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1 INTRODUCTIONIn recent years, considerable evidence has been accumulated regarding the fact that disruptive processes play an important role in galaxy evolution as well as the more dominant hierarchical merging. Observational evidence for these disruptive processes is particularly evident in the dense environment of galaxy clusters. The evidence includes populations of individual intra-cluster objects such as planetary nebulae (; ) and red giant stars , as well as the general diffuse light now thought to make up a significant fraction of the total stellar mass in clusters (,;; ).In this paper, we focus on a relatively new component of intra-cluster space, ultra-compact dwarf (UCD) galaxies. These are compact systems of old stars akin to globular clusters but they are 10–100 times more luminous than Galactic globular clusters and they are located in intra-cluster space between galaxies. The first UCDs were discovered in the Fornax cluster independently in studies of globular clusters (; ) and in studies of compact dwarf galaxies (; ). The UCDs are unlike any known galaxies in terms of luminosity, morphology and size. Several hypotheses have been suggested to explain the origin of UCDs ranging from them being the high-luminosity end of a putative intra-cluster globular cluster distribution to being the evolved super-star clusters formed in galaxy merger events.
In this paper, we focus on the model that UCDs are formed by the global tidal field of a cluster which can strip, or ‘thresh’, the outer stellar envelopes of nucleated dwarf galaxies (dE, Ns and dS0, Ns) as they pass repeatedly through the inner regions of a cluster leaving just the bare nucleus to survive as a UCD (;; ).The motivation for the current work is the subsequent discovery of a larger population of fainter UCDs in the central region of the Fornax cluster (; ). This sample of 60 UCDs is large enough to permit us to test several aspects of the threshing hypothesis using a statistically significant sample. Our focus will be to test simple aspects of the distributions of the UCD and galaxy populations. An alternative approach based on the internal properties of the UCDs is also in progress (e.g.
).Our basic premise for this paper is that if UCDs are descendants of disrupted galaxies, then the UCD parent population can be modelled by the combined current population of Fornax cluster UCDs and dwarf galaxies. We test whether the observed spatial and velocity distributions of the two populations are consistent with this hypothesis and conclude that they are. We then model the orbits of UCDs/galaxies drawn from this joint population to determine what fraction of them passes close enough to the cluster centre to lead to threshing. The relative fraction UCDs to dwarfs seen at large radii in Fornax is inconsistent with this static threshing model.In Section 2, we define the UCD and galaxy samples for our analysis. In Section 3, we test if the luminosity function of the UCDs is consistent with them having been drawn as random sample from the nuclei of dwarf galaxies in the cluster. Section 4 develops a dynamical model for the joint population, and Section 5 calculates the fraction of threshed orbits at each radius. Finally, in Section 6, we summarize our results and draw conclusions about the plausibility of the threshing hypothesis.We adopt a distance of 20 Mpc to the Fornax cluster corresponding to a distance modulus of 31.51 mag.
In this paper, we are not concerned with late-type galaxies. To avoid endless repetition, we use the terms galaxy and dwarf to refer to early-type objects only, as defined in Section 2.1. 2 DATA SAMPLES FROM THE FORNAX CLUSTER 2.1 Early-type galaxy sampleThe hypothesis that we test in this paper is that UCDs form from the disruption of nucleated dwarf galaxies. Our authority for the morphological classification of Fornax cluster galaxies is the Fornax Cluster Catalogue (FCC; ) which was based on photographic data.
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The FCC lists some 291 galaxies as early types (i.e. Not Sa-d, Sm or Im; we include spheroidal galaxies in our sample). Of these, 103 are classified as nucleated. Recent Hubble Space Telescope ( HST) imaging results from the ACS Virgo Cluster Survey (, hereafter CPF06) suggest that the frequency of nucleation in early-type galaxies is actually much higher than suggested from the photographic ground-based surveys. Faint nuclei are difficult to detect because they are washed out by atmospheric seeing, and the central regions of the brightest galaxies are saturated. Notably, CPF06 suggest that potentially all dwarf galaxies may contain nuclei.
We apply the CPF6 model to our Fornax data in Section 3.1 and show that the observed fraction of nucleated dwarfs as a function of magnitude is consistent with this assumption. Also, the spatial distributions of nucleated and non-nucleated dwarfs, shown in, are indistinguishable. The cumulative numbers of nucleated (dashed, blue) and non-nucleated (dotted, red) dwarf galaxies in Fornax as a function of projected radius between 17.5 and 1050 kpc.
Shown also as a solid, black line is the cluster mass profile described in Section 4.3.For the purposes of this current work, therefore, we define the parent galaxy sample to be all early-type dwarf galaxies listed as definite or probable members in the FCC. Where radial velocities are known, we use these to define membership, otherwise we use the FCC membership classifications.
New radial velocities result in the removal of some FCC-classified members and the inclusion of some FCC-classified background galaxies, now known to be members (e.g. More recent radial velocity measurements are taken from. Where the classification is uncertain, we have taken all galaxies fainter than M B=−14 as dwarf; the maximum magnitude for a normal galaxy is then M B=−16.3 and the minimum magnitude for a dwarf galaxy is M B=−17.8. A complete list of the galaxies is given in Table A1.The galaxies in our sample have morphological classifications from the FCC which can include a flag to show that they are nucleated. We use these flags in our discussion below, but we emphasize that there is no HST imaging for most of these galaxies, so we cannot tell with certainty if a given galaxy is really nucleated. We instead adopt the general result of CPF06 that all dwarf galaxies have nuclei, with a magnitude that is related to that of the host galaxy (see Section 3.1).The dwarf galaxy sample that we use is effectively complete to a limit of around M B=−13.5 (see FCC).
The velocity data used to confirm cluster membership are complete for galaxies brighter than M B=−16 and become 50 per cent complete at M B=−14.5. 2.2 UCD sampleThe UCDs were originally discovered as part of the all-object Fornax Cluster Spectroscopic Survey. Although the original survey measured all objects (to b J. The b J photographic APM magnitudes were converted to m B magnitudes by the approximate relation m B= b J+ 0.20based on the relation of b J= B− 0.28( B− V) for an average dwarf galaxy colour of B− V= 0.7 so that M B= b J+ 0.20 − 31.51 = b J− 31.31.The spatial locations of the UCDs are far from circularly symmetric about the centre of Fornax but tend to lie in a band running from northeast to southwest (see fig. This presumably reflects the infall pattern on to the cluster. Provided that the distribution is relaxed, this will not affect the dynamical modelling; however it may confuse the relation between the true three-dimensional positions and velocities and the observed ones.
For the purposes of modelling in this paper, we assume a spherically symmetric distribution. 2.3 Joint sample selectionAccording to our central hypothesis, there was an original parent population of dwarf galaxies, some of which were subsequently disrupted to form UCDs.
She s dating the gangster free download. Unfortunately, the selection effects are different for the two sub-populations and so we need to use different samples for different parts of our analysis. This will be described at the beginning of each relevant section. Here, we make a few general comments on the relative spatial extent of the dwarf and UCD samples.The FCC is a wide-field survey. It covers a rectangular region with a largest inscribed circle that extends to a radius of 3° (1.05 Mpc) from the cluster centre.
Our main UCD sample is limited to a smaller region defined by a maximum radius of (314 kpc) from the cluster centre. We have modelled the density distribution and estimate that there may be up to six missing UCDs at larger radii (although, for the brighter UCDs, two additional regions extending to a radius of 3° have been surveyed and no UCDs were found). Adding six extra UCDs with the appropriate density distribution makes very little difference to the modelling of the spatial distribution of the joint UCD plus dwarf population in Section 4.1.For the UCDs, there is also a need to exclude those at very small radii from the central cluster galaxy, NGC 1399. The distribution of UCD radial velocities shown in shows a trend to smaller velocities (and velocity dispersion) at low radius.
The inner UCDs are clearly moving in the galactic and not the cluster potential and could be considered as bright globular clusters attached to NGC 1399. The choice of where to draw the dividing line between galactic and intracluster UCDs is somewhat arbitrary.
We cut at 3 arcmin (17.5 kpc) which excludes 11 UCDs from our sample (see ), including the two relatively low velocity UCDs seen in the figure at a radius and velocity of approximately 15 kpc and 1140 km s −1, respectively. (Including these two in our analysis makes little difference to the results and would leave the velocity dispersion of the excluded clusters as formally zero once the velocity errors have been accounted for.). A comparison of the UCD and galaxy populations. The radial velocities are plotted as a function of projected radius. UCDs are shown as red triangles, normal galaxies as blue squares, and dwarfs brighter and fainter than M B=−15.0 as blue circles and crosses, respectively. The yellow shaded area shows a running mean of the 1σ velocity dispersion.For reasons that we will describe in Section 3.2, we divide the dwarf population into two. ‘Bright dwarfs’ with M B.
3 COMPARISON OF LUMINOSITY DISTRIBUTIONSIn this section, we develop a unified model for nucleated and non-nucleated dwarf galaxies whereby all galaxies have nuclei but only a fraction of these are bright enough to be detected and classified as such in the FCC. We then go on to compare the predicted luminosity function of nuclei with that of UCDs. As we are interested only in the shape of the magnitude distributions, we use the full samples of dwarfs and UCDs even though two extend over different spatial regions. 3.1 Early-type nucleiAn important property of the parent galaxies is the luminosity distribution of the galaxy nuclei as these will be compared to the UCD luminosities.
We cannot directly measure the luminosities of galaxy nuclei in the Fornax cluster because most do not have high-resolution HST imaging. Instead, we take a statistical approach: we assume that all dwarf galaxies host nuclei and infer the nuclear luminosities from the total galaxy luminosities.CPF06 measured nuclear luminosities for 51 dwarf galaxies in the Virgo cluster.
They confirmed previous suggestions that the nuclear luminosities increase with the galaxy luminosity. They modelled this relation as both a fixed offset between the nuclear and total magnitudes, g′ nuc= g′ gal+ (6.25 ± 0.21), and an offset slowly varying with magnitude, g′ nuc= (0.90 ± 0.18) g′ gal+ (7.59 ± 2.50).
We note that our galaxy sample extends to much fainter magnitudes than did the Virgo sample studied by CPF06, and so we will have to extrapolate their relation. We therefore allow the slope of the relation to vary, but require that it go through the mid-point of the CPF06 data ( g′ gal, g′ nuc= 13.40, 19.65) defined by the crossing point of their two relations.We model the scatter in the relationship by adding a random normal variable with a mean of zero and a standard deviation of 1.5 to the derived nuclear magnitude.
The standard deviation was inferred from the scatter about the fixed-slope fit of CPF06 (their ).To convert the ACS g′ photometry to absolute magnitudes, we first use the mean value of B T− g= 0.30 for the ACS dwarf galaxies to convert g magnitudes to B T. We then apply the distance modulus of 31.09 mag quoted by CPF06, obtaining M B= g′−30.79.To constrain the slope of the g′ nuc– g′ gal relation, we require that it predicts the correct distribution of galaxies that we would expect to have been classified as nucleated in the photographic FCC survey. For each galaxy, we predict its nuclear luminosity as above, then we classify it as nucleated if the nucleus is brighter than the point-source detection limit on the photographic plate (approximately B T= 22.6 or M B=−8.9 for the FCC; H. Ferguson, private communication).
The distribution of dwarf galaxies classified as ‘nucleated’. The leftmost, blue bars show the observed magnitudes of all Fornax dwarfs.
The middle, green bars show only those whose predicted nuclear magnitudes would be greater than −8.9 according to the model developed in the text. Finally, the rightmost, brown bars show the actual magnitude distribution of nucleated dwarfs in Fornax.We show in Section 4.1 that the spatial distributions of the nucleated and non-nucleated dwarfs are identical, thus lending further support to the hypothesis that the presence of a detectable nucleus is the only difference between them. 3.2 UCDsFrom the observed dwarf population, we can now predict the distribution of nuclear magnitudes.
If we assume that the threshing process is independent of galactic (and nuclear) luminosity, then these should have the same shape of distribution as the UCDs. Furthermore, the relative normalization should tell us what fraction of the dwarfs has been threshed. The predicted and actual UCD distributions are given in. Note that the predicted numbers from our model have been scaled down by the completeness values in to allow for the fraction of unmeasured objects. The leftmost, blue bars show the predicted distribution of nuclear magnitudes for Fornax dwarfs, averaged over 100 realizations: the middle, green bars multiply this by the completeness factor for UCD observations. If the threshing hypothesis is correct, then this should be proportional to the rightmost, brown bars that show the observed distribution of UCD magnitudes.The figure shows that the predicted luminosity distribution of UCDs is not perfect.
The model seems to give an excess of UCDs brighter than M B=−11.25 as compared to fainter ones. It is hard to assess the significance of this: given the relatively small number of objects and the uncertainties in the relationship between galactic and nuclear magnitudes, it is probably acceptable.The model predicts that 38 dwarfs should have nuclei that correspond to observable UCDs. This motivates our selection of M B=−15.0 as the dividing line between bright and faint dwarfs, as this gives 38 bright dwarfs. Without scatter, would have predicted a brighter limit, M B≈−15.8, but the greater number of faint galaxies biases things towards fainter magnitudes. Of these 38 dwarfs, only 11 lie within 314 kpc. Thus, the model predicts that the vast majority of dwarfs within this region are likely to be threshed.
Even when averaged over the whole sample, more than half the dwarf population should be threshed. 4 A DYNAMICAL MODEL FOR THE JOINT DWARF/UCD POPULATIONThis section constructs a model of the three-dimensional density distribution of the joint dwarf/UCD population in the cluster.
There will turn out to be some degeneracy in the models which we will attempt to constrain by matching them to observed mass models for Fornax.When comparing dwarfs and UCDs, we restrict our attention to the bright dwarfs, M B −15), then the difference is removed entirely. This observation strengthens the hypothesis of the previous section that dwarfs classified as nucleated or non-nucleated may differ only in the detectability of their central nucleus.Also shown in the figure is the observed mass profile of the Fornax cluster, as described in Section 4.3. The cumulative number density profile of the dwarfs matches that of the cluster mass profile very well and shows no evidence of dwarf galaxy disruption near the cluster core.Next, in we compare the radial distributions of normal galaxies, bright and faint dwarfs and UCDs. Because the UCD survey extends only out to 314 kpc, we have adjusted the normalization of the cumulative distribution to match that of the dwarfs at this radius. The cumulative numbers of normal galaxies (dash–dotted, blue), bright dwarfs (dotted, red), faint dwarfs (dashed, green) and UCDs (solid, black) in Fornax as a function of projected radius between 17.5 and 1050 kpc.
We have adjusted the normalization of the UCD curve to match that of the dwarfs at 314 kpc.It is immediately obvious that the different populations show different degrees of central concentration. Notably, within 314 kpc, the radial distribution of the faint dwarfs is significantly more extended than that of both the bright dwarfs and the UCDs. At first glance, this appears to be at odds with the threshing model developed below (Section 5.1). The model suggests that faint dwarfs are more compact and therefore less likely to be threshed than bright ones, but we have not looked for UCDs at magnitudes corresponding to the faint dwarfs so we cannot test the number that have been threshed. Conversely, we do not see a significant difference between the distributions of UCDs and bright dwarfs, although we would expect the UCDs to be more centrally concentrated than the (surviving) dwarf galaxies according to our model.
In this case, the relatively small number of objects involved may explain why the difference is not significant.Outside 314 kpc, the distributions of bright and faint dwarfs are indistinguishable. There are hints that the UCD distribution is flattening between 200 and 314 kpc and no UCDs have been detected in (incomplete) observations in a few fields beyond this radius. For the purposes of the modelling that follows, we therefore assume that there are no UCDs with cluster-centric radii exceeding 314 kpc. If there are any, the number density of dwarfs rises so rapidly in this region that the latter would dominate anyway.We plot the radial distribution of normal galaxies just for interest. The numbers are so few that it is formally indistinguishable from either the bright or faint dwarf population. We note, however, that it is significantly less centrally concentrated within 314 kpc than the UCD population. 2 where x= r/ a, and a and s are fitting parameters.
(We fit only for the shape of the distribution: the normalization ρ 0 can be chosen so as to match the correct number of objects.) We project each distribution on to the sky and then compare the predicted cumulative mass profile as a function of radius to the observed distribution, using the Kolmogorov–Smirnov test.shows the allowable range of parameters and shows the best-fitting model, although there is a strong degeneracy between a and s such that a wide variety of fits are acceptable. We will show results for s= 3.0, a= 5 kpc and for s= 4.0, a= 90 kpc; both lead to very similar conclusions. Velocity dispersions for different subsamples of the UCD and galaxy populations in Fornax. The completeness of the velocity data can be found by comparing the numbers in this table with those in, but basically it is high except for the faint dwarfs. When calculating velocity dispersions for the different sub-samples, we have used the mean for the full sample of all galaxies (normal, dwarf and UCD) with radii greater than 17.5 kpc, . The final column shows the rms error in the velocity dispersion measurements determined by bootstrap resampling 1000 times.
Velocity dispersions for different subsamples of the UCD and galaxy populations in Fornax. The completeness of the velocity data can be found by comparing the numbers in this table with those in, but basically it is high except for the faint dwarfs. When calculating velocity dispersions for the different sub-samples, we have used the mean for the full sample of all galaxies (normal, dwarf and UCD) with radii greater than 17.5 kpc, . The final column shows the rms error in the velocity dispersion measurements determined by bootstrap resampling 1000 times. The low-velocity dispersion of UCDs as compared to other galaxies is expected in the threshing model, because the UCDs are more centrally concentrated in the cluster potential (i.e.
Have a steeper density profile) – unfortunately, there are too few UCDs to quantify this. However, the table shows a number of other features that are hard to explain.First, why is the velocity dispersion of normal galaxies so much smaller than that of dwarfs, and especially bright dwarfs, given that the two have similar radial distributions within the cluster? In, this difference was interpreted as indicating that the dwarf galaxies were an unrelaxed, infalling, population. In this paper, we are assuming that all galaxies (including UCDs) are relaxed: an alternative explanation is that many of the dwarfs may be orbiting in bound subhaloes, with normal galaxies located at their centres.Secondly, the line-of-sight velocity dispersion for UCDs is significantly higher at small radii than at large ones. Some difference of this kind would be expected if the UCDs are on preferentially radial orbits. Defining the velocity anisotropy parameter as β= 1 −σ 2 t/σ 2 r, where σ r is the radial velocity dispersion with respect to the cluster centre and σ t the tangential one, then this would correspond to β 0.
Unfortunately, the expected variation, calculated in Appendix B, is much too small to explain the observations. The observed decline in velocity dispersion between the inner and outer bin is 1:0.58.
Even if we allow each measurement to move up to 1σ towards agreement (with probability less than 3 per cent), the ratio remains 1:0.80. This can only be explained with β= 1, corresponding to purely radial orbits.
The explanation for this discrepancy may be related to the non-uniform distribution of UCDs within the Fornax cluster. If the outer UCDs have orbits that are preferentially moving perpendicular to the line-of-sight, then that would explain the effect.Despite these uncertainties, we will model the joint UCD plus bright dwarf population as if it is relaxed. As we show in the next section, this provides a marginally acceptable fit to the known mass distribution in the Fornax cluster. 4.3 Cluster mass profile. 8 where M BCG= 2π 2 a 3 BCG ρ BCG,0= 2.0 × 10 12M ⊙; a BCG= 30 kpc; M clus,0= 4πρ clus,0 a 3 clus= 1.1 × 10 14M ⊙; a clus= 400 kpc.
Here, ρ( r) is the density at clustocentric radius r, M r is the mass contained within radius r, x BCG= r/ a BCG and x clus= r/ a clus. Given the uncertainties in the observations, any other model that has M∝ r in the centre, and that passes through the other mass points mentioned above, would be equally acceptable. The observational constraints are shown in as black circles, and the model as a solid, magenta line. 9 We can use this in two ways: to predict the mass distribution, given our dynamical model for the population, or to predict the velocity dispersion profile for the given observed mass profile.shows a comparison between the observed mass profile and that predicted by two of the acceptable density models with constant velocity dispersion of 310 km s −1 and isotropic velocity dispersion tensors, β= 0. We have also tried models with β 0. This makes very little difference to the s= 3 prediction but substantially worsens the s= 4 fit to the data at small radii.Reversing this procedure, gives the predicted velocity dispersion profile for a given density profile and observed cluster mass distribution. In making this prediction, we have taken the approximation that the logarithmic gradient in the velocity dispersion is small compared to that of the density.
Once again, taking β to be greater than zero makes little difference to the s= 3 prediction, but worsens the s= 4 one, giving higher predicted velocity dispersion at small radii. In both these plots, the s= 3 curve provides the closer fit to the data. That it does not match every wiggle in the mass profile in is not surprising given that the latter is somewhat arbitrary and that we have not allowed the velocity dispersion to vary with radius. The normalization is a little too high: lowering the velocity dispersion to 283 km s −1 would provide a very good fit to the mass profile. Given that this is only 1σ away from the measured value in, we regard this as marginally acceptable. The predicted isotropic velocity dispersion profiles for the mass model given in and for density profiles with parameters s= 3, a= 5 kpc (solid, red) and s= 4, a= 90 kpc (dotted, blue).In, it may seem at first sight that the decline in velocity dispersion away from the core of the cluster mimics that seen in the UCD observations.
However, a closer inspection reveals that the minimum in velocity dispersion seen in this plot lies at too small a radius and that by the edge of the UCD observations at around 300 kpc the velocity dispersion has risen to its central value. 5 A STATIC MODEL OF GALAXY THRESHINGIn this section, we investigate the simplest threshing scenario in which dwarf galaxies orbit within the present-day Fornax cluster and are threshed if they pass close to the cluster core. We show that there are too many UCD galaxies at large radii for this model to be viable.
We conclude that in any threshing model, disruption must occur near the cores of smaller subclumps, prior to cluster formation. 5.1 Threshing radiiTo estimate the fraction of dwarf orbits at a given radius which lead to threshing, we calculate the probability for a galaxy with initial projected clustocentric radius and line-of-sight velocity to have R min. The predicted threshing radius as a function of UCD B magnitude.Our approach in estimating the threshing radii is very similar to that used by except for the following differences. First, we specifically use the local gradient of the cluster potential (rather than the point-mass assumption) and we add a core component to the cluster NFW potential.
Secondly, we have used more recent scaling relations to derive the dwarf galaxy core masses as a function of their absolute magnitudes. Our estimates give very similar threshing radii: compare our to their fig. 7.Recently, (2008, hereafter GMK08) have conducted numerical simulations of threshing in a static potential similar to that of the Virgo cluster.
They use two different models of a dwarf galaxy: one which consists solely of an extended dark matter halo with an NFW profile, and one in which this profile has been centrally concentrated by a dissipative baryonic disc. For the latter, the threshing radii they find are similar to ours. The dark-matter-only haloes can have much greater threshing radii, up to 200 kpc, but only for galaxies on quite circular orbits. As we discuss in Section 6, the two models bracket our predictions for UCD fractions as a function of radius, and both lead to the same qualitative results.The detailed threshing simulations of individual dwarf galaxies by showed that several pericentre passages within the threshing radius were necessary to completely strip the dwarf galaxy. In our model below, we do not count the number of orbits, but simply assume that any galaxy with an orbit that passes within its threshing radius will be stripped. This assumption is reasonable for galaxies within about 100 kpc of the cluster centre, but for those galaxies with radii of the order of 300 kpc, on the outskirts of the observed UCD distribution, there may have been only a single pericentric passage in the lifetime of the cluster. This could lead to an overestimate of the UCD fraction at large radii and would strengthen our results.
5.2 Galaxy orbits. 17 Simple iteration of this equation quickly finds the minimum orbital radius (pericentre).For each value of r 0, we draw 10 000 velocities with the appropriate Gaussian distributions in each of the radial and tangential directions, then solve for the pericentric radius. An example histogram is shown in. The sharp spike at r min= r 0 is because any orbit that has an initial radial velocity close to zero and a tangential velocity that exceeds the circular velocity at that radius will already be at pericentre. More importantly, there is a wide distribution of minimum radii extending all the way down to r min≈ 0, even for an isotropic velocity dispersion tensor.
This orbital distribution is in good agreement with that found in cosmological simulations, for example. A histogram showing the probability density for the distribution of minimum orbital radii (pericentres) for a selection of galaxy orbits drawn from the appropriate Gaussian distribution of velocities. For this particular example, the one percentile of minimum radii is at r min≈ 0.03 r 0.The variation in threshing radii for different galaxies is small and so for simplicity we adopt a constant value of 30 kpc. Then, for each radius, r, we can tabulate the fraction of orbits that pass within this radius. This can then be projected along the line-of-sight with the appropriate density weighting to determine the fraction of threshed orbits as a function of projected distance from the cluster centre.
Chuck d autobiography of mistachuck rar file. The results of this calculation are shown in for the two example density profiles discussed above. Comparison of observed and predicted fractions of UCDs. The circles show the observed UCD fraction (of the joint UCD plus bright dwarf sample) as a function of projected radius from the centre of the cluster.
The lines show the predicted fraction of orbits that pass within the threshing radius of 30 kpc for s= 3, a= 5 kpc, β= 0 (solid, red), s= 3, a= 5 kpc, β= 0.5 (dashed, green) and s= 4, a= 90 kpc, β= 0., (dotted, blue).It is immediately apparent that the predicted fraction of threshed galaxies is far too low at radii greater than about 50 kpc. The predicted UCD fraction drops rapidly at this radius, whereas the observed fraction of UCDs stays high out to 250 kpc. (We have checked that this conclusion is unaltered even if the UCDs are distributed on a plane perpendicular to the line-of-sight such that their projected radii are equal to the true distances from the centre of the cluster.) There are many simplifications and uncertainties in the model, but it is hard to see how these could make a difference of a factor of 5. The static threshing model is simply untenable. 6 SUMMARY AND CONCLUSIONSIn this paper, we have investigated the possibility that UCD galaxies are formed by the threshing of nucleated, early-type dwarf galaxies.We first contrast the distribution of nucleated and non-nucleated dwarfs, which are indistinguishable apart from a small excess of bright, nucleated dwarfs at small clustocentric radii.
We concur with the conclusion of CPF06 that the observations are consistent with a single population in which all dwarfs are nucleated, with a ratio of nuclear to total magnitude that varies slowly with magnitude. However, we need to flatten their relation in order to obtain a good fit when extrapolating to fainter magnitudes.Given this hypothesis, we can reproduce the magnitude distribution of the UCD population, except at bright magnitudes where the model predicts more UCDs than are observed. Under the threshing model, the UCDs are likely to have originated from dwarfs with magnitudes brighter than about M B=−15. We use the joint UCD plus bright dwarf population in the modelling that follows.The threshing model predicts that over half of all dwarf galaxies must be disrupted: 38 surviving dwarfs have nuclei of similar magnitude to the 49 observed UCDs. This may seem excessive but corresponds to an intracluster light fraction of just 8 per cent, well within the observed range for clusters of this mass (,;; ).
18 where x= r/ a, and a and s are constants, with s lying between about 3 and 4.5.The velocity dispersion of UCD galaxies shows a sharp decline with radius that is hard to explain. It may in part be due to a radial bias in the orbits, but this is not enough in itself to explain the effect. The velocity dispersion of bright dwarfs is greater than that of the UCDs. When the two are combined, then the joint population with density slope s= 3 provides a marginally acceptable fit to the mass profile of Fornax.We have tested the simplest possible threshing model, in which dwarf galaxies move on orbits in a static cluster potential and are threshed if they pass within a radius at which the tidal force from the cluster exceeds the internal gravity at the core of their dark matter halo. This fails to reproduce the observed fraction of UCDs at radii greater than 50 kpc from the core of Fornax. There are many deficiencies in the model but these are unlikely to raise the threshing radii by a factor of 5, as is required, and so we conclude that this static mode is unviable.Our results have several points of agreement with the earlier work by despite a very different approach: we have used analytic descriptions of the cluster dynamics compared to their numerical computations.
In our work, we have based our prediction on a parent sample of dwarf galaxies generated directly from the known Fornax galaxies, whereas Bekki et al. Generated their galaxy sample from more general empirical relations for the luminosity functions and radial profiles of galaxies within clusters.
In particular, they used a King profile with a core radius of 50 kpc for the density distribution, very different from our model. They demonstrate that dwarf galaxies are disrupted if they pass inside their critical threshing radius when orbiting the cluster centre. They then use this radius to estimate the population of threshed galaxies (UCDs) in the Fornax cluster.
They find this to be consistent with the known distribution of the seven very luminous UCDs known in the cluster at that time.Our conclusion (refuting the simple threshing model) differs from that of Bekki et al. For a number of reasons. First, we use the measured positions of galaxies in Fornax, rather than a generic King model.
We also have many fewer dwarf galaxies than predicted by their Schechter model for the cluster luminosity function. In addition, we have extended the analysis to much lower luminosities of both the UCDs (as new data have become available) and the parent galaxies (due to the greater difference in nuclear to total luminosity now used). This new analysis has clearly revealed a disagreement between the number of UCDs at large clustocentric distances and the threshing predictions.A recent paper by GMK08 undertook an extensive series of simulations to investigate the disruption of UCD host galaxies within a cluster potential similar to that of the Virgo cluster. They considered two different models for the host galaxy with very different degrees of central concentration and followed their threshing in a static potential over 5 Gyr. They then looked at the orbits of particles in a cosmological simulation of cluster formation to assess which of those orbits would lead to threshing.
This latter step follows the dynamical evolution of the halo and is much more realistic than a static potential.GMK08 state that their model ‘leads to the observed spatial distribution of UCDs’, in apparent disagreement with our results above. In fact, our theoretical UCD fractions as a function of radius agree with theirs and are bracketed by their upper and lower predictions.
The difference in the conclusion arises from the very different observed threshing fractions that we adopt. GMK08 use only 15 UCDs in both Virgo and Fornax combined, whereas we use a new sample of 49 UCDs from Fornax alone. Also, GMK08 do not say how they define the nucleated dwarfs corresponding to the parent sample, whereas we are careful to select only those dwarfs that would have nuclei that match those of the observed UCDs.In conclusion, the origin of UCDs as dwarf galaxy nuclei remains unproven. Our modelling has revealed a number of attractive features:The distribution of nuclear magnitudes for dwarf galaxies roughly matches that of known UCD galaxies.UCDs are more centrally concentrated within Fornax than are dwarf galaxies. (However, this would also be true if the UCDs constituted an extended globular cluster population around NGC 1399.)The joint UCD plus bright dwarf population has a smooth density profile with a recognisable (NFW) form and appears to sit in dynamical equilibrium within the Fornax cluster.At the same time, there are several major deficiencies in the model:The model requires that more dwarf galaxies must have been disrupted in Fornax than currently remain. However, the spatial distribution of dwarfs matches that of the total mass profile of the cluster and shows no sign of galaxy disruption near the cluster core.The very low velocity dispersion of UCDs as compared to bright dwarfs is unexplained, as is the sharp decline in velocity dispersion of the UCDs with radius. (However, this would prove true for any dynamical model of the UCD population, regardless of its origin.)A static threshing model for UCD formation, based upon orbits within the current cluster potential, is a hopeless failure.
It predicts far too few UCDs at radii greater than about 30 kpc.The simulations of GMK08 within an evolving cluster potential also give too few UCDs at large radii.The balance of evidence would seem to be against the threshing model. Before dismissing the model altogether, however, we note that the threshing may have occurred within smaller sub-clusters that later fell into Fornax and have not yet reached dynamical equilibrium. This mechanism is suggested by the spatial distribution of UCDs in the Fornax cluster: they show some association with normal galaxies and, in particular, lie in a band across the cluster.In considering the threshing hypothesis for UCD formation, we should not discuss the dynamical properties of the objects in isolation from their internal properties.
Studied the stellar populations of Virgo cluster UCDs and concluded that the Virgo UCDs have stellar populations the globular clusters of the central galaxies M87 and M49 (old ages, a range of metallicity and super-solar alpha-abundances). On this basis, the Virgo UCD stellar populations are not consistent with simple threshing model. On the other hand, found metallicities and (a range of) ages in Fornax cluster UCDs, which are more in agreement with the hypothesis that the Fornax UCDs are threshed nuclei. A detailed analysis of the structure and colours of both Virgo and Fornax UCDs concluded that their structural properties could be consistent with either globular clusters or dwarf galaxy nuclei, with the interesting observation that UCDs are about twice as extended (in effective radius) as the nuclei of dwarf galaxies at the same luminosity.Most of these observational results, as well as our own analysis in this paper, argue against the simple threshing hypothesis for UCD formation. 'We do not have any formal proof of this but note that the weights are equal when σ e, i≪σ and tend to the known optimal weighting w i∝ 1/σ 2 e, i when σ e, i≫σ. A similar, but not identical, expression is given by.This work was initiated while PAT was a visitor to Queensland under ARC Discovery Projects Grant DP0557676, and continued whist MJD was visiting Sussex with partial funding from PPARC Grant PP/D001579/1.
We would like to thank an anonymous referee for many useful suggestions for comparison with previous work. Appendices APPENDIX A: TABLES OF GALAXY AND UCD DATATables A1 and A2 are given in the online version of the article. APPENDIX B: VARIATION IN LINE-OF-SIGHT VELOCITY WITH RADIUSThis Appendix calculates the expected variation in the line-of-sight velocity dispersion of UCDs with radius resulting from anisotropic motions in a declining density profile.We take the velocity dispersion tensor to be aligned with the radial direction and to have diagonal components σ r, σ t and σ t, where σ r and σ t are the radial and tangential components of velocity dispersion, respectively. The velocity anisotropy parameter is defined as β= 1σ 2 t/σ 2 r– thus β= 0 for isotropic orbits and β 0 for preferentially radial orbits. We assume that both σ 2 r and β are constant throughout the cluster.
In practice, one might expect some radial variation in these quantities, but the data are insufficient to constrain more complex models. (B3) where z measures distance along the line of sight from the mid-point through the cluster and r is the radius to a point on that line such that z= R tan θ and r= R/cos θ. The value of the integral quotient in varies between approximately 0.62 and 0.76 for inner and outer radial bins given in (the precise values depend upon the density model for the UCDs but all acceptable fits to the data give similar results). SUPPLEMENTARY MATERIALAdditional may be found in the online version of this article.Table A1. The galaxy sample.Table A2. The UCD sample.Please note: Blackwell Publishing are not responsible for the content or functionality of any supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
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1 INTRODUCTIONIn recent years, considerable evidence has been accumulated regarding the fact that disruptive processes play an important role in galaxy evolution as well as the more dominant hierarchical merging. Observational evidence for these disruptive processes is particularly evident in the dense environment of galaxy clusters. The evidence includes populations of individual intra-cluster objects such as planetary nebulae (; ) and red giant stars , as well as the general diffuse light now thought to make up a significant fraction of the total stellar mass in clusters (,;; ).In this paper, we focus on a relatively new component of intra-cluster space, ultra-compact dwarf (UCD) galaxies. These are compact systems of old stars akin to globular clusters but they are 10–100 times more luminous than Galactic globular clusters and they are located in intra-cluster space between galaxies. The first UCDs were discovered in the Fornax cluster independently in studies of globular clusters (; ) and in studies of compact dwarf galaxies (; ). The UCDs are unlike any known galaxies in terms of luminosity, morphology and size. Several hypotheses have been suggested to explain the origin of UCDs ranging from them being the high-luminosity end of a putative intra-cluster globular cluster distribution to being the evolved super-star clusters formed in galaxy merger events.
In this paper, we focus on the model that UCDs are formed by the global tidal field of a cluster which can strip, or ‘thresh’, the outer stellar envelopes of nucleated dwarf galaxies (dE, Ns and dS0, Ns) as they pass repeatedly through the inner regions of a cluster leaving just the bare nucleus to survive as a UCD (;; ).The motivation for the current work is the subsequent discovery of a larger population of fainter UCDs in the central region of the Fornax cluster (; ). This sample of 60 UCDs is large enough to permit us to test several aspects of the threshing hypothesis using a statistically significant sample. Our focus will be to test simple aspects of the distributions of the UCD and galaxy populations. An alternative approach based on the internal properties of the UCDs is also in progress (e.g.
).Our basic premise for this paper is that if UCDs are descendants of disrupted galaxies, then the UCD parent population can be modelled by the combined current population of Fornax cluster UCDs and dwarf galaxies. We test whether the observed spatial and velocity distributions of the two populations are consistent with this hypothesis and conclude that they are. We then model the orbits of UCDs/galaxies drawn from this joint population to determine what fraction of them passes close enough to the cluster centre to lead to threshing. The relative fraction UCDs to dwarfs seen at large radii in Fornax is inconsistent with this static threshing model.In Section 2, we define the UCD and galaxy samples for our analysis. In Section 3, we test if the luminosity function of the UCDs is consistent with them having been drawn as random sample from the nuclei of dwarf galaxies in the cluster. Section 4 develops a dynamical model for the joint population, and Section 5 calculates the fraction of threshed orbits at each radius. Finally, in Section 6, we summarize our results and draw conclusions about the plausibility of the threshing hypothesis.We adopt a distance of 20 Mpc to the Fornax cluster corresponding to a distance modulus of 31.51 mag.
In this paper, we are not concerned with late-type galaxies. To avoid endless repetition, we use the terms galaxy and dwarf to refer to early-type objects only, as defined in Section 2.1. 2 DATA SAMPLES FROM THE FORNAX CLUSTER 2.1 Early-type galaxy sampleThe hypothesis that we test in this paper is that UCDs form from the disruption of nucleated dwarf galaxies. Our authority for the morphological classification of Fornax cluster galaxies is the Fornax Cluster Catalogue (FCC; ) which was based on photographic data.
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The FCC lists some 291 galaxies as early types (i.e. Not Sa-d, Sm or Im; we include spheroidal galaxies in our sample). Of these, 103 are classified as nucleated. Recent Hubble Space Telescope ( HST) imaging results from the ACS Virgo Cluster Survey (, hereafter CPF06) suggest that the frequency of nucleation in early-type galaxies is actually much higher than suggested from the photographic ground-based surveys. Faint nuclei are difficult to detect because they are washed out by atmospheric seeing, and the central regions of the brightest galaxies are saturated. Notably, CPF06 suggest that potentially all dwarf galaxies may contain nuclei.
We apply the CPF6 model to our Fornax data in Section 3.1 and show that the observed fraction of nucleated dwarfs as a function of magnitude is consistent with this assumption. Also, the spatial distributions of nucleated and non-nucleated dwarfs, shown in, are indistinguishable. The cumulative numbers of nucleated (dashed, blue) and non-nucleated (dotted, red) dwarf galaxies in Fornax as a function of projected radius between 17.5 and 1050 kpc.
Shown also as a solid, black line is the cluster mass profile described in Section 4.3.For the purposes of this current work, therefore, we define the parent galaxy sample to be all early-type dwarf galaxies listed as definite or probable members in the FCC. Where radial velocities are known, we use these to define membership, otherwise we use the FCC membership classifications.
New radial velocities result in the removal of some FCC-classified members and the inclusion of some FCC-classified background galaxies, now known to be members (e.g. More recent radial velocity measurements are taken from. Where the classification is uncertain, we have taken all galaxies fainter than M B=−14 as dwarf; the maximum magnitude for a normal galaxy is then M B=−16.3 and the minimum magnitude for a dwarf galaxy is M B=−17.8. A complete list of the galaxies is given in Table A1.The galaxies in our sample have morphological classifications from the FCC which can include a flag to show that they are nucleated. We use these flags in our discussion below, but we emphasize that there is no HST imaging for most of these galaxies, so we cannot tell with certainty if a given galaxy is really nucleated. We instead adopt the general result of CPF06 that all dwarf galaxies have nuclei, with a magnitude that is related to that of the host galaxy (see Section 3.1).The dwarf galaxy sample that we use is effectively complete to a limit of around M B=−13.5 (see FCC).
The velocity data used to confirm cluster membership are complete for galaxies brighter than M B=−16 and become 50 per cent complete at M B=−14.5. 2.2 UCD sampleThe UCDs were originally discovered as part of the all-object Fornax Cluster Spectroscopic Survey. Although the original survey measured all objects (to b J. The b J photographic APM magnitudes were converted to m B magnitudes by the approximate relation m B= b J+ 0.20based on the relation of b J= B− 0.28( B− V) for an average dwarf galaxy colour of B− V= 0.7 so that M B= b J+ 0.20 − 31.51 = b J− 31.31.The spatial locations of the UCDs are far from circularly symmetric about the centre of Fornax but tend to lie in a band running from northeast to southwest (see fig. This presumably reflects the infall pattern on to the cluster. Provided that the distribution is relaxed, this will not affect the dynamical modelling; however it may confuse the relation between the true three-dimensional positions and velocities and the observed ones.
For the purposes of modelling in this paper, we assume a spherically symmetric distribution. 2.3 Joint sample selectionAccording to our central hypothesis, there was an original parent population of dwarf galaxies, some of which were subsequently disrupted to form UCDs.
She s dating the gangster free download. Unfortunately, the selection effects are different for the two sub-populations and so we need to use different samples for different parts of our analysis. This will be described at the beginning of each relevant section. Here, we make a few general comments on the relative spatial extent of the dwarf and UCD samples.The FCC is a wide-field survey. It covers a rectangular region with a largest inscribed circle that extends to a radius of 3° (1.05 Mpc) from the cluster centre.
Our main UCD sample is limited to a smaller region defined by a maximum radius of (314 kpc) from the cluster centre. We have modelled the density distribution and estimate that there may be up to six missing UCDs at larger radii (although, for the brighter UCDs, two additional regions extending to a radius of 3° have been surveyed and no UCDs were found). Adding six extra UCDs with the appropriate density distribution makes very little difference to the modelling of the spatial distribution of the joint UCD plus dwarf population in Section 4.1.For the UCDs, there is also a need to exclude those at very small radii from the central cluster galaxy, NGC 1399. The distribution of UCD radial velocities shown in shows a trend to smaller velocities (and velocity dispersion) at low radius.
The inner UCDs are clearly moving in the galactic and not the cluster potential and could be considered as bright globular clusters attached to NGC 1399. The choice of where to draw the dividing line between galactic and intracluster UCDs is somewhat arbitrary.
We cut at 3 arcmin (17.5 kpc) which excludes 11 UCDs from our sample (see ), including the two relatively low velocity UCDs seen in the figure at a radius and velocity of approximately 15 kpc and 1140 km s −1, respectively. (Including these two in our analysis makes little difference to the results and would leave the velocity dispersion of the excluded clusters as formally zero once the velocity errors have been accounted for.). A comparison of the UCD and galaxy populations. The radial velocities are plotted as a function of projected radius. UCDs are shown as red triangles, normal galaxies as blue squares, and dwarfs brighter and fainter than M B=−15.0 as blue circles and crosses, respectively. The yellow shaded area shows a running mean of the 1σ velocity dispersion.For reasons that we will describe in Section 3.2, we divide the dwarf population into two. ‘Bright dwarfs’ with M B.
3 COMPARISON OF LUMINOSITY DISTRIBUTIONSIn this section, we develop a unified model for nucleated and non-nucleated dwarf galaxies whereby all galaxies have nuclei but only a fraction of these are bright enough to be detected and classified as such in the FCC. We then go on to compare the predicted luminosity function of nuclei with that of UCDs. As we are interested only in the shape of the magnitude distributions, we use the full samples of dwarfs and UCDs even though two extend over different spatial regions. 3.1 Early-type nucleiAn important property of the parent galaxies is the luminosity distribution of the galaxy nuclei as these will be compared to the UCD luminosities.
We cannot directly measure the luminosities of galaxy nuclei in the Fornax cluster because most do not have high-resolution HST imaging. Instead, we take a statistical approach: we assume that all dwarf galaxies host nuclei and infer the nuclear luminosities from the total galaxy luminosities.CPF06 measured nuclear luminosities for 51 dwarf galaxies in the Virgo cluster.
They confirmed previous suggestions that the nuclear luminosities increase with the galaxy luminosity. They modelled this relation as both a fixed offset between the nuclear and total magnitudes, g′ nuc= g′ gal+ (6.25 ± 0.21), and an offset slowly varying with magnitude, g′ nuc= (0.90 ± 0.18) g′ gal+ (7.59 ± 2.50).
We note that our galaxy sample extends to much fainter magnitudes than did the Virgo sample studied by CPF06, and so we will have to extrapolate their relation. We therefore allow the slope of the relation to vary, but require that it go through the mid-point of the CPF06 data ( g′ gal, g′ nuc= 13.40, 19.65) defined by the crossing point of their two relations.We model the scatter in the relationship by adding a random normal variable with a mean of zero and a standard deviation of 1.5 to the derived nuclear magnitude.
The standard deviation was inferred from the scatter about the fixed-slope fit of CPF06 (their ).To convert the ACS g′ photometry to absolute magnitudes, we first use the mean value of B T− g= 0.30 for the ACS dwarf galaxies to convert g magnitudes to B T. We then apply the distance modulus of 31.09 mag quoted by CPF06, obtaining M B= g′−30.79.To constrain the slope of the g′ nuc– g′ gal relation, we require that it predicts the correct distribution of galaxies that we would expect to have been classified as nucleated in the photographic FCC survey. For each galaxy, we predict its nuclear luminosity as above, then we classify it as nucleated if the nucleus is brighter than the point-source detection limit on the photographic plate (approximately B T= 22.6 or M B=−8.9 for the FCC; H. Ferguson, private communication).
The distribution of dwarf galaxies classified as ‘nucleated’. The leftmost, blue bars show the observed magnitudes of all Fornax dwarfs.
The middle, green bars show only those whose predicted nuclear magnitudes would be greater than −8.9 according to the model developed in the text. Finally, the rightmost, brown bars show the actual magnitude distribution of nucleated dwarfs in Fornax.We show in Section 4.1 that the spatial distributions of the nucleated and non-nucleated dwarfs are identical, thus lending further support to the hypothesis that the presence of a detectable nucleus is the only difference between them. 3.2 UCDsFrom the observed dwarf population, we can now predict the distribution of nuclear magnitudes.
If we assume that the threshing process is independent of galactic (and nuclear) luminosity, then these should have the same shape of distribution as the UCDs. Furthermore, the relative normalization should tell us what fraction of the dwarfs has been threshed. The predicted and actual UCD distributions are given in. Note that the predicted numbers from our model have been scaled down by the completeness values in to allow for the fraction of unmeasured objects. The leftmost, blue bars show the predicted distribution of nuclear magnitudes for Fornax dwarfs, averaged over 100 realizations: the middle, green bars multiply this by the completeness factor for UCD observations. If the threshing hypothesis is correct, then this should be proportional to the rightmost, brown bars that show the observed distribution of UCD magnitudes.The figure shows that the predicted luminosity distribution of UCDs is not perfect.
The model seems to give an excess of UCDs brighter than M B=−11.25 as compared to fainter ones. It is hard to assess the significance of this: given the relatively small number of objects and the uncertainties in the relationship between galactic and nuclear magnitudes, it is probably acceptable.The model predicts that 38 dwarfs should have nuclei that correspond to observable UCDs. This motivates our selection of M B=−15.0 as the dividing line between bright and faint dwarfs, as this gives 38 bright dwarfs. Without scatter, would have predicted a brighter limit, M B≈−15.8, but the greater number of faint galaxies biases things towards fainter magnitudes. Of these 38 dwarfs, only 11 lie within 314 kpc. Thus, the model predicts that the vast majority of dwarfs within this region are likely to be threshed.
Even when averaged over the whole sample, more than half the dwarf population should be threshed. 4 A DYNAMICAL MODEL FOR THE JOINT DWARF/UCD POPULATIONThis section constructs a model of the three-dimensional density distribution of the joint dwarf/UCD population in the cluster.
There will turn out to be some degeneracy in the models which we will attempt to constrain by matching them to observed mass models for Fornax.When comparing dwarfs and UCDs, we restrict our attention to the bright dwarfs, M B −15), then the difference is removed entirely. This observation strengthens the hypothesis of the previous section that dwarfs classified as nucleated or non-nucleated may differ only in the detectability of their central nucleus.Also shown in the figure is the observed mass profile of the Fornax cluster, as described in Section 4.3. The cumulative number density profile of the dwarfs matches that of the cluster mass profile very well and shows no evidence of dwarf galaxy disruption near the cluster core.Next, in we compare the radial distributions of normal galaxies, bright and faint dwarfs and UCDs. Because the UCD survey extends only out to 314 kpc, we have adjusted the normalization of the cumulative distribution to match that of the dwarfs at this radius. The cumulative numbers of normal galaxies (dash–dotted, blue), bright dwarfs (dotted, red), faint dwarfs (dashed, green) and UCDs (solid, black) in Fornax as a function of projected radius between 17.5 and 1050 kpc.
We have adjusted the normalization of the UCD curve to match that of the dwarfs at 314 kpc.It is immediately obvious that the different populations show different degrees of central concentration. Notably, within 314 kpc, the radial distribution of the faint dwarfs is significantly more extended than that of both the bright dwarfs and the UCDs. At first glance, this appears to be at odds with the threshing model developed below (Section 5.1). The model suggests that faint dwarfs are more compact and therefore less likely to be threshed than bright ones, but we have not looked for UCDs at magnitudes corresponding to the faint dwarfs so we cannot test the number that have been threshed. Conversely, we do not see a significant difference between the distributions of UCDs and bright dwarfs, although we would expect the UCDs to be more centrally concentrated than the (surviving) dwarf galaxies according to our model.
In this case, the relatively small number of objects involved may explain why the difference is not significant.Outside 314 kpc, the distributions of bright and faint dwarfs are indistinguishable. There are hints that the UCD distribution is flattening between 200 and 314 kpc and no UCDs have been detected in (incomplete) observations in a few fields beyond this radius. For the purposes of the modelling that follows, we therefore assume that there are no UCDs with cluster-centric radii exceeding 314 kpc. If there are any, the number density of dwarfs rises so rapidly in this region that the latter would dominate anyway.We plot the radial distribution of normal galaxies just for interest. The numbers are so few that it is formally indistinguishable from either the bright or faint dwarf population. We note, however, that it is significantly less centrally concentrated within 314 kpc than the UCD population. 2 where x= r/ a, and a and s are fitting parameters.
(We fit only for the shape of the distribution: the normalization ρ 0 can be chosen so as to match the correct number of objects.) We project each distribution on to the sky and then compare the predicted cumulative mass profile as a function of radius to the observed distribution, using the Kolmogorov–Smirnov test.shows the allowable range of parameters and shows the best-fitting model, although there is a strong degeneracy between a and s such that a wide variety of fits are acceptable. We will show results for s= 3.0, a= 5 kpc and for s= 4.0, a= 90 kpc; both lead to very similar conclusions. Velocity dispersions for different subsamples of the UCD and galaxy populations in Fornax. The completeness of the velocity data can be found by comparing the numbers in this table with those in, but basically it is high except for the faint dwarfs. When calculating velocity dispersions for the different sub-samples, we have used the mean for the full sample of all galaxies (normal, dwarf and UCD) with radii greater than 17.5 kpc, . The final column shows the rms error in the velocity dispersion measurements determined by bootstrap resampling 1000 times.
Velocity dispersions for different subsamples of the UCD and galaxy populations in Fornax. The completeness of the velocity data can be found by comparing the numbers in this table with those in, but basically it is high except for the faint dwarfs. When calculating velocity dispersions for the different sub-samples, we have used the mean for the full sample of all galaxies (normal, dwarf and UCD) with radii greater than 17.5 kpc, . The final column shows the rms error in the velocity dispersion measurements determined by bootstrap resampling 1000 times. The low-velocity dispersion of UCDs as compared to other galaxies is expected in the threshing model, because the UCDs are more centrally concentrated in the cluster potential (i.e.
Have a steeper density profile) – unfortunately, there are too few UCDs to quantify this. However, the table shows a number of other features that are hard to explain.First, why is the velocity dispersion of normal galaxies so much smaller than that of dwarfs, and especially bright dwarfs, given that the two have similar radial distributions within the cluster? In, this difference was interpreted as indicating that the dwarf galaxies were an unrelaxed, infalling, population. In this paper, we are assuming that all galaxies (including UCDs) are relaxed: an alternative explanation is that many of the dwarfs may be orbiting in bound subhaloes, with normal galaxies located at their centres.Secondly, the line-of-sight velocity dispersion for UCDs is significantly higher at small radii than at large ones. Some difference of this kind would be expected if the UCDs are on preferentially radial orbits. Defining the velocity anisotropy parameter as β= 1 −σ 2 t/σ 2 r, where σ r is the radial velocity dispersion with respect to the cluster centre and σ t the tangential one, then this would correspond to β 0.
Unfortunately, the expected variation, calculated in Appendix B, is much too small to explain the observations. The observed decline in velocity dispersion between the inner and outer bin is 1:0.58.
Even if we allow each measurement to move up to 1σ towards agreement (with probability less than 3 per cent), the ratio remains 1:0.80. This can only be explained with β= 1, corresponding to purely radial orbits.
The explanation for this discrepancy may be related to the non-uniform distribution of UCDs within the Fornax cluster. If the outer UCDs have orbits that are preferentially moving perpendicular to the line-of-sight, then that would explain the effect.Despite these uncertainties, we will model the joint UCD plus bright dwarf population as if it is relaxed. As we show in the next section, this provides a marginally acceptable fit to the known mass distribution in the Fornax cluster. 4.3 Cluster mass profile. 8 where M BCG= 2π 2 a 3 BCG ρ BCG,0= 2.0 × 10 12M ⊙; a BCG= 30 kpc; M clus,0= 4πρ clus,0 a 3 clus= 1.1 × 10 14M ⊙; a clus= 400 kpc.
Here, ρ( r) is the density at clustocentric radius r, M r is the mass contained within radius r, x BCG= r/ a BCG and x clus= r/ a clus. Given the uncertainties in the observations, any other model that has M∝ r in the centre, and that passes through the other mass points mentioned above, would be equally acceptable. The observational constraints are shown in as black circles, and the model as a solid, magenta line. 9 We can use this in two ways: to predict the mass distribution, given our dynamical model for the population, or to predict the velocity dispersion profile for the given observed mass profile.shows a comparison between the observed mass profile and that predicted by two of the acceptable density models with constant velocity dispersion of 310 km s −1 and isotropic velocity dispersion tensors, β= 0. We have also tried models with β 0. This makes very little difference to the s= 3 prediction but substantially worsens the s= 4 fit to the data at small radii.Reversing this procedure, gives the predicted velocity dispersion profile for a given density profile and observed cluster mass distribution. In making this prediction, we have taken the approximation that the logarithmic gradient in the velocity dispersion is small compared to that of the density.
Once again, taking β to be greater than zero makes little difference to the s= 3 prediction, but worsens the s= 4 one, giving higher predicted velocity dispersion at small radii. In both these plots, the s= 3 curve provides the closer fit to the data. That it does not match every wiggle in the mass profile in is not surprising given that the latter is somewhat arbitrary and that we have not allowed the velocity dispersion to vary with radius. The normalization is a little too high: lowering the velocity dispersion to 283 km s −1 would provide a very good fit to the mass profile. Given that this is only 1σ away from the measured value in, we regard this as marginally acceptable. The predicted isotropic velocity dispersion profiles for the mass model given in and for density profiles with parameters s= 3, a= 5 kpc (solid, red) and s= 4, a= 90 kpc (dotted, blue).In, it may seem at first sight that the decline in velocity dispersion away from the core of the cluster mimics that seen in the UCD observations.
However, a closer inspection reveals that the minimum in velocity dispersion seen in this plot lies at too small a radius and that by the edge of the UCD observations at around 300 kpc the velocity dispersion has risen to its central value. 5 A STATIC MODEL OF GALAXY THRESHINGIn this section, we investigate the simplest threshing scenario in which dwarf galaxies orbit within the present-day Fornax cluster and are threshed if they pass close to the cluster core. We show that there are too many UCD galaxies at large radii for this model to be viable.
We conclude that in any threshing model, disruption must occur near the cores of smaller subclumps, prior to cluster formation. 5.1 Threshing radiiTo estimate the fraction of dwarf orbits at a given radius which lead to threshing, we calculate the probability for a galaxy with initial projected clustocentric radius and line-of-sight velocity to have R min. The predicted threshing radius as a function of UCD B magnitude.Our approach in estimating the threshing radii is very similar to that used by except for the following differences. First, we specifically use the local gradient of the cluster potential (rather than the point-mass assumption) and we add a core component to the cluster NFW potential.
Secondly, we have used more recent scaling relations to derive the dwarf galaxy core masses as a function of their absolute magnitudes. Our estimates give very similar threshing radii: compare our to their fig. 7.Recently, (2008, hereafter GMK08) have conducted numerical simulations of threshing in a static potential similar to that of the Virgo cluster.
They use two different models of a dwarf galaxy: one which consists solely of an extended dark matter halo with an NFW profile, and one in which this profile has been centrally concentrated by a dissipative baryonic disc. For the latter, the threshing radii they find are similar to ours. The dark-matter-only haloes can have much greater threshing radii, up to 200 kpc, but only for galaxies on quite circular orbits. As we discuss in Section 6, the two models bracket our predictions for UCD fractions as a function of radius, and both lead to the same qualitative results.The detailed threshing simulations of individual dwarf galaxies by showed that several pericentre passages within the threshing radius were necessary to completely strip the dwarf galaxy. In our model below, we do not count the number of orbits, but simply assume that any galaxy with an orbit that passes within its threshing radius will be stripped. This assumption is reasonable for galaxies within about 100 kpc of the cluster centre, but for those galaxies with radii of the order of 300 kpc, on the outskirts of the observed UCD distribution, there may have been only a single pericentric passage in the lifetime of the cluster. This could lead to an overestimate of the UCD fraction at large radii and would strengthen our results.
5.2 Galaxy orbits. 17 Simple iteration of this equation quickly finds the minimum orbital radius (pericentre).For each value of r 0, we draw 10 000 velocities with the appropriate Gaussian distributions in each of the radial and tangential directions, then solve for the pericentric radius. An example histogram is shown in. The sharp spike at r min= r 0 is because any orbit that has an initial radial velocity close to zero and a tangential velocity that exceeds the circular velocity at that radius will already be at pericentre. More importantly, there is a wide distribution of minimum radii extending all the way down to r min≈ 0, even for an isotropic velocity dispersion tensor.
This orbital distribution is in good agreement with that found in cosmological simulations, for example. A histogram showing the probability density for the distribution of minimum orbital radii (pericentres) for a selection of galaxy orbits drawn from the appropriate Gaussian distribution of velocities. For this particular example, the one percentile of minimum radii is at r min≈ 0.03 r 0.The variation in threshing radii for different galaxies is small and so for simplicity we adopt a constant value of 30 kpc. Then, for each radius, r, we can tabulate the fraction of orbits that pass within this radius. This can then be projected along the line-of-sight with the appropriate density weighting to determine the fraction of threshed orbits as a function of projected distance from the cluster centre.
Chuck d autobiography of mistachuck rar file. The results of this calculation are shown in for the two example density profiles discussed above. Comparison of observed and predicted fractions of UCDs. The circles show the observed UCD fraction (of the joint UCD plus bright dwarf sample) as a function of projected radius from the centre of the cluster.
The lines show the predicted fraction of orbits that pass within the threshing radius of 30 kpc for s= 3, a= 5 kpc, β= 0 (solid, red), s= 3, a= 5 kpc, β= 0.5 (dashed, green) and s= 4, a= 90 kpc, β= 0., (dotted, blue).It is immediately apparent that the predicted fraction of threshed galaxies is far too low at radii greater than about 50 kpc. The predicted UCD fraction drops rapidly at this radius, whereas the observed fraction of UCDs stays high out to 250 kpc. (We have checked that this conclusion is unaltered even if the UCDs are distributed on a plane perpendicular to the line-of-sight such that their projected radii are equal to the true distances from the centre of the cluster.) There are many simplifications and uncertainties in the model, but it is hard to see how these could make a difference of a factor of 5. The static threshing model is simply untenable. 6 SUMMARY AND CONCLUSIONSIn this paper, we have investigated the possibility that UCD galaxies are formed by the threshing of nucleated, early-type dwarf galaxies.We first contrast the distribution of nucleated and non-nucleated dwarfs, which are indistinguishable apart from a small excess of bright, nucleated dwarfs at small clustocentric radii.
We concur with the conclusion of CPF06 that the observations are consistent with a single population in which all dwarfs are nucleated, with a ratio of nuclear to total magnitude that varies slowly with magnitude. However, we need to flatten their relation in order to obtain a good fit when extrapolating to fainter magnitudes.Given this hypothesis, we can reproduce the magnitude distribution of the UCD population, except at bright magnitudes where the model predicts more UCDs than are observed. Under the threshing model, the UCDs are likely to have originated from dwarfs with magnitudes brighter than about M B=−15. We use the joint UCD plus bright dwarf population in the modelling that follows.The threshing model predicts that over half of all dwarf galaxies must be disrupted: 38 surviving dwarfs have nuclei of similar magnitude to the 49 observed UCDs. This may seem excessive but corresponds to an intracluster light fraction of just 8 per cent, well within the observed range for clusters of this mass (,;; ).
18 where x= r/ a, and a and s are constants, with s lying between about 3 and 4.5.The velocity dispersion of UCD galaxies shows a sharp decline with radius that is hard to explain. It may in part be due to a radial bias in the orbits, but this is not enough in itself to explain the effect. The velocity dispersion of bright dwarfs is greater than that of the UCDs. When the two are combined, then the joint population with density slope s= 3 provides a marginally acceptable fit to the mass profile of Fornax.We have tested the simplest possible threshing model, in which dwarf galaxies move on orbits in a static cluster potential and are threshed if they pass within a radius at which the tidal force from the cluster exceeds the internal gravity at the core of their dark matter halo. This fails to reproduce the observed fraction of UCDs at radii greater than 50 kpc from the core of Fornax. There are many deficiencies in the model but these are unlikely to raise the threshing radii by a factor of 5, as is required, and so we conclude that this static mode is unviable.Our results have several points of agreement with the earlier work by despite a very different approach: we have used analytic descriptions of the cluster dynamics compared to their numerical computations.
In our work, we have based our prediction on a parent sample of dwarf galaxies generated directly from the known Fornax galaxies, whereas Bekki et al. Generated their galaxy sample from more general empirical relations for the luminosity functions and radial profiles of galaxies within clusters.
In particular, they used a King profile with a core radius of 50 kpc for the density distribution, very different from our model. They demonstrate that dwarf galaxies are disrupted if they pass inside their critical threshing radius when orbiting the cluster centre. They then use this radius to estimate the population of threshed galaxies (UCDs) in the Fornax cluster.
They find this to be consistent with the known distribution of the seven very luminous UCDs known in the cluster at that time.Our conclusion (refuting the simple threshing model) differs from that of Bekki et al. For a number of reasons. First, we use the measured positions of galaxies in Fornax, rather than a generic King model.
We also have many fewer dwarf galaxies than predicted by their Schechter model for the cluster luminosity function. In addition, we have extended the analysis to much lower luminosities of both the UCDs (as new data have become available) and the parent galaxies (due to the greater difference in nuclear to total luminosity now used). This new analysis has clearly revealed a disagreement between the number of UCDs at large clustocentric distances and the threshing predictions.A recent paper by GMK08 undertook an extensive series of simulations to investigate the disruption of UCD host galaxies within a cluster potential similar to that of the Virgo cluster. They considered two different models for the host galaxy with very different degrees of central concentration and followed their threshing in a static potential over 5 Gyr. They then looked at the orbits of particles in a cosmological simulation of cluster formation to assess which of those orbits would lead to threshing.
This latter step follows the dynamical evolution of the halo and is much more realistic than a static potential.GMK08 state that their model ‘leads to the observed spatial distribution of UCDs’, in apparent disagreement with our results above. In fact, our theoretical UCD fractions as a function of radius agree with theirs and are bracketed by their upper and lower predictions.
The difference in the conclusion arises from the very different observed threshing fractions that we adopt. GMK08 use only 15 UCDs in both Virgo and Fornax combined, whereas we use a new sample of 49 UCDs from Fornax alone. Also, GMK08 do not say how they define the nucleated dwarfs corresponding to the parent sample, whereas we are careful to select only those dwarfs that would have nuclei that match those of the observed UCDs.In conclusion, the origin of UCDs as dwarf galaxy nuclei remains unproven. Our modelling has revealed a number of attractive features:The distribution of nuclear magnitudes for dwarf galaxies roughly matches that of known UCD galaxies.UCDs are more centrally concentrated within Fornax than are dwarf galaxies. (However, this would also be true if the UCDs constituted an extended globular cluster population around NGC 1399.)The joint UCD plus bright dwarf population has a smooth density profile with a recognisable (NFW) form and appears to sit in dynamical equilibrium within the Fornax cluster.At the same time, there are several major deficiencies in the model:The model requires that more dwarf galaxies must have been disrupted in Fornax than currently remain. However, the spatial distribution of dwarfs matches that of the total mass profile of the cluster and shows no sign of galaxy disruption near the cluster core.The very low velocity dispersion of UCDs as compared to bright dwarfs is unexplained, as is the sharp decline in velocity dispersion of the UCDs with radius. (However, this would prove true for any dynamical model of the UCD population, regardless of its origin.)A static threshing model for UCD formation, based upon orbits within the current cluster potential, is a hopeless failure.
It predicts far too few UCDs at radii greater than about 30 kpc.The simulations of GMK08 within an evolving cluster potential also give too few UCDs at large radii.The balance of evidence would seem to be against the threshing model. Before dismissing the model altogether, however, we note that the threshing may have occurred within smaller sub-clusters that later fell into Fornax and have not yet reached dynamical equilibrium. This mechanism is suggested by the spatial distribution of UCDs in the Fornax cluster: they show some association with normal galaxies and, in particular, lie in a band across the cluster.In considering the threshing hypothesis for UCD formation, we should not discuss the dynamical properties of the objects in isolation from their internal properties.
Studied the stellar populations of Virgo cluster UCDs and concluded that the Virgo UCDs have stellar populations the globular clusters of the central galaxies M87 and M49 (old ages, a range of metallicity and super-solar alpha-abundances). On this basis, the Virgo UCD stellar populations are not consistent with simple threshing model. On the other hand, found metallicities and (a range of) ages in Fornax cluster UCDs, which are more in agreement with the hypothesis that the Fornax UCDs are threshed nuclei. A detailed analysis of the structure and colours of both Virgo and Fornax UCDs concluded that their structural properties could be consistent with either globular clusters or dwarf galaxy nuclei, with the interesting observation that UCDs are about twice as extended (in effective radius) as the nuclei of dwarf galaxies at the same luminosity.Most of these observational results, as well as our own analysis in this paper, argue against the simple threshing hypothesis for UCD formation. \'We do not have any formal proof of this but note that the weights are equal when σ e, i≪σ and tend to the known optimal weighting w i∝ 1/σ 2 e, i when σ e, i≫σ. A similar, but not identical, expression is given by.This work was initiated while PAT was a visitor to Queensland under ARC Discovery Projects Grant DP0557676, and continued whist MJD was visiting Sussex with partial funding from PPARC Grant PP/D001579/1.
We would like to thank an anonymous referee for many useful suggestions for comparison with previous work. Appendices APPENDIX A: TABLES OF GALAXY AND UCD DATATables A1 and A2 are given in the online version of the article. APPENDIX B: VARIATION IN LINE-OF-SIGHT VELOCITY WITH RADIUSThis Appendix calculates the expected variation in the line-of-sight velocity dispersion of UCDs with radius resulting from anisotropic motions in a declining density profile.We take the velocity dispersion tensor to be aligned with the radial direction and to have diagonal components σ r, σ t and σ t, where σ r and σ t are the radial and tangential components of velocity dispersion, respectively. The velocity anisotropy parameter is defined as β= 1σ 2 t/σ 2 r– thus β= 0 for isotropic orbits and β 0 for preferentially radial orbits. We assume that both σ 2 r and β are constant throughout the cluster.
In practice, one might expect some radial variation in these quantities, but the data are insufficient to constrain more complex models. (B3) where z measures distance along the line of sight from the mid-point through the cluster and r is the radius to a point on that line such that z= R tan θ and r= R/cos θ. The value of the integral quotient in varies between approximately 0.62 and 0.76 for inner and outer radial bins given in (the precise values depend upon the density model for the UCDs but all acceptable fits to the data give similar results). SUPPLEMENTARY MATERIALAdditional may be found in the online version of this article.Table A1. The galaxy sample.Table A2. The UCD sample.Please note: Blackwell Publishing are not responsible for the content or functionality of any supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
...'>Galaxy Scenario File Differs From Host(08.05.2020)1 INTRODUCTIONIn recent years, considerable evidence has been accumulated regarding the fact that disruptive processes play an important role in galaxy evolution as well as the more dominant hierarchical merging. Observational evidence for these disruptive processes is particularly evident in the dense environment of galaxy clusters. The evidence includes populations of individual intra-cluster objects such as planetary nebulae (; ) and red giant stars , as well as the general diffuse light now thought to make up a significant fraction of the total stellar mass in clusters (,;; ).In this paper, we focus on a relatively new component of intra-cluster space, ultra-compact dwarf (UCD) galaxies. These are compact systems of old stars akin to globular clusters but they are 10–100 times more luminous than Galactic globular clusters and they are located in intra-cluster space between galaxies. The first UCDs were discovered in the Fornax cluster independently in studies of globular clusters (; ) and in studies of compact dwarf galaxies (; ). The UCDs are unlike any known galaxies in terms of luminosity, morphology and size. Several hypotheses have been suggested to explain the origin of UCDs ranging from them being the high-luminosity end of a putative intra-cluster globular cluster distribution to being the evolved super-star clusters formed in galaxy merger events.
In this paper, we focus on the model that UCDs are formed by the global tidal field of a cluster which can strip, or ‘thresh’, the outer stellar envelopes of nucleated dwarf galaxies (dE, Ns and dS0, Ns) as they pass repeatedly through the inner regions of a cluster leaving just the bare nucleus to survive as a UCD (;; ).The motivation for the current work is the subsequent discovery of a larger population of fainter UCDs in the central region of the Fornax cluster (; ). This sample of 60 UCDs is large enough to permit us to test several aspects of the threshing hypothesis using a statistically significant sample. Our focus will be to test simple aspects of the distributions of the UCD and galaxy populations. An alternative approach based on the internal properties of the UCDs is also in progress (e.g.
).Our basic premise for this paper is that if UCDs are descendants of disrupted galaxies, then the UCD parent population can be modelled by the combined current population of Fornax cluster UCDs and dwarf galaxies. We test whether the observed spatial and velocity distributions of the two populations are consistent with this hypothesis and conclude that they are. We then model the orbits of UCDs/galaxies drawn from this joint population to determine what fraction of them passes close enough to the cluster centre to lead to threshing. The relative fraction UCDs to dwarfs seen at large radii in Fornax is inconsistent with this static threshing model.In Section 2, we define the UCD and galaxy samples for our analysis. In Section 3, we test if the luminosity function of the UCDs is consistent with them having been drawn as random sample from the nuclei of dwarf galaxies in the cluster. Section 4 develops a dynamical model for the joint population, and Section 5 calculates the fraction of threshed orbits at each radius. Finally, in Section 6, we summarize our results and draw conclusions about the plausibility of the threshing hypothesis.We adopt a distance of 20 Mpc to the Fornax cluster corresponding to a distance modulus of 31.51 mag.
In this paper, we are not concerned with late-type galaxies. To avoid endless repetition, we use the terms galaxy and dwarf to refer to early-type objects only, as defined in Section 2.1. 2 DATA SAMPLES FROM THE FORNAX CLUSTER 2.1 Early-type galaxy sampleThe hypothesis that we test in this paper is that UCDs form from the disruption of nucleated dwarf galaxies. Our authority for the morphological classification of Fornax cluster galaxies is the Fornax Cluster Catalogue (FCC; ) which was based on photographic data.
After running the docker-galaxy-stable container with the command:sudo docker run -i -t. Galaxy Scenario File Differs From Host To Facebook. The Galaxy Tab comes with either 16GB or 32GB of internal storage. It’s like the hard drive in your computer. That storage is used for your apps, music, videos, pictures, and a host of other information. You probably didn’t get a Galaxy Tab because you enjoy managing files on a computer and wanted another gizmo to hone your skills.
The FCC lists some 291 galaxies as early types (i.e. Not Sa-d, Sm or Im; we include spheroidal galaxies in our sample). Of these, 103 are classified as nucleated. Recent Hubble Space Telescope ( HST) imaging results from the ACS Virgo Cluster Survey (, hereafter CPF06) suggest that the frequency of nucleation in early-type galaxies is actually much higher than suggested from the photographic ground-based surveys. Faint nuclei are difficult to detect because they are washed out by atmospheric seeing, and the central regions of the brightest galaxies are saturated. Notably, CPF06 suggest that potentially all dwarf galaxies may contain nuclei.
We apply the CPF6 model to our Fornax data in Section 3.1 and show that the observed fraction of nucleated dwarfs as a function of magnitude is consistent with this assumption. Also, the spatial distributions of nucleated and non-nucleated dwarfs, shown in, are indistinguishable. The cumulative numbers of nucleated (dashed, blue) and non-nucleated (dotted, red) dwarf galaxies in Fornax as a function of projected radius between 17.5 and 1050 kpc.
Shown also as a solid, black line is the cluster mass profile described in Section 4.3.For the purposes of this current work, therefore, we define the parent galaxy sample to be all early-type dwarf galaxies listed as definite or probable members in the FCC. Where radial velocities are known, we use these to define membership, otherwise we use the FCC membership classifications.
New radial velocities result in the removal of some FCC-classified members and the inclusion of some FCC-classified background galaxies, now known to be members (e.g. More recent radial velocity measurements are taken from. Where the classification is uncertain, we have taken all galaxies fainter than M B=−14 as dwarf; the maximum magnitude for a normal galaxy is then M B=−16.3 and the minimum magnitude for a dwarf galaxy is M B=−17.8. A complete list of the galaxies is given in Table A1.The galaxies in our sample have morphological classifications from the FCC which can include a flag to show that they are nucleated. We use these flags in our discussion below, but we emphasize that there is no HST imaging for most of these galaxies, so we cannot tell with certainty if a given galaxy is really nucleated. We instead adopt the general result of CPF06 that all dwarf galaxies have nuclei, with a magnitude that is related to that of the host galaxy (see Section 3.1).The dwarf galaxy sample that we use is effectively complete to a limit of around M B=−13.5 (see FCC).
The velocity data used to confirm cluster membership are complete for galaxies brighter than M B=−16 and become 50 per cent complete at M B=−14.5. 2.2 UCD sampleThe UCDs were originally discovered as part of the all-object Fornax Cluster Spectroscopic Survey. Although the original survey measured all objects (to b J. The b J photographic APM magnitudes were converted to m B magnitudes by the approximate relation m B= b J+ 0.20based on the relation of b J= B− 0.28( B− V) for an average dwarf galaxy colour of B− V= 0.7 so that M B= b J+ 0.20 − 31.51 = b J− 31.31.The spatial locations of the UCDs are far from circularly symmetric about the centre of Fornax but tend to lie in a band running from northeast to southwest (see fig. This presumably reflects the infall pattern on to the cluster. Provided that the distribution is relaxed, this will not affect the dynamical modelling; however it may confuse the relation between the true three-dimensional positions and velocities and the observed ones.
For the purposes of modelling in this paper, we assume a spherically symmetric distribution. 2.3 Joint sample selectionAccording to our central hypothesis, there was an original parent population of dwarf galaxies, some of which were subsequently disrupted to form UCDs.
She s dating the gangster free download. Unfortunately, the selection effects are different for the two sub-populations and so we need to use different samples for different parts of our analysis. This will be described at the beginning of each relevant section. Here, we make a few general comments on the relative spatial extent of the dwarf and UCD samples.The FCC is a wide-field survey. It covers a rectangular region with a largest inscribed circle that extends to a radius of 3° (1.05 Mpc) from the cluster centre.
Our main UCD sample is limited to a smaller region defined by a maximum radius of (314 kpc) from the cluster centre. We have modelled the density distribution and estimate that there may be up to six missing UCDs at larger radii (although, for the brighter UCDs, two additional regions extending to a radius of 3° have been surveyed and no UCDs were found). Adding six extra UCDs with the appropriate density distribution makes very little difference to the modelling of the spatial distribution of the joint UCD plus dwarf population in Section 4.1.For the UCDs, there is also a need to exclude those at very small radii from the central cluster galaxy, NGC 1399. The distribution of UCD radial velocities shown in shows a trend to smaller velocities (and velocity dispersion) at low radius.
The inner UCDs are clearly moving in the galactic and not the cluster potential and could be considered as bright globular clusters attached to NGC 1399. The choice of where to draw the dividing line between galactic and intracluster UCDs is somewhat arbitrary.
We cut at 3 arcmin (17.5 kpc) which excludes 11 UCDs from our sample (see ), including the two relatively low velocity UCDs seen in the figure at a radius and velocity of approximately 15 kpc and 1140 km s −1, respectively. (Including these two in our analysis makes little difference to the results and would leave the velocity dispersion of the excluded clusters as formally zero once the velocity errors have been accounted for.). A comparison of the UCD and galaxy populations. The radial velocities are plotted as a function of projected radius. UCDs are shown as red triangles, normal galaxies as blue squares, and dwarfs brighter and fainter than M B=−15.0 as blue circles and crosses, respectively. The yellow shaded area shows a running mean of the 1σ velocity dispersion.For reasons that we will describe in Section 3.2, we divide the dwarf population into two. ‘Bright dwarfs’ with M B.
3 COMPARISON OF LUMINOSITY DISTRIBUTIONSIn this section, we develop a unified model for nucleated and non-nucleated dwarf galaxies whereby all galaxies have nuclei but only a fraction of these are bright enough to be detected and classified as such in the FCC. We then go on to compare the predicted luminosity function of nuclei with that of UCDs. As we are interested only in the shape of the magnitude distributions, we use the full samples of dwarfs and UCDs even though two extend over different spatial regions. 3.1 Early-type nucleiAn important property of the parent galaxies is the luminosity distribution of the galaxy nuclei as these will be compared to the UCD luminosities.
We cannot directly measure the luminosities of galaxy nuclei in the Fornax cluster because most do not have high-resolution HST imaging. Instead, we take a statistical approach: we assume that all dwarf galaxies host nuclei and infer the nuclear luminosities from the total galaxy luminosities.CPF06 measured nuclear luminosities for 51 dwarf galaxies in the Virgo cluster.
They confirmed previous suggestions that the nuclear luminosities increase with the galaxy luminosity. They modelled this relation as both a fixed offset between the nuclear and total magnitudes, g′ nuc= g′ gal+ (6.25 ± 0.21), and an offset slowly varying with magnitude, g′ nuc= (0.90 ± 0.18) g′ gal+ (7.59 ± 2.50).
We note that our galaxy sample extends to much fainter magnitudes than did the Virgo sample studied by CPF06, and so we will have to extrapolate their relation. We therefore allow the slope of the relation to vary, but require that it go through the mid-point of the CPF06 data ( g′ gal, g′ nuc= 13.40, 19.65) defined by the crossing point of their two relations.We model the scatter in the relationship by adding a random normal variable with a mean of zero and a standard deviation of 1.5 to the derived nuclear magnitude.
The standard deviation was inferred from the scatter about the fixed-slope fit of CPF06 (their ).To convert the ACS g′ photometry to absolute magnitudes, we first use the mean value of B T− g= 0.30 for the ACS dwarf galaxies to convert g magnitudes to B T. We then apply the distance modulus of 31.09 mag quoted by CPF06, obtaining M B= g′−30.79.To constrain the slope of the g′ nuc– g′ gal relation, we require that it predicts the correct distribution of galaxies that we would expect to have been classified as nucleated in the photographic FCC survey. For each galaxy, we predict its nuclear luminosity as above, then we classify it as nucleated if the nucleus is brighter than the point-source detection limit on the photographic plate (approximately B T= 22.6 or M B=−8.9 for the FCC; H. Ferguson, private communication).
The distribution of dwarf galaxies classified as ‘nucleated’. The leftmost, blue bars show the observed magnitudes of all Fornax dwarfs.
The middle, green bars show only those whose predicted nuclear magnitudes would be greater than −8.9 according to the model developed in the text. Finally, the rightmost, brown bars show the actual magnitude distribution of nucleated dwarfs in Fornax.We show in Section 4.1 that the spatial distributions of the nucleated and non-nucleated dwarfs are identical, thus lending further support to the hypothesis that the presence of a detectable nucleus is the only difference between them. 3.2 UCDsFrom the observed dwarf population, we can now predict the distribution of nuclear magnitudes.
If we assume that the threshing process is independent of galactic (and nuclear) luminosity, then these should have the same shape of distribution as the UCDs. Furthermore, the relative normalization should tell us what fraction of the dwarfs has been threshed. The predicted and actual UCD distributions are given in. Note that the predicted numbers from our model have been scaled down by the completeness values in to allow for the fraction of unmeasured objects. The leftmost, blue bars show the predicted distribution of nuclear magnitudes for Fornax dwarfs, averaged over 100 realizations: the middle, green bars multiply this by the completeness factor for UCD observations. If the threshing hypothesis is correct, then this should be proportional to the rightmost, brown bars that show the observed distribution of UCD magnitudes.The figure shows that the predicted luminosity distribution of UCDs is not perfect.
The model seems to give an excess of UCDs brighter than M B=−11.25 as compared to fainter ones. It is hard to assess the significance of this: given the relatively small number of objects and the uncertainties in the relationship between galactic and nuclear magnitudes, it is probably acceptable.The model predicts that 38 dwarfs should have nuclei that correspond to observable UCDs. This motivates our selection of M B=−15.0 as the dividing line between bright and faint dwarfs, as this gives 38 bright dwarfs. Without scatter, would have predicted a brighter limit, M B≈−15.8, but the greater number of faint galaxies biases things towards fainter magnitudes. Of these 38 dwarfs, only 11 lie within 314 kpc. Thus, the model predicts that the vast majority of dwarfs within this region are likely to be threshed.
Even when averaged over the whole sample, more than half the dwarf population should be threshed. 4 A DYNAMICAL MODEL FOR THE JOINT DWARF/UCD POPULATIONThis section constructs a model of the three-dimensional density distribution of the joint dwarf/UCD population in the cluster.
There will turn out to be some degeneracy in the models which we will attempt to constrain by matching them to observed mass models for Fornax.When comparing dwarfs and UCDs, we restrict our attention to the bright dwarfs, M B −15), then the difference is removed entirely. This observation strengthens the hypothesis of the previous section that dwarfs classified as nucleated or non-nucleated may differ only in the detectability of their central nucleus.Also shown in the figure is the observed mass profile of the Fornax cluster, as described in Section 4.3. The cumulative number density profile of the dwarfs matches that of the cluster mass profile very well and shows no evidence of dwarf galaxy disruption near the cluster core.Next, in we compare the radial distributions of normal galaxies, bright and faint dwarfs and UCDs. Because the UCD survey extends only out to 314 kpc, we have adjusted the normalization of the cumulative distribution to match that of the dwarfs at this radius. The cumulative numbers of normal galaxies (dash–dotted, blue), bright dwarfs (dotted, red), faint dwarfs (dashed, green) and UCDs (solid, black) in Fornax as a function of projected radius between 17.5 and 1050 kpc.
We have adjusted the normalization of the UCD curve to match that of the dwarfs at 314 kpc.It is immediately obvious that the different populations show different degrees of central concentration. Notably, within 314 kpc, the radial distribution of the faint dwarfs is significantly more extended than that of both the bright dwarfs and the UCDs. At first glance, this appears to be at odds with the threshing model developed below (Section 5.1). The model suggests that faint dwarfs are more compact and therefore less likely to be threshed than bright ones, but we have not looked for UCDs at magnitudes corresponding to the faint dwarfs so we cannot test the number that have been threshed. Conversely, we do not see a significant difference between the distributions of UCDs and bright dwarfs, although we would expect the UCDs to be more centrally concentrated than the (surviving) dwarf galaxies according to our model.
In this case, the relatively small number of objects involved may explain why the difference is not significant.Outside 314 kpc, the distributions of bright and faint dwarfs are indistinguishable. There are hints that the UCD distribution is flattening between 200 and 314 kpc and no UCDs have been detected in (incomplete) observations in a few fields beyond this radius. For the purposes of the modelling that follows, we therefore assume that there are no UCDs with cluster-centric radii exceeding 314 kpc. If there are any, the number density of dwarfs rises so rapidly in this region that the latter would dominate anyway.We plot the radial distribution of normal galaxies just for interest. The numbers are so few that it is formally indistinguishable from either the bright or faint dwarf population. We note, however, that it is significantly less centrally concentrated within 314 kpc than the UCD population. 2 where x= r/ a, and a and s are fitting parameters.
(We fit only for the shape of the distribution: the normalization ρ 0 can be chosen so as to match the correct number of objects.) We project each distribution on to the sky and then compare the predicted cumulative mass profile as a function of radius to the observed distribution, using the Kolmogorov–Smirnov test.shows the allowable range of parameters and shows the best-fitting model, although there is a strong degeneracy between a and s such that a wide variety of fits are acceptable. We will show results for s= 3.0, a= 5 kpc and for s= 4.0, a= 90 kpc; both lead to very similar conclusions. Velocity dispersions for different subsamples of the UCD and galaxy populations in Fornax. The completeness of the velocity data can be found by comparing the numbers in this table with those in, but basically it is high except for the faint dwarfs. When calculating velocity dispersions for the different sub-samples, we have used the mean for the full sample of all galaxies (normal, dwarf and UCD) with radii greater than 17.5 kpc, . The final column shows the rms error in the velocity dispersion measurements determined by bootstrap resampling 1000 times.
Velocity dispersions for different subsamples of the UCD and galaxy populations in Fornax. The completeness of the velocity data can be found by comparing the numbers in this table with those in, but basically it is high except for the faint dwarfs. When calculating velocity dispersions for the different sub-samples, we have used the mean for the full sample of all galaxies (normal, dwarf and UCD) with radii greater than 17.5 kpc, . The final column shows the rms error in the velocity dispersion measurements determined by bootstrap resampling 1000 times. The low-velocity dispersion of UCDs as compared to other galaxies is expected in the threshing model, because the UCDs are more centrally concentrated in the cluster potential (i.e.
Have a steeper density profile) – unfortunately, there are too few UCDs to quantify this. However, the table shows a number of other features that are hard to explain.First, why is the velocity dispersion of normal galaxies so much smaller than that of dwarfs, and especially bright dwarfs, given that the two have similar radial distributions within the cluster? In, this difference was interpreted as indicating that the dwarf galaxies were an unrelaxed, infalling, population. In this paper, we are assuming that all galaxies (including UCDs) are relaxed: an alternative explanation is that many of the dwarfs may be orbiting in bound subhaloes, with normal galaxies located at their centres.Secondly, the line-of-sight velocity dispersion for UCDs is significantly higher at small radii than at large ones. Some difference of this kind would be expected if the UCDs are on preferentially radial orbits. Defining the velocity anisotropy parameter as β= 1 −σ 2 t/σ 2 r, where σ r is the radial velocity dispersion with respect to the cluster centre and σ t the tangential one, then this would correspond to β 0.
Unfortunately, the expected variation, calculated in Appendix B, is much too small to explain the observations. The observed decline in velocity dispersion between the inner and outer bin is 1:0.58.
Even if we allow each measurement to move up to 1σ towards agreement (with probability less than 3 per cent), the ratio remains 1:0.80. This can only be explained with β= 1, corresponding to purely radial orbits.
The explanation for this discrepancy may be related to the non-uniform distribution of UCDs within the Fornax cluster. If the outer UCDs have orbits that are preferentially moving perpendicular to the line-of-sight, then that would explain the effect.Despite these uncertainties, we will model the joint UCD plus bright dwarf population as if it is relaxed. As we show in the next section, this provides a marginally acceptable fit to the known mass distribution in the Fornax cluster. 4.3 Cluster mass profile. 8 where M BCG= 2π 2 a 3 BCG ρ BCG,0= 2.0 × 10 12M ⊙; a BCG= 30 kpc; M clus,0= 4πρ clus,0 a 3 clus= 1.1 × 10 14M ⊙; a clus= 400 kpc.
Here, ρ( r) is the density at clustocentric radius r, M r is the mass contained within radius r, x BCG= r/ a BCG and x clus= r/ a clus. Given the uncertainties in the observations, any other model that has M∝ r in the centre, and that passes through the other mass points mentioned above, would be equally acceptable. The observational constraints are shown in as black circles, and the model as a solid, magenta line. 9 We can use this in two ways: to predict the mass distribution, given our dynamical model for the population, or to predict the velocity dispersion profile for the given observed mass profile.shows a comparison between the observed mass profile and that predicted by two of the acceptable density models with constant velocity dispersion of 310 km s −1 and isotropic velocity dispersion tensors, β= 0. We have also tried models with β 0. This makes very little difference to the s= 3 prediction but substantially worsens the s= 4 fit to the data at small radii.Reversing this procedure, gives the predicted velocity dispersion profile for a given density profile and observed cluster mass distribution. In making this prediction, we have taken the approximation that the logarithmic gradient in the velocity dispersion is small compared to that of the density.
Once again, taking β to be greater than zero makes little difference to the s= 3 prediction, but worsens the s= 4 one, giving higher predicted velocity dispersion at small radii. In both these plots, the s= 3 curve provides the closer fit to the data. That it does not match every wiggle in the mass profile in is not surprising given that the latter is somewhat arbitrary and that we have not allowed the velocity dispersion to vary with radius. The normalization is a little too high: lowering the velocity dispersion to 283 km s −1 would provide a very good fit to the mass profile. Given that this is only 1σ away from the measured value in, we regard this as marginally acceptable. The predicted isotropic velocity dispersion profiles for the mass model given in and for density profiles with parameters s= 3, a= 5 kpc (solid, red) and s= 4, a= 90 kpc (dotted, blue).In, it may seem at first sight that the decline in velocity dispersion away from the core of the cluster mimics that seen in the UCD observations.
However, a closer inspection reveals that the minimum in velocity dispersion seen in this plot lies at too small a radius and that by the edge of the UCD observations at around 300 kpc the velocity dispersion has risen to its central value. 5 A STATIC MODEL OF GALAXY THRESHINGIn this section, we investigate the simplest threshing scenario in which dwarf galaxies orbit within the present-day Fornax cluster and are threshed if they pass close to the cluster core. We show that there are too many UCD galaxies at large radii for this model to be viable.
We conclude that in any threshing model, disruption must occur near the cores of smaller subclumps, prior to cluster formation. 5.1 Threshing radiiTo estimate the fraction of dwarf orbits at a given radius which lead to threshing, we calculate the probability for a galaxy with initial projected clustocentric radius and line-of-sight velocity to have R min. The predicted threshing radius as a function of UCD B magnitude.Our approach in estimating the threshing radii is very similar to that used by except for the following differences. First, we specifically use the local gradient of the cluster potential (rather than the point-mass assumption) and we add a core component to the cluster NFW potential.
Secondly, we have used more recent scaling relations to derive the dwarf galaxy core masses as a function of their absolute magnitudes. Our estimates give very similar threshing radii: compare our to their fig. 7.Recently, (2008, hereafter GMK08) have conducted numerical simulations of threshing in a static potential similar to that of the Virgo cluster.
They use two different models of a dwarf galaxy: one which consists solely of an extended dark matter halo with an NFW profile, and one in which this profile has been centrally concentrated by a dissipative baryonic disc. For the latter, the threshing radii they find are similar to ours. The dark-matter-only haloes can have much greater threshing radii, up to 200 kpc, but only for galaxies on quite circular orbits. As we discuss in Section 6, the two models bracket our predictions for UCD fractions as a function of radius, and both lead to the same qualitative results.The detailed threshing simulations of individual dwarf galaxies by showed that several pericentre passages within the threshing radius were necessary to completely strip the dwarf galaxy. In our model below, we do not count the number of orbits, but simply assume that any galaxy with an orbit that passes within its threshing radius will be stripped. This assumption is reasonable for galaxies within about 100 kpc of the cluster centre, but for those galaxies with radii of the order of 300 kpc, on the outskirts of the observed UCD distribution, there may have been only a single pericentric passage in the lifetime of the cluster. This could lead to an overestimate of the UCD fraction at large radii and would strengthen our results.
5.2 Galaxy orbits. 17 Simple iteration of this equation quickly finds the minimum orbital radius (pericentre).For each value of r 0, we draw 10 000 velocities with the appropriate Gaussian distributions in each of the radial and tangential directions, then solve for the pericentric radius. An example histogram is shown in. The sharp spike at r min= r 0 is because any orbit that has an initial radial velocity close to zero and a tangential velocity that exceeds the circular velocity at that radius will already be at pericentre. More importantly, there is a wide distribution of minimum radii extending all the way down to r min≈ 0, even for an isotropic velocity dispersion tensor.
This orbital distribution is in good agreement with that found in cosmological simulations, for example. A histogram showing the probability density for the distribution of minimum orbital radii (pericentres) for a selection of galaxy orbits drawn from the appropriate Gaussian distribution of velocities. For this particular example, the one percentile of minimum radii is at r min≈ 0.03 r 0.The variation in threshing radii for different galaxies is small and so for simplicity we adopt a constant value of 30 kpc. Then, for each radius, r, we can tabulate the fraction of orbits that pass within this radius. This can then be projected along the line-of-sight with the appropriate density weighting to determine the fraction of threshed orbits as a function of projected distance from the cluster centre.
Chuck d autobiography of mistachuck rar file. The results of this calculation are shown in for the two example density profiles discussed above. Comparison of observed and predicted fractions of UCDs. The circles show the observed UCD fraction (of the joint UCD plus bright dwarf sample) as a function of projected radius from the centre of the cluster.
The lines show the predicted fraction of orbits that pass within the threshing radius of 30 kpc for s= 3, a= 5 kpc, β= 0 (solid, red), s= 3, a= 5 kpc, β= 0.5 (dashed, green) and s= 4, a= 90 kpc, β= 0., (dotted, blue).It is immediately apparent that the predicted fraction of threshed galaxies is far too low at radii greater than about 50 kpc. The predicted UCD fraction drops rapidly at this radius, whereas the observed fraction of UCDs stays high out to 250 kpc. (We have checked that this conclusion is unaltered even if the UCDs are distributed on a plane perpendicular to the line-of-sight such that their projected radii are equal to the true distances from the centre of the cluster.) There are many simplifications and uncertainties in the model, but it is hard to see how these could make a difference of a factor of 5. The static threshing model is simply untenable. 6 SUMMARY AND CONCLUSIONSIn this paper, we have investigated the possibility that UCD galaxies are formed by the threshing of nucleated, early-type dwarf galaxies.We first contrast the distribution of nucleated and non-nucleated dwarfs, which are indistinguishable apart from a small excess of bright, nucleated dwarfs at small clustocentric radii.
We concur with the conclusion of CPF06 that the observations are consistent with a single population in which all dwarfs are nucleated, with a ratio of nuclear to total magnitude that varies slowly with magnitude. However, we need to flatten their relation in order to obtain a good fit when extrapolating to fainter magnitudes.Given this hypothesis, we can reproduce the magnitude distribution of the UCD population, except at bright magnitudes where the model predicts more UCDs than are observed. Under the threshing model, the UCDs are likely to have originated from dwarfs with magnitudes brighter than about M B=−15. We use the joint UCD plus bright dwarf population in the modelling that follows.The threshing model predicts that over half of all dwarf galaxies must be disrupted: 38 surviving dwarfs have nuclei of similar magnitude to the 49 observed UCDs. This may seem excessive but corresponds to an intracluster light fraction of just 8 per cent, well within the observed range for clusters of this mass (,;; ).
18 where x= r/ a, and a and s are constants, with s lying between about 3 and 4.5.The velocity dispersion of UCD galaxies shows a sharp decline with radius that is hard to explain. It may in part be due to a radial bias in the orbits, but this is not enough in itself to explain the effect. The velocity dispersion of bright dwarfs is greater than that of the UCDs. When the two are combined, then the joint population with density slope s= 3 provides a marginally acceptable fit to the mass profile of Fornax.We have tested the simplest possible threshing model, in which dwarf galaxies move on orbits in a static cluster potential and are threshed if they pass within a radius at which the tidal force from the cluster exceeds the internal gravity at the core of their dark matter halo. This fails to reproduce the observed fraction of UCDs at radii greater than 50 kpc from the core of Fornax. There are many deficiencies in the model but these are unlikely to raise the threshing radii by a factor of 5, as is required, and so we conclude that this static mode is unviable.Our results have several points of agreement with the earlier work by despite a very different approach: we have used analytic descriptions of the cluster dynamics compared to their numerical computations.
In our work, we have based our prediction on a parent sample of dwarf galaxies generated directly from the known Fornax galaxies, whereas Bekki et al. Generated their galaxy sample from more general empirical relations for the luminosity functions and radial profiles of galaxies within clusters.
In particular, they used a King profile with a core radius of 50 kpc for the density distribution, very different from our model. They demonstrate that dwarf galaxies are disrupted if they pass inside their critical threshing radius when orbiting the cluster centre. They then use this radius to estimate the population of threshed galaxies (UCDs) in the Fornax cluster.
They find this to be consistent with the known distribution of the seven very luminous UCDs known in the cluster at that time.Our conclusion (refuting the simple threshing model) differs from that of Bekki et al. For a number of reasons. First, we use the measured positions of galaxies in Fornax, rather than a generic King model.
We also have many fewer dwarf galaxies than predicted by their Schechter model for the cluster luminosity function. In addition, we have extended the analysis to much lower luminosities of both the UCDs (as new data have become available) and the parent galaxies (due to the greater difference in nuclear to total luminosity now used). This new analysis has clearly revealed a disagreement between the number of UCDs at large clustocentric distances and the threshing predictions.A recent paper by GMK08 undertook an extensive series of simulations to investigate the disruption of UCD host galaxies within a cluster potential similar to that of the Virgo cluster. They considered two different models for the host galaxy with very different degrees of central concentration and followed their threshing in a static potential over 5 Gyr. They then looked at the orbits of particles in a cosmological simulation of cluster formation to assess which of those orbits would lead to threshing.
This latter step follows the dynamical evolution of the halo and is much more realistic than a static potential.GMK08 state that their model ‘leads to the observed spatial distribution of UCDs’, in apparent disagreement with our results above. In fact, our theoretical UCD fractions as a function of radius agree with theirs and are bracketed by their upper and lower predictions.
The difference in the conclusion arises from the very different observed threshing fractions that we adopt. GMK08 use only 15 UCDs in both Virgo and Fornax combined, whereas we use a new sample of 49 UCDs from Fornax alone. Also, GMK08 do not say how they define the nucleated dwarfs corresponding to the parent sample, whereas we are careful to select only those dwarfs that would have nuclei that match those of the observed UCDs.In conclusion, the origin of UCDs as dwarf galaxy nuclei remains unproven. Our modelling has revealed a number of attractive features:The distribution of nuclear magnitudes for dwarf galaxies roughly matches that of known UCD galaxies.UCDs are more centrally concentrated within Fornax than are dwarf galaxies. (However, this would also be true if the UCDs constituted an extended globular cluster population around NGC 1399.)The joint UCD plus bright dwarf population has a smooth density profile with a recognisable (NFW) form and appears to sit in dynamical equilibrium within the Fornax cluster.At the same time, there are several major deficiencies in the model:The model requires that more dwarf galaxies must have been disrupted in Fornax than currently remain. However, the spatial distribution of dwarfs matches that of the total mass profile of the cluster and shows no sign of galaxy disruption near the cluster core.The very low velocity dispersion of UCDs as compared to bright dwarfs is unexplained, as is the sharp decline in velocity dispersion of the UCDs with radius. (However, this would prove true for any dynamical model of the UCD population, regardless of its origin.)A static threshing model for UCD formation, based upon orbits within the current cluster potential, is a hopeless failure.
It predicts far too few UCDs at radii greater than about 30 kpc.The simulations of GMK08 within an evolving cluster potential also give too few UCDs at large radii.The balance of evidence would seem to be against the threshing model. Before dismissing the model altogether, however, we note that the threshing may have occurred within smaller sub-clusters that later fell into Fornax and have not yet reached dynamical equilibrium. This mechanism is suggested by the spatial distribution of UCDs in the Fornax cluster: they show some association with normal galaxies and, in particular, lie in a band across the cluster.In considering the threshing hypothesis for UCD formation, we should not discuss the dynamical properties of the objects in isolation from their internal properties.
Studied the stellar populations of Virgo cluster UCDs and concluded that the Virgo UCDs have stellar populations the globular clusters of the central galaxies M87 and M49 (old ages, a range of metallicity and super-solar alpha-abundances). On this basis, the Virgo UCD stellar populations are not consistent with simple threshing model. On the other hand, found metallicities and (a range of) ages in Fornax cluster UCDs, which are more in agreement with the hypothesis that the Fornax UCDs are threshed nuclei. A detailed analysis of the structure and colours of both Virgo and Fornax UCDs concluded that their structural properties could be consistent with either globular clusters or dwarf galaxy nuclei, with the interesting observation that UCDs are about twice as extended (in effective radius) as the nuclei of dwarf galaxies at the same luminosity.Most of these observational results, as well as our own analysis in this paper, argue against the simple threshing hypothesis for UCD formation. \'We do not have any formal proof of this but note that the weights are equal when σ e, i≪σ and tend to the known optimal weighting w i∝ 1/σ 2 e, i when σ e, i≫σ. A similar, but not identical, expression is given by.This work was initiated while PAT was a visitor to Queensland under ARC Discovery Projects Grant DP0557676, and continued whist MJD was visiting Sussex with partial funding from PPARC Grant PP/D001579/1.
We would like to thank an anonymous referee for many useful suggestions for comparison with previous work. Appendices APPENDIX A: TABLES OF GALAXY AND UCD DATATables A1 and A2 are given in the online version of the article. APPENDIX B: VARIATION IN LINE-OF-SIGHT VELOCITY WITH RADIUSThis Appendix calculates the expected variation in the line-of-sight velocity dispersion of UCDs with radius resulting from anisotropic motions in a declining density profile.We take the velocity dispersion tensor to be aligned with the radial direction and to have diagonal components σ r, σ t and σ t, where σ r and σ t are the radial and tangential components of velocity dispersion, respectively. The velocity anisotropy parameter is defined as β= 1σ 2 t/σ 2 r– thus β= 0 for isotropic orbits and β 0 for preferentially radial orbits. We assume that both σ 2 r and β are constant throughout the cluster.
In practice, one might expect some radial variation in these quantities, but the data are insufficient to constrain more complex models. (B3) where z measures distance along the line of sight from the mid-point through the cluster and r is the radius to a point on that line such that z= R tan θ and r= R/cos θ. The value of the integral quotient in varies between approximately 0.62 and 0.76 for inner and outer radial bins given in (the precise values depend upon the density model for the UCDs but all acceptable fits to the data give similar results). SUPPLEMENTARY MATERIALAdditional may be found in the online version of this article.Table A1. The galaxy sample.Table A2. The UCD sample.Please note: Blackwell Publishing are not responsible for the content or functionality of any supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
...'>Galaxy Scenario File Differs From Host(08.05.2020)