Do Halos that Form Early, Have High Concentration, Are Part of a Pair, or Contain a Central Galaxy Potential Host More Pronounced Planes of Satellite Galaxies?

As a first step, we reproduce the earlier analysis, now using the 48 MW- and M31-like host halos of the ELVIS project by Garrison-Kimmel et al. (2014). We use the publicly available present-day (z = 0) halo catalogs and rank all subhalos of a given host by the maximum mass M_peak they had over their history. This is consistent with the ranking used by Buck et al. (2015) and prevalent abundance matching schemes. The mass range covered by the ELVIS halos (M_vir = (1.0–2.8) × 10¹² M_⊙) is comparable with that of the halos analyzed by Buck et al. (2015; M₂₀₀ = (0.8–2.1) × 10¹² M_⊙), especially when considering that M₂₀₀ is systematically smaller than M_vir because the latter is calculated over a larger halo volume (encompassing an average density of 97 instead of 200 times the critical density of the universe). The resolutions of the two simulation suites are comparable, too. ELVIS uses a particle mass of m_p = 1.9 × 10⁵ M_⊙ and a force softening of  = 141 pc for the highest-resolution regions, while the simulations of Buck et al. (2015) have a particle mass of m_p ≈ 1.5 × 10⁵ M_⊙ and force softening of between  = 370 and 540 pc.

To investigate the effect of a central baryonic host galaxy, we additionally analyze the 12 hosts of the Phat ELVIS simulation suite by Kelley et al. (2018). This extension to the ELVIS project consists of 12 dark-matter-only zoom simulations, which were each rerun with an embedded galaxy potential grown to match the observed MW disk and bulge today. The host halos cover a mass range of (M_vir = (0.7–2.0) × 10¹² M_⊙), while the central host disk galaxy is always 6.9 × 10¹⁰ M_⊙ at z = 0. The galaxy potential consists of a stellar and a gaseous disk, as well as a bulge component, and is grown starting from redshift z = 3. The resolution of Phat ELVIS is better than in the ELVIS suite, with a particle mass of m_p = 3 × 10⁴ M_⊙ and a force softening of  = 37 pc for the highest-resolution regions. Due to the differences in resolution and assumed cosmological parameters—Planck 2015 results (Planck Collaboration et al. 2016) instead of WMAP7 (Larson et al. 2011) as in ELVIS—we refrain from combining the ELVIS and Phat ELVIS samples despite the temptation of a larger sample size.⁶ Instead, the Phat ELVIS simulations will be used in Section 5 to determine whether the changes to the orbital properties of a satellite system caused by the presence of a baryonic central galaxy potential can have a substantial effect on the properties of planes of satellite galaxies.

We then look for correlations of the properties of the thinnest and most corotating satellite planes among the subhalos and the following properties of their host halo.

• 1.  
  r_vir, the virial radius measured as the radius of a sphere centered on the host halo that contains a density of 97 times the critical density ρ_crit of the universe. Since this definition implies an unequivocal relation between r_vir and the virial mass M_vir, we could also refer to the latter, which might be seen as more fundamental. However, we decided to refer to the virial radius in the following because it is more directly linked to the issue of spatial distributions.
• 2.  
  c₋₂, the halo concentration determined as c₋₂ = r_vir/r₋₂, where r₋₂ is the radius where ρr² peaks. This differs slightly from the concentration parameter in Buck et al. (2015), who instead of r_vir used r₂₀₀, the radius at which the halo contains a density of 200 times the critical density. Since r₂₀₀ < r_vir, this results in somewhat lower numerical values of concentration for a given halo.
• 3.  
  z_0.5, the formation redshift of the host halo, measured as that redshift at which the host's main progenitor first acquires 50% of the host halo's z = 0 virial mass M_vir.
• 4.  
  ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$, the rms of the radial distances from the center of their host of the selected subhalos (30, or 27 in the case of the PAndAS-like selection volume).

Figure 1 summarizes these host halo properties. Additionally, the lower panel compares the ELVIS halo concentrations c₋₂ to the average concentration relation of Prada et al. (2012), which uses the same cosmology (yellow line) plotted against virial radius r_vir instead of virial mass M_vir. The dashed lines indicate a 1σ scatter of 0.11 dex (or a factor of 1.3) as reported by Dutton & Macciò (2014) and used in Buck et al. (2015). While the study of Dutton & Macciò (2014) is based on a slightly different cosmology, the typical scatter around the average mass–concentration relation is found to be virtually identical among different cosmologies (Macciò et al. 2008) and thus applicable to the ELVIS simulations, too. While the sample of host halos of Buck et al. (2015) was selected to especially sample the wings of the concentration distribution, Figure 1 shows that the ELVIS sample also contains nine hosts that are offset from the mean concentration relation by ≈2σ toward high concentrations.

Zoom In Zoom Out Reset image size

Like Buck et al. (2015), we first select the top N_sh = 30 subhalos within the virial radius of each of our 48 host halos, excluding all subhalos within the innermost 30 kpc. This is our "simulated" sample. We also generate a "randomized" sample of subhalo systems. For this, we keep the radial distances and absolute velocities of all subhalos but draw random directions from an isotropic distribution for the position and velocity vectors. This constitutes a simple but necessary and important test: are potential differences in the properties of satellite planes due to an increase of subhalo coherence that is linked to host halo properties (such as concentration or formation redshift), or are such differences driven by the radial distribution of the subhalo system itself?

To find the thinnest planes for each number of subhalos between 3 and N_sh, we proceed as follows. We generate 10,000 normal directions that are approximately evenly distributed on a hemisphere. Each of these describes a possible satellite plane centered on the host halo. For each of these planes, we rank all N_sh subhalos by their distance from the plane and measure the rms height of the N_inPlane = 3, 4, 5, ... N_sh − 1, N_sh closest subhalos. For the kinematic analysis, we also determine the number of co-orbiting satellites by counting the number of positive and negative angular momenta projected onto the normal vector. The number of co-orbiting satellites N_Coorb is the larger of the two (and thus always N_inPlane/2 ≤ N_Coorb ≤N_inPlane). For each combination of N_inPlane and N_Coorb that occurs in a subhalo system, we record the smallest plane height Δ_rms.

As already pointed out in Pawlowski et al. (2014), the satellite selection volume has a major effect on the distribution of subhalos selected from a simulation and thus on the deduced properties of satellite planes (see Figure 2). Volumes that differ in size and shape from the one actually observed can bias both toward and away from finding narrow satellite planes, depending on their shape. Furthermore, the number of satellites used to find satellite planes has a major influence on the resulting properties: the more satellites in the sample, the higher the chance to find more extreme properties among subsamples of a fixed number. This is why the selection of 30 (instead of the observed 27) satellites from the virial radius (instead of the PAndAS footprint) but allowing for satellites close to the host in projection (in contrast to the observational study by Ibata et al. 2013, which excluded the inner 25 around M31) makes any comparison between the observed GPoA and satellite planes in the simulation futile.

Zoom In Zoom Out Reset image size

Defining the satellite selection volume by the virial radii of the individual host halos furthermore risks introducing the looked-for anticorrelation between host halo concentration and thickness of the narrowest satellite planes. If there is a relation between the overall extent of a satellite system and the height of the narrowest satellite planes (see Section 3.4),⁷ then linking the volume from which satellites are selected to r_vir introduces a correlation between r_vir and the minimum plane heights Δ_rms. The definition of r_vir implies an unequivocal relation to the virial mass M_vir of the form

$$\begin{eqnarray*}&&{M}_{\mathrm{vir}}=97\times {\rho }_{\mathrm{crit}}\times \displaystyle \frac{4}{3}\pi {r}_{\mathrm{vir}}^{3},\end{eqnarray*}$$

such that a correlation with r_vir also implies a correlation with M_vir. In ΛCDM, it is well established that dark matter halos follow a halo mass–concentration relation, in the sense that halos with larger M_vir have lower c₋₂ (Bullock et al. 2001; Ludlow et al. 2014). Thus, a correlation with M_vir also implies an anticorrelation with the concentration parameter. Putting all this together, more concentrated host halos tend to be less massive and have smaller virial radii (see also lower panel of Figure 1); their satellite systems are thus selected from a smaller volume, which biases the satellite planes found in them to be more narrow. Thus, it is conceivable that the selection volume chosen by the previous study introduces the very correlation they reported. However, it is unclear whether this artificially introduced correlation is discernible given the low-number statistics, the substantial scatter in the mass–concentration relation, and the stochasticity of satellite plane heights.

Another distinction in our analysis that improves upon the initial exploration by Buck et al. (2015) is that we restrict the analysis to using only the 1D line-of-sight velocities, in contrast to the previously described analysis (Section 2.1), which uses the full 3D velocities of the subhalos to determine the kinematic coherence. The latter are not available observationally (proper motions at the distance of M31 are extremely difficult to measure; Sohn et al. 2012; van der Marel et al. 2012; Salomon et al. 2016).

Finally, we point out that, in principle, one should consider observational uncertainties, since these are an additional source of dispersion in the satellite coherence (they make planes appear thicker and velocities appear less coherent). We ignore this in the rest of this work for the sake of simplicity—and because the frequency of satellite planes comparable to the observed one turns out to be zero even without considering this effect—but we will revisit the point in a future publication (M. S. Pawlowski et al. 2019, in preparation).

To compare with the observed GPoA, we use the same ELVIS simulations as discussed before but select subhalos from a volume determined by the PAndAS footprint area. For this, we observe each of the isolated host halos from a random direction, while for the paired hosts, the direction of observation is from the partner host. To select only subhalos that fall into the survey area covered by PAndAS, we mock-observe the subhalos by projecting their positions into a spherical coordinate system with angles centered on the host halo. The mock observer is situated at a distance to the host halo of 780 kpc, consistent with the distance to M31. We then select the top 27 subhalos ranked by their mass at infall (m_max) that lie within the PAndAS survey polygon. This number is chosen to be identical to the number of satellites considered by Ibata et al. (2013) and Conn et al. (2013). The maximum allowed distance of a subhalo from the host halo center is 500 kpc, which makes the selection volume consistent with the most-distant M31 satellite in the observed sample (Andromeda XXVII at a most likely distance of ∼480 kpc from M31; Conn et al. 2012). Like Ibata et al. (2013), we also exclude the region within 25 of the host halo in projection and exclude all subhalos from that volume, because the high background this close to the host hampers the detection of satellite galaxies and negatively affects distance measurements. This selection results in a total volume of about 0.07 Mpc³, or a volume corresponding to that of a sphere with radius 257 kpc. As before, we also generate a random sample by randomizing the subhalo positions and velocities before applying the PAndAS selection.

For the plane-fitting analysis, we consider the full 3D position vectors of the 27 selected subhalos for each host, as well as the line-of-sight velocity vectors as seen from the direction from which the PAndAS footprint was applied (within the host halo rest frame). The plane-finding routine itself is identical to the one described before.

Figure 4 presents the minimum plane height for each possible number of satellites in a plane N_inPlane. Each line corresponds to one host's subhalo system, and the lines are color-coded by the concentration of the host halo. While some of the halos hosting the thinnest planes have higher concentrations, no clear trend between the halo concentration and the minimum plane thickness is apparent. We would have expected to see a gradient of higher concentrations for lines at lower $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ at a given satellite number.

Zoom In Zoom Out Reset image size

There are, however, a few minor indications that can be interpreted to be consistent with the findings of Buck et al. (2015). Three of the halos do in fact contain satellite planes of N_inPlane = 15 that are at least as narrow as the 99% upper limit of the GPoA around M31⁸ (Δ_rms ≤ 14.1 kpc). Two of theses three halos seem to be of higher-than-average concentration, too, while the two halos with the largest $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ at N_inPlane = 15 are of lower concentration. In addition, the average of the minimum plane heights for the 12 most-concentrated hosts (thick dashed red line) tends to be slightly below that of the 12 least-concentrated hosts (thick dashed blue line).

However, before we jump to this conclusion, we need to take a step back and compare the findings with our randomized control sample (top right panel in Figure 4). Interestingly, the randomized sample also has a high-concentration halo at the lowest $\min {{\rm{\Delta }}}_{\mathrm{rms}}$. Like in the simulated sample, the two most-pronounced high-$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ halos up to N_inPlane = 20 have low concentration, too. Furthermore, even the average $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for the 12 most- and least-concentrated hosts show the same behavior as in the simulated sample, with the more concentrated ones having slightly lower $\min {{\rm{\Delta }}}_{\mathrm{rms}}$. All indications for a possible correlation between host halo concentration and the height of satellite planes previously discussed for the simulated sample are therefore also present in a sample of satellites drawn from isotropy. This randomized sample does not have any formation history that could be responsible for this. The similarities, therefore, are hints that indeed the radial distributions of the subhalos might be most responsible for driving $\min {{\rm{\Delta }}}_{\mathrm{rms}}$, since this is the only property that the simulated and randomized samples have in common.

More support for this interpretation can be found in the radial profiles of the subhalo systems (Figure 5). The systems belonging to the lowest-concentration hosts tend to be slightly less radially concentrated, especially in the inner parts (compare the dashed red and blue lines, which show the average radial profiles for the high- and low-concentration halos, respectively). More importantly, those systems that contain planes of 15 satellites that are at least as narrow as the GPoA (underlaid with a thick green line) are more radially concentrated than the average subhalo distributions in high-concentration halos. This confirms that the radial concentration is the factor driving the tendency to lower minimum plane heights, but this is only due to an overall more compact scaling of the satellite system that is not accounted for when measuring plane heights in absolute distance.

Zoom In Zoom Out Reset image size

The PAndAS samples do not even show a weak indication of a correlation between $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ and c₋₂ in Figure 4, which demonstrated that the selection volume is an important aspect of any comparison between simulations and observations. None of the 48 ELVIS halos contains a subhalo plane that is as narrow as the observed GPoA. Figure 5 reveals that the PAndAS volume affects the typical radial distribution of selected subhalos compared to the spherical volumes of radius r_vir. It results in a somewhat steeper inner slope within d_host ≲ 150 kpc and then a more extended tail to larger distances, the latter because the selection function allows subhalos to be found up to 500 kpc from the host if they lie within the PAndAS footprint instead of cutting off at the virial radius. Note that the radial profile of the 27 observed M31 satellites among which Ibata et al. (2013) discovered the GPoA (black line in Figure 5) is less radially concentrated than the vast majority of subhalo systems, especially in the inner regions of the halos. This is another indication that it is the radial subhalo distribution that drives $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ to lower values, not the presence of actual satellite planes. In this regard, it is important to note that the analyzed simulations are collisionless, and that the host halos do not contain central galaxy disks, whose tidal effects can result in a depletion of subhalos in the innermost regions, resulting in more radially extended subhalo systems (Garrison-Kimmel et al. 2017; Sawala et al. 2017). This effect on the distribution of satellite subhalos is present in the Phat ELVIS sample that includes a central galaxy potential. As a consequence, for this set of simulations, we find a better match with the observed radial distribution of M31 satellite galaxies, provided that the subhalos are selected from the PAndAS footprint (see Section 5).

Buck et al. (2015) concluded that the narrowness of satellite planes correlates with halo formation time, in the sense that earlier-forming halos contain narrower planes. They based this conclusion on using halo concentration as a proxy for formation time and argued to have found an anticorrelation between plane height and halo concentration. We cannot reproduce the reported correlation between host concentration and the width of the satellite planes, which appears to invalidate this line of argument. Thus, in Figure 6, we more directly check for a possible correlation with halo formation time by comparing to the halo formation redshift z_0.5 (left panels). Maybe unsurprisingly, no correlation is apparent between z_0.5 and the minimum plane heights either. However, color-coding by the virial radius r_vir of the host (middle panels) or the rms radius of the subhalo sample ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$ (right panels) reveals a clear gradient (and thus correlation) that confirms our preceding discussion: systems with a smaller total radial extent result in apparently narrower satellite planes if measured by absolute rms height.

Zoom In Zoom Out Reset image size

As another test, we now invert our approach. Instead of testing whether a halo property results in narrower satellite planes, we now test whether the narrowest satellite planes live in halos that, on average, have different properties. For each number N_inPlane of satellites in a plane, we separate the halos into four bins by the value of $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for these satellite planes. In other words, we split them into groups of 12 halos that range from containing the 12 thinnest satellite planes (thick red line in Figure 7) to the 12 widest (thin blue line). This is done for each number of satellites in the plane N_inPlane, such that the composition of the bins changes for different satellite numbers. We then calculate the average halo concentration, formation redshift, virial radius, and subhalo rms distance for each bin and number of satellites. The results are shown in Figure 7. The averages of the mean properties over all numbers of satellites in the plane (i.e., flattening the x-axis), as well as the scatter around this average, are given at the top of each panel for each bin in the corresponding color.

Zoom In Zoom Out Reset image size

It is clear from the highly fluctuating and crossing curves that the higher concentrations (first row) and formation redshifts (second row) of the host halos do not result in those halos having the thinnest satellite planes. The scatter in the averages over all numbers of satellites in the planes is as large or larger than the difference between them, too. If anything, the halos resulting in the narrowest planes seem to be forming slightly later (smaller z_0.5) than the others for N_inPlane ≥ 15, which is the opposite of the trend suggested by Buck et al. (2015). However, the differences in the averages between the four bins are consistent with the scatter in each bin and therefore not significant, and the same trend is seen for the randomized satellite positions.

There is a tendency that halos that contain narrower satellite planes (for a given number of satellites in the plane) have smaller virial radii if the satellites are selected from within the whole virial radius (third row). Averaged over all satellite numbers, the mean virial radii in the four bins are consistent between the simulated sample and the one with randomized angular positions. This again evidences that the driving variable is the radial extent to which the subhalo system is considered. Consequently, in the case of the fixed-volume PAndAS-like selection, this dependency on r_vir is not as pronounced anymore. The averages are consistent with being identical.

There is a strong tendency that subhalo systems that are more radially concentrated result in narrower planes (fourth row) if selected from the whole virial volume. This is again less clear in the PAndAS samples. However, this effect is again also present for the samples with random subhalo positions (columns 2), which demonstrates that it is merely an effect of considering only the absolute thickness of the subhalo systems. It does not stem from an increase in the spatial and kinematic coherence of subhalo systems in these types of halos, which is completely eradicated by choosing random angular positions of the subhalos.

In addition to these qualitative comparisons, we now apply more formal, quantitative tests of correlation, searching for dependencies between the various halo properties, as well as between these and the satellite plane heights. We use both the Pearson correlation coefficient ρ and the Spearman rank correlation coefficient r_s and report the corresponding p-values, which give the probability of obtaining a more extreme correlation coefficient by chance. We assume that we can reject the hypothesis of no correlation if the p-value is below 0.05 (or $\mathrm{log}\,p\lt -1.3$).

For the top 30 subhalo sample selected from the whole virial volume, we find no evidence for a correlation between the halo concentration c₋₂ and ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$ (ρ = 0.01, p = 0.93; r_s =−0.01, p = 0.95) or the virial radius r_vir and halo formation redshift z_0.5 (ρ = 0.09, p = 0.52; r_s = 0.09, p = 0.55). There are hints of a weak correlation between the formation redshift z_0.5 and ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$, but the two tests are not quite significant (ρ = 0.28, p = 0.06; r_s = 0.20, p = 0.16). We do find a weak, marginally significant correlation between the halo concentration c₋₂ and the halo formation redshift as measured via z_0.5 (ρ = 0.39, p = 0.01; r_s = 0.30, p = 0.04), as well as a strong and highly significant correlation between r_vir and ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$ (ρ = 0.77, p = 1.1 × 10⁻¹⁰; r_s = 0.74, p = 1.4 × 10⁻⁹).

As expected from the discussions in Section 3, our tests reveal no highly significant correlation between the formation redshift or the halo concentration and the satellite plane heights for the different numbers of satellites per plane (or averaged over them). The corresponding p-values of these tests mostly remain well above 0.1 or log p > −1 (see Tables 1–4).⁹ For the sample of 30 subhalos selected from the whole virial volume, we find a correlation with r_vir, which is present and of similar strength for both the simulated and the randomized sample. Unsurprisingly, such a correlation with r_vir is not found for the PAndAS-like selection volume. While the top 30 subhalo samples show a strong correlation between the satellite plane heights and the rms radius of the subhalo samples ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$, only a weak correlation like this exists in the PAndAS-like samples. This quantitatively demonstrates the importance of accurately accounting for the selection volume of the observed M31 satellite galaxies when comparing to subhalos in simulations.

Table 1.  Correlations for Simulated Top 30 Subhalos within r_vir

	$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. c−2				min Δrms vs. z0.5				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. rvir				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$
	Pearson		Spearman		Pearson		Spearman		Pearson		Spearman		Pearson		Spearman
NinPlane	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$
3	−0.17	−0.6	−0.17	−0.6	−0.15	−0.5	−0.18	−0.7	0.38	−2.1	0.41	−2.4	0.39	−2.3	0.42	−2.5
4	0.24	−1.0	0.20	−0.7	0.05	−0.1	−0.03	−0.1	0.22	−0.9	0.18	−0.6	0.27	−1.2	0.24	−1.0
5	−0.03	−0.1	−0.06	−0.2	0.03	−0.1	0.02	−0.1	0.40	−2.4	0.38	−2.1	0.45	−2.9	0.38	−2.1
6	−0.10	−0.3	−0.06	−0.2	−0.04	−0.1	0.00	−0.0	0.39	−2.2	0.32	−1.6	0.54	−4.1	0.49	−3.4
7	−0.14	−0.5	−0.15	−0.5	−0.08	−0.2	−0.09	−0.3	0.52	−3.8	0.50	−3.5	0.58	−4.9	0.56	−4.4
8	−0.15	−0.5	−0.13	−0.4	−0.04	−0.1	0.01	−0.0	0.58	−4.8	0.57	−4.5	0.65	−6.3	0.62	−5.5
9	−0.10	−0.3	−0.14	−0.5	−0.06	−0.2	0.02	−0.0	0.53	−3.9	0.50	−3.5	0.63	−5.7	0.58	−4.7
10	−0.11	−0.3	−0.03	−0.1	−0.11	−0.3	0.01	−0.0	0.47	−3.1	0.47	−3.1	0.61	−5.4	0.61	−5.4
11	−0.11	−0.3	−0.04	−0.1	−0.13	−0.4	−0.10	−0.3	0.42	−2.5	0.37	−2.0	0.54	−4.1	0.47	−3.1
12	−0.12	−0.4	−0.07	−0.2	−0.13	−0.4	−0.13	−0.4	0.41	−2.4	0.37	−2.0	0.56	−4.5	0.51	−3.6
13	−0.08	−0.2	−0.04	−0.1	−0.03	−0.1	−0.02	−0.1	0.42	−2.5	0.41	−2.4	0.65	−6.3	0.63	−5.7
14	−0.06	−0.2	0.01	−0.0	−0.04	−0.1	−0.05	−0.1	0.42	−2.5	0.43	−2.6	0.66	−6.5	0.66	−6.4
15	−0.05	−0.1	0.03	−0.1	0.00	−0.0	0.01	−0.0	0.44	−2.7	0.43	−2.6	0.70	−7.5	0.68	−6.9
16	−0.03	−0.1	0.03	−0.1	0.01	−0.0	0.04	−0.1	0.47	−3.1	0.49	−3.4	0.72	−7.9	0.71	−7.9
17	−0.03	−0.1	−0.00	−0.0	0.04	−0.1	0.05	−0.1	0.51	−3.7	0.52	−3.9	0.73	−8.3	0.72	−8.2
18	0.00	−0.0	0.01	−0.0	0.10	−0.3	0.09	−0.3	0.53	−3.9	0.53	−4.0	0.74	−8.9	0.75	−9.1
19	−0.01	−0.0	0.00	−0.0	0.11	−0.3	0.14	−0.5	0.52	−3.8	0.51	−3.6	0.74	−8.6	0.72	−8.1
20	−0.00	−0.0	0.01	−0.0	0.13	−0.4	0.16	−0.6	0.53	−3.9	0.51	−3.7	0.74	−8.6	0.72	−8.2
21	−0.00	−0.0	0.04	−0.1	0.12	−0.4	0.15	−0.5	0.51	−3.7	0.49	−3.4	0.72	−8.1	0.71	−7.9
22	−0.00	−0.0	0.01	−0.0	0.13	−0.4	0.16	−0.5	0.51	−3.7	0.48	−3.2	0.71	−7.8	0.68	−7.0
23	−0.00	−0.0	−0.01	−0.0	0.16	−0.5	0.16	−0.6	0.50	−3.6	0.46	−3.0	0.71	−7.8	0.66	−6.5
24	0.00	−0.0	−0.00	−0.0	0.17	−0.6	0.16	−0.6	0.49	−3.4	0.44	−2.8	0.71	−7.8	0.64	−6.1
25	−0.01	−0.0	−0.03	−0.1	0.17	−0.6	0.13	−0.4	0.48	−3.3	0.45	−2.8	0.72	−8.0	0.68	−6.9
26	−0.01	−0.0	−0.05	−0.1	0.17	−0.6	0.13	−0.4	0.46	−3.0	0.46	−2.9	0.70	−7.5	0.69	−7.2
27	−0.01	−0.0	−0.03	−0.1	0.16	−0.6	0.14	−0.5	0.45	−2.9	0.48	−3.2	0.70	−7.4	0.69	−7.3
28	−0.00	−0.0	−0.02	−0.1	0.15	−0.5	0.14	−0.4	0.45	−2.9	0.48	−3.3	0.70	−7.4	0.70	−7.6
29	−0.01	−0.0	−0.02	−0.0	0.17	−0.6	0.14	−0.5	0.44	−2.7	0.47	−3.2	0.69	−7.1	0.70	−7.5
30	−0.04	−0.1	−0.06	−0.2	0.14	−0.4	0.11	−0.3	0.45	−2.9	0.47	−3.1	0.68	−7.0	0.69	−7.3
Average	−0.04	−0.2	−0.03	−0.2	0.04	−0.3	0.05	−0.3	0.46	−3.1	0.45	−3.0	0.64	−6.4	0.62	−6.0

Note. Correlation coefficients and logarithms of the corresponding p-values for Pearson (ρ) and Spearman (r_s) tests of correlations between the minimum plane heights $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for different numbers of satellites in a plane N_inPlane vs. various halo parameters: halo concentration c₋₂, formation redshift z_0.5, virial radius r_vir, and rms radius of the subhalo distribution ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$.

Download table as:  ASCIITypeset image

Table 2.  Correlations for Randomized Top 30 Subhalos within r_vir

	$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. c−2				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. z0.5				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. rvir				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$
	Pearson		Spearman		Pearson		Spearman		Pearson		Spearman		Pearson		Spearman
NinPlane	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$
3	−0.06	−0.2	−0.04	−0.1	0.14	−0.5	0.14	−0.5	0.10	−0.3	0.11	−0.3	0.21	−0.8	0.21	−0.8
4	−0.12	−0.4	−0.12	−0.4	0.07	−0.2	0.07	−0.2	0.33	−1.7	0.31	−1.5	0.31	−1.5	0.34	−1.7
5	−0.14	−0.5	−0.09	−0.3	−0.14	−0.5	−0.07	−0.2	0.45	−2.8	0.48	−3.2	0.29	−1.4	0.28	−1.2
6	0.03	−0.1	0.05	−0.1	0.03	−0.1	−0.04	−0.1	0.22	−0.9	0.23	−0.9	0.37	−2.0	0.31	−1.5
7	0.01	−0.0	0.03	−0.1	0.15	−0.5	0.11	−0.4	0.20	−0.7	0.16	−0.6	0.30	−1.4	0.27	−1.2
8	0.11	−0.3	0.10	−0.3	0.07	−0.2	0.05	−0.1	0.24	−1.0	0.27	−1.2	0.48	−3.2	0.49	−3.4
9	−0.03	−0.1	0.00	−0.0	0.04	−0.1	0.02	−0.1	0.34	−1.8	0.34	−1.8	0.50	−3.6	0.48	−3.2
10	−0.02	−0.1	0.00	−0.0	0.13	−0.4	0.11	−0.3	0.33	−1.6	0.33	−1.6	0.52	−3.8	0.49	−3.4
11	0.03	−0.1	0.09	−0.3	0.19	−0.7	0.20	−0.8	0.42	−2.5	0.43	−2.6	0.58	−4.8	0.55	−4.2
12	0.01	−0.0	0.09	−0.3	0.10	−0.3	0.14	−0.4	0.45	−2.9	0.45	−2.9	0.61	−5.3	0.58	−4.7
13	0.07	−0.2	0.12	−0.4	0.10	−0.3	0.13	−0.4	0.42	−2.5	0.43	−2.6	0.60	−5.2	0.57	−4.6
14	0.05	−0.1	0.12	−0.4	0.10	−0.3	0.18	−0.7	0.43	−2.7	0.45	−2.8	0.62	−5.6	0.58	−4.9
15	0.04	−0.1	0.11	−0.3	0.11	−0.3	0.15	−0.5	0.47	−3.1	0.45	−2.8	0.67	−6.8	0.61	−5.4
16	0.02	−0.0	0.09	−0.3	0.14	−0.5	0.16	−0.6	0.49	−3.3	0.44	−2.7	0.67	−6.7	0.58	−4.8
17	−0.03	−0.1	0.05	−0.1	0.15	−0.5	0.14	−0.5	0.52	−3.9	0.46	−2.9	0.68	−6.9	0.61	−5.3
18	−0.05	−0.1	0.02	−0.0	0.16	−0.5	0.16	−0.6	0.53	−3.9	0.45	−2.9	0.69	−7.3	0.62	−5.6
19	−0.05	−0.1	0.02	−0.1	0.15	−0.5	0.19	−0.7	0.52	−3.8	0.46	−3.0	0.68	−7.0	0.62	−5.6
20	−0.04	−0.1	0.00	−0.0	0.17	−0.6	0.19	−0.7	0.50	−3.6	0.44	−2.8	0.67	−6.7	0.62	−5.5
21	−0.01	−0.0	0.01	−0.0	0.21	−0.8	0.23	−0.9	0.51	−3.7	0.46	−3.0	0.69	−7.3	0.64	−5.9
22	−0.01	−0.0	0.02	−0.0	0.21	−0.8	0.23	−0.9	0.52	−3.8	0.49	−3.4	0.69	−7.2	0.64	−6.0
23	−0.01	−0.0	−0.01	−0.0	0.24	−1.0	0.24	−1.0	0.53	−3.9	0.48	−3.2	0.71	−7.9	0.66	−6.5
24	−0.02	−0.0	−0.02	−0.0	0.24	−1.0	0.22	−0.9	0.53	−3.9	0.50	−3.5	0.73	−8.4	0.69	−7.2
25	−0.02	−0.1	−0.02	−0.0	0.23	−1.0	0.20	−0.8	0.53	−3.9	0.50	−3.5	0.74	−8.6	0.69	−7.2
26	−0.05	−0.1	−0.07	−0.2	0.23	−1.0	0.19	−0.7	0.53	−4.0	0.51	−3.6	0.74	−8.9	0.69	−7.2
27	−0.03	−0.1	−0.07	−0.2	0.27	−1.2	0.21	−0.8	0.54	−4.1	0.55	−4.2	0.77	−9.8	0.72	−8.2
28	−0.03	−0.1	−0.07	−0.2	0.29	−1.3	0.22	−0.9	0.58	−4.8	0.58	−4.7	0.79	−10.7	0.73	−8.3
29	0.01	−0.0	−0.02	−0.0	0.33	−1.7	0.23	−0.9	0.61	−5.4	0.62	−5.6	0.81	−11.6	0.74	−8.8
30	−0.01	−0.0	−0.07	−0.2	0.35	−1.8	0.25	−1.0	0.66	−6.6	0.68	−7.0	0.83	−12.5	0.76	−9.4
Average	−0.01	−0.1	0.01	−0.2	0.16	−0.7	0.15	−0.6	0.45	−3.1	0.43	−2.9	0.61	−6.2	0.56	−5.1

Note. Correlation coefficients and logarithms of the corresponding p-values for Pearson (ρ) and Spearman (r_s) tests of correlations between the minimum plane heights $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for different numbers of satellites in a plane N_inPlane vs. various halo parameters: halo concentration c₋₂, formation redshift z_0.5, virial radius r_vir, and rms radius of the subhalo distribution ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$.

Download table as:  ASCIITypeset image

Table 3.  Correlations for Simulated Top 27 Subhalos within PAndAS Volume

	$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. c−2				min Δrms vs. z0.5				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. rvir				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$
	Pearson		Spearman		Pearson		Spearman		Pearson		Spearman		Pearson		Spearman
NinPlane	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$
3	−0.06	−0.2	−0.11	−0.3	0.03	−0.1	0.08	−0.2	0.25	−1.0	0.20	−0.8	0.27	−1.2	0.26	−1.1
4	−0.09	−0.3	−0.16	−0.6	0.08	−0.2	0.07	−0.2	0.14	−0.5	0.12	−0.4	0.36	−2.0	0.37	−2.0
5	−0.09	−0.3	−0.14	−0.5	−0.08	−0.2	−0.03	−0.1	0.01	−0.0	−0.05	−0.1	0.33	−1.6	0.33	−1.7
6	0.13	−0.4	0.11	−0.4	0.01	−0.0	0.05	−0.1	0.03	−0.1	−0.02	−0.1	0.32	−1.6	0.32	−1.6
7	0.14	−0.5	0.18	−0.7	−0.03	−0.1	−0.03	−0.1	−0.04	−0.1	−0.13	−0.4	0.38	−2.1	0.39	−2.3
8	0.20	−0.8	0.25	−1.1	−0.12	−0.4	−0.11	−0.3	−0.13	−0.4	−0.24	−1.0	0.34	−1.8	0.31	−1.5
9	0.18	−0.6	0.23	−1.0	−0.24	−1.0	−0.25	−1.1	−0.08	−0.2	−0.16	−0.6	0.32	−1.6	0.28	−1.3
10	0.06	−0.2	0.14	−0.5	−0.28	−1.3	−0.27	−1.2	0.01	−0.0	−0.08	−0.2	0.35	−1.8	0.37	−2.0
11	0.06	−0.2	0.12	−0.4	−0.31	−1.5	−0.32	−1.6	0.06	−0.2	−0.00	−0.0	0.31	−1.5	0.39	−2.2
12	0.00	−0.0	0.04	−0.1	−0.34	−1.7	−0.36	−1.9	0.03	−0.1	−0.02	−0.1	0.30	−1.4	0.32	−1.6
13	0.04	−0.1	0.05	−0.1	−0.33	−1.6	−0.38	−2.1	−0.04	−0.1	−0.09	−0.3	0.35	−1.8	0.36	−1.9
14	0.04	−0.1	0.06	−0.2	−0.32	−1.6	−0.33	−1.6	−0.01	−0.0	−0.07	−0.2	0.33	−1.7	0.35	−1.8
15	−0.00	−0.0	0.02	−0.0	−0.29	−1.3	−0.30	−1.4	−0.01	−0.0	−0.07	−0.2	0.35	−1.8	0.37	−2.0
16	0.03	−0.1	0.05	−0.1	−0.26	−1.2	−0.29	−1.4	−0.02	−0.1	−0.06	−0.2	0.31	−1.5	0.34	−1.7
17	0.05	−0.1	0.05	−0.1	−0.26	−1.1	−0.27	−1.2	−0.08	−0.2	−0.12	−0.4	0.29	−1.3	0.31	−1.5
18	0.03	−0.1	0.01	−0.0	−0.25	−1.1	−0.29	−1.3	−0.08	−0.2	−0.12	−0.4	0.27	−1.2	0.29	−1.4
19	0.03	−0.1	−0.01	−0.0	−0.24	−1.0	−0.26	−1.1	−0.07	−0.2	−0.12	−0.4	0.24	−1.0	0.24	−1.0
20	0.05	−0.1	0.03	−0.1	−0.16	−0.6	−0.24	−1.0	−0.02	−0.0	−0.09	−0.3	0.18	−0.7	0.20	−0.7
21	0.05	−0.1	0.03	−0.1	−0.10	−0.3	−0.17	−0.6	0.00	−0.0	−0.09	−0.3	0.16	−0.5	0.18	−0.6
22	0.02	−0.1	0.00	−0.0	−0.05	−0.1	−0.09	−0.3	0.04	−0.1	−0.05	−0.1	0.15	−0.5	0.14	−0.5
23	0.01	−0.0	0.05	−0.1	−0.06	−0.2	−0.11	−0.3	0.08	−0.2	0.01	−0.0	0.30	−1.4	0.23	−0.9
24	0.06	−0.2	0.08	−0.2	−0.07	−0.2	−0.09	−0.3	0.10	−0.3	0.07	−0.2	0.32	−1.5	0.26	−1.1
25	0.10	−0.3	0.12	−0.4	−0.08	−0.2	−0.10	−0.3	0.09	−0.3	0.06	−0.2	0.33	−1.7	0.29	−1.3
26	0.09	−0.3	0.11	−0.3	−0.06	−0.2	−0.10	−0.3	0.10	−0.3	0.09	−0.3	0.36	−1.9	0.31	−1.5
27	0.09	−0.3	0.10	−0.3	−0.04	−0.1	−0.06	−0.2	0.09	−0.3	0.11	−0.3	0.44	−2.7	0.37	−2.0
Average	0.05	−0.2	0.06	−0.3	−0.15	−0.7	−0.17	−0.8	0.02	−0.2	−0.04	−0.3	0.31	−1.5	0.30	−1.5

Note. Correlation coefficients and logarithms of the corresponding p-values for Pearson (ρ) and Spearman (r_s) tests of correlations between the minimum plane heights $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for different numbers of satellites in a plane N_inPlane vs. various halo parameters: halo concentration c₋₂, formation redshift z_0.5, virial radius r_vir, and rms radius of the subhalo distribution ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$.

Download table as:  ASCIITypeset image

Table 4.  Correlations for Randomized Top 27 Subhalos within PAndAS Volume

	$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. c−2				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. z0.5				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. rvir				$\min {{\rm{\Delta }}}_{\mathrm{rms}}$ vs. ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$
	Pearson		Spearman		Pearson		Spearman		Pearson		Spearman		Pearson		Spearman
NinPlane	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$	ρ	$\mathrm{log}\,p$	rs	$\mathrm{log}\,p$
3	−0.25	−1.1	−0.33	−1.6	−0.07	−0.2	−0.01	−0.0	0.11	−0.3	0.02	−0.1	0.29	−1.3	0.18	−0.7
4	−0.18	−0.7	−0.21	−0.8	0.03	−0.1	0.01	−0.0	0.01	−0.0	−0.03	−0.1	0.29	−1.4	0.23	−0.9
5	0.06	−0.2	0.05	−0.1	0.07	−0.2	0.08	−0.2	0.06	−0.2	0.04	−0.1	0.31	−1.5	0.24	−1.0
6	−0.03	−0.1	−0.02	−0.1	0.10	−0.3	0.14	−0.5	−0.10	−0.3	−0.05	−0.1	0.13	−0.4	0.09	−0.3
7	−0.16	−0.6	−0.16	−0.6	−0.05	−0.1	−0.03	−0.1	−0.05	−0.1	−0.07	−0.2	0.06	−0.2	0.03	−0.1
8	−0.15	−0.5	−0.21	−0.8	−0.01	−0.0	−0.05	−0.1	−0.08	−0.2	−0.06	−0.2	0.20	−0.7	0.14	−0.5
9	−0.15	−0.5	−0.16	−0.6	−0.13	−0.4	−0.15	−0.5	−0.00	−0.0	−0.03	−0.1	0.16	−0.6	0.15	−0.5
10	−0.13	−0.4	−0.11	−0.3	−0.11	−0.4	−0.14	−0.5	0.07	−0.2	0.02	−0.1	0.13	−0.4	0.12	−0.4
11	−0.09	−0.3	−0.05	−0.1	−0.11	−0.3	−0.11	−0.4	0.11	−0.3	0.06	−0.2	0.13	−0.4	0.09	−0.3
12	−0.03	−0.1	−0.01	−0.0	−0.09	−0.3	−0.12	−0.4	0.06	−0.1	0.02	−0.1	0.15	−0.5	0.11	−0.4
13	0.02	−0.0	0.05	−0.1	−0.06	−0.2	−0.09	−0.2	−0.02	−0.0	0.00	−0.0	0.17	−0.6	0.09	−0.3
14	0.00	−0.0	0.03	−0.1	−0.00	−0.0	0.01	−0.0	−0.08	−0.2	−0.08	−0.2	0.21	−0.8	0.10	−0.3
15	−0.01	−0.0	0.03	−0.1	0.00	−0.0	−0.02	−0.0	−0.07	−0.2	−0.07	−0.2	0.26	−1.2	0.14	−0.5
16	0.03	−0.1	0.06	−0.2	0.05	−0.1	0.04	−0.1	−0.08	−0.2	−0.08	−0.2	0.26	−1.1	0.15	−0.5
17	0.01	−0.0	0.02	−0.0	0.07	−0.2	0.07	−0.2	−0.07	−0.2	−0.06	−0.2	0.23	−0.9	0.17	−0.6
18	0.03	−0.1	0.00	−0.0	0.07	−0.2	0.01	−0.0	−0.05	−0.1	−0.04	−0.1	0.20	−0.8	0.15	−0.5
19	0.01	−0.0	−0.00	−0.0	0.04	−0.1	0.02	−0.0	−0.03	−0.1	−0.04	−0.1	0.21	−0.8	0.16	−0.5
20	0.00	−0.0	−0.02	−0.1	0.02	−0.1	−0.01	−0.0	−0.01	−0.0	−0.02	−0.1	0.15	−0.5	0.14	−0.5
21	−0.02	−0.0	−0.04	−0.1	0.00	−0.0	−0.03	−0.1	0.02	−0.1	0.04	−0.1	0.15	−0.5	0.13	−0.4
22	0.00	−0.0	−0.01	−0.0	−0.02	−0.0	−0.02	−0.1	0.04	−0.1	0.05	−0.1	0.14	−0.5	0.13	−0.4
23	0.01	−0.0	−0.00	−0.0	−0.00	−0.0	−0.01	−0.0	0.07	−0.2	0.08	−0.2	0.16	−0.5	0.11	−0.3
24	−0.00	−0.0	−0.02	−0.0	−0.01	−0.0	0.01	−0.0	0.08	−0.2	0.10	−0.3	0.19	−0.7	0.13	−0.4
25	−0.00	−0.0	−0.04	−0.1	0.01	−0.0	0.02	−0.0	0.09	−0.3	0.10	−0.3	0.21	−0.8	0.16	−0.6
26	0.04	−0.1	−0.00	−0.0	0.03	−0.1	0.01	−0.0	0.05	−0.1	0.06	−0.2	0.23	−1.0	0.17	−0.6
27	0.13	−0.4	0.07	−0.2	0.08	−0.2	0.08	−0.2	−0.00	−0.0	0.05	−0.1	0.25	−1.1	0.24	−1.0
Average	−0.03	−0.2	−0.04	−0.2	−0.00	−0.1	−0.01	−0.2	0.00	−0.2	0.00	−0.1	0.20	−0.8	0.14	−0.5

Note. Correlation coefficients and logarithms of the corresponding p-values for Pearson (ρ) and Spearman (r_s) tests of correlations between the minimum plane heights $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for different numbers of satellites in a plane N_inPlane vs. various halo parameters: halo concentration c₋₂, formation redshift z_0.5, virial radius r_vir, and rms radius of the subhalo distribution ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$.

Download table as:  ASCIITypeset image

Figure 8 shows the correlation between the satellite plane height for planes consisting of 15 satellites and the rms radius of the subhalo samples, ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$. The latter is a good predictor of the height of the narrowest plane if the satellites are selected from the whole virial volume. This is independent of whether the actual subhalo positions of the simulations or randomized positions are used. A linear fit of the form

$$\begin{eqnarray*}&&\min {{\rm{\Delta }}}_{\mathrm{rms}}=a\times {{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}+b\end{eqnarray*}$$

demonstrates the similarity. The fit parameters are a = 0.163 ± 0.001 and b = −9.95 ± 20.93 kpc for the simulated sample and a = 0.145 ± 0.001 and b = −5.73 ± 19.21 kpc for the randomized one. Even the residuals around these best-fit lines have almost identical scatter (3.48 and 3.34 kpc, respectively). This shows how little additional structure is present in the simulated subhalo systems compared to subhalo positions randomly chosen from an isotropic distribution. Knowing the radial distribution of a subhalo system thus allows one to predict the height of its narrowest satellite plane. However, this is not as pronounced if the subhalo positions are constrained by the PAndAS-like selection volume, either for the simulated subhalo positions (a = 0.0393 ± 0.0002, b = 12.61 ± 8.57 kpc, scatter of 3.37 kpc) or for the randomized ones (a = 0.0339 ± 0.0003, b = 14.81 ± 10.45 kpc, scatter of 3.18 kpc).

Zoom In Zoom Out Reset image size

We now split up the ELVIS sample into a subsample containing the 24 isolated hosts (ELVIS isolated) and a subsample containing 24 hosts that are part of 12 pairs of host galaxies (ELVIS paired). The distributions of plane heights for these two sets are shown in the top panels of Figure 10, similar to Figure 4 but now color-coded according to subsample membership. Comparing the subhalo systems of the ELVIS isolated (red) and ELVIS paired (blue) hosts, we find no significant difference in both the average (thick lines) and the scatter (shaded regions) of the plane height. The bottom panels of Figure 10 show the kinematic coherence (as in Figure 9). Again, the two samples of simulated subhalo systems do not display substantial differences. We thus conclude that belonging to a host that is part of a pair configuration does not strongly influence the presence and properties of planes of satellite galaxies in ΛCDM simulations. This is in agreement with Pawlowski & McGaugh (2014b), who looked for analogs of the VPOS of the MW in the ELVIS simulations and did not find a correlation in their incidence or properties with whether the host is in an isolated or paired configuration.

Zoom In Zoom Out Reset image size

As is the case for the whole sample, neither of the two subsamples shows a correlation between the plane heights and halo concentration or formation redshift. There is thus no indication that being part of a paired host halo configuration or an isolated host results in a correlation with these halo properties. As expected from the full sample, if subhalos are selected from the virial volume, a weak correlation with the virial radius and strong correlation with the extent of the subhalo distribution is again present. However, owing to the reduced sample sizes, the respective significances are lower than for the full sample.

It has been found that the addition of a central galaxy potential to a cosmological simulation, whether self-consistently via a hydrodynamical simulation or using an analytic potential, results in enhanced tidal disruption of subhalos compared to a dark-matter-only simulation. This, in turn, changes the radial distribution and orbital properties of the subhalo system (Garrison-Kimmel et al. 2017; Sawala et al. 2017). The inner regions of host halos become depleted in subhalos, and the orbits of surviving subhalo satellites are less radial, on average, than in equivalent dark-matter-only runs. To investigate whether the presence of a central galaxy potential and its effect on the subhalo distribution influence the properties and coherence of planes of satellite galaxies, we now compare the resulting plane heights and kinematic coherence of the two Phat ELVIS simulation samples by Kelley et al. (2018): the 12 dark-matter-only runs that are equivalent to the ELVIS simulations (Phat ELVIS DMO) and the 12 runs started from the same initial conditions but with an added central galaxy potential (Phat ELVIS disk). In the bottom panel of Figure 5, the expected change in the radial distribution of subhalos is apparent: satellite subhalos in the Phat ELVIS disk runs selected from the PAndAS footprint have a radial distribution that is in better agreement with the observed distribution of satellite galaxies in M31 than the original ELVIS runs that did not include a central galaxy potential.

Figure 11 compiles the results of this comparison. The average plane heights (thick lines) are comparable for the dark-matter-only (DMO; red) and disk (blue) runs, though the former are slightly more narrow. The typical scatters (shaded regions) overlap well and show similar width, though there appears to be more scatter in the DMO runs if subhalos are selected from the PAndAS footprint (right panels). For subhalos selected from the PAndAS footprint (right panels), we find $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ to be, on average, 7% larger for the simulations that contain a disk potential compared to their disk-free analogs (compared to 11% if selected from r_vir). This is in line with the general trend of a correlation between the $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ and the radial extent of a subhalo system measured by ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$, discussed in Section 3.4. The median ${{\rm{\Delta }}}_{{\rm{r}}}^{\mathrm{subhalos}}$ is 188 kpc for the DMO and 214 kpc for the disk runs (or 184 and 191 kpc, respectively, if the subhalos are selected from r_vir). Using the corresponding linear fits in Section 3.4, this translates to an expected increase in the width of the subhalo distributions of 5% (6%), which largely accounts for the found increase in plane widths. This further supports the notion that the major driver behind the width of the narrowest planes of satellites found in a given distribution is the distribution's radial extent. The lower panels of Figure 11 further show that the inclusion of a central galaxy potential does not result in a more pronounced kinematic correlation in the narrowest satellite planes. The main difference is again the tendency for the disk-free simulations to have slightly smaller $\min {{\rm{\Delta }}}_{\mathrm{rms}}$ for any number of co-orbiting subhalo satellites. Fundamentally, this finding demonstrates that the addition of baryonic physics to simulations does not appear to offer a solution to the problem of planes of satellite galaxies.

Zoom In Zoom Out Reset image size

Using the concentration parameters of the Phat ELVIS host halos, we have also confirmed that no significant correlations with host halo concentration or formation time are present, either for the DMO or for the disk samples. This is in line with our previously discussed findings for the ELVIS simulations.