THE DISTRIBUTION OF SATELLITES AROUND MASSIVE GALAXIES AT 1 < z < 3 IN ZFOURGE/CANDELS: DEPENDENCE ON STAR FORMATION ACTIVITY^*

Our goal is to measure the distribution of satellites around massive galaxies at 1 < z < 3. We therefore select all galaxies in ZFOURGE with log (M_c/M_☉) > 10.48 (i.e., M_c > 3 × 10¹⁰ M_☉) and a photometric redshift 1 < z < 3 as our sample of central galaxies. We will further consider the subsamples of central galaxies in bins of stellar mass, 10.48 < log (M_c/M_☉) < 10.78 (i.e., M_c = (3–6) × 10¹⁰ M_☉) and log (M_c/M_☉) > 10.78 (i.e., M_c > 6 × 10¹⁰ M_☉). A summary of number and mean stellar mass of centrals in each of the ZFOURGE field and in each subsample is given in Table 1.

According to the central galaxies' selection criteria used by Tal et al. (2013), they consider galaxies as "central" if no other, more massive galaxies are found within a projected radius of 500 kpc. Otherwise, they are counted as satellites of their more massive neighbors. We have tested if the projected radial distribution changes if we exclude galaxies from our sample of central galaxies if there are other more massive galaxies within 10 arcsec (about 80 kpc, projected), which is comparable to our derived halo scale radius (described in Section 3.2, below). We find that our derived projected radial distribution is not significantly changed. Therefore, we do not apply this isolation criteria to select our central sample. However, this may introduce galaxies that are satellites into our sample of centrals. In Section 5.2 we further quantify the effects of the misclassification of centrals and satellites on the number density of satellites using results from a mock galaxy catalog.

We then consider the subsamples of central galaxies divided by star formation activity. Williams et al. (2009) show that the U − V and V − J rest-frame colors are able to distinguish reliably between quiescent galaxies with low specific SFRs (sSFR) and star-forming galaxies with high specific SFRs; see also the discussion in Whitaker et al. (2011). Galaxies are classified as quiescent if their rest-frame colors satisfy these criteria:

$$\begin{eqnarray} &&U-V > 0.88 \times (V-J) +0.49 \nonumber \\ &&U-V > 1.3 \\ &&V-J < 1.6. \nonumber \end{eqnarray} \tag{ 1 }$$

Figure 1 shows the U − V versus V − J diagram (hereafter UVJ diagram) for the centrals in our ZFOURGE samples. We find that between 1 < z < 3 the massive centrals (841 in total with M_c > 3 × 10¹⁰ M_☉) are roughly evenly divided into quiescent galaxies (47%) and star-forming galaxies (53%) based on their UVJ colors. The numbers of the quiescent and star-forming centrals in each ZFOURGE field and mass subsample are shown in Table 1.

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To identify satellites of the central galaxies in our sample, we build on the statistical background subtraction technique, as discussed in Tal et al. (2012, 2013). We first select all galaxies around each central from our ZFOURGE catalogs that satisfy the following conditions

$$\begin{eqnarray} &&| z_\mathrm{c} - z_\mathrm{sat} | \le 0.2 \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} &&10^9\ {{M_\odot }}\le M_\mathrm{sat} < M_\mathrm{c}, \end{eqnarray} \tag{ 3 }$$

where z_c and z_sat are the photometric redshift of the central and satellite, respectively. Similarly, M_c and M_sat are the stellar mass of the central and satellite, respectively. Our requirement that Δz = |z_c − z_sat| ⩽ 0.2 is motivated by our relative photometric uncertainty (σ_z) between centrals and satellites derived above. In each case, the σ_z values for galaxies in each ZFOURGE field are less than about half the Δz ⩽ 0.2 requirement in Equation (2), which argues that this selection criterion is appropriate.

The mass-completeness limits for all galaxies in the ZFOURGE sample at z = 3 are log (M/M_☉) = 9.3 (Tomczak et al. 2014). Below these mass limits, we are incomplete for quiescent galaxies, while our sample remains complete for star-forming galaxies down to log (M/M_☉) = 9. However, in this study, we are comparing the relative number of satellites between quiescent and star-forming centrals, so they have the same relative bias due to incompleteness in satellite detection. Parenthetically, we note that we have also repeated our analysis restricting the centrals to 1 < z < 2, where incompleteness is less of an issue, and our primary conclusions are unchanged.

We consider the possibility that our samples of quiescent and star-forming centrals have different redshift distributions. For example, it could be plausible that the quiescent centrals tend to have lower redshifts, while star-forming centrals tend to have higher redshift. In this hypothetical case, we might expect more satellites around quiescent galaxies because we can see them to lower mass. We therefore compared the redshift distributions of the different subsamples. For the intermediate mass star-forming and quiescent centrals (10.48 < log (M_c/M_☉) < 10.78), there is no difference in their redshift distributions. There is some difference in the redshift distributions between the star-forming and quiescent centrals in the higher mass subsample. However, in Section 5.1 we show that this difference does not effect our main results. Therefore, we conclude that the redshift distributions of central galaxies does not affect the relative number of satellites between the star-forming and quiescent samples.

The method to extract a radial distribution of satellites is illustrated in Figure 2, expanding from the method outlined in Tal et al. (2012). For a given projected distance from each central, we measure the number of all galaxies satisfying our definition of satellite in Equation (2). This includes both physically associated galaxies, as well as chance alignments of foreground and background galaxies. We measure the projected radial distribution by binning the distance from those galaxies to central galaxies in logarithmic bins.

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We remove the contamination from foreground and background galaxies statistically by repeating the measurements in randomly selected positions within the entire area of the ZFOURGE fields. While we use all centrals, some centrals are near the survey edges, which restricts our ability to detect their satellites. To account for this, we correct the galaxy counts in each annulus by the fraction of the annulus that falls outside of the survey boundaries. The locations of random annuli, and the corrections, are determined in the same way as for the central galaxies. The only other restriction we place on the random fields is that they are not centered within 6 arcsec (about 50 kpc, projected) of any central. We have not required that the random fields have zero overlap with areas around our centrals, as the surface density of our centrals is ∼2 arcmin⁻², and such a constraint would be too prohibitive. This is a tradeoff between our requirement to subtract off statistically the foreground and background galaxies, and having a sufficiently high number of the random fields to measure the background accurately in each ZFOURGE field. We then subtract the number density of satellites in the random pointings from the number density of satellites of each central. In practice, we measure the number density of galaxies in 100 random pointings and take the average to estimate the number density of foreground and background galaxies for each central in each ZFOURGE field.

Figure 3 shows the raw number density of galaxies measured around both the centrals and measured in random pointings. In each field there is a strong statistical excess of galaxies around our centrals extending from 10 kpc to ∼100–400 kpc (∼12–50 arcsec), which we attribute to physically associated satellites. There are slight variations in the N_sat distribution inferred from the background, as we would expect from natural field-to-field variations. We see no substantial variation in the N_sat projected distributions between the three separate fields.

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The restriction on the location of the random aperture has little effect on our conclusions. We have tested if this signal changes if we require that no random background aperture is centered within 12 arcsec of a central (compared to the 6 arcsec requirement above), but we find that this does not change significantly the number density of galaxies in the random pointings, and therefore this does not affect our measurement. Similarly, we also find that there is no significant change if we place no restrictions on the locations of the random background apertures.

At smaller projected distances (<10 kpc), we are unable to measure reliably the number density of satellites, as such objects are blended with the isophotes of the central galaxies. For example, we cross-match our central galaxy catalog from ZFOURGE to the morphology parameter catalog for the CANDELS WFC3/F160W imaging from van der Wel et al. (2012). From this, the typical effective radii of our centrals at 1 < z < 3 is ∼3.2 kpc, consistent with measurements of massive galaxies at z ∼ 2 from van Dokkum et al. (2010). Furthermore, van Dokkum et al. show that such galaxies have ∼1% of their stellar mass at a distance of 10 kpc. Therefore, it seems likely that satellites around these galaxies would be indistinguishable from substructure in the centrals for projected distances r < 10 kpc. Indeed, doing a careful analysis by subtracting the light from the central, Tal et al. (2012) find that the number density of satellites around centrals follows a r^1/4-law, consistent with the surface-brightness profile of the central galaxies. This suggests that radial density profile of satellites at small scales is strongly influenced by the baryonic content of the central galaxy, rather than the dark matter halo.

Figure 4 shows the number density of satellites measured for the centrals in each ZFOURGE field, and for the combined sample. The satellite distribution in each field is consistent with that measured in the combined sample for 10 < r/ kpc < 100, and we observe differences at larger and smaller radii. ZFOURGE contains three largely separated fields on the sky, and we interpret the differences at larger radii as a result of field-to-field variations in the number density of background/foreground galaxies in each field.

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We fit the combined projected number-density profile of satellites using a simple powerlaw model, where N_sat∝r^γ. Figure 5 shows that in the range 10 < r/ kpc < 350 the profile is well described by the power-law with γ = −1.24 ± 0.04. The power-law slope of the projected radial profile of satellites around LRGs at z = 0.34 is −1.1 (Tal et al. 2012), which is marginally consistent with our measurement here.

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We also compare our measured projected radial profile of satellites with a projected NFW profile, which Bartelmann (1996) show is

$$\begin{equation*} \Sigma (x) = \left\lbrace \begin{array}{@{}ll@{}}(x^2-1)^{-1}\left(1-\frac{2}{\sqrt{x^2-1}} \arctan \sqrt{\frac{x-1}{x+1}}\right) &{ (x>1)} \\ 1/3 &{(x=1)} \\ (x^2-1)^{-1}\left(1-\frac{2}{\sqrt{1-x^2}} \mathrm{arctanh}\sqrt{\frac{1-x}{1+x}}\right) &{(x<1)}, \\ \end{array} \right. \end{equation*}$$

where x ≡ r/r_s and r_s is the NFW-profile scale radius. We utilize the nonlinear least-squares curve fitting program MPFIT (Markwardt 2009) to fit the projected NFW model to the measured projected radial profile of satellites around centrals at 10 < r/ kpc < 350, where we fit for both the normalization factor and scale radius.

Figure 5 shows that our derived projected radial density of satellites at 1 < z < 3 is well fitted by the projected NFW model with r_s = 61.07 ± 7.8 kpc. Assuming the scale radius is independent of redshift and only scales with a halo mass as $r_s \sim M_h^{0.45}$ (e.g., Bullock et al. 2001), this would predict r_s ≃ 200 kpc at z = 0 (assuming a factor ∼10 growth in halo mass; see, e.g., Moster et al. 2013). This is smaller than that found by Tal et al. (2012), who find r_s ∼ 270 kpc for galaxies at z = 0.02 in Sloan Digital Sky Survey (SDSS), but the results are probably consistent as the galaxies in their sample correspond to progenitors with higher stellar masses by factors of ∼3–5 compared to our sample here (e.g., Tal et al. 2013). Furthermore, this provides us with confidence that our measured satellite distribution is tracing the dark matter halo of the centrals in our ZFOURGE samples.

It is desirable to assign a significance statistic (p value) when comparing the differences between the satellite number densities for different subsamples. The uncertainties of each datum of our projected radial distribution of satellites (N_sat in the figures above) are derived using simple Poisson statistics. When comparing the satellite number density distributions for difference subsamples, we use two methods, a direct rank-sum test and a Monte Carlo simulation. In practice, for reasons described below we find that the Monte Carlo simulation provides more physical probabilities, and we will use those to estimate the significance in our results.

We first apply a one-sided Wilcoxon–Mann–Whitney rank-sum (WMW) test (Mann & Whitney 1947) to quantify a probability that the number density of satellites around quiescent and star-forming centrals have the same parent population. The WMW test measures a probability (p value) using the data and Poisson errors on the satellite distributions between two subsamples (e.g., the quiescent and star-forming centrals). However, the WMW test is not strictly appropriate for our analysis because we are applying it to heavily binned data: each datum is binned (logarithmically) in radius over 10 < r/kpc < 200. In particular, the WMW test is insensitive to the fact that our sample includes hundreds of central galaxies and thousands of satellite galaxies.

To estimate meaningful p values, we use a Monte Carlo approach. We create 10,000 simulations for each subsample of central galaxies. For a given stellar mass range of the central subsample, we randomly select new samples of centrals from the subsample (allowing replacement). We then randomly assign each galaxy to be either quiescent or star-forming. In each simulated subsample, the number of the quiescent and star-forming centrals are equal to the actual number of each in the real subsamples. We then recalculate the radial number density of satellites for each set of random samples and calculate the p_WMW value using the WMW test for each iteration. The likelihood from the Monte Carlo simulations (p_MC) are calculated by determining the fraction of the number of simulations when we have the p_WMW less than the p_WMW value we derive from the real data. A summary of these likelihoods is given in Table 2.

We study how the number density of satellites depends on the stellar mass of centrals by dividing our central galaxy sample into two mass bins: 10.48 < log (M_c/M_☉) < 10.78 and log (M_c/M_☉) > 10.78. We then recompute the number density of satellites for each of these subsamples using the method above. Figure 6 shows that the more massive centrals have a higher number density of satellites compared to the lower mass centrals. Using our Monte Carlo simulations (see Section 4.1), we find that the significance of this result is p_MC = 0.026 (≃1.9σ). Therefore, there is suggestive evidence that the number of satellites increases with the stellar mass of the central galaxy.

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We investigate how the satellite distribution depends on the star formation activity of the central galaxies by dividing our sample of central galaxies into subsamples that are star-forming and quiescent (where these labels correspond to galaxies with high and low sSFRs) using their rest-frame U − V and V − J colors as illustrated in Figure 1 and discussed in Section 2.1. We then recompute the satellite distribution for each subsample.

Figure 7 shows the projected radial distribution of satellites around the star-forming and quiescent centrals with log (M_c/M_☉) > 10.48. We find that quiescent centrals host more satellites than their star-forming counterparts. Using our Monte Carlo simulation the likelihood we would obtain this result by chance has a probability of p_MC = 0.081, corresponding to 1.4σ significance.

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We further investigate how the number density of satellites depends on both star formation activity and stellar mass of the central. Figure 8 shows for centrals with moderate stellar mass 10.48 < log (M_c/M_☉) < 10.78. There is no significant evidence that the number density depends on star formation activity (with a p value p_MC = 0.478): both quiescent and star-forming moderate mass centrals have the same number of satellites. In contrast, all the difference in the number density of satellites occurs for centrals at the high stellar-mass end. For the high mass centrals, log (M_c/M_☉) > 10.78, the quiescent central galaxies have a significant excess of satellites compared to the star-forming centrals, with a p value of p_MC = 0.002 (significant at about ≃ 3.1σ). We discuss the implications of these results in Section 5.

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We integrate the satellite number densities to measure the total (cumulative) number of satellites within a projected distance of the centrals in our samples down to our mass limit for the satellites, log (M/M_☉) > 9. Figure 9 compares the cumulative number density of satellites around quiescent centrals and star-forming centrals with 10.48 < log (M_c/M_☉) < 10.78 and log (M_c/M_☉) > 10.78. On average the intermediate mass centrals have ≈1 satellite more massive than log (M_sat/M_☉) > 9 within 100 kpc. This is true for both the star-forming and quiescent centrals. The intermediate mass star-forming galaxies have an excess of satellites at larger projected radii than the quiescent centrals, but this has <2σ significance.

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Figure 9 also shows that the massive quiescent centrals (log (M_c/M_☉) > 10.78) have nearly double the number of satellites more massive than log (M_sat/M_☉) > 9 within 100–400 kpc compared to the massive star-forming centrals. On average a massive star-forming central has ≈2 such satellites, whereas a massive quiescent central has ≈4. These results are comparable with the number of satellites found around massive centrals by Tal et al. (2013), who find that on average the total number of galaxies with the mass ratio of 1:10 and within 400  kpc around the massive centrals between z = 0.04 to z = 1.6 is 2 to 3.

There is significant evidence that at high stellar mass (log (M_c/M_☉) > 10.78) quiescent galaxies have more satellites than star-forming galaxies. There are two interpretations. One is that there is something intrinsic to a galaxy being quiescent that also causes the galaxy to have more satellites. The second is that the higher number of satellites is related to stellar mass. If the quiescent centrals have higher stellar masses than the star-forming galaxies—even though the stellar mass limit is the same—then they may also be expected to have more satellites.

We test the second of these possibilities by looking at the cumulative stellar mass distribution of the quiescent and star-forming centrals. As shown in Figure 10, indeed the quiescent centrals have a slightly higher median stellar mass, which is higher than the median for the star-forming centrals by 0.05 dex.

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Although this difference in stellar mass between the quiescent and star-forming centrals is small, it could affect the number of satellites. Therefore, we make a new sample of quiescent centrals from our real sample. First, we divide the sample of centrals into narrow stellar mass bins. In each stellar mass bin we randomly select equal numbers of quiescent and star-forming galaxies, therefore creating a new sample matched in stellar mass. The numbers of the quiescent and star-forming centrals in the matched stellar mass samples are shown in Table 2. The right panel of Figure 10 shows that the stellar mass distributions of the matched samples agree very well.

After we match the mass distributions of quiescent and star-forming centrals, we then recalculate the number density profiles of satellites around the centrals for each subsample. Figure 11 shows that the number densities of satellites of moderate mass quiescent and star-forming centrals with 10.48 < log (M_c/M_☉) < 10.78 are nearly identical with no evidence for any difference. Our Monte Carlo tests (Section 4.1) give a 98.5% likelihood (p_MC = 0.985) that the distributions are identical.

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However, the excess of satellites around the massive quiescent centrals with log (M_c/M_☉) > 10.78 compared to the massive star-forming centrals is still significant, where our Monte Carlo tests give a likelihood that we would have obtained this result by chance as 0.4% (i.e., the difference is significant at ≃ 2.7σ (p_MC = 0.004)). Therefore, while the offset in the stellar mass accounts for some of the increase in the number of satellites around the massive centrals, it is unable to account for all of it. Even though the stellar masses are matched, the massive quiescent centrals have more satellites than star-forming centrals.

As another check, one could expect that quiescent and star-forming galaxies may have different redshift distributions, i.e., if at fixed stellar mass the star-forming galaxies lie at higher redshift, then this could possibly affect our results, as the number of satellites (and dark matter halo mass) could build up with time. For example, Moster et al. (2013) show that at fixed stellar mass the halo mass of massive galaxies increases with decreasing redshift.

Figure 12 compares the redshift distributions of quiescent and star-forming centrals for moderate mass and high mass centrals. Using the WMW statistic we find no statistically significant difference between the quiescent/star-forming redshift distributions for moderate mass centrals (p_WMW = 0.46). The median redshift of quiescent and star-forming centrals are 1.63 and 1.71, respectively. For high-mass centrals the quiescent/star-forming redshift distribution is significantly different (p_WMW = 0.002). The median redshift of quiescent and star-forming centrals are 1.57 and 1.79, respectively. This difference is not a surprise, as the quiescent fraction of galaxies at fixed mass increases with decreasing redshift.

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In order to test whether this difference in redshift distributions affects our results, we match the redshift distributions of high-mass quiescent and star-forming centrals and recalculate the number density profiles of satellites for each subsample. We find that the difference in the redshift distributions does not significantly change our main result: there are still more satellites around massive quiescent centrals compared to their star-forming counterparts.

As a final check, we recalculate the number density of satellites for our samples of centrals, restricting the redshift range of centrals to 1 < z < 2. The results are consistent with the satellite distribution measured for the full 1 < z < 3 samples. This also implies that the number of satellites does not change very much over this redshift range. Tal et al. (2013) find that the radial number density of satellites has not evolved much over z = 0.04–1.6. Therefore, our results show that the trend observed by Tal et al. extends to z ∼ 3.

To summarize, there appears to be some physical connection between the quenching of star formation and the presence of an increased number of satellites, at least for massive galaxies. One likely explanation is that the higher number of satellites corresponds to larger dark matter halo masses, and that at fixed stellar mass the quiescent galaxies have higher halo mass. Because we have no direct measures of the halo masses of the galaxies in our sample, we test this conclusion using semi-analytical models of galaxy formation in the next section.

To further explore the physical reasons that the massive (log (M_c/M_☉) > 10.78) quiescent centrals have more satellites than star-forming counterparts at 1 < z < 3, we use predictions from the semi-analytic model (SAM) of Guo et al. (2011). The Guo et al. SAM is derived using the Millennium-I simulation (Springel et al. 2001). Henriques et al. (2012) provide mock "lightcone" catalogs from the Guo et al. models, and these lightcones include galaxies at redshifts and to (low) stellar masses comparable to our ZFOURGE data set.

We select central galaxies from the mock catalogs using the same redshift and stellar mass limits as for our ZFOURGE samples. We further split the mock centrals by sSFR into quiescent (log (sSFR/yr⁻¹) < −10) and star-forming (log (sSFR/yr⁻¹) > −10) subsamples. We use the sSFRs for this classification because currently the Henriques et al. (2012) light cones do not include rest-frame magnitudes (e.g., we are unable to classify them using the UVJ colors as done for the ZFOURGE galaxies). However, this makes little difference as Papovich et al. (2012) show that at z ∼ 1.6 the sSFR threshold of log (sSFR/yr⁻¹) = −10 effectively separates galaxies classified as quiescent or star-forming by a UVJ-type color-color selection. Therefore, the sSFR selection here is equivalent to our UVJ color–color selection above.

We identify centrals and measure the number density of satellites at 1 < z < 2 in the SAM lightcone using the same methods as applied to the data. We restrict ourselves to comparisons between the SAM and our data to 1 < z < 2 and log (M/M_☉) > 9.33 because this is the adopted stellar mass-completeness limit for red satellites at z = 2 in the ZFOURGE data (Tomczak et al. 2014). We note that the SAM is also complete to this mass limit. We then measure the projected radial number density of satellites around centrals in the SAM and in the data using this mass limit and redshift range.

Figure 13 compares the satellite number density profiles in the SAM for the different central samples in our ZFOURGE data. The shape of the distributions is similar between the SAM and the data, but the SAM has ∼3× the satellites than the data at nearly all projected radii. For our comparison here, we are interested in the relative difference between the quiescent and star-forming centrals in the data and the simulation, so this offset is less important. The reason for this offset is an interesting problem (this is similar to the well-known "missing satellite problem" (Bullock 2010)), and may indicate a mistreatment of important physics in the models. For example, the stellar mass functions in the SAM show a higher number density of lower mass galaxies at 1.3 < z < 3.0 compared to observations (see Guo et al. 2011, their Figure 23), and it may be expected that such a disagreement would carry over to the satellite population. However, it is interesting that Wang & White (2012) and Wang et al. (2014) find a good agreement in the abundance of satellites in the low-redshift SDSS data and in the Guo et al. (2011) SAM, while we find such differences at higher redshift. It is plausible that the higher abundance of low-mass galaxies (log (M/M_☉) < 9.5) at z > 1 in the Guo et al. model has been resolved by Henriques et al. (2013, see discussion therein). Henriques et al. comment that in the Guo et al. model low-mass galaxies form too early and are thus overabundant at high redshift. Henriques et al. (2013) introduced modifications to the gas reincorporation timescales and produced an evolving galaxy population which fits observed abundances as a function of stellar mass and luminosity functions up to z = 3. This may help resolve the abundance of satellites as well.

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We fit the projected NFW profiles to the satellite distributions of the centrals in the SAM and the data (using the restricted redshift range, 1 < z < 2, and higher stellar mass-completeness limit for the satellites). The fit to the projected NFW profile for the satellite distribution in the SAM gives r_s = 76.93 ± 6.42 kpc. This is in reasonable agreement with the one we measure for the comparable sample in the ZFOURGE data, where the fit gives r_s = 66.73 ± 10.69 kpc (now restricted to the redshift range 1 < z < 2, which accounts for the differences between r_s derived here and that for the full redshift range in Section 3.2).

To compare with the data, we investigate how the number density of satellites around centrals in the SAM depends on stellar mass and star formation activity. Figure 14 shows the number density of satellites for all the SAM centrals with log (M_c/M_☉) > 10.48, and for the quiescent and star-forming centrals separately. As with the data, there is an excess of satellites around quiescent galaxies and most of the signal comes from the most massive centrals, with log (M_c/M_☉) > 10.78: the p values are p_MC = 0.032 (≃ 1.9σ) and p_MC = 0.001 (≃ 3.7σ) for the centrals with 10.48 < log (M_c/M_☉) < 10.78 and log (M_c/M_☉) > 10.78, respectively. As with the data, we investigate if the excess of the satellites around the quiescent galaxies is a result of a higher average stellar mass. We therefore match the stellar mass distributions between the star-forming and quiescent centrals in the SAM (see Section 5.1). Figure 15 shows the cumulative stellar mass distribution of the SAM centrals after the stellar mass distributions are matched. Figure 14 shows that quiescent centrals in the SAM have a higher number density of satellites compared to the star-forming centrals, even after the stellar mass distributions have been matched. The p values are p_MC = 0.050 (≃ 1.7σ) and p_MC = 0.016 (≃ 2.1σ) for the centrals with 10.48 < log (M_c/M_☉) < 10.78 and log (M_c/M_☉) > 10.78, respectively.

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The difference in number density of satellites between quiescent and star-forming centrals in the SAM is similar to that observed in our centrals in the ZFOURGE data. The massive quiescent centrals (log (M/M_☉) > 10.78) have about twice the number of satellites relative to massive star-forming centrals. This is still the case in a stellar mass matched sample. However, we do note that the difference in satellite content can still be found in the SAM at intermediate masses (10.48 < log (M_c/M_☉) < 10.78), whereas we do not see a significant difference in the data.

It is a concern that our sample of centrals could have some contamination from galaxies misclassified as centrals that are themselves satellites of other centrals. Since this contamination is expected to be worse at intermediate masses than at higher masses, this may affect our results on the mass-dependence of satellite content. In particular, it could contribute to the lack of observed difference in satellite content between intermediate-mass quiescent and star-forming galaxies. One way to circumvent the problem of satellite contamination would be to apply isolation criteria for centrals, however this would reduce our sample size.²¹

Therefore, to test the magnitude of the effect of satellite contamination in our central samples, we use the mock catalog, in which the true central and satellites are known. We find that ∼72% of all galaxies at intermediate mass (10.48 < log (M_c/M_☉) < 10.78) are centrals, while (log (M_c/M_☉) > 10.78) ∼78% of all galaxies in the high-mass sample are centrals, where the rest are misclassified satellites. We excluded these "false centrals" and recalculated the number density of satellites, again divided into subsamples of quiescent and star-forming centrals. For intermediate-mass centrals, the number of satellites around both quiescent and star-forming galaxies decrease by ∼30%. Because this affects both subsamples nearly equally it does not change the relative difference between them, and this should have no impact on our conclusions. For high mass centrals, the number density of satellites declines by ∼40% for star-forming centrals, but only by ∼10% for quiescent centrals. Therefore, while we make no correction for "false centrals" in our analysis, we note that correcting for this affect would reduce the number density of satellites around the high-mass star-forming centrals relative to the high-mass quiescent galaxies, enhancing the significance of difference between these subsamples measured in the data.

Therefore, we use the mock catalog from the SAM to investigate the underlying reason for the excess satellites around massive quiescent galaxies. The main reason appears to be that in the SAM the quiescent centrals have higher halo masses compared to the star-forming centrals at fixed stellar mass. Figure 15 shows that after we have matched the stellar mass distributions of the centrals in the SAM, the quiescent centrals have a higher median halo mass by a factor of ≈0.3 dex (factor of order two).

To test if halo mass is the driving cause, we match the halo mass distributions between the quiescent and star-forming centrals in the SAM using the method to match the stellar mass distributions (see Section 5.1). Figure 16 shows the number density of satellites around quiescent and star-forming centrals after matching their halo mass distributions. The difference in the number density of satellites has almost entirely disappeared. Using our p values from Monte Carlo simulations (see Section 4.3), we derive a likelihood of p_MC = 0.176 (≃ 0.9σ) that there is a difference between the satellite distributions for the centrals with log (M_c/M_☉) > 10.48. Therefore, in the SAM most of the excess in the number density satellites around quiescent galaxies can be attributed to those galaxies having higher halo masses compared to star-forming centrals.

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In ΛCDM, the dark matter halos grow through accretion and mergers. Clearly, this will involve the accretion and merging of smaller halos that contain the satellite galaxies. Our analysis of the SAM suggests that the observed difference in satellite content between different types of galaxies is driven by differences in halo mass (see also Cattaneo et al. 2006), with the number of satellites roughly proportional to the halo mass. Therefore, a plausible interpretation of our results is that, at log (M_c/M_☉) > 10.78, quiescent centrals have a median halo mass that is about a factor of two larger than comparable star-forming galaxies, and that this difference becomes significantly smaller at lower masses.

Based on our analysis of the simulations in Section 5.2, we interpret the excess of satellites around quiescent galaxies as evidence that at fixed stellar mass quiescent centrals have more massive dark matter halos than their star-forming counterparts. Our results are derived from galaxies from the three fields in ZFOURGE (COSMOS, UDS, CDFS), which are well separated on the sky. We see no evidence for strong field-to-field variance (see Section 3.1), and therefore our results seem robust against cosmic variance and/or systematics that vary between the data set in each field.

Our interpretation that quiescent galaxies have higher dark matter halos masses compared to star-forming galaxies agrees with findings from analyses of galaxy clustering. These studies also find that quiescent galaxies have stronger clustering amplitudes, and presumably higher dark mass halo masses, compared to their star-forming counterparts (e.g., Li et al. 2006; Hartley et al. 2013). It is perhaps unsurprising that our results agree because our measurement of the number distribution of satellite galaxies is similar to the "one-halo" term of the galaxy correlation function, but here we measure this to much lower masses and because of our methodology we are able to track the number of satellites and the mass contained within them on average for each central galaxy.

Our results extend trends from the local universe to higher redshifts. For example, More et al. (2011) study the kinematics of satellite galaxies from SDSS to infer the relation between the properties of central galaxies and their halo masses. Similar to our findings, More et al. conclude that central galaxies with the lower stellar masses (log (M/ M_☉) < 10.8) have no significant difference in halo mass regardless of being quiescent or star-forming. Moreover, More et al. find that the more massive quiescent centrals have larger halo masses compared to star-forming centrals even when the stellar mass is fixed, again similar to our findings at high redshift. More et al. find that the difference between halo mass of quiescent and star-forming centrals increases from 0.2 to 0.4 dex as the stellar mass of the central increased from log (M/ M_☉) = 10.8 to log (M/ M_☉) = 11.1.

These similar results also have been found by other studies of low redshift galaxies using the data from SDSS. Wang & White (2012) study the abundance of satellite galaxies in the stellar mass range 9.0 < log (M/ M_☉) < 10.0. They find that red centrals (what they call "primaries") with the stellar masses of log (M/ M_☉) > 10.8, have significantly more satellites than blue centrals of the same stellar mass. For the centrals with stellar masses of log (M/ M_☉) ∼ 11.2, red centrals have more satellites about a factor of 2 relative to the star-forming counterparts. They also compare the observation with the Guo et al. (2011) SAMs and find that the red centrals have more satellites because they reside in more massive halos. Recently, Phillips et al. (2014) study the satellites around bright host galaxies with log (M/ M_☉) = 10.5. The distribution of velocity offset for satellites and their hosts show that at fixed stellar mass the halo mass of passive host galaxies are ∼45% more massive than the those of star-forming galaxies.

These results are all in agreement with our findings. Therefore, it seems as if there is little redshift evolution in the conclusion that quiescent galaxies have higher halo masses than star-forming galaxies at fixed stellar mass, at least for the more massive centrals.

Qualitatively, it may not be surprising that quenched central galaxies occupy more massive halos than star-forming galaxies at fixed stellar mass, regardless of the particular quenching mechanism. Even after a galaxy stops forming new stars, its halo will continue to grow at a rate comparable to the past average (e.g., Conroy & Wechsler 2009; Moster et al. 2013), meaning that the ratio of dark matter mass to stellar mass will begin increasing relative to galaxies that continue to form stars. This is consistent with the results we derive from the Guo et al. (2011) SAM, where the quiescent galaxies have higher median dark matter masses compared to the star-forming galaxies, even when we match the stellar mass distributions.

In this respect it is notable that we find a difference in the number of satellites only in our high-mass sample (∼0.3 dex), and no significant difference at intermediate masses (upper limit ∼0.1 dex). Using the reasoning given above, this could be explained if high-mass galaxies quench first, and thus their halos have had the most time to grow relative to their stellar mass. Indeed, such mass-dependent quenching has been clearly demonstrated by Tomczak et al. (2014, see their Figure 11).

Our observations may have interesting implications for the mechanisms that cause quenching. It has long been recognized that star formation in high-mass halos may be suppressed due to the shock-heating, and the subsequent inefficient cooling, of infalling gas (e.g., White & Rees 1978; Birnboim & Dekel 2003; Keres et al. 2005; Dekel & Birnboim 2006). Here we wish to interpret our results using a simple model in order to test how halo mass and quenching are related. We first use the redshift-dependent parameterization of the stellar-to-halo mass relation from Moster et al. (2013) to populate halos at 1 < z < 3 in the Millennium simulation with galaxies, and add in 0.30 dex scatter in stellar mass. We label the galaxies as star-forming if their halo masses fall below a fixed threshold mass (a few times 10¹² M_☉) and quiescent if their halo masses fall above this threshold (Figure 17, top left panel). We then calculate the quenched fraction and the average halo mass of star-forming and quiescent galaxies in our two mass bins (Figure 17, top center and top right panels, respectively). This fixed halo-mass threshold for quenching results in a quenched fraction that differs significantly between the mass bins, which we do not observe. It also predicts a mean halo mass of quiescent galaxies that is significantly larger than the star-forming galaxies in both stellar mass bins, which we also do not observe.

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Because we cannot reproduce the observations for any single value of quenching halo mass and scatter in stellar mass, rather than using the model with a single halo mass quenching, we assign each galaxy a probability for being quenched based on the halo mass. We set the probability to be a steplike function with a soft cutoff profile, P_quench = 0.5(1 + erf(log (M_h/M_☉) − log (M_0.5/M_☉))/σ), where erf is the error function²². We adjust the parameter M_0.5, which is defined such that P_quench(log (M_0.5/M_☉)) = 0.5, and the parameter σ, as well as the scatter in stellar mass to roughly reproduce the observed quenched fraction and the difference in mean halo mass. We find that a log (M_0.5/M_☉) of 12.3–12.5, a standard deviation of 0.7–0.9, which corresponds to P_quench = 0 for log (M_h/M_☉) ∼ 11–11.5 and P_quench = 1 for log (M_h/M_☉) ∼ 13.5, and a scatter in stellar mass of 0.15–0.2 dex, is able to roughly reproduce the observed quiescent fractions and the difference in the average halo mass of centrals at both stellar mass bins (Figure 17, bottom row). We find that the differences in mean halo mass of quiescent and star-forming galaxies are ∼0.1 dex and ∼0.2 dex for intermediate and high stellar mass bins, respectively (Figure 17, bottom right panel), in better agreement with the observations. The small scatter favored by the model in the stellar-to-halo mass relation is due to the fact that we see significant differences in N_sat over a relatively small range in stellar mass: the mean mass in the intermediate-mass sample is log (M_*/M_☉) ∼ 10.6, while in the high mass sample it is log (M_*/M_☉) ∼ 11.0, and so a large amount of scatter would wash out differences in halo mass over this relatively limited range in stellar mass. We do note that the scatter in our modeling represents intrinsic scatter in the stellar-to-halo mass relation combined with the random errors in our stellar mass estimates, suggesting that the intrinsic scatter must be small indeed.

Our model is simplistic; it is obviously possible to develop it further. For instance, we note that adding a mass-dependent scatter in the stellar masses—where the scatter increases from 0.15 dex at lower masses to 0.3 dex at the higher masses—improves the agreement between the toy model and the data. However, given the uncertainties involved in the current data, particularly with regard to the incompleteness in satellite detection at low masses and the (limited) expected misclassification between centrals and satellites (see Section 2.2), our modeling results can only be regarded as indicative, and we do not push the modeling any further.

If our observation that intermediate mass quiescent and star-forming centrals have the same N_sat is correct, then our toy model strongly favors a scenario where there is no single quenching halo mass threshold: even at relatively high halo masses (log (M/h⁻¹M_☉) ∼ 12 based on the SAM), only about 50% of the galaxies are quiescent while the rest remain star-forming, and galaxies have some likelihood of being quenched over a very wide range in halo masses (log (M_h/M_☉) ∼ 11–13.5). One remaining question is that if halo mass quenching is an important mechanism, why do some galaxies remain star-forming while others quench? Our result implies that halo mass can only be a contributing factor. Other factors may include environmental processes (assembly bias and environmental effects on the gas-accretion process), stochastic processes such as mergers, and galaxy structure (e.g Gao et al. 2005; Wechsler et al. 2006; Croton et al. 2007; Cooper et al. 2010; Papovich et al. 2012; Rudnick et al. 2012; Bassett et al. 2013; Lotz et al. 2013).

This result may be expected on theoretical grounds, as some variation in the quenching mass is expected due to variations in metallicity and perhaps also due to the enhanced ability of cold flows to penetrate halos at the higher redshifts in our sample (Dekel & Birnboim 2006; Dekel et al. 2009). A variation in halo mass is also expected based on the results of Gabor & Davé (2012). In their model galaxy quenching is based on the hot gas content of halos, which is correlated with, but not directly tied to halo mass. Recently, Lu et al. (2013) also show that galaxy models require a quenching probability that increases with mass to explain the color–mass distributions of galaxies in the CANDELS survey.

The mergers that grow massive quiescent galaxies are supposed to be primarily dissipationless and devoid of cold gas available for star formation (e.g., the so-called dry mergers; van Dokkum et al. 2010; Oser et al. 2010, 2012; Hopkins et al. 2010). If this is the case, it is expected that satellites around the quiescent centrals in our sample, which will eventually merge with their central galaxies, should be largely devoid of gas (or some process must cause them to expel or consume their gas prior to merging with the central). Therefore it may be expected that the satellites should show signs of passive colors. A discussion of the color and stellar mass distributions of the satellites is beyond the scope of the present work, but we will study these distributions in a future paper.