An Analysis Framework for Understanding the Origin of Nuclear Activity in Low-Power Radio Galaxies
AAJ,
IN PRESS
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AN ANALYSIS FRAMEWORK FOR UNDERSTANDING THE ORIGIN OF NUCLEAR ACTIVITY IN LOW-POWERRADIO GALAXIES Y EN -T ING L IN , H UNG -J IN H UANG , AND Y EN -C HI C HEN AJ, in press
ABSTRACTUsing large samples containing nearly 2300 active galaxies of low radio luminosity (1.4 GHz luminosity be-tween 2 × and 3 × W/Hz, essentially low-excitation radio galaxies) at z (cid:46) .
3, we present a self-contained analysis of the dependence of the nuclear radio activity on both intrinsic and extrinsic properties ofgalaxies, with the goal of identifying the best predictors of the nuclear radio activity. While confirming theestablished result that stellar mass must play a key role in the triggering of radio activities, we point out thatfor central, most massive galaxies, the radio activity also shows a strong dependence on halo mass, which isunlikely due to enhanced interaction rates in denser regions in massive, cluster-scale halos. We thus furtherinvestigate the effects of various properties of the intracluster medium (ICM) in massive clusters on the radioactivities, employing two standard statistical tools, Principle Component Analysis and Logistic Regression. Itis found that ICM entropy, local cooling time, and pressure are the most effective in predicting the radio activ-ity, pointing to the accretion of gas cooling out of a hot atmosphere to be the likely origin in triggering suchactivities in galaxies residing in massive dark matter halos. Our analysis framework enables us to logicallydiscern the mechanisms responsible for the radio activity separately for central and satellite galaxies.
Keywords: galaxies: active — radio continuum: galaxies — galaxies: clusters: general — galaxies: ellipticaland lenticular, cD INTRODUCTION
The cause of the nuclear radio activity in galaxies has longbeen a unsolved problem in astrophysics (e.g., Tadhunter2016). With the advent of large scale surveys such as NRAOVLA Sky Survey (NVSS; Condon et al. 1998), Faint Im-ages of the Radio Sky at Twenty-Centimeters (FIRST; Beckeret al. 1995), and Sloan Digital Sky Survey (SDSS; Yorket al. 2000), it was clearly shown that the fraction of galaxiesthat are radio-loud (above certain luminosity threshold P th ) is a strong function of stellar mass (e.g., Best et al. 2005a;Pasquali et al. 2009), and it is expected that the radio-loudphase is quite common in the course of the formation of mas-sive galaxies (e.g., Heckman & Best 2014). Indeed, in thecurrent generation of galaxy formation models, feedback fromradio jets emanating from the central super massive black hole(SMBH) has been incorporated as an important mechanismfor keeping massive galaxies “red-and-dead” (e.g., Crotonet al. 2006; Bower et al. 2006; see also McNamara & Nulsen2007). How a very tight feedback loop can be maintainedwhen the physical scales involved span 10 orders of magni-tude remains a deep mystery (Fabian 2012), however.Occupying the most massive end of the galaxy population,the brightest cluster galaxies (BCGs) are found to exhibit thehighest radio active fraction (RAF, defined to be the fractionof galaxies selected with some specified stellar mass or opticalluminosity range with radio luminosity P ≥ P th , and, wherenecessary and possible, also certain specified halo mass range;RAF is about 30-40% with log P th = 23 for BCGs in clusters Institute of Astronomy and Astrophysics, Academia Sinica, Taipei10617, Taiwan; [email protected] Department of Physics, Carnegie Mellon University, Pittsburgh, PA15213, USA Department of Statistics, University of Washington, Seattle, WA98195, USA In the literature, there are different definitions for a galaxy to be radio-loud or radio-quiet/quiescent. Throughout this work we simply use the radioluminosity to classify galaxies into these states. at 1.4 GHz; e.g., Lin & Mohr 2007; Best et al. 2007; von derLinden et al. 2007; here P is in unit of W / Hz). It is longobserved that their nuclear radio activity cannot be solely at-tributed to the high stellar mass, however, as their proximityto the center of galaxy clusters clearly plays important roles intriggering the radio active galactic nuclei (AGN). For exam-ple, Lin & Mohr (2007) find that, compared to cluster galaxiesof comparable stellar mass content (as traced by the near-IRluminosity), BCGs are more likely to be radio loud. It is alsofound that the spatial distribution of non-BCG member ra-dio galaxies is highly concentrated towards the cluster center.Both of these results indicate that galaxies in the central re-gion of clusters have an enhancement of nuclear activity. Itis thus crucial to investigate both the effects of environmentsand internal properties of the galaxies on triggering SMBHactivities.It is suggested that the AGN population can be dividedinto two main categories, primarily based on the configura-tion of the central engine: a radiation dominated class (theso-called “radiative mode”), and a mechanical power domi-nated class (the “jet-mode”) (e.g., Ho 2008; Heckman & Best2014). These roughly correspond to systems of high and lowaccretion rates onto the central SMBH, and therefore could betriggered by different physical mechanisms. While radio-loudobjects are found in both classes, the jet-launching mecha-nisms are likely different (Heckman & Best 2014; Tadhunter2016, and references therein). To understand the phenomenol-ogy of radio-loud AGN, in addition to the central engine, onealso needs to consider the properties and environments of thehost galaxies (e.g., Lin et al. 2010). In this paper, we shallfocus on low-power (e.g., 1.4 GHz luminosity log P ≤ . a r X i v : . [ a s t r o - ph . GA ] M a r L IN , H UANG , & C
HEN properties, both intrinsic and extrinsic to galaxies, that aremost closely linked to the triggering mechanism of the radioactivity in the nucleus. In addition to stellar mass and hosthalo mass, we shall also consider environmental factors suchas local galaxy density and, for galaxies residing in clusters,properties of the intracluster medium (ICM). If such a linkcould be established with high statistical significance, we maybe in a better position in identifying the most likely scenarioamong competing theoretical models (e.g., the precipitationmodel of Voit et al. 2015, the stimulated feedback model ofMcNamara et al. 2016) that aim to explain the radio AGNphenomenon.There have been many studies attempting to discern the pri-mary cause(s) of low-power nuclear radio activity. For ex-ample, Cavagnolo et al. (2008) clearly demonstrate that ra-dio emission is much more pronounced in BCGs when theentropy of the ICM in the cluster center is lower than somethreshold value. Using a sample of 64 nearby clusters, Mittalet al. (2009) examine various correlations between the radioluminosity of BCGs and cluster properties, finding a strongindication for the central cooling time of ICM to play an im-portant role (see also Ineson et al. 2015; McNamara et al.2016). These results suggest the importance of gas coolingout of hot atmosphere/ICM surrounding the galaxies. Extend-ing the host dark matter halo mass range to include lower masssystems, Pasquali et al. (2009) examine the RAF as a func-tion of both stellar and halo mass, finding a dominant stellarmass dependence over that on halo mass. Sabater et al. (2013)find that, at fixed stellar mass, both dense environments andgalaxy interactions enhance the likelihood of a galaxy beingradio-loud.For our investigation, we find it useful to separate galaxiesinto two classes: central and satellite. Central galaxies arelocated close to the bottom of potential well of dark matterhalos, and can grow in stellar mass via mergers with galaxiesbrought in by the dynamical friction, as well as by star forma-tion due to (residual) cooling instability of the ICM. Satellites,on the other hand, refer to all non-central galaxies in a galac-tic system; they are likely once central galaxies in their owndark matter halos before their halos get accreted/merged withthe current halo. In this picture, BCGs are central galaxies inmassive clusters. Given their different locations inside galac-tic systems, it is plausible that the triggering mechanisms forcentral galaxies may be different from that for the satellites.In this work we develop a framework of analysis that al-lows us to investigate the relative importance of various phys-ical properties on the nuclear radio activity. The analysis iscarried out separately for central and satellite galaxies. Usinga large sample of radio galaxies associated with galactic sys-tems that span a wide range in halo mass, we point out in Sec-tion 2 that while for both central and satellite galaxies, stellarmass is a key predictor for radio activity, halo mass also playsan important role, particularly for the central galaxies. Thenin Section 3, utilizing a cluster sample with detailed measure-ments of the ICM properties, we use robust statistical meth-ods to point out that entropy, local cooling time, and pressureplay the most significant role for the triggering of radio activ-ities. We conclude with a discussion on future prospects inSection 4.Throughout this paper we adopt a
WMAP5 (Komatsu et al.2009) Λ CDM cosmological model, where Ω m = 0 . Ω Λ =0 . H = 100 h km s − Mpc − with h = 0 .
71. All optical mag-nitudes are in the AB system. IMPORTANCE OF HALO MASS, STELLAR MASS, AND LOCALGALAXY DENSITY
In the first part of our analysis, we investigate the role ofhost galaxy stellar mass ( M ∗ ), dark matter halo mass ( M h ),and local galaxy density ( Σ ) in triggering nuclear radio ac-tivity, using the radio galaxy (RG) population in groups andclusters found in SDSS. After describing the construction ofour RG sample, we examine the dependence of RAF on thesethree physical properties, obtaining a qualitative picture fromthe global trends (Section 2.1); we then quantitatively com-pare the relative importance of these physical attributes via a logistic regression (LR) analysis (Section 2.2).Our group and cluster sample is taken from the Data Re-lease 7 (DR7) version of the group catalog of Yang et al.(2007). By assuming a one-to-one relationship between thehalo mass and the total luminosity (or stellar mass) con-tent of galaxy groups, Yang et al. (2007) are able to “as-sign” a halo mass to every galactic system they spectroscop-ically identify in SDSS (using essentially a matched-filter al-gorithm), down to single-galaxy systems. For every galaxygroup, they then designate the most massive galaxy closest tothe geometric mean of member galaxy positions as the centralgalaxy; the rest are regarded as satellites. We adopt their cen-tral/satellite designation in this study. We compute the stellarmass and absolute magnitudes of all member galaxies usingthe kcorrect code (Blanton & Roweis 2007).The RG sample used in this Section is based on two largeRG catalogs: one is that of Lin et al. (2010, hereafter L10),which covers the footprint of SDSS DR6 and is available inTable A1, the other is taken from Best & Heckman (2012),covering DR7. Both studies cross match SDSS galaxy sam-ples with 1.4 GHz radio source catalogs from NVSS andFIRST, largely following the methodology outlined in Bestet al. (2005b). To ensure the radio sources are powered (pri-marily) by an active nucleus, a combination of diagnosticsis used to select RGs, including the BPT diagram (Baldwinet al. 1981), and the distributions of objects in the 4000 Å vs . radio power, and H α vs . radio power planes (see modi-fications discussed in Best & Heckman 2012). We refer thereader to the original references for detailed descriptions ofthe ways these catalogs are constructed; here we only pointout two features that distinguish the L10 approach from theBest et al. algorithm. First, we start with a parent galaxy sam-ple with z ≤ . M . r ≤ − .
27 (i.e., more luminous thanthe characteristic magnitude in the galaxy luminosity func-tion; Blanton et al. 2003. Here M . r denotes the SDSS r -bandshifted blueward by a factor of 1.1 in wavelength) from theNew York University Value-Added Galaxy Catalog (Blantonet al. 2005). Selecting RGs with a uniform absolute magni-tude limit makes it straightforward to compute the RAF involume-limited galaxy samples. On the other hand, Best etal. consider matches to a flux-limited radio source sample, andtherefore some radio-loud galaxies may be missed. Second,we have visually inspected all potential matches to improvethe purity, and to combine fluxes from distinct componentsfor complex, extended sources.To construct the parent RG sample, we use all the objectsfrom the L10 sample; in areas unique to DR7, we then usethe Best & Heckman (2012) sample. We further restrict our-selves to galaxies satisfying z ≤ . M . r ≤ − .
57, and23 . ≤ log P . ≤ . P . being the 1.4 GHz radio lumi-nosity in W/Hz) to make the sample volume-limited in bothoptical and radio luminosities; these criteria also make our RIGGERING N UCLEAR R ADIO A CTIVITY Figure 1.
The distribution of our RG sample in the redshift–radio luminosityplane. Our main galaxy sample, volume-limited to z = 0 .
15, is represented bythe union of red and blue-colored points, while the z ≤ .
092 volume-limitedsub-sample is shown as blue points (see Table 1).
Table 1
RG samples in Yang et al. groupsmain ( z ≤ .
15) sample central satelliteparent 97469 21169RG 1861 360 z ≤ .
092 sub-sample central satelliteparent 20529 4972RG 364 96 sample insensitive to the differences in the selection methodsbetween L10 and Best & Heckman (2012). Our selection es-sentially produces a low-excitation radio galaxy (LERG) sam-ple, as only about 3% of our RGs show strong enough [O
III ]emission line to be classified as high-excitation radio galaxies(following the definition of Ching et al. 2017a, that is, theline is detected at ≥ σ , and has equivalent width > M h = M b , themass enclosed in r b , within which the mean overdensity is200 times the mean density of the Universe). Global Trends of Radio Active Fraction
We show in Fig. 2 the dependence of RAF f ( M ∗ , M h ) in thehost galaxy stellar mass vs . host group/cluster mass plane, forcentral (top) and satellite (bottom) galaxies. Here the RAF isthe ratio of number of RGs to that of all galaxies in a given( M ∗ , M h ) bin. The widths of the two dimensional bins are cho-sen such that most of them contain at least 5 RGs, while smallenough to reveal global trends with M ∗ or M h . Our resultsdo not sensitively depend on the choice of bin widths. It canbe seen that the RAF dependence is different for centrals and . . . . . . . halo ) [M h ]10 . . . . . . . l og ( M s t a r ) [ M h ] . . . . . . . . C e n tr a l R A F array([[ 14., 8., 2., 0., 0.], [ 11., 24., 32., 4., 0.], [ 9., 37., 55., 21., 2.], [ 7., 26., 34., 30., 12.], [ 1., 6., 10., 12., 3.]])array([[ 5., 49., 5., 0., 0., 0., 0.], [ 0., 35., 210., 90., 0., 0., 0.], [ 1., 10., 78., 283., 132., 0., 0.], [ 0., 1., 38., 177., 227., 72., 1.], [ 0., 1., 6., 68., 122., 100., 15.], [ 0., 0., 0., 12., 45., 39., 17.], [ 0., 0., 0., 1., 5., 8., 8.]]) RG array
Fig.1 array([[ 4.16500000e+03, 2.10870000e+04, 3.65800000e+03, 4.00000000e+00, 2.00000000e+00, 2.00000000e+00, 2.00000000e+00], [ 2.74000000e+02, 6.35400000e+03, 2.46010000e+04, 4.62100000e+03, 4.00000000e+00, 3.00000000e+00, 2.00000000e+00], [ 3.20000000e+01, 1.37900000e+03, 5.65200000e+03, 8.05100000e+03, 1.92900000e+03, 1.30000000e+01, 0.00000000e+00], [ 1.10000000e+01, 2.15000000e+02, 1.46900000e+03, 2.85800000e+03, 2.17700000e+03, 4.08000000e+02, 3.00000000e+00], [ 1.00000000e+00, 2.00000000e+01, 2.10000000e+02, 7.85000000e+02, 8.91000000e+02, 4.59000000e+02, 5.80000000e+01], [ 0.00000000e+00, 5.00000000e+00, 2.20000000e+01, 1.22000000e+02, 2.43000000e+02, 1.89000000e+02, 6.10000000e+01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 8.00000000e+00, 3.30000000e+01, 2.90000000e+01, 2.30000000e+01]]) . . . . . . . halo ) [M h ]10 . . . . . . . l og ( M s t a r ) [ M h ] . . . . . . . . S a t e lli t e R A F array([[ 2043, 1322, 82, 0 , 0], [ 192, 2847, 938, 71, 2], [ 1413, 2517, 1261, 304, 28], [ 669, 1242, 702, 257, 56], [ 147, 277, 159, 67, 32]]) Figure 2.
The dependence of RAF, defined as the ratio of number of RGsto that of all galaxies in a given ( M ∗ , M h ) bin, on dark matter halo massand stellar mass for central (top panel) and satellite (bottom panel) galaxies,based on our main sample. It is apparent that the RAF depends on both halomass and stellar mass for central galaxies; for satellites, the RAF is primarilydependent on stellar mass. In each ( M h , M ∗ ) bin, the number in the lowerright corner denotes the number of all galaxies, while the one in the upperleft corner is the number of RGs. satellites, in the sense that while satellite RAF is primarily afunction of stellar mass (with only weak dependence on halomass), both stellar mass and halo mass matter for centrals.Our result is consistent with the findings of Pasquali et al.(2009), who also study the stellar mass and halo mass depen-dence of RAF in groups and clusters identified by Yang et al.(although they have combined centrals and satellites in theiranalysis on RGs). Both the group/cluster and the RG sampleswe use are of much larger sizes compared to those used byPasquali et al. (2009). Our RG sample selection is also betterdefined (in terms of radio flux limit, optical luminosity thresh-old, and visual inspection for completeness and purity). Bothof these factors make our results more statistically significant.The trend we see in Fig. 2 may be partially driven by theintrinsic correlation between stellar mass and halo mass forcentral galaxies (e.g., Yang et al. 2007; Mandelbaum et al.2016). To examine how much radio activity is caused by halomass-dependent physical processes additional to the stellarmass–halo mass relation, at fixed stellar mass, we sum theRAF values over all halo mass bins, then normalize the RAFby that sum; in short, the normalized RAF is ˜ f ( M h | M ∗ ) = f ( M h , M ∗ ) / (cid:82) f ( M h , M ∗ ) dM h .Fig. 3 shows the normalized RAF for both central and satel-lite galaxies. There is still a dependence on halo mass afterthe effect of the stellar mass–halo mass relation is removed.Fitting a linear relation between the normalized RAF and log- L IN , H UANG , & C
HEN . . . . . . . halo ) [M h ]10 . . . . . . . l og ( M s t a r ) [ M h ] . . . . . . . . C e n tr a l n o r m a li ze d R A F normalized RAF:[[ 0.03699422 0.03332203 0.01749189 0. 0. 0. 0. ] [ 0. 0.0789898 0.10923883 0.04566077 0. 0. 0. ] [ 0.96300578 0.10398864 0.17660498 0.08240874 0.10587413 0. 0. ] [ 0. 0.06669783 0.33103377 0.14519368 0.16133017 0.20132478 0.27356743] [ 0. 0.71700169 0.36563053 0.2030841 0.21185089 0.24854911 0.21225059] [ 0. 0. 0. 0.23059936 0.28651964 0.23541151 0.22872031] [ 0. 0. 0. 0.29305335 0.23442516 0.3147146 0.28546167]] . . . . . . . halo ) [M h ]10 . . . . . . . l og ( M s t a r ) [ M h ] . . . . S a t e lli t e n o r m a li ze d R A F RAF[[ 0.00685267 0.00605144 0.02439024 0. 0. ] [ 0.00572917 0.00842993 0.03411514 0.05633803 0. ] [ 0.00636943 0.01470004 0.04361618 0.06907895 0.07142857] [ 0.01046338 0.02093398 0.04843305 0.11673152 0.21428571] [ 0.00680272 0.02166065 0.06289308 0.17910448 0.09375 ]]normalized RAF:[[ 0.18920947 0.08431 0.11426802 0. 0. ] [ 0.15818841 0.11744765 0.15982904 0.13373918 0. ] [ 0.17586668 0.2048043 0.2043413 0.16398448 0.18823529] [ 0.28890505 0.29165694 0.22690828 0.27710551 0.56470588] [ 0.18783039 0.30178111 0.29465337 0.42517084 0.24705882]]
Figure 3.
The dependence of normalized RAF on dark matter halo massand stellar mass for central (top panel) and satellite (lower panel) galaxies.At fixed stellar mass, the normalized RAF is positively correlated with halomass, for both central and satellite galaxies. While by definition, at fixedstellar mass, the normalized RAF sums up to unity, it is not meaningful tolook for variation along stellar mass axis at fixed halo mass. arithm of halo mass for each of the stellar mass bin, we findthat all the slopes are positive. To compute the uncertaintiesin the slope of the normalized RAF–halo mass fits, we gener-ate 1000 bootstrap resampling and repeat the fitting process.The halo mass dependence of the normalized RAF is highlysignificant ( > σ ) for all but the most massive central galaxies(with the latter being at 2 σ level, which is likely due to smallnumber statistics). The above exercise is repeated for satel-lite galaxies. Again we find the normalized RAF is positivelycorrelated with halo mass at high significance.We have thus established that the radio activity strongly de-pends on the halo mass the galaxies reside in. This is consis-tent with the findings of some recent studies (e.g., Mendezet al. 2016; Shen et al. 2017); for example, Ching et al.(2017a) find that LERGs are found in higher mass halos than acontrol sample of radio-quiescent galaxies, indicating the im-portance of halo mass in triggering radio activity. As the fu-eling of SMBHs takes place at a scale much smaller than thatof a dark matter halo, we seek to find out what it is in massivehalos that promotes the radio activity. The possibilities in-clude elevated rates of galaxy interaction, and the propertiesof ICM.In Fig. 4 we show the RAF dependence in the local galaxydensity Σ vs . halo mass plane. Here Σ is the surface densityover an area containing the fifth nearest neighbor (also sat-isfying M . r ≤ − .
57 and velocity difference ≤ array([[ 0., 0., 7., 36., 14., 2., 0.], [ 1., 1., 47., 185., 89., 12., 0.], [ 0., 2., 53., 240., 191., 18., 0.], [ 0., 1., 34., 237., 209., 35., 0.], [ 0., 0., 6., 80., 148., 70., 8.], [ 0., 0., 0., 3., 28., 59., 23.], [ 0., 0., 0., 0., 3., 11., 8.]])array([[ 2.70000000e+01, 3.50000000e+02, 6.33500000e+03, 1.53630000e+04, 6.46900000e+03, 5.46000000e+02, 4.00000000e+00], [ 2.20000000e+01, 3.14000000e+02, 6.69000000e+03, 1.89150000e+04, 9.03300000e+03, 8.98000000e+02, 1.10000000e+01], [ 1.20000000e+01, 9.20000000e+01, 2.41200000e+03, 8.95100000e+03, 5.03300000e+03, 5.64000000e+02, 4.00000000e+00], [ 3.00000000e+00, 2.30000000e+01, 5.72000000e+02, 3.33200000e+03, 2.81500000e+03, 4.06000000e+02, 6.00000000e+00], [ 1.00000000e+00, 1.00000000e+00, 5.30000000e+01, 6.31000000e+02, 1.16600000e+03, 5.18000000e+02, 5.70000000e+01], [ 0.00000000e+00, 0.00000000e+00, 1.00000000e+00, 2.90000000e+01, 1.50000000e+02, 3.42000000e+02, 1.21000000e+02], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.40000000e+01, 4.30000000e+01, 3.20000000e+01]]) . . . . . . . halo ) [M h ] l og ( ⌃ ) [ M p c h ] . . . . . . . . . . S a t e lli t e R A F . . . . . . . halo ) [M h ] l og ( ⌃ ) [ M p c h ] . . . . . . . . C e n tr a l R A F array([[ 4., 13., 7., 0., 0.], [ 10., 38., 23., 0., 0.], [ 2., 47., 53., 22., 0.], [ 1., 5., 44., 51., 8.], [ 0., 1., 8., 21., 2.]])array([[ 1.19600000e+03, 2.20300000e+03, 6.33000000e+02, 2.70000000e+01, 1.00000000e+00], [ 1.10700000e+03, 3.44700000e+03, 1.53100000e+03, 1.17000000e+02, 5.00000000e+00], [ 2.02000000e+02, 1.79200000e+03, 2.77200000e+03, 9.80000000e+02, 4.50000000e+01], [ 1.00000000e+01, 1.89000000e+02, 1.49200000e+03, 1.22700000e+03, 1.58000000e+02], [ 0.00000000e+00, 1.20000000e+01, 2.78000000e+02, 3.54000000e+02, 7.00000000e+01]]) Figure 4.
The dependence of RAF on dark matter halo mass and local galaxydensity, Σ , for central (top panel) and satellite (bottom panel) galaxies. TheRAF is largely independent of the local density. We note that the galaxysample used here is primarily composed of luminous galaxies (all in our mainsample), and thus the local density measurements may not be representative,however (see Fig. 5). The meaning of the numbers in each of the ( M h , Σ )bins is the same as in Figure 2. mator of local density as it is related to the dark matter halodensity (Sabater et al. 2013). Our conclusions remain un-changed if we use the density constructed with third nearestneighbor, Σ . There are hints of a weak dependence on the lo-cal galaxy density, although the dependence does not seem tobe monotonic with respect to Σ . We note that, however, theselection of neighbors is limited to very luminous galaxies,which would bias us against effects of minor mergers or inter-actions with less massive companions. We have thus repeatedthe exercise with a different volume limited sample (out to z = 0 . Σ with less luminous ( M . r ≤ − .
27) neighbors,and derived the normalized RAF [this time calculated at fixedhalo mass: ˜ f ( Σ | M h ) = f ( Σ , M h ) / (cid:82) f ( Σ , M h ) d Σ ], to re-move the potential correlation between halo mass and localgalaxy density. The results are presented in Figure 5. Com-pared to the trends shown in Figure 4, for central galaxies inhigh mass halos ( M h ≥ h − M (cid:12) ), the effects of the localdensity on the RAF appears to be weakened. The effect of thelocal density on satellites is more apparent, although we notethe significance of the result is hampered by the small numberof RGs, especially in densest regions (at Σ > h Mpc − ,we only have 4 − RIGGERING N UCLEAR R ADIO A CTIVITY array([[ 0., 4., 6., 7., 0., 0., 0.], [ 3., 13., 24., 15., 4., 0., 0.], [ 0., 10., 28., 33., 13., 2., 1.], [ 0., 2., 12., 32., 38., 17., 3.], [ 0., 0., 0., 7., 28., 22., 9.], [ 0., 0., 0., 0., 6., 11., 4.], [ 0., 0., 0., 0., 2., 4., 4.]])array([[ 5.21000000e+02, 2.43500000e+03, 3.01100000e+03, 1.22600000e+03, 1.80000000e+02, 8.00000000e+00, 0.00000000e+00], [ 2.96000000e+02, 1.67300000e+03, 2.53700000e+03, 1.30000000e+03, 2.41000000e+02, 2.10000000e+01, 1.00000000e+00], [ 4.80000000e+01, 4.48000000e+02, 1.14800000e+03, 9.18000000e+02, 3.35000000e+02, 6.70000000e+01, 7.00000000e+00], [ 3.00000000e+00, 3.70000000e+01, 1.75000000e+02, 4.05000000e+02, 5.77000000e+02, 1.90000000e+02, 2.30000000e+01], [ 0.00000000e+00, 1.00000000e+00, 5.00000000e+00, 5.10000000e+01, 2.02000000e+02, 2.39000000e+02, 5.20000000e+01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.20000000e+01, 4.70000000e+01, 7.50000000e+01, 4.30000000e+01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00, 6.00000000e+00, 1.40000000e+01, 1.20000000e+01]]) . . . . . . . halo ) [M h ] . . . . . . . . . l og ( ⌃ ) [ M p c h ] . . . . . . . . . C e n tr a l n o r m a li ze d R A F array([[ 6., 2., 0., 1., 0.], [ 1., 2., 5., 5., 0.], [ 0., 2., 7., 12., 5.], [ 0., 2., 7., 13., 7.], [ 0., 2., 6., 7., 4.]])array([[ 277., 305., 144., 28., 2.], [ 55., 357., 513., 212., 28.], [ 3., 202., 542., 338., 86.], [ 0., 141., 375., 267., 99.], [ 2., 65., 174., 141., 49.]]) . . . . . . . halo ) [M h ] . . . . . . . . . l og ( ⌃ ) [ M p c h ] . . . . . . . . S a t e lli t e n o r m a li ze d R A F Figure 5.
The dependence of normalized RAF on dark matter halo mass andlocal galaxy density for central (top panel) and satellite (bottom panel) galax-ies. Unlike in Fig. 3, here the RAF is normalized by fixing the halo mass. Thegalaxy sample used here is volume-limited to z = 0 .
092 (see Table 1), differ-ent from that used in Fig. 4, as we would like to include lower luminositygalaxies in the calculation of Σ . It can be seen that while the satellite RAFdepends on the local density, this does not seen to be the case for centrals.The meaning of the numbers in each of the ( M h , Σ ) bins is the same as inFigure 2. Quantitative Analysis with Logistic Regression
We have shown that the RAF strongly depends on both M ∗ and M h , with some hints of dependence on the local galaxydensity. Here we turn to LR as an independent way of eval-uating the importance of these physical quantities on the ra-dio activity of a given galaxy population. We simplify theradio activity into an “on” or “off” state (i.e., when the ra-dio luminosity is within the adopted luminosity range or not),which allows us to transform the question into a classificationproblem, making the LR an appropriate analysis tool. Equiva-lently, we are then asking: which of these physical propertiesare most predictive of the radio activity?The goal of a regression analysis is to study the relation-ships between a response variable Y and an array of m ( ≥ X = ( X , ... X i , ... X m ) in a specified functional form Y = f ( X ) + (cid:15) . In our case, the response variable Y is a bi-nary, taking values of Y = 1 for radio-loud and Y = 0 for radio-quiescent. The regressors considered here are M ∗ , M h and Σ (or Σ ). We apply the standard LR model as the following: Pr ( Y = 1 | X ) = f ( X ) + (cid:15) = e β + β X + ... + β i X i + ... + β m X m + e β + β X + ... + β i X i + ... + β m X m + (cid:15), (1) Strictly speaking, as our RGs are selected to have log P . = 23 . − . Y = 0 and so this state should be understoodas the complement of the “low-power” state. where Pr ( Y = 1 | X ) stands for the probability of a galaxy tobe in the radio-loud state given its physical parameters X , and (cid:15) represents random observational error. Given the observa-tional data of n galaxies ( x , y ) , ( x , y ) , ..., ( x n , y n ) as input,we fit Eq. (1) using the bestglm package in R and derive thebest fit model parameters ˆ β , and ˆ β = ( β , . . . , β m ). A larger | β i | indicates a stronger effect of the regressor X i on Y . It canbe seen that if β i = 0, X i does not have any effect on the finalvalue of Pr ( Y = 1 | X ). Conventionally, the statistical signifi-cance level of regressor X i ’s effect on Y is characterized viathe z -value, defined as the ratio of estimated ˆ β i to its standarderror; a larger | z | implies stronger evidence against the nullhypothesis of β i = 0. Under the assumption that β i is asymp-totically Gaussian, there is a direct link between the z -valueand p -value on the hypothesis test of whether β i = 0 or not. A p -value of 0.05 corresponds to a 95% confidence interval for β i not overlapping with zero.Aiming at selecting a model with predictors (regressors)that are truly associated with nuclear radio activity, we applythe best subset selection method to identify the best model.Generally, a model involving more regressors has more de-grees of freedom to fit the data well, but may suffer fromoverfitting. On the other hand, a model with fewer regressorsis more stable, but may lose its power to predict the behav-ior of Y given all the available information. The best subsetselection method identifies the best model (among all 7 possi-ble regressor combinations of M ∗ , M h , and Σ ) as the one thatminimizes the Bayesian Information Criterion ( BIC ), definedas
BIC ≡ n (cid:0) RSS + log( n ) d ˆ σ (cid:1) , (2)where RSS is the residual sum of squares, d denotes the num-ber of predictors used in the model, n is the total number ofgalaxies, and ˆ σ is an estimate of the variance of observationalerror (cid:15) shown in Eq. (1). The minimum of BIC is reached bybalancing the goodness of fit (
RSS ) and the degree of freedom d . After the best model is identified, we can then evaluate the z - and p -values for each of the predictors in the best model.As mentioned above, the local density calculation for the z ≤ .
15 sample is based on luminous galaxies, and thus maynot be representative of true values. We therefore focus onthe z ≤ .
092 sub-sample here. For central galaxies, the bestmodel consists of M h and M ∗ , irrespective of the local densitydefinition ( Σ or Σ ). As for satellite galaxies, LR prefers amodel consisting of M ∗ and local density (either of Σ and Σ ). The resulting z - and p -values, together with the best-fit β parameter, of these models are shown in Table 2 (for com-pleteness, we present results for both the main sample and the z ≤ .
092 sub-sample). These findings are consistent with thequalitative trends revealed by the RAF plots (Figures 2–5).For the z ≤ .
15 sample, we see from Table 2 that the β values associated with M h are significantly different for thecentrals and satellites. The same also applies to that associ-ated with M ∗ . Therefore we can conclude that the distributionof RAF for centrals and satellites in the M h vs. M ∗ plane mustbe different.The importance of interaction in triggering radio activityhas been noted in a few studies (e.g., Sabater et al. 2013;Pace & Salim 2014). Our distinction of central and satellitegalaxies has enabled us to attribute this environmental factor(and the implied enhancement of tidal interactions) particu-larly to radio AGN phenomenon in satellites. Using a sample L IN , H UANG , & C
HEN
Table 2
Best models based on the LR analysis z ≤ .
15, central galaxiesParameter β z -value p -value M h ± . < × − M ∗ ± . < × − z ≤ .
15, satellite galaxiesParameter β z -value p -value M h ± . < × − M ∗ ± . < × − z ≤ . β z -value p -value M h ± . < × − M ∗ ± . < × − z ≤ . β z -value p -value M ∗ ± . < × − Σ ± . < × − of galaxies in spectroscopically confirmed pairs, Ellison et al.(2015) show that once halo mass and stellar age of galax-ies are controlled, major mergers do not enhance the (low-excitation) radio activity, and thus make the conjecture thatminor mergers or/and accretion from the surrounding mediumcould be possible external gas fueling mechanisms (see alsoKarouzos et al. 2014). Given that the majority of our satel-lite RGs live in cluster-scale halos (75% are in halos with M h ≥ M (cid:12) ), and that the high velocity dispersion in clus-ters makes both merger rates and gas accretion rates low forsatellites, however, it seems that tidal interactions are the mostprobable channel for bringing external gas into nuclear re-gions of satellites.Although it is possible that enhanced interaction amonggalaxies in dense regions may partly contribute to the trigger-ing of radio activity in satellite galaxies, we note that the ma-jority ( ∼ LOCAL ICM PROPERTIES
To investigate the effect of the ICM on triggering of the ra-dio activity, we make use of the X-ray measurements in theACCEPT (Archive of Chandra Cluster Entropy Profile Ta-bles) database (Cavagnolo et al. 2009), which is an attempt tohomogeneously analyze
Chandra observations of about 230galaxy clusters. For each cluster, the database provides, asa function of distance from the cluster center, electron den-sity n e , pressure p , temperature T X , entropy (defined as K ≡ T X n − / e ), cooling time t c , and enclosed gravitational mass,from which we infer the free-fall time t ff = (cid:112) r / GM ( < r ).In addition, the database also provides the location of the X-ray emission peak (which we take as the cluster center), andthe global mean X-ray temperature T . By assuming azimuthalsymmetry, we thus know the local ICM properties of everymember galaxy given its distance from the cluster center.In the redshift range z = 0 . − .
32, there are 54 ACCEPTclusters within the final SDSS imaging footprint (i.e., DR8)with ICM measurements that allow for a robust determina- tion of t ff6 , which will be referred to as the ACCEPT-SDSSsubsample. We can thus use the SDSS (imaging and spectro-scopic) data to identify cluster members and study the corre-lations between the radio activity and the local ICM proper-ties. We have visually inspected these clusters to identify theBCGs. As for the member galaxies, depending on the red-shifts of the clusters, the treatments are somewhat different.For clusters at z ≥ .
1, we make use of the membership proba-bility P mem as given by the redMaPPer algorithm (Rykoff et al.2014, note that all ACCEPT-SDSS clusters have a counterpartin the redMaPPer cluster sample). We regard a galaxy to be apotential cluster member if its P mem ≥ .
8. As the redMaPPercluster sample is incomplete below z = 0 .
1, for the ACCEPT-SDSS clusters at z < .
1, we make use of the spectroscopicredshifts and galaxy color to identify members. Specifically,we regard as members those galaxies within 3000 km/s fromthe cluster restframe, or those with a restframe g − r color con-sistent with the red sequence and are within a projected dis-tance of 1.2 Mpc from the cluster center. We only considergalaxies more luminous than M . r = − .
27, which is aboutthe characteristic magnitude of the galaxy luminosity function(Blanton et al. 2003). Absolute magnitudes, restframe col-ors, and stellar masses are again calculated using kcorrect .Our results below do not depend sensitively on our choiceof parameters for selecting cluster members. Finally, we re-move a few extreme outliers with nonsensical measurementsin physical properties such as stellar mass, pressure, etc.We have run our RG finding algorithm on the ACCEPT-SDSS clusters, with a flux limit of 1 mJy that is suitable forFIRST, and have visually inspected all potential optical-radiomatches to finalize our cluster RG sample (see Table A2).As radio AGN are predominantly hosted by red galaxies (forexample, about 86% of the RGs with log P . ≤ . Chandra observations, out ofwhich 24 have radio power log P . ≥ .
5, a limit chosen toensure our sample is volume limited. Of the 54 BCGs, 16are RGs. This fraction is consistent with that found by Lin &Mohr (2007).Among the available physical properties associated witheach galaxy, we consider a total of six parameters here: clustermass (using the global mean X-ray temperature as a proxy),stellar mass, ICM pressure, entropy, cooling time t c , and theratio of cooling time over free-fall time, t c / t ff . One physicalattribute unfortunately omitted here is the local galaxy den-sity, as we do not possess sufficient number of spectroscopicredshifts for the ACCEPT clusters. Given the small size ofthe ACCEPT-SDSS RG sample, and that many of the ICM-related parameters are highly correlated, we are not able toperform the best subset selection to pick up the most impor-tant predictors, as has been done in Section 2.2, because in thepresent case any potential statistical fluctuations could changethe rank of BIC values among different models. Instead, ourstrategy is to first reduce the dimensionality of the parame-ter space by the application of the the principle componentanalysis (PCA) among the six parameters, and investigate theeffects of the first few dominant principle components (PCs)on the nuclear radio activity. We further strengthen the find- In practice, we keep only clusters with monotonically varying pressureand t ff profiles. RIGGERING N UCLEAR R ADIO A CTIVITY
BCGs
In finding out the PCs , it is necessary to scale each of ourphysical parameters P to Q ≡ P − ¯ P σ P , where ¯ P and σ P are themean and the standard deviation of the parameter. Such anormalization ensures that the derived PCs are not dominatedby a single variable that has the largest standard deviation overthe parameter space.For BCGs, the PCA indicates that only three PCs areneeded to explain up to 90% of variance across the six di-mensional parameter space. As shown in Table 3, the firstPC (hereafter PC1) accounts for ∼
48% of the variance, withits effect mostly on the variation of entropy, pressure and t c .More specifically, we have PC − . (cid:18) ˜ M ∗ − . . (cid:19) + . (cid:18) T − . . (cid:19) + . (cid:18) ˜ K − . . (cid:19) − . (cid:18) ˜ p + . . (cid:19) + . (cid:18) (cid:101) t c − . . (cid:19) + . (cid:18) t c / t ff − . . (cid:19) , (3)where a tilde denotes a quantity in logarithm. A higher en-tropy, lower pressure, and larger t c lead to a larger PC1, asrevealed in the top row of Fig. 6. The second PC (PC2)largely depends on the global temperature T and stellar mass,as shown in the middle row of Fig. 6; the third PC (PC3) ismainly driven by t c / t ff (see the bottom row of Fig. 6).We can further examine the effects of the PCs on the radioactivity of BCGs. Fig. 7 shows the probability density func-tion (pdf) of each PC for radio-loud (red solid histograms) andradio-quiescent (blue dash histograms) BCGs. The p -valuesobtained from a Kolmogorov-Smirnov (KS) test comparingthe two distributions are also shown in each panel. It is clearthat PC1 has the strongest effect, implying that an environ-ment with low entropy, high pressure, and short cooling timeis favorable for triggering the nuclear radio activities. For thedistribution of PC2 and PC3, the large p -value reveals thatthere is no significant difference between RGs and normalgalaxies. But here we note that, the relatively weak effect ofPC2 on the BCG radio activity may be due to the limited massrange our clusters span. As we have seen from Section 2, bothstellar mass and halo mass (basically the PC2 here) are relatedto the RAF of BCGs.We have also performed the LR analysis on the ACCEPT-SDSS BCGs. Given the small sample size, here we only con-sider the one-predictor LR model [i.e. the case when X inEq. (1) is a scalar] for each of the regressors, and tabulatethe resulting z - and p -values in Table 4. The results largelyagree with that given by the PCA, that is, entropy, pressure,and cooling time all show stronger effects on the RG activitythan other covariates. There is some hint of cooling time andentropy being more important than the pressure.Admittedly a sample size of only 54 limits the statisticalsignificance of our inference on the predicting power of phys-ical properties on the radio activity. For BCGs, we could in-crease the sample size by loosening the requirement that theclusters should lie within the SDSS footprint; rather, we onlyneed to be able to identify the BCGs robustly, and to be ableto measure the radio properties of the BCGs. To this end, we expand our cluster sample to include all ACCEPT clusterslying at declination δ > −
40 deg and at z < .
2, and use Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) andTwo-Micron All-Sky Survey (2MASS; Skrutskie et al. 2006)data to identify the BCGs, for clusters lying outside of theSDSS footprint. The WISE channel 1 luminosity is used as aproxy of stellar mass (e.g., Lin et al. 2013). Data from NVSSis used to select radio-loud BCGs and measure their fluxes.For the 105 central galaxies in this ACCEPT-WISE sample,both the PCA and LR results are largely similar to that ofACCEPT-SDSS BCGs. Our conclusions are therefore robustagainst the limited sample size.
Satellites
The PCA results for satellites in the ACCEPT-SDSS sam-ple are summarized in Table 5. As is the case for the BCGs,the first three PCs capture ∼
90% of variance over the sixdimensional parameter space. However, there are slight dif-ferences in the physical information as revealed by the PCsof satellites. As shown in Fig. 8, besides entropy, pressure,and cooling time, the PC1 of satellites has larger contributionfrom t cool / t ff compared with that of BCGs. The PC2 of satel-lites shows mainly the effect of T , and PC3 is totally domi-nated by stellar mass. It is seen that the effect of stellar mass isquite decoupled from other (extrinsic) properties considered.Fig. 9 show the pdf of PCs for radio-loud (red solid his-tograms) and radio-quiescent (blue dash histograms) satel-lites. It is apparent that the radio-loud and radio-quiescentsatellites show different distributions in PC1 and PC3 (withvery low p values), with active satellites showing preferenceto lower PC1 (low entropy, cooling time, and t cool / t ff , and highpressure) and higher PC3 (higher stellar mass) values. This isconsistent with the findings in Section 2.In Table 6 we summarize the significance for each of theparameters via the LR analysis for the satellites. We see thatstellar mass is the most powerful predictor for RG activity,although cooling time, entropy, and pressure all play impor-tant roles. It should be kept in mind that the number of RGsused in our satellite analysis is rather small ( (cid:46)
5% of the satel-lites are radio-loud); a larger cluster sample will be needed tofirmly establish these conclusions. SUMMARY AND DISCUSSION
We have outlined an analysis framework that combines agroup and cluster sample that spans a wide range in halo mass,and a cluster sample that offers detailed ICM measurement.Together with standard statistical analysis tools, the joint sam-ples allow us to investigate the likely sources of nuclear ac-tivity in massive galaxies, making it possible to sort out therelative contributions from halo mass, stellar mass, and otherphysical properties such as local galaxy density, ICM entropy,cooling time.In the first part of our analysis (Section 2), we have used alarge sample of galactic systems to show that, for triggeringthe radio activity, stellar mass is an important factor, irrespec-tive of the type of galaxies (central v.s. satellite). The cen-tral galaxy RAF additionally strongly depends on the mass oftheir host dark matter halo (such dependence is also presentfor the satellites but is weaker). As we do not find convinc-ing evidence linking the elevated RAF in massive halos to thehigher galaxy density therein (which in turn should correlatewith the interaction rates) for central galaxies, the most likelyculprit is the presence of hot gas in massive halos. Thus in thesecond part of our analysis (Section 3), using a cluster sample L IN , H UANG , & C
HEN
Table 3
PCA results for 54 BCGs in the ACCEPT-SDSS samplevariance log M star T log K log p log t c t c / t ff accountedPC1 48% − .
18 0.10 0.56 − .
48 0.58 0.27PC2 28% 0.60 0.67 0.22 0.35 0.07 0.16PC3 14% 0.05 − . − .
09 0.18 − .
12 0.91 N . log(Mstar) P C N . ¯T N . entropy N . pressure N . t c N . t c / t ↵ N . log(Mstar) P C N . ¯T N . entropy N . pressure N . t c N . t c / t ↵ N . log(Mstar) P C N . ¯T N . entropy N . pressure N . t c N . t c / t ↵ Figure 6.
Relation between the parameters and the three dominant principal components for BCGs. The letter “N” in the abscissa stands for “normalized”. − − − − . . . . . . . . . . pd f p : 0 . BCG − − − − . . . . . . p : 0 . BCG
RLRQ − . − . − . − . . . . . . . . . . . . . . . . p : 0 . BCG
Figure 7.
The probability density distribution of PC1, PC2, and PC3 for radio-loud (red) and radio-quiescent (blue) BCGs. The p -values obtained from a KStest comparing the two distributions are also shown in each panel. For PC1, the low p value indicates that the two distributions are highly inconsistent with eachother. that provides spatially resolved measurements of ICM prop-erties, we seek for the best predictor of radio activity amonginternal and environmental factors that could play a role in theevolution of a galaxy.According to our results, entropy, cooling time, and pres-sure play important roles in the triggering of radio activity ingalaxies residing in massive halos. As two of these propertiesare intimately linked to gas cooling out of the hot ICM, a pic-ture that emerges from our study is the following: whether or not a galaxy is a central, the more massive it is, the more likelyit will be active in the radio. The likely source of fuel for theSMBH is from stellar mass loss from evolved stars (e.g., AGBstars). If the galaxy happens to be central in a massive halowhere appreciable amount of ICM is present, then an extrafuel supply, likely gas cooling out of the hot ICM, could trig-ger more radio activity. Confining pressure of the ICM furtherprovides a “working surface” for the jets.Although this picture is certainly not new (e.g., Ciotti & RIGGERING N UCLEAR R ADIO A CTIVITY N . log(Mstar) P C N . ¯T N . entropy N . pressure N . t c N . t c / t ↵ N . log(Mstar) P C N . ¯T N . entropy N . pressure N . t c N . t c / t ↵ N . log(Mstar) P C N . ¯T N . entropy N . pressure N . t c N . t c / t ↵ Figure 8.
Same as Figure 6, but for satellites. − − − − . . . . . . pd f p : 0 . SAT − − − . . . . . . p : 0 . SAT
RLRQ − − . . . . . . . p : 0 . SAT
Figure 9.
The probability density distribution of PC1, PC2, and PC3 for radio-loud (red) and radio-quiescent (blue) satellites. The p -values obtained from a KStest comparing the two distributions are also shown in each panel. For PC3, the low p value indicates that the two distributions are highly inconsistent with eachother. Table 4
LR statistics for BCGs in the ACCEPT-SDSS sampleParameter z -value p -valuelog M star T − .
54 0.592log K − .
16 0.002log p t c − .
18 0.001 t c / t ff − .
08 0.038
Ostriker 2001; Best et al. 2005a; Ho 2008; Heckman &Best 2014), our analysis framework provides a (nearly) self-contained way to demonstrate it. Furthermore, we do not findthe ratio t c / t ff to be a critical parameter for the radio activity(particularly for BCGs), which seems to be at odds to the pre-dictions from the precipitation model advocated by Voit et al.(2015).For our analysis, there are several aspects that can be im- proved or extended. For example, for the ACCEPT clustersample, we do not have a good handle on the local galaxydensity. We could have used clustercentric distance as a verycrude proxy for the local density, which is obviously toosimplistic. Either spectroscopic data from surveys such asGAMA (Galaxy And Mass Assembly; Driver et al. 2011), orgood photometric redshifts with adequate background correc-tion methods, or both, are needed to estimate the local den-sity in a statistical fashion. With a larger cluster sample, suchas that from ACCEPT2, one could also consider high andlow excitation radio galaxies separately, and gain more in-sight into the potentially different triggering mechanisms forthese two types of AGN (e.g., Hardcastle et al. 2007). In ad-dition, applying our approach to dense spectroscopic surveys(e.g., GAMA), we could also study the triggering of AGNs se-lected by (optical) emission lines (e.g., Kauffmann et al. 2003;Sabater et al. 2015). Finally, by combining data from sur-veys such as GAMA (or other dense-sampling spectroscopic0 L IN , H UANG , & C
HEN
Table 5
PCA results for 509 satellites in the ACCEPT-SDSS samplevariance log M star T log K log p log t c t c / t ff accountedPC1 50% − . − .
02 0.52 − .
47 0.57 0.43PC2 23% 0.03 0.83 0.33 0.43 0.03 0.09PC3 17% 1.00 − . − . − .
03 0.01 0.07
Table 6
LR statistics for satellites in the ACCEPT-SDSS sampleParameter z -value p -valuelog M star . < . T .
50 0 . K − .
91 0 . p .
58 0 . t c − .
16 0 . t c / t ff − .
66 0 . surveys such as PRIMUS, Dark Energy Spectroscopic Instru-ment and Prime Focus Spectrograph), ACCEPT2, and Pan-STARRS (Chambers et al. 2016) (or deeper imaging surveyssuch as Kilo Degree Survey, Dark Energy Survey, or HyperSuprime-Cam), it may be possible to extend our analysis tointermediate redshifts ( z ∼ . − z ∼ z , implying an elevatedRAF among satellites. It would thus be exciting to examinethe triggering of radio AGN at different cosmic epochs (e.g.,Williams & Röttgering 2015; Lin et al. 2017).One important omission in the current study is the spin ofthe SMBH. Given the difficulty of estimating the magnitudeof spin, it does not seem feasible to incorporate it in statisticalanalyses like ours, however. Its relevance compared to stellarmass, or extrinsic properties such as entropy and cooling time,has to be assessed with more focused studies (e.g., Schulze etal. 2017), and is beyond the scope of the current paper. ACKNOWLEDGMENTS
APPENDIXRADIO GALAXY SAMPLES
Here we present the radio galaxy samples used in this work.Table A1 is the parent sample for the RGs used in Section 2,which is obtained by combining the L10 RG catalog and thepart of the Best & Heckman (2012) catalog in the area uniqueto SDSS DR7 (with respect to DR6). The sample is completeto M . r ≤ − .
27, with radio flux f ≥ z ≤ . − . r . band, stellar mass, indication ofwhether the source is powered by an AGN, a selection flag,and the origin of the source (L10 or Best & Heckman 2012,B12). Choosing sources with the selection flag with value of1 allows one to obtain the z ≤ .
15 RG sample used in Sec-tion 2 (further restricting the redshift to z ≤ .
092 gives the z ≤ .
092 sub-sample).We list in Table A2 the galaxies used in the analysis inSection 3, providing the coordinates, cluster redshift, clus-tercentric distance, stellar mass, a flag indicating whether thegalaxy is the BCG, radio luminosity (a value of − P th = 23 . Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559Best, P. N., & Heckman, T. M. 2012, MNRAS, 421, 1569Best, P. N., Kauffmann, G., Heckman, T. M., Brinchmann, J., Charlot, S.,Ivezi´c, Ž., & White, S. D. M. 2005a, MNRAS, 362, 25Best, P. N., Kauffmann, G., Heckman, T. M., & Ivezi´c, Ž. 2005b, MNRAS,362, 9Best, P. N., von der Linden, A., Kauffmann, G., Heckman, T. M., & Kaiser,C. R. 2007, MNRAS, 379, 894Blanton, M. R., & Roweis, S. 2007, AJ, 133, 734Blanton, M. R., et al. 2003, ApJ, 592, 819—. 2005, AJ, 129, 2562Bower, R. G., Benson, A. J., Malbon, R., Helly, J. C., Frenk, C. S., Baugh,C. M., Cole, S., & Lacey, C. G. 2006, MNRAS, 370, 645Cavagnolo, K. W., Donahue, M., Voit, G. M., & Sun, M. 2008, ApJ, 683,L107
RIGGERING N UCLEAR R ADIO A CTIVITY Table A1
Radio galaxy sample used in Section 2R.A. Decl. z f . log P . M . r − h log M ∗ AGN? Selection Ref(J2000) (J2000) (mJy) (W Hz − ) ( h − M (cid:12) )2.814975 − . − .
844 11.36 1 0 L107.887342 − . − .
585 11.25 1 0 L106.942545 − . − .
711 11.31 1 0 L108.979727 0 . − .
746 11.35 1 0 L105.067143 0 . − .
722 11.34 1 0 L10260.534205 30 . − .
409 10.64 0 0 B12260.374455 30 . − .
239 10.74 1 1 B12
Table A2
Radio galaxy sample used in Section 3R.A. Decl. z distance log M ∗ BCG? log P . T log K log p log t c t c / t ff Cluster(J2000) (J2000) (kpc) ( h − M (cid:12) ) (W Hz − ) (keV) (keV cm ) (dyne cm − ) (Gyr)230.833830 8 . . − .
84 1 . . . − .
97 1 . . . − . − . . . − . − . . . − .
41 0 ..