Quantifying the Effect of Black Hole Feedback from the Central Galaxy on the Satellite Populations of Groups and Clusters

In the local universe, every massive dark matter halo, and therefore every massive galaxy, hosts a supermassive black hole in the center (Kormendy & Ho 2013). Supermassive black holes grow in mass mainly through gas accretion (Croton et al. 2006), and the total energy released during this process is on the order of a few percent of the final black hole mass (M_•). For black holes more massive than ∼10⁹ solar masses (M_⊙), the energy released is similar to the binding energy of the host halo itself and can therefore potentially alter the evolution of galaxies residing within. In fact, in state-of-the-art cosmological numerical simulations, the energetic feedback radiated by growing black holes is responsible for reproducing the observed properties of massive galaxies (Schaye et al. 2015; Weinberger et al. 2018). Moreover, the effect of black hole feedback is expected to become increasingly important with increasing halo mass.

Galaxy groups and clusters are massive, gravitationally bound systems, and feedback from the supermassive black hole at the center of the dark matter halo is expected to play a dominant role in regulating their internal thermodynamics. In particular, numerical simulations of galaxy clusters show that the energy injected by the central supermassive black hole into the intragroup/intracluster medium (IGM/ICM) is able to heat the existing gas, preventing the formation of cooling flows (Churazov et al. 2002; Martizzi et al. 2019). Moreover, this feedback is thought to be strong enough to actually regulate the star formation of satellites living within these massive (M ≳ 10¹² M_⊙) dark matter halos (Dashyan et al. 2019).

Observationally, the clearest indication of the effect of black hole feedback on cluster scales is the existence of large X-ray cavities likely sustained by the energetic input from the central black hole (McNamara & Nulsen 2007; Fabian 2012). However, an empirical assessment of whether black hole feedback actually regulates star formation has proven to be a challenging task. Arguably, the main observational difficulty arises from the fact that black hole feedback is highly nonlinear, with time variations much shorter than those associated with the quenching processes of galaxies (Hickox et al. 2014). The observed connection between the properties of central and satellite galaxies, known as galaxy conformity (Weinmann et al. 2006), has also been proposed to be a consequence of the aforementioned black-hole-regulated star formation of the satellite population (e.g., Kauffmann et al. 2013), although it may also arise from the hierarchical nature of a Λ-Cold Dark Matter (Λ-CDM) universe (Bray et al. 2016). Direct observational evidence of black-hole-suppressed star formation therefore stands as a fundamental open question, motivating the development of this study.

In this Letter we explore how the properties of satellite galaxies in groups and clusters depend on the mass of the black hole of the central galaxy. We find that dark matter halos hosting more massive black holes in their centers exhibit an enhanced fraction of quiescent satellites and are able to sustain a hotter IGM/ICM. The outline of this work is as follows. Data are presented in Section 2. We describe our main metric, the M_•–M_halo relation, in Section 3, and our main results are presented in Section 4. Finally, these results are discussed in Section 5.

We have based our analysis on a sample of 4308 galaxy groups and clusters (Tempel et al. 2014) selected from the Sloan Digital Sky Survey (SDSS; Ahn et al. 2014). An extensive discussion about the sample properties is provided in Tempel et al. (2014; see also Section 3.1). We briefly note that group and cluster halo masses and virial radii are measured by assuming that the system is in virial equilibrium. The quoted halo masses and sizes are then estimated using the velocity dispersion and the radial extent of the detected group and cluster members, assuming a Navarro–Frenk–White profile (Navarro et al. 1997). The location of the most luminous galaxy (hereafter central galaxy) is also provided for each object in the catalog. In total, the original catalog contains 82,458 (flux-limited) groups and clusters, at a median redshift of 0.0864, expanding a range in halo mass from ∼10¹² to ∼10¹⁴ M_⊙.

We complemented our sample with total star formation rate (SFR; Brinchmann et al. 2004) and stellar mass (Kauffmann et al. 2003; Salim et al. 2007) measurements also based on the SDSS for each group and cluster member. We did not include in the analysis individual galaxies flagged out by the Max Planck for Astrophysics (MPA) and Johns Hopkins University (JHU) group. Further details on this data set can be found on the MPA–JHU project website.⁵

In order to explore the connection between central black hole feedback and star formation in satellite galaxies, we first constructed a relation between the group or cluster halo mass (M_halo) and the mass of the black hole (M_•) hosted by the central galaxy as shown in Figure 1. Black hole masses were estimated using the M_•–σ_e relation presented in van den Bosch (2016), where stellar velocity dispersions correspond to a fixed aperture of 1 R_e.

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For each central galaxy, the velocity dispersion and the redshift were measured from its SDSS optical spectrum using the pPXF algorithm (Cappellari & Emsellem 2004) fed with the MILES stellar population synthesis models (Vazdekis et al. 2010). We then used the measured redshift to estimate the distance to the central galaxy, from which we derived the fraction of its effective radius covered by the SDSS fiber (R_SDSS = 15). Finally, the stellar velocity dispersion at 1 R_e was calculated by applying an aperture correction to the value directly measured from the spectra (Cappellari et al. 2006).

Having halo and central black hole mass estimations, we calculated the average M_•–M_halo  relation using a two-step running median scheme. First, we measured the median central black hole mass over 150 equally log-spaced halo mass bins (from log M_halo/M_⊙ = 12 to log M_halo/M_⊙ = 14). Then, we fit these 150 median halo and central black hole masses with a low-order polynomial. This allowed us to have a well-behaved M_•(M_halo) function, which is shown in Figure 1 as a black dashed line. The results presented in this Letter are based on a fourth-order polynomial for the M_•(M_halo) function, but we also repeated the analysis with higher and lower polynomial orders, finding similar and consistent trends.

The M_•–M_halo relation shown in Figure 1 allowed us to define a metric that is effectively sensitive to the amount of energy radiated by the central black hole (Martín-Navarro et al. 2016; Terrazas et al. 2016). We labeled as overmassive black hole halos those systems lying above the mean M_•–M_halo relation. Complementarily, undermassive black hole halos are those that, at a given mass, have a central black hole less massive than the average. The reasoning behind this separation and its relation with the effect of black hole feedback is simple. Halo mass is thought to be the main parameter describing the properties of gravitationally bound structures in a Λ-CDM universe, from individual galaxies to groups and clusters (Blumenthal et al. 1984). Hence the (vertical) scatter in Figure 1 is expected to probe systems with very similar properties but with a variety of central black hole masses. Since the net energy released by supermassive black holes is expected to scale with their total mass from theoretical arguments, feedback-related processes such as galaxy quenching are likely enhanced in overmassive black hole halos compared to undermassive black hole ones. Thus, the scatter in the M_•–M_halo relation probes the effect of black hole feedback on group and cluster scales, modulo the assumption that overmassive and undermassive black hole halos only differ with respect to their central black hole masses.

3.1. Homogenizing Overmassive and Undermassive Black Hole Halos

3.2. Stellar Velocity Dispersion as a Proxy for M_•

Using the M_halo–M_• relation as a local metric, we then analyzed the SFRs of satellite galaxies in overmassive and undermassive black hole halos. The left panel in Figure 2 shows that non-central members in both overmassive and undermassive black hole halos follow similar distributions in the SFR–stellar mass parameter space, with notably coinciding star formation main sequences (SFMSs) highlighted by the dashed line.⁶ However, a striking difference is revealed in the right panel when analyzing the distribution of distances from the main sequence (ΔSFMS): the population of quiescent satellites (ΔSFMS < −1.2)⁷ is enhanced in groups and clusters hosting more massive black holes in their centers. Because the number of satellite galaxies in overmassive and undermassive black hole halos is almost identical, by normalization, the number of star-forming galaxies is enhanced in the latter.

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In order to investigate the dependence of this effect on halo mass, we binned galaxies in Figure 2 according to the masses of the halos to which they belong. We then calculated the fraction of quiescent satellite galaxies and their average SFR. Figure 3 shows these two quantities for overmassive and undermassive black hole halos as a function of halo mass. The fraction of quiescent galaxies increases and the average SFR decreases with increasing halo mass, as expected (Wetzel et al. 2013). On top of these trends, the differences between overmassive and undermassive black hole halos are clear for all masses. At a given halo mass, when a cluster or a group hosts a more massive black hole in the center, the fraction of quiescent galaxies is enhanced and the average SFR is lower.

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A final piece of evidence comes from the analysis of the X-ray properties of 196 optically confirmed groups and clusters (Takey et al. 2013). These systems were identified as extended X-ray sources with an optical galaxy overdensity counterpart detected in the SDSS. Unfortunately, there was little overlap between this sample and that shown in Figure 1, so we did not have a dynamical measurement of the halo mass. Thus, for the analysis of the 196 groups and clusters with X-ray measurements we used M₅₀₀, an estimate of the average halo mass within an aperture of R₅₀₀ (where the mean mass density is 500 times the critical density of the universe at the halo redshift), rather than M_halo.⁸ This M₅₀₀ halo mass was calculated iteratively based on the X-ray bolometric flux assuming a β model (see details in Takey et al. 2011, 2013).

For each of the 196 groups and clusters, the temperature of the IGM/ICM was derived from X-ray spectral fitting (Takey et al. 2011), and the mass of the central black hole was estimated in the same manner as before. As in Figure 1, we divided the sample into overmassive and undermassive black hole halos and then calculated the average X-ray temperature in different mass bins. Figure 4 shows the T_gas–M₅₀₀ relation for overmassive and undermassive black hole halos. Two features clearly emerge from this figure. First, as expected by virial arguments (Birnboim & Dekel 2003), X-ray temperatures increase with increasing halo mass (Bogdán et al. 2018). Second, the gas has been heated above the expected virial temperature, and this excess of energy correlates with the mass of the black hole in the center of the halo. At fixed mass, halos with more massive central black holes sustain hotter IGM/ICMs.

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Explaining the trends shown in Figures 3 and 4 in the absence of feedback from the black hole in the center of the halos would require a highly fine-tuned mechanism. By construction, our overmassive and undermassive black hole halos are indistinguishable in mass, size, total stellar mass, and stellar mass distribution. The effect of a possible assembly bias (Wechsler & Tinker 2018) is likely negligible as there is little difference in the normalization of the SFMS between overmassive and undermassive black hole halos (ΔSFMS₀ ∼ 0.13 ± 0.22). Satellites in groups and clusters with more massive black holes form on average fewer stars, and there is an enhanced fraction of quiescent galaxies compared to undermassive black hole halos, suggesting that longer timescale quenching processes such as strangulation may play a greater role in overmassive black hole halos. A hotter ICM would be more conducive to stripping the gaseous halos of infalling galaxies (Burchett et al. 2018; Zinger et al. 2018), depriving them of their immediate reservoirs for star formation.

Moreover, given the departure from a simple scaling of the virial temperature (dashed line in Figure 4), it is not trivial to explain the higher X-ray temperature of the IGM/ICM in those halos hosting more massive black holes in their centers without invoking feedback effects. Our analysis is certainly a simplified assessment of the effect of black hole feedback. We have assumed that the central galaxy is the only galaxy contributing to the heating of the IGM/ICM. Additionally, group and cluster galaxies likely formed under particular conditions in dense filaments even before falling into the group/cluster environment, and it is therefore possible that some differences between overmassive and undermassive black hole halos have been inherited. We note, however, that SFR measurements are sensitive to timescales much shorter (Calzetti 2013) than the dynamical timescales within halos, and therefore they should be largely driven by recent IGM/ICM conditions.

Black hole heating acting on group and cluster scales emerges as a simple explanation to the observed trends, consistent with our cosmological understanding of galaxy formation (Dashyan et al. 2019). If the temperatures of halos, and their internal thermodynamics in general, are set by a combination of virial plus black hole heating, quenching processes such as strangulation or ram pressure stripping would become more efficient in those groups and clusters with more massive central black holes, resulting in a higher number of quiescent galaxies as shown in Figure 3. Moreover, this group/cluster-wide feedback process would emerge from accreting black holes in the center of individual massive galaxies, where similar trends between SFR, X-ray temperatures, and black hole masses have been reported (Martín-Navarro et al. 2018, 2019). Interestingly, a unified black hole heating scenario, from galactic to cluster scales, would naturally predict a certain degree of (one halo) galactic conformity (Weinmann et al. 2006; Kauffmann et al. 2013), as quenched galaxies are also found to host higher-mass black holes (Terrazas et al. 2016). Our results observationally support a scenario where the baryonic cycle in galaxies is regulated by the joint effects of black holes and dark matter halos across cosmic time.

We would like to thank the anonymous referee for useful and constructive comments on our manuscript. I.M.N. acknowledges support from the AYA2016-77237-C3-1-P grant from the Spanish Ministry of Economy and Competitiveness (MINECO) and from the Marie Skłodowska-Curie Individual SPanD Fellowship 702607. M.M. acknowledges support from the Spanish Juan de la Cierva program (IJCI-2015-23944) and the Beatriu de Pinos fellowship (2017-BP-00114).