Environmental Dependence of Self-Regulating Black-hole Feedback in Massive Galaxies

In the universe's most massive galaxies, kinetic feedback from a central supermassive black hole appears to limit star formation. Abundant circumstantial evidence suggests that accumulation of cold gas near the central black hole strongly boosts the feedback output, keeping the ambient medium in a state marginally unstable to condensation and formation of cold gas clouds. However, the ability of that mechanism to self-regulate may depend on numerous environmental factors, including the depth of the potential well and the pressure of the surrounding circumgalactic medium (CGM). Here we present a suite of numerical simulations that explores the dependence of cold-fuelled bipolar kinetic feedback on those environmental factors. Halo mass in this simulation suite ranges from $2 \times 10^{12} \, M_\odot$ to $8 \times 10^{14} \, M_\odot$. We include the spatially extended mass and energy input from the massive galaxy's old stellar population, which is capable of sweeping gas out of the galaxy and away from the central black hole if the confining CGM pressure is sufficiently low. Our simulations show that this feedback mechanism is tightly self-regulating in a massive galaxy with a deep central potential and low CGM pressure, permitting only small amounts of multiphase gas to accumulate and allowing almost no star formation. In a massive galaxy of similar mass but a shallower central potential and greater CGM pressure the same feedback mechanism is more episodic, producing extended multiphase gas and occasionally allowing small rates of star formation ($\sim 0.1 \, M_\odot \, {\rm yr}^{-1}$). At the low-mass end of the explored range the mechanism becomes implausibly explosive, perhaps because the ambient gas initially has no angular momentum, which would have reduced the amount of condensed gas capable of fueling feedback.


INTRODUCTION
X-ray observations during the past two decades have revolutionized the astronomical community's understanding of how AGNs regulate cooling, condensation, and star formation at the centers of galaxy clusters. The high X-ray surface brightness of a cool-core cluster allows detection of cavities created in the hot gas by AGN outflows, along with measurements of their size, which show that AGN kinetic power is comparable to the radiative cooling rate of the cluster core (Churazov et al. 2001;McNamara & Nulsen 2007). Among galaxy clusters in the nearby universe, high-power radio AGNs, multiphase gas, and star formation are found only in those with low-entropy gas at their centers (Cavagnolo et al. 2009a(Cavagnolo et al. , 2008Rafferty et al. 2006;Sun 2009;Hoffer et al. 2012;Rawle et al. 2012). These relationships indicate that AGN heating self-regulates through a feedback loop in which accretion of cold clouds condensing out of the hot medium strongly boosts AGN feedback power, thereby maintaining the core in a state marginally unstable to precipitation of cold clouds. The minimum ratio of gas cooling time (t cool ) to free-fall time (t ff ) in such a self-regulating system tends to be in the range 10 < min(t cool /t ff ) < 20 Sharma et al. 2012;Gaspari et al. 2012b;Prasad et al. 2015Prasad et al. , 2018Li et al. 2015;Voit et al. 2015bVoit et al. ,a, 2017. Many cool-core clusters observed with Chandra do indeed fall into this range (Voit et al. 2015b;Hogan et al. 2017), strongly supporting the hypothesis that AGN feedback in cluster cores is throttled by a transition to precipitation.
These findings raise an important question: Does precipitation-regulated AGN feedback also limit cooling and condensation of circumgalactic gas around smaller galaxies? The hot atmospheres of those galaxies tend to be harder to observe with X-ray telescopes, but preliminary investigations indicate that the AGN feedback loop observed in the universes largest galaxies may also limit the density of circumgalactic gas all the way down through Milky-Way scales (Voit et al. 2018;Voit 2019). X-ray observations of massive ellipticals (Werner et al. 2012(Werner et al. , 2014 show that the lower bound on t cool in the ambient medium tracks the min(t cool /t ff ) ∼ 10 locus across two orders of magnitude in radius, from ∼20 kpc down to ∼200 pc (Voit et al. 2015b(Voit et al. ,c, 2020. Also, the general features of precipitation-regulated star formation are consistent with several of the major scaling relations observed among galaxies (Voit et al. 2015a).
Several different channels can feed accretion of cold gas onto the central black hole. Numerical simulations show that cold gas can stream along cosmological dark matter filaments and accrete onto a halo's central galaxy if those cold streams are not disrupted by a surrounding hot gaseous halo (Kereš et al. 2005;Dekel et al. 2009). In a galaxy cluster, radiative cooling of the halo's hot gas can produce a central cooling flow (Fabian 1994). And in massive elliptical galaxies, accumulations of gas ejected from the old stellar population can also produce a central cooling flow (Mathews & Loewenstein 1986;Voit & Donahue 2011). All of these supply channels are capable of fueling star formation at rates greatly exceeding those observed in massive elliptical galaxies, requiring a feedback mechanism to quench star formation.
Numerical simulations demonstrate that bipolar AGN jets fuelled by cold accretion can effectively quench star formation (Gaspari et al. 2012b(Gaspari et al. , 2013Li & Bryan 2014;Li et al. 2015;Prasad et al. 2015Prasad et al. , 2018Yang & Reynolds 2016;Meece et al. 2017). However, both the amount of cold gas that accumulates and its spatial distribution appear to depend on galactic environment. In galaxy clusters, 10 9 -10 11 M of molecular gas can accumulate, extending to tens of kiloparsecs from the center. Less molecular gas accumulates at the centers of smaller halos, and its spatial distribution appears to depend on the galaxy's stellar velocity dispersion. In massive elliptical galaxies with central velocity dispersion σ v < 240 km s −1 , the cold gas typically extends beyond the central 2 kpc, but it tends to be more centrally concentrated in galaxies with σ v > 240 km s −1 , as long as they are not at the centers of galaxy clusters (Voit et al. 2015c(Voit et al. , 2020. This relationship between σ v and the distribution of cold gas is intriguing, particularly in light of optical observations showing that nquenching of star formation is more closely related to the stellar velocity dispersion of the central galaxy than to any other observable property (Wake et al. 2012;Bluck et al. 2016;Terrazas et al. 2016;Bluck et al. 2020).
Here, we present a suite of 3-D hydrodynamic simulations motivated by the observed relationships between AGN feedback and galactic environment. The simulations were designed to investigate how bipolar AGN outflows fuelled by cold accretion depend on halo mass, central velocity dispersion, and the pressure of the circumgalactic medium (CGM). Section 2 provides additional background on how the central stellar velocity dispersion is thought to influence the relationship between AGN feedback and CGM pressure. Section 3 describes the numerical setup for our simulations. Section 4 specifies the initial conditions for each numerical experiment. Section 5 presents the main results. Section 6 discusses the limitations of our simulations and their potential effects on the results. With those limitations in mind, §7 discusses our results, comparing them to theoretical models and prior simulations. Section 8 summarizes the paper's main findings.

THE BLACK-HOLE FEEDBACK VALVE
Spatially extended gas and energy input from the central galaxy's old stellar population is an essential feature of the simulation suite we are presenting, because of how it links CGM pressure to AGN feedback. In a massive elliptical galaxy, energy input from SNIa heating cannot by itself push ejected stellar gas out of the galaxy's halo. Instead, that gas accumulates until its ambient density becomes great enough for radiative cooling to exceed supernova heating (Mathews & Loewenstein 1986;Ciotti et al. 1991;Binney & Tabor 1995). That process can take a few billion years. But eventually, the resulting cooling flow should make AGN feedback the dominant heating mechanism. It is therefore rather surprising that X-ray observations of nearby elliptical galaxies with σ v > 240 km s −1 are often consistent with models of steady subsonic outflows driven by SNIa heating, at least within the central 1-10 kpc (Voit et al. 2015c(Voit et al. , 2020. In those models, AGN feedback and SNIa heating play complementary roles. Feedback from the AGN is necessary to lift circumgalactic gas out of the galaxy's potential well. However, lifting of the CGM lowers its pressure, causing conditions within the galaxy to change. As AGN feedback drives CGM pressure down, gas pressure and density within the galaxy also decline. AGN feedback therefore enables SNIa heating to become more competitive with radiative cooling within the galaxy. Once the galaxy's ambient gas density becomes low enough for SNIa heating to exceed radiative cooling, SNIa heating can limit the cooling flow that powers AGN feedback. Stellar mass and energy sources can therefore couple with AGN feedback to maintain a nearly steady state in which SNIa heating slightly exceeds radiative cooling of gas within the galaxy. Voit et al. (2020) refers to this tuning mechanism as a "black-hole feedback valve." It operates when the specific energy of gas ejected from the old stellar population ( * ) is not much greater than the square of the galaxy's stellar velocity dispersion (σ v ). In a steady outflow driven by SNIa heating, the gradients of gas pressure, density, and entropy depend on the ratio * /σ 2 v . As that ratio declines, the proportion of SNIa energy needed to lift gas out of the galaxy becomes greater and the gradients of gas properties become larger.
A simple calculation in Voit et al. (2020) demonstrates that the tuning mechanism for a galaxy with a stellar population age ∼ 10 Gyr works best if σ v > 240 km s −1 . At that limiting value of σ v , the gradient of specific entropy 1 approximately corresponds to K ∝ r 2/3 , making the pressure and density gradients approximately ∝ 1/r. For greater values of σ v , the density gradient is steeper, causing radiative cooling to exceed SNIa heating at small radii, even if SNIa heating exceeds radiative cooling at larger radii. The result is a cooling flow at small radii (< 1 kpc) surrounded by a slow SNIa-heated outflow extending to beyond ∼ 10 kpc. Consequently, the CGM pressure confining the slow outflow determines the cooling-flow rate at small radii. That coupling is what enables the mechanism to tune itself. It should inevitably shut down star formation by suppressing accumulation of extended multiphase gas in galaxies with a central velocity dispersion exceeding the critical limiting value, as long as the AGN produces enough power to lift the CGM out of the halo's potential well.
One of this paper's motivations was to see whether this black-hole feedback valve mechanism would naturally arise in a 3-D numerical simulation with the required properties. That is why σ v is an important environmental parameter and also why we pay particular attention to the relationship between SNIa heating and radiative cooling. Our attempt to replicate the mechanism was only partially successful. Section 6 discusses some future improvements to simulations that may help 1 This paper quantifies specific entropy in terms of the entropy index K ≡ kT n −2/3 e . to replicate the mechanism with greater realism.

NUMERICAL SETUP
We modified Enzo, an adaptive mesh refinement (AMR) code Brummel-Smith et al. 2019), to simulate AGN and stellar feedback in idealized galactic environments across a broad mass range. The masses of the simulated halos span the range 2 × 10 12 M ≤ M 200 ≤ 8 × 10 14 M , where M 200 is the mass contained within the radius r 200 encompassing a mean mass density 200 times the cosmological critical density. We solve the standard hydrodynamic equations in Cartesian coordinates, including radiative cooling, gravity, star formation, stellar feedback, and AGN feedback, along with mass and energy input from an old stellar population (see §3.4 for details). These simulations employ the piecewise parabolic method (PPM) with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver.

Grids
The simulation domain is a (4 Mpc) 3 box with a 64 3 root grid and up to 10 levels of refinement. The central (128 kpc) 3 region enforces static regions of grid refinement ranging from level 6 to level 9, with the refinement level increasing toward the center. In the central (2 kpc) 3 , the mesh is fixed to be at the highest level of refinement. This design ensures that the CGM is highly resolved at all times with a minimum cell size ∆l ≈ 61 pc and a maximum cell size ∆l < 1 kpc.

Environmental Parameters
The gravitational potentials in our simulations have three components, and they do not change with time. We use an NFW form (Navarro et al. 1997) for the darkmatter halo, with mass density ρ DM ∝ r −1 (1 + r/r s ) −2 , where r s is the NFW scale radius and c 200 = r 200 /r s is a halo concentration parameter. For the central galaxy, we use a Hernquist profile (Hernquist 1990), with a stellar mass density ρ * ∝ r −1 (1 + r/r H ) −3 , where r H is the Hernquist scale radius. The potential of the central supermassive black hole of mass M BH follows a Paczynski-Witta form (Paczyńsky & Wiita 1980). Table 1 provides the parameter values for each model. Two of those models are based on particular galaxies. The multiphase galaxy (MPG) model is intended to resemble NGC 5044, which has a central stellar velocity dispersion 2 σ v ≈ 225 km s −1 , and represents the population of massive elliptical galaxies with extended mul- tiphase gas. The single phase galaxy (SPG) model is intended to resemble NGC 4472, which has a central stellar velocity dispersion σ v ≈ 282 km s −1 , and represents the population of massive elliptical galaxies without much multiphase gas beyond the central kiloparsec.
The brightest cluster galaxy (BCG) model is meant to represent the central region of a typical massive galaxy cluster. The smaller elliptical galaxy (SEG) model is designed to test how the AGN feedback mechanism used in the larger halos operates when the halo mass and central stellar velocity dispersion are reduced.

Star Formation
A simulation cell forms a star particle if its gas satisfies several criteria based on the Cen & Ostriker (1992) prescription: • The baryon density must exceed a threshold density (∼ 1 cm −3 ).
• The gas mass of the cell (m b ) must exceed 10 3 M .
• The cooling time of the gas must be less than the dynamical time for that cell's gas, t dyn = 3π/(32Gρ gas ).
A star particle is then formed with mass m * = f * ,eff (∆t/t dyn )m b , where the star-formation efficiency parameter is set to f * ,eff = 0.1 in this simulation suite.

Stellar Mass and Energy Input
The central galaxy's stars heat the gas through two separate channels: 1. New stars forming during the course of the simulation produce supernovae (SNII) that impart both thermal energy and momentum.
2. Old stars with the density distribution of the Hernquist potential ( §3.2) add heat through SNIa explosions and thermalization of stellar kinetic energy.
Feedback from stars formed during the simulation follows the prescription from Bryan et al. (2014). After a star particle of mass m * forms, a fraction f m, * of its mass is added back to the cell, along with thermal energy E SN = f SN m * c 2 . Our simulations adopt the parameter values f SN = 1 × 10 −5 and f m, * = 0.25. The returned gas formally has a metallicity f Z, * = 0.02, which can be used as a passive tracer but is not included in our radiative cooling calculations. This process starts immediately after the formation of the star particle and decays exponentially, with a time constant of 1 Myr.
SNIa heating is modelled with steady, spherically symmetric injection of thermal energy into the simulation domain at a rate proportional to the stellar mass density. The total energy ejected from SNIa explosions assumes 10 51 erg of per SNIa at a specific rate of 3 × 10 −14 SNIa yr −1 M −1 , following Voit et al. 2015c. At this rate, an old stellar population of mass ∼ 10 11 M adds ∼ 10 41 erg s −1 of thermal energy. The old stellar population also injects kinetic energy as it sheds gas mass in the form of stellar winds and SNIa explosions. Our simulations assume that this kinetic energy immediately thermalizes. We assume a specific gas ejection rate α * = 10 −19 s −1 , such that the net ejected matter per unit time per unit volume is α * ρ * . To simplify the calculation of thermalized kinetic energy, we assume an isotropic 1-D stellar velocity dispersion of 300 km s −1 at all radii in all of our runs, following Wang et al. 2019. The difference between this uniform value of σ v and the actual one is inconsequential, because energy input from SNIa heating is several times ( 5) greater than the kinetic energy injection in all cases.

AGN Feedback
AGN feedback is introduced into the simulation using a feedback zone attached to the AGN particle , which is always located at the geometric center of the halo. We drive AGN feedback in the form of a bipolar outflow by putting source terms for mass, momentum and energy into the fluid equations as follows: where S ρ , S p and S e are the density, momentum and energy source terms, respectively. The specific energy e includes kinetic energy, and the corresponding equation of state is P = (γ − 1)ρ(e − v 2 /2).

Accretion and AGN Feedback Efficiency
The accretion rateṀ acc onto the central supermassive black hole is calculated by assuming that all the cold gas (T < 10 5 K) within r < 0.5 kpc accretes onto the central black hole on a 1 Myr time scale. This mass accretion rate fuels AGN feedback at an energy output rate given by:Ė where c is the speed of light and the feedback efficiency parameter AGN is taken to be 10 −4 for all our runs with AGN feedback. A cold gas mass equal toṀ acc ∆t is removed from the spherical accretion zone (r < 0.5 kpc) by subtraction of gas mass from each cell in that zone with a temperature below 10 5 K, and the amount of gas mass subtracted from the cell is proportional to its total gas mass.

Feedback Energy Deposition
The AGN output energy is partitioned into kinetic and thermal parts and introduced using the source terms described above. The source regions are cylinders of radius 0.5 kpc extending along the jet axis from r = 0.5 kpc to r = 1 kpc in each direction. Each jet therefore subtends 1 radian at r = 1 kpc.
In each cell of volume ∆V cell within the source region of volume V jet , the density source term is S ρ = ∆m cell /∆V cell , where ∆m cell = (∆V cell /V jet )Ṁ acc ∆t and ∆t is the time step. Within the source region, the corresponding energy source term in each cell is For all our runs the ratio of kinetic to total AGN output energy is fixed at f kin = 0.9. The momentum source term in each cell is andn is a unit vector pointing away from the origin along the jet injection axis.

ATMOSPHERIC INITIAL CONDITIONS
All of the simulations in this paper begin with hydrostatic, single-phase galactic atmospheres having profiles of density, pressure, and specific entropy consistent with observations of nearby counterparts. Figure 1 shows the initial atmospheric properties for each simulation, along with the properties of the gravitational potentials and central galaxies outlined in Table 1. Solid lines in the upper panels of Figure 1 show the total mass M (r) enclosed within radius r and the corresponding circular velocity, v c = GM (r)/r, while dashed lines show the same quantities for just the stellar mass component. Each initial entropy profile is modelled using the form K(r) = K 0 +K 100 (r/100 kpc) α (Cavagnolo et al. 2009a). Table 2 gives the starting values of K 0 , K 100 and α for each halo, which are based on observations by Cavagnolo et al. (2009b) for the BCG model, Werner et al. (2012Werner et al. ( , 2014 for the MPG and SPG models, and Lakhchaura et al. (2018); Babyk et al. (2018) for the SEG model.
The bottom left panel shows each galaxy's initial entropy profile, and the bottom left panel shows the initial ratio of SNIa heating to radiative cooling at each radius. Initial atmospheric pressure in the BCG and MPG is large enough that radiative cooling significantly exceeds SNIa heating everywhere. In the initial state of the SPG, SNIa heating nearly equals radiative cooling inside of ∼ 5 kpc but is less significant at larger radii. However, the lower-pressure atmosphere of the smaller elliptical galaxy (SEG) allows SNIa heating to exceed radiative cooling within the central ∼ 5 kpc. In all cases, the initial electron number density is set to a constant value (n e = 5 × 10 −6 cm −3 ) at an outer domain radius corresponding to 2r 200 in the three lower-mass halos and to r 200 in the most massive halo.
Throughout the simulation, atmospheric gas is allowed to cool to 10 3 K using tabulated Sutherland & Dopita (1993) cooling functions with one-third solar metallicity for the BCG simulation and solar metallicity for all other runs.

RESULTS
This section describes the key results from our simulations. We first examine how the atmospheres evolve without AGN feedback. In each case a cooling flow results, even if SNIa heating initially exceeds radiative cooling. Then we analyze how each atmosphere changes when AGN feedback is active. We find that the three more massive systems each settle into a selfregulated state within ∼ 1 Gyr. The fluctuations in AGN feedback are larger in the two massive halos with greater CGM pressure and lower central velocity dispersion (σ v ≈ 230 km s −1 ), causing larger changes in core  conditions and producing more multiphase gas over a larger region. In contrast, the massive halo with lower CGM pressure and greater central velocity dispersion (σ v ≈ 280 km s −1 ) quickly settles into a nearly steady self-regulating state in which SNIa heating exceeds radiative cooling within the central ∼ 10 kpc. However, the lowest-mass halo (M 200 = 2 × 10 12 M ) fails to selfregulate because AGN feedback becomes too explosive.

Simulations without AGN feedback
To see how quickly star formation begins and what its rate would be without AGN feedback, we ran simulations of the three smaller halos with AGN = 0. We did not perform a similar simulation of the BCG, because stellar feedback is obviously insufficient to limit star formation in such a massive halo. Figure 2 shows the resulting star formation rates as functions of time. Unsurprisingly, the MPG model begins to form stars almost immediately, because radiative cooling exceeds SNIa heating at all radii. More than 10 9 M of cold gas (T < 10 5 K) accumulates by t ≈ 250 Myr, and star formation then proceeds at a steady rate ∼ 25 M yr −1 . According to Voit (2011), the steady cooling-flow rate associated with an entropy profile K(r) ∝ r iṡ in an isothermal potential. The asymptotic star formation rate observed in the MPG simulation without AGN feedback is therefore consistent with its initial entropy profile, which is K/r ≈ 1 keV cm 2 kpc −1 at ∼ 10 kpc.
The asymptotic star-formation rate is again consistent with equation (6), but with kT ∼ 0.3 keV.
Cooling and star formation begins within ∼ 100 Myr in the SEG model despite the central SNIa heating, because the weight of its CGM prevents the gas ejected by old stars from leaving the galaxy. The initial gas mass density at ∼ 1 kpc is ρ ≈ 5 × 10 −26 g cm −3 . At similar radii, the stellar mass density is ρ * ≈ 10 −22 g cm −3 , meaning that stellar ejecta can double the gas-mass density there on a timescale ρ(α * ρ * ) −1 ∼ 150 Myr if the gas cannot be pushed outward. Some of the gas is pushed outward, but not enough to prevent a buildup of gas within the central 5 kpc. Meanwhile, radiative cooling of gas just beyond ∼ 5 kpc produces an entropy inversion that makes the atmosphere convectively unstable and promotes thermal instability. Condensing gas clouds then sink to the center and initiate star formation. The resulting SNII explosions briefly suppress additional star formation but result in uplift of low-entropy ambient gas that precipitates at ∼ 10 kpc, forming new cold clouds. Those clouds then rain down toward the galaxy's center, and during the next 50 Myr the ambient gas settles into a steady cooling flow.
Star formation requires more time to reach a steady state in the SPG simulation without AGN feedback. A brief burst of star formation happens at t ∼ 50 Myr, because radiative cooling initially exceeds SNIa heating everywhere. SNII feedback from that initial burst then lowers the central density, which allows SNIa heating to exceed radiative cooling out to ∼ 1 kpc. Star formation remains suppressed for the next ∼ 1.3 Gyr, while the central gas pressure gradually rises. The central pressure goes up during this period because SNIa heating cannot push ejected stellar gas outward as fast as it accumulates and also because cooling of the overlying layers increases their weight. Eventually, the central gas density becomes great enough for radiative cooling to exceed SNIa heating, and the resulting cooling flow boosts the star formation to a steady state rate of ∼ 3.5 M yr −1 at t ∼ 2.0 Gyr.

Massive halos with AGN feedback
In all of our simulations with AGN feedback, star formation is highly suppressed relative to the respective no-AGN counterparts (see Figure 2). However, condensation of the ambient medium couples with AGN feedback differently, depending on both the depth of the central potential well the and atmospheric pressure at larger radii. In the SPG simulation, coupling between condensation and AGN feedback is remarkably tight and maintains a nearly steady feedback-regulated state. In contrast, the MPG and BCG simulations exhibit greater feedback bursts. This section examines how these three massive halos self-regulate, while §5.3 looks at what happens in the SEG simulation, which fails to self-regulate. Figure 3 shows the median emissivity-weighted radial entropy profiles in the SPG, MPG, and BCG simulations with AGN feedback. A dashed magenta line indicates the initial entropy profile in each simulation. A solid red line traces the median profile for the entire period from 0.5 to 1.5 Gyr. Dark grey shading shows the 20-80 percentile range of the median entropy profile during that period, and light grey shading shows the 1-99 percentile range.

Radial profiles
In each case, the median entropy profile shifts from its initial state into a different self-regulated state. The BCG entropy profile settles from a flat-entropy core into a self-regulated state with K ∝ r 2/3 in the central ∼ 30 kpc. The MPG entropy profile rises to a selfregulated state with a mean entropy at < 10 kpc several times greater than the initial state. The SPG entropy profile also rises within the central ∼ 10 kpc by a factor of ∼ 2. However, the shading shows that tightlycoupled feedback confines the SPG entropy profile to a much narrower range than in the BCG or MPG.
Comparing the data in Figure 3 with the simulation results reveals a significant discrepancy in the vicinity of 1 kpc, where specific entropy in the SPG and MPG simulations exceeds the observations by a factor of 2 to 3. In the middle panel showing the MPG simulation, some of that discrepancy might arise from a selection effect. The galaxies shown have particularly bright X-ray emission produced by atmospheres denser than average for their mass, meaning that they have lower than average specific entropy, but the data still remain within the fluctuation range of the simulation. However, the data in the SPG panel are well outside the fluctuation range of the SPG simulation. We therefore suspect that the entropy excess near 1 kpc results from a limitation of our simulation, which is the thickness of the AGN jet there. Section 6 discusses that limitation in more detail. Figure 4 shows the median radial profiles of both t cool (upper panels) and the t cool /t ff ratio (lower panels) during the same time period for the same three simulations. The left panels show that the SPG simulation self-regulates with min(t cool /t ff ) > 20 at > 1 kpc and t cool > 1 Gyr at 10 kpc. The middle panels show that the MPG self-regulates with most of its time spent in the 10 < min(t cool /t ff ) < 20 range, with t cool < 1 Gyr at 10 kpc. The right panels show that the BCG self regulates with min(t cool /t ff ) fluctuating in and out of that range, also with t cool < 1 Gyr at 10 kpc.

Self-regulation and SNIa heating
Self-regulation in these three simulations depends on how multiphase condensation couples AGN feedback with the state of the ambient medium. The upper panels in Figure 5 show how jet power (P jet ) is related to X-ray luminosity (L X ) over the time period 0-1.5 Gyr. After the initial AGN outburst of ∼ 10 43 erg s −1 , the single phase galaxy settles into a nearly steady state with time-averaged AGN jet power that is similar to the Xray luminosity from within the central 30 kpc. Frequent bursts fuelled by fluctuations in the amount of cold gas  . Median radial profiles of t cool (upper panels) and t cool /t ff (lower panels) for simulations with AGN feedback. Red lines and grey shading have the same meanings as in Figure 3. Black lines in the lower panels indicate the range 10 < t cool /t ff < 20 characteristic of precipitation-regulated feedback. The single phase galaxy (left panels) remains above that range outside of 1 kpc, with min(t cool /t ff ) ∼ 30. The multiphase galaxy (middle panels) self-regulates with 10 < t cool /t ff < 20 near 10 kpc during most of the 0.5-1.5 Gyr period, with brief excursions down to min(t cool /t ff ) ∼ 6 at smaller radii. The brightest cluster galaxy fluctuates in and out of the 10 < t cool /t ff < 20 range, with brief excursions to min(t cool /t ff ) ∼ 5 within the central few kiloparsecs.
within the central 0.5 kpc cause jet power to vary by a factor ∼ 10, but the power output remains steady when smoothed over timescales > 100 Myr. However, the other two simulations experience much greater fluctuations in jet power.
In the multiphase galaxy, AGN feedback is bimodal. The simulation starts with an outburst of jet power ∼ 10 44 erg s −1 . Heat input from that outburst causes the galaxy's atmosphere to expand, lowering its density and significantly reducing radiative cooling of the central 30 kpc. The AGN then enters a low-power state with P jet fluctuating on a ∼ 100 Myr timescale between < 10 41 erg s −1 and a few times 10 42 erg s −1 . Meanwhile, the atmosphere's X-ray luminosity climbs, because timeaveraged AGN power is much less than L X from within 30 kpc. Those radiative losses allow the weight of the CGM to compress the galactic atmosphere, gradually raising its density and pressure. The AGN remains in this low-power mode for ≈ 800 Myr but then reverts back to a high-power state, similar to the initial one, for another ≈ 200 Myr.
The BCG simulation remains in a state similar to the high-power mode of the MPG simulation most of the time and does not have a low-power mode. It is either near P jet ∼ 10 44 erg s −1 or at P jet < 10 41 erg s −1 . The state of extremely low power is likely to be artificial, resulting from the fact that our feedback algorithm sets AGN power to zero if there is no cold gas within the central 0.5 kpc. A more realistic model would include AGN power resulting from Bondi-like accretion of hot ambient gas, but jet power in that mode would be far too low to significantly affect the surrounding atmosphere.
The lower panels of Figure 5 show how the mode of AGN feedback is related to the ratio of SNIa heating to radiative cooling in the central few kiloparsecs. Initially, radiative cooling in the single phase galaxy is slightly greater than SNIa heating within ∼ 5 kpc of the center. Cooling of that gas fuels a ∼ 100 Myr burst of feedback that lowers the central gas density until SNIa heating exceeds radiative cooling from ∼ 0.5 kpc to ∼ 5 kpc. AGN feedback then enters the low-power mode, fueled only by cooling of gas within ∼ 0.5 kpc of the center. And that mode is sufficient to keep the single-phase galaxy in a steady state, for at least ∼ 1.5 Gyr.
In the multiphase galaxy, a larger initial burst of AGN power is needed to lower the atmosphere's density because its confining CGM pressure is greater. However, SNIa heating becomes comparable to radiative cooling at ∼ 1 kpc by t ≈ 300 Myr. The simulation then settles into the low-power feedback mode for nearly 1 Gyr.   Ia) to radiative cooling as a function of radius every 150 Myr during the evolution of each halo. In the single phase galaxy (left), AGN feedback promptly lowers the atmosphere's density, enabling SNIa heating to exceed radiative cooling from ∼ 0.5 kpc to ∼ 5 kpc. That state corresponds in time to the steady low-power mode of self-regulation. The high-power feedback mode in the multiphase galaxy (center) expands the galactic atmosphere, lowering its X-ray luminosity until SNIa heating becomes comparable to radiative cooling near ∼ 1 kpc. AGN feedback then switches to a low-power mode that is insufficient to replace radiative losses within ∼ 30 kpc, causing feedback to revert to a high-power mode at 1.2 Gyr, when radiative cooling once again exceeds SNIa heating everywhere. In the BCG simulation (right), radiative cooling rapidly exceeds SNIa heating everywhere, fueling only the high-power feedback mode.
During that time, AGN power is less steady than in the single phase galaxy because near-equality of SNIa heating and radiative cooling at r < 3 kpc allows larger condensation events to intermittently feed the AGN. The BCG simulation, on the other hand, is in a cooling-dominated state everywhere during virtually the entire time period. AGN feedback cannot lower the atmosphere's central density enough for SNIa heating to equal radiative cooling. Therefore, the mode of selfregulation connects AGN feedback to large condensation events, which occur well outside of the central kiloparsec.

Cold Gas and Star Formation
In these simulations, central accumulation of cold gas couples atmospheric conditions with AGN feedback while accumulations of cold gas at larger radii facilitate star formation. Figure 6 shows how the masses of cold gas (M cold ) and new stars change with time. In the single phase galaxy, the accumulations of cold gas are always small (10 4 -10 6 M ), and star formation is neg-ligible. Note that the feedback algorithm described in §3.5.1 produces an AGN feedback poweṙ E AGN = 6 × 10 42 erg s −1 M cold (< 0.5 kpc) 10 6 M , (7) given AGN = 10 −4 . The fluctuations in feedback power shown for this galaxy in Figure 5 are therefore consistent with the fluctuations in cold gas mass shown in Figure  6, as long as a large proportion of that gas ends up accreting onto the central black hole. Cold gas clouds forming through condensation are therefore consumed before they can form stars, linking the precipitation rate within 0.5 kpc directly to AGN feedback. In the multiphase galaxy, the mass of cold gas is ∼ 10 7 M in the high-power mode and ∼ 10 5 -10 6 M in the low-power mode. Those amounts of cold gas are also largely consistent with the fluctuations in feedback power shown in Figure 5. Furthermore, the periods when cold gas extends beyond 1 kpc correlate with periods of greater star formation and AGN power. Feedback events that cause multiphase precipitation at larger radii therefore promote star formation in our simulations, because the cold gas clouds have time to form stars before sinking into the AGN accretion region in the central 0.5 kpc. Figure 2 shows that those starformation events briefly peak at a rate ∼ 1 M yr −1 , but the accumulated stellar mass in figure 6 implies a timeaveraged rate ∼ 1 M yr −1 and a specific star-formation rate ∼ 10 −12 yr −1 . The brightest cluster galaxy experiences several condensation events that push M cold up to ∼ 10 8 M , producing surges of AGN power exceeding 10 44 erg s −1 . Figure 5 shows that surges of this magnitude with a significant duty cycle are necessary to compensate for the radiative losses from within 30 kiloparsecs. Note that increasing the parameter AGN in our feedback algorithm would result in greater accumulation of cold gas, because balance between AGN feedback and radiative cooling would require less cold gas to be reprocessed within the accretion zone. The amount of star formation in this simulation is therefore contingent on the choice of AGN . For the choice AGN = 10 −4 , the time-averaged star formation rate is ∼ 0.4 M yr −1 . Figure 7 shows the maximum radial extent of cold gas (T < 10 5 K) as these different systems evolve. In the single phase galaxy simulation, cold gas remains concentrated within 1 kpc and usually within 0.5 kpc, except during the initial outburst. In contrast, cold gas in the multiphase galaxy generally extends beyond 1 kpc (sometimes as far as ∼ 10 kpc), but cold gas in the BCG simulation tends to be less extended. Comparing cold gas radial extent to P jet in Figure 5 shows that cold gas becomes most extended following periods of strong AGN feedback, indicating that uplift of central gas promotes condensation at greater altitudes (Revaz et al. 2008;Mc-Namara et al. 2016;Voit et al. 2017).  Radial extent of cold gas (T < 10 5 K) in the AGN-feedback simulations of the single phase galaxy (red line), multiphase galaxy (blue line) and brightest cluster galaxy (black line). In the single phase galaxy, cold gas almost always remains within 1 kpc. In all cases, cold gas reaches its maximum extent following high-power bursts of AGN feedback.

AGN feedback in a smaller halo
Our AGN-feedback simulation in a lower-mass halo (the SEG with M 200 = 2 × 10 12 M ) dramatically differs from the others. Figure 8 shows that the simulation produces a large AGN outburst and some star formation during the first 0.4 Gyr and then enters a state in which AGN feedback does not compensate for radiative losses. Instead, star formation and AGN power shut down, while L X and M cold steadily decline with time.
As in the SEG simulation without AGN feedback (see §5.1), the action begins at ∼ 50 Myr when the central gas starts to condense. Those first cold clouds then trigger a self-exciting AGN feedback outburst. Uplift of low-entropy ambient gas simulates multiphase condensation that causes ∼ 5 × 10 8 M of cold gas to precipitate by t = 200 Myr. Much of that cold gas falls radially back into the accretion zone (< 0.5 kpc), boosting the jet power by a few times -up to ∼ 10 44 erg s −1 , more than an order of magnitude greater than the radiative losses from the ambient medium (L X ). This powerful feedback event blows out much of the hot-gas atmosphere but does not destroy the cold gas clouds, which can continue to rain back down in the accretion zone. The result is a decaying AGN feedback mode, in which intermittent accretion events produce smaller feedback outbursts that gradually lower the X-ray luminosity. Figure 9 shows the evolution of entropy (left panel), t cool (middle panel), and t cool /t ff ratio (right panel) during the first 600 Myr of the SEG simulation with AGN feedback. During the first 300 Myr, strong AGN feedback pushes some of the low-entropy ambient gas from the central region to beyond ∼ 10 kpc and heats the rest. The radiatively cooling outflow becomes most unstable to condensation near 10 kpc, where t cool /t ff remains near unity for tens of Myr. That low-entropy gas then sinks inward and becomes the cold gas that sustains runaway feedback. A similar runaway does not happen in the more massive halos, because AGN feedback in those systems does not produce as much uplift and convection. Later in the simulation, we find t cool /t ff < 10 at ∼ 100 kpc, but that gas condenses slowly because the cooling time there is several Gyr.

LIMITATIONS OF OUR SIMULATIONS
The primary limitation of our AGN-feedback simulations is the thickness of the jets within the central few kiloparsecs, which is inherently a numerical limitation. In order to model a high-velocity AGN jet in a way that is numerically stable, we need to represent the outflow by modifying a "disk" of cells that is several cell widths in radius. At 1 kpc, the injected jets in our calculations subtend 1 radian, which is several times greater than the observed widths of powerful jets among the galaxies we are trying to model. For example, the angular width of the jet in NGC 4261 is ∼ 0.2 radian at ∼ 1 kpc (Nakahara et al. 2018). If our simulations had comparably narrow jets with the same kinetic power they would likely drill more effectively through the gas at ∼ 1 kpc, coupling less strongly with the local ambient medium and thermalizing less of their kinetic energy there. We therefore hypothesize that the excess entropy at ∼ 1 kpc in the SPG and MPG simulations, relative to the data in Figure 3, results from simulated jets that are too wide at that radius. We are currently testing that hypothesis with simulations that have narrower jets.
Another limitation of our simulations is the initial lack of angular momentum in the galactic atmosphere. Injection of feedback energy produces turbulence that gives the cold clouds forming in that atmosphere some stochastic angular momentum, but often not enough angular momentum to prevent the clouds from sinking nearly radially down into the accretion zone at r < 0.5 kpc. In the three more massive halos (SPG, MPG, and BCG), the AGN feedback mechanism nevertheless manages to self-regulate, but in the SEG simulation it does not. We hypothesize that the initial lack of angular momentum is one of the factors that stymies self-regulation of the SEG, because it allows a self-exciting runaway of AGN feedback.
As mentioned in §5.3, uplift of ambient gas by the initial AGN feedback outburst in the SEG simulation stimulates condensation of > 10 8 M of cold gas, much of which falls directly back into the accretion zone. Jet power therefore spikes to several times 10 44 erg s −1 (see Equation 7), dramatically heating and disrupting the CGM (see Figure 8). However, fewer of the cold clouds condensing out of the ambient medium would fall directly into the accretion zone if the atmosphere as a whole had greater net angular momentum. More of the condensing cold gas would then settle down in a torus around the central SMBH and get decoupled from the feedback cycle (Prasad et al. 2015). We are therefore preparing simulations to explore the role of angular momentum in moderating this AGN feedback mechanism in lower-mass galaxies. The SPG and MPG simulations presented here were designed, in part, to test the "black-hole feedback valve" mechanism proposed by Voit et al. (2015cVoit et al. ( , 2020 and  Figure 9. Evolution of the SEG simulation (M200 = 2 × 10 12 M ) with AGN feedback in entropy (left panel), cooling time (middle panel) and t cool /t ff ratio (right panel) during the first 600 Myr. Colored lines show the median radial profiles at 30 Myr intervals. Central cooling initiates feedback at ∼ 50 Myr. The AGN outflow then lifts low-entropy gas out of the central region and creates a thermally unstable entropy inversion at ∼ 10 kpc. Condensing low-entropy gas subsequently sinks to the center and boosts the AGN fedback power. The resulting runaway overheats the CGM, raising its entropy level to ∼ 10 2 keV cm 2 out to ∼ 100 kpc by ∼ 400 Myr. summarized in §2. Qualitatively, the SPG and MPG simulations with AGN feedback do indeed self-regulate as envisioned, with AGN feedback tuning itself so that local radiative cooling is similar to SNIa heating out to distances several kiloparsecs from the galaxy's center. Figure 5 shows that the SPG simulation (σ v ≈ 280 km s −1 ) begins with cooling exceeding heating everywhere and settles into a steady state with SNIa heating exceeding radiative cooling from ∼ 1 kpc to ∼ 5 kpc, as predicted by the feedback-valve model for galaxies with σ v > 240 km s −1 . AGN feedback in this mode is fueled by cooling of gas within the central 0.5 kpc, while SNIa heating sweeps much of the gas released by stars at larger radii out of the galaxy. This state can remain steady as long as AGN feedback prevents the confining CGM pressure from building up, and it succeeds for at least 1.5 Gyr because the time-averaged jet power roughly matches radiative losses from the inner 30 kpc. However, we have not yet tested whether a galaxy with the SPG potential but a higher-pressure CGM (like the initial state of the MPG) tunes itself to this same steady state.
The MPG simulation (σ v ≈ 230 km s −1 ) also begins with cooling exceeding SNIa heating everywhere. Kinetic AGN feedback with power ∼ 10 44 erg s −1 then lowers the atmospheric density and abates when radiative cooling becomes similar to SNIa heating within ∼ 3 kpc. The galaxy remains in this low-power state for nearly 1 Gyr, but cannot sustain it because radiative losses from the inner 30 kpc exceed the jet power. The CGM pressure there remains high and gradually increases, preventing supernova heating from sweeping ejected stellar gas out of the galaxy. Gas density and radiative cooling within the galaxy therefore both rise until the gas density reaches a ceiling imposed by the condition min(t cool /t ff ) ≈ 10 (see Figure 4), at which precipitation of cold clouds inevitably triggers a large increase in feedback power. This second burst of feedback again lowers the central gas density until SNIa heating is comparable to local radiative cooling (see the yellow line in the lower center panel of Figure 5). Consequently, the configuration of the ambient medium fluctuates but is bracketed by the state in which SNIa heating exceeds radiative cooling and the state with min(t cool /t ff ) ≈ 10, in alignment with the black-hole feedback valve model for galaxies with σ v ≈ 230 km s −1 .
Quantitatively, however, the simulations do not match the black-hole feedback valve model in detail. One of the model's key predictions is that the power-law slope of the entropy profile should exceed K ∝ r 2/3 at r ∼ 1-10 kpc in galaxies with σ v > 240 km s −1 . The entropy profile at 1-10 kpc in our SPG simulation is much flatter than this prediction, which assumes that SNIa heating exceeds AGN heating within the galaxy. While it is difficult to measure with precision how much of the heating at ∼ 1 kpc is resulting from thermalization of jet energy, the excess entropy at that radius in the SPG simulation, relative to both the data and the analytical steady-flow models of Voit et al. (2020), suggests that the discrepancy results from excessive thermalization of jet kinetic energy at ∼ 1 kpc in the simulation (see §6).
The predictions made in Voit et al. (2020) for galaxies like the SEG and BCG are less specific, but the results of our simulations of the SEG and BCG with AGN feedback generally conform to the model's expectations. According to the model, a galaxy that does not supply enough feedback power to lift its CGM and alleviate the confining pressure should remain in a precipitationlimited state that self-regulates through multiphase condensation. The BCG simulation is consistent with that expectation of the model. For the SEG, the model predicts that multiphase circulation should be inevitable, because feedback overturns the atmosphere's entropy gradient. And indeed, the feedback events observed in the simulation lift low-entropy ambient gas out of the center, catalyzing widespread condensation and production of cold gas, much of which falls back toward the center.

Comparisons with Prior Simulations
Several earlier numerical studies have explored the role of kinetic AGN feedback fueled by cold-gas accretion in massive elliptical galaxies like the ones simulated in this paper. The efforts most closely related to our SPG and MPG simulations were published by Gaspari et al. (2011aGaspari et al. ( , 2012a and Wang et al. (2019). The ones most closely related to our BCG simulation were published by Gaspari et al. (2011bGaspari et al. ( , 2012b, Li et al. (2015), Prasad et al. (2018), and Meece et al. (2017). Gaspari et al. (2011aGaspari et al. ( ,b, 2012a performed the first suite of simulations to demonstrate that bipolar jets fueled by cold accretion can tune themselves to balance radiative cooling without overheating the central gas. Collectively, those three papers explored a range of halo mass similar to the range spanned by our SPG, MPG, and BCG models, but with substantially lower spatial resolution. Also, they adjusted their AGN feedback efficiency parameter, equivalent to our AGN , to optimize agreement with observations, finding the best results for AGN 3 × 10 −4 in lower-mass halos and AGN 5 × 10 −3 in cluster-scale halos. While mass and energy input from the old stellar population were included in these simulations, the role of the old stellar population in the overall feedback loop was not specifically analyzed. The simulations of Wang et al. (2019), like ours, were motivated by the analysis of Voit et al. (2015c) and focused on distinguishing the roles of the central gravitational potential and the stellar mass and energy sources. Wang et al. (2019) performed two simulations similar to our SPG and MPG simulations with AGN feedback. The initial conditions in those simulations were not identical to ours but were inspired by the same two galaxies, with NGC 4472 representing single phase elliptical galaxies and NGC 5044 representing multiphase galaxies. In alignment with our simulation results, Wang et al. (2019) found that AGN feedback in the galaxy similar to NGC 4472 maintained a relatively steady hotgas atmosphere with small amounts of centrally concentrated cold gas, while the same AGN feedback algorithm in the galaxy similar to NGC 5044 caused greater fluctuations in the hot-gas atmosphere and produced larger quantities of extended cold gas. Their general findings therefore also support the black-hole feedback valve model. However, the details of our simulation results differ from those of Wang et al. (2019). First, the median AGN power in Wang et al. (2019) is much greater, with jet power often rising above 10 43 erg s −1 in the single phase galaxy and rarely dropping below 10 43 erg s −1 in the multiphase galaxy. Their large AGN feedback efficiency (equivalent to AGN = 5×10 −3 ) allows the same amount of cold-gas accretion to produce much more power, but that cannot be the whole explanation for the power difference, because self-regulation over a 1.5 Gyr period requires time-integrated heat input within the central 10 to 30 kpc (with t cool 1.5 Gyr) to balance radiative losses from the same region. Therefore, kinetic AGN power in Wang et al. (2019) must be thermalizing over a larger region, implying that it is propagating farther from the center. Second, specific entropy near ∼ 1 kpc in the single phase galaxy of Wang et al. (2019) remains below 10 keV cm 2 most of the time, and is typically ≈ 5 keV cm 2 , in better agreement with observations of single phase galaxies than our SPG simulation. In §6, we hypothesized that the excess entropy at ∼ 1 kpc in our SPG simulation resulted from jets that were insufficiently narrow. And indeed, the jets implemented by Wang et al. (2019) are narrower, having a transverse momentum profile ∝ exp(−r 2 /2r 2 jet ) with r jet = 183 pc. With greater power and a smaller cross-section, the jets in Wang et al. (2019) have a much greater momentum flux than ours and are capable of propagating to much greater distances, also accounting for why the simulations of Wang et al. (2019) require more AGN power to self-regulate.
Self-regulation of AGN feedback in our BCG simulation is broadly similar to what is observed in other simulations of its type (e.g., Gaspari et al. 2011bGaspari et al. , 2012bLi & Bryan 2014;Li et al. 2015;Prasad et al. 2015Prasad et al. , 2018Meece et al. 2017). Our BCG simulation's typical value of min(t cool /t ff ) is greater than most, with a median ratio ∼ 25. In a future paper, we will show that the self-regulated K(r) profile of our BCG simulation, which has an inner slope K ∝ r 2/3 (see Figure 3) is in excellent agreement with the observations of Hogan et al. (2017) and Babyk et al. (2018). However, unlike some of the other simulations, it produces less cold gas than is observed in cluster cores, and the cold gas it does produce rarely extends beyond 3 kpc.
The main reason for the lack of cold gas in our BCG simulation is the low feedback efficiency parameter we have chosen. For AGN = 10 −4 , the cold-gas accretion rate required to sustain 10 44 erg s −1 of feedback power is 18 M yr −1 . Our algorithm converts all of that cold gas to hot gas and expels it from the central region in a jet. Over the course of 1 Gyr, more than 10 10 M would otherwise have accumulated, and much it would likely have formed stars at a rate ∼ 10 M yr −1 . In some of the other cluster-scale simulations (e.g., Gaspari et al. 2012b;Li & Bryan 2014;Prasad et al. 2015), much of the cold gas persists indefinitely in a torus orbiting outside of the accretion zone because of the stochastic angular momentum it gains during kinetic feedback bursts. Our simulation does not produce such a torus and we will analyze what inhibits torus formation in a future paper.

CONCLUSIONS
The suite of simulations in this paper was designed to explore how a particular cold-fueled kinetic AGN feedback mechanism responds to differences in the surrounding potential well and initial atmospheric conditions. In halos ranging from galaxy-cluster scale (8 × 10 14 M ), through galaxy-group scale (4 × 10 13 M ), down to smaller elliptical galaxies (2 × 10 12 M ), we performed high resolution 3D hydrodynamic simulations with radiative cooling, stellar feedback, and AGN feedback. We were particularly interested in testing the "black-hole feedback valve" mechanism (see §2), which hypothesizes that coupling between AGN feedback and SNIa heating tunes the confining CGM pressure so that SNIa heating approximately equals radiative cooling within the galaxy.
The main results from those numerical experiments are: 1. AGN feedback is necessary to quench star formation in all of our simulated galaxies.
2. The cold-fueled kinetic AGN feedback mechanism we implement becomes self-regulating within ∼ 200 Myr in all three of the higher mass halos (M 200 > 10 13 M ).
3. AGN feedback in the two group-scale halos selftunes to a state with SNIa heating approximately equal to radiative cooling inside the central galaxy, and the nature of that self-regulated state depends on galactic velocity dispersion (σ v ) and confining CGM pressure. Those findings, which mirror those of Wang et al. (2019), are in general agreement with the black-hole feedback valve hypothesis.
4. AGN feedback in our single phase galaxy (SPG) simulation with σ v ≈ 280 km s −1 maintains a nearly steady state, with time-averaged AGN power several times 10 41 erg s −1 . Condensation of cold gas is focused within the central kiloparsec, as predicted by the black-hole feedback valve model for galaxies with σ v > 240 km s −1 . SNIa heating exceeds radiative cooling at ∼ 1-5 kpc and sweeps much of the gas ejected by stars out of the galaxy, while star formation is completely quenched. However, kinetic AGN feedback appears to overheat the region near ∼ 1 kpc, producing excess entropy, relative to observations. We hypothesize that the bipolar jets implemented in our simulations overheat that region because they are too wide and therefore couple too strongly to the ambient gas there.
5. AGN feedback in our multiphase galaxy (MPG) simulation with σ v ≈ 230 km s −1 is less steady, switching back and forth between a high-power state (∼ 10 44 erg s −1 ) and a low-power state (∼ 10 42 erg s −1 ). The high-power state is characterized by min(t cool /t ff ) ∼ 10, extending to ∼ 15 kpc, which allows precipitation of cold clouds out of the hot ambient medium to produce extended multiphase gas. AGN power fueled by accretion of the cold gas then heats the CGM and lowers its pressure until SNIa heating approximately matches radiative cooling within the central few kiloparsecs.
As that happens, the MPG simulation enters a low-power state but cannot maintain it, eventually reverting back to the high-power state with min(t cool /t ff ) ∼ 10. These features are consistent with the black-hole feedback valve model for galaxies with σ v 240 km s −1 .
6. CGM pressure in our brightest cluster galaxy (BCG) simulation is always great enough to ensure that radiative cooling exceeds SNIa heating everywhere. It self-regulates with AGN power exceeding 10 44 erg s −1 for much of the simulation runtime. However, not much cold gas accumulates compared to other similar galaxy-cluster simulations, probably because of our comparatively low feedback efficiency parameter ( AGN = 10 −4 ).
7. In the smaller elliptical galaxy (SEG) simulation, with σ v ≈ 150 km s −1 , the cold-fueled kinetic feedback mechanism dramatically fails to self-regulate. As AGN feedback turns on and begins to lift the ambient gas, it stimulates copious multiphase condensation. Much of that cold gas then rains back down into the accretion region, causing an even stronger feedback response. This runaway of AGN feedback then overheats the ambient gas and blows out much of it out to ∼ 100 kpc. We suspect that the outcome of this simulation might have been different if the galaxy's initial atmosphere had some net angular momentum. Much of the precipitating cold gas might then have avoided falling into the accretion zone and fueling the runaway response.
Future papers will present more detailed analyses of each of these simulations.
DP is supported by Chandra theory grant no. TM8-19006X (G. M. Voit as PI) and NSF grant no. AST-1517908 (B.W.O'Shea as PI). BWO acknowledges further support from NSF grant no. AST-1908109 and NASA ATP grants NNX15AP39G and 80NSSC18K1105. DP thanks Yuan Li and Philipp Grete for providing support during the start of this project. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562 and TG-AST190022, as well as the resources of the Michigan State University High Performance Computing Center (operated by the Institute for Cyber-Enabled Research). Enzo Brummel-Smith et al. 2019) and yt (Turk et al. 2011) are developed by a large number of independent researchers from numerous institutions around the world.
Their commitment to open science has helped make this work possible.