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Jeremiah P. Ostriker

Publications and source records attributed to Jeremiah P. Ostriker.

At least 55 records · Page 3Linked to original sources

Quantifying Supernovae-Driven Multiphase Galactic Outflows

Galactic outflows are ubiquitously observed in star-forming disk galaxies and are critical for galaxy formation. Supernovae (SNe) play the key role in driving the outflows, but there is no consensus as to how much energy, mass and metal they can launch out of the disk. We perform 3D, high-resolution hydrodynamic simulations to study SNe-driven outflows from stratified media. Assuming SN rate scales with gas surface density $Σ_{\rm{gas}}$ as in the Kennicutt-Schmidt (KS) relation, we find the mass loading factor, $η_m$, defined as the mass outflow flux divided by the star formation surface density, decreases with increasing $Σ_{\rm{gas}}$ as $η_m \propto Σ^{-0.61}_{\rm{gas}}$. Approximately $Σ_{\rm{gas}}$ $\lesssim$ 50 $M_\odot/\rm{pc}^2$ marks when $η_m \gtrsim$1. About 10-50\% of the energy and 40-80\% of the metals produced by SNe end up in the outflows. The tenuous hot phase ($T>3\times 10^5$ K), which fills 60-80\% of the volume at mid-plane, carries the majority of the energy and metals in outflows. We discuss how various physical processes, including vertical distribution of SNe, photoelectric heating, external gravitational field and SN rate, affect the loading efficiencies. The relative scale height of gas and SNe is a very important factor in determining the loading efficiencies.

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AGN feedback, quiescence and CGM metal enrichment in early-type galaxies

We present three-dimensional hydrodynamical simulations showing the effect of kinetic and radiative AGN feedback on a model galaxy representing a massive quiescent low-redshift early-type galaxy of $M_* = 8.41\times 10^{10} M_\odot$, harbouring a $M_\mathrm{BH} = 4\times 10^8 M_\odot $ black hole surrounded by a cooling gaseous halo. We show that, for a total baryon fraction of $\sim 20\%$ of the cosmological value, feedback from the AGN can keep the galaxy quiescent for about 4.35 Gyr and with properties consistent with black hole mass and X-ray luminosity scaling relations. However, this can only be achieved if the AGN feedback model includes both kinetic and radiative feedback modes. The simulation with only kinetic feedback fails to keep the model galaxy fully quiescent, while one with only radiative feedback leads to excessive black-hole growth. For higher baryon fractions (e.g. 50\% of the cosmological value), the X-ray luminosities exceed observed values by at least one order of magnitude, and rapid cooling results in a star-forming galaxy. The AGN plays a major role in keeping the circumgalactic gas at observed metallicities of $Z/Z_\odot \gtrsim 0.3 $ within the central $\sim 30$ kpc by venting nuclear gas enriched with metals from residual star formation activity. As indicated by previous cosmological simulations, our results are consistent with a model for which the black hole mass and the total baryon fraction are set at higher redshifts $z > 1$ and the AGN alone can keep the model galaxy on observed scaling relations. Models without AGN feedback violate both the quiescence criterion as well as CGM metallicity constraints.

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Ultralight scalars as cosmological dark matter

An intriguing alternative to cold dark matter (CDM) is that the dark matter is a light ( $m \sim 10^{-22}$ eV) boson having a de Broglie wavelength $λ\sim 1$ kpc, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos smaller than about $10^7 (m/10^{-22} {\rm eV})^{-3/2} M_\odot$ do not form. (ii) FDM halos are comprised of a core that is a stationary, minimum-energy configuration called a "soliton", surrounded by an envelope that resembles a CDM halo. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating systems, which proceeds as if the halo were composed of particles with mass $\sim ρλ^3$ where $ρ$ is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies. (v) Relaxation can produce FDM disks but an FDM disk in the solar neighborhood must have a half-thickness of at least $300 (m/10^{-22} {\rm eV})^{-2/3}$ pc. (vi) Solitonic FDM sub-halos evaporate by tunneling through the tidal radius and this limits the minimum sub-halo mass inside 30 kpc of the Milky Way to roughly $10^8 (m/10^{-22} {\rm eV})^{-3/2} M_\odot$. (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM.

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OVI Emission From the Supernovae-regulated Interstellar Medium: Simulation Vs Observation

The OVI $λλ$1032, 1038Å doublet emission traces collisionally ionized gas with $T\approx 10^{5.5}$ K, where the cooling curve peaks for metal-enriched plasma. This warm-hot phase is usually not well-resolved in numerical simulations of the multiphase interstellar medium (ISM), but can be responsible for a significant fraction of the emitted energy. Comparing simulated OVI emission to observations is therefore a valuable test of whether simulations predict reasonable cooling rates from this phase. We calculate OVI $λ$1032Å emission, assuming collisional ionization equilibrium, for our small-box simulations of the stratified ISM regulated by supernovae. We find that the agreement is very good for our solar neighborhood model, both in terms of emission flux and mean OVI density seen in absorption. We explore runs with higher surface densities and find that, in our simulations, the OVI emission from the disk scales roughly linearly with the star formation rate. Observations of OVI emission are rare for external galaxies, but our results do not show obvious inconsistency with the existing data. Assuming the solar metallicity, OVI emission from the galaxy disk in our simulations accounts for roughly 0.5\% of supernovae heating.

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Modeling for Stellar Feedback in Galaxy Formation Simulations

Various heuristic approaches to model unresolved supernova (SN) feedback in galaxy formation simulations exist to reproduce the formation of spiral galaxies and the overall inefficient conversion of gas into stars. Some models, however, require resolution dependent scalings. We present a sub-resolution model representing the three major phases of supernova blast wave evolution $-$free expansion, energy conserving Sedov-Taylor, and momentum conserving snowplow$-$ with energy scalings adopted from high-resolution interstellar-medium simulations in both uniform and multiphase media. We allow for the effects of significantly enhanced SN remnant propagation in a multiphase medium with the cooling radius scaling with the hot volume fraction, $f_{\mathrm{hot}}$, as $(1 - f_{\mathrm{hot}})^{-4/5}$. We also include winds from young massive stars and AGB stars, Strömgren sphere gas heating by massive stars, and a gas cooling limiting mechanism driven by radiative recombination of dense HII regions. We present initial tests for isolated Milky-Way like systems simulated with the GADGET based code SPHgal with improved SPH prescription. Compared to pure thermal SN input, the model significantly suppresses star formation at early epochs, with star formation extended both in time and space in better accord with observations. Compared to models with pure thermal SN feedback, the age at which half the stellar mass is assembled increases by a factor of 2.4, and the mass loading parameter and gas outflow rate from the galactic disk increase by a factor of 2. Simulation results are converged for a two order of magnitude variation in particle mass in the range (1.3$-$130)$\times 10^4$ solar masses.

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Towards Self-Consistent Modelling of the Sgr A* Accretion Flow: Linking Theory and Observation

The interplay between supermassive black holes (SMBHs) and their environments is believed to command an essential role in galaxy evolution. The majority of these SMBHs are in the radiative inefficient accretion phase where this interplay remains elusive, but suggestively important, due to few observational constraints. To remedy this, we directly fit 2-D hydrodynamic simulations to Chandra observations of Sgr A* with Markov Chain Monte Carlo sampling, self-consistently modelling the 2-D inflow-outflow solution for the first time. We find the temperature and density at flow onset are consistent with the origin of the gas in the stellar winds of massive stars in the vicinity of Sgr A*. We place the first observational constraints on the angular momentum of the gas and estimate the centrifugal radius, r$_c$ $\approx$ 0.056 r$_b$ $\approx8\times10^{-3}$ pc, where r$_b$ is the Bondi radius. Less than 1\% of the inflowing gas accretes onto the SMBH, the remainder being ejected in a polar outflow. For the first time, we decouple the quiescent point-like emission from the spatially extended flow. We find this point-like emission, accounting for $\sim4$\% of the quiescent flux, is spectrally too steep to be explained by unresolved flares, nor Bremsstrahlung, but is likely a combination of a relatively steep synchrotron powerlaw and the high energy tail of inverse-Compton emission. With this self-consistent model of the accretion flow structure, we make predictions for the flow dynamics and discuss how future X-ray spectroscopic observations can further our understanding of the Sgr A* accretion flow.

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Theoretical Challenges in Galaxy Formation

Numerical simulations have become a major tool for understanding galaxy formation and evolution. Over the decades the field has made significant progress. It is now possible to simulate the formation of individual galaxies and galaxy populations from well defined initial conditions with realistic abundances and global properties. An essential component of the calculation is to correctly estimate the inflow to and outflow from forming galaxies since observations indicating low formation efficiency and strong circum-glactic presence of gas are persuasive. Energetic 'feedback' from massive stars and accreting super-massive black holes - generally unresolved in cosmological simulations - plays a major role for driving galactic outflows, which have been shown to regulate many aspects of galaxy evolution. A surprisingly large variety of plausible sub-resolution models succeeds in this exercise. They capture the essential characteristics of the problem, i.e. outflows regulating galactic gas flows, but their predictive power is limited. In this review we focus on one major challenge for galaxy formation theory: to understand the underlying physical processes that regulate the structure of the interstellar medium, star formation and the driving of galactic outflows. This requires accurate physical models and numerical simulations, which can precisely describe the multi-phase structure of the interstellar medium on the currently unresolved few hundred parsecs scales of large scale cosmological simulations. Such models ultimately require the full accounting for the dominant cooling and heating processes, the radiation and winds from massive stars and accreting black holes, an accurate treatment of supernova explosions as well as the non-thermal components of the interstellar medium like magnetic fields and cosmic rays.

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Formation of Massive Black Holes in Galactic Nuclei: Runaway Tidal Encounters

Nuclear star clusters (NSCs) and supermassive black holes (SMBHs) both inhabit galactic nuclei, coexisting in a range of bulge masses, but excluding each other in the largest or smallest galaxies. We propose that the transformation of NSCs into SMBHs occurs via runaway tidal captures, once NSCs exceed a certain critical central density and velocity dispersion. The bottleneck in this process, as with all collisional runaways, is growing the first e-fold in black hole mass. The growth of a stellar mass black hole past this bottleneck occurs as tidally captured stars are consumed in repeated episodes of mass transfer at pericenter. Tidal captures may turn off as a growth channel once the black hole reaches a mass ~100-1000 solar masses, but tidal disruption events will continue and appear capable of growing the seed SMBH to larger sizes. The runaway slows (becomes sub-exponential) once the seed SMBH consumes the core of its host NSC. While the bulk of the cosmic mass density in SMBHs is ultimately produced (via the Soltan-Paczynski argument) by episodic gaseous accretion in very massive galaxies, the smallest SMBHs have probably grown from strong tidal encounters with NSC stars. SMBH seeds that grow for a time $t$ entirely through this channel will follow simple power law relations with the velocity dispersion, $σ$, of their host galaxy. In the simplest regime it is $M_\bullet \sim σ^{3/2}\sqrt{M_\star t / G} \sim 10^{6}M_\odot (σ/ 50~{\rm km~s}^{-1})^{3/2}(t/10^{10}~{\rm yr})^{1/2}$, but the exponents and prefactor can differ slightly depending on the details of loss cone refilling. Current tidal disruption event rates predicted from this mechanism are consistent with observations.

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Hyper-Eddington accretion flows onto massive black holes

We study very-high rate spherically symmetric accretion flows onto a massive black hole (BH; 10^2 < M_BH < 10^6 Msun) embedded in a dense gas cloud with a low abundance of metals, performing one-dimensional hydrodynamical simulations which include multi-frequency radiation transfer and non-equilibrium primordial chemistry. We find that rapid gas supply from the Bondi radius at a hyper-Eddington rate can occur without being impeded by radiation feedback when (n/10^5 cm^-3) > (M_BH/10^4Msun)^{-1}(T/10^4 K)^{3/2}, where n and T are the density and temperature of ambient gas outside of the Bondi radius. The resulting accretion rate in this regime is steady, and larger than 3000 times the Eddington rate. At lower Bondi rates, the accretion is episodic due to radiative feedback and the average rate is limited below the Eddington rate. For the hyper-Eddington case, the steady solution consists of two parts: a radiation-dominated central core, where photon trapping due to electron scattering is important, and an accreting envelope which follows a Bondi profile with T~8000 K. When the emergent luminosity is limited below the Eddington luminosity because of photon trapping, radiation from the central region does not affect the gas dynamics at larger scales. We apply our result to the rapid formation of massive BHs in protogalaxies with a virial temperature of T_vir> 10^4 K. Once a seed BH forms at the center of the galaxy, it can grow up to a maximum ~10^5 (T_vir/10^4 K) Msun via gas accretion independent of the initial BH mass. Finally, we discuss possible observational signatures of rapidly accreting BHs with/without allowance for dust. We suggest that these systems could explain Lya emitters without X-rays and luminous infrared sources with hot dust emission, respectively.

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Launching cosmic-ray-driven outflows from the magnetized interstellar medium

We present a hydrodynamical simulation of the turbulent, magnetized, supernova (SN)-driven interstellar medium (ISM) in a stratified box that dynamically couples the injection and evolution of cosmic rays (CRs) and a self-consistent evolution of the chemical composition. CRs are treated as a relativistic fluid in the advection-diffusion approximation. The thermodynamic evolution of the gas is computed using a chemical network that follows the abundances of H+, H, H2, CO, C+, and free electrons and includes (self-)shielding of the gas and dust. We find that CRs perceptibly thicken the disk with the heights of 90% (70%) enclosed mass reaching ~1.5 kpc (~0.2 kpc). The simulations indicate that CRs alone can launch and sustain strong outflows of atomic and ionized gas with mass loading factors of order unity, even in solar neighborhood conditions and with a CR energy injection per SN of 10^50 erg, 10% of the fiducial thermal energy of an SN. The CR-driven outflows have moderate launching velocities close to the midplane (~100 km/s) and are denser (ρ~1e-24 - 1e-26 g/cm^3), smoother, and colder than the (thermal) SN-driven winds. The simulations support the importance of CRs for setting the vertical structure of the disk as well as the driving of winds.

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Supernova Feedback and the Hot Gas Filling Fraction of the Interstellar Medium

Supernovae (SN), the most energetic stellar feedback mechanism, are crucial for regulating the interstellar medium (ISM) and launching galactic winds. We explore how supernova remnants (SNRs) create a multiphase medium by performing 3D hydrodynamical simulations at various SN rates, $S$, and ISM average densities, $\bar{n}$. The evolution of a SNR in a self-consistently generated three-phase ISM is qualitatively different from that in a uniform or a two-phase warm/cold medium. By travelling faster and further in the low-density hot phase, the domain of a SNR increases by $>10^{2.5}$. Varying $\bar{n}$ and $S$, we find that a steady state can only be achieved when the hot gas volume fraction $f_{\rm{V,hot}}\lesssim 0.6 \pm 0.1 $. Above that level, overlapping SNRs render connecting topology of the hot gas, and the ISM is subjected to thermal runaway. Photoelectric heating (PEH) has a surprisingly strong impact on $f_{\rm{V,hot}}$. For $\bar{n}\gtrsim 3 \cm-3 $, a reasonable PEH rate is able to suppress the thermal runaway. Overall, we determine the critical SN rate for the onset of thermal runaway to be $S_{\rm{crit}} = 200 (\bar{n}/1\cm-3)^k (E_{\rm{SN}}/10^{51}\erg)^{-1} \kpc^{-3} \myr-1$, where $k = (1.2,2.7)$ for $\bar{n} \leq 1$ and $> 1\cm-3 $, respectively. We present a fitting formula of the ISM pressure $P(\bar{n}$, $S$), which can be used as an effective equation of state in cosmological simulations. Despite the 5 orders of magnitude span of $(\bar{n},S)$, the average Mach number varies little: $\mathcal{M} \approx \ 0.5\pm 0.2, \ 1.2\pm 0.3,\ 2.3\pm 0.9$ for the hot, warm and cold phases, respectively.

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A Dynamical Potential-Density Pair for Star Clusters With Nearly Isothermal Interiors

We present a potential-density pair designed to model nearly isothermal star clusters (and similar self-gravitating systems) with a central core and an outer turnover radius, beyond which density falls off as $r^{-4}$. In the intermediate zone, the profile is similar to that of an isothermal sphere (density $ρ\propto r^{-2}$), somewhat less steep than the King 62 profile, and with the advantage that many dynamical quantities can be written in a simple closed form. We derive new analytic expressions for the cluster binding energy and velocity dispersion, and apply these to create toy models for cluster core collapse and evaporation. We fit our projected surface brightness profiles to observed globular and open clusters, and find that the quality of the fit is generally at least as good as that for the surface brightness profiles of King 62. This model can be used for convenient computation of the dynamics and evolution of globular and nuclear star clusters.

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Kinetic energy from supernova feedback in high-resolution galaxy simulations

We describe a new method for adding a prescribed amount of kinetic energy to simulated gas modeled on a cartesian grid by directly altering grid cells' mass and velocity in a distributed fashion. The method is explored in the context of supernova feedback in high-resolution ($\sim 10$ pc) hydrodynamic simulations of galaxy formation. Resolution-dependence is a primary consideration in our application of the method and simulations of isolated explosions (performed at different resolutions) motivate a resolution-dependent scaling for the injected fraction of kinetic energy that we apply in cosmological simulations of a $10^9$ Msun dwarf halo. We find that in high density media ($\gtrsim$ 50 cm$^{-3}$) with coarse resolution ($\gtrsim 4$ pc per cell), results are sensitive to the initial kinetic energy fraction due to early and rapid cooling. In our galaxy simulations, the deposition of small amounts of supernova energy in kinetic form (as little as 1%) has a dramatic impact on the evolution of the system, resulting in an order of magnitude suppression of stellar mass. The overall behavior of the galaxy in the two highest resolution simulations we perform appears to converge. We discuss the resulting distribution of stellar metallicities, an observable sensitive to galactic wind properties, and find that while the new method demonstrates increased agreement with observed systems, significant discrepancies remain, likely due to simplistic assumptions that neglect contributions from Type Ia supernovae and stellar winds.

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A Two-Parameter Matching Scheme for Massive Galaxies and Dark Matter Haloes

Halo Abundance Matching has been used to construct a one-parameter mapping between galaxies and dark matter haloes by assuming that halo mass and galaxy luminosity (or stellar mass) are monotonically related. While this approach has been reasonably successful, it is known that galaxies must be described by at least two parameters, as can be seen from the two-parameter Fundamental Plane on which massive early-type galaxies lie. In this paper, we derive a connection between initial dark matter density perturbations in the early universe and present-day virialized dark matter haloes by assuming simple spherical collapse combined with conservation of mass and energy. We find that $z = 0$ halo concentration, or alternatively the inner slope of the halo density profile $α$, is monotonically and positively correlated with the collapse redshift of the halo. This is qualitatively similar to the findings of some previous works based on numerical simulations, with which we compare our results. We then describe how the halo mass and concentration (or inner slope $α$) can be used as two halo parameters in combination with two parameters of early-type galaxies to create an improved abundance matching scheme.

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The impact of mechanical AGN feedback on the formation of massive early-type galaxies

We employ cosmological hydrodynamical simulations to investigate the effects of AGN feedback on the formation of massive galaxies with present-day stellar masses of $M_{stel} = 8.8 \times 10^{10} - 6.0 \times 10^{11} M_{sun}$. Using smoothed particle hydrodynamics simulations with a pressure-entropy formulation that allows an improved treatment of contact discontinuities and fluid mixing, we run three sets of simulations of 20 halos with different AGN feedback models: (1) no feedback, (2) thermal feedback, and (3) mechanical and radiation feedback. We assume that seed black holes are present at early cosmic epochs at the centre of emerging dark matter halos and trace their mass growth via gas accretion and mergers with other black holes. Both feedback models successfully recover the observed M_BH - sigma relation and black hole-to-stellar mass ratio for simulated central early-type galaxies. The baryonic conversion efficiencies are reduced by a factor of two compared to models without any AGN feedback at all halo masses. However, massive galaxies simulated with thermal AGN feedback show a factor of ~10-100 higher X-ray luminosities than observed. The mechanical/radiation feedback model reproduces the observed correlation between X-ray luminosities and velocity dispersion, e.g. for galaxies with sigma = 200 km/s, the X-ray luminosity is reduced from $10^{42}$ erg/s to $10^{40}$ erg/s. It also efficiently suppresses late time star formation, reducing the specific star formation rate from $10^{-10.5}$ $yr^{-1}$ to $10^{-14}$ $yr^{-1}$ on average and resulting in quiescent galaxies since z=2, whereas the thermal feedback model shows higher late time in-situ star formation rates than observed.

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The stellar accretion origin of stellar population gradients in massive galaxies at large radii

We investigate the evolution of stellar population gradients from $z=2$ to $z=0$ in massive galaxies at large radii ($r > 2R_{\mathrm{eff}}$) using ten cosmological zoom simulations of halos with $6 \times 10^{12} M_{\odot} < M_{\mathrm{halo}} < 2 \times 10^{13}M_{\odot}$. The simulations follow metal cooling and enrichment from SNII, SNIa and AGB winds. We explore the differential impact of an empirical model for galactic winds that reproduces the mass-metallicity relation and its evolution with redshift. At larger radii the galaxies, for both models, become more dominated by stars accreted from satellite galaxies in major and minor mergers. In the wind model, fewer stars are accreted, but they are significantly more metal poor resulting in steep global metallicity ($\langle \nabla Z_{\mathrm{stars}} \rangle= -0.35$ dex/dex) and color (e.g. $\langle \nabla g-r \rangle = -0.13$ dex/dex) gradients in agreement with observations. In contrast, colour and metallicity gradients of the models without winds are inconsistent with observations. Age gradients are in general mildly positive at $z=0$ ($\langle \nabla Age_{\mathrm{stars}} \rangle= 0.04$ dex/dex) with significant differences between the models at higher redshift. We demonstrate that for the wind model, stellar accretion is steepening existing in-situ metallicity gradients by about 0.2 dex by the present day and helps to match observed gradients of massive early-type galaxies at large radii. Colour and metallicity gradients are significantly steeper for systems which have accreted stars in minor mergers, while galaxies with major mergers have relatively flat gradients, confirming previous results. This study highlights the importance of stellar accretion for stellar population properties of massive galaxies at large radii, which can provide important constraints for formation models.

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Understanding black hole mass assembly via accretion and mergers at late times in cosmological simulations

Accretion is thought to primarily contribute to the mass accumulation history of supermassive black holes throughout cosmic time. While this may be true at high redshifts, at lower redshifts and for the most massive black holes mergers themselves might add significantly to the mass budget. We evolve SMBHs from $4 > z > 0$ using merger trees derived from hydrodynamical cosmological simulations of a cluster and void region, scaled to the observed value of the stellar mass fraction to account for overcooling. Mass gains from gas accretion proportional to bulge growth and BH-BH mergers are tracked, as are black holes that remain "orbiting" due to insufficient dynamical friction in a merger remnant, as well as those that are ejected due to gravitational recoil. We find that gas accretion remains the dominant source of mass accumulation in almost all SMBHs; mergers contribute $2.5\pm0.1\%$ for all SMBHs in the cluster and $1.0\pm0.1\%$ in the void since $z = 4$. However, mergers are significant for massive SMBHs. The fraction of mass accumulated from mergers for central BHs generally increases for larger values of the host bulge mass: in the void, the fraction is $2\%$ at $M_{*, bul} = 10^{10} M_{\odot}$, increasing to $4\%$ at $M_{*, bul} \gtrsim 10^{11} M_{\odot}$, and in the cluster it is $4\%$ at $M_{*, bul} = 10^{10} M_{\odot}$ and $23\%$ at $10^{12} M_{\odot}$. We find that $40\%$ of SMBHs and $\approx 8\%$ of the total SMBH mass is found orbiting in the cluster region at $z = 0$. The existence of orbiting and ejected SMBHs requires modification of the Soltan argument. We estimate this correction to the integrated accreted mass density of SMBHs to be in the range $6-21\%$, with a mean value of $11\pm3\%$. We also calculate the total energy output and strain from gravitational waves emitted by merging SMBHs, and obtain a signal potentially detectable by pulsar timing arrays.

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AGN feedback in an isolated elliptical galaxy: the effect of strong radiative feedback in the kinetic mode

Based on two-dimensional high resolution hydrodynamic numerical simulation, we study the mechanical and radiative feedback effects from the central AGN on the cosmological evolution of an isolated elliptical galaxy. Physical processes such as star formation and supernovae are considered. The inner boundary of the simulation domain is carefully chosen so that the fiducial Bondi radius is resolved and the accretion rate of the black hole is determined self-consistently. In analogy to previous works, we assume that the specific angular momentum of the galaxy is low. It is well-known that when the accretion rates are high and low, the central AGNs will be in cold and hot accretion modes, which correspond to the radiative and kinetic feedback modes, respectively. The emitted spectrum from the hot accretion flows is harder than that from the cold accretion flows, which could result in a higher Compton temperature accompanied by a more efficient radiative heating, according to previous theoretical works. Such a difference of the Compton temperature between the two feedback modes, the focus of this study, has been neglected in previous works. Significant differences in the kinetic feedback mode are found as a result of the stronger Compton heating and accretion becomes more chaotic. More importantly, if we constrain models to correctly predict black hole growth and AGN duty cycle after cosmological evolution, we find that the favored model parameters are constrained: mechanical feedback efficiency diminishes with decreasing luminosity (the maximum efficiency being $\simeq 10^{-3.5}$) and X-ray Compton temperature increases with decreasing luminosity, although models with fixed mechanical efficiency and Compton temperature can be found that are satisfactory as well. We conclude that radiative feedback in the kinetic mode is much more important than previously thought.

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