Luca Ciotti

COOLING FLOWS AND QUASARS. II. DETAILED MODELS OF FEEDBACK-MODULATED ACCRETION FLOWS

Most elliptical galaxies contain central black holes (BHs), and most also contain significant amounts of hot gas capable of accreting on to the central BH as a result of having cooling times that are short compared to the Hubble time. Why, therefore, do we not see active galactic nuclei (AGNs) at the center of most elliptical galaxies rather than in only (at most) a few percent of them? We here propose the simple idea that feedback from accretion events heats the ambient gas, retarding subsequent infall, in a follow-up to papers by Binney & Tabor and Ciotti & Ostriker. Even small amounts of accretion on a central BH can cause the release of enough energy to reverse the central inflow, when the Compton temperature (TX) of the emitted radiation is higher than the mean galactic gas temperature, the basic assumption of this paper. Well-observed nearby AGNs (3C 273, 3C 279), having TX near 5 × 108 K, amply satisfy this requirement. In this context, we present a new class of one-dimensional hydrodynamical evolutionary sequences for the gas flows in elliptical galaxies with massive central BHs. The model galaxies are constrained to lie on the fundamental plane of elliptical galaxies, and are surrounded by variable amounts of dark matter. Two source terms operate: mass loss from evolving stars, and a secularly declining heating by Type Ia supernovae (SNe Ia). Like the previous models investigated by Ciotti et al., these new models can evolve up to three consecutive evolutionary stages: the wind, outflow, and inflow phases. At this point the presence of the BH dramatically alters the subsequent evolution, because of the energy emitted by the accreting gas flow. The effects of Compton heating and cooling, hydrogen and helium photoionization heating, and bremsstrahlung recycling on the gas flow are investigated by numerical integration of the nonstationary equations of hydrodynamics, in the simplifying assumption of spherical symmetry, and for various values of the accretion efficiency and supernova rates. The resulting evolution is characterized by strong oscillations, in which very fast and energetic bursts from the BH are followed by longer periods during which the X-ray galaxy emission comes from the coronal gas. For a fixed galaxy total mass and structure, the length and the intensity of the bursts depend sensitively on the accretion efficiency and the SN Ia rate. For high efficiency and SN Ia rate values, short and strong bursts are followed by a degassing of the galaxy, with a consequent shut-off of the BH followed by a long period when the mass loss from the stellar population replenishes the galaxy, and after which a new cooling catastrophe another accretion event takes place. In this case, high accretion rates characterize the BH evolution, but the total mass accreted by the BH is very small. For low efficiency and SN Ia rate values, the luminosity evolution is still characterized by strong intermittencies, but the number of global degassing events is considerably reduced, and for very low efficiency values it completely disappears. The remaining instability is then concentrated in the central galactic regions. We also allow for departures from spherical symmetry by examining scenarios in which the central engine is either an advection-dominated accretion flow or a more conventional accretion disk that is optically thick except for a polar region. The general property of highly unstable accretion remains true, with central BHs growing episodically to the mass range 108-109 M☉ (in contrast to ΔMBH 1010-1011 M☉, if feedback is ignored). In all cases the duty cycle (fraction of the time that the system will be seen as an AGN) is quite small and in the range fBH 10-4-2 × 10-3. Thus, for any reasonable value of the efficiency, the presence of a massive BH at the center of a galaxy seems to be incompatible with the presence of a long-lived cooling flow.

Cooling Flows and Quasars: Different Aspects of the Same Phenomenon? I. Concepts

We present a new class of solutions for the gas flows in elliptical galaxies containing massive central black holes (BHs). Modified King model galaxies are assumed. Two source terms operate: mass loss from evolving stars, and a secularly declining heating by supernovae (SNe Ia). Relevant atomic physical processes are modeled in detail. Like the previous models investigated by Ciotti et al., these new models first evolve through three consecutive evolutionary stages: wind, outflow, and inflow. At this point the presence of the BH alters dramatically the subsequent evolution because the energy emitted by the BH can heat the surrounding gas to above virial temperatures, causing the formation of a hot expanding central bubble. Short and strong nuclear bursts of radiation (LBH) are followed by longer periods during which the X-ray galaxy emission comes from the coronal gas (LX). The range and approximate distribution spanned by LX are found to be in accordance with observations of X-ray early-type galaxies. Moreover, although high accretion rates occur during bursting phases when the central BH has a luminosity characteristic of quasars, the total mass accreted is very small when compared to that predicted by stationary cooling-flow solutions and computed masses are in accord with putative BH nuclear masses. In the bursting phases the X-ray gas luminosity is low and the surface brightness profile is very low compared to preburst or to cooling flow models. We propose that these new models, while solving some long-standing problems of the cooling flow scenario, can provide a unified description of QSO-like objects and X-ray-emitting elliptical galaxies, these being the same objects observed at two different evolutionary phases.

Reasoning From Fossils: Learning from the Local Black Hole Population about the Evolution of Quasars

We discuss a simple working scenario for the growth of supermassive black holes (BHs) at the center of spheroidal stellar systems. In particular, we assess the hypotheses that (1) star formation in spheroids and BH fueling are proportional to one another, and (2) the BH accretion luminosity stays near the Eddington limit during luminous quasar phases. With the aid of this simple picture, we are able to interpret many properties of the QSO luminosity function, including the puzzling steep decline of the characteristic luminosity from redshift z ≈ 2 to z = 0: indeed the residual star formation in spheroidal systems is today limited to a small number of bulges, characterized by stellar velocity dispersions a factor of 2-3 smaller than those of the elliptical galaxies hosting QSOs at z 2. A simple consequence of our hypotheses is that the redshift evolution of the QSO emissivity and of the star formation history in spheroids should be roughly parallel. We find this result to be broadly consistent with our knowledge of the evolution of both the global star formation rate and the QSO emissivity, but we identify interesting discrepancies at both low and high redshifts, to which we offer tentative solutions. Our hypotheses allow us to present a robust method to derive the duty cycle of QSO activity, based on the observed QSO luminosity function and the present-day relation between the masses of supermassive BHs and those of their spheroidal host stellar systems. The duty cycle is found to be substantially less than unity, with characteristic values in the range (3-6) × 10-3, and we compute that the average bolometric radiative efficiency is ≈ 0.07. Finally, we find that the growth in mass of individual BHs at high redshift (z 2) can be dominated by mergers and is therefore not necessarily limited by accretion.

Radial orbital anisotropy and the Fundamental Plane of elliptical galaxies

The existence of the Fundamental Plane imposes strong constraints on the structure and dynamics of elliptical galaxies, and thus contains important information on the processes of their formation and evolution. Here we focus on the relations between the Fundamental Plane thinness and tilt and the amount of radial orbital anisotropy: in fact, the problem of the compatibility between the observed thinness of the Fundamental Plane and the wide spread of orbital anisotropy admitted by galaxy models has often been raised. By using N-body simulations of galaxy models characterized by observationally motivated density profiles, and also allowing for the presence of live, massive dark matter haloes, we explore the impact of radial orbital anisotropy and instability on the Fundamental Plane properties. The numerical results confirm a previous semi-analytical finding (based on a different class of one-component galaxy models): the requirement of stability matches almost exactly the thinness of the Fundamental Plane. In other words, galaxy models that are radially anisotropic enough to be found outside the observed Fundamental Plane (with their isotropic parent models lying on the Fundamental Plane) are unstable, and their end-products fall back on the Fundamental Plane itself. We also find that a systematic increase of radial orbit anisotropy with galaxy luminosity cannot explain by itself the whole tilt of the Fundamental Plane, the galaxy models becoming unstable at moderately high luminosities: at variance with the previous case, their end-products are found well outside the Fundamental Plane itself. Some physical implications of these findings are discussed in detail.

Two-body relaxation in modified Newtonian dynamics

A naive extension to modified Newtonian dynamics (MOND) of the standard computation of the two-body relaxation time t 2b implies that t 2b is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MONDs field equation. A non-standard approach to the calculation of t 2b is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case, we find that in the deep-MOND regime t 2b scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Near the centre of a spherical system that is in the deep-MOND regime, we show that the fluctuating component of the gravitational force is never small compared to the mean-field force; this conclusion surprisingly even applies to systems with a density cusp that keeps the mean-field force constant to arbitrarily small radius, and suggests that a cuspy centre can never be in the deep-MOND regime. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two-body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ∼10 M ○. should have spiralled to the centres of dwarf galaxies.

Alignment and morphology of elliptical galaxies: the influence of the cluster tidal field

We investigate two possible effects of the tidal field induced by a spherical cluster on its elliptical galaxy members: the modification of the ellipticity of a spherical galaxy and the isophotal alignment in the cluster radial direction of a misaligned prolate galaxy. Numerical N-body simulations have been performed for radial and circular galactic orbits. The properties of the stars zero--velocity surfaces in the perturbed galaxies are explored briefly, and the adiabaticity of the galaxy to the external field is discussed. For a choice of parameters characteristic of rich clusters we find that the induced ellipticity on a spherical galaxy is below or close to the detectability level. But we find that the tidal torque can result in significant isophotal alignment of the galaxies major axis with the cluster radial direction if the galaxy is outside the cluster core radius. The time required for the alignment is very short compared with the Hubble time. A significant increase in the ellipticity of the outer isophotes of the prolate model is also found, but with no observable isophotal twisting. Our main prediction is an alignment segregation of the elliptical galaxy population according to whether their orbits lie mostly outside or inside the cluster core radius. These results also suggest that galactic alignment in rich clusters is not incompatible with a bottom-up galaxy formation scenario.

The Scaling Relations of Galaxy Clusters and Their Dark Matter Halos

Like early-type galaxies, nearby galaxy clusters also define fundamental plane, luminosity-radius, and luminosity-velocity dispersion relations, whose physical origins are still unclear. By means of high-resolution N-body simulations of massive dark matter halos in a ΛCDM (Λ cold dark matter) cosmology, we find that scaling relations similar to those observed for galaxy clusters are already defined by their dark matter hosts. The slopes, however, are not the same, and among the various possibilities in principle able to bring the simulated and the observed scaling relations into mutual agreement, we show that the preferred solution is a luminosity-dependent mass-to-light ratio (M/L ∝ L~0.3) that corresponds well to what is inferred observationally. We then show that at galactic scales there is a conflict between the cosmological predictions of structure formation, the observed trend of the mass-to-light ratio in elliptical galaxies, and the slope of their luminosity-velocity dispersion relation (which significantly differs from the analogous one followed by clusters). The conclusion is that the scaling laws of elliptical galaxies might be the combined result of the cosmological collapse of density fluctuations at the epoch when galactic scales became nonlinear plus important modifications afterward due to early-time dissipative merging. Finally, we briefly discuss the possible evolution of the cluster scaling relations with redshift.

On the use of X-rays to determine dynamical properties of elliptical galaxies

The extended and X-ray-emitting interstellar medium of early-type galaxies is often used as a tool to determine their total mass M and stellar orbital anisotropy β profiles, based on the hypothesis of hydrostatic equilibrium for the hot gas. Here we investigate the effects that deviations from equilibrium have on M and β estimates, by using simple analytical calculations and hydrodynamical simulations representative of gas-rich galaxies. We show that the deviations of the X-ray-determined β est and M est from the true values are linked by a remarkably simple relation; in particular, M is underestimated if β is overestimated. Also, more radially anisotropic orbital distributions than the true one are deduced in presence of gas infall velocities of the order of the local stellar velocity dispersion (as are likely in the central regions of galactic cooling flows). The results of this analysis are applied to the most thoroughly investigated bright elliptical, NGC 4472. First we show that β est recently derived from X-rays corresponds to a galaxy that is unstable by radial orbit instability. Then, assuming as true β and M the optically derived values, we show that the differences β est - β and M est - M agree with the predictions found here in the case of lack of hydrostatic equilibrium, which points to the latter as a possible explanation for the discrepancies. This analysis casts doubts on the possibility of using X-ray information to determine accurately the dynamical properties of bright X-ray-emitting ellipticals, at least within their R e .

Self‐consistent stellar dynamical tori

We present preliminary results on a new family of distribution functions that are able to generate axisymmetric, truncated (i.e., finite size) stellar dynamical models characterized by toroidal shapes. The relevant distribution functions generalize those that are known to describe polytropic spheres, for which all the dynamical and structural properties of the system can be expressed in explicit form as elementary functions of the system gravitational potential. The model construction is then completed by a numerical study of the associated Poisson equation. We note that our axisymmetric models can also include the presence of an external gravitational field, such as that produced by a massive disk or by a central mass concentration (e.g., a supermassive black hole).

The role of Compton heating in cluster cooling flows

Recent observations by Chandra and XMM‐Newton demonstrate that the central gas in “cooling flow” galaxy clusters has a mass cooling rate that decreases rapidly with decreasing temperature. This contrasts the predictions of a steady state cooling flow model. On the basis of these observational results, the gas can be in a steady state only if a steady temperature dependent heating mechanism is present; alternatively the gas could be in an unsteady state, i.e., heated intermittently. Intermittent heating can be produced by accretion on the supermassive black hole residing in the central cluster galaxy, via Compton heating. This mechanism can be effective provided that the radiation temperature of the emitted spectrum is higher than the gas temperature. Here we explore whether this heating mechanism can be at the origin of the enigmatic behavior of the hot gas in the central regions of “cooling flow” clusters. Although several characteristics of Compton heating appear attractive in this respect, we find that...