I use numerical simulations to understand the connection between black holes and their host galaxies.
Imagine trying to work out the theory of stellar structure with no knowledge of nuclear physics. Remarkably, some progress was made on that project (e.g Eddington MNRAS 77:16 1916), but one can hardly say that one has a complete and coherent theory of stellar structure without a detailed calculation of nuclear energy generation rates given the measured nuclear cross sections. The expressions for energy generation are combined with the equations of mass conservation and hydrostatic equilibrium to produce stellar lifetimes and luminosities that can be compared to observational data.
If one were ignorant of or uninterested in nuclear physics, one might say "Suppose there is some energy generation mechanism relevant in stars that is a power law function of density and temperature. After all, energy generation must be some function of density and temperature, and a power law seems as good a choice as any." One would then try many different values power law indices, make plots of the stellar main sequence as a function of the two parameters, and compare to observations. One may even be able to place some limits on the values the parameters may take.
Would one then rest and say that stars are understood? Absolutely not: the theory is incomplete without a detailed calculation to determine whether the microphysics actually implies that nuclear energy generation takes the form that observations of real stars require.
I am working out the "nuclear physics" of galaxies. I would like to use basic physics to calculate the how the state of gas in a galaxy determines the central black hole (BH) mass accretion rate, and how the BH accretion in turn affects the state of gas in the galaxy.
Sub-resolution models that assume, for example, that a fixed fraction of the luminosity of the BH is converted to thermal energy on a scale of 100 parsecs may be useful for determining the broad contours of the observational requirements, but they can never substitute for a detailed calculation of the implications of the basic physics.
The "nuclear physics" of galaxies is far more complex than the nuclear physics of atoms. In the latter case, one can compute the required energy generation rates using a hypothetical cube of material much smaller than a star, within which the density and temperature is constant. It does not matter whether or not the cube is inside a star, and the material within the cube is homogeneous. Energy is then transported to overlying layers of the star solely by processes that act on timescales much longer than the dynamical time of the star itself.
Nature has not been so kind to physicists with respect to the problem of BHs and galaxies: gas within galaxies is inhomogeneous on all scales of interest. Worse, energy liberated by accretion onto the BH is easily capable of directly affecting the state of gas 1 kiloparsec or more from the center of the galaxy on timescales much shorter than the dynamical timescale of the galaxy. Galactic nuclear physics is both non-local and depends crucially on an enormous range of spatial scales. It is not possible to take advantage of the difference of spatial and temporal scales to decouple energy generation from the response, as is the case with stars. One cannot separate BH fueling from feedback, using the current terminology in the extragalactic literature.
There has for many years been a concerted effort to understand accretion disk physics on sub-parsec scales both analytically and using numerical simulations. This is a necessary ingredient to achieve a full understanding of the growth and evolution of BHs in the universe, but it cannot serve as a complete picture. The gas supplied to BHs comes from much larger radii and the BH is capable of directly affecting the thermodynamic state of the gas—and therefore the fuel supply of the accretion disk—out to many kiloparsecs or more. I see no alternative but to capture within a simulation all of the physical scales over which feedback is occurring at once: we must simulate gas dynamics from galactic scales to at least the edge of the BH accretion disk.
It is important to remember that over their lifetimes, black holes emit of order enough energy to unbind the host galaxy, including the dark matter halo. With such an enormous amount of energy available, BH feedback can in principle solve nearly any problem in astrophysics. Rearranging the mass in a galaxy to change the logarithmic slope of the density profile, or heating up galactic gas to terminate star formation, is no problem at all in principle.
Of course, BHs do not unbind their host galaxies because the vast majority of the photons produced by the BH escape from the galaxy—we do after all observe active galactic nuclei (AGN). Thus the crucial question concerning AGN is coupling: when, where, and how do AGN photons couple to the gas in a galaxy? Simple sub-resolution models of AGN feedback cannot answer this question—only detailed simulations of the actual physics involved can tell us how AGN affect galaxies.
The physics of accretion is exceedingly complex and serves to couple vastly disparate length scales, making the problem rich, difficult and interesting. I have extended the ZEUS hydrodynamics code to implement a physically rich model of AGN feedback and used it to perform high spatial resolution (cell size 0.1 pc near the BH) simulations of BH fueling in galaxies. These simulations resolve both the length scales where the state of the gas begins to be dominated by the BH (the Bondi radius, a few parsecs for gas radiatively heated to the Compton temperature in the simulations) and the length and timescales associated with galaxies and stellar evolution (kiloparsecs and gigayears).
The AGN feedback model includes a wide array of physical processes, and the numerical implementation is focused on being faithful to the underlying physics rather than forcing the model to match any particular observation. One hopes that a dispassionate implementation of the underlying physics will either reproduce all observations, or its discrepancies will point the way to gaps in our understanding (or problems with the observations). What seems clear is that it is difficult to learn about AGN from models that include freely adjustable parameters that ensure that observations are always reproduced.
We already know the basic physical theories that govern the connection between BHs and their host galaxies; the real problem at present is complexity. The emphasis must be on increasing our conceptual understanding of the coupling between galaxies and BHs rather than than simply finding a model that reproduces observations. In order to untangle the complexity it is also essential that our implementation of the connection between galaxies and BHs be firmly rooted in our best understanding of the underlying physics. A model that successfully reproduces observations but is not faithful to the physics cannot be said to have increased our understanding of this complex problem. It is of the highest importance to work toward developing a clear conceptual understanding of how the many physical processes operate to couple BHs and galaxies.
The problem of BH fueling and feedback in galaxies is both physically and computationally complex enough that there is little danger that we will run out of questions for the foreseeable future. As observations, simulations, and our conceptual understanding improve, we can look forward to an ever more subtle understanding of the exquisite links between the small-scale physics of accretion and the large-scale physics of galactic evolution.
J. P. Ostriker
J. R. Primack