Feedback from Central Black Holes in Elliptical Galaxies:
  Two-dimensional Models Compared to One-dimensional Models
  We extend the black hole (BH) feedback models of Ciotti, Ostriker, and Proga
to two dimensions. In this paper, we focus on identifying the differences
between the one-dimensional and two-dimensional hydrodynamical simulations. We
examine a normal, isolated $L_*$ galaxy subject to the cooling flow instability
of gas in the inner regions. Allowance is made for subsequent star formation,
Type Ia and Type II supernovae, radiation pressure, and inflow to the central
BH from mildly rotating galactic gas which is being replenished as a normal
consequence of stellar evolution. The central BH accretes some of the infalling
gas and expels a conical wind with mass, momentum, and energy flux derived from
both observational and theoretical studies. The galaxy is assumed to have low
specific angular momentum in analogy with the existing one-dimensional case in
order to isolate the effect of dimensionality. The code then tracks the
interaction of the outflowing radiation and winds with the galactic gas and
their effects on regulating the accretion. After matching physical modeling to
the extent possible between the one-dimensional and two-dimensional treatments,
we find essentially similar results in terms of BH growth and duty cycle
(fraction of the time above a given fraction of the Eddington luminosity). In
the two-dimensional calculations, the cool shells forming at 0.1--1 kpc from
the center are Rayleigh--Taylor unstable to fragmentation, leading to a
somewhat higher accretion rate, less effective feedback, and a more irregular
pattern of bursting compared to the one-dimensional case.
