Dt. Woods et al., X-RAY-HEATED CORONAE AND WINDS FROM ACCRETION DISKS - TIME-DEPENDENT 2-DIMENSIONAL HYDRODYNAMICS WITH ADAPTIVE MESH REFINEMENT, The Astrophysical journal, 461(2), 1996, pp. 767-804
We perform for the first time time-dependent, two-dimensional, axisymm
etric hydrodynamic simulations using local adaptive mesh refinement of
thermally driven rotating winds from X-ray-irradiated accretion disks
. The disk is assumed to flare in height with radius allowing direct e
xposure from the central X-ray source. The heating and cooling are tre
ated strictly in the optically thin approximation. We adopt two spectr
a characteristic of active galactic nuclei (AGNs) which have Compton t
emperatures of T-IC approximate to 1.3 x 10(7) K and 10(8) K. We have
computed a number of models which cover a large range in luminosity (0
.002 less than or equal to L/L(Eddington) less than or equal to 1) and
radius (less than or similar to 20 Compton radii). Our models enable
us to extend and improve on the analytic predictions of Begelman, McKe
e, & Shields (BMS) for Compton-heated winds by including non-Compton p
rocesses such as photoionization heating and line cooling, typical of
X-ray-heated winds. These non-Compton processes can be dominant at low
temperatures (less than or similar to 10(7) K), thus being important
in the wind regions of AGNs. Our results agree well with a number of p
redictions given by EMS, even when non-Compton processes dominate, sug
gesting that their analytic approximations of the hydrodynamics of dis
k winds are applicable to the more general area of X-ray-heated winds.
In the regime in which Compton processes dominate (i.e., T-IC = 10(8)
K spectrum), we have used our results to improve the analytic predict
ions of BMS, providing a new expression for the mass-loss rate and a m
odified view of the wind solution topology. We find that beginning fro
m a basically static state, the time-dependent flow which develops eve
ntually settles into a steady wind, without any evidence of hydrodynam
ic instabilities. The solution topology consists of a corona with an e
xponentially truncated wind at small radii, and a vigorous wind at lar
ge radii which can be impeded by gravity for small luminosities. We ha
ve constructed radius-luminosity parameter space plots of our numerica
l results in analogy to EMS for both the high and low T-IC, cases, dep
icting the range of solutions. The plots are strikingly similar to the
analytic predictions, especially for high T-IC. We find the radial ex
tent of the corona to be independent of luminosity, as predicted by BM
S, extending out to about 0.25R(IC); this is a direct consequence of C
ompton heating. The transition from an isothermal to nonisothermal cor
ona occurs at a luminosity within about a factor of 2 of the critical
luminosity (L(cr) approximate to 0.03T(IC8)(-1/2)L(E)) predicted by BM
S. The mass flux density in the corona shows an exponential rise, peak
ing at around 0.2R(IC) nearly independent of luminosity. The wind solu
tions can be characterized mainly by steadily heated, free winds (regi
on B in BMS) and gravity-inhibited winds (region C in BMS). Nearly iso
thermal winds with temperatures of the order T-IC also exist (region A
in BMS) but require higher luminosities than was first estimated by B
MS. A necessary condition for the winds to approach isothermality is t
hat the luminosity exceed the critical luminosity. The change in wind
solutions from regions B and C is characterized by a nearly discontinu
ous change in the sonic point location from large heights in region C
to small heights in region B. The mass-loss rate, however, appears con
tinuous across this boundary. For a streamline leaving the disk surfac
e at a radius R(0), the sonic point distance along the streamline, s(s
onic), is such that s(sonic)/R(0) approximate to 0.6 in region B and s
(sonic)/R(0) much greater than 1 in region C. An unexpected conclusion
from our numerical results is that the area of a flow tube can actual
ly be smaller at the sonic point than at the disk surface. This is bec
ause of the presence of an unbalanced radial pressure gradient of the
flow at low heights upon being heated. Incorporating this effect into
the simple analytical formulae for the mass-loss rate given by EMS yie
lds results which are typically within about a factor of 2 (3) of our
numerical results over a wide range of luminosities and radii for the
high (low) Compton temperature models. We provide fitting formulae of
our numerical results which give the mass flux density as a function o
f radius and luminosity. We also discuss briefly the implications of o
ur results for the prediction of Fe K alpha lines which have recently
been observed in AGNs.