We consider the X-ray emission due to bremsstrahlung processes from hot, low
radiative-efficiency accretion flows around supermassive and galactic black
holes. We calculate surface brightness profiles and Michelson visibility
functions for a range of density profiles, rho ~ r^(-3/2+p), with 0 < p < 1, to
allow for the presence of outflows. We find that although the 1 keV emitting
region in these flows can always extend up to 10^6 Schwarzschild radii (R_S),
their surface brightness profiles and visibility functions are strongly
affected by the specific density profile. The advection-dominated solutions
with no outflows (p=0) lead to centrally peaked profiles with characteristic
sizes of only a few tens of R_S. Solutions with strong outflows (p~1) lead to
flat intensity profiles with significantly larger characteristic sizes of up to
10^6 R_S. This implies that low luminosity galactic nuclei, such as M87, may
appear as extended X-ray sources when observed with current X-ray imaging
instruments. We show that X-ray brightness profiles and their associated
visibility functions may be powerful probes for determining the relevant mode
of accretion and, in turn, the properties of hot accretion flows. We discuss
the implications of our results for observations with the Chandra X-ray
Observatory and the planned X-ray interferometer MAXIM.Comment: 14 pages, 4 figures, accepted by The Astrophysical Journal, minor
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