For small values of the dimensionless viscosity parameter , namely \alpha \lesssim 0.1 , the dynamics of non-radiating accretion flows is dominated by convection ; convection strongly suppresses the accretion of matter onto the central object and transports a luminosity \sim 10 ^ { -3 } -10 ^ { -2 } \dot { M } c ^ { 2 } from small to large radii in the flow .
A fraction of this convective luminosity is likely to be radiated at large radii via thermal bremsstrahlung emission .
We show that this leads to a correlation between the frequency of maximal bremsstrahlung emission and the luminosity of the source , \nu _ { peak } \propto L ^ { 2 / 3 } .
Accreting black holes with X-ray luminosities 10 ^ { -4 } L _ { Edd } \gtrsim L _ { X } ( 0.5 - 10 { keV } ) \gtrsim 10 ^ { -7 } L _ { Edd } are expected to have hard X-ray spectra , with photon indices \Gamma \sim 2 , and sources with L _ { X } \lesssim 10 ^ { -9 } L _ { Edd } are expected to have soft spectra , with \Gamma \sim 3.5 .
This is testable with Chandra and XMM .