Recent studies of the cosmic X-ray background ( XRB ) have suggested the possible existence of a population of relatively faint sources with hard X-ray spectra ; however , the emission mechanism remains unclear .
If the hard X-ray emission is from the radiatively inefficient , advection-dominated accretion flows ( ADAFs ) around massive black holes in galactic nuclei , X-ray luminosity and radio luminosity satisfy the approximate relation L _ { R } \sim 7 \times 10 ^ { 35 } ( \nu / 15 GHz ) ^ { 7 / 5 } ( M / 10 ^ { 7 } M _ { \odot } ) ( L _ { x } / 10 ^ { 40 } erg% ~ { } s ^ { -1 } ) ^ { 1 / 10 } ~ { } erg~ { } s ^ { -1 } where L _ { R } = \nu L _ { \nu } is the radio luminosity at frequency \nu , M is the mass of the accreting black hole , and 10 ^ { 40 } \mathrel { \hbox to 0.0 pt { \raise 2.1973 pt \hbox { $ < $ } } { \lower 2.1973 pt \hbox% { $ \sim$ } } } L _ { x } \mathrel { \hbox to 0.0 pt { \raise 2.1973 pt \hbox { $ < $ } } { \lower 2.197 % 3 pt \hbox { $ \sim$ } } } 10 ^ { 42 } erg~ { } s ^ { -1 } is the 2-10 keV X-ray luminosity .
These sources are characterized by inverted radio spectra I _ { \nu } \propto \nu ^ { 2 / 5 } .
For example , an ADAF X-ray source with luminosity L _ { x } \sim 10 ^ { 41 } erg~ { } s ^ { -1 } has a nuclear radio luminosity of \sim 4 \times 10 ^ { 36 } ( M / 3 \times 10 ^ { 7 } M _ { \odot } ) ~ { } erg~ { } s ^ { -1 } at \sim 20 GHz and if at a distance of \sim 10 ( M / 3 \times 10 ^ { 7 } M _ { \odot } ) ^ { 1 / 2 } ~ { } Mpc would be detected as a \sim 1 mJy point radio source .
High frequency ( \sim 20 GHz ) , high angular resolution radio observations provide an important test of the ADAF emission mechanism .
Since L _ { R } depends strongly on black hole mass and only weakly on X-ray luminosity , the successful measurement of nuclear radio emission could provide an estimate of black hole mass .
Because the X-ray spectra produced by ADAFs are relatively hard , sources of this emission are natural candidates for contributing to the hard , > 2 keV , background .