We present new accurate near-infrared ( NIR ) spheroid ( bulge ) structural parameters obtained by two-dimensional image analysis for all galaxies with a direct black hole ( \mathrm { BH } ) mass determination .
As expected , NIR bulge luminosities L _ { \mathrm { bul } } and \mathrm { BH } masses are tightly correlated , and if we consider only those galaxies with secure \mathrm { BH } mass measurement and accurate L _ { \mathrm { bul } } ( 27 objects ) , the spread of M _ { \mathrm { BH } } - L _ { \mathrm { bul } } is similar to M _ { \mathrm { BH } } - \sigma _ { e } , where \sigma _ { e } is the effective stellar velocity dispersion .
We find an intrinsic rms scatter of \simeq 0.3 dex in log M _ { \mathrm { BH } } .
By combining the bulge effective radii R _ { e } measured in our analysis with \sigma _ { e } , we find a tight linear correlation ( rms \simeq 0.25 dex ) between M _ { \mathrm { BH } } and the virial bulge mass ( \propto R _ { e } \sigma _ { e } ^ { 2 } ) , with \langle M _ { \mathrm { BH } } / M _ { \mathrm { bul } } \rangle \sim 0.002 .
A partial correlation analysis shows that M _ { \mathrm { BH } } depends on both \sigma _ { e } and R _ { e } , and that both variables are necessary to drive the correlations between M _ { \mathrm { BH } } and other bulge properties .