We have conducted an image analysis of the ( current ) full sample of 44 spiral galaxies with directly measured supermassive black hole ( SMBH ) masses , M _ { BH } , to determine each galaxy ’ s logarithmic spiral arm pitch angle , \phi .
For predicting black hole masses , we have derived the relation : \log ( { M _ { BH } / { M _ { \sun } } } ) = ( 7.01 \pm 0.07 ) - ( 0.171 \pm 0.017 ) \left [ | \phi| - % 15 \degr \right ] .
The total root mean square scatter associated with this relation is 0.43 dex in the \log { M _ { BH } } direction , with an intrinsic scatter of 0.33 \pm 0.08 dex .
The M _ { BH } – \phi relation is therefore at least as accurate at predicting SMBH masses in spiral galaxies as the other known relations .
By definition , the existence of an M _ { BH } – \phi relation demands that the SMBH mass must correlate with the galaxy discs in some manner .
Moreover , with the majority of our sample ( 37 of 44 ) classified in the literature as having a pseudobulge morphology , we additionally reveal that the SMBH mass correlates with the large-scale spiral pattern and thus the discs of galaxies hosting pseudobulges .
Furthermore , given that the M _ { BH } – \phi relation is capable of estimating black hole masses in bulge-less spiral galaxies , it therefore has great promise for predicting which galaxies may harbour intermediate-mass black holes ( IMBHs , M _ { BH } < 10 ^ { 5 } { M _ { \sun } } ) .
Extrapolating from the current relation , we predict that galaxies with | \phi| \geq 26 \fdg 7 should possess IMBHs .