# The mass function of nearby black hole candidates

## TL;DR

This paper derives a volume-limited mass function of nearby supermassive black hole candidates using 2MASS data, revealing a curved distribution that informs models of ultra high energy cosmic ray sources.

## Contribution

It provides the first comprehensive, volume-limited black hole mass function for the local universe, based on a large catalog and correlation with galaxy bulges.

## Key findings

- Mass function is curved, with a power-law index of -3 above 10^8 M_sun.
- Number of black holes with M_BH > 10^7 M_sun within z<0.025 is about 24,000.
- Distribution supports models linking black holes to ultra high energy cosmic rays.

## Abstract

The mass function of super-massive black holes in our cosmic neighborhood is required to understand the statistics of their activity and consequently the origin of the ultra high energy particles. We determine a mass function of black hole candidates from the entire sky except for the Galactic plane. Using the 2MASS catalogue as a starting point, and the well established correlation between black hole mass and the bulge of old population of stars, we derive a list of nearby black hole candidates within the redshift range z < 0.025, then do a further selection based on the Hubble-type, and give this as a catalogue elsewhere. The final list of black hole candidates above a mass of M_BH > 3*10^{6} M_sol has 5,829 entries; moreover doing a further Hubble type correction to account for the selection effects cuts down the number to 2,919 black hole candidates. We also correct for volume, so that this mass function is a volume limited distribution to redshift 0.025 The differential mass function of nearby black hole candidates is a curved function, with a straight simple power-law of index -3 above 10^{8} M_sol, growing progressively flatter towards lower masses, turning off towards a gap below 3*10^{6} M_sol, and then extending into the range where nuclear star clusters replace black holes. The shape of this mass function can be explained in a simple merger picture. Integrating this mass function over the redshift range, from which it has been derived, gives a total number of black holes with z < 0.025, and M_BH > 10^{7} M_sol of about 2.4*10^{4}, or, if we just average uniformly, 0.6 for every square degree on the sky. In different models many of these are candidates for ultra high energy particles sources. If a very small fraction of the super-massive black holes produces ultra high energy cosmic rays, this should be enough to observe the highly inhomogeneous distribution of the galaxies.