# Observational signatures of the black hole Mass Distribution in the Galactic Center

## TL;DR

This study simulates the star cluster around SgrA* to analyze the black hole mass distribution, its impact on galactic center dynamics, and the potential gravitational wave signals detectable by LISA.

## Contribution

It introduces a detailed simulation framework for the black hole mass function in the Galactic Center and links it to observable signatures and gravitational wave event rates.

## Key findings

- Black hole mass function influences SgrA* growth and dynamics.
- Estimated LISA detection rate of inspiraling stellar-mass black holes is 10^-5 per year.
- Massive initial black hole populations dominate inspiral event rates.

## Abstract

We simulate the star cluster, made of stars in the main sequence and different black hole (BH) remnants, around SgrA* at the center of the Milky Way galaxy. Tracking stellar evolution, we find the BH remnant masses and construct the BH mass function. We sample 4 BH species and consider the impact of the mass-function in the dynamical evolution of system. Starting from an initial 6 dimensional family of parameters and using an MCMC approach, we find the best fits to various parameters of model by directly comparing the results of the simulations after $t = 10.5$ Gyrs with current observations of the stellar surface density, stellar mass profile and the mass of SgrA*. Using these parameters, we study the dynamical evolution of system in detail. We also explore the mass-growth of SgrA* due to tidally disrupted stars and swallowed BHs. We show that the consumed mass is dominated for the BH component with larger initial normalization as given by the BH mass-function. Assuming that about 10% of the tidally disrupted stars contribute in the growth of SgrA* mass, stars make up the second dominant effect in enhancing the mass of SgrA*. We consider the detectability of the GW signal from inspiralling stellar mass BHs around SgrA* with LISA. Computing the fraction of the lifetime of every BH species in the LISA band, with signal to noise ratio $\gtrsim 8$, to their entire lifetime, and rescaling this number with the total number of BHs in the system, we find that the total expected rate of inspirals per Milky-Way sized galaxy per year is $10^{-5}$. Quite interestingly, the rate is dominated for the BH component with larger initial normalization as dictated by the BH mass-function. We interpret it as the second signature of the BH mass-function.