# The lifetime of binary black holes in S\'ersic galaxy models

## TL;DR

This study estimates the upper limits on the lifetime of binary black holes in galaxies with different stellar profiles, highlighting how galaxy structure influences merger timescales relevant for gravitational wave detection.

## Contribution

It introduces a method to constrain binary black hole lifetimes using galaxy stellar profiles and local scaling relations, focusing on the transition to gravitational wave-driven inspiral.

## Key findings

- Binary black hole lifetimes vary from less than 1 Gyr to over 10 Gyr.
- Different stellar density profiles lead to distinct lifetime predictions.
- Uncertainties in observed correlations significantly affect lifetime estimates.

## Abstract

In the local universe, black holes of $10^{5-6}$ M$_{\odot}$ are hosted in galaxies displaying a variety of stellar profiles and morphologies. These black holes are the anticipated targets of LISA, the Laser Interferometer Space Antenna that will detect the low-frequency gravitational-wave signal emitted by binary black holes in this mass interval. In this paper, we infer upper limits on the lifetime of binary black holes of $10^{5-6}$ M$_{\odot}$ and up to $10^8$ M$_{\odot}$, forming in galaxy mergers, exploring two underlying stellar density profiles, by Dehnen and by Prugniel & Simien, and by exploiting local scaling relations between the mass of the black holes and several quantities of their hosts. We focus on the phase of the dynamical evolution when the binary is transitioning from the hardening phase ruled by the interaction with single stars to the phase driven by the emission of gravitational waves. We find that different stellar profiles predict very distinct trends with binary mass, with lifetimes ranging between fractions of a Gyr to more than 10 Gyr, and with a spread of about one order of magnitude, given by the uncertainties in the observed correlations, which are larger in the low-mass tail of the observed black hole population.