# Fitting formulae for evolution tracks of massive stars under extreme metal poor environments for population synthesis calculations and star cluster simulations

## TL;DR

This paper presents new fitting formulae for the evolution of massive stars in extremely metal-poor environments, enabling improved population synthesis and star cluster simulations, especially for binary black hole formation.

## Contribution

The authors developed and validated fitting formulae for massive EMP star evolution, including phases like blue supergiants and blue loops, compatible with popular simulation codes.

## Key findings

- Fitting formulae accurately reproduce stellar evolution models.
- Formulae include phases like blue supergiants and blue loops.
- Applicable to population synthesis and star cluster simulations.

## Abstract

We have devised fitting formulae for evolution tracks of massive stars with $8 \lesssim M/M_\odot \lesssim 160$ under extreme metal poor (EMP) environments for $\log (Z/Z_\odot) = -2, -4, -5, -6$, and $-8$, where $M_\odot$ and $Z_\odot$ are the solar mass and metallicity, respectively. Our fitting formulae are based on reference stellar models which we have newly obtained by simulating the time evolutions of EMP stars. Our fitting formulae take into account stars ending with blue supergiant (BSG) stars, and stars skipping Hertzsprung gap (HG) phases and blue loops, which are characteristics of massive EMP stars. In our fitting formulae, stars may remain BSG stars when they finish their core Helium burning (CHeB) phases. Our fitting formulae are in good agreement with our stellar evolution models. We can use these fitting formulae on the SSE, BSE, NBODY4, and NBODY6 codes, which are widely used for population synthesis calculations and star cluster simulations. These fitting formulae should be useful to make theoretical templates of binary black holes formed under EMP environments.