# Formation time-scales for stellar bars in diverse galactic discs

## TL;DR

This paper explores how long it takes for stellar bars to form in galaxies, using simulations to study the effects of disc structure and dark matter haloes.

## Contribution

The study introduces an empirical relation for bar formation time-scales in live haloes and compares bar growth in live versus static haloes.

## Key findings

- Bars form within a Hubble time in Milky Way-like discs if specific stability criteria are met.
- Discs with higher velocity dispersion experience delayed bar growth.
- Bars in static haloes grow at roughly half the rate of those in live haloes.

## Abstract

We study the formation of stellar bars using 145 simulations of disc galaxies embedded in live and static dark matter haloes. We use the exponential bar growth time-scale, \documentclass[12pt]{minimal}
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$\tau _{\rm bar}$\end{document}, to quantify how disc structure and kinematics regulate the onset and rate of secular bar formation. We extend previous work to thicker and more turbulent discs, motivated by those observed at high redshift (\documentclass[12pt]{minimal}
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$z\,\gt\,1$\end{document}). By revisiting several commonly used disc stability criteria – the Efstathiou-Lake-Negroponte parameter (\documentclass[12pt]{minimal}
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$\epsilon _{\rm ELN}$\end{document}), the Ostriker-Peebles ratio (\documentclass[12pt]{minimal}
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$t_{\rm OP}$\end{document}), and the disc stellar mass fraction within 2.2 disc scale radii (\documentclass[12pt]{minimal}
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$f_{\rm disc}$\end{document}) – we find that \documentclass[12pt]{minimal}
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$\tau _{\rm bar}$\end{document}, when expressed in terms of the disc’s orbital period, follows a tight power law with each criteria. In Milky Way-like discs embedded in live haloes, bars form within a Hubble time if \documentclass[12pt]{minimal}
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$f_{\rm disc} \ge 0.18$\end{document}, \documentclass[12pt]{minimal}
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$t_{\rm OP} \ge 0.27$\end{document}, and \documentclass[12pt]{minimal}
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$\epsilon _{\rm ELN} \le 1.44$\end{document}. We show discs with higher velocity dispersion experience delayed bar growth and introduce an empirical relation that correctly describes the bar formation time-scales of all our live halo models. Bars in static haloes grow at roughly half the rate of those in live haloes and require substantially greater disc instability to do so.