Formation time-scales for stellar bars in diverse galactic discs

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, [Formula: see text], 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 ([Formula: see text]). By revisiting several commonly used disc stability criteria - the Efstathiou-Lake-Negroponte parameter ([Formula: see text]), the Ostriker-Peebles ratio ([Formula: see text]), and the disc stellar mass fraction within 2.2 disc scale radii ([Formula: see text]) - we find that [Formula: see text], 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 [Formula: see text], [Formula: see text], and [Formula: see text]. 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.