A double power-law fit to the computed stellar $\log(\tau/{\rm y})$-$\log(m/m_\odot)$ relation

Abstract

The computed $\log(\tau/{\rm y})$-$\log(m/m_\odot)$ relation for the stellar initial mass range, 0.6-120.0, and the stellar initial metallicity range, 0.0004-0.0500, tabulated in an earlier attempt (Portinari et al. 1998) is fitted to a good extent by a four-parameter curve, expressed by a double power-law, for assigned stellar initial metallicity, which can be reduced to a three-parameter curve, expressed by a single power-law, for the whole set of stellar initial metallicities. The relative errors do not exceed about 2% and 4%, respectively. The extent to which the interpolation curve, expressed by a single power-law, can be extrapolated towards both high-mass and low-mass stars, is also investigated. High-mass star lifetimes are understimated by a factor less than 2 up to $m/m_\odot= 1000$ and by a fiducial factor less than 4 up to infinite. Low-mass star lifetimes are overstimated by a factor of about 3 down to $m/m_\odot=0.25$ and by an unacceptably large factor down to $m/m_\odot=0.08$. As a simple application, the star mass fraction of a single star generation with stellar initial mass function defined by a power-law, is plotted vs. the logarithmic stellar lifetime. The star mass fraction declines in time at a decreasing rate for mild stellar initial mass function and at an increasing rate for steep stellar initial mass function, where a linear trend is exhibited for a value of the exponent close to the Salpeter's value, equal to -2.35.