vice.mlr.pm1993

Compute either the lifetime or the mass of a dying star according to the mass-lifetime relation of Padovani & Matteucci (1993) [1].

Signature: vice.mlr.pm1993(qty, postMS = 0.1, which = “mass”)

New in version 1.3.0.

Note

This parameterization of the mass-lifetime relation predicts the lives of solar mass stars to be shorter than most other forms (~7.8 Gyr compared to ~10 Gyr).

Parameters

qtyfloat

Either the mass of a star in \(M_\odot\) or the age of a stellar population in Gyr. Interpretion set by the keyword argument which.

postMSfloat [default0.1]

The ratio of a star’s post main sequence lifetime to its main sequence lifetime. Zero to compute the main sequence lifetime alone, or the main sequence turnoff mass when which == "age".

whichstr [case-insensitive] [default“mass”]

The interpretation of qty: either "mass" or "age" (case-insensitive). If which == "mass", then qty represents a stellar mass in \(M_\odot\) and this function will compute a lifetime in Gyr. Otherwise, qty represents the age of a stellar population and the mass of a star with the specified lifetime will be calculated.

Returns

xfloat

If which == "mass", the lifetime of a star of that mass and metallicity in Gyr according to Padovani & Matteucci (1993). If which == "age", the mass of a star in \(M_\odot\) with the specified lifetime in Gyr.

Notes

Padovani & Matteucci (1993) parameterize the mass-lifetime relation according to:

\[\log_{10}\tau = \frac{\alpha - \sqrt{ \beta - \gamma(\eta - \log_{10}(M/M_\odot)) }}{\mu}\]

for stellar masses below 6.6 \(M_\odot\) with \(\tau\) in Gyr, and

\[\tau = 1.2(M/M_\odot)^{-1.85} + 0.003\text{ Gyr}\]

for masses above 6.6 \(M_\odot\). Below 0.6 \(M_\odot\), the lifetime flattens off at 160 Gyr. The coefficients \(\alpha\), \(\beta\), \(\gamma\), \(\eta\), and \(\mu\) are given below:

\(\alpha\)

0.334

\(\beta\)

1.790

\(\gamma\)

0.2232

\(\eta\)

7.764

\(\mu\)

0.1116

Though this form was originally published in Padovani & Matteucci (1993), in detail the form here is taken from Romano et al. (2005) [2].

The timescale \(\tau\) quantifies only the main sequence lifetime of stars; the parameter postMS specifies the length of the post main sequence lifetime. This parameterization neglects the metallicity dependence of the mass-lifetime relation.

Example Code

>>> import vice
>>> vice.mlr.pm1993(1) # the lifetime of the sun
7.825388414293052
>>> vice.mlr.pm1993(1, postMS = 0) # main sequence lifetime only
7.113989467539137
>>> vice.mlr.pm1993(1, which = "age") # what mass lives 1 Gyr?
1.8113833345909132
>>> vice.mlr.pm1993(2, which = "age") # 2 Gyr?
1.4492132883063318
>>> vice.mlr.pm1993(2, postMS = 0, which = "age") # MS turnoff mass
1.4079983006192527
>>> vice.mlr.pm1993(3)
0.2571838372046172
>>> vice.mlr.pm1993(3, postMS = 0)
0.23380348836783377
>>> vice.mlr.pm1993(3, which = "age")
1.285731894196999