vice.mlr.larson1974

Compute either the lifetime or the mass of a dying star according to the mass-lifetime relation of Larson (1974) [1].

Signature: vice.mlr.larson1974(qty, postMS = 0.1, which = “mass”)

New in version 1.3.0.

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 Larson (1974). If which == "age", the mass of a star in \(M_\odot\) with the specified lifetime in Gyr.

Notes

Larson (1974) present the following fit to the compilation of evolutionary lifetimes presented in Tinsley (1972) [2]:

\[\log_{10} \tau = \alpha + \beta \log_{10}(M/M_\odot) + \gamma (\log_{10}(M/M_\odot))^2\]

where \(\alpha\) = 1 for \(\tau\) measured in Gyr, \(\beta\) = -3.42, and \(\gamma\) = 0.88. Though this form was originally presented in Larson (1974), the values of the coefficients were taken from David, Forman & Jones (1990) [3] and Kobayashi (2004) [4].

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.

In solving the inverse function (i.e. mass as a function of lifetime), the solution proceeds analytically according to the quadratic formula where subtraction is chosen in the numerator over addition as this is the physical solution.

Example Code

>>> import vice
>>> vice.mlr.larson1974(1) # the lifetime of the sun
11.0
>>> vice.mlr.larson1974(1, postMS = 0) # main sequence lifetime only
10.0
>>> vice.mlr.larson1974(1, which = "age") # what mass lives 1 Gyr?
2.1529829084164525
>>> vice.mlr.larson1974(2, which = "age") # 2 Gyr?
1.698651828235309
>>> vice.mlr.larson1974(2, postMS = 0, which = "age") # MS lifetime only
1.6460010348842196
>>> vice.mlr.larson1974(3)
0.40734775084938435
>>> vice.mlr.larson1974(3, postMS = 0)
0.3703161371358039
>>> vice.mlr.larson1974(3, which = "age")
1.4882047037330677