vice.mlr.mm1989¶
Compute either the lifetime or the mass of a dying star according to the mass-lifetime relation of Maeder & Meynet (1989) [1].
Signature: vice.mlr.mm1989(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). Ifwhich == "mass"
, thenqty
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 Maeder & Meynet (1989). Ifwhich == "age"
, the mass of a star in \(M_\odot\) with the specified lifetime in Gyr.
Notes¶
The mass-lifetime relation of Maeder & Meynet (1989) is given by:
for stellar masses below 60 \(M_\odot\). Above this mass, the lifetime is given by:
and in both cases, \(\tau\) is in Gyr.
Though this form was originally published in Maeder & Meynet (1989), 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.
The values of the coefficients \(\alpha\) and \(\beta\) vary with stellar mass according to (\(m = M/M_\odot\)):
Mass Range |
\(\alpha\) |
\(\beta\) |
\(m \leq 1.3\) |
-0.6545 |
1 |
\(1.3 < m \leq 3\) |
-3.7 |
1.35 |
\(3 < m \leq 7\) |
-2.51 |
0.77 |
\(7 < m \leq 15\) |
-1.78 |
0.17 |
\(15 < m \leq 60\) |
-0.86 |
-0.94 |
In calculating stellar masses from ages (i.e. when which == "age"
),
the equation must be solved numerically. For this, VICE makes use of
the bisection root-finding algorithm described in chapter 9 of Press,
Teukolsky, Vetterling & Flannery (2007) [3].
Example Code¶
>>> import vice
>>> vice.mlr.mm1989(1) # the lifetime of the sun
11.0
>>> vice.mlr.mm1989(1, postMS = 0) # main sequence lifetime only
10.0
>>> vice.mlr.mm1989(1, which = "age") # what mass lives 1 Gyr?
2.3775540199279783
>>> vice.mlr.mm1989(2, which = "age") # 2 Gyr?
1.9712891674041746
>>> vice.mlr.mm1989(2, postMS = 0, which = "age") # MS turnoff mass
1.9207444791793824
>>> vice.mlr.mm1989(3)
0.42271148013148074
>>> vice.mlr.mm1989(3, postMS = 0)
0.38428316375589155
>>> vice.mlr.mm1989(3, which = "age")
1.721426746368408