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). 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 Padovani & Matteucci (1993). Ifwhich == "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:
for stellar masses below 6.6 \(M_\odot\) with \(\tau\) in Gyr, and
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