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")

.. versionadded:: 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
----------
qty : float
	Either the mass of a star in :math:`M_\odot` or the age of a
	stellar population in Gyr. Interpretion set by the keyword
	argument ``which``.
postMS : float [default : 0.1]
	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"``.
which : str [case-insensitive] [default : "mass"]
	The interpretation of ``qty``: either ``"mass"`` or ``"age"``
	(case-insensitive). If ``which == "mass"``, then ``qty`` represents
	a stellar mass in :math:`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
-------
x : float
	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 :math:`M_\odot` with
	the specified lifetime in Gyr.

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

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

for stellar masses below 6.6 :math:`M_\odot` with :math:`\tau` in
Gyr, and

.. math:: \tau = 1.2(M/M_\odot)^{-1.85} + 0.003\text{ Gyr}

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

+------------------+----------+
| :math:`\alpha`   | 0.334    |
+------------------+----------+
| :math:`\beta`    | 1.790    |
+------------------+----------+
| :math:`\gamma`   | 0.2232   |
+------------------+----------+
| :math:`\eta`     | 7.764    |
+------------------+----------+
| :math:`\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 :math:`\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

.. [1] Padovani & Matteucci (1993), ApJ, 416, 26
.. [2] Romano et al. (2005), A&A, 430, 491