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")

.. versionadded:: 1.3.0

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 Larson (1974).
	If ``which == "age"``, the mass of a star in :math:`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]_:

.. math:: \log_{10} \tau = \alpha + \beta \log_{10}(M/M_\odot) +
	\gamma (\log_{10}(M/M_\odot))^2

where :math:`\alpha` = 1 for :math:`\tau` measured in Gyr,
:math:`\beta` = -3.42, and :math:`\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 :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.

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

.. [1] Larson (1974), MNRAS, 166, 585
.. [2] Tinsley (1972), A&A, 20, 383
.. [3] David, Forman & Jones (1990), ApJ, 359, 29
.. [4] Kobayashi (2004), MNRAS, 347, 740