vice.yields.sneia.fractional
============================

Calculate a delay-time distribution integrated fractional nucleosynthetic
yield of a given element from type Ia supernovae.

**Signature**: vice.yields.sneia.fractional(element, study = "seitenzahl13",
model = "N1", n = 2.2e-03)

Parameters
----------
element : ``str`` [case-insensitive]
	The symbol of the element to calculate the yield for.
study : ``str`` [case-sensitive] [default : "seitenzahl13"]
	A keyword denoting which study to adopt SN Ia mass yields from.

	Keywords and their Associated Studies:

		- "seitenzahl13" : Seitenzahl et al. (2013) [1]_
		- "iwamoto99" : Iwamoto et al. (1999), [2]_
		- "gronow21" : Gronow et al. (2021a, b) [3]_ [4]_

model : ``str`` [case-insensitive] [default : "N1"]
	The model from the associated study to adopt.

	Keywords and their Associated Models:

		- 	"seitenzahl13" : N1, N3, N5, N10, N20, N40, N100H, N100,
				N100L, N150, N200, N300C, N1600, N1600C, N100_Z0.5,
				N100_Z0.1, N100_Z0.01
		- 	"iwamoto99" : W7, W70, WDD1, WDD2, WDD3, CDD1, CDD2
		- 	| "gronow21" : M08_03_001, M08_03_01, M08_03_1, M08_03_3,
			| 	M08_05_001, M08_05_01, M08_05_1, M08_05_3,
			| 	M08_10_001, M08_10_01, M08_10_1, M08_10_3,
			| 	M09_03_001, M09_03_01, M09_03_1, M09_03_3,
			| 	M09_05_001, M09_05_01, M09_05_1, M09_05_3,
			| 	M09_10_001, M09_10_01, M09_10_1, M09_10_3,
			| 	M10_02_001, M10_02_01, M10_02_1, M10_02_3,
			| 	M10_03_001, M10_03_01, M10_03_1, M10_03_3,
			| 	M10_05_001, M10_05_01, M10_05_1, M10_05_3,
			| 	M10_10_001, M10_10_01, M10_10_1, M10_10_3,
			| 	M11_05_001, M11_05_01, M11_05_1, M11_05_3

n : real number [default : 2.2e-03]
	The average number of type Ia supernovae produced per unit stellar
	mass formed :math:`N_\text{Ia}/M_\star` in :math:`M_\odot^{-1}`.

	.. note:: The default value for this parameter is adopted from
		Maoz & Mannucci (2012) [5]_.

Returns
-------
y : real number
	The delay-time distribution integrated yield. This quantity represents
	the mass of some element produced over all SN Ia associated with a
	given stellar population in units of that stellar population's mass.
	This quantity is thus unitless (:math:`M_\odot` per :math:`M_\odot`).

.. note:: Unlike vice.yields.ccsne.fractional, there is no associated
	numerical error with this function, because the solution is analytic.

Raises
------
* ValueError
	- 	The element is not built into VICE.
	- 	The study is not built into VICE.
	- 	n < 0
* LookupError
	- 	The model is not recognized for the given study.
* IOError [Occurs only if VICE's file structure has been modified]
	- 	The parameters passed to this function are allowed but the data
		file is not found.

Notes
-----
This function evaluates the solution to the following equation:

.. math:: y_x^\text{Ia} = \left(\frac{N_\text{Ia}}{M_\star}\right)M_x

where :math:`M_x` is the value returned by vice.yields.sneia.single, and
:math:`N_\text{Ia}/M_\star` is specified by the parameter ``n``.

The data stored in this module are reported for each corresponding study
*as published*. The Seitenzahl et al. (2013) and Gronow et al. (2021a, b)
models reported mass yields after complete decay of all radioactive
nuclides with half-lives less than 2 Gyr, and the Iwamoto et al. (1999)
study fully decayed *all* unstable isotopes; any additional treatment for
radioactive isotopes is thus unnecessary.

The Gronow et al. (2021a, b) models are named for the mass of the
carbon-oxygen core, the mass of the helium shell, and the metallicity of
the progenitor relative to solar, in that order.
For example, the "M09_05_01" model refers to one with a 0.9 :math:`M_\odot`
carbon-oxygen core and a 0.05 :math:`M_\odot` helium shell produced by a
star that was initially at a metallicity of 0.1 :math:`Z_\odot`.

Example Code
------------
>>> import vice
>>> vice.yields.sneia.fractional("fe")
0.0025825957080000002
>>> vice.yields.sneia.fractional("fe", study = "iwamoto99", model = "W70")
0.001705352
>>> vice.yields.sneia.fractional("fe", study = "iwamoto99", model = "CDD1")
0.0014255185999999997
>>> vice.yields.sneia.fractional("ni", model = "n100l")
8.610998000011574e-05
>>> vice.yields.sneia.fractional("ni", model = "N150")
0.00016497607368
>>> vice.yields.sneia.fractional("co", study = "gronow21",
	model = "M10_10_1")
2.3276e-06
>>> vice.yields.sneia.fractional("co", study = "gronow21",
	model = "M09_05_001")
3.4584000000000003e-07

.. seealso::

	- vice.yields.sneia.single
	- vice.yields.sneia.gronow21
	- vice.yields.sneia.iwamoto99
	- vice.yields.sneia.seitenzahl13

.. [1] Seitenzahl et al. (2013), MNRAS, 429, 1156
.. [2] Iwamoto et al. (1999), ApJ, 124, 439
.. [3] Gronow et al. (2021a), A&A, 649, 155
.. [4] Gronow et al. (2021b), arxiv:2103.14050
.. [5] Maoz & Mannucci (2012), PASA, 29, 447