vice.yields.ccsne.fractional

Calculate an IMF-integrated fractional net nucleosynthetic yield of a given element from core-collapse supernovae.

Signature: vice.yields.ccsne.fractional(element, study = “LC18”, MoverH = 0, rotation = 0, IMF = “kroupa”, method = “simpson”, m_lower = 0.08, m_upper = 100, tolerance = 1.0e-03, Nmin = 64, Nmax = 2.0e+08)

Parameters

elementstr [case-insensitive]

The symbol of the element to calculate the IMF-integrated fractional yield for.

studystr [case-insensitive] [default“LC18”]

A keyword denoting which study to adopt the yields from

Keywords and their Associated Studies:

• “LC18”: Limongi & Chieffi (2018) 1

• “CL13”: Chieffi & Limongi (2013) 2

• “CL04”: Chieffi & Limongi (2004) 3

• “WW95”: Woosley & Weaver (1995) 4

MoverHreal number [default0]

The total metallicity [M/H] of the exploding stars. There are only a handful of metallicities recognized by each study.

Keywords and their Associated Metallicities:

• “LC18”: [M/H] = -3, -2, -1, 0

• “CL13”: [M/H] = 0

• “CL04”: [M/H] = -inf, -4, -2, -1, -0.37, 0.15

• “WW95”: [M/H] = -inf, -4, -2, -1, 0

rotationreal number [default0]

The rotational velocity of the exploding stars in km/s. There are only a handful of rotational velocities recognized by each study.

Keywords and their Associated Rotational Velocities:

• “LC18”: v = 0, 150, 300

• “CL13”: v = 0, 300

• “CL04”: v = 0

• “WW95”: v = 0

IMFstr [case-insensitive] [default“kroupa”]

The stellar initial mass function (IMF) to assume. Strings denote built-in IMFs, which must be either “Kroupa” 5 or “Salpeter” 6.

methodstr [case-insensitive] [default“simpson”]

The method of quadrature.

Recognized Methods:

• “simpson”

• “trapezoid”

• “midpoint”

• “euler”

Note

These methods of quadrature are implemented according to Chapter 4 of Press, Teukolsky, Vetterling & Flannery (2007) 7.

m_lowerreal number [default0.08]

The lower mass limit on star formation in \(M_\odot\).

m_upperreal number [default100]

The upper mass limit on star formation in \(M_\odot\).

tolerancereal number [default0.001]

The numerical tolerance. VICE will not return a result until the fractional change between two successive integrations is smaller than this value.

Nminreal number [default64]

The minimum number of bins in quadrature.

Nmaxreal number [default2.0e+08]

The maximum number of bins in quadrature. Included as a failsafe against solutions that din’t converge numerically.

Returns

yreal number

The numerically calculated yield.

errorreal number

The estimated numerical error.

Raises

• ValueError

  • The element is not built into VICE

  • The study is not built into VICE

  • The tolerance is not between 0 and 1

  • m_lower > m_upper

  • Custom IMF does not accept exactly 1 positional argument

  • Built-in IMF is not recognized

  • The method of quadrature is not built into VICE

  • Nmin > Nmax

• LookupError

  • The study did not report yields at the specified metallicity

  • The study did not report yields at the specified rotational velocity.

• ScienceWarning

  • m_upper is larger than the largest mass on the grid reported by the specified study. VICE extrapolates to high masses in this case.

  • study is either “CL04” or “CL13” and the atomic number of the element is between 24 and 28 (inclusive). VICE warns against adopting these yields for iron peak elements.

  • Numerical quadrature did not converge within the maximum number of allowed quadrature bins to within the specified tolerance.

Notes

This function evaluates the solution to the following equation.

\[y_x^\text{CC} \frac{ \int_8^u m_x \frac{dN}{dm} dm }{ \int_l^u m_x \frac{dN}{dm} dm }\]

Note

The nucleosynthetic yield tables built into VICE do not include any treatment of radioactive isotopes. The above equation is evaluated directly from the total mass yield of stable isotopes only. In this regard, if any element has a significant contribution to its nucleosynthesis from radioactive decay products, then the values returned from this function should be interpreted as lower bounds rather than estimates of the true nucleosynthetic yield.

Example Code

>>> y, err = vice.yields.ccsne.fractional("o")
>>> y
        0.004859197708207693
>>> err
        5.07267151987336e-06
>>> y, err = vice.yields.ccsne.fractional("mg", study = "CL13")
>>> y
        0.0009939371276697314

1

Limongi & Chieffi (2018), ApJS, 237, 13

2

Chieffi & Limongi (2013), ApJ, 764, 21

3

Chieffi & Limongi (2004), ApJ, 608, 405

4

Woosley & Weaver (1995), ApJ, 101, 181

5

Kroupa (2001), MNRAS, 231, 322

6

Salpeter (1955), ApJ, 121, 161

7

Press, Teukolsky, Vetterling & Flannery (2007), Numerical Recipes, Cambridge University Press