vice.yields.ccsne.fractional

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

Signature: vice.yields.ccsne.fractional(element, study = “LC18”, MoverH = 0, rotation = 0, explodability = None, wind = True, net = True, IMF = “kroupa”, method = “simpson”, m_lower = 0.08, m_upper = 100, tolerance = 1e-3, 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]

  • “S16/W18”: Sukhbold et al. (2016) [2] (W18 explosion engine)

  • “S16/W18F”: Sukhbold et al. (2016) (W18 engine, forced explosions)

  • “S16/N20”: Sukhbold et al. (2016) (N20 explosion engine)

  • “CL13”: Chieffi & Limongi (2013) [3]

  • “NKT13”: Nomoto, Kobayashi & Tominaga (2013) [4]

  • “CL04”: Chieffi & Limongi (2004) [5]

  • “WW95”: Woosley & Weaver (1995) [6]

Note

The S16/W18F yields force a supernova explosion in the progenitors which otherwise did not explode in the S16/W18 set, producing a yield sample for which all progenitors explode. This allows new black hole landscapes to be used in computing yields under similar explosion physics; the IMF-averaged S16/W18 yields are similar to what is computed with the S16/W18F yields and S16/W18 explodability function (see below). For details on the forced explosion models, see discussion in Griffith et al. (2021) [7].

MoverHreal number [default0]

The total metallicity [M/H] = \(\log_{10}(Z/Z_\odot)\) 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

  • “S16/*”: [M/H] = 0

  • “CL13”: [M/H] = 0

  • “NKT13”: [M/H] = -inf, -1.15, -0.54, -0.24, 0.15, 0.55

  • “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

  • “S16/*”: v = 0

  • “CL13”: v = 0, 300

  • “NKT13”: v = 0

  • “CL04”: v = 0

  • “WW95”: v = 0

explodability<function> or None [defaultNone]

Stellar explodability as a function of mass. This function is expected to take stellar mass in \(M_\odot\) as the only numberical parameter, and to return a number between 0 and 1 denoting the fraction of stars at that mass which explode as a CCSN.

New in version 1.2.0.

Tip

The vice.yields.ccsne.engines module provides a number of popular mathematical forms for the black hole landscape, both simple and complex.

Note

Explodability criteria will be overspecified when calculating yields from the Limongi & Chieffi (2018) study, in which stars above 25 \(M_\odot\) were not forced to explode. The same applies to the W18 and N20 yield sets from the Sukhbold et al. (2016) study, for which the reported yields already reflect the more complicated black hole landscape predicted by the explosion engine.

windbool [defaultTrue]

If True, the stellar wind contribution to the yield will be included in the yield calculation. If False, the calculation will run considering only the supernova explosion yield.

New in version 1.2.0.

Note

Wind and explosive yields are only separated for the Limongi & Chieffi (2018) and Sukhbold et al. (2016) studies. Wind yields are not separable from explosive yields or are not included for other studies supported by this function.

netbool [defaultTrue]

If True, the initial abundance of each simulated CCSN progenitor star will be subtracted from the gross yield to convert the reported value to a net yield.

New in version 1.2.0.

Note

Net yields cannot be calculated for the Woosley & Weaver (1995) study as they do not report birth abundances. Conversely, gross yields cannot be calculated for the Nomoto, Kobayashi & Tominaga (2013) study, because their data is already reported as net yields for each individual progenitor.

IMFstr [case-insensitive] or <function> [default“kroupa”]

The stellar initial mass function (IMF) to assume. Strings denote built-in IMFs, which must be either “Kroupa” [8] or “Salpeter” [9]. Functions must accept stellar mass in \(M_\odot\) as the only numerical paraneter and will be interpreted as a custom, arbitrary stellar IMF.

New in version 1.2.0: Prior to version 1.2.0, only the built-in Kroupa and Salpeter IMFs were supported.

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) [10].

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 don’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.

      The upper mass limits of each study:

      • Limongi & Chiefii (2018) : 120 \(M_\odot\)

      • Sukhbold et al (2016) : 120 \(M_\odot\)

      • Nomoto, Kobayash & Tominaga (2013) : 40 \(M_\odot\)

      • Chieffi & Limongi (2013) : 120 \(M_\odot\)

      • Chieffi & Limongi (2004) : 35 \(M_\odot\)

      • Woosley & Weaver (1995) : 40 \(M_\odot\)

    • 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.

    • explodability is not None and study == "LC18", "S16/N20", "S16/W18". The mass yields these studies report are already under a given model for the black hole landscape.

    • wind = False and study is anything other than LC18 or S16. These are the only studies for which wind yields were reported separate from explosive yields.

    • net == True and study == "WW95". The Woosley & Weaver (1995) study did not report a detailed initial composition of their model CCSN progenitors; VICE can only calculate gross yields in this instance.

    • net == False and study == NKT13. The Nomoto, Kobayashi & Tominaga (2013) study reported net yields in their model core collapse supernova ejeta. VICE can only calculate net yields in this instance.

Notes

This function evaluates the solution to the following equation:

\[y_x^\text{CC} = \frac{ \int_8^u (E(m)m_x + w_x - Z_{x,\text{prog}}(m - m_\text{rem}(m))) \frac{dN}{dm} dm }{ \int_l^u m \frac{dN}{dm} dm }\]

where \(E(m)\) is the stellar explodability for progenitors of initial mass \(m\), \(m_x\) is the mass of the element \(x\) produced in the explosion, \(w_x\) is the mass of the element \(x\) ejected in the wind, \(dN/dm\) is the assumed stellar IMF, \(m_\text{rem}\) is the mass of the remnant left behind by a star of initial mass \(m\), and \(Z_{x,\text{prog}}\) is the abundance by mass of the element \(x\) in the CCSN progenitor stars, whose values are stored in VICE’s internal data. If the keyword arg net = False, \(Z_{x,\text{prog}}\) is simply set to zero to calculate a gross yield. Remnant masses are computed according to the parametrization in Weinberg, Andrews & Freudenburg (2017 [11]; based on Kalirai et al. 2008 [12]) where \(m \geq 8 M_\odot\) stars leave behind a 1.44 \(M_\odot\) remnant. Although there is debate surrounding the details of the initial-final remnant mass relation, Weinberg, Andrews & Freudenburg (2017) demonstrate that the details of how stellar envelopes are returned to the ISM is a small correction in chemical evolution models, indicating that these effects should not significantly impact conclusions.

If a study does not report wind yields, or doesn’t separate them from the explosive yields (i.e. anything other than LC18 or S16/* yield sets), then \(w_x\) = 0 everywhere by definition. In these cases, VICE weights the term correcting for the birth abundance \(Z_{x,\text{prog}}m\) by the explodability \(E(m)\) for net yield calculations. Because high mass stars tend to return their birth abundance with the wind yield (see discussion in Griffith et al. 2021), \(w_x\) = 0 is unrealistic in these cases. Weighting \(Z_{x,\text{prog}}m\) by \(E(m)\) prevents this function from returning very negative net yields in this scenario, approximately correcting for the neglected return of the birth abundance in the wind. For gross yield calculations, this is unnecessary because VICE simply sets \(Z_{x,\text{prog}}m\) = 0 anyway.

The above equation is evaluated always for stable isotopes only. See the notes in the vice.yields.ccsne docstring for details on the studies to which VICE applies a treatment of radioactive isotopes in its built-in tables.

New in version 1.3.1: Prior versions did not subtract the remnant mass from the initial mass of the star for calculating net yields. This is a small correction for metals but is more noticeable for helium. In this version, only the simplified remnant mass model is adopted whereby massive stars of all masses produce a 1.44 \(M_\odot\) white dwarf. We plan to expand upon these options for remnant mass models in future versions.

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