Supernovae Type Ia

Class providing models of Type Ia supernovae from a stellar population, specifically the cumulative number of Type Ia events and the associated metal yield (iron-peak elements) as a function of initial stellar population mass, age, and metallicity. Type Ia supernovae are thermonuclear explosions of white dwarfs in binary systems and are the dominant source of iron in the universe. Their delay-time distribution governs the iron enrichment history of galaxies and is expected to vary across different prescriptions (e.g. power-law vs. single-degenerate vs. double-degenerate channels).

Default implementation: supernovaeTypeIaNagashima2005

Methods

massInitialRange

Return the range of initial stellar masses that contribute to the Type Ia population.

  • class(initialMassFunctionClass) initialMassFunction_ [inout]

  • double precision age [in]

  • double precision metallicity [in]

  • double precision massInitialMinimum [out]

  • double precision massInitialMaximum [out]

number → double precision

Return the cumulative number of Type Ia supernovae from a stellar population of the given initialMass, age, and metallicity.

  • class(initialMassFunctionClass) initialMassFunction_ [inout]

  • double precision initialMass [in]

  • double precision age [in]

  • double precision metallicity [in]

yield → double precision

Return the cumulative yield from Type Ia supernovae from a stellar population of the given initialMass, age, and metallicity.

  • class(initialMassFunctionClass) initialMassFunction_ [inout]

  • double precision initialMass [in]

  • double precision age [in]

  • double precision metallicity [in]

  • integer atomIndex (optional) [in]

supernovaeTypeIaDifferentialDTD

A supernovae type Ia class which operates through the differential delay time distribution.

Methods

numberDifferential → double precision

Return the number of type Ia supernovae per Solar mass of stars formed per unit time at a given population age and metallicity.

  • double precision age [in]

  • double precision metallicity [in]

timeDelayMinimum → double precision

Return the minimum time in the type Ia supernovae delay time distribution.

timeDelayMaximum → double precision

Return the maximum time in the type Ia supernovae delay time distribution.

supernovaeTypeIaFixedYield

A supernovae type Ia class in which the yield is independent of progenitor mass. The yields are read from an XML file, which may optionally tabulate them at several metallicities, in which case they are interpolated linearly in metallicity (and held constant beyond the tabulated range). The file should have the following structure:

<supernovaeYields>
 <isotope>
   <name>56Fe</name>
   <atomicMass>56</atomicMass>
   <atomicNumber>26</atomicNumber>
   <yield>6.26e-1</yield>
 </isotope>
 .
 .
 .
</supernovaeYields>

Only metals should be included—the total metal yield is formed by summing over every isotope present in the file. To make the yields depend on metallicity, wrap each set of isotopes in a yieldsMetallicity element carrying the metallicity at which that set applies:

<supernovaeYields>
 <yieldsMetallicity>
   <metallicity>1.49e-4</metallicity>
   <isotope>
     .
     .
   </isotope>
 </yieldsMetallicity>
 <yieldsMetallicity>
   <metallicity>1.49e-2</metallicity>
   .
   .
 </yieldsMetallicity>
</supernovaeYields>

Methods

initialize

Initialize yield data.

supernovaeTypeIaMassIndependentDTD

A supernovae type Ia class for delay time distributions that are independent of progenitor mass.

Methods

numberCumulative → double precision

Return the cumulative number of type Ia supernovae per Solar mass of stars formed at a given population age and metallicity.

  • double precision age [in]

  • double precision metallicity [in]

supernovaeTypeIaMetallicityDependentRate

A supernovae type Ia class which takes the rate of Type Ia supernovae from another supernovaeTypeIa class and multiplies it by a power of the metallicity,

\[f(Z) = \left( \frac{\max(Z,Z_\mathrm{min})}{\mathrm{Z}_\odot} \right)^\beta,\]

where \(\beta=\) [exponent] and \(Z_\mathrm{min}=\) [metallicityMinimum]. Both the number of events and the yields are scaled, the latter being proportional to the former.

Johnson et al. (2023) argue that the anti-correlation of the close binary fraction with metallicity should enhance the Type Ia supernova rate at low metallicity, and find that a scaling of approximately \(Z^{-1/2}\) on top of the differing star formation histories accounts for the high specific rates observed in dwarf galaxies. That is the default adopted here.

The scaling is unity at \(Z=\mathrm{Z}_\odot\), so the normalization of the wrapped class retains its usual meaning as the rate at Solar metallicity. Because the scaling diverges as \(Z \rightarrow 0\) for negative \(\beta\), the metallicity is floored at [metallicityMinimum]; with the default values this caps the enhancement at a factor of ten. The floor should be chosen with the range over which the adopted scaling was calibrated in mind—it is not itself a physical statement.

Separating the metallicity dependence of the rate from the shape of the delay time distribution in this way means it can be applied to any of the other supernovaeTypeIa classes.

Parameters

  • [exponent] (real; default -0.5d0) — The exponent \(\beta\) in the scaling of the Type Ia supernova rate with metallicity, \(f(Z) \propto Z^\beta\); the default value of \(-1/2\) follows Johnson et al. (2023). Default from: (Johnson et al., 2023).

  • [metallicityMinimum] (real; default 1.0d-2*metallicitySolar) — The metallicity below which the scaling of the Type Ia supernova rate with metallicity is held constant. This is required because the scaling diverges as \(Z \rightarrow 0\) for negative [exponent]; with the default values it caps the enhancement of the rate at a factor of ten.

supernovaeTypeIaNagashima2005

A supernovae type Ia class which uses the prescriptions from Nagashima et al. (2005) to compute the numbers and yields of Type Ia supernovae.

(Default implementation)

Parameters

  • [fileName] (string; default inputPath(pathTypeDataStatic)//'stellarAstrophysics/Supernovae_Type_Ia_Yields.xml') — The name of the XML file from which to read the yields of Type Ia supernovae.

supernovaeTypeIaPowerLawDTD

A supernovae type Ia class with a power-law delay time distribution.

Parameters

  • [timeMinimum] (real; default 40.0d-3) — The minimum time before which the delay time distribution is zero. Default from: (Freundlich and Maoz, 2021).

  • [exponent] (real; default -1.07d0) — The power-law index \(\alpha\) in the Type Ia supernova delay time distribution \(\mathrm{d}N/\mathrm{d}t \propto t^\alpha\), describing how the rate declines with time after star formation; the default value of \(-1.07\) follows Freundlich and Maoz (2021). Default from: (Freundlich and Maoz, 2021).

  • [normalization] (real; default 0.21d-3) — The normalization \(R_1\) of the delay time distribution at 1 Gyr in units of Gyr\(^{-1}\,\mathrm{M}_\odot^{-1}\). Default from: (Freundlich and Maoz, 2021).

  • [fileName] (string; default inputPath(pathTypeDataStatic)//'stellarAstrophysics/Supernovae_Type_Ia_Yields.xml') — The name of the XML file from which to read the yields of Type Ia supernovae.

supernovaeTypeIaPowerLawDTDDifferential

A supernovae type Ia class with a power-law delay time distribution. This class implements the differential form of the delay time distribution and is intended primarily for testing.

Parameters

  • [timeMinimum] (real; default 40.0d-3) — The minimum time before which the delay time distribution is zero. Default from: (Freundlich and Maoz, 2021).

  • [exponent] (real; default -1.07d0) — The power-law index \(\alpha\) in the Type Ia supernova delay time distribution \(\mathrm{d}N/\mathrm{d}t \propto t^\alpha\) (differential form), describing how the rate declines with time after star formation; the default value of \(-1.07\) follows Freundlich and Maoz (2021). Default from: (Freundlich and Maoz, 2021).

  • [normalization] (real; default 0.21d-3) — The normalization \(R_1\) of the delay time distribution at 1 Gyr in units of Gyr\(^{-1}\,\mathrm{M}_\odot^{-1}\). Default from: (Freundlich and Maoz, 2021).

  • [fileName] (string; default inputPath(pathTypeDataStatic)//'stellarAstrophysics/Supernovae_Type_Ia_Yields.xml') — The name of the XML file from which to read the yields of Type Ia supernovae.

supernovaeTypeIaZero

A supernovae type Ia class which produces zero supernovae.