uvex_transients.utils.cosmology.supernovae_Ia_rate#

uvex_transients.utils.cosmology.supernovae_Ia_rate(z: float | ~numpy._typing._array_like.NDArray[~numpy.float64], cosmology: ~astropy.cosmology._src.core.Cosmology | None = None, dtd_slope: float = -1.1, t_min: float | ~astropy.units.quantity.Quantity = <Quantity 0.04 Gyr>, n_ia_per_m: float | ~astropy.units.quantity.Quantity = 0.0013, t_norm: float | ~astropy.units.quantity.Quantity = <Quantity 13.7 Gyr>, sfr_shape: ~typing.Literal['md14', 'mf17'] = 'md14', imf: ~typing.Literal['salpeter', 'kroupa', 'chabrier'] = 'kroupa', z_form: float = 20.0, n_tau: int = 2000) → Quantity[source]#

Compute the volumetric Type Ia supernova rate.

The rate is the cosmic star formation history convolved with a power-law delay-time distribution (DTD),

\[\mathcal{R}_{\rm Ia}(z) = \int_{t_{\min}}^{t(z) - t(z_{\rm form})} \dot{\rho}_\star\big(t(z) - \tau\big)\,\Psi(\tau)\,d\tau, \qquad \Psi(\tau) = A\left(\frac{\tau}{\rm Gyr}\right)^{\alpha}\ (\tau > t_{\min}),\]

with \(A\) set so that \(\int_{t_{\min}}^{t_{\rm norm}}\Psi\,d\tau = N_{\rm Ia}/M_\star\). Values are taken from Maoz and Graur[1].

Parameters:

  • z (float or ndarray) – Redshift.

  • cosmology (~astropy.cosmology.FLRW, optional) – Cosmology used for the redshift–cosmic-time relation. If None, the configured default cosmology is used; see get_cosmology.

  • dtd_slope (float, optional) – DTD power-law index \(\alpha\). Default -1.1 (Maoz & Graur 2017).

  • t_min (float or Quantity, optional) – Minimum delay time. Bare numbers are in Gyr. Default 40 Myr.

  • n_ia_per_m (float or Quantity, optional) – Number of SNe Ia per unit stellar mass formed, \(N_{\rm Ia}/M_\star\), integrated from t_min to t_norm. Bare numbers are per \({\rm M_\odot}\). Default \(1.3\times10^{-3}\) (Maoz & Graur 2017).

  • t_norm (float or Quantity, optional) – Upper limit of the normalization integral. Bare numbers are in Gyr. Default 13.7 Gyr, the convention used for literature \(N_{\rm Ia}/M_\star\).

  • sfr_shape ({"md14", "mf17"}, optional) – Cosmic star formation history; see star_formation_rate. Default "md14".

  • imf ({"salpeter", "kroupa", "chabrier"}, optional) – IMF used to normalize the star formation rate. It must match the IMF that n_ia_per_m is defined for. Default "kroupa", matching the Maoz & Graur (2017) efficiency.

  • z_form (float, optional) – Redshift at which star formation begins. Default 20.

  • n_tau (int, optional) – Number of log-spaced delay-time samples used in the convolution.

Returns:

Volumetric Type Ia supernova rate in \({\rm yr^{-1}\,Mpc^{-3}}\).

Return type:

Quantity

Raises:

ValueError – If t_min is not strictly between 0 and t_norm.

References