VillarLightcurve

class uvex_transients.models.lightcurves.generic.VillarLightcurve(**overrides: Parameter | Quantity | float | int)

A parametric supernova-like light curve.

\[\begin{split}L(t) = A \times \begin{cases} \dfrac{1 + \beta(t - t_0)}{1 + \exp[-(t-t_0)/\tau_\mathrm{rise}]}, & t < t_1, \\[8pt] \dfrac{(1 + \beta\gamma)\, \exp[-(t-t_1)/\tau_\mathrm{fall}]}{1 + \exp[-(t-t_0)/\tau_\mathrm{rise}]}, & t \ge t_1, \end{cases}\end{split}\]

with \(t_1 = t_0 + \gamma\). A logistic rise (timescale \(\tau_\mathrm{rise}\)) turns on around \(t_0\); the light curve then declines linearly with slope \(\beta\) (a plateau, for small \(|\beta|\)) until \(t_1\), after which it switches to an exponential decline with timescale \(\tau_\mathrm{fall}\). The two branches agree exactly at \(t_1\), by construction.

This is the parametric form used by Villar et al.[1] to fit multi-band supernova photometry, adapted here to a bolometric luminosity rather than a per-band flux.

Parameters

The light curve parameters are summarized below.

Parameter	Symbol	Description
amplitude	\(A\)	Overall luminosity normalization.
t0	\(t_0\)	Reference time at which the logistic rise is centered.
gamma	\(\gamma\)	Duration of the plateau, measured from t0.
beta	\(\beta\)	Linear slope of the plateau.
tau_rise	\(\tau_\mathrm{rise}\)	Logistic rise timescale.
tau_fall	\(\tau_\mathrm{fall}\)	Exponential decline timescale, after the plateau.

See also

uvex_transients.models.supernovae.VillarCoolingBlackbodySED

Pairs this bolometric light curve with a cooling-blackbody spectrum.

References

[1]

V. A. Villar, E. Berger, G. Miller, R. Chornock, A. Rest, D. O. Jones, M. R. Drout, R. J. Foley, R. Kirshner, R. Lunnan, E. Magnier, D. Milisavljevic, N. Sanders, and D. Scolnic. Supernova photometric classification pipelines trained on spectroscopically classified supernovae from the Pan-STARRS1 medium-deep survey. The Astrophysical Journal, 884(1):83, 2019. arXiv:1905.07422, doi:10.3847/1538-4357/ab418c.

Methods

eval(t, **parameters)	Evaluate the bolometric luminosity at the given time.
eval_cgs(t, **parameters)	Bolometric luminosity, taking and returning plain cgs numbers.
eval_from_arrays(t, *parameters)	Positional-argument form of eval().
eval_log(t, **parameters)	Natural log of the bolometric luminosity, given physical-unit inputs.
eval_log_cgs(t, **parameters)	Natural log of the bolometric luminosity, taking and returning plain cgs numbers.
get(k[,d])
items()
keys()
pack_params_to_arrays(**parameters)	Convert a dict of parameter values into an ordered sequence.
sample_parameters([size, rng, parameters])	Draw random samples of some or all of this model's parameters.
simulate(t[, size, rng])	Draw random parameter realizations and evaluate the model at the given time.
unpack_params_from_arrays(*parameters)	Convert an ordered sequence of parameter values back into a dict.
values()