SmoothBrokenPowerLawLightcurve

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

A smoothly broken power-law transient.

The asymptotic behavior is

\[\begin{split}L(t) \propto \begin{cases} t^{\alpha_\mathrm{rise}}, & t \ll t_\mathrm{peak}, \\ t^{-\alpha_\mathrm{decline}}, & t \gg t_\mathrm{peak}, \end{cases}\end{split}\]

with a smooth transition between the two branches. The implementation uses

\[f(x) = \left[ x^{-s\alpha_\mathrm{rise}} + x^{s\alpha_\mathrm{decline}} \right]^{-1/s},\]

but rescales the argument and normalization so that the maximum occurs exactly at t_peak and

\[L(t_\mathrm{peak}) = A.\]

The positive smoothness parameter \(s\) controls the sharpness of the transition: larger values approach a sharply broken power law.

Parameters

The light curve parameters are summarized below.

Parameter	Symbol	Description
amplitude	\(A\)	Peak bolometric luminosity.
t_peak	\(t_\mathrm{peak}\)	Time of peak luminosity.
rise_index	\(\alpha_\mathrm{rise}\)	Positive asymptotic rise index.
decline_index	\(\alpha_\mathrm{decline}\)	Positive asymptotic decline index.
smoothness	\(s\)	Sharpness of the transition between power-law branches.

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()