BrokenPowerLawSpectrum#

class uvex_transients.models.spectra.powerlaw.BrokenPowerLawSpectrum(**overrides: Parameter | Quantity | float | int)[source]#

Finite-band, two-segment power-law spectral shape.

Represents

\[S(\nu) = \nu_{\rm break}^{-1} \left(\frac{\nu}{\nu_{\rm break}}\right)^{\alpha_1 \,\mathrm{or}\,\alpha_2},\]

using index \(\alpha_1\) below break_frequency and \(\alpha_2\) above it, and zero outside [frequency_min, frequency_max]. Because both segments are anchored to the same break_frequency, \(S(\nu)\) is automatically continuous there (both give \(\nu_{\rm break}^{-1}\)) without any extra matching condition.

The default indices are sampled from Gaussian priors centered on -1 (below the break) and -2 (above it) – a generic steepening spectrum; like any other parameter, both can be overridden per instance. break_frequency and the cutoffs use constant priors by default, making them deterministic unless replaced or overridden explicitly.

Parameters

The spectral shape parameters are summarized below.

Parameter	Symbol	Description
`spectral_index_1`	\(\alpha_1\)	Power-law index below `break_frequency`.
`spectral_index_2`	\(\alpha_2\)	Power-law index above `break_frequency`.
`break_frequency`	\(\nu_{\rm break}\)	Frequency at which the spectral index switches from alpha_1 to alpha_2.
`frequency_min`	\(\nu_{\min}\)	Lower frequency cutoff of the spectrum.
`frequency_max`	\(\nu_{\max}\)	Upper frequency cutoff of the spectrum.

Methods

`eval`(nu, **parameters)	Evaluate the spectral shape at the given frequency.
`eval_cgs`(nu, **parameters)	Spectral shape, taking and returning plain cgs numbers.
`eval_from_arrays`(nu, *parameters)	Positional-argument form of `eval()`.
`eval_log`(nu, **parameters)	Natural log of the spectral shape, given physical-unit inputs.
`eval_log_cgs`(nu, **parameters)	Natural log of the spectral shape, taking and returning plain cgs numbers.
`eval_normalization`(**parameters)	Evaluate \(\int S(\nu)\,d\nu\).
`eval_normalization_cgs`(**parameters)	Return the shape's frequency integral as plain cgs numbers; see `eval_normalization_log_cgs()`.
`eval_normalization_log`(**parameters)	Natural log of the shape's frequency integral, given physical-unit inputs.
`eval_normalization_log_cgs`(**parameters)	Natural log of the shape's frequency integral, 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`(nu[, size, rng])	Draw random parameter realizations and evaluate the model at the given frequency.
`unpack_params_from_arrays`(*parameters)	Convert an ordered sequence of parameter values back into a dict.
`values`()