uvex_transients.models.spectra.powerlaw

Power-law spectral shapes.

PowerLawSpectrum represents a single truncated power law

\[S(\nu) = \frac{1}{\nu_0}\left(\frac{\nu}{\nu_0}\right)^\alpha,\]

between finite lower and upper frequency cutoffs and zero elsewhere. The reference frequency \(\nu_0\) fixes the otherwise arbitrary dimensional normalization of the power law, while the finite cutoffs make the frequency integral well-defined – a pure, unbroken power law cannot have a finite integral over \(0 < \nu < \infty\), since at least one end always diverges.

BrokenPowerLawSpectrum generalizes this to two power-law segments that meet continuously at a break_frequency, which doubles as the reference frequency for both segments (so no separate normalization constant is needed to keep the two pieces continuous).

Neither shape is normalized to integrate to 1 by construction; each overrides _eval_normalization() with the closed-form integral of its own shape (see powerlaw_shape_integral_cgs()).

Classes

BrokenPowerLawSpectrum(**overrides)	Finite-band, two-segment power-law spectral shape.
PowerLawSpectrum(**overrides)	Finite-band power-law spectral shape.