TypeIIPSED#

class uvex_transients.models.supernovae.IIp.TypeIIPSED(**overrides: Parameter | Quantity | float | int)[source]#

Type IIP supernova SED: two shared-onset exponentials and a switched radioactive tail.

With a cooling blackbody photosphere.

\[L_\mathrm{bol}(t) = S_0(t)\,\bigl[1-S_P(t)\bigr] \Bigl[L_\mathrm{pk}\,e^{-(t-t_0)/\tau_\mathrm{cool}} + L_p\Bigr] + S_P(t)\, L_\mathrm{Co}\, e^{-(t-t_P)/\tau_\mathrm{Co}},\]

with two logistic switches

\[S_0(t) = \frac{1}{1+e^{-(t-t_0)/\tau_\mathrm{rise}}}, \qquad S_P(t) = \frac{1}{1+e^{-(t-t_P)/\tau_\mathrm{drop}}}.\]

\(S_0\) turns the photospheric emission on at the explosion/rise epoch \(t_0\); \(S_P\) turns it back off – and the radioactive tail on – at the plateau-end epoch \(t_P\). Well before \(t_0\), \(L_\mathrm{bol} \to 0\). Well after the rise but before the plateau ends, \(L_\mathrm{bol} \simeq L_\mathrm{pk}\,e^{-(t-t_0)/\tau_\mathrm{cool}} + L_p\): an early cooling-phase decline from \(L_\mathrm{pk}\) onto a constant plateau \(L_p\). After \(t_P\), \(L_\mathrm{bol} \to L_\mathrm{Co}\, e^{-(t-t_P)/\tau_\mathrm{Co}}\), a pure radioactive-tail exponential.

A deliberately minimum-complexity stand-in for the classic three-phase Type IIP morphology (shock-cooling decline, hydrogen-recombination plateau, radioactive tail): two logistic switches, two exponentials, three luminosity scales.

The photospheric temperature reuses the light curve’s own \(t_0\) and \(t_P\) and is a smooth, doubly-broken power law with three regimes – an early regime, a cooling-phase regime around \(t_0\), and a recombination/plateau regime around \(t_P\) –

\[T(t) = T_0\, \left(\frac{t}{t_0}\right)^{\alpha_r} \left(\frac{1 + (t/t_0)^{s_0}}{2}\right)^{\frac{\alpha_c - \alpha_r}{s_0}} \left(\frac{1 + (t/\sqrt{t_0 t_P})^{s_1}}{2}\right)^{-\frac{\alpha_c - \alpha_p}{s_1}},\]

(\(t\) in days). Both bracketed terms are normalized to equal 1 exactly at their own break (\(t=t_0\), \(t=\sqrt{t_0 t_P}\)), so \(T(t_0) \approx T_0\) (up to a small correction from the second bracket, negligible when \(t_0 \ll t_P\)). For \(t \ll t_0\), \(T(t) \to T_0\, (t/t_0)^{\alpha_r}\); between the two breaks (\(t_0 \ll t \ll \sqrt{t_0 t_P}\)), \(T(t) \propto t^{\alpha_c}\); for \(t \gg \sqrt{t_0 t_P}\) (approaching and past \(t_P\)), \(T(t) \propto t^{\alpha_p}\). With \(\alpha_r > 0 > \alpha_c > \alpha_p\), the temperature rises through the early, pre-\(t_0\) region (where \(L_\mathrm{bol} \approx 0\) anyway, so this region is not otherwise constrained), peaks near \(t_0\), then declines – fast through the cooling regime, and much more slowly (nearly flat) through the recombination/plateau regime. \(s_0\)/\(s_1\) set the sharpness of the two breaks (smooth, unlike the light curve’s logistic switches, but the same role); the second break has no epoch of its own, so it is centered on the geometric mean of \(t_0\) and \(t_P\).

Parameters

Parameter	Symbol
`t0`	\(t_0\)
`tau_rise`	\(\tau_\mathrm{rise}\)
`L_pk`	\(L_\mathrm{pk}\)
`tau_cool`	\(\tau_\mathrm{cool}\)
`L_p`	\(L_p\)
`t_P`	\(t_P\)
`tau_drop`	\(\tau_\mathrm{drop}\)
`L_Co`	\(L_\mathrm{Co}\)
`tau_Co`	\(\tau_\mathrm{Co}\)
`T_0`	\(T_0\)
`alpha_r`	\(\alpha_r\)
`alpha_c`	\(\alpha_c\)
`alpha_p`	\(\alpha_p\)
`s_0`	\(s_0\)
`s_1`	\(s_1\)

Notes

tau_drop/tau_Co are fixed shape constants. Light-curve priors (t0 through tau_Co) come from a scipy.optimize.curve_fit() to SN 1999em and SN 2003hn; temperature-law priors (T_0 through s_1) are hand-tuned against the aggregate Type IIP photospheric-temperature dataset in test_data/transients (SN 1999em, SN 2003hn, SN 2012aw, SN 2012A, SN 2008in), following Dall’Ora et al.[1] and Faran et al.[2].

Methods

`as_astropy_model`([x_type, y_type, y_kind, ...])	Build an `Model` of this `SpectralModel` for a given parameter set.
`as_source_spectrum`(t, *[, redshift, ...])	Build a `SourceSpectrum` giving the observed flux at one fixed time \(t\).
`eval`(nu, t, **parameters)	Evaluate the spectral luminosity at the given frequency and time.
`eval_bolometric`(t, **parameters)	Evaluate the bolometric luminosity at the given time.
`eval_bolometric_cgs`(t, **parameters)	Bolometric luminosity, taking and returning plain cgs numbers.
`eval_bolometric_log`(t, **parameters)	Natural log of the bolometric luminosity, given physical-unit inputs.
`eval_bolometric_log_cgs`(t, **parameters)	Natural log of the bolometric luminosity, taking and returning plain cgs numbers.
`eval_cgs`(nu, t, **parameters)	Spectral luminosity, taking and returning plain cgs numbers.
`eval_from_arrays`(nu, t, *parameters)	Positional-argument form of `eval()`.
`eval_log`(nu, t, **parameters)	Natural log of the spectral luminosity, given physical-unit inputs.
`eval_log_cgs`(nu, t, **parameters)	Natural log of the spectral luminosity, taking and returning plain cgs numbers.
`eval_spectrum`(nu, t, **parameters)	Evaluate the normalized spectral shape at the given frequency and time.
`eval_spectrum_cgs`(nu, t, **parameters)	Return the normalized spectral shape as plain cgs numbers; see `eval_log_cgs()`.
`eval_spectrum_log`(nu, t, **parameters)	Natural log of the normalized spectral shape, given physical-unit inputs.
`eval_spectrum_log_cgs`(nu, t, **parameters)	Natural log of the normalized spectral shape, taking and returning plain cgs numbers.
`flux`(nu, t, *[, redshift, ...])	Evaluate the observed flux density at the given frequency and time.
`flux_band`(nu, throughput, t, *[, redshift, ...])	Evaluate the throughput-weighted mean observed flux density over a band.
`flux_band_cgs`(nu, throughput, t, redshift, ...)	Band-averaged observed flux density as plain cgs numbers; see `flux_band_log_cgs()`.
`flux_band_log`(nu, throughput, t, *[, ...])	Natural log of the band-averaged observed flux density, given physical-unit inputs.
`flux_band_log_cgs`(nu, throughput, t, ...[, ...])	Natural log of the throughput-weighted mean flux density over a band, plain cgs numbers.
`flux_bolometric`(t, *[, redshift, ...])	Evaluate the observed bolometric flux at the given time.
`flux_bolometric_cgs`(t, redshift, ...)	Observed bolometric flux, taking and returning plain cgs numbers.
`flux_bolometric_log`(t, *[, redshift, ...])	Natural log of the observed bolometric flux, given physical-unit inputs.
`flux_bolometric_log_cgs`(t, redshift, ...)	Natural log of the observed bolometric flux, taking and returning plain cgs numbers.
`flux_cgs`(nu, t, redshift, luminosity_distance, *)	Observed flux density, taking and returning plain cgs numbers.
`flux_log`(nu, t, *[, redshift, ...])	Natural log of the observed flux density, given physical-unit inputs.
`flux_log_cgs`(nu, t, redshift, ...[, ...])	Natural log of the observed flux density, taking and returning plain cgs numbers.
`get`(k[,d])
`items`()
`keys`()
`mag`(nu, t, *[, redshift, ...])	Evaluate the apparent AB magnitude at the given frequency and time.
`mag_band`(nu, throughput, t, *[, redshift, ...])	Evaluate the apparent AB magnitude of the band-averaged flux density.
`mag_band_cgs`(nu, throughput, t, redshift, ...)	Apparent AB magnitude of the band-averaged flux density.
`mag_bandpass`(bandpass, t, *[, redshift, ...])	Evaluate the apparent AB magnitude of the flux averaged over bandpass.
`mag_cgs`(nu, t, redshift, luminosity_distance, *)	Apparent AB magnitude: \(m_\mathrm{AB} = -2.5 \log_{10}(F_\nu / F_{\mathrm{AB},0})\).
`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, t[, size, rng])	Draw random parameter realizations and evaluate the model at the given frequency and time.
`simulate_photometry`(t, exptime, detector, ...)	Simulate noisy synthetic photometry of this model at given time(s), against a real detector.
`temperature`(t, **parameters)	\(T(t)\) in Kelvin.
`unpack_params_from_arrays`(*parameters)	Convert an ordered sequence of parameter values back into a dict.
`values`()