VanVelzenTDESED

class uvex_transients.models.tdes.van_velzen.VanVelzenTDESED(**overrides: Parameter | Quantity | float | int)

A constant-temperature blackbody modulated by a Gaussian-rise, exponential-decay light curve.

\[L_\nu(\nu, t) = L_0 \cdot \ell(t) \cdot \frac{\pi B_\nu(\nu, T)}{\sigma_\mathrm{SB} T^4},\]

where

\[\begin{split}\ell(t) = \begin{cases} \exp\left[-\dfrac{(t-t_\mathrm{peak})^2}{2\sigma^2}\right] & t < t_\mathrm{peak} \\[6pt] \exp\left[-\dfrac{t-t_\mathrm{peak}}{\tau}\right] & t \ge t_\mathrm{peak} \end{cases}\end{split}\]

with \(t_\mathrm{peak} = 5\sigma\) (GREDLightcurve’s own convention – the rise is always exactly 5 Gaussian widths long, not a separate free parameter). This is a fairly typical parameterization for a TDE SED [1]: a constant-temperature blackbody photosphere (the \(\pi B_\nu(\nu, T)/(\sigma_\mathrm{SB} T^4)\) factor is exactly BlackbodySpectrum’s normalized shape, \(\int_0^\infty S(\nu, T)\,d\nu = 1\)), so \(L_0\) here is literally \(L_\mathrm{bol}(t_\mathrm{peak})\). Composed from GREDLightcurve (already bolometric – \(L_0 \cdot \ell(t)\)) and BlackbodySpectrum; see ComposedSpectralModel for how the two are combined.

The default priors are informed by the log-normal fits to the ZTF TDE sample reported by van Velzen et al.[1] (their Section 4.1 / Table 4), though the values below have since been hand-tuned away from those exact fits and are not currently a literal reproduction of them: log-normal in \(L_0\), \(T\), \(\sigma\), and \(\tau\), each parameterized here via a base-10 log transform on a NormalPrior.

Parameters

The model parameters are summarized below.

Parameter	Symbol	Description
amplitude	\(L_0\)	Peak bolometric luminosity, \(L_0 = L_\mathrm{bol}(t_\mathrm{peak})\). \(\log_{10}(L_0/\mathrm{erg\,s^{-1}}) \sim \mathcal{N}(43.8, 0.3^2)\).
sigma_rise	\(\sigma\)	Gaussian width of the pre-peak rise. \(\log_{10}(\sigma/\mathrm{d}) \sim \mathcal{N}(0.91, 0.25^2)\).
tau_decline	\(\tau\)	Exponential decline timescale after peak. \(\log_{10}(\tau/\mathrm{d}) \sim \mathcal{N}(1.7, 0.2^2)\).
temperature	\(T\)	Photospheric blackbody temperature. \(\log_{10}(T/\mathrm{K}) \sim \mathcal{N}(4.3, 0.1^2)\).

References

[1] (1,2)

Sjoert van Velzen, Suvi Gezari, Erica Hammerstein, Nathaniel Roth, Sara Frederick, Charlotte Ward, Tiara Hung, S. Bradley Cenko, Robert Stein, Daniel A. Perley, Kirsty Taggart, Jesper Sollerman, Igor Andreoni, Eric C. Bellm, Kishalay De, Richard Dekany, Ryan J. Foley, Christoffer Fremling, Anna Y. Q. Ho, Mansi M. Kasliwal, and Shrinivas R. Kulkarni. Seventeen tidal disruption events from the first half of ZTF survey observations: entering a new era of population studies. The Astrophysical Journal, 908(1):4, 2021. arXiv:2001.01409, doi:10.3847/1538-4357/abc258.

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.
unpack_params_from_arrays(*parameters)	Convert an ordered sequence of parameter values back into a dict.
values()