r"""Composite tidal disruption event SED, following the Van Velzen et al. (2021) ZTF sample."""
from typing import ClassVar
from astropy import units as u
from uvex_transients.models.core.base import ComposedSpectralModel
from uvex_transients.models.core.parameters import Parameter
from uvex_transients.models.core.priors import NormalPrior
from uvex_transients.models.lightcurves.generic import GREDLightcurve
from uvex_transients.models.spectra.thermal import BlackbodySpectrum
__all__ = ["VanVelzenTDESED"]
[docs]
class VanVelzenTDESED(ComposedSpectralModel):
r"""
A constant-temperature blackbody modulated by a Gaussian-rise, exponential-decay light curve.
.. math::
L_\nu(\nu, t) = L_0 \cdot \ell(t) \cdot \frac{\pi B_\nu(\nu, T)}{\sigma_\mathrm{SB} T^4},
where
.. math::
\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}
with :math:`t_\mathrm{peak} = 5\sigma` (:class:`~uvex_transients.models.lightcurves.generic.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 :footcite:p:`2021ApJ...908....4V`: a constant-temperature
blackbody photosphere (the :math:`\pi B_\nu(\nu, T)/(\sigma_\mathrm{SB}
T^4)` factor is exactly :class:`~uvex_transients.models.spectra.thermal.BlackbodySpectrum`'s
normalized shape, :math:`\int_0^\infty S(\nu, T)\,d\nu = 1`), so
:math:`L_0` here is literally :math:`L_\mathrm{bol}(t_\mathrm{peak})`.
Composed from :class:`~uvex_transients.models.lightcurves.generic.GREDLightcurve`
(already bolometric -- :math:`L_0 \cdot \ell(t)`) and
:class:`~uvex_transients.models.spectra.thermal.BlackbodySpectrum`; see
:class:`~uvex_transients.models.core.base.ComposedSpectralModel` for how the two
are combined.
The default priors are informed by the log-normal fits to the ZTF TDE sample
reported by :footcite:t:`2021ApJ...908....4V` (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
:math:`L_0`, :math:`T`, :math:`\sigma`, and :math:`\tau`, each parameterized
here via a base-10 log transform on a
:class:`~uvex_transients.models.core.priors.NormalPrior`.
.. rubric:: Parameters
The model parameters are summarized below.
.. list-table::
:header-rows: 1
:widths: 18 18 64
* - Parameter
- Symbol
- Description
* - ``amplitude``
- :math:`L_0`
- Peak bolometric luminosity, :math:`L_0 = L_\mathrm{bol}(t_\mathrm{peak})`.
:math:`\log_{10}(L_0/\mathrm{erg\,s^{-1}}) \sim \mathcal{N}(43.8, 0.3^2)`.
* - ``sigma_rise``
- :math:`\sigma`
- Gaussian width of the pre-peak rise.
:math:`\log_{10}(\sigma/\mathrm{d}) \sim \mathcal{N}(0.91, 0.25^2)`.
* - ``tau_decline``
- :math:`\tau`
- Exponential decline timescale after peak.
:math:`\log_{10}(\tau/\mathrm{d}) \sim \mathcal{N}(1.7, 0.2^2)`.
* - ``temperature``
- :math:`T`
- Photospheric blackbody temperature.
:math:`\log_{10}(T/\mathrm{K}) \sim \mathcal{N}(4.3, 0.1^2)`.
References
----------
.. footbibliography::
"""
_LIGHTCURVE_CLASS = GREDLightcurve
_SPECTRUM_CLASS = BlackbodySpectrum
_DEFAULT_PARAMETERS: ClassVar[dict[str, Parameter]] = {
"amplitude": Parameter(
prior=NormalPrior(mean=43.8, sigma=0.3),
scale=1.0 * u.erg / u.s,
transform="log10",
description="Peak bolometric luminosity, L_0 = L_bol(t_peak). log10(L_0/[erg/s]) ~ N(43.8, 0.3^2).",
latex=r"L_0",
),
"temperature": Parameter(
prior=NormalPrior(mean=4.3, sigma=0.1),
scale=1.0 * u.K,
transform="log10",
description="Photospheric blackbody temperature. log10(T/K) ~ N(4.3, 0.1^2).",
latex=r"T",
),
"sigma_rise": Parameter(
prior=NormalPrior(mean=0.91, sigma=0.25),
scale=1.0 * u.day,
transform="log10",
description="Gaussian width of the pre-peak rise. log10(sigma/day) ~ N(0.91, 0.25^2).",
latex=r"\sigma",
),
"tau_decline": Parameter(
prior=NormalPrior(mean=1.7, sigma=0.2),
scale=1.0 * u.day,
transform="log10",
description="Exponential decline timescale after peak. log10(tau/day) ~ N(1.7, 0.2^2).",
latex=r"\tau",
),
}
