r"""Luminous Fast Blue Optical Transient (LFBOT) SED model."""
from typing import ClassVar
import numpy as np
from astropy import units as u
from uvex_transients.models._typing import CGSParameterValue, FloatArray
from uvex_transients.models._util_functions import cooling_temperature_cgs
from uvex_transients.models._utils import to_cgs_value
from uvex_transients.models.core.base import SpectralModel
from uvex_transients.models.core.parameters import Parameter
from uvex_transients.models.core.priors import LogNormalPrior, NormalPrior, UniformPrior
from uvex_transients.models.lightcurves.generic import GaussianRisePowerLawLightcurve
from uvex_transients.models.spectra.thermal import BlackbodySpectrum
__all__ = ["LFBOTCoolingBlackbodySED"]
[docs]
class LFBOTCoolingBlackbodySED(SpectralModel):
r"""
A Gaussian-rise/power-law-decline light curve with a Villar-type cooling blackbody photosphere.
This model pairs
:class:`~uvex_transients.models.lightcurves.generic.GaussianRisePowerLawLightcurve`
with a time-dependent blackbody spectral shape,
.. math::
L_\nu(\nu, t)
=
L_\mathrm{bol}(t)\,
S_\mathrm{BB}\!\left[\nu, T(t)\right],
where :math:`S_\mathrm{BB}` is the normalized blackbody spectrum provided
by :class:`~uvex_transients.models.spectra.thermal.BlackbodySpectrum`.
The photosphere follows the same cooling-law form as
:class:`~uvex_transients.models.supernovae.villar.VillarCoolingBlackbodySED`,
but with the cooling timescale fixed to the light curve's own
:math:`t_\mathrm{peak}` rather than a separate free parameter,
.. math::
T(t) = T_\mathrm{floor} + (T_0 - T_\mathrm{floor})(1 + t/t_\mathrm{peak})^{-\alpha_T},
which has the correct :math:`T \to T_\mathrm{floor} + (T_0 -
T_\mathrm{floor})(t/t_\mathrm{peak})^{-\alpha_T}` power-law asymptote at late times.
.. rubric:: Parameters
The model parameters are summarized below.
.. list-table::
:header-rows: 1
:widths: 18 18 64
* - Parameter
- Symbol
- Description
* - ``amplitude``
- :math:`A`
- Peak bolometric luminosity.
* - ``t_peak``
- :math:`t_\mathrm{peak}`
- Time of peak luminosity since explosion.
* - ``decline_index``
- :math:`\alpha_\mathrm{decline}`
- Positive post-peak power-law decline index of the bolometric
light curve.
* - ``T0``
- :math:`T_0`
- Photospheric temperature at t=0 (the T(t) -> T0 limit, not
literally T at peak).
* - ``T_floor``
- :math:`T_\mathrm{floor}`
- Asymptotic late-time photospheric temperature (T(t) -> T_floor
as t -> infinity).
* - ``alpha_T``
- :math:`\alpha_T`
- Late-time photospheric cooling power-law index.
"""
_DEFAULT_PARAMETERS: ClassVar[dict[str, Parameter]] = {
"amplitude": Parameter(
prior=NormalPrior(mean=44.5, sigma=0.5),
scale=1.0 * u.erg / u.s,
transform="log10",
description="Peak bolometric luminosity. log10(L_0/[erg/s]) ~ N(44.5, 0.1^2), "
"spanning the ~1e44 (CSS161010) to a few 1e45 erg/s range reported by Ho & Lu et al. 2026.",
latex=r"L_0",
),
"t_peak": Parameter(
prior=NormalPrior(mean=np.log10(3), sigma=0.1),
scale=1.0 * u.day,
transform="log10",
description="Time of peak bolometric luminosity since explosion. Log-normal around "
"2 d with fairly small scatter (Ho & Lu et al. 2026).",
latex=r"t_\mathrm{peak}",
),
"decline_index": Parameter(
prior=UniformPrior(lower=1.5, upper=4),
scale=1 * u.dimensionless_unscaled,
description="Positive post-peak power-law decline index; L_bol ~ t^-decline_index. "
"Late-time light curves are broadly consistent with a t^-3 decline (Ho & Lu et al. 2026).",
latex=r"\alpha_\mathrm{decline}",
),
"T0": Parameter(
prior=LogNormalPrior(mean=0.0, sigma=0.15),
scale=4e4 * u.K,
description="Photospheric temperature at t=0 (the T(t) -> T0 limit, not literally T at peak).",
latex=r"T_0",
),
"T_floor": Parameter(
prior=LogNormalPrior(mean=0.0, sigma=0.01),
scale=1e4 * u.K,
description="Asymptotic late-time photospheric temperature (T(t) -> T_floor as t -> infinity). "
"Log-normal, tightly centered on 1e4 K.",
latex=r"T_\mathrm{floor}",
),
"alpha_T": Parameter(
prior=UniformPrior(lower=1 / 3, upper=1),
scale=1,
description="Late-time photospheric cooling power-law index; T ~ t^-alpha_T for t >> t_peak. "
"~1/3 is a reasonable fit for most events (e.g. AT2018cow); CSS161010 was closer to "
"constant temperature (Ho & Lu et al. 2026).",
latex=r"\alpha_T",
),
}
# -------------------------------------- #
# Cooling Law: T(t) #
# -------------------------------------- #
@classmethod
def _temperature_cgs(
cls,
t: FloatArray,
*,
T0: CGSParameterValue,
T_floor: CGSParameterValue,
t_peak: CGSParameterValue,
alpha_T: CGSParameterValue,
**_ignored: CGSParameterValue,
) -> FloatArray:
r"""
:math:`T(t) = T_\mathrm{floor} + (T_0 - T_\mathrm{floor})(1 + t/t_\mathrm{peak})^{-\alpha_T}`.
Parameters
----------
t : numpy.ndarray
Time since explosion, in seconds.
T0, T_floor, t_peak, alpha_T : float or numpy.ndarray
This model's parameter values, in cgs units; see the class docstring.
**_ignored
Any other model parameter values, ignored.
Returns
-------
numpy.ndarray
:math:`T(t)`, in Kelvin.
"""
return cooling_temperature_cgs(t, T0=T0, T_floor=T_floor, timescale=t_peak, alpha=alpha_T)
[docs]
@classmethod
def temperature(cls, t: FloatArray, **parameters: CGSParameterValue) -> FloatArray:
r"""
:math:`T(t)` in Kelvin.
Parameters
----------
t : numpy.ndarray
Time since explosion, in seconds.
**parameters
This model's parameter values, in cgs units.
Returns
-------
numpy.ndarray
:math:`T(t)`, in Kelvin.
"""
cgs_parameters: dict[str, CGSParameterValue] = {name: to_cgs_value(value) for name, value in parameters.items()}
return cls._temperature_cgs(t.cgs.value, **cgs_parameters) * u.K
# -------------------------------------- #
# Bolometric Luminosity: L_bol(t) #
# -------------------------------------- #
@classmethod
def _eval_bolometric(cls, t: FloatArray, **parameters: CGSParameterValue) -> FloatArray:
r"""
:math:`\log L_\mathrm{bol}(t)`, delegated directly to :class:`GaussianRisePowerLawLightcurve`.
Exact -- no integration needed.
Parameters
----------
t : numpy.ndarray
Time since explosion, in seconds.
**parameters
This model's parameter values, in cgs units.
Returns
-------
numpy.ndarray
The natural log of :math:`L_\mathrm{bol}(t)`, in erg/s.
"""
lightcurve_parameters = {name: parameters[name] for name in GaussianRisePowerLawLightcurve._DEFAULT_PARAMETERS}
return GaussianRisePowerLawLightcurve._eval(t, **lightcurve_parameters)
# -------------------------------------- #
# Normalized Spectral Shape: S(nu, t) #
# -------------------------------------- #
@classmethod
def _eval_spectrum(cls, nu: FloatArray, t: FloatArray, **parameters: CGSParameterValue) -> FloatArray:
r"""
:math:`\log S(\nu, T(t))`, delegated to :class:`BlackbodySpectrum`.
Evaluated at this ``t``'s own cooling-law temperature.
Parameters
----------
nu : numpy.ndarray
Frequency, in Hz.
t : numpy.ndarray
Time since explosion, in seconds.
**parameters
This model's parameter values, in cgs units.
Returns
-------
numpy.ndarray
The natural log of the normalized spectral shape, in 1/Hz.
"""
temperature = cls._temperature_cgs(t, **parameters)
return BlackbodySpectrum._eval(nu, temperature=temperature)
# -------------------------------------- #
# Spectral Luminosity: L_nu(nu, t) #
# -------------------------------------- #
@classmethod
def _eval(cls, nu: FloatArray, t: FloatArray, **parameters: CGSParameterValue) -> FloatArray:
r"""
:math:`\log L_\nu(\nu, t) = \log L_\mathrm{bol}(t) + \log S(\nu, T(t))`.
Parameters
----------
nu : numpy.ndarray
Frequency, in Hz.
t : numpy.ndarray
Time since explosion, in seconds.
**parameters
This model's parameter values, in cgs units.
Returns
-------
numpy.ndarray
The natural log of :math:`L_\nu(\nu, t)`, in erg/s/Hz.
"""
return cls._eval_bolometric(t, **parameters) + cls._eval_spectrum(nu, t, **parameters)
