Supernova cooling neutrino source approximated using a Fermi-Dirac distribution. More...

#include <NeutrinoSource.hh>

Inheritance diagram for marley::FermiDiracNeutrinoSource:

Public Member Functions
	FermiDiracNeutrinoSource (int particle_id=marley_utils::ELECTRON_NEUTRINO, double Emin=0., double Emax=50., double temp=3.5, double eta=0.)

virtual double	get_Emax () const override
	Get the maximum neutrino energy (MeV) that can be sampled by this source.

virtual double	get_Emin () const override
	Get the minimum neutrino energy (MeV) that can be sampled by this source.

virtual double	pdf (double E) const override
	Probability density function describing the incident neutrino energy distribution.

Public Member Functions inherited from marley::NeutrinoSource
	NeutrinoSource (int particle_id)

virtual int	get_pid () const
	Get the PDG particle ID for the neutrino type produced by this source.

virtual double	sample_incident_neutrino (int &pdg, marley::Generator &gen) const
	Samples an incident neutrino energy and loads pdg with the PDG code of the appropriate neutrino type.

Protected Attributes
double	C_
	normalization constant (MeV²)

double	Emax_
	maximum neutrino energy (MeV)

double	Emin_
	minimum neutrino energy (MeV)

double	eta_
	dimensionless pinching parameter

double	temperature_
	temperature (MeV)

Protected Attributes inherited from marley::NeutrinoSource
int	pid_
	PDG particle ID for the neutrinos produced by this source.

Additional Inherited Members
Static Public Member Functions inherited from marley::NeutrinoSource
static bool	pdg_is_allowed (const int pdg)

Detailed Description

Supernova cooling neutrino source approximated using a Fermi-Dirac distribution.

Neutrino energies from this source are sampled from a Fermi-Dirac distribution with temperature \(T\) (MeV) and pinching parameter \(\eta\). The probability density function is given by

\begin{align*} P(E) &= \frac{C\,E^2} {T^4\left[1+\exp\left(\frac{E}{T} - \eta\right)\right]} & \text{E}_\text{min} \leq E \leq \text{E}_\text{max} \end{align*}

where \(C\) is a normalization constant.

Definition at line 124 of file NeutrinoSource.hh.

Constructor & Destructor Documentation

◆ FermiDiracNeutrinoSource()

marley::FermiDiracNeutrinoSource::FermiDiracNeutrinoSource	(	int	particle_id = marley_utils::ELECTRON_NEUTRINO,
		double	Emin = 0.,
		double	Emax = 50.,
		double	temp = 3.5,
		double	eta = 0. )

Parameters

particle_id	PDG particle ID for the neutrinos produced by this source
Emin	minimum allowed neutrino energy (MeV)
Emax	maximum allowed neutrino energy (MeV)
temp	temperature (MeV)
eta	pinching parameter

Definition at line 66 of file NeutrinoSource.cc.

  : NeutrinoSource(particle_id), Emin_(Emin), Emax_(Emax), temperature_(temp),
  eta_(eta), C_(1.)
{
  // Normalize the source spectrum (not strictly necessary, but having the
  // spectrum approximately normalized makes the default rejection sampling
  // tolerance of 1e-8 reliable for finding the maximum of the spectrum)
  double integral = marley_utils::num_integrate(
    [this](double E) -> double { return this->pdf(E); }, Emin_, Emax_);
 
  // Update the normalization constant, thereby normalizing this object's
  // pdf in the process.
  C_ /= integral;
}

References marley::NeutrinoSource::NeutrinoSource(), C_, Emax_, Emin_, eta_, pdf(), and temperature_.

Member Function Documentation

◆ get_Emax()

double marley::FermiDiracNeutrinoSource::get_Emax ( ) const

inlineoverridevirtual

Get the maximum neutrino energy (MeV) that can be sampled by this source.

Implements marley::NeutrinoSource.

Definition at line 343 of file NeutrinoSource.hh.

343{ return Emax_; }

References Emax_.

◆ get_Emin()

double marley::FermiDiracNeutrinoSource::get_Emin ( ) const

inlineoverridevirtual

Get the minimum neutrino energy (MeV) that can be sampled by this source.

Implements marley::NeutrinoSource.

Definition at line 344 of file NeutrinoSource.hh.

344{ return Emin_; }

References Emin_.

◆ pdf()

double marley::FermiDiracNeutrinoSource::pdf ( double E ) const

overridevirtual

Probability density function describing the incident neutrino energy distribution.

The neutrino spectrum produced by this source will be folded with the relevant cross sections by a Generator object during event creation

Parameters

E	neutrino energy (MeV)

Returns: Probability density (MeV^-1)

Implements marley::NeutrinoSource.

Definition at line 82 of file NeutrinoSource.cc.

                                                         {
  if (E < Emin_ || E > Emax_) return 0.;
  else return (C_ / std::pow(temperature_, 4)) * (std::pow(E, 2)
    / (1 + std::exp((E / temperature_) - eta_)));
}