blackbody.hpp File Reference

Blackbody radiation model. More...

#include "cphot/rquantities.hpp"

Go to the source code of this file.

Functions
QSpectralFluxDensity	bb_flux_function (QLength lam, Number amp, QTemperature teff)
	Blackbody as a flux distribution as function of wavelength, temperature and amplitude. More...
double	bb_flux_function (double lam_nm, double amp, double teff_K)
	default units blackbody as a flux distribution as function of wavelength, temperature and amplitude. More...

Detailed Description

Blackbody radiation model.

Version

0.1

Date

2021-12-01

References:

• Rybicki, G. B.; Lightman, A. P. (1979). Radiative Processes in Astrophysics. John Wiley & Sons. ISBN 0-471-82759-2.

Planck's law of black-body radiation states that

\begin{eqnarray*} f_{\lambda }(T) &=& a\,\cdot\,{\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /kT}-1}}\\ &=& a\,\cdot\,\frac{2hc^2}{\lambda^5}{\frac {1}{e^{hc /\lambda kT}-1}}, \end{eqnarray*}

where

• \(f_\lambda(T)\) is the spectral flux density at thermal equilibrium of temperature \(T\).
• \(h\) is the Planck constant ( \(6.6260693\cdot10^{-34}\) J/s);
• \(c\) is the speed of light in a vacuum ( \(299792458\cdot 10^6\mu m/s\));
• \(k\) is the Boltzmann constant ( \(1.3806505\cdot 10^{-23}\) J/K);
• \(\nu\) is the frequency of the electromagnetic radiation;
• \(\lambda\) is the wavelength of the electromagnetic radiation;
• \(T\) is the absolute temperature of the body;
• and \(a\) is a dimensionless normalization factor.

Note that $a$ can alternatively links to the angular size $\theta$

\[ \theta = \sqrt{\frac{a}{\pi}} = \frac{R}{d} \]

where \(R\) is the radius, and \(d\) is the distance to the star.

Definition in file blackbody.hpp.

Function Documentation

bb_flux_function() [1/2]

double bb_flux_function	(	double	lam_nm,
		double	amp,
		double	teff_K
	)

default units blackbody as a flux distribution as function of wavelength, temperature and amplitude.

Parameters

lam	wavelength in nm
amp	dimensionless normalization factor
teff	temperature in Kelvins

Returns

evaluation of the blackbody radiation in flam units (erg/s/cm2/AA)

Definition at line 80 of file blackbody.hpp.

bb_flux_function() [2/2]

QSpectralFluxDensity bb_flux_function	(	QLength	lam,
		Number	amp,
		QTemperature	teff
	)

Blackbody as a flux distribution as function of wavelength, temperature and amplitude.

This function deals with unit conversions

Parameters

lam	wavelength
amp	dimensionless normalization factor
teff	temperature

Returns

evaluation of the blackbody radiation in flam units (erg/s/cm2/AA)

Note that amp is alternatively represented as the angular size θ = R/d = sqrt(amp/pi)

Definition at line 52 of file blackbody.hpp.