Planck’s radiation law¶
- PyAstronomy.pyasl.planck(T, lam=None, nu=None)¶
Evaluate Planck’s radiation law.
Depending on whether wavelength or frequency is specified as input, the function evaluates:
\[B_{\nu} = \frac{2\pi h \nu^3}{c^2} \frac{1}{e^{\frac{h\nu}{kT}} - 1}\]or
\[B_{\lambda} = \frac{2\pi h c^2}{\lambda^5} \frac{1}{e^{\frac{h c}{\lambda kT}} - 1} \; .\]If lambda is given (in meters), the output units are W/(m^2 m). To convert into erg/(cm^2 A s), the output has to be multiplied by a factor of 1e-7.
- Parameters
- Tfloat
Temperature in Kelvin.
- lamfloat or array, optional
Wavelength in meters.
- nufloat or array, optional
Frequency in Hz.
- Returns
- Spectral radiancefloat or array
Depending on whether lam or nu were specified, returns the spectral radiance per area and wavelength or frequency. The unit (SI) will be W/(m^2 m) if lam was given and W/(m^2 Hz) if nu was specified.
Example¶
from __future__ import print_function
import numpy as np
import matplotlib.pylab as plt
from PyAstronomy.pyasl import planck
# Define wavelength in meters
lam = np.arange(1000.0*1e-10, 20000.*1e-10, 20e-10)
# Get the Planck spectrum in [W/(m**2 m)] for a temperature of 7000 K
s7 = planck(7000., lam=lam)
# Get the Planck spectrum in [W/(m**2 m)] for a temperature of 5000 K
s5 = planck(5000., lam=lam)
# Convert into erg/(cm**2 * A * s)
s5erg = s5 * 1e-7
s7erg = s7 * 1e-7
# Integrate the spectrum and compare with Stefan-Boltzmann law
i5 = np.sum(s5) * (lam[1] - lam[0])
i7 = np.sum(s7) * (lam[1] - lam[0])
print("5000 K integral: %.3e W/m**2 (Stefan-Boltzmann predicts %.3e W/m**2)" % (i5, (5.67e-8*5000.**4)))
print("7000 K integral: %.3e W/m**2 (Stefan-Boltzmann predicts %.3e W/m**2)" % (i7, (5.67e-8*7000.**4)))
plt.xlabel("Wavelength [$\AA$]")
plt.ylabel("Flux [erg/cm$^2$/A/s]")
plt.plot(lam*1e10, s5erg, 'r-')
plt.plot(lam*1e10, s7erg, 'b-')
plt.show()
