astropy:docs

brightness_temperature

astropy.units.equivalencies.brightness_temperature(beam_area, disp)[source] [edit on github]

“Antenna Gain” or “sensitivity” equivalency: Defines the conversion between Jy/beam and “brightness temperature”, T_B, in Kelvins. This is a unit very commonly used in radio astronomy. Typically, the gain refers to the conversion between corrected antenna temperature T_A^* and flux density. See, e.g., “Tools of Radio Astronomy” (Wilson 2009) eqn 8.16 and eqn 8.19 (these pages are available on google books).

T_B \equiv S_\nu / \left(2 k \nu^2 / c^2 \right)

However, the beam area is essential for this computation: the brighntess temperature is inversely proportional to the beam area

Parameters:

beam_area : Beam Area equivalent

Beam area in angular units, i.e. steradian equivalent

disp : Quantity with spectral units

The observed spectral equivalent Unit (e.g., frequency or wavelength)

Examples

Arecibo C-band beam gain ~ 7 K/Jy:

>>> import numpy as np
>>> from astropy import units as u
>>> beam_area = np.pi*(50*u.arcsec)**2
>>> freq = 5*u.GHz
>>> u.Jy.to(u.K, equivalencies=u.brightness_temperature(beam_area,freq))
7.052588858...
>>> (1*u.Jy).to(u.K, equivalencies=u.brightness_temperature(beam_area,freq))
<Quantity 7.05258...

VLA synthetic beam:

>>> beam_area = np.pi*(15*u.arcsec)**2
>>> freq = 5*u.GHz
>>> u.Jy.to(u.K, equivalencies=u.brightness_temperature(beam_area,freq))
78.36209843...

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