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# brightness_temperature

`astropy.units.equivalencies.``brightness_temperature`(beam_area, disp)

  “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...