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- Units and Quantities (`astropy.units`) »
- brightness_temperature

# brightness_temperature

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

  Defines the conversion between Jy/beam and “brightness temperature”, T_B, in Kelvins. The brightness temperature is a unit very commonly used in radio astronomy. 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 brightness 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:

      >>> import numpy as np
      >>> from astropy import units as u
      >>> beam_sigma = 50*u.arcsec
      >>> beam_area = 2*np.pi*(beam_sigma)**2
      >>> freq = 5*u.GHz
      >>> equiv = u.brightness_temperature(beam_area, freq)
      >>> u.Jy.to(u.K, equivalencies=equiv)
      3.526294429423223
      >>> (1*u.Jy).to(u.K, equivalencies=equiv)
      <Quantity 3.526294429423223 K>

  VLA synthetic beam:

      >>> bmaj = 15*u.arcsec
      >>> bmin = 15*u.arcsec
      >>> fwhm_to_sigma = 1./(8*np.log(2))**0.5
      >>> beam_area = 2.*np.pi*(bmaj*bmin/fwhm_to_sigma**2)
      >>> freq = 5*u.GHz
      >>> equiv = u.brightness_temperature(beam_area, freq)
      >>> u.Jy.to(u.K, equivalencies=equiv)
      7.065788175060084