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# brightness_temperature

astropy.units.brightness_temperature(frequency, beam_area=None)

  Defines the conversion between Jy/sr 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).

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

  If the input is in Jy/beam or Jy (assuming it came from a single beam), the beam area is essential for this computation: the brightness temperature is inversely proportional to the beam area.

  Parameters:
    frequency `Quantity`

      The observed `spectral` equivalent `Unit` (e.g., frequency or wavelength). The variable is named ‘frequency’ because it is more commonly used in radio astronomy. BACKWARD COMPATIBILITY NOTE: previous versions of the brightness temperature equivalency used the keyword `disp`, which is no longer supported.

    beam_area `Quantity` [:ref: ‘solid angle’]

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

  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(freq)
      >>> (1*u.Jy/beam_area).to(u.K, equivalencies=equiv)
      <Quantity 3.526295144567176 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(freq)
      >>> (u.Jy/beam_area).to(u.K, equivalencies=equiv)
      <Quantity 217.2658703625732 K>

  Any generic surface brightness:

      >>> surf_brightness = 1e6*u.MJy/u.sr
      >>> surf_brightness.to(u.K, equivalencies=u.brightness_temperature(500*u.GHz))
      <Quantity 130.1931904778803 K>