From the temperature power to the flux

For a point source, it is more natural to express the signal, and thus the sensitivity, in unit of flux. The flux ( \ensuremath{F}) of a point source is linked to its brightness temperature \ensuremath{T} through

  $\displaystyle \ensuremath{F}= \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensurema...
...thrm{sd}}} = \frac{2\ensuremath{k}}{\ensuremath{A_\ensuremath{\mathrm{eff}}}},
$ (5)
where \ensuremath{k} is the Boltzman constant, and \ensuremath{A_\ensuremath{\mathrm{eff}}} is the effective area of the antenna (eq. 3-113 in Kraus , 1982), and \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}} the conversion factor for a typical interferometer antenna. The effective area depends on the observing wavelength when the surface rms accuracy becomes a significant fraction of the wavelength. For NOEMA, the effective area is close to 1 at 3 mm but significantly lower than 1 at 1 mm.

Using the same conversion factor for the sensitivity, we yield

  $\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{...
...{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}}}.
$ (6)