Calibrating maps in Jy/beam

If your images show a lot of structure, you will need to calibrate your maps in Jy/beam. This is true for most observations of dark and molecular clouds, young supernovae, protostars or young stars and even for nearby galaxies. However, if you are only dealing with faint point sources and low S/N maps, you probably need to integrate over the map. If this is the case, it does not matter whether you calibrate in Jy/beam or Jy/aperture, both methods will give the same result. Since Starlink packages do not deal with Jy/beam, it may appear more complicated to integrate over an image calibrated in Jy/beam, but the only difference is that one needs to normalize the integral over the source with the beam integral, $\int F(\Omega)_\nu d\Omega$, where F($\Omega$) is the normalized power pattern of the telescope. For a Gaussian beam the beam integral is simply $1.134 \times \theta_A^2$. Radio astronomical reduction packages of course do this normalization automatically. Since the JCMT beam is not a simple Gaussian beam, we need to account for the error beam, which is equivalent to having an FCF which varies with aperture, when we calibrate in Jy/aperture. We discuss how this is done towards the end of this section.

To calibrate in Jy/beam we have to know the beam size. Ideally we would derive both the flux density conversion factor and the beam size, $\theta_{A}$, from planet observations. If there are no planets available, we can use one of the secondary calibrators. To determine the beam size at 850 $\mu$m it is usually sufficient to make a weighted average from our pointing observations during the run, if we don't have a planet observation or a point like secondary calibrator, but for 450 $\mu$m we need a planet or a secondary calibrator. All JCMT secondary calibrators are directly calibrated in Jy/beam. In this case the FCF is simply the quoted flux divided by the peak signal of the source.