Sensitivity Model
The ‘system equivalent flux density’ (SEFD) for a single dish is given by:
where:
\(k\) is the Boltzmann constant so that \(kT_{sys}\) measures the power received from background emission and all other sources of unwanted signal within the system, that is \(T_{sys} = T_{spl} + T_{sky} + T_{rcv} + T_{cmb} + ...\)
\(\eta_A\) is the dish efficiency
\(A\) is the geometric dish area.
The SEFD for an interferometer array made up of two types of dish is given by:
where \(n_{\mathrm{SKA}}\) is the number of SKA antennas, \(n_{\mathrm{MeerKAT}}\) is the number of MeerKAT antennas, \(SEFD_{\mathrm{SKA}}\) is the SEFD computed for an individual SKA antenna, and \(SEFD_{\mathrm{MeerKAT}}\) is the SEFD computed for an individual MeerKAT antenna.
We define the telescope sensitivity here as the minimum detectable Stokes I flux (1 \(\sigma\)). This is equal to the noise on the background power, obtained using the radiometer equation \(\sigma = SEFD / \sqrt{2 B t}\), corrected for atmospheric absorption:
where:
\(\Delta S_{min}\) is the source flux density above the atmosphere
\(\eta_s\) is the efficiency factor of the interferometer
\(B\) is bandwidth
\(t\) is integration time
\(\tau_{atm}\) is the optical depth of the atmosphere towards the target
See Implementation for more details.