Signal to Noise

The rms noise can be computed from

$$\sigma = \frac{\JpK\mbox{$T_{\rm sys}$}} {\eta \sqrt{\Na (\Na -1) \Nc T_{\rm ON} B}}$$ (1)

where

• $T_{\rm sys}$ is the system temperature (150 K below 110 GHz, 200 K at 115 GHz, 400 K at 230 GHz for sources at $\ge 20^\circ$)
• $\hbox{$J_{\rm pK}$}$ is the conversion factor from Kelvin to Jansky (22 Jy/K at 3mm, 35 Jy/K at 1.3mm)

• $\eta$ is an efficiency factor due to atmospheric phase noise (0.9 at 3 mm, 0.8 at 1.3 mm).
• $\hbox{$N_{\rm a}$}$ is the number of antennas (6), and $\hbox{$N_{\rm c}$}$ is the number of configurations: 1 for D, 2 for CD, 2 for BC, and so on.
• $T_{\rm ON}$ is the on-source integration time per configuration in seconds (2 to 8 hours, depending on source declination). Because of various calibration observations the total observing time is typically 1.4 $T_{\rm ON}$.
• $B$ is the spectral bandwidth in Hz (580 MHz for continuum, 40 kHz to 2.5 MHz for spectral line, according to the spectral correlator setup)

Investigators have to specify the $1\sigma$ noise level which is necessary to achieve each individual goal of a proposal, and particularly for projects aiming at deep integrations.