Signal to Noise

The rms noise can be computed from

$$\sigma = \frac{J_{\rm pK} T_{\rm sys}} {\eta \sqrt{N_{\rm a... ...m a}-1) N_{\rm c} T_{\rm ON} B}} \frac{1}{\sqrt{N_{\rm pol}}}$$ (1)

where

• $J_{\rm pK}$ is the conversion factor from Kelvin to Jansky (22 Jy/K at 3mm, 35 Jy/K at 1.3mm)
• $T_{\rm sys}$ is the system temperature ($T_{\rm sys}$ = 100K below 110GHz, 180K at 115GHz, 250K at 230GHz for sources at $\delta \ge 20^\circ$ and for typical summer conditions.)
• $\eta$ is an efficiency factor due to atmospheric phase noise (0.9 at 3mm, 0.8 at 1.3mm).
• $N_{\rm a}$ is the number of antennas (5), and $N_{\rm c}$ is the number of configurations: 1 for D, 2 for CD, 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 (up to 2 GHz for continuum, 40 kHz to 2.5 MHz for spectral line, according to the spectral correlator setup)
• $N_{\rm pol}$ is the number of polarizations: 1 for single polarization and 2 for dual polarization (see section Correlator for details).

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