Detection experiments

The point source sensitivity (one $\sigma$ level) for an N antenna array, over a bandwith $\delta\nu$ in a time $\delta t$ is given by

$$\delta S = \frac{\rho _{e} T_{sys}}{\eta _{c}\eta _{p}\eta _{j} \sqrt{N(N-1)} \sqrt{\delta\nu \delta t}}$$ (1)

where

• T_sys is the system temperature outside the atmosphere, i.e. corrected for atmospheric transmission (typically 150K SSB below 110 GHz, but 300K (250) at 115 GHz, and 500K (350) at 230 GHz in summer. Bracked values are for typical winter conditions),
• $\rho _{e}$ is the antenna efficiency (Jy K^-1) i.e. $2k/(\eta _a A)$ with $\eta _{a}$ the aperture efficiency, A the antenna collecting area, and k the Boltzmann constant (22 Jy.K^-1 at 85 GHz, 35 Jy.K^-1 at 230 GHz),
• $\eta _{c}$ is the correlator efficiency (0.88)
• $\eta _{j}$ is the instrumental decorrelation coefficient, related to the oscillator phase jitter by $\eta _{j} = e^{-\sigma_{j}^2/2}$ (0.90 to 0.98), and
• $\eta _{p}$ is the atmospheric decorrelation coefficient, related to the atmospheric phase noise by $\eta _{p} = e^{-\sigma_{p}^2/2}$ (0.6 to 0.98).

For the correlator, $\delta\nu$ is the noise equivalent bandwidth, equal to 1.87 times the channel separation; the effective channel width is 1.60 times the channel separation.

The instrumental phase jitter $\sigma _{j}$ typically ranges between 3 and 5 degrees at 90 GHz, and increases linearly with frequency. The short and long term atmospheric phase fluctuations $\sigma _{p}$ depend on the baseline length and water vapor content, ranging up to 60 degrees on the longest baseline under ``not optimum'' conditions (7 mm water vapor). 15 degrees is more typical for short (< 100 m) baselines.

With typical values for Plateau de Bure we find at 90 GHz $\delta S =$0.4mJy (best) to 0.8mJy (worst) for a one hour integration in a 580MHz bandwidth. For a full synthesis (2 configurations, or 16 hours on source), this goes down to about 0.1 mJy. At 115 GHz, the sensitivity is degraded by about a factor 2 because of higher system noise and atmospheric phase fluctuations. At 230 GHz, the expected rms noise is 1.5 to 3 mJy in one hour 0.4 mJy to 0.8 mJy after 16 hours).