Detection experiments

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

$$\delta S = \frac{\rho _{e} T_{sys}}{\eta _{p}\eta _{j} \sqrt... ... \sqrt{\delta\nu \delta t}} \cdot \frac{1}{\sqrt{N_{\rm pol}}}$$ (1)

where

• $\rho _{e}$ 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 (22Jy.K$^{-1}$ at 85GHz, 29Jy.K$^{-1}$ at 150GHz, 35Jy.K$^{-1}$ at 230GHz and 45 Jy/K at 350GHz),
• $T_{sys}$ is the system temperature outside the atmosphere, i.e. corrected for atmospheric transmission (typically 100K SSB below 110 GHz, but 180K (170K) at 115 GHz, 150K (130K) below 150GHz, 200K (170K) above 150GHz, and 250K (200K) at 230 GHz in summer (values in brackets are for typical winter conditions)). Use $T_{sys}=370K$ at 350GHz,
• $\eta _{j}$ is the instrumental decorrelation coefficient, related to the oscillator phase jitter by $\eta _{j} = e^{-\sigma_{j}^2/2}$ (0.90 to 0.98),
• $\eta _{p}$ is the atmospheric decorrelation coefficient, related to the atmospheric phase noise by $\eta _{p} = e^{-\sigma_{p}^2/2}$ (0.6 to 0.98),
• $\delta\nu$ is the noise equivalent bandwidth of the correlator in Hz, equal to 1.88 times the channel separation; the effective channel width for standard apodization (using a Welch time-lag window) is 1.60 times the channel separation,
• $\delta t$ 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 1.6 $\delta t$, and
• $N_{\rm pol}$ is the number of polarizations: 1 for single polarization and 2 for dual polarization (see Section  for details).

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 of the atmosphere. 15 degrees is a typical value for short ($<$ 100m) baselines.

With typical values for Plateau de Bure and assuming 6 antennas, we find at 90 GHz $\delta S =$ 0.08mJy ( $\eta _{j}*\eta _{j}=0.96$) to 0.15mJy ( $\eta _{j}*\eta _{j}=0.54$) for a one hour integration in a 3600MHz bandwidth and using both polarizations. For a full synthesis (2 configurations, or 11 hours on source), this goes down to about 0.03mJy ( $\eta _{j}*\eta _{j}=0.96$) to 0.04mJy ( $\eta _{j}*\eta _{j}=0.54$). 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 0.26 to 0.53mJy in one hour (0.08 mJy to 0.14 mJy after 11 hours in average winter conditions).