Sensitivity

The 1 sigma point source sensitivity (in Jy) can be derived with:

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

where

• $J_{pK}$ 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.

• $\eta$ is an additional efficiency factor due to atmospheric decorrelation. The short and long term atmospheric phase fluctuations depend on the baseline length, atmospheric stability and frequency.

• $T_{\rm sys}$ is the system temperature outside the atmosphere, i.e. corrected for atmospheric transmission.

• $N_{\rm a}$ is the number of antennas

• $T_{\rm ON}$ is the on-source integration time in seconds. Because of various calibration overheads, the total observing time is typically at least 1.6 $T_{\rm ON}$ .

• $B$ is the noise equivalent bandwidth of the correlator in Hz, equal to $\sim$1.8 times the channel separation; the effective channel width for standard apodization (using a Hanning time-lag window) is 1.772 times the channel separation.

• $N_{\rm pol}$ is the number of polarizations: 1 for single polarization and 2 for dual polarization

To provide the most realistic and up-to-date estimates of the sensitivity of NOEMA, NOEMA provides sophisticated sensitivity calculators via PMS (see Section ) and via the GILDAS software package ASTRO (please use the most recent GILDAS version when preparing your proposals). Both softwares use the same calculations, based on equation (1) given above, and are regularly updated with the latest NOEMA characteristics.

The point source sensitivity obviously depends on the observing frequency and hence a so called representative frequency has to be choosen in order to calculate the sensitivity in ASTRO and PMS. In PMS, the representative frequency has to be within the frequency range and for high spectral resolution projects within one of the high resolution spectral windows that are selected in the respective technical sheet. The representative frequency does not have to be identical to the actual tuning frequency. Please note, that due to the large bandwidth and the dual-sideband mode, the noise can vary significantly with frequency in the available frequency range. Especially, if one of the sidebands is close to a receiver band edge, significant differences in the noise can occur within and between the sidebands. This should be taken into consideration when setting the representative frequency for each tuning. Please note that PMS and ASTRO take into account variations of the noise across the entire 15.488 GHz bandwidth to calculate the continuum sensitivity. Both tools also account for the declination of the source to estimate the rms noise levels. Longer telescope times are needed for sources at low declinations ( $\delta < -10^\circ$) to achieve the same point-source sensitivity.