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Mapping

The rms brightness temperature is related to the point source sensitivity by

\begin{displaymath}
\delta T_m = \frac{\rho \lambda^{2}}{ \theta _{1} \theta _{2} } \sigma
\end{displaymath} (2)

where $\lambda$ is the wavelength in millimeters, $\theta _1$ and $\theta_2$ are the beam major and minor axis in arcseconds, $\sigma$ is the point source sensitivity in Jy, and $\rho$$\simeq$15 for untapered maps with natural weighting.

For a typical experiment with configuration BC or CD, tracking the source for 8 hours (but spending 2 hours on calibration) on each configuration, we obtain $\delta T_{BC}$=0.11 K and $\delta T_{CD}$=0.03 K, for 0.625 MHz channel spacing with the spectral correlator, with the same assumptions as above at 90 GHz. The factor $\rho$ is increased by uniform weighting and tapering: the amount depends on the uv-coverage and on the phase noise as a function of baseline lengths, but tapering also increases the synthesized beam size.

An equivalent way to look at noise in a map is by comparison to the single-dish sensitivity (given here for position switching)

\begin{displaymath}
\delta T_s = \frac{2 T_{sys}}{\sqrt{B T_{ON}}}
\cdot \frac{1}{\sqrt{N_{\rm pol}}}
\end{displaymath} (3)

which is typically $\delta T_s$=4.5 mK in one hour (for a channel spacing of 0.625 MHz and a frequency below 110 GHz).

The mapping sensitivity is roughly related to $\delta T_s$ by

\begin{displaymath}
\delta T_m = \frac{\Omega ^2}{(\theta _1 \theta _2)} \frac{\delta T_s}
{\eta \sqrt{N(N-1)} }
\end{displaymath} (4)

where $\Omega$ is the size of the antenna primary beam in seconds of arc. Then $\delta T_{CD} = 40 \delta T_s$, $\delta T_{BC} = 190
\delta T_s$, and $\delta T_{AB} = 590 \delta T_s$. In practice, a source that is well detected but unresolved at the 30 m telescope can easily be imaged at NOEMA.


next up previous contents index
Next: Array Operation Up: Sensitivity Previous: Detection experiments   Contents   Index
Gildas manager 2015-03-19