10 IMAGE SENSITIVITY

Image sensitivity is the RMS thermal noise ( $\Delta I_{\rm m}$) expected in a single-polarization image. Image sensitivities with the 10-station VLBA, for typical observing parameters, are listed in Table 3.

Alternatively, the image sensitivity for a homogeneous array with natural weighting can be calculated using the following formula (Wrobel 1995; Wrobel & Walker 1999).

$$\Delta I_{\rm m} = {1 \over \eta_{\rm s}} \times { {\rm SE... ...s \Delta\nu \times t_{\rm int}} }\ \ {\rm Jy~beam}^{-1},$$ (4)

Parameters $\eta_{\rm s}$, SEFD, and $\Delta\nu$ are those described in Section 9. $N$ is the number of observing stations, and $t_{\rm int}$ is the total integration time on source in seconds.

The expression for image noise becomes rather more complicated for a heterogeneous array such as the HSA, and may depend quite strongly on the data weighting that is chosen in imaging. The EVN sensitivity calculator at http://www.evlbi.org/cgi-bin/EVNcalc provides a convenient estimate. For example, the RMS noise at 22 GHz for the 10-station VLBA in a 1-hr integration is reduced by a factor between 4 and 5 by adding the GBT and the phased VLA.

If simultaneous dual polarization data are available with the above value of $\Delta I_{\rm m}$ per polarization, then for an image of Stokes $I$, $Q$, $U$, or $V$,

$$\Delta I = \Delta Q = \Delta U = \Delta V = {\Delta I_{\rm m} \over \sqrt2}.$$ (5)

For a polarized intensity image of $P = \sqrt{Q^2 + U^2}$,

$$\Delta P = 0.655 \times \Delta Q = 0.655 \times \Delta U.$$ (6)

It is sometimes useful to express $\Delta I_{\rm m}$ in terms of an RMS brightness temperature in Kelvins ( $\Delta T_{\rm b}$) measured within the synthesized beam. An approximate formula for a single-polarization image is

$$\Delta T_{\rm b} \sim 320 \times \Delta I_{\rm m} \times (B^{\rm km}_{\rm max})^2\ \ {\rm K},$$ (7)

where $B^{\rm km}_{\rm max}$ is as in Table 5 and in Equation 2.