IMAGE SENSITIVITY

Typical image sensitivities for the VLBA are listed in Table 3. Alternatively, the following formula may be used in conjunction with the typical zenith $SEFD\/$s for VLBA antennas given in Table 3 (or a different $SEFD\/$ for lower elevations or poor weather) to calculate the RMS thermal noise ( $\Delta I_{\rm m}$) expected in a single-polarization image, assuming natural weighting (Wrobel 1995; Wrobel & Walker 1999):

$$\Delta I_{\rm m} = {1 \over \eta_{\rm s}} \times { SEFD \o... ...s \Delta\nu \times t_{\rm int}} }\ \ {\rm Jy~beam}^{-1},$$ (8)

where $\eta_{\rm s}$ is discussed in Section 14; $N$ is the number of VLBA antennas available; $\Delta\nu$ is the bandwidth [Hz]; and $t_{\rm int}$ is the total integration time on source [s]. The expression for image noise becomes rather more complicated for a set of non-identical antennas such as the HSA, and may depend quite strongly on the data weighting that is chosen in imaging. The best strategy in this case is to estimate image sensitivity using the EVN sensitivity calculator at http://www.evlbi.org/cgi-bin/EVN/calc . As an example, note that the rms noise at 22 GHz for the 10 antenna 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 $V$,

$$\Delta I = \Delta Q = \Delta U = \Delta V = {\Delta I_{\rm m} \over \sqrt2}.$$ (9)

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

$$\Delta P = 0.655 \times \Delta Q = 0.655 \times \Delta U.$$ (10)

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

$$\Delta T_{\rm b} \sim 320 \times \Delta I_{\rm m} \times (B^{\rm km}_{\rm max})^2\ \ {\rm K},$$ (11)

where $B^{\rm km}_{\rm max}$ is as in Equation 1.