Image Sensitivity

Image sensitivity is the RMS thermal noise (ΔI_m) expected in a single-polarization image. Image sensitivities for the 10-station VLBA, for typical observing parameters, are listed in column [7] of table 5.1.

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

$$\mathrm{\Delta }{I}_m=\mathrm{S}\mathrm{E}\mathrm{F}\mathrm{D}/[{\eta }_s\cdot (N\cdot (N-1)\cdot \mathrm{\Delta }\nu \cdot t_{\mathrm{i}\mathrm{n}\mathrm{t}}{)}^{1/2}]\mathrm{J}\mathrm{y}\mathrm{b}\mathrm{e}\mathrm{a}{\mathrm{m}}^{-1}$$

Parameters SEFD, ${\eta }_s$, and $\mathrm{\Delta }\nu$ are the same as those used in computing baseline sensitivity, $N$ is the number of observing stations, and $t_{\mathrm{i}\mathrm{n}\mathrm{t}}$ 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 new EVN Observation Planner and the EVN sensitivity calculator both provide 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 ΔI_m per polarization, then for an image of Stokes I, Q, U, or V,

$$\mathrm{\Delta }I=\mathrm{\Delta }Q=\mathrm{\Delta }U=\mathrm{\Delta }V=\frac{\mathrm{\Delta }{I}_m}{\sqrt{2}}$$

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

$$\mathrm{\Delta }P=0.655\times \mathrm{\Delta }Q=0.655\times \mathrm{\Delta }U$$

It is sometimes useful to express $\mathrm{\Delta }{I}_m$ in terms of an RMS brightness temperature in Kelvins ($\mathrm{\Delta }{T}_B$) measured within the synthesized beam. An approximate formula for a single-polarization image is

$$\mathrm{\Delta }{T}_b\sim 320\times \mathrm{\Delta }{I}_m\times (B_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{k}\mathrm{m}}{)}^2\mathrm{K}$$

where $B_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{k}\mathrm{m}}$ is as in Table 8.2.

The new EVN Observation Planner is a versatile tool for estimating the image sensitivity of an observation, along with a great deal of other useful information, especially when the science target location is known. When submitting a VLBA proposal, user must upload either a copy of the PDF file generated by EVN Observation Planner or a screen shot from the EVN sensitivity calculator in the NRAO Proposal Submission Tool.