Pointing-list estimate for PMS technical preparation

In the Proposal Management System, the technical preparation of an observation can define the actual mosaic pointing offsets. In this case, the sensitivity estimation can use the actual the actual mosaic layout instead of an idealized layout deduced from the area. It can use the same radiometer equation and the same observing overheads as above, but distribute the time over the actual number of pointings, $n_\ensuremath{\mathrm{point}}$, and then compute the gain in sensitivity from the overlap of the primary beams.

For a given receiver band and reference frequency $\nu$, the expected rms noise of one pointing is

$$\ensuremath{\sigma_\ensuremath{\mathrm{Jy,point}}}(\ensuremath{\n... ...uremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on,point}}}}},$$ (60)

with

$$\ensuremath{\Delta t_\ensuremath{\mathrm{on,point}}}= \ensuremath... ...remath{\mathrm{setup}}}}{\ensuremath{n_\ensuremath{\mathrm{point}}}} \right) }.$$ (61)

Here, $n_\ensuremath{\mathrm{point}}$ is the actual number of offsets in the pointing list. The mosaic efficiency $\eta_\ensuremath{\mathrm{mos}}$ is computed with the same slew and cycling constraints as in the area-based estimate, but using this actual pointing list. When an area is needed in the scan-time or aliasing constraint of the pointing-list method, the area used is the imaged area defined below.

This estimate assumes that all pointings in a given receiver band have the same expected rms noise. This is not a claim about the exact noise in the future calibrated data: the weather, flagging, and detailed observing history of each individual pointing cannot be known at proposal time. This assumption is nevertheless consistent with the mosaic observing strategy, which cycles through the pointings to keep the observing conditions and the $uv$ coverage as homogeneous as possible across the mosaic.

Let $B_i(p,\ensuremath{\nu})$ be the normalized primary beam of pointing $i$, evaluated at sky pixel $p$ and frequency $\nu$. Under the equal expected rms assumption, the dimensionless noise factor between one pointing and the mosaic is

$$\ensuremath{f}_\ensuremath{\nu}(p) = \ensuremath{\displaystyle\le... ...ath{n_\ensuremath{\mathrm{point}}}} B_i^2(p,\ensuremath{\nu}) \right] }^{-1/2}.$$ (62)

The local mosaic sensitivity is therefore

$$\ensuremath{\sigma_\ensuremath{\mathrm{Jy,mos}}}(p,\ensuremath{\n... ...math{\mathrm{Jy,point}}}(\ensuremath{\nu})\,\ensuremath{f}_\ensuremath{\nu}(p),$$ (63)

or, equivalently,

$$\ensuremath{\sigma_\ensuremath{\mathrm{Jy,mos}}}(p,\ensuremath{\n... ...ath{n_\ensuremath{\mathrm{point}}}} B_i^2(p,\ensuremath{\nu}) \right] }^{-1/2}.$$ (64)

The valid imaged area at frequency $\nu$ is defined as the set of non-blanked pixels in the final sensitivity-factor map,

$$\mathcal{A}_\ensuremath{\nu}= \ensuremath{\displaystyle\left\{ p\,\vert\, \ensuremath{f}_\ensuremath{\nu}(p) \mbox{ is not blanked} \right\}}.$$ (65)

The single representative sensitivity reported by the pointing-list method is the median over this band-specific valid area:

$$\ensuremath{\sigma_\ensuremath{\mathrm{Jy,typ}}}(\ensuremath{\nu}... ...\ensuremath{\sigma_\ensuremath{\mathrm{Jy,mos}}}(p,\ensuremath{\nu}) \right\}}.$$ (66)

Equivalently,

$$\ensuremath{\sigma_\ensuremath{\mathrm{Jy,typ}}}(\ensuremath{\nu}... ...\mathrm{Jy,point}}}(\ensuremath{\nu})\,\tilde{\ensuremath{f}}_\ensuremath{\nu}, \quad \tilde{\ensuremath{f}}_\ensuremath{\nu}= \ensuremath{\mathr... ... \ensuremath{\displaystyle\left\{ \ensuremath{f}_\ensuremath{\nu}(p) \right\}}.$$ (67)

In dual-band mode, this median is computed independently for each band, using each band's own non-blanked area $\mathcal{A}_\ensuremath{\nu}$. It is not computed on the common overlap area of the two bands.

The minimum and maximum values over the same valid area could also be reported as

$$\ensuremath{\sigma_\ensuremath{\mathrm{Jy,min}}}(\ensuremath{\nu}... ...nu}), \quad \ensuremath{\sigma_\ensuremath{\mathrm{Jy,max}}}(\ensuremath{\nu}).$$ (68)

The maximum value mainly indicates the sensitivity degradation at the accepted mosaic edge. With a primary-beam truncation at 20%, a relative factor close to 5 can occur by construction in the least-covered accepted pixels. Pixels outside this support are blanked rather than assigned still larger formal noise values.