Some Notes on the S4R2 Paper
Uniform templates in equatorial plane
Testing the intuitive idea that the sky-metric we used is isotropic in the equatorial plane: this might have been thought from
Fig.4 in the Paper, showing the sky-templates in the equatorial plane are approximately uniform.
We generated the metric ellipses for an observation time of
hours sampled over the northern hemisphere of the
sky, both projected onto a Freq = const. surface ("projected") and simply ''restricted'' to Freq = const ("unprojected"), in
three coordinate systems for the sky: equatorial sky-angles, unit vectors in equatorial plane, and unit-vectors in the ecliptic plane:
| Northern hemisphere using sky-angles
|| Northern hemisphere represented in the equatorial plane
|| Northern hemisphere represented in the ecliptic plane
We see that the (frequency-projected) sky-ellipses in the equatorial plane are '''not''' circular.
The reason for the approximately uniform distribution of sky-templates in the equatorial plane
therefore lies with the gridding algorithm in the sky, i.e.
To illustrate that this is in principle possible, consider the following simple example: a non-isotropic metric (ellipses are not circles),
still we can construct a uniform, square template lattice!
These plots were produced using the octave scripts ''plotSkyMetrics_S4R2.m'' and ''fakeFlatGrid.m'' respectively, which
are found in this tarball
. Note: you need to install ''octapps'' for these scripts to work, which
you can download using: