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 $T=30$ 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. http://www.lsc-group.phys.uwm.edu/lal/slug/nightly/doxygen/html/TwoDMesh_8c.html LALCreate2DMesh()

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: git-clone git://n0.aei.uni-hannover.de:shared/octapps.git