Geometric Biases in Power-Spectrum Measurements
  The observed distribution of galaxies has local transverse isotropy around
the line-of- sight (LOS) with respect to the observer. The difference in the
statistical clustering signal along and across the line-of-sight encodes
important information about the ge- ometry of the Universe, its expansion rate
and the rate of growth of structure within it. Because the LOS varies across a
survey, the standard Fast Fourier Transform (FFT) based methods of measuring
the Anisotropic Power-Spectrum (APS) cannot be used for surveys with wide
observational footprint, other than to measure the monopole moment. We derive a
simple analytic formula to quantify the bias for higher-order Legendre moments
and we demonstrate that it is scale independent for a simple sur- vey model,
and depends only on the observed area. We derive a similar numerical correction
formula for recently proposed alternative estimators of the APS that are based
on summing over galaxies rather than using an FFT, and can therefore in-
corporate a varying LOS. We demonstrate that their bias depends on scale but
not on the observed area. For a quadrupole the bias is always less than 1 per
cent for k > 0.01h/Mpc at z > 0.32. For a hexadecapole the bias is below 5 per
cent for k>0.05h/Mpc at z>0.32.
