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Abstract
In this paper, we study how to directly measure the effect of peculiar velocities in the observed angular power spectra. We do this by constructing a new anti-symmetric estimator of Large Scale Structure using different dark matter tracers. We show that the Doppler term is the major component of our estimator and we show that we can measure it with a signal-to-noise ratio up to ∼ 50 using a futuristic SKAO HI galaxy survey. We demonstrate the utility of this estimator by using it to provide constraints on the Euler equation.
Highlights
Detectable, such as lensing magnification [11] and effects which are linearly dependent on the velocity, commonly referred to as the Doppler term [12]
The authors of [20,21,22] have studied the observational asymmetries in galaxy cross-correlations induced by the Doppler term, which will be the focus of our paper
Our set goal for this paper was to build an estimator based on the observed angular power spectrum which was the angular equivalent to the Doppler dipole proposed by [12] with the two-point function
Summary
Let us assume that the galaxy type A has an average proper number density of sources nA. The first term of Equation 2.5 is the conventional density contrast term in Newtonian gauge, the second the redshift space distortions (or the first Kaiser term for the aficionados), the following is the Doppler term and the last is the lensing contribution. Which measures how the comoving number of sources changes with redshift Introducing another tracer of dark matter as galaxy type B, the angular power spectrum can be written in terms of the primordial power spectra of the curvature perturbation P(k) and transfer functions ∆W as [5]. The transfer function ∆WA takes into account the fact that any survey will have a redshift distribution of sources A pA(z) and a window function W A(z, zi). Where we called “δ” for density only, “R” for RSD, “L” for the lensing contribution from κ, and “D” for Doppler
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