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Register a new userQuantification of the multi-streaming effect in Redshift Space Distortion
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Yi Zheng
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Both multi-streaming (random motion) and bulk motion cause the Finger-of-God (FoG) effect in redshift space distortion (RSD). We apply a direct measurement of the multi-streaming effect in RSD from simulations, proving that it induces an additional, non-negligible FoG damping to the redshift space density power spectrum. We show that, including the multi-streaming effect, the RSD modelling is significantly improved. We also provide a theoretical explanation based on halo model for the measured effect, including a fitting formula with one to two free parameters. The improved understanding of FoG helps break the $fsigma_8-sigma_v$ degeneracy in RSD cosmology, and has the potential of significantly improving cosmological constraints.
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We show that spherical infall models (SIMs) can better describe some galaxy clusters in redshift slice space than in traditional axially-convolved projection space. This is because in SIM, the presence of transverse motion between cluster and observer, and/or shear flow about the cluster (such as rotation), causes the infall artifact to tilt, obscuring the characteristic two-trumpet profile; and some clusters resemble such tilted artifacts. We illustrate the disadvantages of applying SIM to convolved data and, as an alternative, introduce a method fitting a tilted 2D envelope to determine a 3D envelope. We also introduce a fitting algorithm and test it on toy SIM simulations as well as three clusters (Virgo, A1459, and A1066). We derive relations useful for using the tilt and width-to-length ratio of the fitted envelopes to analyze peculiar velocities. We apply them to our three clusters as a demonstration. We find that transverse motion between cluster and observer can be ruled out as sole cause of the observed tilts, and that a multi-cluster study could be a feasible way to find our infall toward Virgo cluster.
The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors ${bf k_1,k_2,k_3}$ with respect to the line of sight. Here we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane parallel approximation only the first four even $ell$ multipoles have non-zero values, and we present explicit analytical expressions for all the non-zero multipoles {it i.e.} upto $ell=6,m=4$. The ratio of the different multipole moments to the real space bispectrum depends only on $beta_1$ the linear redshift distortion parameter and the shape of the triangle. Considering triangles of all possible shapes, we have studied how this ratio depends on the shape of the triangle for $beta_1=1$. We have also studied the $beta_1$ dependence for some of the extreme triangle shapes. If measured in future, these multipole moments hold the potential of constraining $beta_1$. The results presented here are also important if one wishes to constrain $f_{text{NL}}$ using redshift surveys.
We apply the Minkowski tensor statistics to three dimensional Gaussian random fields. Minkowski tensors contain information regarding the orientation and shape of excursion sets, that is not present in the scalar Minkowski functionals. They can be used to quantify globally preferred directions, and additionally provide information on the mean shape of subsets of a field. This makes them ideal statistics to measure the anisotropic signal generated by redshift space distortion in the low redshift matter density field. We review the definition of the Minkowski tensor statistics in three dimensions, focusing on two coordinate invariant quantities $W^{0,2}_{1}$ and $W^{0,2}_{2}$. We calculate the ensemble average of these $3 times 3$ matrices for an isotropic Gaussian random field, finding that they are proportional to products of the identity matrix and a corresponding scalar Minkowski functional. We show how to numerically reconstruct $W^{0,2}_{1}$ and $W^{0,2}_{2}$ from discretely sampled fields and apply our algorithm to isotropic Gaussian fields generated from a linear $Lambda$CDM matter power spectrum. We then introduce anisotropy by applying a linear redshift space distortion operator to the matter density field, and find that both $W^{0,2}_{1}$ and $W^{0,2}_{2}$ exhibit a distinct signal characterised by inequality between their diagonal components. We discuss the physical origin of this signal and how it can be used to constrain the redshift space distortion parameter $Upsilon equiv f/b$.
The post-reionization ${rm HI}$ 21-cm signal is an excellent candidate for precision cosmology, this however requires accurate modelling of the expected signal. Sarkar et al. (2016) have simulated the real space ${rm HI}$ 21-cm signal, and have modelled the ${rm HI}$ power spectrum as $P_{{rm HI}}(k)=b^2 P(k)$ where $P(k)$ is the dark matter power spectrum and $b(k)$ is a (possibly complex) scale dependent bias for which fitting formulas have been provided. This paper extends these simulations to incorporate redshift space distortion and predict the expected redshift space ${rm HI}$ 21-cm power spectrum $P^s_{{rm HI}}(k_{perp},k_{parallel})$ using two different prescriptions for the ${rm HI}$ distributions and peculiar velocities. We model $P^s_{{rm HI}}(k_{perp},k_{parallel})$ assuming that it is the product of $P_{{rm HI}}(k)=b^2 P(k)$ with a Kaiser enhancement term and a Finger of God (FoG) damping which has $sigma_p$ the pair velocity dispersion as a free parameter. Considering several possibilities for the bias and the damping profile, we find that the models with a scale dependent bias and a Lorentzian damping profile best fit the simulated $P^s_{{rm HI}}(k_{perp},k_{parallel})$ over the entire range $1 le z le 6$. The best fit value of $sigma_p$ falls approximately as $(1+z)^{-m}$ with $m=2$ and $1.2$ respectively for the two different prescriptions. The model predictions are consistent with the simulations for $k < 0.3 , {rm Mpc}^{-1}$ over the entire $z$ range for the monopole $P^s_0(k)$, and at $z le 3$ for the quadrupole $P^s_2(k)$. At $z ge 4$ the models underpredict $P^s_2(k)$ at large $k$, and the fit is restricted to $k < 0.15 , {rm Mpc}^{-1}$.
We study potential systematic effects of assembly bias on cosmological parameter constraints from redshift space distortion measurements. We use a semi-analytic galaxy formation model applied to the Millennium N-body WMAP-7 simulation to study the effects of halo assembly bias on the redshift space distortions of the galaxy correlation function. We look at the pairwise velocities of galaxies living in haloes with concentrations and ages in the upper and lower quintiles, and find that the velocity differences between these are consistent with those reported for real-space clustering analyses, i.e. samples with higher clustering also exhibit stronger infall pairwise motions. This can also be seen in the monopole and quadrupole of the redshift-space correlation function. We find that regardless of the method of measurement, the changes in the $beta$ parameter due to different secondary halo parameters fully tracks the change in the bias Parameter. Hence, assembly bias does not introduce detectable systematics in the inferred logarithmic growth factor.
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