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Register a new userAngular power spectrum of galaxies in the 2MASS Redshift Survey
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We present the measurement and interpretation of the angular power spectrum of nearby galaxies in the 2MASS Redshift Survey catalog with spectroscopic redshifts up to $zapprox 0.1$. We detect the angular power spectrum up to a multipole of $ellapprox 1000$. We find that the measured power spectrum is dominated by galaxies living inside nearby galaxy clusters and groups. We use the halo occupation distribution (HOD) formalism to model the power spectrum, obtaining a fit with reasonable parameters. These HOD parameters are in agreement with the 2MASS galaxy distribution we measure toward the known nearby galaxy clusters, confirming validity of our analysis.
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We use data from the first-year (Y1) observations of the DES collaboration to measure the galaxy angular power spectrum (APS), and search for its BAO feature using a template-fitting method. We test our methodology in a sample of 1800 DES Y1-like mock catalogs. The APS is measured with the pseudo-$C_ell$ method, using pixelized maps constructed from the mock catalogs and the DES mask. The covariance matrix of the $C_ell$s in these tests are also obtained from the mock catalogs. We use templates to model the measured spectra and estimate template parameters firstly from the $C_ell$s of the mocks using two different methods, a maximum likelihood estimator and a MCMC, finding consistent results with a good reduced $chi^2$. Robustness tests are performed to estimate the impact of different choices of settings used in our analysis. After these tests on mocks, we apply our method to a galaxy sample constructed from DES Y1 data specifically for LSS studies. This catalog comprises galaxies within an effective area of 1318 deg$^2$ and $0.6<z<1.0$. We fit the observed spectra with our optimized templates, considering models with and without BAO features. We find that the DES Y1 data favors a model with BAO at the $2.6,sigma$ C.L. with a best-fit shift parameter of $alpha=1.023pm 0.047$. However, the goodness-of-fit is somewhat poor, with $chi^2/$(dof) = 1.49. We identify a possible cause of this issue and show that using a theoretical covariance matrix obtained from $C_ell$s that are better adjusted to data results in an improved value of $chi^2/$(dof) = 1.36 which is similar to the value obtained with the real-space analysis. Our results correspond to a distance measurement of $D_A(z_{rm eff} = 0.81)/r_d = 10.65 pm 0.49$, consistent with the main DES BAO findings. This is a companion paper to the main DES BAO article showing the details of the harmonic space analysis.
We analyse the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 (DR11) sample, which consists of $690,827$ galaxies in the redshift range $0.43 < z < 0.7$ and has a sky coverage of $8,498,text{deg}^2$. We perform our analysis in Fourier space using a power spectrum estimator suggested by Yamamoto et al. (2006). We measure the multipole power spectra in a self-consistent manner for the first time in the sense that we provide a proper way to treat the survey window function and the integral constraint, without the commonly used assumption of an isotropic power spectrum and without the need to split the survey into sub-regions. The main cosmological signals exploited in our analysis are the Baryon Acoustic Oscillations and the signal of redshift space distortions, both of which are distorted by the Alcock-Paczynski effect. Together, these signals allow us to constrain the distance ratio $D_V(z_{rm eff})/r_s(z_d) = 13.89pm 0.18$, the Alcock-Paczynski parameter $F_{rm AP}(z_{rm eff}) = 0.679pm0.031$ and the growth rate of structure $f(z_{rm eff})sigma_8(z_{rm eff}) = 0.419pm0.044$ at the effective redshift $z_{rm eff}=0.57$. We did not find significant systematic uncertainties for $D_V/r_s$ or $F_{rm AP}$ but include a systematic error for $fsigma_8$ of $3.1%$. Combining our dataset with Planck to test General Relativity (GR) through the simple $gamma$-parameterisation, reveals a $sim 2sigma$ tension between the data and the prediction by GR. The tension between our result and GR can be traced back to a tension in the clustering amplitude $sigma_8$ between CMASS and Planck.
Long-wavelength matter inhomogeneities contain cleaner information on the nature of primordial perturbations as well as the physics of the early universe. The large-scale coherent overdensity and tidal force, not directly observable for a finite-volume galaxy survey, are both related to the Hessian of large-scale gravitational potential and therefore of equal importance. We show that the coherent tidal force causes a homogeneous anisotropic distortion of the observed distribution of galaxies in all three directions, perpendicular and parallel to the line-of-sight direction. This effect mimics the redshift-space distortion signal of galaxy peculiar velocities, as well as a distortion by the Alcock-Paczynski effect. We quantify its impact on the redshift-space power spectrum to the leading order, and discuss its importance for the ongoing and upcoming galaxy surveys.
As the determination of density fluctuations becomes more precise with larger surveys, it becomes more important to account for the increased covariance due to the non-linearity of the field. Here I have focussed on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory in real space. I carried out an exact and exhaustive derivation of all tree-level terms of the non-Gaussian covariance of the galaxy $C_ell$, with the computation developed up to the third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method was used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance was derived in all trispectra cases with and without Limbers approximation, with the formulae being of potential interest for other observables than galaxies. The effect of subtracting shot-noise from the measured spectrum is also discussed, and does simplify the covariance, though some non-Gaussian shot-noise terms still remain. I make the link between this complete derivation and partial terms which have been used previously in the literature, including super-sample covariance (SSC). I uncover a wealth of additional terms which were not previously considered, including a whole new class which I dub braiding terms as it contains multipole-mixing kernels. The importance of all these new terms is discussed with analytical arguments. I find that they become comparable to, if not bigger than, SSC if the survey is large or deep enough to probe scales comparable with the matter-radiation equality $k_mathrm{eq}$. A short self-contained summary of the equations is provided in Section 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.
We study an efficient way to enhance the measurability of the galaxy density and/or velocity power spectrum in redshift space. It is based on the angular decomposition with the Tripolar spherical harmonic (TripoSH) basis and applicable even to galaxy distributions in wide-angle galaxy surveys. While nontrivial multipole-mode mixings are inevitable in the covariance of the Legendre decomposition coefficient commonly used in the small-angle power spectrum analysis, our analytic computation of the covariance of the TripoSH decomposition coefficient shows that such mixings are absent by virtue of high separability of the TripoSH basis, yielding the minimum variance. Via the simple signal-to-noise ratio assessment, we confirm that the detectability improvement by the TripoSH decomposition approach becomes more significant at higher multipole modes, and, e.g., the hexadecapole of the density power spectrum has two orders of magnitude improvement. The TripoSH decomposition approach is expected to be applied to not only currently available survey data but also forthcoming wide-angle one, and to bring about something new or much more accurate cosmological information.
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