scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

scholarly journals Covariance of the galaxy angular power spectrum with the halo model

2018 ◽  
Vol 615 ◽  
pp. A1 ◽  
Author(s):  
Fabien Lacasa
Keyword(s):  
Perturbation Theory ◽  
Shot Noise ◽  
Real Space ◽  
Density Fluctuations ◽  
Tree Level ◽  
Analytical Prediction ◽  
Angular Power Spectrum ◽  
Sample Covariance ◽  
The Galaxy ◽  
Non Gaussian

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 galaxyCℓ, 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 Limber’s 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 equalitykeq. A short self-contained summary of the equations is provided in Sect. 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.

scholarly journals Studying high-z galaxies with [C ii]  intensity mapping

2019 ◽  
Vol 490 (2) ◽  
pp. 1928-1943 ◽  
Author(s):  
B Yue ◽  
A Ferrara
Keyword(s):  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Contamination Level ◽  
Microwave Background ◽  
Noise Component ◽  
Intensity Mapping ◽  
Detection Depth ◽  
Infrared Background ◽  
Full Power

ABSTRACT We investigate the [C ii] line intensity mapping (IM) signal from galaxies in the Epoch of Reionization (EoR) to assess its detectability, the possibility to constrain the $L_{\rm C\,{\small II}}\!-\!{\rm SFR}$ relation, and to recover the [C ii] luminosity function (LF) from future experiments. By empirically assuming that ${\rm log}\,L_{\rm C\,{\small II}}={\rm log}\,A+\gamma {\rm SFR}\pm \sigma _\mathrm{ L}$, we derive the [C ii] LF from the observed UV LF, and the [C ii] IM power spectrum. We study the shot noise and the full power spectrum separately. Although, in general, the shot-noise component has a much higher signal-to-noise ratio than the clustering one, it cannot be used to put independent constraints on log A and γ. Full power spectrum measurements are crucial to break such degeneracy and reconstruct the [C ii] LF. In our fiducial survey S1 (inspired by CCAT-p/1000 h) at z ∼ 6, the shot-noise (clustering) signal is detectable for two (one) of the five considered $L_{\rm C\,{\small II}}\!-\!{\rm SFR}$ relations. The shot noise is generally dominated by galaxies with $L_{\rm C\,{\small II}}\gtrsim 10^{8}\!-\!10^{9}~ \mathrm{L}_\odot$ (MUV ∼ −20 to −22), already at reach of ALMA pointed observations. However, given the small field of view of such telescope, an IM experiment would provide unique information on the bright end of the LF. The detection depth of an IM experiment crucially depends on the (poorly constrained) $L_{\rm C\,{\small II}}\!-\!{\rm SFR}$ relation in the EoR. If the $L_{\rm C\,{\small II}}\!-\!{\rm SFR}$ relation varies in a wide log A–γ range, but still consistent with ALMA [C ii] LF upper limits, even the signal from galaxies with $L_{\rm C\,{\small II}}$ as faint as ∼107 L⊙ could be detectable. Finally, we consider the contamination by continuum foregrounds (cosmic infrared background, dust, cosmic microwave background) and CO interloping lines, and derive the requirements on the residual contamination level to reliably extract the [C ii] signal.

scholarly journals Cosmological parameters from the likelihood analysis of the galaxy power spectrum and bispectrum in real space

2021 ◽  
Vol 2021 (11) ◽  
pp. 038
Author(s):  
Andrea Oddo ◽  
Federico Rizzo ◽  
Emiliano Sefusatti ◽  
Cristiano Porciani ◽  
Pierluigi Monaco
Keyword(s):  
Power Spectrum ◽  
Cosmological Parameters ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Real Space ◽  
Tree Level ◽  
Large Set ◽  
Cross Covariance ◽  
Likelihood Analysis ◽  
The Galaxy

Abstract We present a joint likelihood analysis of the halo power spectrum and bispectrum in real space. We take advantage of a large set of numerical simulations and of an even larger set of halo mock catalogs to provide a robust estimate of the covariance properties. We derive constraints on bias and cosmological parameters assuming a theoretical model from perturbation theory at one-loop for the power spectrum and tree-level for the bispectrum. By means of the Deviance Information Criterion, we select a reference bias model dependent on seven parameters that can describe the data up to k max,P = 0.3 h Mpc-1 for the power spectrum and k max,B = 0.09 h Mpc-1 for the bispectrum at redshift z = 1. This model is able to accurately recover three selected cosmological parameters even for the rather extreme total simulation volume of 1000h -3 Gpc3. With the same tools, we study how relations among bias parameters can improve the fit while reducing the parameter space. In addition, we compare common approximations to the covariance matrix against the full covariance estimated from the mocks, and quantify the (non-negligible) effect of ignoring the cross-covariance between the two statistics. Finally, we explore different selection criteria for the triangular configurations to include in the analysis, showing that excluding nearly equilateral triangles rather than simply imposing a fixed maximum k max,B on all triangle sides can lead to a better exploitation of the information contained in the bispectrum.

scholarly journals Probing delayed-end reionization histories with the 21-cm LAE cross-power spectrum

2020 ◽  
Vol 494 (1) ◽  
pp. 703-718 ◽  
Author(s):  
Lewis H Weinberger ◽  
Girish Kulkarni ◽  
Martin G Haehnelt
Keyword(s):  
Power Spectrum ◽  
Dynamic Range ◽  
Signal To Noise Ratio ◽  
High Dynamic Range ◽  
Integration Time ◽  
Signal To Noise ◽  
Total Signal ◽  
The Cross ◽  
Noise Ratio ◽  
Cross Power Spectrum

ABSTRACT We model the 21-cm signal and Lyman-α emitter (LAE) population evolution during the epoch of reionization in order to predict the 21-cm LAE cross-power spectrum. We employ high-dynamic-range simulations of the intergalactic medium to create models that are consistent with constraints from the cosmic microwave background, Lyman-α forest, and LAE population statistics. Using these models we consider the evolution of the cross-power spectrum for a selection of realistic reionization histories and predict the sensitivity of current and upcoming surveys to measuring this signal. We find that the imprint of a delayed end to reionization can be observed by future surveys, and that strong constraints can be placed on the progression of reionization as late as z = 5.7 using a Subaru–SKA survey. We make predictions for the signal-to-noise ratios achievable by combinations of Subaru/PFS (Prime Focus Spectrograph) with the MWA, LOFAR, HERA, and SKA interferometers for an integration time of 1000 h. We find that a Subaru–SKA survey could measure the cross-power spectrum for a late reionization at z = 6.6 with a total signal-to-noise ratio greater than 5, making it possible to constrain both the timing and bubble size at the end of reionization. Furthermore, we find that expanding the current Subaru/PFS survey area and depth by a factor of three would double the total signal-to-noise ratio.

scholarly journals Minimum variance estimation of galaxy power spectrum in redshift space

2020 ◽  
Vol 498 (1) ◽  
pp. L77-L81
Author(s):  
Maresuke Shiraishi ◽  
Teppei Okumura ◽  
Naonori S Sugiyama ◽  
Kazuyuki Akitsu
Keyword(s):  
Power Spectrum ◽  
Variance Estimation ◽  
Signal To Noise Ratio ◽  
Minimum Variance ◽  
Wide Angle ◽  
Decomposition Approach ◽  
Galaxy Surveys ◽  
Angle Data ◽  
The Galaxy ◽  
Decomposition Coefficient

ABSTRACT 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 non-trivial multipole-mode mixings are inevitable in the covariance of the Legendre decomposition coefficient commonly used in the small-angle power spectrum analysis, our analytical 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 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 data, and to bring about something new or much more accurate cosmological information.

scholarly journals Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Fangfang ◽  
Sun Shuli
Keyword(s):  
Computational Cost ◽  
Covariance Matrices ◽  
The State ◽  
Multirate Systems ◽  
Multiplicative Noises ◽  
Cross Covariance ◽  
Sampling Points ◽  
Optimal Fusion ◽  
The Cross ◽  
Local Filters

This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

scholarly journals Perturbation theory approach for the power spectrum: from dark matter in real space to massive haloes in redshift space

2012 ◽  
Vol 2012 (11) ◽  
pp. 029-029 ◽  
Author(s):  
Héctor Gil-Marín ◽  
Christian Wagner ◽  
Licia Verde ◽  
Cristiano Porciani ◽  
Raul Jimenez
Keyword(s):  
Dark Matter ◽  
Perturbation Theory ◽  
Power Spectrum ◽  
Real Space ◽  
Theory Approach

scholarly journals Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

2019 ◽  
Vol 490 (4) ◽  
pp. 4688-4714 ◽  
Author(s):  
Matteo Rizzato ◽  
Karim Benabed ◽  
Francis Bernardeau ◽  
Fabien Lacasa
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Principal Component ◽  
Weak Lensing ◽  
Galaxy Surveys ◽  
Point Correlation ◽  
Non Gaussian ◽  
The Impact

ABSTRACT We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum–bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

scholarly journals Cross-correlation between cosmological and astrophysical datasets: the Planck and Herschel case

2014 ◽  
Vol 10 (S306) ◽  
pp. 202-205 ◽  
Author(s):  
Federico Bianchini ◽  
Andrea Lapi
Keyword(s):  
Power Spectrum ◽  
Cross Correlation ◽  
Forthcoming Paper ◽  
Joint Analysis ◽  
Atlas Data ◽  
Λcdm Model ◽  
The Galaxy ◽  
The Cross ◽  
Galaxy Bias ◽  
Cross Power Spectrum

AbstractWe present the first measurement of the correlation between the map of the CMB lensing potential derived from the Planck nominal mission data and z ≳ 1.5 galaxies detected by Herschel-ATLAS (H-ATLAS) survey covering about 550 deg2. We detect the cross-power spectrum with a significance of ∼ 8.5σ, ruling out the absence of correlation at 9σ. We check detection with a number of null tests. The amplitude of cross-correlation and the galaxy bias are estimated using joint analysis of the cross-power spectrum and the galaxy survey auto-spectrum, which allows to break degeneracy between these parameters. The estimated galaxy bias is consistent with previous estimates of the bias for the H-ATLAS data, while the cross-correlation amplitude is higher than expected for a ΛCDM model. The content of this work is to appear in a forthcoming paper Bianchini, et al. (2014).

Sign in / Sign up

Export Citation Format

Share Document