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Modeling the cross power spectrum of Sunyaev-Zeldovich and X-ray surveys

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 Added by Hurier Guillaume Dr
 Publication date 2017
  fields Physics
and research's language is English




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Thermal Sunyaev-Zeldovich (tSZ) effect and X-ray emission from galaxy clusters have been extensively used to constrain cosmological parameters. These constraints are highly sensitive to the relations between cluster masses and observables (tSZ and X-ray fluxes). The cross-correlation of tSZ and X-ray data is thus a powerful tool, in addition of tSZ and X-ray based analysis, to test our modeling of both tSZ and X-ray emission from galaxy clusters. We chose to explore this cross correlation as both emissions trace the hot gas in galaxy clusters and thus constitute one the easiest correlation that can be studied. We present a complete modeling of the cross correlation between tSZ effect and X-ray emission from galaxy clusters, and focuses on the dependencies with clusters scaling laws and cosmological parameters. We show that the present knowledge of cosmological parameters and scaling laws parameters leads to an uncertainties of 47% on the overall normalization of the tSZ-X cross correlation power spectrum. We present the expected signal-to-noise ratio for the tSZ-X cross-correlation angular power spectrum considering the sensitivity of actual tSZ and X-ray surveys from {it Planck}-like data and ROSAT. We demonstrate that this signal-to-noise can reach 31.5 in realistic situation, leading to a constraint on the amplitude of tSZ-X cross correlation up to 3.2%, fifteen times better than actual modeling limitations. Consequently, used in addition to other probes of cosmological parameters and scaling relations, we show that the tSZ-X is a powerful probe to constrain scaling relations and cosmological parameters.

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We use numerical simulations to predict the soft X-ray ([0.4-0.6] keV) and Sunyaev-Zeldovich signal (at 150 GHz) from the large scale structure in the Universe and then compute 2-point statistics to study the spatial distribution and time evolution of the signals. The average X-ray signal predicted for the WHIM is in good agreement with observational constraints that set it at about 10% of the total Diffuse X-ray Background. The characteristic angle computed with the Autocorrelation Function is of the order of some arcminutes and becomes smaller at higher redshift. The power spectrum peak of the SZ due to the WHIM is at l~10000 and has amplitude of ~0.2 muK^2, about one order of magnitude below the signal measured with telescopes like Planck, ACT, and SPT. Even if the high-redshift WHIM signal is too weak to be detected using X-rays only, the small-scale correlation between X-ray and SZ maps is dominated by the high-redshift WHIM. This makes the analysis of the SZ signal in support of X-rays a promising tool to study the early time WHIM.
X-ray emission and the thermal Sunyaev-Zeldovich distortion to the Cosmic Microwave Background are two important handles on the gas content of the Universe. The cross-correlation between these effects eliminates noise bias and reduces observational systematic effects. Using analytic models for the cluster profile, we develop a halo model formalism to study this cross-correlation and apply it to forecast the signal-to-noise of upcoming measurements from eROSITA and the Simons Observatory. In the soft X-ray band (0.5--2 keV), we forecast a signal-to-noise of 174 for the cross-power spectrum. Over a wide range of the scales, the X-rays will be signal-dominated, and so sample variance is important. In particular, non-Gaussian (4-point) contributions to the errors highlight the utility of masking massive clusters. Masking clusters down to $10^{14} M_odot$ increases the signal-to-noise of the cross-spectrum to 201. We perform a Fisher Analysis on the fitting coefficients of the Battaglia et al. gas profiles and on cosmological parameters. We find that the cross spectrum is most sensitive to the overall scale of the profiles of pressure and electron density, as well as cosmological parameters $sigma_8$ and $H_0$, but that the large number of parameters form a degenerate set, which makes extracting the information more challenging. Our modeling framework is flexible, and in the future, we can easily extend it to forecast the spatial cross-correlations of surveys of X-ray lines available to high-energy-resolution microcalorimetry, to studies of the Warm-Hot Intergalactic Medium, and other effects.
We measure the Cosmic Microwave Background (CMB) skewness power spectrum in $textit{Planck}$, using frequency maps of the HFI instrument and the Sunyaev-Zeldovich (SZ) component map. The two-to-one skewness power spectrum measures the cross-correlation between CMB lensing and the thermal SZ effect. We also directly measure the same cross-correlation using $textit{Planck}$ CMB lensing map and the SZ map and compare it to the cross-correlation derived from the skewness power spectrum. We model fit the SZ power spectrum and CMB lensing-SZ cross power spectrum via the skewness power spectrum to constrain the gas pressure profile of dark matter halos. The gas pressure profile is compared to existing measurements in the literature including a direct estimate based on the stacking of SZ clusters in $textit{Planck}$.
Cosmography provides a direct method to map the expansion history of the Universe in a model-independent way. Recently, different kinds of observations have been used in cosmographic analyses, such as SNe Ia and gamma ray bursts measurements, weak and strong lensing, cosmic microwave background anisotropies, etc. In this work we examine the prospects for constraining cosmographic parameters from current and future measurements of galaxy clusters distances based on their Sunyaev-Zeldovich effect (SZE) and X-ray observations. By assuming the current observational error distribution, we perform Monte Carlo simulations based on a well-behaved parameterization for the deceleration parameter to generate samples with different characteristics and study the improvement on the determination of the cosmographic parameters from upcoming data. The influence of galaxy clusters (GC) morphologies on the $H_0- q_0$ plane is also investigated.
We consistently include the effect of massive neutrinos in the thermal Sunyaev Zeldovich (SZ) power spectrum and cluster counts analyses, highlighting subtle dependencies on the total neutrino mass and data combination. In particular, we find that using the transfer functions for Cold Dark Matter (CDM) + baryons in the computation of the halo mass function, instead of the transfer functions including neutrino perturbations, as prescribed in recent work, yields a $approx$ 0.25% downward shift of the $sigma_8$ constraint from tSZ power spectrum data, with a fiducial neutrino mass $Sigma m_ u=0.06$ eV. In $Lambda$CDM, with an X-ray mass bias corresponding to the expected hydrostatic mass bias, i.e., $(1-b)simeq0.8$, our constraints from Planck SZ data are consistent with the latest results from SPT, DES-Y1 and KiDS+VIKING-450. In $ uLambda$CDM, our joint analyses of Planck SZ with Planck 2015 primary CMB yield a small improvement on the total neutrino mass bound compared to the Planck 2015 primary CMB constraint, as well as $(1-b)=0.64pm0.04$~(68%~CL). For forecasts, we find that competitive neutrino mass measurements using cosmic variance limited SZ power spectrum require masking the heaviest clusters and probing the small-scale SZ power spectrum up to $ell_mathrm{max}approx10^4$. Although this is challenging, we find that SZ power spectrum can realistically be used to tightly constrain intra-cluster medium properties: we forecast a 2% determination of the X-ray mass bias by combining CMB-S4 and our mock SZ power spectrum with $ell_mathrm{max}=10^3$.
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