Mass selection bias in galaxy cluster peculiar velocities from the kinetic Sunyaev–Zel'dovich effect

Upcoming surveys for galaxy clusters using the Sunyaev–Zel'dovich effect are potentially sensitive enough to create a peculiar velocity catalogue. The statistics of these peculiar velocities are sensitive to cosmological parameters. We develop a method to explore parameter space using N -body simulations in order to quantify dark matter halo velocity statistics which will be useful for cluster peculiar velocity observations. We show that mass selection bias from a kinetic Sunyaev–Zel'dovich velocity catalogue forecasts rms peculiar velocities with a much more complicated  Ω_m  dependency than suggested by linear perturbation theory. In addition, we show that both two-point functions for velocities disagree with linear theory predictions out to  ∼40  h ⁻¹ Mpc  separations. A pedagogical appendix is included developing linear theory notation with respect to the two-point peculiar velocities functions.     

Statistics of the Sunyaev–Zel'dovich effect power spectrum

Using large numbers of simulations of the microwave sky, incorporating the cosmic microwave background (CMB) and the Sunyaev–Zel'dovich (SZ) effect due to clusters, we investigate the statistics of the power spectrum at microwave frequencies between spherical multipoles of 1000 and 10 000. From these virtual sky maps, we find that the spectrum of the SZ effect has a larger standard deviation by a factor of 3 than would be expected from purely Gaussian realizations, and has a distribution that is significantly skewed towards higher values, especially when small map sizes are used. The standard deviation is also increased by around 10 per cent compared to the trispectrum calculation due to the clustering of galaxy clusters. We also consider the effects of including residual point sources and uncertainties in the gas physics. This has implications for the excess power measured in the CMB power spectrum by the Cosmic Background Imager (CBI) and Berkeley–Illinois–Maryland Association (BIMA) experiments. Our results indicate that the observed excess could be explained using a lower value of σ₈ than previously suggested, however the effect is not enough to match  σ₈= 0.825  . The uncertainties in the gas physics could also play a substantial role. We have made our maps of the SZ effect available online.     

Cluster formation and the Sunyaev–Zel'dovich power spectrum in modified gravity: the case of a phenomenologically extended DGP model

We investigate the effect of modified gravity on cluster abundance and the Sunyaev–Zel'dovich (SZ) angular power spectrum. Our modified gravity is based on a phenomenological extension of the Dvali–Gabadadze–Porrati model which includes two free parameters characterizing deviation from Λ cold dark matter cosmology. Assuming that Birkhoff's theorem gives a reasonable approximation, we study the spherical collapse model of structure formation and show that while the growth function changes to some extent, modified gravity gives rise to no significant change in the linear density contrast at collapse time. The growth function is enhanced in the so called normal branch, while in the 'self-accelerating' branch it is suppressed. The SZ angular power spectrum is computed in the normal branch, which allows us to put observational constraints on the parameters of the modified gravity model using small scale cosmic microwave background observation data.     

Measurement of the Sunyaev–Zel'dovich increment in massive galaxy clusters

We have detected the Sunyaev–Zel'dovich (SZ) increment at 850 μm in two galaxy clusters (Cl 0016+16 and MS 1054.4−0321) using the Submillimetre Common User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. Fits to the isothermal β model yield a central Compton y parameter of  (2.2 ± 0.7) × 10⁻⁴  and a central 850-μm flux of  Δ I ₀= 2.2 ± 0.7 mJy beam⁻¹  in Cl 0016. This can be combined with decrement measurements to infer   y = (2.38 ±^0.36_0.34) × 10⁻⁴  and   v _pec= 400±¹⁹⁰⁰₁₄₀₀ km s⁻¹  . In MS 1054 we find a peak 850-μm flux of  Δ I ₀= 2.0 ± 1.0 mJy beam⁻¹  and   y = (2.0 ± 1.0) × 10⁻⁴  . To be successful such measurements require large chop throws and non-standard data analysis techniques. In particular, the 450-μm data are used to remove atmospheric variations in the 850-μm data. An explicit annular model is fit to the SCUBA difference data in order to extract the radial profile, and separately fit to the model differences to minimize the effect of correlations induced by our scanning strategy. We have demonstrated that with sufficient care, SCUBA can be used to measure the SZ increment in massive, compact galaxy clusters.     

Determination of the linear mass power spectrum from the mass function of galaxy clusters

We develop a new method to determine the linear mass power spectrum using the mass function of galaxy clusters. We obtain the rms mass fluctuation  σ( M )  using the expression for the mass function in the Press & Schechter, Sheth, Mo & Tormen and Jenkins et al. formalisms. We apply different techniques to recover the adimensional power spectrum  Δ²( k )  from  σ( M )  namely the   k _eff  approximation, the singular value decomposition and the linear regularization method. The application of these techniques to the τCDM and ΛCDM GIF simulations shows a high efficiency in recovering the theoretical power spectrum over a wide range of scales. We compare our results with those derived from the power spectrum of the spatial distribution of the same sample of clusters in the simulations obtained by application of the classical Feldman, Kaiser & Peacock (FKP) method. We find that the mass function based method presented here can provide a very accurate estimate of the linear power spectrum, particularly for low values of k . This estimate is comparable to, or even better behaved than, the FKP solution.
The principal advantage of our method is that it allows the determination of the linear mass power spectrum using the joint information of objects of a wide range of masses without dealing with specific assumptions on the bias relative to the underlying mass distribution.     

Sunyaev–Zel'dovich cluster survey simulations for Planck

We examine the ability of the future Planck mission to provide a catalogue of galaxy clusters observed via their Sunyaev–Zel'dovich (SZ) distortion in the cosmic microwave background (CMB). For this purpose we produce full-sky SZ maps based on N -body simulations and scaling relations between cluster properties for several cosmological models. We extrapolate the N -body simulations by a mass function to high redshifts in order to obtain a realistic SZ background. The simulated Planck observations include, besides the thermal and kinematic SZ effects, contributions from the primordial CMB, extragalactic point sources as well as Galactic dust, free–free and synchrotron emission. A harmonic-space maximum-entropy method is used to separate the SZ signal from contaminating components in combination with a cluster detection algorithm based on thresholding and flux integration to identify clusters and to obtain their fluxes. We estimate a survey sensitivity limit (depending on the quality of the recovered cluster flux) and provide cluster survey completeness and purity estimates. We find that, given our modelling and detection algorithm, Planck will reliably detect at least several thousands of clusters over the full sky. The exact number depends on the particular cosmological model (up to 10 000 cluster detections in a concordance ΛCDM model with  σ₈= 0.9  ). We show that the Galaxy does not significantly affect the cluster detection. Furthermore, the dependence of the thermal SZ power spectrum on the matter variance on scales of  8 h ⁻¹  Mpc and the quality of its reconstruction by the employed method are investigated. Our simulations suggest that the Planck cluster sample will not only be useful as a basis for follow-up observations, but also will have the ability to provide constraints on cosmological parameters.     

The redshift-space power spectrum in the halo model

Recently there has been a lot of attention focused on a virialized halo-based approach to understanding the properties of the matter and galaxy power spectrum. We show that this model allows a natural treatment of the large- and small-scale redshift-space distortions, which we develop here, which extends the pedagogical value of the approach.     

Decorrelating the power spectrum of galaxies

We show how to decorrelate the (pre-whitened) power spectrum measured from a galaxy survey into a set of high-resolution uncorrelated band-powers. The treatment includes non-linearity, but not redshift distortions. Amongst the infinitely many possible decorrelation matrices, the square root of the Fisher matrix, or a scaled version thereof, offers a particularly good choice, in the sense that the band-power windows are narrow, approximately symmetric, and well-behaved in the presence of noise. We use this method to compute band-power windows for, and the information content of, the Sloan Digital Sky Survey, the Las Campanas Redshift Survey, and the IRAS 1.2-Jy Survey.     

Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues

We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies.
By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the three-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the matter density parameter of the Universe, which occurs in linear analysis of 3D galaxy catalogues. In previous papers, we have shown how a similar analysis can be done in three dimensions, and we show here through an error analysis and by implementing the method on a simulated projected catalogue that ongoing three-dimensional galaxy redshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift-space distortions and smaller numbers) will do far better than all-sky projected catalogues with similar selection function.     

Peaks in the cosmological density field: sensitivity to initial power spectrum, redshift distortions and galaxy halo occupation

We investigate the number density of maxima in the cosmological galaxy density field smoothed with a filter as a probe of clustering. In previous work it has been shown that this statistic is closely related to the slope of the linear power spectrum, even when the directly measured power spectrum is non-linear. In the present paper we investigate the sensitivity of the peak number density to various models with differing power spectra, including rolling index models, cosmologies with massive neutrinos and different baryon densities. We find that rolling index models which have given an improved fit to CMB/LSS (cosmic microwave background/large scale structure) data yield a ∼10 per cent difference in peak density compared to the scale invariant case. Models with 0.3 eV neutrinos have effects of similar magnitude and it should be possible to constrain them with data from current galaxy redshift surveys. Baryon oscillations in the power spectrum also give rise to distinctive features in the peak density. These are preserved without modification when measured from the peak density in fully non-linear N -body simulations. Using the simulations, we also investigate how the peak density is modified in the presence of redshift distortions. Redshift distortions cause a suppression of the number of peaks, largely due to fingers of God overlapping in redshift space. We find that this effect can be modelled by using a modification of the input power spectrum. We also study the results when the simulation density field is traced by galaxies obtained by populating haloes with a halo occupation distribution consistent with observations. The peak number density is consistent with that in the dark matter for filter scales  >4  h ⁻¹ Mpc  , for which we find good agreement with the linear theory predictions. In a companion paper we analyse data from the 2dF Galaxy Redshift Survey.