Modelling the Power Spectrum of Density Fluctuations: A Phenomenological Approach

We show how, based on considerations on the observed form of the galaxy 2-point spatial correlation function xi(r), a very simplified -- yet surprisingly effective -- model for the linear density fluctuations power spectrum can be constructed. We first relate the observed large-scale shape of xi(r) to a power-law form for the power spectrum, P(k)\propto k^{-2.2}. For a plausible value of the bias parameter b = 1/sigma_8 ~ 1.8, one has (delta_rho / rho)_{rms} ~ 1 r ~ 3.5/h Mpc, suggesting that the change of slope observed in xi(r) around this scale marks the transition between the linear and nonlinear gravitational regimes. Under this working hypothesis, we use a simple analytical form to fit the large-scale correlations constraints together with the COBE CMB anisotropy measurement, thus constructing a simple phenomenological model for the linear power spectrum. Despite its simplicity, the model fits remarkably well directly estimated power spectra from different optical galaxy samples, and when evolved through an N-body simulation it provides a good match to the observed galaxy correlations. One of the most interesting features of the model is the small-scale one-dimensional velocity dispersion produced: sigma_{1d} = 450 Km s^{-1} at 0.5/h Mpc and sigma_{1d} = 350 Km s^{-1} for separations larger than ~ 2/h Mpc.Comment: ApJL in press, 10 pages in plain TeX, 3 figures available from [email protected], SISSA 110/93/

The velocity field of 2MRS Ks=11.75 galaxies: constraints on beta and bulk flow from the luminosity function

Using the nearly full sky Ks=11.75 2MASS Redshift Survey [2MRS]of ~45,000 galaxies we reconstruct the underlying peculiar velocity field and constrain the cosmological bulk flow within ~100. These results are obtained by maximizing the probability to estimate the absolute magnitude of a galaxy given its observed apparent magnitude and redshift. At a depth of ~60 Mpc/h we find a bulk flow Vb=(90\pm65,-230\pm65,50\pm65) km/s in agreement with the theoretical predictions of the LCDM model. The reconstructed peculiar velocity field that maximizes the likelihood is characterized by the parameter beta=0.323 +/- 0.08. Both results are in agreement with those obtained previously using the ~23,000 galaxies of the shallower Ks=11.25 2MRS survey. In our analysis we find that the luminosity function of 2MRS galaxies is poorly fitted by the Schechter form and that luminosity evolves such that objects become fainter with increasing redshift according to L(z)=L(z=0)(1+z)^(+2.7 +/-0.15).Comment: 10 pages, 6 figure

A comparison of the galaxy peculiar velocity field with the PSCz gravity field-- A Bayesian hyper-parameter method

We constructed a Bayesian hyper-parameter statistical method to quantify the difference between predicted velocities derived from the observed galaxy distribution in the \textit{IRAS}-PSC$z$ redshift survey and peculiar velocities measured using different distance indicators. In our analysis we find that the model--data comparison becomes unreliable beyond 70 \hmpc because of the inadequate sampling by \textit{IRAS} survey of prominent, distant superclusters, like the Shapley Concentration. On the other hand, the analysis of the velocity residuals show that the PSC$z$ gravity field provides an adequate model to the local, \le 70 \hmpc, peculiar velocity field. The hyper-parameter combination of ENEAR, SN, A1SN and SFI++ catalogues in the Bayesian framework constrains the amplitude of the linear flow to be $\beta=0.53 \pm 0.014$. For an rms density fluctuations in the PSC$z$ galaxy number density $\sigma_8^{\rm gal}=0.42\pm0.03$, we obtain an estimate of the growth rate of density fluctuations $f\sigma_{8}(z\sim0) = 0.42 \pm 0.033$, which is in excellent agreement with independent estimates based on different techniques.Comment: 14 pages, 32 figures, MNRAS in press, matched the MNRAS published versio

Simultaneous constraints on bias, normalization and growth index through power spectrum measurements

In this Letter we point out that redshift surveys can break the degeneracy between the galaxy bias, the power spectrum normalization, \sigma_{8,0} and the growth factor, without the need for external information by using a simple and rather general parametrization for the growth rate, the well known \gamma-parametrization and measuring the power spectrum at least at two different redshifts. We find that in next-generation surveys like Euclid, \sigma_{8,0} and \gamma can be measured to within 1% and 5%, respectively, while the bias b(z) can be measured to within 1-2% in each of 14 equal-width redshift bins spanning 0.7<=z<=2.Comment: 6 pages, 4 figures, version matching the one published by MNRAS Letter

Growth factor and galaxy bias from future redshift surveys: a study on parametrizations

Many experiments in the near future will test dark energy through its effects on the linear growth of matter perturbations. In this paper we discuss the constraints that future large-scale redshift surveys can put on three different parameterizations of the linear growth factor and how these constraints will help ruling out different classes of dark energy and modified gravity models. We show that a scale-independent bias can be estimated to a few percent per redshift slice by combining redshift distortions with power spectrum amplitude, without the need of an external estimation. We find that the growth rate can be constrained to within 2-4% for each $\Delta z=0.2$ redshift slice, while the equation of state $w$ and the index $\gamma$ can be simultaneously estimated both to within 0.02. We also find that a constant dimensionless coupling between dark energy and dark matter can be constrained to be smaller than 0.14.Comment: 22 pages, 11 figure

Euclid: Constraining ensemble photometric redshift distributions with stacked spectroscopy

The ESA Euclid mission will produce photometric galaxy samples over 15000 square degrees of the sky that will be rich for clustering and weak lensing statistics. The accuracy of the cosmological constraints derived from these measurements will depend on the knowledge of the underlying redshift distributions based on photometric redshift calibrations. A new approach is proposed to use the stacked spectra from Euclid slitless spectroscopy to augment broad-band photometric information to constrain the redshift distribution with spectral energy distribution fitting. The high spectral resolution available in the stacked spectra complements the photometry and helps to break the colour-redshift degeneracy and constrain the redshift distribution of galaxy samples. We modelled the stacked spectra as a linear mixture of spectral templates. The mixture may be inverted to infer the underlying redshift distribution using constrained regression algorithms. We demonstrate the method on simulated Vera C. Rubin Observatory and Euclid mock survey data sets based on the Euclid Flagship mock galaxy catalogue. We assess the accuracy of the reconstruction by considering the inference of the baryon acoustic scale from angular two-point correlation function measurements. We selected mock photometric galaxy samples at redshift z>1 using the self-organising map algorithm. Considering the idealised case without dust attenuation, we find that the redshift distributions of these samples can be recovered with 0.5% accuracy on the baryon acoustic scale. The estimates are not significantly degraded by the spectroscopic measurement noise due to the large sample size. However, the error degrades to 2% when the dust attenuation model is left free. We find that the colour degeneracies introduced by attenuation limit the accuracy considering the wavelength coverage of Euclid near-infrared spectroscopy