Bayesian methods for fitting Baryon Acoustic Oscillations in the Lyman-α forest

We study and compare fitting methods for the Lyman-α (Lyα) forest 3D correlation function. We use the nested sampler PolyChord and the community code picca to perform a Bayesian analysis which we compare with previous frequentist analyses. By studying synthetic correlation functions, we find that the frequentist profile likelihood produces results in good agreement with a full Bayesian analysis. On the other hand, Maximum Likelihood Estimation with the Gaussian approximation for the uncertainties is inadequate for current data sets. We compute for the first time the full posterior distribution from the Lyα forest correlation functions measured by the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We highlight the benefits of sampling the full posterior distribution by expanding the baseline analysis to better understand the contamination by Damped Lyα systems (DLAs). We make our improvements and results publicly available as part of the picca package

Optimal 1D Ly α forest power spectrum estimation – I. DESI-lite spectra

The 1D Ly α forest flux power spectrum P1D is sensitive to scales smaller than a typical galaxy survey, and hence ties to the intergalactic medium’s thermal state, suppression from neutrino masses, and new dark matter models. It has emerged as a competitive framework to study new physics, but also has come with various challenges and systematic errors in analysis. In this work, we revisit the optimal quadratic estimator for P1D, which is robust against the relevant problems such as pixel masking, time evolution within spectrum, and quasar continuum errors. We further improve the estimator by introducing a fiducial power spectrum, which enables us to extract more information by alleviating the discreteness of band powers. We meticulously apply our method to synthetic Dark Energy Spectroscopic Instrument (DESI) spectra and demonstrate how the estimator overcomes each challenge. We further apply an optimization scheme that approximates the Fisher matrix to three elements per row and reduces computation time by 60 per cent. We show that we can achieve per cent precision in P1D with 5-yr DESI data in the absence of systematics and provide forecasts for different spectral qualities

Cosmology beyond BAO from the 3D distribution of the Lyman-α forest

We propose a new method for fitting the full-shape of the Lyman-α (Ly α) forest 3D correlation function in order to measure the Alcock-Paczynski (AP) effect. Our method preserves the robustness of baryon acoustic oscillations (BAO) analyses, while also providing extra cosmological information from a broader range of scales. We compute idealized forecasts for the Dark Energy Spectroscopic Instrument (DESI) using the Ly α autocorrelation and its cross-correlation with quasars, and show how this type of analysis improves cosmological constraints. The DESI Ly α BAO analysis is expected to measure H(zeff)rd and DM(zeff)/rd with a precision of ∼0.9 per cent⁠, where H is the Hubble parameter, rd is the comoving BAO scale, DM is the comoving angular diameter distance, and the effective redshift of the measurement is zeff ≃ 2.3. By fitting the AP parameter from the full shape of the two correlations, we show that we can obtain a precision of ∼0.5−0.6 per cent on each of H(zeff)rd and DM(zeff)/rd. Furthermore, we show that a joint full-shape analysis of the Ly α auto and cross-correlation with quasars can measure the linear growth rate times the amplitude of matter fluctuations in spheres of 8 h−1Mpc, fσ8(zeff). Such an analysis could provide the first ever measurement of fσ8(zeff) at redshift zeff > 2. By combining this with the quasar autocorrelation in a joint analysis of the three high-redshift two-point correlation functions, we show that DESI could be able to measure fσ8(zeff ≃ 2.3) with a precision of 5−12 per cent⁠, depending on the smallest scale fitted

The Effect of High Column Density Systems on the Measurement of the Lyman \alpha Forest Correlation Function

We present a study of the effect of High Column Density (HCD) systems on the Lyman \alpha forest correlation function on large scales. We study the effect both numerically, by inserting HCD systems on mock spectra for a specific model, and analytically, in the context of two-point correlations and linear theory. We show that the presence of HCDs substantially contributes to the noise of the correlation function measurement, and systematically alters the measured redshift-space correlation function of the Lyman \alpha forest, increasing the value of the density bias factor and decreasing the redshift distortion parameter $\beta_\alpha$ of the Lyman \alpha forest. We provide simple formulae for corrections on these derived parameters, as a function of the mean effective optical depth and bias factor of the host halos of the HCDs, and discuss the conditions under which these expressions should be valid. In practice, precise corrections to the measured parameters of the Lyman \alpha forest correlation for the HCD effects are more complex than the simple analytical approximations we present, owing to non-linear effects of the damped wings of the HCD systems and the presence of three-point terms. However, we conclude that an accurate correction for these HCD effects can be obtained numerically and calibrated with observations of the HCD-Lyman \alpha cross-correlation. We also discuss an analogous formalism to treat and correct for the contaminating effect of metal lines overlapping the Lyman \alpha forest spectra.Comment: 26 pages, 11 figure

Bias of damped Lyman--α systems from their cross-correlation with CMB lensing

We cross-correlate the positions of damped Lyman-α systems (DLAs) and their parent quasar catalog with a convergence map derived from the Planck cosmic microwave background (CMB) temperature data. We make consistent measurements of the lensing signal of both samples in both Fourier and configuration space. By interpreting the excess signal present in the DLA catalog with respect to the parent quasar catalog as caused by the large scale structure traced by DLAs, we are able to infer the bias of these objects: bDLA=2.6±0.9. These results are consistent with previous measurements made in cross-correlation with the Lyman-α forest, although the current noise in the lensing data and the low number density of DLAs limits the constraining power of this measurement. We discuss the robustness of the analysis with respect to a number different systematic effects and forecast prospects of carrying out this measurement with data from future experiments

Broadband distortion modeling in Lyman-α\alpha forest BAO fitting

In recent years, the Lyman-$\alpha$ absorption observed in the spectra of high-redshift quasars has been used as a tracer of large-scale structure by means of the three-dimensional Lyman-$\alpha$ forest auto-correlation function at redshift $z\simeq 2.3$, but the need to fit the quasar continuum in every absorption spectrum introduces a broadband distortion that is difficult to correct and causes a systematic error for measuring any broadband properties. We describe a $k$-space model for this broadband distortion based on a multiplicative correction to the power spectrum of the transmitted flux fraction that suppresses power on scales corresponding to the typical length of a Lyman-$\alpha$ forest spectrum. Implementing the distortion model in fits for the baryon acoustic oscillation (BAO) peak position in the Lyman-$\alpha$ forest auto-correlation, we find that the fitting method recovers the input values of the linear bias parameter $b_{F}$ and the redshift-space distortion parameter $\beta_{F}$ for mock data sets with a systematic error of less than 0.5\%. Applied to the auto-correlation measured for BOSS Data Release 11, our method improves on the previous treatment of broadband distortions in BAO fitting by providing a better fit to the data using fewer parameters and reducing the statistical errors on $\beta_{F}$ and the combination $b_{F}(1+\beta_{F})$ by more than a factor of seven. The measured values at redshift $z=2.3$ are $\beta_{F}=1.39^{+0.11\ +0.24\ +0.38}_{-0.10\ -0.19\ -0.28}$and$b_{F}(1+\beta_{F})=-0.374^{+0.007\ +0.013\ +0.020}_{-0.007\ -0.014\ -0.022}$(1$\sigma$, 2$\sigma$and 3$\sigma$ statistical errors). Our fitting software and the input files needed to reproduce our main results are publicly available.Comment: 28 pages, 15 figures, matches the published versio

Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology

Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, N-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COmoving Lagrangian Acceleration (COLA) simulations with a box size of 250 h−1Mpc⁠, varying the amplitude of scalar fluctuations (As), matter density (Ωm), and neutrino mass (∑mν). The power spectrum P and bispectrum B are measured for wavenumbers between 0.125 and 0.5 hMpc−1⁠, while a corresponding lower cut of ∼12.6 h−1Mpc is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved 1σ constraints of ∼17 per cent (⁠∼12 per cent⁠) on Ωm and ∼12 per cent (⁠∼10 per cent⁠) on As with respect to P (P + B) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics

The impact of temperature fluctuations on the large-scale clustering of the Lyα forest

We develop a semi-analytic method for assessing the impact of the large-scale IGM temperature fluctuations expected following He ii reionization on three-dimensional clustering measurements of the Lyα forest. Our methodology builds upon the existing large volume, mock Lyα forest survey simulations presented by Greig et al. by including a prescription for a spatially inhomogeneous ionizing background, temperature fluctuations induced by patchy He ii photoheating and the clustering of quasars. This approach enables us to achieve a dynamic range within our semi-analytic model substantially larger than currently feasible with computationally expensive, fully numerical simulations. The results agree well with existing numerical simulations, with large-scale temperature fluctuations introducing a scale-dependent increase in the spherically averaged 3D Lyα forest power spectrum of up to 20–30 per cent at wavenumbers k ∼ 0.02 Mpc− 1. Although these large-scale thermal fluctuations will not substantially impact upon the recovery of the baryon acoustic oscillation scale from existing and forthcoming dark energy spectroscopic surveys, any complete forward modelling of the broad-band term in the Lyα correlation function will none the less require their inclusion

Cosmological Hydrodynamic Simulations with Suppressed Variance in the Ly alpha Forest Power Spectrum

We test a method to reduce unwanted sample variance when predicting Lyα forest power spectra from cosmological hydrodynamical simulations. Sample variance arises due to sparse sampling of modes on large scales and propagates to small scales through nonlinear gravitational evolution. To tackle this, we generate initial conditions in which the density perturbation amplitudes are fixed to the ensemble average power spectrum—and are generated in pairs with exactly opposite phases. We run 50 such simulations (25 pairs) and compare their performance against 50 standard simulations by measuring the Lyα 1D and 3D power spectra at redshifts z = 2, 3, and 4. Both ensembles use periodic boxes of $40\,{h}^{-1}\mathrm{Mpc}$ containing 5123 particles each of dark matter and gas. As a typical example of improvement, for wavenumbers $k=0.25\,h{\mathrm{Mpc}}^{-1}$ at z = 3, we find estimates of the 1D and 3D power spectra converge 34 and 12 times faster in a paired–fixed ensemble compared with a standard ensemble. We conclude that, by reducing the computational time required to achieve fixed accuracy on predicted power spectra, the method frees up resources for exploration of varying thermal and cosmological parameters—ultimately allowing the improved precision and accuracy of statistical inference