Redshift-space Distortion Parameter Research Articles

Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative

Focusing on the redshift space observations with plane-parallel approximation and relying on the rotational dependency of the general definition of excursion sets, we introduce the so-called conditional moments of the first derivative (cmd) measures for the smoothed matter density field in three dimensions. We derive the perturbative expansion of cmd for the real space and redshift space where peculiar velocity disturbs the galaxies’ observed locations. Our criteria can successfully recognize the contribution of linear Kaiser and Finger-of-God effects. Our results demonstrate that the cmd measure has significant sensitivity for pristine constraining the redshift space distortion parameter β = f/b and interestingly, the associated normalized quantity in the Gaussian linear Kaiser limit has only β dependency. Implementation of the synthetic anisotropic Gaussian field approves the consistency between the theoretical and numerical results. Including the first-order contribution of non-Gaussianity perturbatively in the cmd criterion implies that the N-body simulations for the Quijote suite in the redshift space have been mildly skewed with a higher value for the threshold greater than zero. The non-Gaussianity for the perpendicular direction to the line of sight in the redshift space for smoothing scales R ≳ 20 Mpc h −1 is almost the same as in the real space. In contrast, the non-Gaussianity along the line-of-sight direction in the redshift space is magnified. The Fisher forecasts indicate a significant enhancement in constraining the cosmological parameters Ω m , σ 8, and n s when using cmd + cr jointly.

The cross-correlation of galaxies in absorption with the Lyman α forest

ABSTRACT We present the first clustering measurement of Strong Blended Lyman α (SBLA) absorption systems by measuring their cross-correlation with the Lyman α forest. SBLAs are a new population of absorbers detected within the Lyman α forest. We find a bias of 2.329 ± 0.057, consistent with that of Damped Lyman α absorbers (DLAs). For DLAs, we recover a bias of 2.331 ± 0.057 larger than previously reported. We also find a redshift space distortion parameter β = 0.417 ± 0.010, also consistent with the recovered value for DLAs (β = 0.416 ± 0.010). This is consistent with SBLA and DLA systems tracing different portions of the circumgalactic medium of a broadly common population of galaxies. Given these common clustering properties, we combined them to perform a cross-correlation of galaxies in absorption with the Lyα forest. We find that the BAO scale uncertainty of this new measurement is 1.75 × that of Lyα autocorrelation and 1.6 × that of the quasar cross-correlation with the Lyα forest. We note that the current preferred metal contamination model for fitting the correlation functions with respect to the Lyα forest is not realistic enough for SBLA systems, likely due to their status as high redshift precision sites of high metal enrichment. Mock spectra including SBLA systems and their associated metal absorption are required to understand this sample fully. We conclude that SBLAs have the potential to complement the standard Lyα cosmological analyses in future surveys.

Cosmological Fisher forecasts for next-generation spectroscopic surveys

ABSTRACT Next-generation spectroscopic surveys such as the MegaMapper, MUltiplexed Survey Telescope (MUST), MaunaKea Spectroscopic Explorer (MSE), and WideField Spectroscopic Telescope (WST) are foreseen to increase the number of galaxy/quasar redshifts by an order of magnitude, with hundred millions of spectra that will be measured at z > 2. We perform a Fisher matrix analysis for these surveys on the baryonic acoustic oscillation (BAO), the redshift-space distortion (RSD) measurement, the non-Gaussianity (NG) amplitude fNL, and the total neutrino mass Mν. For BAO and RSD parameters, these surveys may achieve precision at sub-per cent level (<0.5 per cent), representing an improvement of factor 10 w.r.t. the latest data base. For NG, these surveys may reach an accuracy of σ(fNL) ∼ 1. They can also put a tight constraint on Mν with $\sigma (M_\nu) \sim 0.02\, \rm eV$ if we do joint analysis with Planck and even $0.01\, \rm eV$ if combined with other data. In addition, we introduce a general survey model to derive the cosmic volume and number density of tracers, given instrumental facilities and survey strategy. Using our Fisher formalism, we can explore (continuously) a wide range of survey observational parameters and propose different survey strategies that optimize the cosmological constraints. Fixing the fibre number and survey duration, we show that the best strategy for fNL and Mν measurement is to observe large volumes, despite the noise increase. However, the strategy differs for the apparent magnitude limit. Finally, we prove that increasing the fibre number improves Mν measurement but not significantly fNL.

Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing

ABSTRACT We test general relativity (GR) at the effective redshift $\bar{z} \sim 1.5$ by estimating the statistic EG, a probe of gravity, on cosmological scales $19 - 190\, h^{-1}{\rm Mpc}$. This is the highest redshift and largest scale estimation of EG so far. We use the quasar sample with redshifts 0.8 < z < 2.2 from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 as the large-scale structure (LSS) tracer, for which the angular power spectrum $C_\ell ^{qq}$ and the redshift-space distortion parameter β are estimated. By cross-correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $C_\ell ^{\kappa q}$ signal at $12\, \sigma$ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of EG at five bins covering different scales, with the later preferred for its better constraints on the covariances. We find EG estimates agree with the GR prediction at $1\, \sigma$ level over all these scales. With the CM estimated with 300 simulations, we report a best-fitting scale-averaged estimate of $E_G(\bar{z})=0.30\pm 0.05$, which is in line with the GR prediction $E_G^{\rm GR}(\bar{z})=0.33$ with Planck 2018 CMB + BAO matter density fraction Ωm = 0.31. The statistical errors of EG with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.

The clustering of the SDSS-IV extended baryon oscillation spectroscopic survey DR16 luminous red galaxy and emission-line galaxy samples: cosmic distance and structure growth measurements using multiple tracers in configuration space

ABSTRACTWe perform a multitracer analysis using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and the DR16 emission-line galaxy (ELG) samples in the configuration space, and successfully detect a cross-correlation between the two samples, and find the growth rate to be fσ8=0.342 ± 0.085 (∼25 per cent accuracy) from the cross-sample alone. We perform a joint measurement of the baryonic acoustic oscillation (BAO) and redshift space distortion (RSD) parameters at a single effective redshift of zeff = 0.77, using the autocorrelation and cross-correlation functions of the LRG and ELG samples, and find that the comoving angular diameter distance DM(zeff)/rd = 18.85 ± 0.38, the Hubble distance DH(zeff)/rd = 19.64 ± 0.57, and fσ8(zeff) = 0.432 ± 0.038, which is consistent with a ΛCDM model at $68{\ \rm per\ cent}$ CL. Compared to the single-tracer analysis on the LRG sample, the Figure of Merit of α⊥, α∥, andfσ8 is improved by a factor of 1.11 in our multitracer analysis, and in particular, the statistical uncertainty of fσ8 is reduced by $11.6{\ \rm per\ cent}$.

Cosmological angular trispectra and non-Gaussian covariance

Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity is drastically reduced for correlators in a “separable” form—we define a suitable notion of separability for cosmological trispectra, and derive formulas for angular correlators of different separability classes. As an application of our formalism, we compute the angular galaxy trispectrum at tree level, with and without primordial non-Gaussianity. This includes effects of redshift space distortion and bias parameters up to cubic order. We also compute the non-Gaussian covariance of the angular matter power spectrum due to the connected four-point function, beyond the Limber approximation. We demonstrate that, in contrast to the standard lore, the Limber approximation can fail for the non-Gaussian covariance computation even for large multipoles.

Joint growth-rate measurements from redshift-space distortions and peculiar velocities in the 6dF Galaxy Survey

ABSTRACT We present a new model for the cross-covariance between galaxy redshift-space distortions and peculiar velocities. We combine this with the autocovariance models of both probes in a fully self-consistent, maximum-likelihood method, allowing us to extract enhanced cosmological parameter constraints. When applying our method to the 6-degree Field Galaxy Survey (6dFGS), our constraint on the growth rate of structure is $f\sigma _8 = 0.384 \pm 0.052 \rm {(stat)} \pm 0.061 \rm {(sys)}$ and our constraint for the redshift-space distortion parameter is $\beta = 0.289^{+0.044}_{-0.043} \rm {(stat)} \pm 0.049 \rm {(sys)}$. We find that the statistical uncertainty for the growth rate of structure is reduced by 64 per cent when using the complete covariance model compared to the redshift-space distortion autocovariance model and 50 per cent when compared to using the peculiar-velocity autocovariance model. Our constraints are consistent with those from the literature on combining multiple tracers of large-scale structure, as well as those from other 6dFGS analyses. Our measurement is also consistent with the standard cosmological model.

Ensemble Average of Three-dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space

Abstract We present the ensemble expectation values for the translation-invariant, rank-2 Minkowski tensors in three dimensions, for a linearly redshift-space-distorted Gaussian random field. The Minkowski tensors , are sensitive to global anisotropic signals present within a field, and by extracting these statistics from the low-redshift matter density one can place constraints on the redshift-space distortion parameter β = f/b. We begin by reviewing the calculation of the ensemble expectation values , for isotropic, Gaussian random fields, then consider how these results are modified by the presence of a linearly anisotropic signal. Under the assumption that all fields remain Gaussian, we calculate the anisotropic correction due to redshift-space distortion in a coordinate system aligned with the line of sight, finding inequality between the diagonal elements of , . The ratio of diagonal elements of these matrices provides a set of statistics that are sensitive only to the redshift-space distortion parameter β. We estimate the Fisher information that can be extracted from the Minkowski tensors, and find is more sensitive to β than , and a measurement of accurate to ∼1% can yield a constraint on β. Finally, we discuss the difference between using the matrix elements of the Minkowski tensors directly against measuring the eigenvalues. For the purposes of cosmological parameter estimation we advocate the use of the matrix elements, to avoid spurious anisotropic signals that can be generated by the eigenvalue decomposition.

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measuring the evolution of the growth rate using redshift-space distortions between redshift 0.8 and 2.2

We measure the growth rate and its evolution using the anisotropic clustering of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample, which includes $148\,659$ quasars covering the wide redshift range of $0.8 < z < 2.2$ and a sky area of $2112.90$ $\rm deg^2$. To optimise measurements we deploy a redshift-dependent weighting scheme, which allows us to avoid binning, and perform the data analysis consistently including the redshift evolution across the sample. We perform the analysis in Fourier space, and use the redshift evolving power spectrum multipoles to measure the redshift space distortion parameter $f\sigma_8$ and parameters controlling the anisotropic projection of the cosmological perturbations. We measure $f \sigma_8(z=1.52)=0.43 \pm 0.05 $ and $df\sigma_8/dz (z=1.52)= - 0.16 \pm 0.08$, consistent with the expectation for a $\Lambda$CDM cosmology as constrained by the Planck experiment.

Minkowski Tensors in Three Dimensions: Probing the Anisotropy Generated by Redshift Space Distortion

Abstract We apply the Minkowski tensor statistics to three-dimensional Gaussian random fields. Minkowski tensors contain information regarding the orientation and shape of excursion sets that is not present in the scalar Minkowski functionals. They can be used to quantify globally preferred directions and also provide information on the mean shape of the subsets of a field. This makes them ideal statistics to measure the anisotropic signal generated by redshift space distortion in the low-redshift matter density field. We review the definition of the Minkowski tensor statistics in three dimensions, focusing on two coordinate invariant quantities, and . We calculate the ensemble average of these 3 × 3 matrices for an isotropic Gaussian random field, finding that they are proportional to products of the identity matrix and a corresponding scalar Minkowski functional. We show how to numerically reconstruct and from discretely sampled fields and apply our algorithm to isotropic Gaussian fields generated from a linear ΛCDM matter power spectrum. We then introduce anisotropy by applying a linear redshift space distortion operator to the matter density field and find that both and exhibit a distinct signal characterized by inequality between their diagonal components. We discuss the physical origin of this signal and how it can be used to constrain the redshift space distortion parameter ϒ ≡ f/b.

Quasar – CIV forest cross-correlation with SDSS DR12

We present a new determination of the large-scale clustering of the CIV forest (i.e., the absorption due to all CIV absorbers) using its cross-correlation with quasars in the Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12). We fit a linear bias model to the measured cross-correlation. We find that the transmission bias of the CIV forest, $b_{Fc}$, at a mean redshift of $z=2.3$, obeys the relation $(1+\beta_c)b_{F c} = -0.024 \pm 0.003$. Here, $\beta_{c}$ is the linear redshift space distortion parameter of the CIV absorption, which can only be poorly determined at $\beta_c=1.1\pm 0.6$ from our data. This transmission bias is related to the bias of CIV absorbers and their host halos through the effective mean optical depth of the CIV forest, $\bar\tau_c$. Estimating a value $\bar \tau_c(z) \simeq 0.01$ from previous studies of the CIV equivalent width distribution, our measurement implies a CIV absorber bias near unity, with a large error due to uncertainties in both $\beta_c$ and $\bar\tau_c$. This makes it compatible with the higher DLA bias $b_{\rm DLA}\simeq 2$ measured previously from the cross-correlation of DLAs and the Lyman-$\alpha$ forest. We discuss the implications of the CIV absorber bias for the mass distribution of their host halos. More accurate determinations of $\bar \tau_c(z)$ and $\beta_c$ are necessary to obtain a more robust measurement of this CIV absorber bias.

The triply-ionized carbon forest from eBOSS: cosmological correlations with quasars in SDSS-IV DR14

We present measurements of the cross-correlation of the triply-ionized carbon (CIV) forest with quasars using Sloan Digital Sky Survey Data Release 14. The study exploits a large sample of new quasars from the first two years of observations by the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). The CIV forest is a weaker tracer of large-scale structure than the Lyα forest, but benefits from being accessible at redshifts z<2 where the quasar number density from eBOSS is high. Our data sample consists of 287,651 CIV forest quasars in the redshift range 1.4<z<3.5 and 387,315 tracer quasars with 1.2<z<3.5. We measure large-scale correlations from CIV absorption occuring in three distinct quasar rest-frame wavelength bands of the spectra referred to as the CIV forest, the SiIV forest and the Lyα forest. From the combined fit to the quasar-CIV cross-correlations for the CIV forest and the SiIV forest, the CIV redshift-space distortion parameter is βCIV=0.27 −0.14 −0.26 +0.16 +0.34 and its combination with the CIV linear transmission bias parameter is bCIV(1+βCIV)=−0.0183 −0.0014 −0.0029 +0.0013 +0.0025 (1σ and 2σ statistical errors) at the mean redshift z=2.00. Splitting the sample at z=2.2 to constrain the bias evolution with redshift yields the power-law exponent γ=0.60±0.63, indicating a significantly weaker redshift-evolution than for the Lyα forest linear transmission bias. Additionally, we demonstrate that CIV absorption has the potential to be used as a probe of baryon acoustic oscillations (BAO). While the current data set is insufficient for a detection of the BAO peak feature, the final quasar samples for redshifts 1.4<z<2.2 from eBOSS and the Dark Energy Spectroscopic Instrument (DESI) are expected to provide measurements of the isotropic BAO scale to ∼7% and ∼3% precision, respectively, at z≃1.6.

Impact of large-scale tides on cosmological distortions via redshift-space power spectrum

Although the large-scale perturbations beyond a finite-volume survey region are not direct observables, these affect measurements of clustering statistics of small-scale (sub-survey) perturbations in the large-scale structure, compared with the ensemble average, via the mode-coupling effect. In this paper we show that the large-scale tides induced by scalar perturbations cause apparent anisotropic distortions in the redshift-space power spectrum of galaxies in a way depending on an alignment between the tides, the wavevector of small-scale modes and the line-of-sight direction. Using the perturbation theory of structure formation, we derive the $\textit{response}$ function of the redshift-space power spectrum to the large-scale tides. We then investigate the impact of the large-scale tides on estimation of cosmological distances and the redshift-space distortion parameter via the measured redshift-space power spectrum for a hypothetical large-volume survey, based on the Fisher matrix formalism. To do this, we treat the large-scale tides as a signal, rather than an additional source of the statistical errors, and show that a degradation in the parameter is restored if we can employ the prior on the rms amplitude expected for the standard cold dark matter (CDM) model. We also discuss whether the large-scale tides can be constrained at an accuracy better than the CDM prediction, if the effects up to a larger wavenumber in the nonlinear regime can be included.

Constraints on Dynamical Dark Energy with Precision Cosmological Data

We present a Dark Energy (DE) model based on a scalar field with an inverse power law potential (IPL) V(∅)=M4+n∅−n. We consider three different models n=1/2, n=3/4 and n=1 and we vary the value of M and the initial amount of energy density Ω∅ at the scale factor ac. We obtain a time dependent equation of state (EoS) , with w∅=1/3 at early times for a scale factor ac with a steep transition to w∅=1 at , , , lasting a long period of time and a subsequent descent w∅=-1 to for to finally grow to w∅= -0.906, w∅=-0.932, w∅=-0.924 for n=1/2, n=3/4 and n=1 respectively. The values of M and Ω∅(ac) are M(eV)= 4.63,127.31,2465.46 and Ω∅(ac)=0.038,0.148,0.227 for n= 1/2, n= 3/4 and n=1 respectively. We show the differences in the evolution of H, the CMB and Matter power spectra, and the redshift space distortion (RSD)parameter. Precision cosmological data allow us to test the dynamics of Dark Energy and we obtain in all three cases a reduction of compared to ∧CDM with and an equivalent fit for CMB and SNIa data.

The VIMOS Public Extragalactic Redshift Survey

We identified voids in the completed VIMOS Public Extragalactic Redshift Survey (VIPERS), using an algorithm based on searching for empty spheres. We measured the cross-correlation between the centres of voids and the complete galaxy catalogue. The cross-correlation function exhibits a clear anisotropy in both VIPERS fields (W1 and W4), which is characteristic of linear redshift space distortions. By measuring the projected cross-correlation and then deprojecting it we are able to estimate the undistorted cross-correlation function. We propose that given a sufficiently well measured cross-correlation function one should be able to measure the linear growth rate of structure by applying a simple linear Gaussian streaming model for the redshift space distortions (RSD). Our study of voids in 306 mock galaxy catalogues mimicking the VIPERS fields would suggest that VIPERS is capable of measuring $\beta$ with an error of around $25\%$. Applying our method to the VIPERS data, we find a value for the redshift space distortion parameter, $\beta = 0.423^{+0.104}_{-0.108}$, which given the bias of the galaxy population we use gives a linear growth rate of $f\sigma_8 = 0.296^{+0.075}_{-0.078}$ at $z = 0.727$. These results are consistent with values observed in parallel VIPERS analysis using standard techniques.

Multipole analysis of redshift-space distortions around cosmic voids

We perform a comprehensive redshift-space distortion analysis based on cosmic voids in the large-scale distribution of galaxies observed with the Sloan Digital Sky Survey. To this end, we measure multipoles of the void-galaxy cross-correlation function and compare them with standard model predictions in cosmology. Merely considering linear-order theory allows us to accurately describe the data on the entire available range of scales and to probe void-centric distances down to about 2 h−1Mpc. Common systematics, such as the Fingers-of-God effect, scale-dependent galaxy bias, and nonlinear clustering do not seem to play a significant role in our analysis. We constrain the growth rate of structure via the redshift-space distortion parameter β at two median redshifts, β(z̄=0.32)=0.599+0.134−0.124 and β(z̄=0.54)=0.457+0.056−0.054, with a precision that is competitive with state-of-the-art galaxy-clustering results. While the high-redshift constraint perfectly agrees with model expectations, we observe a mild 2σ deviation at z̄=0.32, which increases to 3σ when the data is restricted to the lowest available redshift range of 0.15<z<0.33.

Improving constraints on the growth rate of structure by modelling the density–velocity cross-correlation in the 6dF Galaxy Survey

We present the first simultaneous analysis of the galaxy overdensity and peculiar velocity fields by modelling their cross-covariance. We apply our new maximum-likelihood approach to data from the 6-degree Field Galaxy Survey (6dFGS), which has the largest single collection of peculiar velocities to date. We present a full derivation of the analytic expression for the cross-covariance between the galaxy overdensity and peculiar velocity fields and find direct evidence for a non-zero correlation between the fields on scales up to $\sim50 h^{-1}$ Mpc. When utilising the cross-covariance, our measurement of the normalised growth rate of structure is $f\sigma_8(z=0) = 0.424^{+0.067}_{-0.064}$ (15% precision), and our measurement of the redshift-space distortion parameter is $\beta=0.341^{+0.062}_{-0.058}$ (18% precision). Both measurements improve by $\sim$20% compared to only using the auto-covariance information. This is consistent with the literature on multiple-tracer approaches, as well as Fisher matrix forecasts and previous analyses of 6dFGS. Our measurement of $f\sigma_8$ is consistent with the standard cosmological model, and we discuss how our approach can be extended to test alternative models of gravity.

The cross-correlation between 21 cm intensity mapping maps and the Lyα forest in the post-reionization era

We investigate the cross-correlation signal between 21cm intensity mapping maps and the Lyα forest in the fully non-linear regime using state-of-the-art hydrodynamic simulations. The cross-correlation signal between the Lyα forest and 21cm maps can provide a coherent and comprehensive picture of the neutral hydrogen (HI) content of our Universe in the post-reionization era, probing both its mass content and volume distribution. We compute the auto-power spectra of both fields together with their cross-power spectrum at z = 2.4 and find that on large scales the fields are completely anti-correlated. This anti-correlation arises because regions with high (low) 21cm emission, such as those with a large (low) concentration of damped Lyα systems, will show up as regions with low (high) transmitted flux. We find that on scales smaller than k ≃ 0.2 hMpc−1 the cross-correlation coefficient departs from −1, at a scale where non-linearities show up. We use the anisotropy of the power spectra in redshift-space to determine the values of the bias and of the redshift-space distortion parameters of both fields. We find that the errors on the value of the cosmological and astrophysical parameters could decrease by 30% when adding data from the cross-power spectrum, in a conservative analysis. Our results point out that linear theory is capable of reproducing the shape and amplitude of the cross-power up to rather non-linear scales. Finally, we find that the 21cm-Lyα cross-power spectrum can be detected by combining data from a BOSS-like survey together with 21cm intensity mapping observations by SKA1-MID with a S/N ratio higher than 3 in k∊[0.06,1] hMpc−1. We emphasize that while the shape and amplitude of the 21cm auto-power spectrum can be severely affected by residual foreground contamination, cross-power spectra will be less sensitive to that and therefore can be used to identify systematics in the 21cm maps.

The 2-degree Field Lensing Survey: design and clustering measurements

We present the 2-degree Field Lensing Survey (2dFLenS), a new galaxy redshift survey performed at the Anglo-Australian Telescope. 2dFLenS is the first wide-area spectroscopic survey specifically targeting the area mapped by deep-imaging gravitational lensing fields, in this case the Kilo-Degree Survey. 2dFLenS obtained 70,079 redshifts in the range z < 0.9 over an area of 731 sq deg, and is designed to extend the datasets available for testing gravitational physics and promote the development of relevant algorithms for joint imaging and spectroscopic analysis. The redshift sample consists first of 40,531 Luminous Red Galaxies (LRGs), which enable analyses of galaxy-galaxy lensing, redshift-space distortion, and the overlapping source redshift distribution by cross-correlation. An additional 28,269 redshifts form a magnitude-limited (r < 19.5) nearly-complete sub-sample, allowing direct source classification and photometric-redshift calibration. In this paper, we describe the motivation, target selection, spectroscopic observations, and clustering analysis of 2dFLenS. We use power spectrum multipole measurements to fit the redshift-space distortion parameter of the LRG sample in two redshift ranges 0.15 < z < 0.43 and 0.43 < z < 0.7 as beta = 0.49 +/- 0.15 and beta = 0.26 +/- 0.09, respectively. These values are consistent with those obtained from LRGs in the Baryon Oscillation Spectroscopic Survey. 2dFLenS data products will be released via our website http://2dflens.swin.edu.au.

Broadband distortion modeling in Lyman-α forest BAO fitting

In recent years, the Lyman-α 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-α forest auto-correlation function at redshift z≃ 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-α forest spectrum. Implementing the distortion model in fits for the baryon acoustic oscillation (BAO) peak position in the Lyman-α forest auto-correlation, we find that the fitting method recovers the input values of the linear bias parameter bF and the redshift-space distortion parameter βF 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 βF and the combination bF(1+βF) by more than a factor of seven. The measured values at redshift z=2.3 are βF=1.39+0.11 +0.24 +0.38−0.10 −0.19 −0.28 and bF(1+βF)=−0.374+0.007 +0.013 +0.020−0.007 −0.014 −0.022 (1σ, 2σ and 3σ statistical errors). Our fitting software and the input files needed to reproduce our main results are publicly available.