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Register a new userThe Ly$alpha$ forest flux correlation function: a perturbation theory perspective
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The Ly$alpha$ forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Ly$alpha$ forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the `renormalization of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics.
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The Ly$alpha$ forest transmission probability distribution function (PDF) is an established probe of the intergalactic medium (IGM) astrophysics, especially the temperature-density relationship of the IGM. We measure the transmission PDF from 3393 Baryon Oscillations Spectroscopic Survey (BOSS) quasars from SDSS Data Release 9, and compare with mock spectra that include careful modeling of the noise, continuum, and astrophysical uncertainties. The BOSS transmission PDFs, measured at $langle z rangle = [2.3,2.6,3.0]$, are compared with PDFs created from mock spectra drawn from a suite of hydrodynamical simulations that sample the IGM temperature-density relationship, $gamma$, and temperature at mean-density, $T_0$, where $T(Delta) = T_0 Delta^{gamma-1}$. We find that a significant population of partial Lyman-limit systems with a column-density distribution slope of $beta_mathrm{pLLS} sim -2$ are required to explain the data at the low-transmission end of transmission PDF, while uncertainties in the mean Ly$alpha$ forest transmission affect the high-transmission end. After modelling the LLSs and marginalizing over mean-transmission uncertainties, we find that $gamma=1.6$ best describes the data over our entire redshift range, although constraints on $T_0$ are affected by systematic uncertainties. Within our model framework, isothermal or inverted temperature-density relationships ($gamma leq 1$) are disfavored at a significance of over 4$sigma$, although this could be somewhat weakened by cosmological and astrophysical uncertainties that we did not model.
An analytical framework is presented to understand the effects of a fluctuating intensity of the cosmic ionising background on the correlations of the Ly{alpha} forest transmission fraction measured in quasar spectra. In the absence of intensity fluctuations, the Ly{alpha} power spectrum should have the expected cold dark matter power spectrum with redshift distortions in the linear regime, with a bias factor b_{delta} and a redshift distortion parameter {beta} that depend on redshift but are independent of scale. The intensity fluctuations introduce a scale dependence in both b_{delta} and {beta}, but keeping their product b_{delta}{beta} fixed. Observations of the Ly{alpha} correlations and cross-correlations with radiation sources like those being done at present in the BOSS survey of SDSS-III (Busca et al. 2013; Slosar et al. 2013; Font-Ribera et al. 2014) have the potential to measure this scale dependence, which reflects the biasing properties of the sources and absorbers of the ionising background. We also compute a second term affecting the Ly{alpha} spectrum, due to shot noise in the sources of radiation. This term is very large if luminous quasars are assumed to produce the ionising background and to emit isotropically with a constant luminosity, but should be reduced by a contribution from galaxies, and by the finite lifetime and anisotropic emission of quasars.
We use the probability distribution function (PDF) of the lya forest flux at z=2-3, measured from high-resolution UVES/VLT data, and hydrodynamical simulations to obtain constraints on cosmological parameters and the thermal state of the intergalactic medium (IGM) at z 2-3. The observed flux PDF at z=3 alone results in constraints on cosmological parameters in good agreement with those obtained from the WMAP data, albeit with about a factor two larger errors. The observed flux PDF is best fit with simulations with a matter fluctuation amplitude of sigma_8=0.8-0.85 pm 0.07 and an inverted IGM temperature-density relation (gamma ~ 0.5-0.75), consistent with our previous results obtained using a simpler analysis. These results appear to be robust to uncertainties in the quasar (QSO) continuum placement. We further discuss constraints obtained by a combined analysis of the high-resolution flux PDF and the power spectrum measured from the Sloan Digital Sky Survey (SDSS) lya forest data. The joint analysis confirms the suggestion of an inverted temperature-density relation, but prefers somewhat higher values (sigma_8 ~ 0.9) of the matter fluctuation amplitude than the WMAP data and the best fit to the flux PDF alone. The joint analysis of the flux PDF and power spectrum (as well as an analysis of the power spectrum data alone) prefers rather large values for the temperature of the IGM, perhaps suggesting that we have identified a not yet accounted for systematic error in the SDSS flux power spectrum data or that the standard model describing the thermal state of the IGM at z ~ 2-3 is incomplete.
We have developed two independent methods to measure the one-dimensional power spectrum of the transmitted flux in the Lyman-$alpha$ forest. The first method is based on a Fourier transform, and the second on a maximum likelihood estimator. The two methods are independent and have different systematic uncertainties. The determination of the noise level in the data spectra was subject to a novel treatment, because of its significant impact on the derived power spectrum. We applied the two methods to 13,821 quasar spectra from SDSS-III/BOSS DR9 selected from a larger sample of over 60,000 spectra on the basis of their high quality, large signal-to-noise ratio, and good spectral resolution. The power spectra measured using either approach are in good agreement over all twelve redshift bins from $<z> = 2.2$ to $<z> = 4.4$, and scales from 0.001 $rm(km/s)^{-1}$ to $0.02 rm(km/s)^{-1}$. We determine the methodological and instrumental systematic uncertainties of our measurements. We provide a preliminary cosmological interpretation of our measurements using available hydrodynamical simulations. The improvement in precision over previously published results from SDSS is a factor 2--3 for constraints on relevant cosmological parameters. For a $Lambda$CDM model and using a constraint on $H_0$ that encompasses measurements based on the local distance ladder and on CMB anisotropies, we infer $sigma_8 =0.83pm0.03$ and $n_s= 0.97pm0.02$ based on ion{H}{i} absorption in the range $2.1<z<3.7$.
We report a detection of the baryon acoustic oscillation (BAO) feature in the three-dimensional correlation function of the transmitted flux fraction in the Lya forest of high-redshift quasars. The study uses 48,640 quasars in the redshift range $2.1le z le 3.5$ from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third generation of the Sloan Digital Sky Survey (SDSS-III). At a mean redshift $z=2.3$, we measure the monopole and quadrupole components of the correlation function for separations in the range $20hMpc<r<200hMpc$. A peak in the correlation function is seen at a separation equal to $(1.01pm0.03)$ times the distance expected for the BAO peak within a concordance $Lambda$CDM cosmology. This first detection of the BAO peak at high redshift, when the universe was strongly matter dominated, results in constraints on the angular diameter distance $da$ and the expansion rate $H$ at $z=2.3$ that, combined with priors on $H_0$ and the baryon density, require the existence of dark energy. Combined with constraints derived from Cosmic Microwave Background (CMB) observations, this result implies $H(z=2.3)=(224pm8){rm km,s^{-1}Mpc^{-1}}$, indicating that the time derivative of the cosmological scale parameter $dot{a}=H(z=2.3)/(1+z)$ is significantly greater than that measured with BAO at $zsim0.5$. This demonstrates that the expansion was decelerating in the range $0.7<z<2.3$, as expected from the matter domination during this epoch. Combined with measurements of $H_0$, one sees the pattern of deceleration followed by acceleration characteristic of a dark-energy dominated universe.
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