arXiv subjects

David H. Weinberg

Publications and source records attributed to David H. Weinberg.

At least 145 records · Page 8Linked to original sources

arXiv2013

Dark Energy: A Short Review

The accelerating expansion of the universe is the most surprising cosmological discovery in many decades. In this short review, we briefly summarize theories for the origin of cosmic acceleration and the observational methods being used to test these theories. We then discuss the current observational state of the field, with constraints from the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), Type Ia supernovae (SN), direct measurements of the Hubble constant ($H_0$), and measurements of galaxy and matter clustering. Assuming a flat universe and dark energy with a constant equation-of-state parameter $w = P/ρ$, the combination of Planck CMB temperature anisotropies, WMAP CMB polarization, the Union2.1 SN compilation, and a compilation of BAO measurements yields $w = -1.10^{+0.08}_{-0.07}$, consistent with a cosmological constant ($w=-1$). However, with these constraints the cosmological constant model predicts a value of $H_0$ that is lower than several of the leading recent estimates, and it predicts a parameter combination $σ_8(Ω_m)^{0.5}$ that is higher than many estimates from weak gravitational lensing, galaxy clusters, and redshift-space distortions. Individually these tensions are only significant at the ~$2σ$ level, but they arise in multiple data sets with independent statistics and distinct sources of systematic uncertainty. The tensions are stronger with Planck CMB data than they were with WMAP because of the smaller statistical errors and the higher central value of $Ω_m.$ With the improved measurements expected from the next generation of data sets, these tensions may diminish, or they may sharpen in a way that points towards a more complete physical understanding of cosmic acceleration.

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arXiv2013

The one-dimensional Ly-alpha forest power spectrum from BOSS

We have developed two independent methods to measure the one-dimensional power spectrum of the transmitted flux in the Lyman-$α$ 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 $ = 2.2$ to $ = 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 $Λ$CDM model and using a constraint on $H_0$ that encompasses measurements based on the local distance ladder and on CMB anisotropies, we infer $σ_8 =0.83\pm0.03$ and $n_s= 0.97\pm0.02$ based on \ion{H}{i} absorption in the range $2.1<z<3.7$.

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arXiv2013

A response to arXiv:1310.2791: A self-consistent public catalogue of voids and superclusters in the SDSS Data Release 7 galaxy surveys

Recently, Nadathur & Hotchkiss (2013) submitted a paper discussing a new cosmic void catalog. This paper includes claims about the void catalog described in Sutter et al. (2012). In this note, we respond to those claims, clarify some discrepancies between the text of Sutter et al. (2012) and the most recent version of the catalog, and provide some comments on the differences between our catalog and that of Nadathur & Hotchkiss (2013). All updates and documentation for our catalog are available at http://www.cosmicvoids.net.

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arXiv2013

Hydrogen and Metal Line Absorption Around Low-Redshift Galaxies in Cosmological Hydrodynamic Simulations

We study the physical conditions of the circum-galactic medium (CGM) around z=0.25 galaxies as traced by HI and metal line absorption, using cosmological hydrodynamic simulations that include galactic outflows. Using lines of sight targeted at impact parameters from 10 kpc to 1 Mpc around galaxies with halo masses from 10^11-10^13 M_solar, we study the physical conditions and their variation with impact parameter b and line-of-sight velocity delta v in the CGM as traced by HI, MgII, SiIV, CIV, OVI, and NeVIII absorbers. All ions show a strong excess of absorption near galaxies compared to random lines of sight. The excess continues beyond 1 Mpc, reflecting the correlation of metal absorption with large-scale structure. Absorption is particularly enhanced within about v<300 km/sec and roughly 300 kpc of galaxies (with distances somewhat larger for the highest ion), approximately delineating the CGM; this range contains the majority of global metal absorption. Low ions like MgII and SiIV predominantly arise in denser gas closer to galaxies and drop more rapidly with b, while high ions OVI and NeVIII trace more diffusely distributed gas with a comparatively flat radial profile; CIV is intermediate. All ions predominantly trace T~10^4-4.5 K photo-ionised gas at all b, but when hot CGM gas is present (mostly in larger halos), we see strong collisionally-ionised OVI and NeVIII at b <= 100 kpc. Larger halo masses generally produce more absorption, though overall the trends are not as strong as that with impact parameter. These findings arise using our favoured outflow scalings as expected for momentum-driven winds; with no winds, the CGM gas remains mostly unenriched, while our outflow model with a constant velocity and mass loading factor produce hotter, more widely dispersed metals.

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arXiv2013

Tracing Inflows and Outflows with Absorption Lines in Circumgalactic Gas

We examine how HI and metal absorption lines within low-redshift galaxy halos trace the dynamical state of circumgalactic gas, using cosmological hydrodynamic simulations that include a well-vetted heuristic model for galactic outflows. We categorize inflowing, outflowing, and ambient gas based on its history and fate as tracked in our simulation. Following our earlier work showing that the ionisation level of absorbers was a primary factor in determining the physical conditions of absorbing gas, we show here that it is also a governing factor for its dynamical state. Low-ionisation metal absorbers (e.g. MgII) tend to arise in gas that will fall onto galaxies within several Gyr, while high-ionisation metal absorbers (e.g. OVI) generally trace material that was deposited by outflows many Gyr ago. Inflowing gas is dominated by enriched material that was previously ejected in an outflow, hence accretion at low redshifts is typically substantially enriched. Recycling wind material is preferentially found closer to galaxies, and is more dominant in lower-mass halos since high-mass halos have more hot gas that is able to support itself against infall. Low-mass halos also tend to re-eject more of their accreted material, owing to our outflow prescription that employs higher mass loading factors for lower-mass galaxies. Typical HI absorbers trace unenriched ambient material that is not participating in the baryon cycle, but stronger HI absorbers arise in cool, enriched inflowing gas. Instantaneous radial velocity measures of absorbers are generally poor at distinguishing between inflowing and outflowing gas, except in the case of very recent outflows. These results suggest that probing halo gas using a range of absorbers can provide detailed information about the amount and physical conditions of material that is participating in the baryon cycle.

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arXiv2013

The Neutral Hydrogen Content of Galaxies in Cosmological Hydrodynamic Simulations

We examine the global HI properties of galaxies in quarter-billion particle cosmological simulations using Gadget-2, focusing on how galactic outflows impact HI content. We consider four outflow models, including a new one (ezw) motivated by recent interstellar medium simulations in which the wind speed and mass loading factor scale as expected for momentum-driven outflows for larger galaxies and energy-driven outflows for dwarfs (sigma<75 km/s). To obtain predicted HI masses, we employ a simple but effective local correction for particle self-shielding, and an observationally-constrained transition from neutral to molecular hydrogen. Our ezw simulation produces an HI mass function whose faint-end slope of -1.3 agrees well with observations from the ALFALFA survey; other models agree less well. Satellite galaxies have a bimodal distribution in HI fraction versus halo mass, with smaller satellites and/or those in larger halos more often being HI-deficient. At a given stellar mass, HI content correlates with star formation rate and inversely correlates with metallicity, as expected if driven by stochasticity in the accretion rate. To higher redshifts, massive HI galaxies disappear and the mass function steepens. The global cosmic HI density conspires to remain fairly constant from z~5-0, but the relative contribution from smaller galaxies increases with redshift.

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arXiv2013

Inside Out and Upside Down: Tracing the Assembly of a Simulated Disk Galaxy Using Mono-Age Stellar Populations

We analyze the present-day structure and assembly history of a high resolution hydrodynamic simulation of the formation of a Milky Way (MW)-like disk galaxy, from the "Eris" simulation suite, dissecting it into cohorts of stars formed at different epochs of cosmic history. At z=0, stars with t_form < 2 Gyr mainly occupy the stellar spheroid, with the oldest (earliest forming) stars having more centrally concentrated profiles. The younger age cohorts populate disks of progressively longer radial scale length and shorter vertical scale height. At a given radius, the vertical density profiles and velocity dispersions of stars vary smoothly as a function of age, and the superposition of old, vertically-extended and young, vertically-compact cohorts gives rise to a double-exponential profile like that observed in the MW. Turning to formation history, we find that the trends of spatial structure and kinematics with stellar age are largely imprinted at birth, or immediately thereafter. Stars that form during the active merger phase at z>3 are quickly scattered into rounded, kinematically hot configurations. The oldest disk cohorts form in structures that are radially compact and relatively thick, while subsequent cohorts form in progressively larger, thinner, colder configurations from gas with increasing levels of rotational support. The disk thus forms "inside-out" in a radial sense and "upside-down" in a vertical sense. Secular heating and radial migration influence the final state of each age cohort, but the changes they produce are small compared to the trends established at formation. The predicted correlations of stellar age with spatial and kinematic structure are in good qualitative agreement with the correlations observed for mono-abundance stellar populations in the MW.

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arXiv2013

Cold dark matter: controversies on small scales

The cold dark matter (CDM) cosmological model has been remarkably successful in explaining cosmic structure over an enormous span of redshift, but it has faced persistent challenges from observations that probe the innermost regions of dark matter halos and the properties of the Milky Way's dwarf galaxy satellites. We review the current observational and theoretical status of these "small scale controversies." Cosmological simulations that incorporate only gravity and collisionless CDM predict halos with abundant substructure and central densities that are too high to match constraints from galaxy dynamics. The solution could lie in baryonic physics: recent numerical simulations and analytic models suggest that gravitational potential fluctuations tied to efficient supernova feedback can flatten the central cusps of halos in massive galaxies, and a combination of feedback and low star-formation efficiency could explain why most of the dark matter subhalos orbiting the Milky Way do not host visible galaxies. However, it is not clear that this solution can work in the lowest mass galaxies where discrepancies are observed. Alternatively, the small-scale conflicts could be evidence of more complex physics in the dark sector itself. For example, elastic scattering from strong dark matter self-interactions can alter predicted halo mass profiles, leading to good agreement with observations across a wide range of galaxy mass. Gravitational lensing and dynamical perturbations of tidal streams in the stellar halo provide evidence for an abundant population of low mass subhalos in accord with CDM predictions. These observational approaches will get more powerful over the next few years.

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arXiv2013

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Luminosity and Color Dependence and Redshift Evolution

We measure the luminosity and color dependence and the redshift evolution of galaxy clustering in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Ninth Data Release. We focus on the projected two-point correlation function (2PCF) of subsets of its CMASS sample, which includes about 260,000 galaxies over ~3,300 sq. deg in the redshift range 0.43<z<0.7. To minimize the selection effect on galaxy clustering, we construct well-defined luminosity and color subsamples by carefully accounting for the CMASS galaxy selection cuts. The 2PCF of the whole CMASS sample, if approximated by a power-law, has a correlation length of r_0=7.93\pm0.06Mpc/h and an index of γ=1.85\pm0.01. Clear dependences on galaxy luminosity and color are found for the projected 2PCF in all redshift bins, with more luminous and redder galaxies generally exhibiting stronger clustering and steeper 2PCF. The color dependence is also clearly seen for galaxies within the red sequence, consistent with the behavior of SDSS-II main sample galaxies at lower redshifts. At a given luminosity (k+e corrected), no significant evolution of the projected 2PCFs with redshift is detected for red sequence galaxies. We also construct galaxy samples of fixed number density at different redshifts, using redshift-dependent magnitude thresholds. The clustering of these galaxies in the CMASS redshift range is found to be consistent with that predicted by passive evolution. Our measurements of the luminosity and color dependence and redshift evolution of galaxy clustering will allow for detailed modeling of the relation between galaxies and dark matter halos and new constraints on galaxy formation and evolution.

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arXiv2013

The Redshift-Space Cluster-Galaxy Cross-Correlation Function: I. Modeling Galaxy Infall onto Millennium Simulation Clusters and SDSS Groups

The large scale infall of galaxies around massive clusters provides a potentially powerful diagnostic of structure growth, dark energy, and cosmological deviations from General Relativity. We develop and test a method to recover galaxy infall kinematics (GIK) from measurements of the redshift-space cluster-galaxy cross-correlation function ξ_{cg}(r_p,r_π). Using galaxy and halo samples from the Millennium simulation, we calibrate an analytic model of the galaxy kinematic profiles comprised of a virialized component with an isotropic Gaussian velocity distribution and an infall component described by a skewed 2D t-distribution with a characteristic infall velocity v_r and separate radial and tangential dispersions. We show that convolving the real-space cross-correlation function with this velocity distribution accurately predicts the redshift-space ξ_{cg}, and we show that measurements of ξ_{cg} can be inverted to recover the four distinct elements of the GIK profiles. These in turn provide diagnostics of cluster mass profiles, and we expect the characteristic infall velocity v_r(r) in particular to be insensitive to galaxy formation physics that can affect velocity dispersions within halos. As a proof of concept we measure ξ_{cg} for rich galaxy groups in the Sloan Digital Sky Survey and recover GIK profiles for groups in two bins of central galaxy stellar mass. The higher mass bin has a v_r(r) curve very similar to that of 10^{14} Msun halos in the Millennium simulation, and the recovered kinematics follow the expected trends with mass. GIK modeling of cluster-galaxy cross-correlations can be a valuable complement to stacked weak lensing analyses, allowing novel tests of modified gravity theories that seek to explain cosmic acceleration.

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arXiv2013

Measurement of Baryon Acoustic Oscillations in the Lyman-alpha Forest Fluctuations in BOSS Data Release 9

We use the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) to detect and measure the position of the Baryonic Acoustic Oscillation (BAO) feature in the three-dimensional correlation function in the Lyman-alpha forest flux fluctuations at a redshift z=2.4. The feature is clearly detected at significance between 3 and 5 sigma (depending on the broadband model and method of error covariance matrix estimation) and is consistent with predictions of the standard LCDM model. We assess the biases in our method, stability of the error covariance matrix and possible systematic effects. We fit the resulting correlation function with several models that decouple the broadband and acoustic scale information. For an isotropic dilation factor, we measure 100x(alpha_iso-1) = -1.6 ^{+2.0+4.3+7.4}_{-2.0-4.1-6.8} (stat.) +/- 1.0 (syst.) (multiple statistical errors denote 1,2 and 3 sigma confidence limits) with respect to the acoustic scale in the fiducial cosmological model (flat LCDM with Omega_m=0.27, h=0.7). When fitting separately for the radial and transversal dilation factors we find marginalised constraints 100x(alpha_par-1) = -1.3 ^{+3.5+7.6 +12.3}_{-3.3-6.7-10.2} (stat.) +/- 2.0 (syst.) and 100x(alpha_perp-1) = -2.2 ^{+7.4+17}_{-7.1-15} +/- 3.0 (syst.). The dilation factor measurements are significantly correlated with cross-correlation coefficient of ~ -0.55. Errors become significantly non-Gaussian for deviations over 3 standard deviations from best fit value. Because of the data cuts and analysis method, these measurements give tighter constraints than a previous BAO analysis of the BOSS DR9 Lyman-alpha forest sample, providing an important consistency test of the standard cosmological model in a new redshift regime.

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arXiv2013

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Measuring D_A and H at z=0.57 from the Baryon Acoustic Peak in the Data Release 9 Spectroscopic Galaxy Sample

We present measurements of the angular diameter distance to and Hubble parameter at z=0.57 from the measurement of the baryon acoustic peak in the correlation of galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey. Our analysis is based on a sample from Data Release 9 of 264,283 galaxies over 3275 square degrees in the redshift range 0.43<z<0.70. We use two different methods to provide robust measurement of the acoustic peak position across and along the line of sight in order to measure the cosmological distance scale. We find D_A(0.57) = 1408 +/- 45 Mpc and H(0.57) = 92.9 +/- 7.8 km/s/Mpc for our fiducial value of the sound horizon. These results from the anisotropic fitting are fully consistent with the analysis of the spherically averaged acoustic peak position presented in Anderson et al, 2012. Our distance measurements are a close match to the predictions of the standard cosmological model featuring a cosmological constant and zero spatial curvature.

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arXiv2013

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological constraints from the full shape of the clustering wedges

We explore the cosmological implications of the clustering wedges, xi_perp(s) and xi_para(s), of the CMASS Data Release 9 (DR9) sample of the Baryon Oscillation Spectroscopic Survey (BOSS). These clustering wedges are defined by averaging the full two-dimensional correlation function, xi(mu,s), over the ranges 0<mu<0.5 and 0.5<mu<1, respectively. These measurements allow us to constrain the parameter combinations D_A(z)/r_s(z_d)=9.03 +- 0.21 and cz/(r_s(z_d)H(z)) = 12.14 +- 0.43 at the mean redsfhit of the sample, z=0.57. We combine the information from the clustering wedges with recent measurements of CMB, BAO and type Ia supernovae to obtain constraints on the cosmological parameters of the standard LCDM model and a number of potential extensions. The information encoded in the clustering wedges is most useful when the dark energy equation of state is allowed to deviate from its standard LCDM value. The combination of all datasets shows no evidence of a deviation from a constant dark energy equation of state, in which case we find w_DE = -1.013 +- 0.064, in complete agreement with a cosmological constant. We explore potential deviations from general relativity by constraining the growth rate f(z)=d ln D(a)/ d ln a, in which case the combination of the CMASS clustering wedges with CMB data implies f(z=0.57)=0.719 +- 0.094, in accordance with the predictions of GR. Our results clearly illustrate the additional constraining power of anisotropic clustering measurements with respect to that of angle-averaged quantities.

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arXiv2013

Observational Probes of Cosmic Acceleration

The accelerating expansion of the universe is the most surprising cosmological discovery in many decades, implying that the universe is dominated by some form of "dark energy" with exotic physical properties, or that Einstein's theory of gravity breaks down on cosmological scales. The profound implications of cosmic acceleration have inspired ambitious experimental efforts to measure the history of expansion and growth of structure with percent-level precision or higher. We review in detail the four most well established methods for making such measurements: Type Ia supernovae, baryon acoustic oscillations (BAO), weak gravitational lensing, and galaxy clusters. We pay particular attention to the systematic uncertainties in these techniques and to strategies for controlling them at the level needed to exploit "Stage IV" dark energy facilities such as BigBOSS, LSST, Euclid, and WFIRST. We briefly review a number of other approaches including redshift-space distortions, the Alcock-Paczynski test, and direct measurements of H_0. We present extensive forecasts for constraints on the dark energy equation of state and parameterized deviations from GR, achievable with Stage III and Stage IV experimental programs that incorporate supernovae, BAO, weak lensing, and CMB data. We also show the level of precision required for other methods to provide constraints competitive with those of these fiducial programs. We emphasize the value of a balanced program that employs several of the most powerful methods in combination, both to cross-check systematic uncertainties and to take advantage of complementary information. Surveys to probe cosmic acceleration produce data sets with broad applications, and they continue the longstanding astronomical tradition of mapping the universe in ever greater detail over ever larger scales.

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arXiv2013

Baryon Acoustic Oscillations in the Ly-α forest of BOSS quasars

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 $2.1\le z \le 3.5$ 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 $20\hMpc<r<200\hMpc$. A peak in the correlation function is seen at a separation equal to $(1.01\pm0.03)$ times the distance expected for the BAO peak within a concordance $Λ$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 $H(z=2.3)=(224\pm8){\rm km\,s^{-1}Mpc^{-1}}$, 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 $z\sim0.5$. 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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arXiv2013

Fitting Methods for Baryon Acoustic Oscillations in the Lyman-α Forest Fluctuations in BOSS Data Release 9

We describe fitting methods developed to analyze fluctuations in the Lyman-α forest and measure the parameters of baryon acoustic oscillations (BAO). We apply our methods to BOSS Data Release 9. Our method is based on models of the three-dimensional correlation function in physical coordinate space, and includes the effects of redshift-space distortions, anisotropic non-linear broadening, and broadband distortions. We allow for independent scale factors along and perpendicular to the line of sight to minimize the dependence on our assumed fiducial cosmology and to obtain separate measurements of the BAO angular and relative velocity scales. Our fitting software and the input files needed to reproduce our main BOSS Data Release 9 results are publicly available.

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arXiv2012

A first application of the Alcock-Paczynski test to stacked cosmic voids

We report on the first application of the Alcock-Paczynski test to stacked voids in spectroscopic galaxy redshift surveys.We use voids from the Sutter et al. (2012) void catalog, which was derived from the Sloan Digital Sky Survey Data Release 7 main sample and luminous red galaxy catalogs. The construction of that void catalog removes potential shape measurement bias by using a modified version of the ZOBOV algorithm and by removing voids near survey boundaries and masks. We apply the shape-fitting procedure presented in Lavaux & Wandelt (2012) to ten void stacks out to redshift z=0.36. Combining these measurements, we determine the mean cosmologically induced "stretch" of voids in three redshift bins, with 1-sigma errors of 5-15%. The mean stretch is consistent with unity, providing no indication of a distortion induced by peculiar velocities. While the statistical errors are too large to detect the Alcock-Paczynski effect over our limited redshift range, this proof-of-concept analysis defines procedures that can be applied to larger spectroscopic galaxy surveys at higher redshifts to constrain dark energy using the expected statistical isotropy of structures that are minimally affected by uncertainties in galaxy velocity bias.

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arXiv2012

The BOSS Lyman-alpha Forest Sample from SDSS Data Release 9

We present the BOSS Lyman-alpha (Lya) Forest Sample from SDSS Data Release 9, comprising 54,468 quasar spectra with zqso > 2.15 suitable for Lya forest analysis. This data set probes the intergalactic medium with absorption redshifts 2.0 < z_alpha < 5.7 over an area of 3275 square degrees, and encompasses an approximate comoving volume of 20 h^-3 Gpc^3. With each spectrum, we have included several products designed to aid in Lya forest analysis: improved sky masks that flag pixels where data may be unreliable, corrections for known biases in the pipeline estimated noise, masks for the cores of damped Lya systems and corrections for their wings, and estimates of the unabsorbed continua so that the observed flux can be converted to a fractional transmission. The continua are derived using a principal component fit to the quasar spectrum redwards of restframe Lya (lambda > 1216 Ang), extrapolated into the forest region and normalized by a linear function to fit the expected evolution of the Lya forest mean-flux. The estimated continuum errors are ~5% rms. We also discuss possible systematics arising from uncertain spectrophotometry and artifacts in the flux calibration; global corrections for the latter are provided. Our sample provides a convenient starting point for users to analyze clustering in BOSS Lya forest data, and it provides a fiducial data set that can be used to compare results from different analyses of baryon acoustic oscillations in the Lya forest. The full data set is available from the SDSS-III DR9 web site.

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