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Donald P. Schneider

Publications and source records attributed to Donald P. Schneider.

At least 91 records · Page 5Linked to original sources

Exploratory X-Ray Monitoring of Luminous Radio-Quiet Quasars at High Redshift: Extended Time-Series Analyses and Stacked Imaging Spectroscopy

We present three new Chandra X-ray epochs along with new ground-based optical-UV observations as the third installment in a time-series analysis of four high-redshift ($z\sim4.1-4.4$) radio-quiet quasars (RQQs). In total, we present nine epochs for these sources with rest-frame temporal baselines of $\sim1300-2000$ days. We utilize the X-ray data to determine basic variability properties, as well as produce mean spectra and stacked images based on effective exposure times of $\sim40-70$ ks per source. We perform time-series analyses in the soft and hard bands, separately, and compare variability properties to those of sources at lower redshifts and luminosities. The magnitude of X-ray variability of our sources remains consistent with or lower than that of similar sources at lower redshifts, in agreement with the variability-luminosity anti-correlation. The mean power-law photon indices in the stacked Chandra spectra of our sources are consistent with the values measured from their archival XMM-Newton spectra separated by about three years in the rest frame. Along with the X-ray observations we provide near-simultaneous optical monitoring of the sources in the optical-UV regime. The overall variability in the optical-to-X-ray spectral slope is consistent with sources at lower redshifts and the optical-UV observations display mild variability on monthly timescales.

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The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Survey Design, Reductions, and Detections

We describe the survey design, calibration, commissioning, and emission-line detection algorithms for the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). The goal of HETDEX is to measure the redshifts of over a million Ly$α$ emitting galaxies between 1.88<z<3.52, in a 540 deg^2 area encompassing a co-moving volume of 10.9 Gpc^3. No pre-selection of targets is involved; instead the HETDEX measurements are accomplished via a spectroscopic survey using a suite of wide-field integral field units distributed over the focal plane of the telescope. This survey measures the Hubble expansion parameter and angular diameter distance, with a final expected accuracy of better than 1%. We detail the project's observational strategy, reduction pipeline, source detection, and catalog generation, and present initial results for science verification in the COSMOS, Extended Groth Strip, and GOODS-N fields. We demonstrate that our data reach the required specifications in throughput, astrometric accuracy, flux limit, and object detection, with the end products being a catalog of emission-line sources, their object classifications, and flux-calibrated spectra.

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The $z \sim 2$ $\rm{[O\ III]}$ Luminosity Function of Grism-selected Emission-line Galaxies

Upcoming missions such as Euclid and the Nancy Grace Roman Space Telescope (Roman) will use emission-line selected galaxies to address a variety of questions in cosmology and galaxy evolution in the $z>1$ universe. The optimal observing strategy for these programs relies upon knowing the number of galaxies that will be found and the bias of the galaxy population. Here we measure the $\rm{[O\ III]}\ λ5007$ luminosity function for a vetted sample of 1951 $m_{\rm J+JH+H} < 26$ galaxies with unambiguous redshifts between $1.90 < z < 2.35$, which were selected using HST/WFC3 G141 grism frames made available by the 3D-HST program. These systems are directly analogous to the galaxies that will be identified by the Euclid and Roman missions, which will utilize grism spectroscopy to find $\rm{[O\ III]}\ λ5007$-emitting galaxies at $0.8 \lesssim z \lesssim 2.7$ and $1.7 \lesssim z \lesssim 2.8$, respectively. We interpret our results in the context of the expected number counts for these upcoming missions. Finally, we combine our dust-corrected $\rm{[O\ III]}$ luminosities with rest-frame ultraviolet star formation rates to present a new calibration of the SFR density associated with $1.90 < z < 2.35$ $\rm{[O\ III]}$-emitting galaxies. We find that these grism-selected galaxies contain roughly half of the total star formation activity at $z\sim2$.

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Chemical Cartography with APOGEE: Mapping Disk Populations with a Two-Process Model and Residual Abundances

We apply a novel statistical analysis to measurements of 16 elemental abundances in 34,410 Milky Way disk stars from the final data release (DR17) of APOGEE-2. Building on recent work, we fit median abundance ratio trends [X/Mg] vs. [Mg/H] with a 2-process model, which decomposes abundance patterns into a "prompt" component tracing core collapse supernovae and a "delayed" component tracing Type Ia supernovae. For each sample star, we fit the amplitudes of these two components, then compute the residuals Δ[X/H] from this two-parameter fit. The rms residuals range from ~0.01-0.03 dex for the most precisely measured APOGEE abundances to ~0.1 dex for Na, V, and Ce. The correlations of residuals reveal a complex underlying structure, including a correlated element group comprised of Ca, Na, Al, K, Cr, and Ce and a separate group comprised of Ni, V, Mn, and Co. Selecting stars poorly fit by the 2-process model reveals a rich variety of physical outliers and sometimes subtle measurement errors. Residual abundances allow comparison of populations controlled for differences in metallicity and [α/Fe]. Relative to the main disk (R=3-13 kpc, |Z|<2 kpc), we find nearly identical abundance patterns in the outer disk (R=15-17 kpc), 0.05-0.2 dex depressions of multiple elements in LMC and Gaia Sausage/Enceladus stars, and wild deviations (0.4-1 dex) of multiple elements in ωCen. Residual abundance analysis opens new opportunities for discovering chemically distinctive stars and stellar populations, for empirically constraining nucleosynthetic yields, and for testing chemical evolution models that include stochasticity in the production and redistribution of elements.

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First HETDEX Spectroscopic Determinations of Ly$α$ and UV Luminosity Functions at $z=2-3$: Bridging a Gap Between Faint AGN and Bright Galaxies

We present Ly$α$ and ultraviolet-continuum (UV) luminosity functions (LFs) of galaxies and active galactic nuclei (AGN) at $z=2.0-3.5$ determined by the un-targetted optical spectroscopic survey of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). We combine deep Subaru imaging with HETDEX spectra resulting in $11.4$ deg$^2$ of fiber-spectra sky coverage, obtaining $18320$ galaxies spectroscopically identified with Ly$α$ emission, $2126$ of which host type 1 AGN showing broad (FWHM$~>1000$ km s$^{-1}$) Ly$α$ emission lines. We derive the Ly$α$ (UV) LF over 2 orders of magnitude covering bright galaxies and AGN in $\log L_\mathrm{Lyα}/\mathrm{[erg~s^{-1}]}=43.3-45.5$ ($-27 -21$) type 1 AGN increases from $z\sim2$ to $z\sim0$ as opposed to the evolution of bright ($M_\mathrm{UV}<-21$) type 1 AGN, suggesting the AGN downsizing in the rest-frame UV luminosity.

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Detection of Lyman Continuum from 3.0 < z < 3.5 Galaxies in the HETDEX Survey

Questions as to what drove the bulk reionization of the Universe, how that reionization proceeded, and how the hard ionizing radiation reached the intergalactic medium remain open and debated. Observations probing that epoch are severely hampered by the increasing amounts of neutral gas with increasing redshift, so a small, but growing number of experiments are targeting star forming galaxies ($z\sim3$) as proxies. However, these studies, while providing fantastic detail, are time intensive, contain relatively few targets, and can suffer from selection biases. As a complementary alternative, we investigate whether stacking the already vast (and growing) numbers of low-resolution ($Δλ/ λ= 800$) Lyman-$α$ Emitting (LAE) galaxy spectra from the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) can be used to measure ionizing photons (restframe 880-910Å) escaping their galaxy hosts. As a blind survey, HETDEX avoids the biases from continuum selected galaxies and its planned 540 square degree coverage promotes the statistical power of large numbers. In this paper, we confirm the feasibility of Lyman continuum detection by carefully selecting a sample of \lyccount\ high redshift ($z\sim$3) LAEs from a subset of HETDEX observations, stacking their spectra and measuring a $\gtrsim$3$σ$ detection of $0.10 μ$Jy restframe Lyman continuum emission, uncorrected for attenuation in the intergalactic medium, over the full sample stack ($3.0 < z < 3.5$ and $-22.0 \lesssim M_{\text{UV}} \lesssim -19.0$).

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Double-lined spectroscopic binaries in the APOGEE DR16 and DR17 data

APOGEE spectra offer $\lesssim$1 km s$^{-1}$ precision in the measurement of stellar radial velocities (RVs). This holds even when multiple stars are captured in the same spectrum, as happens most commonly with double-lined spectroscopic binaries (SB2s), although random line of sight alignments of unrelated stars can also occur. We develop a code that autonomously identifies SB2s and higher order multiples in the APOGEE spectra, resulting in 7273 candidate SB2s, 813 SB3s, and 19 SB4s. We estimate the mass ratios of binaries, and for a subset of these systems with sufficient number of measurements we perform a complete orbital fit, confirming that most systems with period $<$10 days have circularized. Overall, we find a SB2 fraction ($F_{SB2}$) $\sim$3\% among main sequence dwarfs, and that there is not a significant trend in $F_{SB2}$ with temperature of a star. We are also able to recover a higher $F_{SB2}$ in sources with lower metallicity, however there are some observational biases. We also examine light curves from TESS to determine which of these spectroscopic binaries are also eclipsing. Such systems, particularly those that are also pre- and post-main sequence, are good candidates for a follow-up analysis to determine their masses and temperatures.

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The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: The Damped Lyman-$α$ systems Catalog

We present the characteristics of the Damped Lyman-$α$ (DLA) systems found in the data release DR16 of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) of the Sloan Digital Sky Survey (SDSS). DLAs were identified using the convolutional neural network (CNN) of~\cite{Parks2018}. A total of 117,458 absorber candidates were found with $2 \leq \zdla \leq 5.5$ and $19.7 \leq \lognhi \leq 22$, including 57,136 DLA candidates with $\lognhi \geq 20.3$. Mock quasar spectra were used to estimate DLA detection efficiency and the purity of the resulting catalog. Restricting the quasar sample to bright forests, i.e. those with mean forest fluxes $\meanflux>2\times\fluxunit$, the completeness and purity are greater than 90\% for DLAs with column densities in the range $20.1\leq \lognhi \leq 22$.

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The clustering of galaxies in the completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Primordial non-Gaussianity in Fourier Space

We present measurements of the local primordial non-Gaussianity parameter \fNLloc from the clustering of 343,708 quasars with redshifts 0.8 < z < 2.2 distributed over 4808 square degrees from the final data release (DR16) of the extended Baryon acoustic Oscillation Spectroscopic Survey (eBOSS), the largest volume spectroscopic survey up to date. Our analysis is performed in Fourier space, using the power spectrum monopole at very large scales to constrain the scale dependent halo bias. We carefully assess the impact of systematics on our measurement and test multiple contamination removal methods. We demonstrate the robustness of our analysis pipeline with EZ-mock catalogues that simulate the eBOSS DR16 target selection. We find $f_\mathrm{NL}=-12\pm 21$ (68\% confidence) for the main clustering sample including quasars with redshifts between 0.8 and 2.2, after exploiting a novel neural network scheme for cleaning the DR16 sample and in particular after applying redshift weighting techniques, designed for non-Gaussianity measurement from large scales structure, to optimize our analysis, which improve our results by 37\%.

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Primordial non-Gaussianity from the Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey I: Catalogue Preparation and Systematic Mitigation

We investigate the large-scale clustering of the final spectroscopic sample of quasars from the recently completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). The sample contains $343708$ objects in the redshift range $0.8<z<2.2$ and $72667$ objects with redshifts $2.2<z<3.5$, covering an effective area of $4699~{\rm deg}^{2}$. We develop a neural network-based approach to mitigate spurious fluctuations in the density field caused by spatial variations in the quality of the imaging data used to select targets for follow-up spectroscopy. Simulations are used with the same angular and radial distributions as the real data to estimate covariance matrices, perform error analyses, and assess residual systematic uncertainties. We measure the mean density contrast and cross-correlations of the eBOSS quasars against maps of potential sources of imaging systematics to address algorithm effectiveness, finding that the neural network-based approach outperforms standard linear regression. Stellar density is one of the most important sources of spurious fluctuations, and a new template constructed using data from the Gaia spacecraft provides the best match to the observed quasar clustering. The end-product from this work is a new value-added quasar catalogue with the improved weights to correct for nonlinear imaging systematic effects, which will be made public. Our quasar catalogue is used to measure the local-type primordial non-Gaussianity in our companion paper, Mueller et al. in preparation.

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Taking a Long Look: A Two-Decade Reverberation Mapping Study of High-Luminosity Quasars

Reverberation mapping (RM) of active galactic nuclei (AGNs) has been used over the past three decades to determine AGN broad-line region (BLR) sizes and central black-hole masses, and their relations with the AGN's luminosity. Until recently the sample of objects with RM data was limited to low-luminosity AGNs ($L_{\rm opt} \lesssim 10^{46}$ ergs s$^{-1}$) and low redshifts ($z \lesssim 0.5$). Here we present results from a reverberation-mapping project of some of the most luminous and highest redshift quasars that have been mapped to date. The study is based on almost twenty years of photometric monitoring of 11 quasars, six of which were monitored spectrophotometrically for 13 years. This is the longest reverberation-mapping project carried out so far on this type of AGNs. We successfully measure a time lag between the CIV$λ$1549 broad emission line and the quasar continuum in three objects, and measure a CIII$λ$1909 lag in one quasar. Together with recently published data on CIV reverberation mapping, the BLR size is found to scale as the square root of the UV luminosity over eight orders of magnitude in AGN luminosity. There is a significant scatter in the relation, part of which may be intrinsic to the AGNs. Although the CIV line is probably less well suited than Balmer lines for determination of the mass of the black hole, virial masses are tentatively computed and in spite of a large scatter we find that the mass of the black hole scales as the square root of the UV luminosity.

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The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey quasar sample: Testing observational systematics on the Baryon Acoustic Oscillation measurement

Baryon Acoustic Oscillations are considered to be a very robust standard ruler against various systematics. This premise has been tested against observational systematics, but not to the level required for the next generation of galaxy surveys such as the Dark Energy Spectroscopic Instrument (DESI) and Euclid. In this paper, we investigate the effect of observational systematics on the BAO measurement of the final sample of quasars from the extended Baryon Oscillation Spectroscopic Survey Data Release 16 in order to prepare and hone a similar analysis for upcoming surveys. We employ catalogues with various treatments of imaging systematic effects using linear and neural network-based nonlinear approaches and consider how the BAO measurement changes. We also test how the variations to the BAO fitting model respond to the observational systematics. As expected, we confirm that the BAO measurements obtained from the DR16 quasar sample are robust against imaging systematics well within the statistical error, while reporting slightly modified constraints that shift the line-of-sight BAO signal by less than 1.1% . We use realistic simulations with similar redshift and angular distributions as the DR16 sample to conduct statistical tests for validating the pipeline, quantifying the significance of differences, and estimating the expected bias on the BAO scale in future high-precision data sets. Although we find a marginal impact for the eBOSS QSO data, the work presented here is of vital importance for constraining the nature of dark energy with the BAO feature in the new era of big data cosmology with DESI and Euclid.

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The HETDEX Survey: The Ly$α$ Escape Fraction from 3D-HST Emission Line Galaxies at $z \sim 2$

We measure the Ly$α$ escape fraction of 935 [OIII]-emitting galaxies between $1.9 < z < 2.35$ by comparing stacked spectra from the Hubble Space Telescope/WFC3's near-IR grism to corresponding stacks from the Hobby Eberly Telescope Dark Energy Experiment's Internal Data Release 2. By measuring the stacks' H$β$ to Ly$α$ ratios, we determine the Ly$α$ escape fraction as a function of stellar mass, star formation rate, internal reddening, size, and [OIII]/H$β$ ratio. We show that the escape fraction of Ly$α$ correlates with a number of parameters, such as galaxy size, star formation rate, and nebular excitation. However, we also demonstrate that most of these relations are indirect, and the primary variables that control the escape of Ly$α$ are likely stellar mass and internal extinction. Overall, the escape of Ly$α$ declines from $\gtrsim 18\%$ in galaxies with $\log M/M_{\odot} \lesssim 9$ to $\lesssim 1\%$ for systems with $\log M/M_{\odot} \gtrsim 10$, with the sample's mean escape fraction being $6.0^{+0.6\%}_{-0.5\%}$.

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The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: a multi-tracer analysis in Fourier space for measuring the cosmic structure growth and expansion rate

We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of $z\in[0.6,1.1]$, and detect a RSD signal from the cross power spectrum at a $\sim4σ$ confidence level, i.e., $fσ_8=0.317\pm0.080$ at $z_{\rm eff}=0.77$. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measurement the BAO distances and growth rate simultaneously at two effective redshifts, namely, $D_{\rm M}/r_{\rm d} \ (z=0.70)=17.96\pm0.51, \ D_{\rm H}/r_{\rm d} \ (z=0.70)=21.22\pm1.20, \ fσ_8 \ (z=0.70) =0.43\pm0.05$, and $D_{\rm M}/r_{\rm d} \ (z=0.845)=18.90\pm0.78, \ D_{\rm H}/r_{\rm d} \ (z=0.845)=20.91\pm2.86, \ fσ_8 \ (z=0.845) =0.30\pm0.08$. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-$α$ sample, our measurement has raised the significance level of a nonzero $Ω_{\rm Λ}$ to $\sim11σ$.

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The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1

We analyse the large-scale clustering in Fourier space of emission line galaxies (ELG) from the Data Release 16 of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey. The ELG sample contains 173,736 galaxies covering 1,170 square degrees in the redshift range $0.6 < z < 1.1$. We perform a BAO measurement from the post-reconstruction power spectrum monopole, and study redshift space distortions (RSD) in the first three even multipoles. Photometric variations yield fluctuations of both the angular and radial survey selection functions. Those are directly inferred from data, imposing integral constraints which we model consistently. The full data set has only a weak preference for a BAO feature ($1.4σ$). At the effective redshift $z_{\rm eff} = 0.845$ we measure $D_{\rm V}(z_{\rm eff})/r_{\rm drag} = 18.33_{-0.62}^{+0.57}$, with $D_{\rm V}$ the volume-averaged distance and $r_{\rm drag}$ the comoving sound horizon at the drag epoch. In combination with the RSD measurement, at $z_{\rm eff} = 0.85$ we find $fσ_8(z_{\rm eff}) = 0.289_{-0.096}^{+0.085}$, with $f$ the growth rate of structure and $σ_8$ the normalisation of the linear power spectrum, $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 20.0_{-2.2}^{+2.4}$ and $D_{\rm M}(z_{\rm eff})/r_{\rm drag} = 19.17 \pm 0.99$ with $D_{\rm H}$ and $D_{\rm M}$ the Hubble and comoving angular distances, respectively. These results are in agreement with those obtained in configuration space, thus allowing a consensus measurement of $fσ_8(z_{\rm eff}) = 0.315 \pm 0.095$, $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 19.6_{-2.1}^{+2.2}$ and $D_{\rm M}(z_{\rm eff})/r_{\rm drag} = 19.5 \pm 1.0$. This measurement is consistent with a flat $Λ$CDM model with Planck parameters.

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The Stars of the HETDEX Survey. I. Radial Velocities and Metal-Poor Stars from Low-Resolution Stellar Spectra

The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) is an unbiased, massively multiplexed spectroscopic survey, designed to measure the expansion history of the universe through low-resolution ($R\sim750$) spectra of Lyman-Alpha Emitters. In its search for these galaxies, HETDEX will also observe a few 10$^{5}$ stars. In this paper, we present the first stellar value-added catalog within the internal second data release of the HETDEX Survey (HDR2). The new catalog contains 120,571 low-resolution spectra for 98,736 unique stars between $10 < G < 22$ spread across the HETDEX footprint at relatively high ($b\sim60^\circ$) Galactic latitudes. With these spectra, we measure radial velocities (RVs) for $\sim$42,000 unique FGK-type stars in the catalog and show that the HETDEX spectra are sufficient to constrain these RVs with a 1$σ$ precision of 28.0 km/s and bias of 3.5 km/s with respect to the LAMOST surveys and 1$σ$ precision of 27.5 km/s and bias of 14.0 km/s compared to the SEGUE survey. Since these RVs are for faint ($G\geq16$) stars, they will be complementary to Gaia. Using t-Distributed Stochastic Neighbor Embedding (t-SNE), we also demonstrate that the HETDEX spectra can be used to determine a star's T${\rm{eff}}$, and log g and its [Fe/H]. With the t-SNE projection of the FGK-type stars with HETDEX spectra we also identify 416 new candidate metal-poor ([Fe/H] $< -1$~dex) stars for future study. These encouraging results illustrate the utility of future low-resolution stellar spectroscopic surveys.

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The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the Quasar Sample in configuration space between redshift 0.8 and 2.2

We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of $343,708$ spectroscopically confirmed quasars between redshift $0.8<z<2.2$ are used as tracers of the underlying dark matter field. In comparison with DR14 sample, the final sample doubles the number of objects as well as the survey area. In this paper, we present the analysis in configuration space by measuring the two-point correlation function and decompose using the Legendre polynomials. For the full-shape analysis of the Legendre multipole moments, we measure the BAO distance and the growth rate of the cosmic structure. At an effective redshift of $z_{\rm eff}=1.48$, we measure the comoving angular diameter distance $D_{\rm M}(z_{\rm eff})/r_{\rm drag} = 30.66\pm0.88$, the Hubble distance $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 13.11\pm0.52$, and the growth rate $fσ_8(z_{\rm eff}) = 0.439\pm0.048$. The accuracy of these measurements is confirmed using an extensive set of mock simulations developed for the quasar sample. The uncertainties on the distance and growth rate measurements have been reduced substantially ($\sim 45\%$ and $\sim30\%$) with respect to the DR14 results. We also perform a BAO-only analysis to cross check the robustness of the methodology of the full-shape analysis. Combining our analysis with the Fourier space analysis, we arrive at $D^{\bf{c}}_{\rm M}(z_{\rm eff})/r_{\rm drag} = 30.22 \pm 0.79$, $D^{\bf{c}}_{\rm H}(z_{\rm eff})/r_{\rm drag} = 13.26 \pm 0.47$, and $fσ_8^{\bf{c}}(z_{\rm eff}) = 0.464 \pm 0.045$.

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The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic power spectrum between redshifts 0.6 and 1.0

We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 luminous red galaxy sample (DR16 eBOSS LRG) in combination with the high redshift tail of the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12 BOSS CMASS). We measure the redshift space distortions (RSD) and also extract the longitudinal and transverse baryonic acoustic oscillation (BAO) scale from the anisotropic power spectrum signal inferred from 377,458 galaxies between redshifts 0.6 and 1.0, with effective redshift of $z_{\rm eff}=0.698$ and effective comoving volume of $2.72\,{\rm Gpc}^3$. After applying reconstruction we measure the BAO scale and infer $D_H(z_{\rm eff})/r_{\rm drag} = 19.30\pm 0.56$ and $D_M(z_{\rm eff})/r_{\rm drag} =17.86 \pm 0.37$. When we perform a redshift space distortions analysis on the pre-reconstructed catalogue on the monopole, quadrupole and hexadecapole we find, $D_H(z_{\rm eff})/r_{\rm drag} = 20.18\pm 0.78$, $D_M(z_{\rm eff})/r_{\rm drag} =17.49 \pm 0.52$ and $fσ_8(z_{\rm eff})=0.454\pm0.046$. We combine both sets of results along with the measurements in configuration space of \cite{LRG_corr} and report the following consensus values: $D_H(z_{\rm eff})/r_{\rm drag} = 19.77\pm 0.47$, $D_M(z_{\rm eff})/r_{\rm drag} = 17.65\pm 0.30$ and $fσ_8(z_{\rm eff})=0.473\pm 0.044$, which are in full agreement with the standard $Λ$CDM and GR predictions. These results represent the most precise measurements within the redshift range $0.6\leq z \leq 1.0$ and are the culmination of more than 8 years of SDSS observations.

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