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At least 37 records · Page 2

Full calibration of the tomographic redshift distribution from the HSC PDR3 Shape Catalog with DESI

The calibration of tomographic redshift distributionsis essential for cosmological analysis of weak lensing data.In this work, we calibrate all four tomographic bins of the Hyper Suprime Camera (HSC) weak lensing catalog with the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 and 2 using the clustering redshifts technique. We include z > 1.2 redshift sources such as emission line galaxies (ELG) and quasars (QSO) sources in our calibration, which were not available in the previous HSC calibration (Rau et al. (2022), Mon. Not. Roy. Astron. Soc. 524 (2023) 5109), allowing a complete calibration of all the redshift bins. We find the first tomographic bin exhibits a small shift towards low redshifts. The second bin is in good agreement with the photometric calibration, while third and fourth bin exhibit a shift towards higher redshifts. However, these shifts are considerably smaller than the shifts obtained in the HSC Year 3 cosmic shear analyses. We evaluate the impact of galaxy bias and magnification effects from all the samples on the measurements, finding them to be small, and we propose corrections to reduce them further. Specifically, we relax the assumption of linear bias and only assume no redshift evolution of the cross-correlation coefficient, allowing us to leverage smaller clustering scales. We model the redshift distributions with splines and compare our results to previous analyses as well as to other parameterizations found in literature. For the two high-redshift tomographic bins, we find the shifts to higher redshifts with respect to the measurements performed in Rau+2022 to be Δz$_{3}$ =-0.039$^{+0.020}$$_{-0.021}$ and Δz$_{4}$ = -0.048$^{+0.012}$$_{-0.012}$.

Choppin de Janvry, J. [LBL, Berkeley; UC, Berkeley↗

Photometric Redshifts for Next-Generation Surveys

Photometric redshifts are essential in studies of both galaxy evolution and cosmology, as they enable analyses of objects too numerous or faint for spectroscopy. The Rubin Observatory, Euclid, and Roman Space Telescope will soon provide a new generation of imaging surveys with unprecedented area coverage, wavelength range, and depth. To take full advantage of these data sets, further progress in photometric redshift methods is needed. In this review, we focus on the greatest common challenges and prospects for improvement in applications of photometric redshifts to the next generation of surveys: ∙ Gains in performance (i.e., the precision of redshift estimates for individual galaxies) could greatly enhance studies of galaxy evolution and some probes of cosmology. ∙ Improvements in characterization (i.e., the accurate recovery of redshift distributions of galaxies in the presence of uncertainty on individual redshifts) are urgently needed for cosmological measurements with next-generation surveys. To achieve both of these goals, improvements in the scope and treatment of the samples of spectroscopic redshifts that make high-fidelity photometric redshifts possible will also be needed. For the full potential of the next generation of surveys to be reached, the characterization of redshift distributions must improve by roughly an order of magnitude compared with the current state of the art, requiring progress on a wide variety of fronts. We conclude by presenting a speculative evaluation of how photometric redshift methods and the collection of the necessary spectroscopic samples may improve by the time near-future surveys are completed.

Astronomy & Astrophysics↗

Inferring the Redshift of More than 150 GRBs with a Machine-learning Ensemble Model

Gamma-ray bursts (GRBs), due to their high luminosities, are detected up to a redshift of 10, and thus have the potential to be vital cosmological probes of early processes in the Universe. Fulfilling this potential requires a large sample of GRBs with known redshifts, but due to observational limitations, only 11% have known redshifts (z). There have been numerous attempts to estimate redshifts via correlation studies, most of which have led to inaccurate predictions. To overcome this, we estimated GRB redshift via an ensemble-supervised machine-learning (ML) model that uses X-ray afterglows of long-duration GRBs observed by the Neil Gehrels Swift Observatory. The estimated redshifts are strongly correlated (a Pearson coefficient of 0.93) and have an rms error, namely, the square root of the average squared error $\langle$Δz 2 $\rangle$, of 0.46 with the observed redshifts showing the reliability of this method. The addition of GRB afterglow parameters improves the predictions considerably by 63% compared to previous results in peer-reviewed literature. Finally, we use our ML model to infer the redshifts of 154 GRBs, which increase the known redshifts of long GRBs with plateaus by 94%, a significant milestone for enhancing GRB population studies that require large samples with redshift.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey Year 3 results: redshift calibration of the weak lensing source galaxies

ABSTRACT Determining the distribution of redshifts of galaxies observed by wide-field photometric experiments like the Dark Energy Survey (DES) is an essential component to mapping the matter density field with gravitational lensing. In this work we describe the methods used to assign individual weak lensing source galaxies from the DES Year 3 Weak Lensing Source Catalogue to four tomographic bins and to estimate the redshift distributions in these bins. As the first application of these methods to data, we validate that the assumptions made apply to the DES Y3 weak lensing source galaxies and develop a full treatment of systematic uncertainties. Our method consists of combining information from three independent likelihood functions: self-organizing map p(z) (sompz), a method for constraining redshifts from galaxy photometry; clustering redshifts (WZ), constraints on redshifts from cross-correlations of galaxy density functions; and shear ratios (SRs), which provide constraints on redshifts from the ratios of the galaxy-shear correlation functions at small scales. Finally, we describe how these independent probes are combined to yield an ensemble of redshift distributions encapsulating our full uncertainty. We calibrate redshifts with combined effective uncertainties of σ〈z〉 ∼ 0.01 on the mean redshift in each tomographic bin.

79 ASTRONOMY AND ASTROPHYSICS↗

Redshift drift cosmography with ELT and SKAO measurements

ABSTRACT Mapping the expansion history of the universe is a compelling task of physical cosmology, especially in the context of the observational evidence for the recent acceleration of the universe, which demonstrates that canonical theories of cosmology and particle physics are incomplete and that there is new physics still to be discovered. Cosmography is a phenomenological approach to cosmology, where (with some caveats) physical quantities are expanded as a Taylor series in the cosmological redshift z, or analogous parameters such as the rescaled redshift y = z/(1 + z) or the logarithmic redshift x = ln (1 + z). Moreover, the redshift drift of objects following cosmological expansion provides a model-independent observable, detectable by facilities currently under construction, viz. the Extremely Large Telescope and the Square Kilometre Array Observatory (at least in its full configuration). Here, we use simulated redshift drift measurements from the two facilities to carry out an assessment of the cosmological impact and model discriminating power of redshift drift cosmography. We find that the combination of measurements from the two facilities can provide a stringent test of the Λ cold dark matter paradigm, and that overall the logarithmic-based expansions of the spectroscopic velocity drift are the most reliable ones, performing better than analogous expansions in the redshift or the rescaled redshift: the former nominally gives the smaller error bars for the cosmographic coefficients but is vulnerable to biases in the higher order terms (in other words, it is only reliable at low redshifts), while the latter always performs poorly.

Rocha, B. A. R.↗

Optimizing the shape of photometric redshift distributions with clustering cross-correlations

We present an optimization method for the assignment of photometric galaxies to a chosen set of redshift bins. This is achieved by combining simulated annealing, an optimization algorithm inspired by solid-state physics, with an unsupervised machine learning method, a self-organizing map (SOM) of the observed colours of galaxies. Starting with a sample of galaxies that is divided into redshift bins based on a photometric redshift point estimate, the simulated annealing algorithm repeatedly reassigns SOM-selected subsamples of galaxies, which are close in colour, to alternative redshift bins. We optimize the clustering cross-correlation signal between photometric galaxies and a reference sample of galaxies with well-calibrated redshifts. Depending on the effect on the clustering signal, the reassignment is either accepted or rejected. By dynamically increasing the resolution of the SOM, the algorithm eventually converges to a solution that minimizes the number of mismatched galaxies in each tomographic redshift bin and thus improves the compactness of their corresponding redshift distribution. This method is demonstrated on the synthetic Legacy Survey of Space and Time cosmoDC2 catalogue. We find a significant decrease in the fraction of catastrophic outliers in the redshift distribution in all tomographic bins, most notably in the highest redshift bin with a decrease in the outlier fraction from 57 percent to 16 percent.

79 ASTRONOMY AND ASTROPHYSICS↗

The riddle of the redshifts

Somewhat more than 40 years ago Hubble and Humason conclusively established that the redshifts of the galaxies are proportional to their apparent brightnesses. With this discovery came the general conclusion that the redshifts were due to the Doppler effect and that the universe is expanding. The discovery of QSOs with large redshifts led to the conclusion that if the redshifts were measures of distance the objects were at immense distances and in general some 50 times brighter than most luminous galaxies. Arguments for and against the cosmological redshift hypothesis are evaluated, giving attention to QSO variability, questions of relativistic expansion, the redshift-apparent magnitude diagram, the redshift-angular diameter relation, the distribution of redshifts, multiple redshifts, and distance measurements in extragalactic astronomy.

Burbidge, G.↗

A study of the absorption-line spectra of six high-redshift quasi-stellar objects

High-resolution spectrograms of six QSOs with apparent visual magnitudes of 17.0 to 18.5 and redshifts greater than 2 are studied for absorption lines. Accurate wavelengths are measured for all the absorption lines that could be detected, attempts are made to identify redshift systems, and the redshifts in each object are examined. Analysis of the absorption-line spectra shows that: (1) a large number of redshifts covering a wide range of values are present in five of the QSOs; (2) about two-thirds of the absorption lines remain unidentified, cannot be of Galactic origin, and are not associated with existing redshift systems; (3) many comparatively small absorption redshifts exist which, if they are due to intervening galaxies, must be produced by very large halos; and (4) in one QSO there is a possible redshift system containing five lines with an absorption redshift that is significantly greater than the emission redshift.

Roberts, D. H.↗

Impact of systematic redshift errors on the cross-correlation of the Lyman-α forest with quasars at small scales using DESI Early Data

The Dark Energy Spectroscopic Instrument (DESI) will measure millions of quasar spectra by the end of its 5 year survey. Quasar redshift errors impact the shape of the Lyman-α forest correlation functions, which can affect cosmological analyses and therefore cosmological interpretations. Here, using data from the DESI Early Data Release and the first two months of the main survey, we measure the systematic redshift error from an offset in the cross-correlation of the Lyman-α forest with quasars. We find evidence for a redshift dependent bias causing redshifts to be underestimated with increasing redshift, stemming from improper modeling of the Lyman-α optical depth in the templates used for redshift estimation. New templates were derived for the DESI Year 1 quasar sample at z > 1.6 and we found the redshift dependent bias, Δr ∥ , increased from -1.94 ± 0.15 h -1 Mpc to -0.08 ± 0.04 h -1 Mpc (-205 ± 15 km s -1 to -9.0 ± 4.0 km s -1 ). These new templates will be used to provide redshifts for the DESI Year 1 quasar sample.

Lyman alpha forest↗

The Swift Gamma-Ray Burst Host Galaxy Legacy Survey. I. Sample Selection and Redshift Distribution

We introduce the Swift Gamma-Ray Burst Host Galaxy Legacy Survey (SHOALS), a multi-observatory high redshift galaxy survey targeting the largest unbiased sample of long-duration gamma-ray burst (GRB) hosts yet assembled (119 in total). We describe the motivations of the survey and the development of our selection criteria, including an assessment of the impact of various observability metrics on the success rate of afterglow-based redshift measurement. We briefly outline our host galaxy observational program, consisting of deep Spitzer/IRAC imaging of every field supplemented by similarly deep, multicolor optical/near-IR photometry, plus spectroscopy of events without preexisting redshifts. Our optimized selection cuts combined with host galaxy follow-up have so far enabled redshift measurements for 110 targets (92%) and placed upper limits on all but one of the remainder. About 20% of GRBs in the sample are heavily dust obscured, and at most 2% originate from z > 5.5. Using this sample, we estimate the redshift-dependent GRB rate density, showing it to peak at z approx. 2.5 and fall by at least an order of magnitude toward low (z = 0) redshift, while declining more gradually toward high (z approx. 7) redshift. This behavior is consistent with a progenitor whose formation efficiency varies modestly over cosmic history. Our survey will permit the most detailed examination to date of the connection between the GRB host population and general star-forming galaxies, directly measure evolution in the host population over cosmic time and discern its causes, and provide new constraints on the fraction of cosmic star formation occurring in undetectable galaxies at all redshifts.

galaxies: evolution – galaxies: high-redshift â€↗

XXL-HSC: An updated catalogue of high-redshift ( z ≥ 3.5) X-ray AGN in the XMM-XXL northern field

X-rays offer a reliable method to identify active galactic nuclei (AGNs). However, in the high-redshift Universe, X-ray AGNs are poorly sampled due to their relatively low space density and the small areas covered by X-ray surveys. In addition to wide-area X-ray surveys, it is important to have deep optical data in order to locate the optical counterparts and determine their redshifts. Here, in this work, we built a high-redshift (z ≥ 3.5) X-ray-selected AGN sample in the XMM-XXL northern field using the most updated [0.5–2 keV] catalogue along with a plethora of new spectroscopic and multi-wavelength catalogues, including the deep optical Subaru Hyper Suprime-Cam (HSC) data, reaching magnitude limits i ~ 26 mag. We selected all the spectroscopically confirmed AGN and complement this sample with high-redshift candidates that are HSC g- and r-band dropouts. To confirm the dropouts, we derived their photometric redshifts using spectral energy distribution techniques. We obtained a sample of 54 high-z sources (28 with spec-z), the largest in this field so far (almost three times larger than in previous studies), and we estimated the possible contamination and completeness. We calculated the number counts (log N-log S) in different redshift bins and compared our results with previous studies and models. We provide the strongest high-redshift AGN constraints yet at bright fluxes (f 0.5 – 2 keV > 10 –15 erg s –1 cm –2 ). The samples of z ≥ 3.5, z ≥ 4, and z ≥ 5 are in agreement with an exponential decline model similar to that witnessed at optical wavelengths. Our work emphasises the importance of using wide-area X-ray surveys with deep optical data to uncover high-redshift AGNs.

79 ASTRONOMY AND ASTROPHYSICS↗

Correcting correlation functions for redshift-dependent interloper contamination

ABSTRACT The construction of catalogues of a particular type of galaxy can be complicated by interlopers contaminating the sample. In spectroscopic galaxy surveys this can be due to the misclassification of an emission line; for example in the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX) low-redshift [O ii] emitters may make up a few per cent of the observed Ly α emitter (LAE) sample. The presence of contaminants affects the measured correlation functions and power spectra. Previous attempts to deal with this using the cross-correlation function have assumed sources at a fixed redshift, or not modelled evolution within the adopted redshift bins. However, in spectroscopic surveys like HETDEX, where the contamination fraction is likely to be redshift dependent, the observed clustering of misclassified sources will appear to evolve strongly due to projection effects, even if their true clustering does not. We present a practical method for accounting for the presence of contaminants with redshift-dependent contamination fractions and projected clustering. We show using mock catalogues that our method, unlike existing approaches, yields unbiased clustering measurements from the upcoming HETDEX survey in scenarios with redshift-dependent contamination fractions within the redshift bins used. We show our method returns autocorrelation functions with systematic biases much smaller than the statistical noise for samples with at least as high as 7 per cent contamination. We also present and test a method for fitting for the redshift-dependent interloper fraction using the LAE–[O ii] galaxy cross-correlation function, which gives less biased results than assuming a single interloper fraction for the whole sample.

79 ASTRONOMY AND ASTROPHYSICS↗

No redshift evolution in the rest-frame ultraviolet emission line properties of quasars from z = 1.5 to z = 4.0

We analyse the rest-frame ultraviolet (UV) spectra of 2531 high-redshift (3.5 < z < 4.0) quasars from the Sloan Digital Sky Survey DR16Q catalogue. In combination with previous work, we study the redshift evolution of the rest-frame UV line properties across the entire redshift range, 1.5 < z < 4.0. We improve the systemic redshift estimates at z > 3.5 using a cross-correlation algorithm that employs high signal-to-noise template spectra spanning the full range in UV emission line properties. We then quantify the evolution of C iv and He ii emission line properties with redshift. The increase in C iv blueshifts with cosmological redshift can be fully explained by the higher luminosities of quasars observed at high redshifts. We recover broadly similar trends between the He ii equivalent width and C iv blueshift at both 1.5 < z < 2.65 and 3.5 < z < 4.0 suggesting that the blueshift depends systematically on the spectral energy density (SED) of the quasar and there is no evolution in the SED over the redshift range 1.5 < z < 4.0. C iv blueshifts are highest when L/L Edd ≥ 0.2 and M BH ≥ 10 9 M ⊙ for the entire 1.5 < z < 4.0 sample. We find that luminosity matching samples as a means to explore the evolution of their rest-frame UV emission line properties is only viable if the samples are also matched in the M BH –L/L Edd plane. Quasars at z ≥ 6 are on average less massive and have higher Eddington-scaled accretion rates than their luminosity-matched counterparts at 1.5 < z < 4.0, which could explain the observed evolution in their UV line properties.

79 ASTRONOMY AND ASTROPHYSICS↗

Random Forests as a Viable Method to Select and Discover High-redshift Quasars

We present a method of selecting quasars up to redshift ≈6 with random forests, a supervised machine-learning method, applied to Pan-STARRS1 and WISE data. We find that, thanks to the increasing set of known quasars, we can assemble a training set that enables supervised machine-learning algorithms to become a competitive alternative to other methods up to this redshift. We present a candidate set for the redshift range 4.8–6.3, which includes the region around z = 5.5 where selecting quasars is difficult due to their photometric similarity to red and brown dwarfs. We demonstrate that, under our survey restrictions, we can reach a high completeness (66% ± 7% below redshift 5.6/83{sub -9}{sup +6}% above redshift 5.6) while maintaining a high selection efficiency (78{sub -8}{sup +10}%/94{sub -8}{sup +5}%). Our selection efficiency is estimated via a novel method based on the different distributions of quasars and contaminants on the sky. The final catalog of 515 candidates includes 225 known quasars. We predict the candidate catalog to contain additional 148{sub -33}{sup +41} new quasars below redshift 5.6 and 45{sub -8}{sup +5} above, and we make the catalog publicly available. Spectroscopic follow-up observations of 37 candidates led us to discover 20 new high redshift quasars (18 at 4.6 ≤ z ≤ 5.5, 2 z ~ 5.7). These observations are consistent with our predictions on efficiency. We argue that random forests can lead to higher completeness because our candidate set contains a number of objects that would be rejected by common color cuts, including one of the newly discovered redshift 5.7 quasars.

79 ASTRONOMY AND ASTROPHYSICS↗

Redshift Evolution of the Feedback–Cooling Equilibrium in the Core of 48 SPT Galaxy Clusters: A Joint Chandra–SPT–ATCA Analysis

We analyze the cooling and feedback properties of 48 galaxy clusters at redshifts 0.4 < z < 1.3 selected from the South Pole Telescope (SPT) catalogs to evolve like the progenitors of massive and well-studied systems at z ~ 0. We estimate the radio power at the brightest cluster galaxy (BCG) location of each cluster from an analysis of Australia Telescope Compact Array data. Assuming that the scaling relation between the radio power and active galactic nucleus (AGN) cavity power P cav observed at low redshift does not evolve with redshift, we use these measurements in order to estimate the expected AGN cavity power in the core of each system. We estimate the X-ray luminosity within the cooling radius L cool of each cluster from a joint analysis of the available Chandra X-ray and SPT Sunyaev–Zel'dovich (SZ) data. This allows us to characterize the redshift evolution of the P cav /L cool ratio. When combined with low-redshift results, these constraints enable investigations of the properties of the feedback–cooling cycle across 9 Gyr of cluster growth. We model the redshift evolution of this ratio measured for cool-core clusters by a log-normal distribution Log-N (α + βz, σ 2 ) and constrain the slope of the mean evolution to β = -0.05 ± 0.47. This analysis improves the constraints on the slope of this relation by a factor of two. We find no evidence of redshift evolution of the feedback–cooling equilibrium in these clusters, which suggests that the onset of radio-mode feedback took place at an early stage of cluster formation. High values of P cav /L cool are found at the BCG location of noncool-core clusters, which might suggest that the timescales of the AGN feedback cycle and the cool core–noncool core transition are different. This work demonstrates that the joint analysis of radio, SZ, and X-ray data solidifies the investigation of AGN feedback at high redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

On the Anticorrelation between Duration and Redshift in Gamma-Ray Bursts

Abstract For gamma-ray bursts (GRBs) with durations greater than two seconds (so-called long GRBs), the intrinsic prompt gamma-ray emission appears, on average, to last longer for bursts at lower redshifts. We explore the nature of this duration–redshift anticorrelation, describing systems and conditions in which this cosmological evolution could arise. In particular, we explore its dependence on the metallicity of a massive star progenitor, because we can securely count on the average stellar metallicity to increase with decreasing redshift. Although stars with higher metallicity/lower redshift lose mass and angular momentum through line-driven winds, in some cases these stars are able to form more extended accretion disks when they collapse, potentially leading to longer-duration GRBs. We also examine how this duration–redshift trend may show up in interacting binary models composed of a massive star and compact object companion, recently suggested to be the progenitors of radio-bright GRBs. Under certain conditions, mass loss and equation-of-state effects from massive stars with higher metallicity and lower redshift can decrease the binary separation. This can then lead to spin-up of the massive star and allow for a longer-duration GRB upon the massive star’s collapse. Finally, the duration–redshift trend may also be supported by a relatively larger population of small-separation binaries born in situ at low redshift.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian Component Separation for DESI LAE Automated Spectroscopic Redshifts and Photometric Targeting

Lyα emitters (LAEs) are valuable high-redshift cosmological probes traditionally identified using specialized narrowband photometric surveys. In ground-based spectroscopy, it can be difficult to distinguish the sharp LAE peak from residual sky emission lines using automated methods, leading to misclassified redshifts. We present a Bayesian spectral component separation technique to automatically determine spectroscopic redshifts for LAEs while marginalizing over sky residuals. We use visually inspected spectra of LAEs obtained using the Dark Energy Spectroscopic Instrument (DESI) to create a data-driven prior and can determine redshift by jointly inferring sky residual, LAE, and residual components for each individual spectrum. We demonstrate this method on 881 spectroscopically observed z = 2–4 DESI LAE candidate spectra and determine their redshifts with >90% accuracy when validated against visually inspected redshifts. Using the Δχ$^{2}$ value from our pipeline as a proxy for detection confidence, we then explore potential survey design choices and implications for targeting LAEs with medium-band photometry. This method allows for scalability and accuracy in determining redshifts from DESI spectra, and the results provide recommendations for LAE targeting in anticipation of future high-redshift spectroscopic surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Absorption in X-ray spectra of high-redshift quasars

We present evidence that X-ray absorption is common in high-redshift quasars. We have studied six high-redshift (z approximately 3) quasars with the ROSAT Position Sensitive Proportional Counter (PSPC) of which four are in directions of low Galactic N(sub H). Three out of these four show excess absorption, while only three in approximately 50 z approximately less than 0.4 quasars do, indicating that such absorption must be common, but not ubiquitous, at high redshifts, and that the absorbers must lie at z greater than 0.4. The six quasars were: S5 0014+81, Q0420-388, PKS 0438-436, S4 0636+680. PKS 2000-330, PKS 2126-158, which have redshifts between 2.85 and 3.78. PKS 0438-436 and PKS 2126-158 show evidence for absorption above the local Galactic value at better than 99.999% confidence level. If the absorber is at the redshift of the quasar, then values of N(sub H) = (0.86(+0.49, -0.28)) x 10(exp 22) atoms/sq cm for PKS 0438-436, and N(sub H) = (1.45(+1.20, -0.64)) x 10(exp 22) atoms/ sq cm for PKS 2126-158, are implied, assuming solar abundances. The spectrum of S4 0636+680 also suggests the presence of a similarly large absorption column density at the 98% confidence level. This absorption reverses the trend for the most luminous active galactic nuclei (AGN) to have the least X-ray absorption, so a new mechanism is likely to be responsible. Intervening absorption due to damped Lyman(alpha) systems is a plausible cause. We also suggest, as an intrinsic model, that intracluster material, e.g., a cooling flow, around the quasar could account for both the X-ray spectrum and other properties of these quasars. All the quasars are radio-loud and three are gigahertz peaked (two of the three showing absorption). No excess absorption above the Galactic value is seen toward Q0420-388. This quasar has two damped Lyman(alpha) systems at z = 3.08. The limit on the X-ray column density implies a low ionization fraction, N(H I)/N(H) approximately greater than 4 x 10(exp -3) (3 (sigma)), for solar abundances, for these systems, and can set a weak limit on the size of the absorber. In the emitted frame these PSPC spectra cover the band approximately 0.5-10 keV, which has been well observed for low-redshift quasars and AGN. Comparison of high and low-redshift spectra in this emitted band shows no change of mean spectral index greater than Delta alpha(sub E) greater than 0.3 (99% confidence) with either redshift or luminosity, for radio-loud quasars.

Elvis, Martin↗