arXiv subjects

S. Desai

Publications and source records attributed to S. Desai.

At least 109 records · Page 6Linked to original sources

arXiv2023

Detection of the significant impact of source clustering on higher-order statistics with DES Year 3 weak gravitational lensing data

We demonstrate and measure the impact of source galaxy clustering on higher-order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show this effect can exceed measurement uncertainties for common higher-order statistics for certain analysis choices. Source clustering effects are larger at small scales and for statistics applied to combinations of low and high redshift samples, and diminish at high redshift. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey Year 3 data we construct null tests for the source-clustering-free case, finding a $p$-value of $p=4\times10^{-3}$ (2.6 $σ$) using third-order map moments and $p=3\times10^{-11}$ (6.5 $σ$) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either be included in the model or minimized through \textit{ad-hoc} procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses (using map moments and peaks) were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher-order gravitational lensing statistics, e.g. higher-order N-point functions, wavelet-moment observables (including phase harmonics and scattering transforms), and deep learning or field level summary statistics of weak lensing maps. We provide recipes both to minimise the impact of source clustering and to incorporate source clustering effects into forward-modelled mock data.

astro-ph.CO↗

arXiv2023

The second data release from the European Pulsar Timing Array II. Customised pulsar noise models for spatially correlated gravitational waves

The nanohertz gravitational wave background (GWB) is expected to be an aggregate signal of an ensemble of gravitational waves emitted predominantly by a large population of coalescing supermassive black hole binaries in the centres of merging galaxies. Pulsar timing arrays, ensembles of extremely stable pulsars, are the most precise experiments capable of detecting this background. However, the subtle imprints that the GWB induces on pulsar timing data are obscured by many sources of noise. These must be carefully characterized to increase the sensitivity to the GWB. In this paper, we present a novel technique to estimate the optimal number of frequency coefficients for modelling achromatic and chromatic noise and perform model selection. We also incorporate a new model to fit for scattering variations in the pulsar timing package temponest and created realistic simulations of the European Pulsar Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise modelling algorithms. We present an in-depth analysis of the noise properties of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the EPTA and investigate the effect of incorporating low-frequency data from the Indian PTA collaboration. We use enterprise and temponest packages to compare noise models with those reported with the EPTA DR1. We find that, while in some pulsars we can successfully disentangle chromatic from achromatic noise owing to the wider frequency coverage in DR2, in others the noise models evolve in a more complicated way. We also find evidence of long-term scattering variations in PSR J1600$-$3053. Through our simulations, we identify intrinsic biases in our current noise analysis techniques and discuss their effect on GWB searches. The results presented here directly help improve sensitivity to the GWB and are already being used as part of global PTA efforts.

astro-ph.HE↗

arXiv2023

The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals

We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of $4\%$. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of $60$ and a false alarm probability of about $0.1\%$ ($\gtrsim 3σ$ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The inferred spectrum from the latest EPTA data from new generation observing systems is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of ($2.5\pm0.7)\times10^{-15}$ at a reference frequency of $1\,{\rm yr}^{-1}$. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.

astro-ph.HE↗

arXiv2023

A measurement of the mean central optical depth of galaxy clusters via the pairwise kinematic Sunyaev-Zel'dovich effect with SPT-3G and DES

We infer the mean optical depth of a sample of optically-selected galaxy clusters from the Dark Energy Survey (DES) via the pairwise kinematic Sunyaev-Zel'dovich (kSZ) effect. The pairwise kSZ signal between pairs of clusters drawn from the DES Year-3 cluster catalog is detected at $4.1 σ$ in cosmic microwave background (CMB) temperature maps from two years of observations with the SPT-3G camera on the South Pole Telescope. After cuts, there are 24,580 clusters in the $\sim 1,400$ deg$^2$ of the southern sky observed by both experiments. We infer the mean optical depth of the cluster sample with two techniques. The optical depth inferred from the pairwise kSZ signal is $\barτ_e = (2.97 \pm 0.73) \times 10^{-3}$, while that inferred from the thermal SZ signal is $\barτ_e = (2.51 \pm 0.55^{\text{stat}} \pm 0.15^{\rm syst}) \times 10^{-3}$. The two measures agree at $0.6 σ$. We perform a suite of systematic checks to test the robustness of the analysis.

astro-ph.CO↗

arXiv2023

Cool Cores in Clusters of Galaxies in the Dark Energy Survey

We search for the presence of cool cores in optically-selected galaxy clusters from the Dark Energy Survey (DES) and investigate their prevalence as a function of redshift and cluster richness. Clusters were selected from the redMaPPer analysis of three years of DES observations that have archival Chandra X-ray observations, giving a sample of 99 clusters with a redshift range of $0.11 < z < 0.87$ and a richness range of $25 < λ< 207$. Using the X-ray data, the core temperature was compared to the outer temperature to identify clusters where the core temperature is a factor of 0.7 or less than the outer temperature. We found a cool core fraction of approximately 20% with no significant trend in the cool core fraction with either redshift or richness.

astro-ph.CO↗

arXiv2023

The XMM Cluster Survey: Exploring scaling relations and completeness of the Dark Energy Survey Year 3 redMaPPer cluster catalogue

We cross-match and compare characteristics of galaxy clusters identified in observations from two sky surveys using two completely different techniques. One sample is optically selected from the analysis of three years of Dark Energy Survey observations using the redMaPPer cluster detection algorithm. The second is X-ray selected from XMM observations analysed by the XMM Cluster Survey. The samples comprise a total area of 57.4 deg$^2$, bounded by the area of 4 contiguous XMM survey regions that overlap the DES footprint. We find that the X-ray selected sample is fully matched with entries in the redMaPPer catalogue, above $λ>$20 and within 0.1$< z <$0.9. Conversely, only 38\% of the redMaPPer catalogue is matched to an X-ray extended source. Next, using 120 optically clusters and 184 X-ray selected clusters, we investigate the form of the X-ray luminosity-temperature ($L_{X}-T_{X}$), luminosity-richness ($L_{X}-λ$) and temperature-richness ($T_{X}-λ$) scaling relations. We find that the fitted forms of the $L_{X}-T_{X}$ relations are consistent between the two selection methods and also with other studies in the literature. However, we find tentative evidence for a steepening of the slope of the relation for low richness systems in the X-ray selected sample. When considering the scaling of richness with X-ray properties, we again find consistency in the relations (i.e., $L_{X}-λ$ and $T_{X}-λ$) between the optical and X-ray selected samples. This is contrary to previous similar works that find a significant increase in the scatter of the luminosity scaling relation for X-ray selected samples compared to optically selected samples.

astro-ph.CO↗

arXiv2023

Photometry of outer Solar System objects from the Dark Energy Survey I: photometric methods, light curve distributions and trans-Neptunian binaries

We report the methods of and initial scientific inferences from the extraction of precision photometric information for the $>800$ trans-Neptunian objects (TNOs) discovered in the images of the Dark Energy Survey (DES). Scene-modelling photometry is used to obtain shot-noise-limited flux measures for each exposure of each TNO, with background sources subtracted. Comparison of double-source fits to the pixel data with single-source fits are used to identify and characterize two binary TNO systems. A Markov Chain Monte Carlo method samples the joint likelihood of the intrinsic colors of each source as well as the amplitude of its flux variation, given the time series of multiband flux measurements and their uncertainties. A catalog of these colors and light curve amplitudes $A$ is included with this publication. We show how to assign a likelihood to the distribution $q(A)$ of light curve amplitudes in any subpopulation. Using this method, we find decisive evidence (i.e. evidence ratio $<0.01$) that cold classical (CC) TNOs with absolute magnitude $6<H_r<8.2$ are more variable than the hot classical (HC) population of the same $H_r$, reinforcing theories that the former form in situ and the latter arise from a different physical population. Resonant and scattering TNOs in this $H_r$ range have variability consistent with either the HC's or CC's. DES TNOs with $H_r<6$ are seen to be decisively less variable than higher-$H_r$ members of any dynamical group, as expected. More surprising is that detached TNOs are decisively less variable than scattering TNOs, which requires them to have distinct source regions or some subsequent differential processing.

astro-ph.EP↗

arXiv2023

Non-local contribution from small scales in galaxy-galaxy lensing: Comparison of mitigation schemes

Recent cosmological analyses with large-scale structure and weak lensing measurements, usually referred to as 3$\times$2pt, had to discard a lot of signal-to-noise from small scales due to our inability to accurately model non-linearities and baryonic effects. Galaxy-galaxy lensing, or the position-shear correlation between lens and source galaxies, is one of the three two-point correlation functions that are included in such analyses, usually estimated with the mean tangential shear. However, tangential shear measurements at a given angular scale $θ$ or physical scale $R$ carry information from all scales below that, forcing the scale cuts applied in real data to be significantly larger than the scale at which theoretical uncertainties become problematic. Recently there have been a few independent efforts that aim to mitigate the non-locality of the galaxy-galaxy lensing signal. Here we perform a comparison of the different methods, including the Y-transformation, the Point-Mass marginalization methodology and the Annular Differential Surface Density statistic. We do the comparison at the cosmological constraints level in a combined galaxy clustering and galaxy-galaxy lensing analysis. We find that all the estimators yield equivalent cosmological results assuming a simulated Rubin Observatory Legacy Survey of Space and Time (LSST) Year 1 like setup and also when applied to DES Y3 data. With the LSST Y1 setup, we find that the mitigation schemes yield $\sim$1.3 times more constraining $S_8$ results than applying larger scale cuts without using any mitigation scheme.

astro-ph.CO↗

arXiv2023

The Dark Energy Survey Supernova Program: Corrections on photometry due to wavelength-dependent atmospheric effects

Wavelength-dependent atmospheric effects impact photometric supernova flux measurements for ground-based observations. We present corrections on supernova flux measurements from the Dark Energy Survey Supernova Program's 5YR sample (DES-SN5YR) for differential chromatic refraction (DCR) and wavelength-dependent seeing, and we show their impact on the cosmological parameters $w$ and $Ω_m$. We use $g-i$ colors of Type Ia supernovae (SNe Ia) to quantify astrometric offsets caused by DCR and simulate point spread functions (PSFs) using the GalSIM package to predict the shapes of the PSFs with DCR and wavelength-dependent seeing. We calculate the magnitude corrections and apply them to the magnitudes computed by the DES-SN5YR photometric pipeline. We find that for the DES-SN5YR analysis, not accounting for the astrometric offsets and changes in the PSF shape cause an average bias of $+0.2$ mmag and $-0.3$ mmag respectively, with standard deviations of $0.7$ mmag and $2.7$ mmag across all DES observing bands (\textit{griz}) throughout all redshifts. When the DCR and seeing effects are not accounted for, we find that $w$ and $Ω_m$ are lower by less than $0.004\pm0.02$ and $0.001\pm0.01$ respectively, with $0.02$ and $0.01$ being the $1σ$ statistical uncertainties. Although we find that these biases do not limit the constraints of the DES-SN5YR sample, future surveys with much higher statistics, lower systematics, and especially those that observe in the $u$ band will require these corrections as wavelength-dependent atmospheric effects are larger at shorter wavelengths. We also discuss limitations of our method and how they can be better accounted for in future surveys.

astro-ph.CO↗

arXiv2023

Ultracool dwarfs candidates based on six years of the Dark Energy Survey data

We present a sample of 19,583 ultracool dwarf candidates brighter than z $\leq 23$ selected from the Dark Energy Survey DR2 coadd data matched to VHS DR6, VIKING DR5 and AllWISE covering $\sim$ 4,800 $deg^2$. The ultracool candidates were first pre-selected based on their (i-z), (z-Y), and (Y-J) colours. They were further classified using a method that compares their optical, near-infrared and mid-infrared colours against templates of M, L and T dwarfs. 14,099 objects are presented as new L and T candidates and the remaining objects are from the literature, including 5,342 candidates from our previous work. Using this new and deeper sample of ultracool dwarf candidates we also present: 20 new candidate members to nearby young moving groups (YMG) and associations, variable candidate sources and four new wide binary systems composed of two ultracool dwarfs. Finally, we also show the spectra of twelve new ultracool dwarfs discovered by our group and presented here for the first time. These spectroscopically confirmed objects are a sanity check of our selection of ultracool dwarfs and photometric classification method.

astro-ph.SR↗

arXiv2023

Synchronous rotation in the (136199) Eris-Dysnomia system

We combine photometry of Eris from a 6-month campaign on the Palomar 60-inch telescope in 2015, a 1-month Hubble Space Telescope WFC3 campaign in 2018, and Dark Energy Survey data spanning 2013--2018 to determine a light curve of definitive period $15.771\pm 0.008$~days (1-$σ$ formal uncertainties), with nearly sinusoidal shape and peak-to-peak flux variation of 3\%. This is consistent at part-per-thousand precision with the $P=15.78590\pm0.00005$~day period of Dysnomia's orbit around Eris, strengthening the recent detection of synchronous rotation of Eris by Szakats et al (2022) with independent data. Photometry from Gaia is consistent with the same light curve. We detect a slope of $0.05\pm0.01$~mag per degree of Eris' brightness with respect to illumination phase, intermediate between Pluto's and Charon's values. Variations of $0.3$~mag are detected in Dysnomia's brightness, plausibly consistent with a double-peaked light curve at the synchronous period. The synchronous rotation of Eris is consistent with simple tidal models initiated with a giant-impact origin of the binary, but is difficult to reconcile with gravitational capture of Dysnomia by Eris.

astro-ph.EP↗

arXiv2023

Core-collapse Supernovae in the Dark Energy Survey: Luminosity Functions and Host Galaxy Demographics

We present the luminosity functions and host galaxy properties of the Dark Energy Survey (DES) core-collapse supernova (CCSN) sample, consisting of 69 Type II and 50 Type Ibc spectroscopically and photometrically-confirmed supernovae over a redshift range $0.045<z<0.25$. We fit the observed DES $griz$ CCSN light-curves and K-correct to produce rest-frame $R$-band light curves. We compare the sample with lower-redshift CCSN samples from Zwicky Transient Facility (ZTF) and Lick Observatory Supernova Search (LOSS). Comparing luminosity functions, the DES and ZTF samples of SNe II are brighter than that of LOSS with significances of 3.0$σ$ and 2.5$σ$ respectively. While this difference could be caused by redshift evolution in the luminosity function, simpler explanations such as differing levels of host extinction remain a possibility. We find that the host galaxies of SNe II in DES are on average bluer than in ZTF, despite having consistent stellar mass distributions. We consider a number of possibilities to explain this -- including galaxy evolution with redshift, selection biases in either the DES or ZTF samples, and systematic differences due to the different photometric bands available -- but find that none can easily reconcile the differences in host colour between the two samples and thus its cause remains uncertain.

astro-ph.HE↗

arXiv2023

Concerning Colour: The Effect of Environment on Type Ia Supernova Colour in the Dark Energy Survey

Recent analyses have found intriguing correlations between the colour ($c$) of type Ia supernovae (SNe Ia) and the size of their 'mass-step', the relationship between SN Ia host galaxy stellar mass ($M_\mathrm{stellar}$) and SN Ia Hubble residual, and suggest that the cause of this relationship is dust. Using 675 photometrically-classified SNe Ia from the Dark Energy Survey 5-year sample, we study the differences in Hubble residual for a variety of global host galaxy and local environmental properties for SN Ia subsamples split by their colour. We find a $3σ$ difference in the mass-step when comparing blue ($c<0$) and red ($c>0$) SNe. We observe the lowest r.m.s. scatter ($\sim0.14$ mag) in the Hubble residual for blue SNe in low mass/blue environments, suggesting that this is the most homogeneous sample for cosmological analyses. By fitting for $c$-dependent relationships between Hubble residuals and $M_\mathrm{stellar}$, approximating existing dust models, we remove the mass-step from the data and find tentative $\sim 2σ$ residual steps in rest-frame galaxy $U-R$ colour. This indicates that dust modelling based on $M_\mathrm{stellar}$ may not fully explain the remaining dispersion in SN Ia luminosity. Instead, accounting for a $c$-dependent relationship between Hubble residuals and global $U-R$, results in $\leq1σ$ residual steps in $M_\mathrm{stellar}$ and local $U-R$, suggesting that $U-R$ provides different information about the environment of SNe Ia compared to $M_\mathrm{stellar}$, and motivating the inclusion of galaxy $U-R$ colour in SN Ia distance bias correction.

astro-ph.CO↗

arXiv2023

OzDES Reverberation Mapping Program: H$β$ lags from the 6-year survey

Reverberation mapping measurements have been used to constrain the relationship between the size of the broad-line region and luminosity of active galactic nuclei (AGN). This $R-L$ relation is used to estimate single-epoch virial black hole masses, and has been proposed for use to standardise AGN to determine cosmological distances. We present reverberation measurements made with H$β$ from the six-year Australian Dark Energy Survey (OzDES) Reverberation Mapping Program. We successfully recover reverberation lags for eight AGN at $0.12<z< 0.71$, probing higher redshifts than the bulk of H$β$ measurements made to date. Our fit to the $R-L$ relation has a slope of $α=0.41\pm0.03$ and an intrinsic scatter of $σ=0.23\pm0.02$ dex. The results from our multi-object spectroscopic survey are consistent with previous measurements made by dedicated source-by-source campaigns, and with the observed dependence on accretion rate. Future surveys, including LSST, TiDES and SDSS-V, which will be revisiting some of our observed fields, will be able to build on the results of our first-generation multi-object reverberation mapping survey.

astro-ph.GA↗

arXiv2023

Mapping Variations of Redshift Distributions with Probability Integral Transforms

We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.

astro-ph.CO↗

arXiv2022

The Dark Energy Survey Year 3 and eBOSS: constraining galaxy intrinsic alignments across luminosity and colour space

We present direct constraints on galaxy intrinsic alignments using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift $z\sim0.2-1.0$, luminous red galaxies (LRGs) from eBOSS at $z\sim0.8$, and also a SDSS-III BOSS CMASS sample at $z\sim0.5$. We measure two point intrinsic alignment correlations, which we fit using a model that includes lensing, magnification and photometric redshift error. Fitting on scales $6<r_{\rm p} < 70$ Mpc$/h$, we make a detection of intrinsic alignments in each sample, at $5σ-22σ$ (assuming a simple one parameter model for IAs). Using these red samples, we measure the IA-luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim2-18\%$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of Emission Line Galaxies (ELGs) from eBOSS at $z\sim 0.8$. We report a null detection, constraining the IA amplitude (assuming the nonlinear alignment model) to be $A_1=0.07^{+0.32}_{-0.42}$ ($|A_1|<0.78$ at $95\%$ CL).

astro-ph.CO↗

arXiv2022

Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing using the MagLim lens sample

Two of the most sensitive probes of the large scale structure of the universe are the clustering of galaxies and the tangential shear of background galaxy shapes produced by those foreground galaxies, so-called galaxy-galaxy lensing. Combining the measurements of these two two-point functions leads to cosmological constraints that are independent of the galaxy bias factor. The optimal choice of foreground, or lens, galaxies is governed by the joint, but conflicting requirements to obtain accurate redshift information and large statistics. We present cosmological results from the full 5000 sq. deg. of the Dark Energy Survey first three years of observations (Y3) combining those two-point functions, using for the first time a magnitude-limited lens sample (MagLim) of 11 million galaxies especially selected to optimize such combination, and 100 million background shapes. We consider two cosmological models, flat $Λ$CDM and $w$CDM. In $Λ$CDM we obtain for the matter density $Ω_m = 0.320^{+0.041}_{-0.034}$ and for the clustering amplitude $S_8 = 0.778^{+0.037}_{-0.031}$, at 68% C.L. The latter is only 1$σ$ smaller than the prediction in this model informed by measurements of the cosmic microwave background by the Planck satellite. In $w$CDM we find $Ω_m = 0.32^{+0.044}_{-0.046}$, $S_8=0.777^{+0.049}_{-0.051}$, and dark energy equation of state $w=-1.031^{+0.218}_{-0.379}$. We find that including smaller scales while marginalizing over non-linear galaxy bias improves the constraining power in the $Ω_m-S_8$ plane by $31$% and in the $Ω_m-w$ plane by $41$% while yielding consistent cosmological parameters from those in the linear bias case. These results are combined with those from cosmic shear in a companion paper to present full DES-Y3 constraints from the three two-point functions (3x2pt).

astro-ph.CO↗

arXiv2022

Dark Energy Survey Year 3 Results: Measurement of the Baryon Acoustic Oscillations with Three-dimensional Clustering

The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, $ξ_{\rm p}$ to measure the Baryonic Acoustic Oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range $ 0.6 < z_{\rm p } < 1.1 $ over a footprint of $4108 \, \mathrm{deg}^2 $. Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-$z$ approximation. To increase the signal-to-noise of the measurements, a Gaussian stacking window function is adopted in place of the commonly used top-hat. Using the full sample, $ D_{\rm M}(z_{\rm eff} ) / r_{\rm s} $, the ratio between the comoving angular diameter distance and the sound horizon, is constrained to be $ 19.00 \pm 0.67 $ (top-hat) and $ 19.15 \pm 0.58 $ (Gaussian) at $z_{\rm eff} = 0.835$. The constraint is weaker than the angular correlation $w$ constraint ($18.84 \pm 0.50$) because the BAO signals are heterogeneous across redshift. When a homogeneous BAO-signal sub-sample in the range $ 0.7 < z_{\rm p } < 1.0 $ ($z_{\rm eff} = 0.845$) is considered, $ξ_{\rm p} $ yields $ 19.80 \pm 0.67 $ (top-hat) and $ 19.84 \pm 0.53 $ (Gaussian). The latter is mildly stronger than the $w$ constraint ($19.86 \pm 0.55 $). We find that the $ξ_{\rm p} $ results are more sensitive to photo-$z$ errors than $w$ because $ξ_{\rm p}$ keeps the three-dimensional clustering information causing it to be more prone to photo-$z$ noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. $ξ_{\rm p}$ and the angular statistics such as $w$ have their own pros and cons, and they serve an important crosscheck with each other.

astro-ph.CO↗