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The Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) is expected to obtain observations of over ten million quasars. The survey’s exceptional cadence and sensitivity will enable a significant fraction of these objects to be monitored in theugrizybands, spanning observed wavelengths of approximately 0.3 − 1.0 μm. The unprecedented number of sources makes spectroscopic follow-up for the vast majority of them unfeasible in the near future, so most studies will have to rely on photometric redshift estimates which are traditionally much less reliable for Active Galactic Nuclei (AGNs) than for inactive galaxies. This work presents a novel methodology to constrain the photometric redshift of AGNs that leverages the effects of cosmological time dilation, and of the luminosity and wavelength dependence of AGN variability. Specifically, we assume that the variability can be modeled as a damped random walk (DRW) process, and we adopted a parametric model to characterize the DRW timescale (τ) and asymptotic amplitude of the variability (SF_∞) based on the redshift, the rest-frame wavelength, and the AGN luminosity. We constructed variability-based photometric redshift (photo-z) priors by modeling the observed variability using the expected DRW parameters at a given redshift. These variability-based photo-z(VAR-PZ) priors were then combined with traditional spectral energy distribution (SED) fitting to improve the redshift estimates from SED fitting. Validation was performed using observational data from the Sloan Digital Sky Survey (SDSS), demonstrating significant reduction in catastrophic outliers by more than 10% in comparison with SED fitting techniques and improvements in redshift precision. The simulated light curves with both SDSS and LSST-like cadences and baselines confirm thatVAR-PZwill be able to constrain the photometric redshifts of SDSS-like AGNs by bringing the outlier fractions down to below 15% from 32% (SED alone) at the end of the survey. 

Context. In November 2019, eROSITA on board of the Spektrum-Roentgen-Gamma (SRG) observatory started to map the entire sky in X-rays. After the four-year survey program, it will reach a flux limit that is about 25 times deeper than ROSAT. During the SRG performance verification phase, eROSITA observed a contiguous 140 deg 2 area of the sky down to the final depth of the eROSITA all-sky survey (eROSITA Final Equatorial-Depth Survey; eFEDS), with the goal of obtaining a census of the X-ray emitting populations (stars, compact objects, galaxies, clusters of galaxies, and active galactic nuclei) that will be discovered over the entire sky. Aims. This paper presents the identification of the counterparts to the point sources detected in eFEDS in the main and hard samples and their multi-wavelength properties, including redshift. Methods. To identifyy the counterparts, we combined the results from two independent methods ( NWAY and ASTROMATCH ), trained on the multi-wavelength properties of a sample of 23k XMM-Newton sources detected in the DESI Legacy Imaging Survey DR8. Then spectroscopic redshifts and photometry from ancillary surveys were collated to compute photometric redshifts. Results. Of the eFEDS sources, 24 774 of 27 369 have reliable counterparts (90.5%) in the main sample and 231 of 246 sourcess (93.9%) have counterparts in the hard sample, including 2514 (3) sources for which a second counterpart is equally likely. By means of reliable spectra, Gaia parallaxes, and/or multi-wavelength properties, we have classified the reliable counterparts in both samples into Galactic (2695) and extragalactic sources (22 079). For about 340 of the extragalactic sources, we cannot rule out the possibility that they are unresolved clusters or belong to clusters. Inspection of the distributions of the X-ray sources in various optical/IR colour-magnitude spaces reveal a rich variety of diverse classes of objects. The photometric redshifts are most reliable within the KiDS/VIKING area, where deep near-infrared data are also available. Conclusions. This paper accompanies the eROSITA early data release of all the observations performed during the performance and verification phase. Together with the catalogues of primary and secondary counterparts to the main and hard samples of the eFEDS survey, this paper releases their multi-wavelength properties and redshifts. 

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown.Euclidis a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg²of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.