Context. The main element of the observing program of the Spectrum-Roentgen-Gamma orbital observatory is a four-year all-sky survey, in the course of which the entire sky will be scanned eight times. Aims. We analyze the statistical properties of active galactic nuclei (AGN) and quasars/quasi-stellar objects (QSOs ) that are expected to be detected in the course of the eROSITA all-sky survey (eRASS). Methods. According to the currently planned survey strategy and based on the parameters of the Galactic and extragalactic X-ray background as well as on the results of the recent calculations of the eROSITA instrumental background, we computed a sensitivity map of the eRASS. Using the best available redshift-dependent AGN X-ray luminosity function (XLF), we computed various characteristics of the eRASS AGN sample, such as their luminosity-and redshift distributions, and the brightness distributions of their optical counterparts. Results. After four years of the survey, a sky-average sensitivity of about 1 × 10 −14 erg s −1 cm −2 will be achieved in the 0.5−2.0 keV band. With this sensitivity, eROSITA is expected to detect about 3 million AGN on the extragalactic sky (|b| > 10 • ). The median redshift of the eRASS AGN will be z ≈ 1 with approximately 40% of the objects in the z = 1−2 redshift range. About 10 4 −10 5 AGN are predicted beyond redshift z = 3 and about 2000−30 000 AGN beyond redshift z = 4, the exact numbers depend on the poorly known behavior of the AGN XLF in the high-redshift and high-luminosity regimes. Of the detected AGN, the brightest 10% will be detected with more than ≈38 counts per point-spread-function (half-energy width), while the faintest 10% will have fewer than ≈9 counts. The optical counterparts of approximately 95% of the AGN will be brighter than I AB = 22.5 mag. The planned scanning strategy will allow one to search for transient events on a timescale of half a year and a few hours with a 0.5−2.0 keV sensitivity of ≈2 × 10 −14 to ≈2 × 10 −13 erg s −1 cm −2 , respectively.

We report the first statistical detection of X-ray emission from cosmic web filaments in ROSAT data. We selected 15 165 filaments at 0.2 <  z <  0.6 ranging from 30 Mpc to 100 Mpc in length, identified in the Sloan Digital Sky Survey survey. We stacked the X-ray count-rate maps from ROSAT around the filaments, excluding resolved galaxy groups and clusters above the mass of ∼3 × 1013 M⊙ as well as the detected X-ray point sources from the ROSAT, Chandra, and XMM-Newton observations. The stacked signal results in the detection of the X-ray emission from the cosmic filaments at a significance of 4.2σ in the energy band of 0.56−1.21 keV. The signal is interpreted, assuming the Astrophysical Plasma Emission Code model, as an emission from the hot gas in the filament-core regions with an average gas temperature of 0.9−0.6+1.0 keV and a gas overdensity of δ ∼ 30 at the center of the filaments. Furthermore, we show that stacking the SRG/eROSITA data for ∼2000 filaments only would lead to a ≳5σ detection of their X-ray signal, even with an average gas temperature as low as ∼0.3 keV.