Context. The circumgalactic medium (CGM) provides the material needed for galaxy formation and influences galaxy evolution. The hot (T > 106K) CGM is poorly detected around galaxies with stellar masses (M*) lower than 3 × 1011 M⊙ due to the low surface brightness. Aims. We aim to detect the X-ray emission from the hot CGM around Milky Way-mass (MW-mass, log(M*/M⊙) = 10.5 − 11.0) and M31-mass (log(M*/M⊙) = 11.0 − 11.25) galaxies, in addition to measuring the X-ray surface brightness profile of the hot CGM. Methods. We applied a stacking technique to gain enough statistics to detect the hot CGM. We used the X-ray data from the first four SRG/eROSITA All-Sky Surveys (eRASS:4). We discussed how the satellite galaxies could bias the stacking and the method we used to carefully build the central galaxy samples. Based on the SDSS spectroscopic survey and halo-based group finder algorithm, we selected central galaxies with spectroscopic redshifts of zspec < 0.2 and stellar masses of 10.0 < log(M*/M⊙) < 11.5 (85 222 galaxies) – or halo masses of 11.5 < log(M200m/M⊙) < 14.0 (125,512 galaxies). By stacking the X-ray emission around galaxies, we obtained the mean X-ray surface brightness profiles. We masked the detected X-ray point sources and carefully modeled the X-ray emission from the unresolved active galactic nuclei (AGN) and X-ray binaries (XRB) to obtain the X-ray emission from the hot CGM. Results. We measured the X-ray surface brightness profiles for central galaxies of log(M*/M⊙) > 10.0 or log(M200m/M⊙) > 11.5. We detected the X-ray emission around MW-mass and more massive central galaxies extending up to the virial radius (Rvir). The signal-to-noise ratio (S/N) of the extended emission around MW-mass (M31-mass) galaxy is about 3.1σ (4.7σ) within Rvir. We used a β model to describe the X-ray surface brightness profile of the hot CGM (SX, CGM). We obtained a central surface brightness of log(SX,0[erg s−1 kpc−2]) = 36.7−0.4+1.4 (37.1−0.4+1.5) and β = 0.43−0.06+0.10 (0.37−0.02+0.04) for MW-mass (M31-mass) galaxies. For galaxies with log(M200m/M⊙) > 12.5, the extended X-ray emission is detected with S/N > 2.8σ and the SX, CGM can be described by a β model with β ≈ 0.4 and log(SX,0[erg s−1 kpc−2]) > 37.2. We estimated the baryon budget of the hot CGM and obtained a value that is lower than the prediction of ΛCDM cosmology, indicating significant gas depletion in these halos. We extrapolated the hot CGM profile measured within Rvir to larger radii and found that within ≈3Rvir, the baryon budget is close to the ΛCDM cosmology prediction. Conclusions. We measured the extended X-ray emission from representative populations of central galaxies around and above MW-mass out to Rvir. Our results set a firm footing for the presence of the hot CGM around such galaxies. These measurements constitute a new benchmark for galaxy evolution models and possible implementations of feedback processes therein.
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