Baryonic Ecosystem IN Galaxies (BEINGMgII)

We search for the galaxies associated with the intervening Mg <ns0:sc>II</ns0:sc> absorbers over a redshift range of 0.4 ≤ z ≤ 1 using imaging data from DESI Legacy Imaging Surveys and measure the redshift based on the direct detection of nebular emission in the background quasar spectra from the SDSS survey. We find 270 Mg <ns0:sc>II</ns0:sc> absorbers associated with strong O [<ns0:sc>II</ns0:sc>] or O [<ns0:sc>III</ns0:sc>] and Hβ nebular emissions, at a 2.5σ level. Among them, for 213 Mg <ns0:sc>II</ns0:sc> absorbers, we detect an absorber host galaxy at impact parameters of 4 ≤ ρ ≤ 16 kpc, including three absorbers associated with a galaxy pair, with a best-fit galaxy spectral energy distribution model based on multi-passband photometric data from DESI Legacy Imaging surveys, supplemented with the infrared VISTA and unWISE imaging surveys. The detection rate of the Mg <ns0:sc>II</ns0:sc> absorber host with strong O [<ns0:sc>II</ns0:sc>] nebular emission in the finite SDSS fibre of a 2–3 arcsec diameter increases from 0.2% to ∼3% with an increasing equivalent width from 0.3 Å to ∼3.5 Å, which remains near-constant across the probed redshift range. The associated Mg <ns0:sc>II</ns0:sc> host galaxies exhibit a wide range of stellar mass from 7.94 ≤ log(M⋆/M⊙)≤11.11, with an average star formation rate (SFR) of 5.81 M⊙ yr−1. The Mg <ns0:sc>II</ns0:sc> absorber hosts selected based on O [<ns0:sc>II</ns0:sc>] nebular emission mostly exhibit active star-forming systems including 13.4% starburst systems, but 10.2% with a suppressed SFR. The near-constant absorption strength at low-impact parameters suggests a high gas covering fraction. We find that the Mg <ns0:sc>II</ns0:sc> equivalent width (W2796) positively correlates with the SFR and specific SFR, likely indicating their wind origin. The average velocity offset between the host and the absorber suggests that the Mg <ns0:sc>II</ns0:sc> gas is bound within the dark matter halo.