ABSTRACT We report spectroscopic identification of the host galaxies of 18 ultra-strong Mg ii systems (USMg ii) at 0.6 ≤ z ≤ 0.8. We created the largest sample by merging these with 20 host galaxies from our previous survey within 0.4 ≤ z ≤ 0.6. Using this sample, we confirm that the measured impact parameters ($\rm 6.3\leqslant D[kpc] \leqslant 120$ with a median of 19 kpc) are much larger than expected, and the USMg ii host galaxies do not follow the canonical $\rm {\it W}_{2796}-{\it D}$ anticorrelation. We show that the presence and significance of this anticorrelation may depend on the sample selection. The $\rm {\it W}_{2796}-{\it D}$ anticorrelation seen for the general Mg ii absorbers show a mild evolution at low $\rm W_{2796}$ end over the redshift range 0.4 ≤ z ≤ 1.5 with an increase of the impact parameters. Compared to the host galaxies of normal Mg ii absorbers, USMg ii host galaxies are brighter and more massive for a given impact parameter. While the USMg ii systems preferentially pick star-forming galaxies, they exhibit slightly lower ongoing star-forming rates compared to main sequence galaxies with the same stellar mass, suggesting a transition from star-forming to quiescent states. For a limiting magnitude of mr < 23.6, at least 29 per cent of the USMg ii host galaxies are isolated, and the width of the Mg ii absorption in these cases may originate from gas flows (infall/outflow) in isolated haloes of massive star forming but not starbursting galaxies. We associate more than one galaxy with the absorber in $\ge 21~{{\ \rm per\ cent}}$ cases, where interactions may cause wide velocity spread.
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