Mg II absorption profile around isolated galaxies. Left: $W_{\mathrm{r}}^{2796}$-b relation for the sample of isolated galaxies. The blue dots represent our isolated galaxy sample and small gray dots represent log(M_⋆/M_⊙) < 9 isolated galaxies. The blue line is the $W_{\mathrm{r}}^{2796}$-b fit for log(M_⋆/M_⊙) > 9 isolated galaxies and the shaded area shows the 1-σ interval. $W_{\mathrm{r}}^{2796}$-b fits from Dutta et al. (2020), Nielsen et al. (2013a) and Huang et al. (2021) are also represented, along with the binned values from Lan & Mo (2018). Right: Mg II covering fraction as a function of impact parameter for the 66 log(M_⋆/M_⊙) > 9 isolated galaxies for different W_t thresholds. The shaded areas are 1-σ uncertainties. The dotted line represents the covering fraction computed by Schroetter et al. (2021) for MEGAFLOW for a 0.1 Å detection limit for primary galaxies (no mass selection). The squares represent the differential covering fraction from Dutta et al. (2020) for different W_t thresholds. The lower panel shows the impact parameter, b, corresponding to the 50% covering fraction as a function of the W_t threshold value for our sample (dashed blue line) and interpolated from the covering fraction values from Dutta et al. (2020) (dotted green line). We also show the b₅₀ from DeFelippis et al. (2021) (TNG50), DeFelippis et al. (2024) (RAMSES with cosmic rays), Ho et al. (2020) (EAGLE), and Ramesh & Nelson (2024) (GIBLE at z = 1).