The MAGPI survey: The interdependence of the mass, star formation rate, and metallicity in galaxies at z~0.3

Star formation rates (SFRs), gas-phase metallicities, and stellar masses are crucial for studying galaxy evolution. The different relations resulting from these properties give insights into the complex interplay of gas inside galaxies and their evolutionary trajectory and current characteristics. We aim to characterize these relations at $z\sim 0.3$, corresponding to a 3-4 Gyr lookback time. We utilized optical integral field spectroscopy of 65 emission-line galaxies from the MAGPI survey at a redshift of $0.28<z<0.35$ and spanning a total stellar mass range of $8.2<\log(M_{*}/M_{\odot}) < 11.4$. We derived the resolved star formation main sequence (rSFMS), resolved mass metallicity relation (rMZR), and resolved fundamental metallicity relation (rFMR) at $z\sim 0.3$. We find a relatively shallow rSFMS slope of $\sim 0.425 \pm 0.014$ compared to the expected slope at this redshift for an ordinary least square (OLS) fitting routine. For an orthogonal distance regression (ODR) routine, a much steeper slope of $\sim 1.162 \pm 0.022$ is measured. We confirm the existence of an rMZR at $z\sim 0.3$ with an average metallicity located $\sim 0.03$ dex above the local Universe's metallicity. Via partial correlation coefficients, evidence is found that the local metallicity is predominantly determined by the stellar mass surface density and has a weak secondary (inverse) dependence on the SFR surface density $\Sigma_{SFR}$. Additionally, a significant dependence of the local metallicity on the total stellar mass $M_{*}$ is found. Furthermore, we find that the stellar mass surface density $\Sigma_{*}$ and $M_{*}$ have a significant influence in determining the strength with which $\Sigma_{SFR}$ correlates with the local metallicity. We observe that at lower stellar masses, there is a tighter correlation between $\Sigma_{SFR}$ and the gas-phase metallicity, resulting in a more pronounced rFMR.