Magnetic Inflation and Stellar Mass. V. Intensification and saturation of M dwarf absorption lines with Rossby number

In young sun-like stars and field M dwarf stars, chromospheric and coronal magnetic activity indicators such as H$α$, X-ray and radio emission are known to saturate with low Rossby number ($Ro \lesssim 0.1$), defined as the ratio of rotation period to convective turnover time. The mechanism for the saturation is unclear. In this paper, we use photospheric Ti I and Ca I absorption lines in $Y$ band to investigate magnetic field strength in M dwarfs for Rossby numbers between 0.01 and 1.0. The equivalent widths of the lines are magnetically enhanced by photospheric spots, a global field or a combination of the two. The equivalent widths behave qualitatively similar to the chromospheric and coronal indicators: we see increasing equivalent widths (increasing absorption) with decreasing $Ro$ and saturation of the equivalent widths for $Ro \lesssim 0.1$. The majority of M dwarfs in this study are fully convective. The results add to mounting evidence that the magnetic saturation mechanism occurs at or beneath the stellar photosphere.