Determining stellar accretion rates from $P{a}_{\alpha }$ and $B{r}_{\beta }$ emission lines with JWST NIRSpec

In this letter we present the first systematic spectroscopic measurements of the Near-InfraRed (NIR) hydrogen recombination lines Paschen alpha ($P{a}_{\alpha }$ $\lambda =1.875\mu m$) and Brackett beta ($B{r}_{\beta }$ $\lambda =2.626\mu m$), produced by pre-main-sequence (PMS) stars. These stars, consisting of T Tauri and Herbig AeBe stars are located in the massive Galactic star-formation region NGC 3603. The measurements were obtained from JWST NIRSpec, using multi-object spectroscopy (MOS) mode. Utilising existing empirical relations between $L_{acc}$ and $L_{B{r}_{\gamma }}$, we have used our new measurements to formulate, for the first time, an empirical relationship between the accretion luminosity $L_{acc}$ of the stars, and the line luminosities $L_{line}$ of both $P{a}_{\alpha }$ and $B{r}_{\beta }$. These relationships are: ${\log }_{10}(\frac{L_{acc}}{L_{\odot }})=1.42(\pm 0.18)\times {\log }_{10}(\frac{L_{P{a}_{\alpha }}}{L_{\odot }})+3.33(\pm 0.42)$ and ${\log }_{10}(\frac{L_{acc}}{L_{\odot }})=1.47(\pm 0.18)\times {\log }_{10}(\frac{L_{B{r}_{\beta }}}{L_{\odot }})+4.60(\pm 0.57)$. These new relationships are key for roughly estimating the accretion rates for large samples of PMS stars with JWST.