Determining stellar accretion rates from $Pa_{\alpha}$ and $Br_{\beta}$ 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 ($Pa_{\alpha}$ $\lambda = 1.875 \mu m$) and Brackett beta ($Br_{\beta}$ $\lambda = 2.626 \mu m$), 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 $L_{Br_{\gamma}}$, 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 $Pa_{\alpha}$ and $Br_{\beta}$. These relationships are: $\log_{10}( \frac{L_{acc}}{L_{\odot}}) = 1.42 (\pm 0.18) \times \log_{10}( \frac{L_{Pa_{\alpha}}}{L_{\odot}}) + 3.33 (\pm 0.42)$ and $\log_{10}( \frac{L_{acc}}{L_{\odot}}) = 1.47 (\pm 0.18) \times \log_{10}( \frac{L_{Br_{\beta}}}{L_{\odot}}) + 4.60 (\pm 0.57)$. These new relationships are key for roughly estimating the accretion rates for large samples of PMS stars with JWST.