Probing stellar accretion with mid-infrared hydrogen lines

In this paper we investigate the origin of the mid-infrared (IR) hydrogen recombination lines for a sample of 114 disks in different evolutionary stages (full, transitional and debris disks) collected from the {\it Spitzer} archive. We focus on the two brighter {H~{\sc i}} lines observed in the {\it Spitzer} spectra, the {H~{\sc i}}(7-6) at 12.37$\mu$m and the {H~{\sc i}}(9-7) at 11.32$\mu$m. We detect the {H~{\sc i}}(7-6) line in 46 objects, and the {H~{\sc i}}(9-7) in 11. We compare these lines with the other most common gas line detected in {\it Spitzer} spectra, the {[Ne~{\sc iii}]} at 12.81$\mu$m. We argue that it is unlikely that the {H~{\sc i}} emission originates from the photoevaporating upper surface layers of the disk, as has been found for the {[Ne~{\sc iii}]} lines toward low-accreting stars. Using the {H~{\sc i}}(9-7)/{H~{\sc i}}(7-6) line ratios we find these gas lines are likely probing gas with hydrogen column densities of 10$^{10}$-10$^{11}$~cm$^{-3}$. The subsample of objects surrounded by full and transitional disks show a positive correlation between the accretion luminosity and the {H~{\sc i}} line luminosity. These two results suggest that the observed mid-IR {H~{\sc i}} lines trace gas accreting onto the star in the same way as other hydrogen recombination lines at shorter wavelengths. A pure chromospheric origin of these lines can be excluded for the vast majority of full and transitional disks.We report for the first time the detection of the {H~{\sc i}}(7-6) line in eight young (< 20~Myr) debris disks. A pure chromospheric origin cannot be ruled out in these objects. If the {H~{\sc i}}(7-6) line traces accretion in these older systems, as in the case of full and transitional disks, the strength of the emission implies accretion rates lower than 10$^{-10}$M$_{\odot}$/yr. We discuss some advantages of extending accretion indicators to longer wavelengths.