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We report infrared spectroscopic observations of HD 105, a nearby ($\sim 40$pc) and relatively young ($\sim 30$ Myr) G0 star with excess infrared continuumemission, which has been modeled as arising from an optically thincircumstellar dust disk with an inner hole of size $\gtrsim 13$ AU. We haveused the high spectral resolution mode of the Infrared Spectrometer (IRS) onthe Spitzer Space Telescope to search for gas emission lines from the disk. Theobservations reported here provide upper limits to the fluxes of H$_2$ S(0)28$\mu$m, H$_2$ S(1) 17$\mu$m, H$_2$ S(2) 12 $\mu$m, [FeII] 26$\mu$m, [SiII]35$\mu$m, and [SI] 25$\mu$m infrared emission lines. The H$_2$ line upperlimits directly place constraints on the mass of warm molecular gas in thedisk: $M({\rm H_2})< 4.6$, 3.8$\times 10^{-2}$, and $3.0\times 10^{-3}$ M$_J$at $T= 50$, 100, and 200 K, respectively. We also compare the line flux upperlimits to predictions from detailed thermal/chemical models of various gasdistributions in the disk. These comparisons indicate that if the gasdistribution has an inner hole with radius $r_{i,gas}$, the surface density atthat inner radius is limited to values ranging from $\lesssim 3$ gm cm$^{-2}$at $r_{i,gas}=0.5$ AU to 0.1 gm cm$^{-2}$ at $r_{i,gas}= 5-20$ AU. These valuesare considerably below the value for a minimum mass solar nebula, and suggestthat less than 1 M$_J$ of gas (at any temperature) exists in the 1-40 AUplanet-forming region. Therefore, it is unlikely that there is sufficient gasfor gas giant planet formation to occur in HD 105 at this time.Comment: To appear in the Astrophysical Journa

Formation and Evolution of Planetary Systems: Upper Limits to the Gas Mass in HD 105