Fermi LAT Observation of Diffuse Gamma-Rays Produced Through Interactions between Local Interstellar Matter and High Energy Cosmic Rays

Observations by the Large Area Telescope (LAT) on the \textit{Fermi} mission of diffuse $\gamma$-rays in a mid-latitude region in the third quadrant (Galactic longitude $l$ from $200\arcdeg$ to $260\arcdeg$ and latitude $| b |$ from $22\arcdeg$ to $60\arcdeg$) are reported. The region contains no known large molecular cloud and most of the atomic hydrogen is within 1 kpc of the solar system. The contributions of $\gamma$-ray point sources and inverse Compton scattering are estimated and subtracted. The residual $\gamma$-ray intensity exhibits a linear correlation with the atomic gas column density in energy from 100 MeV to 10 GeV. The measured integrated $\gamma$-ray emissivity is $(1.63 \pm 0.05) \times 10^{-26} {\rm photons s^{-1} sr^{-1} H\mathchar`-atom^{-1}}$ and $(0.66 \pm 0.02) \times 10^{-26} {\rm photons s^{-1} sr^{-1} H\mathchar`-atom^{-1}}$ above 100 MeV and above 300 MeV, respectively, with additional systematic error of $\sim 10%$. The differential emissivity in 100 MeV--10 GeV agrees with calculations based on cosmic ray spectra consistent with those directly measured, at the 10% level. The results obtained indicate that cosmic ray nuclei spectra within 1 kpc from the solar system in regions studied are close to the local interstellar spectra inferred from direct measurements at the Earth within $\sim 10%$.