We have observed warm molecular hydrogen in two nearby edge-on disk galaxies , NGC 4565 and NGC 5907 , using the Spitzer high-resolution infrared spectrograph . The 0–0 S ( 0 ) 28.2 \mu m and 0–0 S ( 1 ) 17.0 \mu m pure rotational lines were detected out to 10 kpc from the center of each galaxy on both sides of the major axis , and in NGC 4565 the S ( 0 ) line was detected at r = 15 kpc on one side . This location is beyond the transition zone where diffuse neutral atomic hydrogen starts to dominate over cold molecular gas , and marks a transition from a disk dominated by high surface-brightness far-IR emission to that of a more quiescent disk . It also lies beyond a steep drop in the radio continuum emission from cosmic rays in the disk . Despite indications that star formation activity decreases with radius , the { H _ { 2 } } excitation temperature and the ratio of the { H _ { 2 } } line and the far-IR luminosity surface densities , \Sigma ( L _ { H 2 } ) / \Sigma ( L _ { TIR } ) , change very little as a function of radius , even into the diffuse outer region of the disk of NGC 4565 . This suggests that the source of excitation of the { H _ { 2 } } operates over a large range of radii , and is broadly independent of the strength and relative location of UV emission from young stars . Although excitation in photodissociation regions is the most common explanation for the widespread { H _ { 2 } } emission , cosmic ray heating or shocks can not be ruled out . At r = 15 kpc in NGC 4565 , outside the main UV and radio continuum-dominated disk , we derived a higher than normal { H _ { 2 } } to 7.7 \mu m PAH emission ratio , but this is likely due to a transition from mainly ionized PAH molecules in the inner disk to mainly neutral PAH molecules in the outer disk . The inferred mass surface densities of warm molecular hydrogen in both edge-on galaxies differ substantially , being 4 ( –60 ) M _ { \sun } pc ^ { -2 } and 3 ( –50 ) M _ { \sun } pc ^ { -2 } at r = 10 kpc for NGC 4565 and NGC 5907 , respectively . The higher values represent very unlikely point-source upper limits . The point source case is not supported by the observed emission distribution in the spectral slits . These mass surface densities can not support the observed rotation velocities in excess of 200 km s ^ { -1 } . Therefore , warm molecular hydrogen can not account for dark matter in these disk galaxies , contrary to what was implied by a previous ISO study of the nearby edge-on galaxy NGC 891 .