Molecular Gas and Nuclear Activity in Ultraluminous Infrared Galaxies with Double Nuclei

High-resolution CO(1-0) observations of five ultraluminous infrared galaxies (ULIGs: L_IR [8-1000um] >~ 10^12 L_sun) with double nuclei are analyzed. These sources constitute a complete subset of local ULIGs expected to be in an intermediate stage of merging and selected with projected nuclear separations of 2.0-5.4 (3-5 kpc) so they could be resolved with the Owens Valley Radio Observatory Millimeter Array. The observed pairs include two mergers with cool far-infrared colors (25um to 60um flux density ratio f_25um/f_60um < 0.2) from the Infrared Astronomical Satellite (IRAS) Bright Galaxy Sample (IRAS 12112+0305 and IRAS 14348-1447) and three mergers with warm infrared dust temperatures f_25um/f_60um >~ 0.2) selected from the IRAS Warm Galaxy Sample (IRAS 08572+3915, IRAS 13451+1232 = PKS 1345+12, and IRAS 13536+1836 = Mrk 463). These ULIGs are further distinguished by the presence of pairs of active nuclei; among the ten nuclei, nine have Seyfert or LINER classifications and one is unclassified. Molecular gas is detected only on the redder, more radio-luminous nucleus of the warm objects, whereas both nuclei of the cool ULIGs are detected in CO. The inferred molecular gas masses for the detected nuclei are 0.1-1.2x10^10 M_sun, and the undetected nuclei have molecular gas masses at least 1.2--2.8 times less than that of their CO-luminous companions. Upper limits on the extent of the CO emitting regions of each detected nucleus range from 2--4 kpc, which is about 3-6 times smaller than the average effective CO diameter of nearby spiral galaxies...