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We present the detection and morphological characterization of hot moleculargas outflows in nearby ultra-luminous infrared galaxies, using the near-IRintegral-field spectrograph SINFONI on the VLT. We detect outflows observed inthe 2.12 micron H$_{2}$ 1-0 S(1) line for three out of four ULIRGs analyzed;IRAS 12112+0305, 14348-1447, and 22491-1808. The outflows are mapped on scalesof 0.7-1.6 kpc, show typical outflow velocities of 300-500 km/s, and appear tooriginate from the nuclear region. The outflows comprise hot molecular gasmasses of ~6-8x10$^3$ M(sun). Assuming a hot-to-cold molecular gas mass ratioof 6x10$^{-5}$, as found in nearby luminous IR galaxies, the total (hot+cold)molecular gas mass in these outflows is expected to be ~1x10$^{8}$ M(sun). Thistranslates into molecular mass outflow rates of ~30-85 M(sun)/yr, which is afactor of a few lower than the star formation rate in these ULIRGs. Inaddition, most of the outflowing molecular gas does not reach the escapevelocity of these merger systems, which implies that the bulk of the outflowingmolecular gas is re-distributed within the system and thus remains availablefor future star formation. The fastest H$_{2}$ outflow is seen in theCompton-thick AGN of IRAS 14348-1447, reaching a maximum outflow velocity of~900 km/s. Another ULIRG, IRAS 17208-0014, shows asymmetric H$_{2}$ lineprofiles different from the outflows seen in the other three ULIRGs. We discussseveral alternative explanations for its line asymmetries, including a verygentle galactic wind, internal gas dynamics, low-velocity gas outside the disk,or two superposed gas disks. We do not detect the hot molecular counterpart tothe outflow previously detected in CO(2-1) in IRAS 17208-0014, but we note thatour SINFONI data are not sensitive enough to detect this outflow if it has asmall hot-to-cold molecular gas mass ratio of < 9x10$^{-6}$.

Outflows of hot molecular gas in ultra-luminous infra-red galaxies mapped with VLT-SINFONI