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We present a high-resolution (R~16,000) spectrum and a narrow-band imagecentered on the [NeII]12.8 micron line of the central kpc region of thestarburst/Seyfert2 galaxy NGC 7582. The galaxy has a rotating circum-nuclearstarburst disk, shown at great detail at a diffraction-limited resolution of0.4 arcsec. The high spatial resolution allows us to probe the dynamics of the[NeII] gas in the nuclear regions, and to estimate the mass of the centralblack hole. We construct models of gas disks rotating in the combinedgravitational potential from the stellar bulge and a central black hole, andderive a black hole mass of 5.5 x 10^7 solar masses with a 95% confidenceinterval of [3.6,8.1] x 10^7 solar masses. The black hole mass combined withstellar velocity dispersion measurements from the literature shows that thegalaxy is consistent with the local M-sigma relation. This is the first timethat a black hole mass in a galaxy except our own Milky Way system has beenestimated from gas dynamics in the mid-infrared. We show that spatiallyresolved mid-infrared spectroscopy may be competitive with similar techniquesin the optical and near-infrared, and may prove to be important for estimatingblack hole masses in galaxies with strong nuclear dust obscuration. The highspectral resolution allows us to determine the heliocentric systemic velocityof the galaxy to between 1614 and 1634 km/s. The mid-infrared image revealsseveral dense knots of dust-embedded star formation in the circum-nuclear disk,and we briefly discuss its morphology.Comment: 11 pages, 7 figures, accepted for publication in A&

The nuclear regions of NGC 7582 from [Ne II] spectroscopy at 12.8μm – an estimate of the black hole mass