We present near-infrared VLT ISAAC imaging and spectroscopy of the peculiar Virgo galaxy NGC 4438, whose nucleus has been classified as a LINER. The data are supplemented by mid-infrared imaging, and compared to previous WFPC2 HST broadband images. Images and position-velocity maps of the [Fe II] and H2 line emissions are presented and compared with the distribution of the optical narrow-line region and radio features. Our results show that shocks (possibly driven by a radio jet) contribute to an important fraction of the excitation of [Fe II], while X-ray heating from a central AGN may be responsible for the H2 excitation. We address the question whether the outflow has an AGN or a starburst origin by providing new estimates of the central star formation rate and the kinetic energy associated with the gas. By fitting a Sersic bulge, an exponential disc and a compact nuclear source to the light distribution, we decomposed NGC 4438s light distribution and found an unresolved nuclear source at 0.8 arcsec resolution with M_K = -18.7 and J-H = 0.69. Our measured bulge velocity dispersion, 142 km/s, together with the standard M_bh-sigma relation, suggests a central black hole mass of log(M_bh/Msun) ~ 7.0. The stellar kinematics measured from the near-infrared CO lines shows a strong peak in the velocity dispersion of 178 km/s in the central 0.5 arcsec, which is possible kinematic evidence of a central black hole. We calculated a general expression for the integrated Sersic profile flux density in elliptical geometry, including the case of disky isophotes.
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