We present the first NIR spectro-interferometry of the LBV Eta Carinae. The K
band observations were performed with the AMBER instrument of the ESO Very
Large Telescope Interferometer using three 8.2m Unit Telescopes with baselines
from 42 to 89m. The aim of this work is to study the wavelength dependence of
Eta Car's optically thick wind region with a high spatial resolution of 5 mas
(11 AU) and high spectral resolution. The medium spectral resolution
observations (R=1,500) were performed in the wavelength range around both the
HeI 2.059 micron and the Br gamma 2.166 micron emission lines, the high
spectral resolution observations (R=12,000) only in the Br gamma line region.
In the K-band continuum, a diameter of 4.0 +/-0.2 mas (Gaussian FWHM, fit range
28-89m) was measured for Eta Car's optically thick wind region. If we fit
Hillier et al. (2001) model visibilities to the observed AMBER visibilities, we
obtain 50 % encircled-energy diameters of 4.2, 6.5 and 9.6mas in the 2.17
micron continuum, the HeI, and the Br gamma emission lines, respectively. In
the continuum near the Br gamma line, an elongation along a position angle of
120+/-15 degrees was found, consistent with previous VLTI/VINCI measurements by
van Boekel et al. (2003). We compare the measured visibilities with predictions
of the radiative transfer model of Hillier et al. (2001), finding good
agreement. Furthermore, we discuss the detectability of the hypothetical hot
binary companion. For the interpretation of the non-zero differential and
closure phases measured within the Br gamma line, we present a simple geometric
model of an inclined, latitude-dependent wind zone. Our observations support
theoretical models of anisotropic winds from fast-rotating, luminous hot stars
with enhanced high-velocity mass loss near the polar regions.Comment: 22 pages, 14 figures, 2 tables; A&A in pres