| Abstract
| - Context. IRC +10420 is a massive evolved star belonging to the group of yellow hypergiants. Currently, this star is rapidly evolving through the Hertzprung-Russell diagram, crossing the so-called yellow void. IRC +10420 is suffering from intensive mass loss which led to the formation of an extended dust shell. Moreover, the dense stellar wind of IRC +10420 is subject to strong line emission. Aims. Our goal was to probe the photosphere and the innermost circumstellar environment of IRC +10420, to measure the size of its continuum- as well as the Br $\gamma\,$line-emitting region on milliarcsecond scales, and to search for evidence of an asymmetric distribution of IRC +10420's dense, circumstellar gas. Methods. We obtained near-infrared long-baseline interferometry of IRC +10420 with the AMBER instrument of ESO's Very Large Telescope Interferometer (VLTI). The measurements were carried out in May/June 2007 and May 2008 in low-spectral resolution mode in the JHK bands using three auxillary telescopes (ATs) at projected baselines ranging from 30 to 96 m, and in October 2008 in high-spectral resolution mode in the K band around the Br $\gamma\,$emission line using three unit telescopes (UTs) with projected baselines between 54 and 129 m. The high-spectral resolution mode observations were analyzed by means of radiative transfer modeling using CMFGEN and the 2D Busche & Hillier codes. Results. For the first time, we have been able to absolutely calibrate the H- and K-band data and, thus, to determine the angular size of IRC+10420's continuum- and Br γ line-emitting regions. We found that both the low resolution differential and closure phases are zero within the uncertainty limits across all three bands. In the high-spectral resolution observations, the visibilities show a noticeable drop across the Br γ line on all three baselines. We found differential phases up to -25° in the redshifted part of the Br γ line and a non-zero closure phase close to the line center. The calibrated visibilities were corrected for AMBER's limited field-of-view to appropriately account for the flux contribution of IRC +10420's extended dust shell. From our low-spectral resolution AMBER data we derived FWHM Gaussian sizes of 1.05 ±0.07 and 0.98 ±0.10 mas for IRC +10420's continuum-emitting region in the H and K bands, respectively. From the high-spectral resolution data, we obtained a FWHM Gaussian size of 1.014 ±0.010 mas in the K-band continuum. The Br $\gamma\,$-emitting region can be fitted with a geometric ring model with a diameter of $4.18^{\rm +0.19}_{-0.09}~$mas, which is approximately 4 times the stellar size. The geometric model also provides some evidence that the Br $\gamma\,$line-emitting region is elongated towards a position angle of 36°, well aligned with the symmetry axis of the outer reflection nebula. Assuming an unclumped wind and a luminosity of 6 $\times$10 5${\,{L}_{odot}}$, the spherical radiative transfer modeling with CMGFEN yields a current mass-loss rate of 1.5-2.0 $\times$10 -5${\,{M}_{odot}\,{\rm yr}^{-1}}$ based on the Br $\gamma\,$equivalent width. However, the spherical CMFGEN model poorly reproduces the observed line shape, blueshift, and extension, definitively showing that the IRC +10420 outflow is asymmetric. Our 2D radiative transfer modeling shows that the blueshifted Br $\gamma\,$emission and the shape of the visibility across the emission line can be explained with an asymmetric bipolar outflow with a high density contrast from pole to equator (8-16), where the redshifted light is substantially diminished.
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