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 2-D 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 \gamma 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 \gamma line on all three baselines .
We found differential phases up to -25° in the redshifted part of the Br \gamma 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 \pm 0.07 and 0.98 \pm 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 \pm 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 ^ { +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 } \mathrm { L } _ { \odot } , the spherical radiative transfer modeling with CMGFEN yields a current mass-loss rate of 1.5 - 2.0 \times 10 ^ { -5 } \mathrm { M } _ { \odot } { 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 2-D 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 .

Conclusions :