To probe the circumstellar environment of IRAS 13481-6124, a 20 M_sun high-mass young stellar object (HMYSO) with a parsec-scale jet and accretion disc, we investigate the origin of its Brgamma-emission line through NIR interferometry. We present the first AMBER/VLTI observations of the Brgamma-emitting region in an HMYSO at R~1500. Our AMBER/VLTI observations reveal a spatially and spectrally resolved Brgamma-line in emission with a strong P Cygni profile, indicating outflowing matter with a terminal velocity of ~500 km/s. Visibilities, differential phases, and closure phases are detected in our observations within the spectral line and in the adjacent continuum. Both total visibilities (continuum plus line emitting region) and pure-line visibilities indicate that the Brgamma-emitting region is more compact (2-4 mas in diameter or ~6-13 au at 3.2 kpc) than the continuum-emitting region (~5.4 mas or ~17 au). The absorption feature is also spatially resolved at the longest baselines (81 and 85 m) and has a visibility that is slightly smaller than the continuum-emitting region. The differential phases at the four longest baselines display an u2018Su2019-shaped structure across the line, peaking in the blue- and red-shifted high-velocity components. The calibrated photocentre shifts are aligned with the known jet axis, i.e they are probably tracing an ionised jet. The high-velocity components (v_r~100-500 km/s) are located far from the source, whereas the low-velocity components (0-100 km/s) are observed to be closer, indicating a strong acceleration of the gas flow in the inner 10 au. Finally, a non-zero closure phase along the continuum is detected. By comparing our observations with the synthetic images of the continuum around 2.16 um, we confirm that this feature originates from the asymmetric brightness distribution of the continuum owing to the inclination of the inner disc.
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