The stellar population in the central parsec of the Galaxy is dominated by an old (several Gyr) population, but young, massive stars dominate the luminosity function. We have studied the most luminous of these stars, GCIRS 7, in order to constrain the age of the recent star formation event in the Galactic Centre and to characterise it as an interferometric reference for observations of the Galactic Centre with the instrument GRAVITY, which will equip the Very Large Telescope Interferometer in the near future. We present the first H-band interferometric observations of GCIRS 7, obtained using the PIONIER visitor instrument on the VLTI using the four 8.2-m unit telescopes. In addition, we present unpublished K-band VLTI/AMBER data, build JHKL light-curves based on data spanning 4 decades, and measured the stars effective temperature using SINFONI spectroscopy. GCIRS 7 is marginally resolved at H-band (in 2013: uniform-disk diameter=1.076+/-0.093mas, R=960+/-92Rsun at 8.33+/-0.35kpc). We detect a significant circumstellar contribution at K-band. The star and its environment are variable in brightness and in size. The photospheric H-band variations are well modelled with two periods: P0~470+/-10 days (amplitude ~0.64mag) and long secondary period LSP~2700-2850 days (~1.1mag). As measured from CO equivalent width, <Teff>=3600+/-195K. The size, periods, luminosity (<Mbol>=-8.44+/-0.22) and effective temperature are consistent with an M1 supergiant with an initial mass of 22.5+/-2.5Msun and an age of 6.5-10Myr (depending on rotation). This age is in remarkable agreement with most estimates for the recent star formation event in the central parsec. Caution should be taken when using this star as an interferometric reference as it is variable in size, is surrounded by a variable circumstellar environment and large convection cells may form on its photosphere.
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