Abstract: Context: The Gaia Radial Velocity Spectrometer (RVS) provides the unique opportunity of a spectroscopic analysis of millions of stars at medium resolution (500) in the near-infrared (845-872 nm). This wavelength range includes the Ca II infrared triplet (IRT) at 850.03, 854.44, and 866.45 nm, which is a good indicator of magnetic activity in the chromosphere of late-type stars. Aims: Here we present the method devised for inferring the Gaia stellar activity index from the analysis of the Ca II IRT in the RVS spectrum, together with its scientific validation. Methods: The Gaia stellar activity index is derived from the Ca II IRT excess equivalent width with respect to a reference spectrum, taking the projected rotational velocity (vsini) into account. We performed scientific validation of the Gaia stellar activity index by deriving a RIIRT index, which is largely independent of the photospheric parameters, and considering the correlation with the RIHK index for a sample of stars. A sample of well-studied pre-main-sequence (PMS) stars is considered to identify the regime in which the Gaia stellar activity index may be affected by mass accretion. The position of these stars in the colour-magnitude diagram and the correlation with the amplitude of the photometric rotational modulation is also scrutinised. Results: Gaia DR3 contains a stellar activity index derived from the Ca II IRT for some 2 × 106 stars in the Galaxy. This represents a "gold mine" for studies on stellar magnetic activity and mass accretion in the solar vicinity. Three regimes of the chromospheric stellar activity are identified, confirming suggestions made by previous authors based on much smaller RIHK datasets. The highest stellar activity regime is associated with PMS stars and RS CVn systems, in which activity is enhanced by tidal interaction. Some evidence of a bimodal distribution in main sequence (MS) stars with Teff [menor o igual] 5000 K is also found, which defines the two other regimes, without a clear gap in between. Stars with 3500 K [menor o igual] Teff [menor o igual] 5000 K are found to be either very active PMS stars or active MS stars with a unimodal distribution in chromospheric activity. A dramatic change in the activity distribution is found for Teff [menor o igual] 3500 K, with a dominance of low activity stars close to the transition between partially- and fully convective stars and a rise in activity down into the fully convective regime.

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