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In this work we investigate the effect of the H$\alpha$ bandpass width in thecorrelation between the CaII H&K and H$\alpha$ indices with the aim ofimproving the H$\alpha$ index to better identify and model the signals comingfrom activity variability. We used a sample of 152 FGK dwarfs observed withHARPS for more than 13 years with enough cadence to be able to detectrotational modulations and cycles in activity proxies. We calculated the CaIIH&K and H$\alpha$ activity indices using a range of bandwidths for H$\alpha$between 0.1 and 2.0 Ang. We studied the correlation between the indices timeseries at long and short timescales and analysed the impact of stellarparameters, activity level and variability on the correlations. The correlationbetween CaII H&K and H$\alpha$ both at short and long timespans is maximisedwhen using narrow H$\alpha$ bandwidths, with a maximum at 0.6 Ang. For someinactive stars, as the activity level increases, the flux in the H$\alpha$ linecore increases while the flux in the line wings decreases as the line becomesshallower and broader. The balance between these fluxes can cause stars to showthe negative correlations observed in the literature when using a widebandwidth on H$\alpha$. These anti-correlations may become positivecorrelations if using the 0.6 Ang bandwidth. Calculating the H$\alpha$ indexusing a bandpass of 0.6 Ang maximises the correlation between CaII H&K andH$\alpha$ both at short and long timescales. On the other hand, the use of thebroader 1.6 Ang, generally used in exoplanet detection to identify stellaractivity signals, degrades the signal by including the flux in the line wings.In face to these results we strongly recommend the use of a 0.6 Ang bandwidthwhen computing the H$\alpha$ index for the identification of activityrotational modulation and magnetic cycle signals in solar-type stars.(Abridged)

astronomy and astrophysics

Optimising the H$\alpha$ index for the identification of activity  signals in FGK stars. Improvement of the correlation between H$\alpha$ and  CaII H&K