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(Abridged) We perform a detailed study of the main optical activityindicators (Ca II H & K, Balmer lines, Na I D$_{\rm 1}$ D$_{\rm 2}$, and He ID$_{\rm 3}$) measured for the Sun using the data provided by the HARPS-Nsolar-telescope feed at the Telescopio Nazionale Galileo. The value of thesolar rotation period is found in all the activity indicators, with the onlyexception being H$\delta$. The derived values vary from 26.29 days (H$\gamma$line) to 31.23 days (He I). From an analysis of sliding periodograms we findthat in most of the activity indicators the spectral power is split intoseveral "bands" of periods around 26 and 30 days, that might be explained bythe migration of active regions between the equator and a latitude of $\sim$30$^{\circ}$, spot evolution or a combination of both effects. In agreementwith previous works a typical lifetime of active regions of $\sim$ ten rotationperiods is inferred from the pooled variance diagrams. We find that H$\alpha$,H$\beta$, H$\gamma$, H$\epsilon$, and He I show a significant correlation withthe S index. Significant correlations between the contrast, bisector span, andthe heliocentric radial velocity with the activity indexes are also found. Weshow that the full width at half maximum, the bisector, and the disc-integratedmagnetic field correlate with the radial velocity variations. The correlationof the S index and H$\alpha$ changes with time, increasing with larger sun spotnumbers and solar irradiance. A similar tendency with the S index - radialvelocity correlation is also present in the data. Our results are consistentwith a scenario in which higher activity favours the correlation between the Sindex and the H$\alpha$ activity indicators and between the S index and radialvelocity variations.

Temporal evolution and correlations of optical activity indicators measured in Sun-as-a-star observations