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The Isaac Newton Telescope monitoring survey of Local Group dwarf galaxies. II. The star formation history of Andromeda I derived from long period variables

An optical monitoring survey in the nearby dwarf galaxies was carried out with the 2.5-m Isaac Newton Telescope (INT). 55 dwarf galaxies and four isolated globular clusters in the Local Group (LG) were observed with the Wide Field Camera (WFC). The main aims of this survey are to identify the most evolved asymptotic giant branch (AGB) stars and red supergiants at the end-point of their evolution based on their pulsational instability, use their distribution over luminosity to reconstruct the star formation history (SFH), quantify the dust production and mass loss from modelling the multi-wavelength spectral energy distributions, and relate this to luminosity and radius variations. In this second of a series of papers, we present the methodology used to estimate SFH based on long-period variable (LPV) stars and then derive it for Andromeda\,I (And\,I) dwarf galaxy as an example of the survey. Using our identified 59 LPV candidates within two half-light radii of And\,I and Padova stellar evolution models, we estimated the SFH of this galaxy. A major epoch of star formation occurred in And\,I peaking around 6.6 Gyr ago, reaching $0.0035\pm0.0016$ M$_\odot$ yr$^{-1}$ and only slowly declining until 1--2 Gyr ago. The presence of some dusty LPVs in this galaxy corresponds to a slight increase in recent star formation peaking around 800 Myr ago. We evaluate a quenching time around 4 Gyr ago ($z<0.5$), which makes And\,I a late-quenching dSph. A total stellar mass $(16\pm7)\times10^6$ M$_\odot$ is calculated within two half-light radii of And\,I for a constant metallicity $Z=0.0007$.