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An optical monitoring survey in the nearby dwarf galaxies was carried outwith the 2.5-m Isaac Newton Telescope (INT). 55 dwarf galaxies and fourisolated globular clusters in the Local Group (LG) were observed with the WideField Camera (WFC). The main aims of this survey are to identify the mostevolved asymptotic giant branch (AGB) stars and red supergiants at theend-point of their evolution based on their pulsational instability, use theirdistribution over luminosity to reconstruct the star formation history (SFH),quantify the dust production and mass loss from modelling the multi-wavelengthspectral energy distributions, and relate this to luminosity and radiusvariations. In this second of a series of papers, we present the methodologyused to estimate SFH based on long-period variable (LPV) stars and then deriveit for Andromeda\,I (And\,I) dwarf galaxy as an example of the survey. Usingour identified 59 LPV candidates within two half-light radii of And\,I andPadova stellar evolution models, we estimated the SFH of this galaxy. A majorepoch 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 Gyrago. The presence of some dusty LPVs in this galaxy corresponds to a slightincrease in recent star formation peaking around 800 Myr ago. We evaluate aquenching time around 4 Gyr ago ($z<0.5$), which makes And\,I a late-quenchingdSph. A total stellar mass $(16\pm7)\times10^6$ M$_\odot$ is calculated withintwo half-light radii of And\,I for a constant metallicity $Z=0.0007$.

astrophysical journal/the astrophysical journal

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