The Isaac Newton Telescope monitoring survey of Local Group dwarf galaxies -- IV. The star formation history of Andromeda VII derived from long period variable stars.

We have examined the star formation history (SFH) of Andromeda VII (And VII), the brightest and most massive dwarf spheroidal (dSph) satellite of the Andromeda galaxy (M 31). Although M 31 is surrounded by several dSph companions with old stellar populations and low metallicity, it has a metal-rich stellar halo with an age of 6$-$8 Gyr. This indicates that any evolutionary association between the stellar halo of M 31 and its dSph system is frail. Therefore, the question is whether And VII (a high-metallicity dSph located $\sim$220 kpc from M 31), can be associated with M 31's young, metal-rich halo. Here, we perform the first reconstruction of the SFH of And VII employing long-period variable (LPV) stars. As the most-evolved asymptotic giant branch (AGB) and red supergiant (RSG) stars, the birth mass of LPVs can be determined by connecting their near-infrared photometry to theoretical evolutionary tracks. We found 55 LPV candidates within two half-light radii, using multi-epoch imaging with the Isaac Newton Telescope in the $i$ and $V$ bands. Based on their birth mass function, the star-formation rate (SFR) of And VII was obtained as a function of cosmic time. The main epoch of star formation occurred $\simeq 6.2$ Gyr ago with a SFR of $0.006\pm0.002$ M$_\odot$ yr$^{-1}$. Over the past 6 Gyr, we find slow star formation, which continued until 500 Myr ago with a SFR $\sim0.0005\pm0.0002$ M$_\odot$ yr$^{-1}$. We determined And VII's stellar mass $M=(13.3\pm5.3)\times10^6$ M$_\odot$ within a half-light radius $r_{\frac{1}{2}}=3.8\pm0.3$ arcmin and metallicity $Z=0.0007$, and also derived its distance modulus of $\mu=24.38$ mag.