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.
