OGLE-ing the Magellanic System: Photometric Metallicity from Fundamental
  Mode RR Lyrae Stars
  In an era of extensive photometric observations, the catalogs of RR Lyr type
variable stars number tens of thousands of objects. The relation between the
iron abundance [Fe/H] and the Fourier parameters of the stars light curve
allows us to investigate mean metallicities and metallicity gradients in
various stellar environments, independently of time-consuming spectroscopic
observations. In this paper we use almost 6500 $V$- and $I$-band light curves
of fundamental mode RR Lyr stars from the OGLE-IV survey to provide a relation
between the $V$- and $I$-band phase parameter $\varphi_{31}$ used to estimate
[Fe/H]. The relation depends on metallicity, which limits its applicability. We
apply this relation to metallicity formulae developed for the Johnson $V$- and
the Kepler $Kp$-band to obtain the relation between [Fe/H] and $\varphi_{31}$
for the $I$-band photometry. Last, we apply the new relation of Nemec to the
OGLE-IV fundamental mode RR Lyr stars data and construct a metallicity map of
the Magellanic Clouds. Median [Fe/H] is $-1.39\pm0.44$ dex for the LMC and
$-1.77\pm0.48$ dex for the SMC, on the Jurcsik metallicity scale. We also find
a metallicity gradient within the LMC with a slope of $-0.029\pm0.002$ dex/kpc
in the inner 5 kpc and $-0.030 \pm0.003$ dex/kpc beyond 8 kpc, and no gradient
in-between ($-0.019\pm0.002$ dex/kpc integrally). We do not observe a
metallicity gradient in the SMC, although we show that the metal-rich RRab
stars are more concentrated toward the SMC center than the metal-poor.
