Using classical Cepheids to study the far side of the Milky Way disk: I.
  Spectroscopic classification and the metallicity gradient
  The structure, kinematics, and chemical composition of the far side of the
Milky Way disk, beyond the bulge, are still to be revealed. Classical Cepheids
(CCs) are young and luminous standard candles. We aim to use a
well-characterized sample of these variable stars to study the present time
properties of the far side of the Galactic disk. A sample of 45 Cepheid
variable star candidates were selected from near infrared time series
photometry obtained by the VVV survey. We characterized this sample using high
quality near infrared spectra obtained with VLT/X-Shooter, deriving radial
velocities and iron abundances for all the sample Cepheids. This allowed us to
separate the CCs, which are metal rich and with kinematics consistent with the
disk rotation, from type II Cepheids (T2Cs), which are more metal poor and with
different kinematics. We estimated individual distances and extinctions using
VVV photometry and period-luminosity relations, reporting the characterization
of 30 CCs located on the far side of the Galactic disk, plus 8 T2Cs mainly
located in the bulge region, of which 10 CCs and 4 T2Cs are new discoveries.
This is the first sizeable sample of CCs in this distant region of our Galaxy
that has been spectroscopically confirmed. We use their positions, kinematics,
and metallicities to confirm that the general properties of the far disk are
similar to those of the well-studied disk on the solar side of the Galaxy. In
addition, we derive for the first time the radial metallicity gradient on the
disk's far side. Considering all the CCs with $R_{\mathrm{GC}} < 17\,\rm{kpc}$,
we measure a gradient with a slope of $-0.062 \, \mathrm{dex\, kpc^{-1}}$ and
an intercept of $+0.59 \, \rm{dex}$, which is in agreement with previous
determinations based on CCs on the near side of the disk.
