Chemical abundances and radial velocities in the extremely metal-poor
  galaxy DDO 68
  We present chemical abundances and radial velocities of six HII regions in
the extremely metal-poor star-forming dwarf galaxy DDO 68. They are derived
from deep spectra in the wavelength range 3500 - 10,000 {\AA}, acquired with
the Multi Object Double Spectrograph (MODS) at the Large Binocular Telescope
(LBT). In the three regions where the [O III]$\lambda$4363 {\AA} line was
detected, we inferred the abundance of He, N, O, Ne, Ar, and S through the
"direct" method. We also derived the oxygen abundances of all the six regions
adopting indirect method calibrations. We confirm that DDO 68 is an extremely
metal-poor galaxy, and a strong outlier in the luminosity - metallicity
relation defined by star-forming galaxies. With the direct-method we find
indeed an oxygen abundance of 12+log(O/H)=7.14$\pm$0.07 in the northernmost
region of the galaxy and, although with large uncertainties, an even lower
12+log(O/H)=6.96$\pm$0.09 in the "tail". This is, at face value, the most
metal-poor direct abundance detection of any galaxy known. We derive a radial
oxygen gradient of -0.06$\pm$0.03 dex/kpc (or -0.30 dex $R_{25}^{-1}$) with the
direct method, and a steeper gradient of -0.12$\pm$0.03 dex/kpc (or -0.59 dex
$R_{25}^{-1}$) from the indirect method. For the $\alpha$-element to oxygen
ratios we obtain values in agreement with those found in other metal-poor
star-forming dwarfs. For nitrogen, instead, we infer much higher values,
leading to log(N/O)$\sim-1.4$, at variance with the suggested existence of a
tight plateau at $-1.6$ in extremely metal poor dwarfs. The derived helium mass
fraction ranges from Y=0.240$\pm$0.005 to Y=0.25$\pm$0.02, compatible with
standard big bang nucleosynthesis. Finally, we measured HII region radial
velocities in the range 479$-$522 km/s from the tail to the head of the
"comet", consistent with the rotation derived in the HI.
