  In this second paper of the series, we present the 2-dimensional (2D)
emission line abundance analysis of NGC 628, the largest object within the PPAK
Integral Field Spectroscopy (IFS) Nearby Galaxies Survey: PINGS. We introduce
the methodology applied to the 2D IFS data in order to extract and deal with
large spectral samples, from which a 2D abundance analysis can be later
performed. We obtain the most complete and reliable abundance gradient of the
galaxy up-to-date, by using the largest number of spectroscopic points sampled
in the galaxy, and by comparing the statistical significance of different
strong-line metallicity indicators. We find features not previously reported
for this galaxy that imply a multi-modality of the abundance gradient
consistent with a nearly flat-distribution in the innermost regions of the
galaxy, a steep negative gradient along the disc and a shallow gradient or
nearly-constant metallicity beyond the optical edge of the galaxy. The N/O
ratio seems to follow the same radial behaviour. We demonstrate that the
observed dispersion in metallicity shows no systematic dependence with the
spatial position, signal-to-noise or ionization conditions, implying that the
scatter in abundance for a given radius is reflecting a true spatial physical
variation of the oxygen content. Furthermore, by exploiting the 2D IFS data, we
were able to construct the 2D metallicity structure of the galaxy, detecting
regions of metal enhancement, and showing that they vary depending on the
choice of the metallicity estimator. The analysis of axisymmetric variations in
the disc of NGC 628 suggest that the physical conditions and the star formation
history of different-symmetric regions of the galaxy have evolved in a
different manner.

Cosmology and Nongalactic Astrophysics