Evolution of N/O Abundance Ratios and Ionization Parameters from z~0 to
  2 Investigated by the Direct Temperature Method
  We present N/O abundance ratios, ionization parameters {$q_{\rm ion}$}, and
oxygen abundance O/H for a total of 41 galaxies (11 individual galaxies and a
30-galaxy stack) including {Ly$\alpha$} emitters and Lyman break galaxies at
$z\sim 2$, and investigate galaxy evolution from $z\sim 0$ to $2$ in
conjunction with 208,529 local SDSS galaxies and 9 green pea galaxies (GPs). In
contrast with most of the recent studies, we obtain the N/O ratio, {$q_{\rm
ion}$}, and O/H measurements by direct $T_{\rm e}$ methods with
{[O\,\textsc{iii}]} $\lambda$4363 and {O\,\textsc{iii}]} $\lambda$1665 lines.
Based on these reliable measurements, we find that there exist $z\sim 2$
galaxies with an excess of N/O falling beyond the local average of N/O--O/H
relation, while the majority of the $z\sim 2$ galaxies have the N/O ratios
nearly comparable with $z\sim 0$ galaxies in the N/O--stellar mass relation.
Our galaxies place the upper limit of N/O ratio $\log ({\rm N/O})\le -1.26$ on
average, suggesting that the N/O ratio evolves, if at all, by $<0.17$ dex.
Exploiting our reliable measurements free from the N/O--{$q_{\rm ion}$}--O/H
degeneracies, we identify, for the first time, that $z\sim 2$ galaxies with
offsets in the BPT diagram indicate either 1) only an N/O excess, 2) only a
{$q_{\rm ion}$} excess, or 3) both N/O and {$q_{\rm ion}$} excesses. We argue
that the BPT offsets at $z\sim 2$ are not made by one of 1)--3) galaxy
populations alone, but the composite of 1)--3) populations. We confirm that
these 1)--3) populations also exist at $z\sim 0$, such as GPs and SDSS low-mass
and high-SFR galaxies (LMHSs).
