Big Three Dragons: A [N II] 122 $\mu$m Constraint and New Dust-continuum
  Detection of A $z = 7.15$ Bright Lyman Break Galaxy with ALMA
  We present new Atacama Large Millimeter/submillimeter Array Band 7
observational results of a Lyman break galaxy at $ z=7.15 $, B14-65666 ("Big
Three Dragons"), which is an object detected in [OIII] 88 $\rm{\mu m}$, [CII]
158 $\rm{\mu m}$, and dust-continuum emission during the epoch of reionization.
Our targets are the [NII] 122 $\rm{\mu m}$ fine-structure emission line and
underlying 120 $\rm{\mu m}$ dust continuum. The dust continuum is detected with
a $ \sim $19$ \sigma $ significance. From far-infrared spectral energy
distribution sampled at 90, 120, and 160 $\rm{\mu m}$, we obtaine a best-fit
dust temperature of $ 40 $ K ($ 79 $ K) and an infrared luminosity of $
\log_{10}(L_{\rm IR}/{\rm L}_\odot)=11.6$ ($12.1$) at the emissivity index $
\beta = 2.0 $ (1.0). The [NII] 122 $\rm{\mu m}$ line is not detected. The 3$
\sigma $ upper limit of the [NII] luminosity is $ 8.1 \times 10^7\ {\rm
L}_\odot$. From the [NII], [OIII], and [CII] line luminosities, we use the
Cloudy photoionization code to estimate nebular parameters as functions of
metallicity. If the metallicity of the galaxy is high ($ Z > 0.4\ {\rm
Z}_\odot$), the ionization parameter and hydrogen density are $ \log_{10} U
\simeq -2.7\pm0.1$ and $ n_\text{H} \simeq 50$-$250\ {\rm cm}^{-3}$,
respectively, which are comparable to those measured in low-redshift galaxies.
The nitrogen-to-oxygen abundance ratio, $\rm{N/O}$, is constrained to be
sub-solar. At $ Z < 0.4\ {\rm Z}_\odot$, the allowed $ U $ drastically
increases as the assumed metallicity decreases. For high ionization parameters,
the $\rm{N/O}$ constraint becomes weak. Finally, our Cloudy models predict the
location of B14-65666 on the BPT diagram, thereby allowing a comparison with
low-redshift galaxies.
