ALMA [NII] 205 micron Imaging Spectroscopy of the Interacting Galaxy
  System BRI 1202-0725 at Redshift 4.7
  We present the results from Atacama Large Millimeter/submillimeter Array
(ALMA) imaging in the [NII] 205 micron fine-structure line (hereafter [NII])
and the underlying continuum of BRI 1202-0725, an interacting galaxy system at
$z =$ 4.7, consisting of an optical QSO, a sub-millimeter galaxy (SMG) and two
Lyman-$\alpha$ emitters (LAEs), all within $\sim$25 kpc of the QSO. We detect
the QSO and SMG in both [NII] and continuum. At the $\sim$$1"$ (or 6.6 kpc)
resolution, both QSO and SMG are resolved in [NII], with the de-convolved major
axes of $\sim$9 and $\sim$14 kpc, respectively. In contrast, their continuum
emissions are much more compact and unresolved even at an enhanced resolution
of $\sim$$0.7"$. The ratio of the [NII] flux to the existing CO (7$-$6) flux is
used to constrain the dust temperature ($T_{\rm dust}$) for a more accurate
determination of the FIR luminosity $L_{\rm FIR}$. Our best estimated $T_{\rm
dust}$ equals $43 (\pm 2)$ K for both galaxies (assuming an emissivity index
$\beta = 1.8$). The resulting $L_{\rm CO(7-6)}/L_{\rm FIR}$ ratios are
statistically consistent with that of local luminous infrared galaxies,
confirming that $L_{\rm CO(7-6)}$ traces the star formation (SF) rate (SFR) in
these galaxies. We estimate that the on-going SF of the QSO (SMG) has a SFR of
5.1 $(6.9) \times 10^3 M_{\odot}$ yr$^{-1}$ ($\pm$ 30%) assuming Chabrier
initial mass function, takes place within a diameter (at half maximum) of 1.3
(1.5) kpc, and shall consume the existing 5 $(5) \times 10^{11} M_{\odot}$ of
molecular gas in 10 $(7) \times 10^7$ years.
