We present the results from Atacama Large Millimeter/submillimeter Array ( ALMA ) imaging in the [ N ii ] 205 \mu { m } fine-structure line ( hereafter [ N ii ] ) 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 [ N ii ] and continuum .
At the \sim 1″ ( or 6.6 kpc ) resolution , both QSO and SMG are resolved in [ N ii ] , 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 [ N ii ] flux to the existing CO ( 7 - 6 ) flux is used to constrain the dust temperature ( T _ { dust } ) for a more accurate determination of the FIR luminosity L _ { FIR } .
Our best estimated T _ { dust } equals 43 ( \pm 2 ) K for both galaxies ( assuming an emissivity index \beta = 1.8 ) .
The resulting L _ { CO ( 7 - 6 ) } / L _ { FIR } ratios are statistically consistent with that of local luminous infrared galaxies , confirming that L _ { 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 .