We present secure [ N ii ] _ { 205 \mu m } detections in two mm-bright , strongly lensed objects at high redshift , APM 08279+5255 ( z =3.911 ) and MM 18423+5938 ( z =3.930 ) , using the IRAM Plateau de Bure Interferometer .
Due to its ionization energy [ N ii ] _ { 205 \mu m } is a good tracer of the ionized gas phase in the interstellar medium .
The measured fluxes are S ( [ N ii ] _ { 205 \mu m } ) = ( 4.8 \pm 0.8 ) Jy km s ^ { -1 } and ( 7.4 \pm 0.5 ) Jy km s ^ { -1 } respectively , yielding line luminosities of L ( [ N ii ] _ { 205 } ) = ( 1.8 \pm 0.3 ) \times 10 ^ { 9 } \mu ^ { -1 } L _ { \odot } for APM 08279+5255 and L ( [ N ii ] _ { 205 } ) = ( 2.8 \pm 0.2 ) \times 10 ^ { 9 } \mu ^ { -1 } L _ { \odot } for MM 18423+5938 .
Our high-resolution map of the [ N ii ] _ { 205 \mu m } and 1 mm continuum emission in MM 18423+5938 clearly resolves an Einstein ring in this source , and reveals a velocity gradient in the dynamics of the ionized gas .
A comparison of these maps with high-resolution EVLA CO observations enables us to perform the first spatially-resolved study of the dust continuum-to-molecular gas surface brightness ( \Sigma _ { FIR } \propto \Sigma _ { CO } ^ { N } , which can be interpreted as the star formation law ) in a high-redshift object .
We find a steep relation ( N = 1.4 \pm 0.2 ) , consistent with a starbursting environment .
We measure a [ N ii ] _ { 205 \mu m } /FIR luminosity ratio in APM 08279+5255 and MM 18423+5938 of 9.0 \times 10 ^ { -6 } and 5.8 \times 10 ^ { -6 } , respectively .
This is in agreement with the decrease of the [ N ii ] _ { 205 \mu m } /FIR ratio at high FIR luminosities observed in local galaxies .