We present secure [N ii ] 205 μm detections in two millimeter-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 μm is a good tracer of the ionized gas phase in the interstellar medium. The measured fluxes are S ([N ii ] 205 μm ) = (4.8 ± 0.8) Jy km s −1 and (7.4 ± 0.5) Jy km s −1 , respectively, yielding line luminosities of L ([N ii ] 205 μm ) = (1.8 ± 0.3) × 10 9 μ −1 L ☉ for APM 08279+5255 and L ([N ii ] 205 μm ) = (2.8 ± 0.2) × 10 9 μ −1 L ☉ for MM 18423+5938. Our high-resolution map of the [N ii ] 205 μm 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 (Σ FIR ∝Σ N CO , which can be interpreted as the star formation law) in a high-redshift object. We find a steep relation ( N = 1.4 ± 0.2), consistent with a starbursting environment. We measure a [N ii ] 205 μm /FIR luminosity ratio in APM 08279+5255 and MM 18423+5938 of 9.0 × 10 −6 and 5.8 × 10 −6 , respectively. This is in agreement with the decrease of the [N ii ] 205 μm /FIR ratio at high FIR luminosities observed in local galaxies.
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