Physical Constraints on the Extended Interstellar Medium of the z=6.42 Quasar J1148+5251: [C II](158 mu m), [N II](205 mu m), and [O I](146 mu m) Observations

We report new Northern Extended Millimeter Array observations of the [C II](158 mu m), [N II](205 mu m), and [O I](146 mu m) atomic fine structure lines (FSLs) and dust continuum emission of J1148+5251, a z = 6.42 quasar, which probe the physical properties of its interstellar medium (ISM). The radially averaged [C II](158 mu m) and dust continuum emission have similar extensions (up to theta = 2.51(-0.25)(+0.46) arcsec, corresponding to r = 9.8(-2.1)(+3.3) kpc, accounting for beam convolution), confirming that J1148+5251 is the quasar with the largest [C II](158 mu m)-emitting reservoir known at these epochs. Moreover, if the [C II](158 mu m), emission is examined only along its NE-SW axis, a significant excess (>5.8 sigma) of [C II](158 mu m) emission (with respect to the dust) is detected. The new wide-bandwidth observations enable us to accurately constrain the continuum emission, and do not statistically require the presence of broad [C II](158 mu m) line wings that were reported in previous studies. We also report the first detection of the [O I](146 mu m) and (tentatively) [N II](205 mu m) emission lines in J1148+5251. Using FSL ratios of the [C II](158 mu m), [N II](205 mu m), [O I](146 mu m), and previously measured [C II](369 mu m) emission lines, we show that J1148+5251 has similar ISM conditions compared to lower-redshift (ultra)luminous infrared galaxies. CLOUDY modeling of the FSL ratios excludes X-ray-dominated regions and favors photodissociation regions as the origin of the FSL emission. We find that a high radiation field (10(3.5-4.5) G(0)), a high gas density (n similar or equal to 10(3.5-4.5) cm(-3)), and an H I column density of 10(23) cm(-2) reproduce the observed FSL ratios well.