We report the detection of 158 micron [CII] fine-structure line emission from MIPS J142824.0+352619, a hyperluminous (L_IR ~ 10^13 L_sun) starburst galaxy at z=1.3. The line is bright, and corresponds to a fraction L_[CII]/L_FIR = 2 x 10^-3 of the far-IR (FIR) continuum. The [CII], CO, and FIR continuum emission may be modeled as arising from photodissociation regions (PDRs) that have a characteristic gas density of n ~ 10^4.2 cm^-3, and that are illuminated by a far-UV radiation field ~10^3.2 times more intense than the local interstellar radiation field. The mass in these PDRs accounts for approximately half of the molecular gas mass in this galaxy. The L_[CII]/L_FIR ratio is higher than observed in local ULIRGs or in the few high-redshift QSOs detected in [CII], but the L_[CII]/L_FIR and L_CO/L_FIR ratios are similar to the values seen in nearby starburst galaxies. This suggests that MIPS J142824.0+352619 is a scaled-up version of a starburst nucleus, with the burst extended over several kiloparsecs.
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