Deuterium fractionation is known to enhance the [DCO+]/[HCO+] abundance ratio over the D/H elemental ratio of about 1e-5 in the cold and dense gas typically found in pre-stellar cores. We report the first detection and mapping of very bright DCO+ J=3-2 and J=2-1 lines (3 and 4 K respectively) towards the Horsehead photodissociation region (PDR) observed with the IRAM-30m telescope. The DCO+ emission peaks close to the illuminated warm edge of the nebula (< 50 or about 0.1 pc away). Detailed nonlocal, non-LTE excitation and radiative transfer analyses have been used to determine the prevailing physical conditions and to estimate the DCO+ and H13CO+ abundances from their line intensities. A large [DCO+]/[HCO+] abundance ratio (>= 0.02) is inferred at the DCO+ emission peak, a condensation shielded from the illuminating far-UV radiation field where the gas must be cold (10-20 K) and dense (>= 2x10^5 cm-3). DCO+ is not detected in the warmer photodissociation front, implying a lower [DCO+]/[HCO+] ratio (< 1e-3). According to our gas phase chemical predictions, such a high deuterium fractionation of HCO+ can only be explained if the gas temperature is below 20 K, in good agreement with DCO+ excitation calculations.
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