Context :

Aims : For the first time we investigate the role of the grain surface chemistry in the Horsehead Photo-dissociation region ( PDR ) .

Methods : We performed deep observations of several \text { H } _ { 2 } \text { CO } rotational lines toward the PDR and its associated dense-core in the Horsehead nebula , where the dust is cold ( T _ { \mathrm { dust } } \simeq 20 - 30 K ) .
We complemented these observations with a map of the \text { p - H } _ { 2 } \text { CO } ~ { } 3 _ { 03 } -2 _ { 02 } line at 218.2 GHz ( with 12 ” angular resolution ) .
We determine the \text { H } _ { 2 } \text { CO } abundances using a detailed radiative transfer analysis and compare these results with PDR models that include either pure gas-phase chemistry or both gas-phase and grain surface chemistry .

Results : The \text { H } _ { 2 } \text { CO } abundances ( \simeq 2 - 3 \times 10 ^ { -10 } ) with respect to H-nuclei are similar in the PDR and dense-core .
In the dense-core the pure gas-phase chemistry model reproduces the observed \text { H } _ { 2 } \text { CO } abundance .
Thus , surface processes do not contribute significantly to the gas-phase \text { H } _ { 2 } \text { CO } abundance in the core .
In contrast , the formation of \text { H } _ { 2 } \text { CO } on the surface of dust grains and subsequent photo-desorption into the gas-phase are needed in the PDR to explain the observed gas-phase \text { H } _ { 2 } \text { CO } abundance , because the gas-phase chemistry alone does not produce enough \text { H } _ { 2 } \text { CO } .
The assignments of different formation routes are strengthen by the different measured ortho-to-para ratio of \text { H } _ { 2 } \text { CO } : the dense-core displays the equilibrium value ( \sim 3 ) while the PDR displays an out-of-equilibrium value ( \sim 2 ) .

Conclusions : Photo-desorption of \text { H } _ { 2 } \text { CO } ices is an efficient mechanism to release a significant amount of gas-phase \text { H } _ { 2 } \text { CO } into the Horsehead PDR .