Linking ice and gas in the lambda Orionis Barnard 35A cloud

Dust grains play an important role in the synthesis of molecules in the interstellar medium, from the simplest species to complex organic molecules. How some of these solid-state molecules are converted into gas-phase species is still a matter of debate. Our aim is to directly compare ice and gas abundances of methanol (CH$_3$OH) and CO, and to investigate the relationship between ice and gas in low-mass protostellar envelopes. We present Submillimeter Array and Atacama Pathfinder EXperiment observations of gas-phase CH$_3$OH and CO towards the multiple protostellar system IRAS05417+0907 located in the B35A cloud. We use archival AKARI ice data toward the same target to calculate CH$_3$OH and CO gas-to-ice ratios. The CO isotopologues emissions are extended, whereas the CH$_3$OH emission is compact and traces the giant outflow emanating from IRAS05417+0907. A discrepancy between submillimeter dust emission and H$_2$O ice column density is found for B35A$-$4 and B35A$-$5, similar to what has previously been reported. B35A$-$2 and B35A$-$3 are located where the submillimeter dust emission peaks and show H$_2$O column densities lower than for B35A$-$4. The difference between the submillimeter continuum emission and the infrared H$_2$O ice observations suggests that the distributions of dust and H$_2$O ice differ around the young stellar objects in this dense cloud. The reason for this may be that the sources are located in different environments resolved by the interferometric observations: B35A$-$2, B35A$-$3 and in particular B35A$-$5 are situated in a shocked region plausibly affected by sputtering and heating impacting the submillimeter dust emission pattern, while B35A$-$4 is situated in a more quiescent part of the cloud. Gas and ice maps are essential to connect small-scale variations in the ice composition with large-scale astrophysical phenomena probed by gas observations.