Cosmic-ray melt windows in interstellar ice make a four-carbon ketose but not the sugar pattern of G+0.693-0.027
Erythrulose (ERU), a four-carbon (C4) ketose, is reported towards the Galactic-centre cloud G+0.693-0.027 at a column density comparable to that of glycolaldehyde (GA), while the three-carbon (C3) sugars are not detected. We test whether melt windows opened in interstellar ice by cosmic-ray heavy ions can reproduce this pattern, with each rate fixed to a published value where available. A track model for eleven cosmic-ray nuclei determines the rate and duration of the liquid windows and the energy deposited inside and outside the melts. A radical network including C1 radicals from formaldehyde and methanol follows the inventory through repeated events. Radiolysis between events uses measured half-life doses of organics in cold ice. Hydrated GA opens a channel that preferentially forms the C4 ketose, so the melt-window chemistry can account for the ketose identity of ERU, although cold surface chemistry also yields it. The overall pattern, however, is not reproduced. The C1 radicals add one carbon at a time: dihydroxyacetone is at 15 times its limit when ERU/GA reaches the observed value. The ions deposit 0.41 eV per molecule per event outside the melts, which destroys the sugars between events; the ratio is reached only for half-life doses above 1000 eV, against measured values below 5 eV. The exposure is less certain: 2940 whole-grain melting events, 65 Myr at an ionisation rate $ζ=10^{-14}$ s$^{-1}$. Within 7 Myr it needs $ζ\gtrsim9.3\times10^{-14}$ s$^{-1}$, 9.3 times the dense-gas limit in the Central Molecular Zone, or $5.8\times10^{-15}$ s$^{-1}$ if the trapped radicals recombine. With standard assumptions the sugars of G+0.693 are not made in cosmic-ray melt windows. The pattern would need C1 radicals that do not add to the sugar radicals, sugars that survive the solid-phase dose and a local source of MeV ions with $ζ\gtrsim2\times10^{-13}$ s$^{-1}$.