  Astrophysical observations show complex organic molecules (COMs) in the gas
phase of protoplanetary disks. X-rays emitted from the central young stellar
object (YSO) that irradiate interstellar ices in the disk, followed by the
ejection of molecules in the gas phase, are a possible route to explain the
abundances observed in the cold regions. This process, known as X-ray
photodesorption, needs to be quantified for methanol-containing ices. We aim at
experimentally measuring X-ray photodesorption yields of methanol and its
photo-products from binary mixed ices: $^{13}$CO:CH$_3$OH ice and
H$_2$O:CH$_3$OH ice. We irradiated these ices at 15 K with X-rays in the 525 -
570 eV range. The release of species in the gas phase was monitored by
quadrupole mass spectrometry, and photodesorption yields were derived. For
$^{13}$CO:CH$_3$OH ice, CH$_3$OH X-ray photodesorption yield is estimated to be
10$^{-2}$ molecule/photon at 564 eV. X-ray photodesorption of larger COMs,
which can be attributed to either ethanol, dimethyl ether, and/or formic acid,
is detected with a yield of 10$^{-3}$ molecule/photon. When methanol is mixed
with water, X-ray photodesorption of methanol and of the previous COMs is not
detected. X-ray induced chemistry, dominated by low-energy secondary electrons,
is found to be the main mechanism that explains these results. We also provide
desorption yields that are applicable to protoplanetary disk environments for
astrochemical models. The X-ray emission from YSOs should participate in the
enrichment of the protoplanetary disk gas phase with COMs such as methanol in
the cold and X-ray dominated regions because of X-ray photodesorption from
methanol-containing ices.
