2013ApJ...769..119X

We report our search for γ-ray emission in the energy range from 100 MeV to 300 GeV from four accreting millisecond pulsars (AMPs), SAX J1808.4-3658, IGR J00291+5934, XTE J1814-338, and XTE J0929-314. The data are from four-year observations carried out by the Large Area Telescope on board the Fermi Gamma-Ray Space Telescope. The AMPs were not detected, and the γ-ray luminosity upper limits we obtain are 5.1x10³³ erg/s for SAX J1808.4-3658, 2.1 x10³³ erg/s for IGR J00291+5934, 1.2x10³⁴ erg/s for XTE J1814-338, and 2.2x10³³ erg/s for XTE J0929-314. We compare our results with γ-ray irradiation luminosities required for producing optical modulations seen from the companions in the AMPs, which has been suggested by Takata et al., and our upper limits have excluded γ-ray emission as the heating source in these systems except XTE J0929-314, the upper limit of which is not deep enough. Our results also do not support the model proposed by Takata et al. that relatively strong γ-ray emission could arise from the outer gap of a high-mass neutron star controlled by the photon-photon pair creation for the AMPs. Two AMPs, SAX J1808.4-3658 and IGR J00291+5934, have measurements of their spin-down rates, and we derive the upper limits of their γ-ray conversion efficiencies, which are 57% and 3%, respectively. We discuss the implications to the AMP systems by comparing the efficiency upper limit values with that of 20 γ-ray millisecond pulsars (MSP) detected by Fermi and the newly discovered transitional MSP binary J1023+0038.