Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are
magnetar candidates, i.e., neutron stars powered by strong magnetic field. If
they are indeed magnetars, they will emit high-energy gamma-rays which are
detectable by Fermi-LAT according to the outer gap model. However, no
significant detection is reported in recent Fermi-LAT observations of all known
AXPs and SGRs. Considering the discrepancy between theory and observations, we
calculate the theoretical spectra for all AXPs and SGRs with sufficient
observational parameters. Our results show that most AXPs and SGRs are
high-energy gamma-ray emitters if they are really magnetars. The four AXPs 1E
1547.0-5408, XTE J1810-197, 1E 1048.1-5937, and 4U 0142+61 should have been
detected by Fermi-LAT. Then there is conflict between out gap model in the case
of magnetars and Fermi observations. Possible explanations in the magnetar
model are discussed. On the other hand, if AXPs and SGRs are fallback disk
systems, i.e., accretion-powered for the persistent emissions, most of them are
not high-energy gamma-ray emitters. Future deep Fermi-LAT observations of AXPs
and SGRs will help us make clear whether they are magnetars or fallback disk
systems.Comment: 15 pages, 3 figures, 1 table, accepted for publication in The
Astrophysical Journa
