Recently, it discovered two ultra-long period radio transients GLEAM-X
J162759.5-523504.3 (J1627) and GPM J1839β10 (J1839) with spin periods longer
than 1000 s. The origin of these two ultra-long period radio transients is
intriguing in understanding the spin evolution of neutron stars (NSs). In this
work, we diagnose whether the interaction between strong magnetized NSs and
fallback disks can spin NSs down to the observed ultra-long period. Our
simulations found that the magnetar+fallback disk model can account for the
observed period, period derivative, and X-ray luminosity of J1627 in the
quasi-spin-equilibrium stage. To evolve to the current state of J1627, the
initial mass-accretion rate of the fallback disk and the magnetic field of the
NS are in the range of (1.1β30)Γ1024Β gsβ1 and
(2β5)Γ1014Β G, respectively. In an active lifetime of fallback
disk, J1839 is impossible to achieve the observed upper limit of period
derivative. Therefore, we propose that J1839 may be in the second ejector phase
after the fallback disk becomes inactive. Those NSs with a magnetic field of
(2β6)Γ1014Β G and a fallback disk with an initial mass-accretion
rate of βΌ1024β1026Β gsβ1 are the possible progenitors of
J1839.Comment: 12 pages, 10 figures, ApJ in pres