On the fallback disk around the slowest isolated pulsar, 1E 161348$-$5055

The central compact object 1E 161348$-$5055 in the supernova remnant RCW 103 has a spin period $\sim 6.67$ hr, making it the slowest isolated pulsar. It is believed that a supernova fallback disk is required to spin down the neutron star to the current spin period within a few $10^3$ yr. The mass of the fallback disk around newborn neutron stars can provide useful information on the supernova processes and the possible detection limit with optical/infrared observations. However, it is controversial how massive the disk is in the case of 1E 161348$-$5055. In this work we simulate the spin evolution of a magnetar that is driven by the interaction between the disk and the star's magnetic field. Compared with previous studies, we take into account various critical conditions that affect the formation and evolution of the fallback disk. Our calculation shows that we can reproduce the extremely slow spin of 1E 161348$-$5055 when taking the initial disk mass $M_{\rm d} \sim 10^{-7} M_{\odot}$ and the neutron star magnetic field $B\geq 5 \times 10^{15}$ G. This implies that 1E 161348$-$5055 may be a magnetar with very special initial parameters. However, if future observations reveal more objects like 1E 161348$-$5055, then stringent constraints can be obtained on the supernova fallback.