Continued Brightening of the Afterglow of GW170817/GRB 170817A as Being Due to a Delayed Energy Injection

The brightness of the multi-wavelength afterglow of GRB 170817A is increasing unexpectedly even $\sim$ 160 days after the associated gravitational burst. Here we suggest that the brightening can be caused by a late-time energy injection process. We use an empirical expression to mimic the evolution of the injection luminosity, which is consisted of a power-law rising phase and a power-law decreasing phase. It is found that the power-law indices of the two phases are $0.92$ and $-2.8$, respectively, with the peak time of the injection being $\sim 110$ days. The energy injection could be due to some kind of accretion, with the total accreted mass being $\sim 0.006 M_\odot$. However, normal fall-back accretion, which usually lasts for a much shorter period, cannot provide a natural explanation. Our best-fit decaying index of $-2.8$ is also at odds with the expected value of $-5/3$ for normal fall-back accretion. Noting that the expansion velocities of the kilonova components associated with GW170817 is $0.1-0.3\,c$, we argue that there should also be some ejecta with correspondingly lower velocities during the coalescence of the double neutron star system. They are bound by the gravitational well of the remnant central compact object and might be accreted at a timescale of about 100 days, providing a reasonable explanation for the energy injection. Detailed studies on the long-lasting brightening of GRB 170817A thus may provide useful information on the matter ejection during the merger process of binary neutron stars.