SIMBAD references

We propose a geometrical explanation for periodically and non-periodically repeating fast radio bursts (FRBs) under neutron star (NS)-companion systems. We suggest a constant critical binary separation, r_c, within which the interaction between the NS and companion can trigger FRBs. For an elliptic orbit with the minimum and maximum binary separations, r_min and r_max, a periodically repeating FRB with an active period could be reproduced if r_min < r_c < r_max. However, if r_max < r_c, the modulation of orbital motion will not work due to persistent interaction, and this kind of repeating FRBs should be non-periodic. We test relevant NS-companion binary scenarios on the basis of FRB 180916.J0158+65 and FRB 121102 under this geometrical frame. It is found that the pulsar-asteroid belt impact model is more suitable to explain these two FRBs since this model is compatible with different companions (e.g. massive stars and black holes). At last, we point out that FRB 121102-like samples are potential objects that can reveal the evolution of star-forming region.