Abstract
We propose a geometrical explanation about neutron star (NS)-companion system
in order to explain the periodically and nonperiodicly repeating fast radio
bursts (FRBs). We propose that there is a critical binary separation $r_\rm
c$ under which the interaction between the NS and its companion can trigger
FRBs. If the maximum and minimum binary separation of elliptic orbit, i.e.,
$r_max$ and $r_min$, satisfy $r_max>r_c>r_min$,
the orbital motion of the binary can induce periodicly FRBs, and the
interaction between the NS and companion when they get close enough in their
elliptic orbit will result an active period of periodicly FRBs. If the maximum
binary separation $r_max<r_c$, the modulation of orbital motion
will not work since the interaction is always there, such that a repeating FRB
can be nonperiodic.
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