Probing the formation of planetesimals in the Galactic Centre using Sgr
  A* flares
  Flares in X-ray and near infrared are observed above the quiescent emission
of the supermassive black hole (SBH) in the Galactic Centre (GC) at a rate of
approximately once per day. One proposed energy source for these flares is the
tidal disruption of planetesimals with radius $\gtrsim 10$ km passing within
$\sim$ 1 AU of the SBH. Very little is known about the formation and evolution
of planetesimals in galactic nuclei such as the GC, making predictions for
flaring event rates uncertain. We explore two scenarios for the formation of
planetesimals in the GC: (1) in a large-scale cloud bound to the SBH, and (2)
in debris discs around stars. We model their orbital evolution around the SBH
using the Fokker-Planck equation and investigate the effect of gravitational
interactions with various relevant perturbers. Our predicted flaring rate,
$\approx 0.6 \, \mathrm{day^{-1}}$, is nearly independent of the distribution
of perturbers. Moreover, it is insensitive to scenarios (1) or (2). The assumed
number of planetesimals per star is consistent with debris discs around stars
in the Solar neighbourhood. In scenario (1) this implies that the number of
planetesimals formed in the large-scale cloud is strongly correlated with the
number of stars, and this requires finetuning for our results to be consistent
with the observed flaring rate. We favour the alternative explanation that
planetesimals in the GC are formed in debris discs around stars, similar to the
Solar neighbourhood.
