We revisit the flip-flop instability of two-dimensional planar accretion using high-fidelity numerical simulations .
By starting from an initially steady-state axisymmetric solution , we are able to follow the growth of this overstability from small amplitudes .
In the small-amplitude limit , before any transient accretion disk is formed , the oscillation period of the accretion shock is comparable to the Keplerian period at the Hoyle-Lyttleton accretion radius ( R _ { a } ) , independent of the size of the accreting object .
The growth rate of the overstability increases dramatically with decreasing size of the accretor , but is relatively insensitive to the upstream Mach number of the flow .
We confirm that the flip-flop does not require any gradient in the upstream flow .
Indeed , a small density gradient as used in the discovery simulations has virtually no influence on the growth rate of the overstability .
The ratio of specific heats does influence the overstability , with smaller \gamma leading to faster growth of the instability .
For a relatively large accretor ( a radius of 0.037 R _ { a } ) planar accretion is unstable for \gamma = 4 / 3 , but stable for \gamma \geq 1.6 .
Planar accretion is unstable even for \gamma = 5 / 3 provided the accretor has a radius of < 0.0025 R _ { a } .
We also confirm that when the accretor is sufficiently small , the secular evolution is described by sudden jumps between states with counter-rotating quasi-Keplerian accretion disks .