  Our result is a construction of infinitely many radial self-similar implosion
profiles for the gravitational Euler-Poisson system. The problem can be
expressed as solving a system of non-autonomous non-linear ODEs. The first
rigorous existence result for a non-trivial solution to these ODEs is due to
Guo, Had\v{z}i\'c and Jang [Comm. Math. Phys. 386.3 (2021)], in which they
construct a solution found numerically by Larson and Penston independently
[Monthly Notices of the Royal Astronomical Society 145.3 (1969), Monthly
Notices of the Royal Astronomical Society 144.4 (1969)]. The solutions we
construct belong to a different regime and correspond to a strict subset of the
family of profiles discovered numerically by Hunter. Our proof adapts a
technique developed by Collot, Rapha\"el and Szeftel in [Mem. Amer. Math. Soc.
260.1255 (2019)], in which they study blowup for a family of
energy-supercritical focusing semilinear heat equations. In our case, the
quasilinearity presents complications, most severely near the sonic point where
the system degenerates.
