  We study self-gravitating stars in the bootstrapped Newtonian picture for
polytropic equations of state. We consider stars that span a wide range of
compactness values. Both matter density and pressure are sources of the
gravitational potential. Numerical solutions show that the density profiles can
be well approximated by Gaussian functions. Later we assume Gaussian density
profiles to investigate the interplay between the compactness of the source,
the width of the Gaussian density profile and the polytropic index. We also
dedicate a section to comparing the pressure and density profiles of the
bootstrapped Newtonian stars to the corresponding General Relativistic
solutions. We also point out that no Buchdahl limit is found, which means that
the pressure can in principle support a star of arbitrarily large compactness.
In fact, we find solutions representing polytropic stars with compactness above
the Buchdhal limit.
