Hyperbolic components and cubic polynomials

In the space of cubic polynomials, Milnor defined a notable curve $\mathcal S_p$, consisting of cubic polynomials with a periodic critical point, whose period is exactly $p$. In this paper, we show that for any integer $p\ge 1$, any bounded hyperbolic component on ${\mathcal{S}}_p$ is a Jordan disk.