  We introduce the moduli stack of pointed curves equipped with effective
$r$-spin structures: these are effective divisors $D$ such that $rD$ is a
canonical divisor modified at marked points. We prove that this moduli space is
smooth and compute its dimension. We also prove that it always contains a
component that projects birationally to the locus $S^0$ in the moduli space of
$r$-spin curves consisting of $r$-spin structures $L$ such that $h^0(L)\neq 0$.
Finally, we study the relation between the locus $S^0$ and Witten's virtual top
Chern class.
