  The Witten-Kontsevich theorem states that a certain generating function for
intersection numbers on the moduli space of stable curves is a tau-function for
the KdV integrable hierarchy. This generating function can be recovered via the
topological recursion applied to the Airy curve $x=\frac{1}{2}y^2$. In this
paper, we consider the topological recursion applied to the irregular spectral
curve $xy^2=\frac{1}{2}$, which we call the Bessel curve. We prove that the
associated partition function is also a KdV tau-function, which satisfies
Virasoro constraints, a cut-and-join type recursion, and a quantum curve
equation. Together, the Airy and Bessel curves govern the local behaviour of
all spectral curves with simple branch points.
