Compactified Jacobians of N\'eron type

We characterize stable curves $X$ whose compactified degree-$d$ Jacobian is of N'eron type. This means the following: for any one-parameter regular smoothing of $X$, the special fiber of the N'eron model of the Jacobian of the generic fiber is isomorphic to a dense open subset of the degree-$d$ compactified Jacobian. It is well known that compactified Jacobians of N'eron type have the best modular properties, and that they are endowed with a mapping property useful for applications.