The subalgebra of the tautological ring of the moduli of curves of compact type generated by the κ classes is studied in all genera. Relations, constructed via the virtual geometry of the moduli of stable quotients, are used to obtain minimal sets of generators. Bases and Betti numbers of the κ rings are computed. A universality property relating the higher genus κ rings to the genus 0 rings is proven using the virtual geometry of the moduli space of stable maps. The λ_g-formula for Hodge integrals arises as the simplest consequence.