  For distinct odd primes $p$ and $q$, we define the Catalan curve $C_{p,q}$ by
the affine equation $y^q=x^p-1$. In this article we construct the Sato-Tate
groups of the Jacobians in order to study the limiting distributions of
coefficients of their normalized L-polynomials.Catalan Jacobians are
nondegenerate and simple with noncyclic Galois groups (of the endomorphism
fields over $\mathbb Q$), thus making them interesting varieties to study in
the context of Sato-Tate groups. We compute both statistical and numerical
moments for the limiting distributions. Lastly, we determine the Galois
endomorphism types of the Jacobians using both old and new techniques.
