  Pulsar timing arrays (PTA) are a promising probe to the cosmologically novel
nanohertz gravitational wave (GW) regime through the stochastic GW background.
In this work, we consider subluminal GW modes as a possible source of
correlations in a PTA, utilizing the public code PTAfast and the 12.5 years
correlations data by NANOGrav, which we hypothesize are sourced by GWs. Our
results show no evidence in support of tensor- or vector-induced GW
correlations in the data, and that vector correlations are disfavored. This
places an upper bound to the graviton mass, $m_{\rm g} \lesssim 10^{-22}$ eV,
characteristic of the PTA GW energy scale.
