Neutron stars in scalar-tensor theories: Analytic scalar charges and universal relations

Neutron stars are ideal astrophysical sources to probe general relativity due their large compactnesses and strong gravitational fields. For example, binary pulsar wave observations have placed stringent bounds on certain scalar-tensor theories in which a massless scalar field is coupled the metric through matter. A remarkable phenomenon of neutron such spontaneous scalarization, where normalized charge remains order unity even if matter-scalar coupling vanishes asymptotically far from star. While most works scalarization focus numerical analysis, this paper aims derive accurate charges analytically. To achieve this, we consider simple energy density profile Tolman VII form work weak-field expansion. We solve modified Tolman-Oppenheimer-Volkoff equations by apply Pad\'e resummation account for higher-order effects. find that our analytic terms stellar compactness beautifully model those computed numerically. also quasi-universal relation between binding insensitive underlying state. Comparison constant mathematically support relation. The results found here provide physically motivated, ready-to-use expressions charges.