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Neutron stars (NSs) in scalar-tensor theories of gravitation with thephenomenon of spontaneous scalarization can develop significant deviations fromgeneral relativity. Cases with a massless scalar were studied widely. Here wecompare the NS scalarizations in the Damour--Esposito-Far{\`e}se theory, theMendes-Ortiz theory, and the $\xi$-theory with a massive scalar field.Numerical solutions for slowly rotating NSs are obtained. They are used toconstruct the X-ray pulse profiles of a pair of extended hot spots on thesurface of NSs. We also calculate the tidal deformability for NSs withspontaneous scalarization which is done for the first time with a massivescalar field. We show the universal relation between the moment of inertia andthe tidal deformability. The X-ray pulse profiles, the tidal deformability, andthe universal relation may help to constrain the massive scalar-tensor theoriesin X-ray and gravitational-wave observations of NSs, including the Neutron starInterior Composition Explorer (NICER) satellite, Square Kilometre Array (SKA)telescope, and LIGO/Virgo/KAGRA laser interferometers.

Scalarized neutron stars in massive scalar-tensor gravity: X-ray pulsars and tidal deformability