Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings

In Horndeski theories containing a scalar coupling with the Gauss-Bonnet (GB) curvature invariant RGB2, we study the existence and linear stability of neutron star (NS) solutions on a static and spherically symmetric background. For a scalar-GB coupling of the form αζ(φ)RGB2, where ζ is a function of the scalar field φ, the existence of linearly stable stars with a nontrivial scalar profile without instabilities puts an upper bound on the strength of the dimensionless coupling constant |α|. To realize maximum masses of NSs for a linear (or dilatonic) GB coupling αGBφRGB2 with typical nuclear equations of state, we obtain the theoretical upper limit |αGB|<0.7 km. This is tighter than those obtained by the observations of gravitational waves emitted from binaries containing NSs. We also incorporate cubic-order scalar derivative interactions, quartic derivative couplings with nonminimal couplings to a Ricci scalar besides the scalar-GB coupling, and show that NS solutions with a nontrivial scalar profile satisfying all the linear stability conditions are present for certain ranges of the coupling constants. In regularized four-dimensional Einstein-GB gravity obtained from a Kaluza-Klein reduction with an appropriate rescaling of the GB coupling constant, we find that NSs in this theory suffer from a strong coupling problem as well as Laplacian instability of even-parity perturbations. We also study NS solutions with a nontrivial scalar profile in power-law F(RGB2) models, and show that they are pathological in the interior of stars and plagued by ghost instability together with the asymptotic strong coupling problem in the exterior of stars.