Modeling compact objects with quark matter and dark energy: A comparative study of the radial oscillation modes of HESS J1731-347 and PSR J0740+6620

We model the massive pulsar J0740+6620 and the light HESS J1731-347 compact object assuming (i) quark matter and (ii) dark energy stars. Within Einstein’s General Relativity, and assuming objects made of isotropic matter, we adopt analytic equations-of-state for both matter contents. Although the inner composition of the objects is very different in each case, both equations-of-state imply qualitatively very similar mass-to-radius relationships. We compute the spectra of radial equations for all four cases and the corresponding wave functions as well as the large frequency separations. A comparison between the different matter contents is made as well.