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The observations of PSR J0952-0607 and the second object in GW190814 eventindicate the possible existence of supermassive neutron stars. In this work, byusing the Constant-Sound-Speed (CSS) parametrization to describe the equationof state (EOS) of quark matter, the constraints on the EOS parameters fromsupermassive hybrid stars are investigated through the Maxwell and Gibbsconstructions. It is shown that to support a supermassive hybrid star, a lowertransition energy density, a smaller energy density discontinuity and a highersound speed of quark matter are favored. For the constructed hybrid star EOSmodel, the maximum mass of the corresponding hybrid stars will not meet thelower mass limit of the second object in GW190814 if the energy densitydiscontinuity takes a value higher than $180~{\rm MeV~fm^{-3}}$. Moreover, itis confirmed that the supermassive neutron star observation can also rule outthe existence of twin stars as a supermassive hybrid star requires a relativelysmall energy density discontinuity. Finally, we give a rough estimate of thelower limit of the dimensionless tidal deformability of neutron stars whichranges from 2 to 3.

Implications of supermassive neutron stars for the form of the equation of state of hybrid stars