Core EoS vs. Total EoS including quarks missmatch

Hello everyone,

We are finding some strange behaviour for the equation of state when including quarks. Other than our previous question regarding the Gibbs construction, using simply the Maxwell construction in the core yields the yellow points on this pressure vs baryon density plot.

Those look quite normal, with the expected discontinuity. However, when we go forward and perform the remaining two syntheses (cust+ChEFT and that with core) using the hyperbolic tangent method, we find the blue points.

Those represent the final equation of state data of pressure and, as you can see, at large pressure, they go above the data of the quark phase. We’re performing the final synthesis at nB = 0.23, with a gamma of 0.02, so it should be narrow enough such that at nB=0.5 the curve should strictly follow the core behaviour of the yellow points.

Are we missing something regarding how the synthesis module works for the quark case? How is it possible it reaches a larger value of pressure at the very centre than what is predicted by the quark EOS? It seems as if the hadronic phase had been extrapolated somehow.

We checked, by the way, that this strange behaviour is not present when quarks are not included: in the EOS we created with Octet/Decuplet, the final EOS correctly follows the Core EOS after the final synthesis.

Thanks very much in advance,

Federico and Fernando

HI, I’m tagging @mrpelicer who I’m sure will get back to you soon (although he’s sick at the moment so I ask for your patience). Also, @cnc6 may have some insights in the meantime.

Hi Federico,

To be honest, we haven’t tried matching the EOS smoothly after having a first order phase transition, as this would smooth out the discontinuity – like you are seeing.

In which variable are you matching the EOSs? I think each Y(x) case would have its own problems in matching with a phase transition.