Correlations between nuclear incompressibility, liquid-gas critical point, and quarkyonic transition

We systematically probe different parametrizations of the attractive nuclear force based on real gas models to construct the nuclear matter equation of state. In each of the cases, the repulsion between nucleons is treated in the framework of excluded volume, and interaction parameters are fitted to the empirical properties of the nuclear ground state. We calculate the critical temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>T</a:mi><a:mi>c</a:mi></a:msub></a:math> and critical particle number density <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>n</b:mi><b:mi>c</b:mi></b:msub></b:math>, and find that they are strongly correlated. Both are also correlated with the incompressibility <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>K</c:mi><c:mn>0</c:mn></c:msub></c:math> in the nuclear ground state. We also include a quarkyonic matter phase in the quasiparticle description and investigate the relationships among <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>K</d:mi><d:mn>0</d:mn></d:msub></d:math>, transition density to the quarkyonic phase, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>n</e:mi><e:mi>tr</e:mi></e:msub></e:math>, and corresponding peak in the speed of sound, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msubsup><f:mi>v</f:mi><f:mrow><f:mi>s</f:mi><f:mo>,</f:mo><f:mi>max</f:mi></f:mrow><f:mn>2</f:mn></f:msubsup></f:math>. At each density, the quark fraction is found by minimizing the energy density. We find that both <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>n</g:mi><g:mi>tr</g:mi></g:msub></g:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msubsup><h:mi>v</h:mi><h:mrow><h:mi>s</h:mi><h:mo>,</h:mo><h:mi>max</h:mi></h:mrow><h:mn>2</h:mn></h:msubsup></h:math> are negatively correlated with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>K</i:mi><i:mn>0</i:mn></i:msub><i:mo>,</i:mo><i:mo> </i:mo><i:msub><i:mi>n</i:mi><i:mi>c</i:mi></i:msub></i:math>, and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>T</j:mi><j:mi>c</j:mi></j:msub></j:math>.