Probing the nonstrange quark star equation of state with compact stars and gravitational waves

A recent study shows that incorporating a new term into the thermodynamic potential density, as required by the thermodynamic consistency criterion, can effectively resolve the thermodynamic inconsistency problems of the conventional perturbative QCD model. This additional term plays a crucial role in resolving inconsistencies at relatively low densities and becomes negligible at extremely high densities. Within this revised perturbative QCD model, we find that if we require only that the energy per baryon of up-down ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>u</a:mi> <a:mi>d</a:mi> </a:math> ) quark matter exceeds 930 MeV so as not to contradict the standard nuclear physics, the maximum mass of an <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>u</c:mi> <c:mi>d</c:mi> </c:math> quark star allowed by the revised perturbative QCD model can reach up to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>2.17</e:mn> <e:msub> <e:mi>M</e:mi> <e:mo stretchy="false">⊙</e:mo> </e:msub> </e:math> . From this perspective, the observed <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mn>2.14</h:mn> <h:msub> <h:mi>M</h:mi> <h:mo stretchy="false">⊙</h:mo> </h:msub> </h:math> pulsar PSR <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi mathvariant="normal">J</k:mi> <k:mn>0740</k:mn> <k:mo>+</k:mo> <k:mn>6620</k:mn> </k:mrow> </k:math> may be an <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>u</n:mi> <n:mi>d</n:mi> </n:math> quark star. However, if we further impose the constraint that the tidal deformability of a <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mn>1.4</p:mn> <p:msub> <p:mi>M</p:mi> <p:mo stretchy="false">⊙</p:mo> </p:msub> </p:math> <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>u</s:mi> <s:mi>d</s:mi> </s:math> quark star must be consistent with the GW170817 event, the maximum mass allowed by the revised perturbative QCD model would decrease to no more than <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mn>2.08</u:mn> <u:msub> <u:mi>M</u:mi> <u:mo stretchy="false">⊙</u:mo> </u:msub> </u:math> . Consequently, our results suggest that the compact object with a mass of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mrow> <x:mn>2.50</x:mn> <x:mo>−</x:mo> <x:mn>2.67</x:mn> <x:msub> <x:mi>M</x:mi> <x:mo stretchy="false">⊙</x:mo> </x:msub> </x:mrow> </x:math> , as observed in the GW190814 event, cannot be an <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>u</ab:mi> <ab:mi>d</ab:mi> </ab:math> quark star, according to the revised perturbative QCD model.