Theoretical calculation of tidal Love numbers of the Moon with a new spectral element method

The tidal Love numbers of the Moon are a set of nondimensional parameters that describe the deformation responses of the Moon to the tidal forces of external celestial bodies.They play an important role in the theoretical calculation of the Moon’s tidal deformation and the inversion of its internal structure.In this study,we introduce the basic theory for the theoretical calculation of the tidal Love numbers and propose a new method of solving the tidal Love numbers:the spectral element method.Moreover,we explain the mathematical theory and advantages of this method.On the basis of this new method,using 10 published lunar internal structure reference models,the lunar surface and lunar internal tidal Love numbers were calculated,and the influence of different lunar models on the calculated Love numbers was analyzed.Results of the calculation showed that the difference in the second-degree lunar surface Love numbers among different lunar models was within 8.5%,the influence on the maximum vertical displacement on the lunar surface could reach±8.5 mm,and the influence on the maximum gravity change could reach±6μGal.Regarding the influence on the Love numbers inside the Moon,different lunar models had a greater impact on the Love numbers h_(2) and l_(2) than on k_(2) in the lower lunar mantle and core.

Symmetry energy of strange quark matter and tidal deformability of strange quark stars

Research performed during the past decade revealed an important role of symmetry energy in the equation of state(EOS)of strange quark matter(SQM).By introducing an isospin-dependent term into the quark mass scaling,the SQM stability window in the equivparticle model was studied.The results show that a sufficiently strong isospin dependence C_(I)can significantly widen the SQM region of absolute stability,yielding results that simultaneously satisfy the constraints of the astrophysical observations of PSR J1614-2230 with 1.928±0.017 Mand tidal deformability 70≤Λ_(1:4)≤580 measured in the event GW170817.With increasing C_(I),the difference between the u,d,and s quark fractions for the SQM inβ-equilibrium becomes inconspicuous for C>0,leading to small isospin asymmetryδ,and further resulting in similar EOS and structures of strange quark stars(SQSs).Moreover,unlike the behavior of the maximum mass of ud QSs,which varies with C_(I)depending on the sign of the parameter C,the maximum mass of the SQSs decreases monotonously with increasing CI.

Dependence of the tidal deformability of neutron stars on the nuclear equation of state

Within the Bayesian framework,using an explicitly isospin-dependent parametric equation of state(EOS)for the core of neutron stars(NSs),we studied how the NS EOS behaves when we confront it with the tidal deformabilitiesΛ1.4abilities of massive NSs.We found that it does not significantly improve the constraints on the NS EOS but has a weak effect on narrowing down the slope parameter of the symmetry energy by decreasing the measurement errors ofΛ1.4.Both the isospin-dependent and isospin-independent parts of the NS EOS were significantly constrained and raised as the tidal deformabilities of massive NSs were adopted in the calculations,especially in high-density regions.We also found thatΛ1.4symmetry energy,whereas the opposite occurs for the radius of canonical NSs R1.4.The tidal deformability of an NS with two times the solar massΛ2.0ergy,andΛ1.4and R1.4have no correlation with the former.

Key factor for determining relation between radius and tidal deformability of neutron stars: Slope of symmetry energy

The constraints on tidal deformability Λ of neutron stars were first extracted from GW170817 by LIGO and Virgo Collaborations.However,the relationship between the radius R and tidal deformability Λ is still under debate.Using an isospin-dependent parameterized equation of state(EOS),we study the relation between R andΛand its dependence on parameters of symmetry energy Esym and EOS of symmetric nuclear matter E0 when the mass is fixed at 1.4 M⊙,1.0 M⊙,and 1.8 M⊙.We find that,although the changes of high order parameters of Esym and E 0 can shift individual values of R1.4 and Λ1.4,the R1.4~Λ1.4 relation remains approximately at the same fitted curve.The slope L of the symmetry energy plays the dominant role in determining the R1.4~Λ1.4 relation.By investigating the mass dependence of the R~Λ relation,we find that the well fitted R~Λ relation for 1.4 M⊙ is broken for massive neutron stars.

Hyperonic neutron stars: reconciliation between nuclear properties and NICER and LIGO/VIRGO results

Using an extended version of quantum hadrodynamics,I propose a new microscopic equation of state(EoS)that is able to correctly reproduce the main properties of symmetric nuclear matter at the saturation density,as well as produce massive neutron stars and satisfactory results for the radius and the tidal parameter.I show that this EoS can reproduce at least a 2.00 solar mass neutron star,even when hyperons are present.The constraints about the radius of a 2.00 M_(⊙) and the minimum mass that enables a direct Urea effect are also checked.

Strange quark star and the parameter space of the quasi-particle model

The properties of strange quark stars are studied within the quasi-particle model. Taking into account chemical equilibrium and charge neutrality, the equation of state(EOS) of(2+ 1)-flavor quark matter is obtained. We illustrate the parameter spaces with constraints from two aspects: one is based on the astronomical results of PSR J0740+ 6620 and GW 170 817,and the other is based on the constraints proposed from the theoretical study of a compact star that the EOS must ensure the tidal deformability Λ_(1.4)=190_(-120)^(+390) and support a maximum mass above 1.97M⊙. It is found that neither type of constraints can restrict the parameter space of the quasi-particle model in a reliable region and thus we conclude that the low mass compact star cannot be a strange quark star.

Neutron star cooling and GW170817 constraint within quark-meson coupling models

In the present work,we used five different versions of the quark-meson coupling(QMC)model to compute astrophysical quantities related to the GW170817 event and the neutron star cooling process.Two of the models are based on the original bag potential structure and three versions consider a harmonic oscillator potential to confine quarks.The bag-like models also incorporate the pasta phase used to describe the inner crust of neutron stars.With a simple method studied in the present work,we show that the pasta phase does not play a significant role.Moreover,the QMC model that satisfies the GW170817 constraints with the lowest slope of the symmetry energy exhibits a cooling profile compatible with observational data.

Chiral phase transition and equation of state in chiral imbalance

The chiral phase transition and equation of state are studied within a novel self-consistent mean-field approximation of the two-flavor Nambu-Jona-Lasinio model.In this newly developed model,modifications to the chemical μand chiral chemical μ5 potentials are naturally included by introducing vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian.In the proper-time scheme,the chiral phase transition is a crossover in the T-μ plane.However,when μ5 is incorporated,our study demonstrates that a first order phase transition may emerge.Furthermore,the chiral imbalance will soften the equation of state of quark matter.The mass-radius relationship and tidal deformability of quark stars are calculated.The maximum mass and radius decrease as μ5 increases.Our study also indicates that the vector and axial-vector channels exhibit an opposite influence on the equation of state.