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Register a new userFrom nuclei to neutron stars: simple binding energy computer modelling in the classroom (part 2)
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We introduce two simple online activities to explore the physics of neutron stars. These provide an introduction to the basic properties of compact objects, like their masses and radii, for secondary school students. The first activity explores the idea of the minimum mass of a neutron star. It is directly linked to the concept of binding energy and follows on from our previous activities. The second activity focuses on the maximum mass of neutron stars using a solvable model of the neutron star interior. The activities are based on spreadsheets, provided as Supplementary Material, and can be easily adapted to different levels, age groups and discussion topics. In particular, these activities can naturally lead towards discussions on extrapolations and limits of theoretical models.
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We present a simple activity based on the liquid-drop model which allows secondary school students to explore the uses of mathematical models and gain an intuitive understanding of the concept of binding energy, and in particular the significance of positive binding energy. Using spreadsheets provided as Supplementary Material, students can perform simple manipulations on the different coefficients of the model to understand the role of each of its five terms. Students can use the spreadsheets to determine model parameters by optimising the agreement with real atomic mass data. %This will subsequently be used to predict the limit of existence of the Segre chart and to find the minimum mass of a neutron star. This activity can be used as the starting point of a discussion about theoretical models, their validation when it comes to describing experimental data and their predictive power towards unexplored regimes.
The symmetry energy obtained with the effective Skyrme energy density functional is related to the values of isoscalar effective mass and isovector effective mass, which is also indirectly related to the incompressibility of symmetric nuclear matter. In this work, we analyze the values of symmetry energy and its related nuclear matter parameters in five-dimensional parameter space by describing the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u, neutron skin of $^{208}$Pb, and tidal deformability and maximum mass of neutron star. We obtain the parameter sets which can describe the isospin diffusion, neutron skin, tidal deformability and maximum mass of neutron star, and give the incompressibility $K_0$=250.23$pm$20.16 MeV, symmetry energy coefficient $S_0$=31.35$pm$2.08 MeV, the slope of symmetry energy $L$=59.57$pm$10.06 MeV, isoscalar effective mass $m_s^*/m$=0.75$pm$0.05 and quantity related to effective mass splitting $f_I$=0.005$pm$0.170. At two times normal density, the symmetry energy we obtained is in 35-55 MeV. To reduce the large uncertainties of $f_I$, more critical works in heavy ion collisions at different beam energies are needed.
{it Background.} We investigate possible correlations between neutron star observables and properties of atomic nuclei. Particularly, we explore how the tidal deformability of a 1.4 solar mass neutron star, $M_{1.4}$, and the neutron skin thickness of ${^{48}}$Ca and ${^{208}}$Pb are related to the stellar radius and the stiffness of the symmetry energy. {it Methods.} We examine a large set of nuclear equations of state based on phenomenological models (Skyrme, NLWM, DDM) and {it ab-initio} theoretical methods (BBG, Dirac-Brueckner, Variational, Quantum Monte Carlo). {it Results.} We find strong correlations between tidal deformability and NS radius, whereas a weaker correlation does exist with the stiffness of the symmetry energy. Regarding the neutron skin thickness, weak correlations appear both with the stiffness of the symmetry energy, and the radius of a $M_{1.4}$. {it Conclusion.} The tidal deformability of a $M_{1.4}$ and the neutron-skin thickness of atomic nuclei show some degree of correlation with nuclear and astrophysical observables, which however depends on the ensemble of adopted EoS.
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of nuclear symmetry energy leads to large changes in the binding energy of neutron stars. The difference in predictions using the GR and the scalar-tensor theory appears only for massive neutron stars, and even then is significantly smaller than the difference resulting from variations in the symmetry energy.
The recent announcement of the PREX-II measurement of the neutron skin of $^{208}$Pb that suggests a stiff symmetry energy near nuclear matter density $n_0$ and its impact on the EoS of massive compact stars raise the issue as to whether the widely accepted lore in nuclear astrophysics that the EoS determined at $n_0$ necessarily gives a stringent ``constraint at high densities relevant to massive compact stars. We present the argument that the ``cusp structure in the symmetry energy at $n_{1/2}gsim 2 n_0$ predicted by a topology change in dense matter could obstruct the validity of the lore. The topology change, encoding the emergence of QCD degrees of freedom in terms of hidden local and scale symmetries, predicts an EoS that is soft below and stiff above $ngsim n_{1/2}$, involving no low-order phase transitions, and yields the macrophysical properties of neutron stars overall consistent with the astrophysical observations including the maximum mass $ 2.0lsim M/ M_odotlsim 2.2$ as well as the GW data. Furthermore it describes the interior core of the massive stars constituted of baryon-charge-fractionalized quasi-fermions, that are neither baryonic nor quarkonic, with the ``pseudo-conformal sound speed $v^2_{pcs}/c^2approx 1/3$ converged from below at $n_{1/2}$ with a nonzero trace of energy-momentum tensor. { In the renormalization-group approach to interacting fermions dubbed $Gn$EFT, the strangeness degrees of freedom play no role in the density regime relevant to the massive stars considered.}
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