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Register a new userConstraints on the symmetry energy and its associated parameters from nuclei to neutron stars
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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.
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A number of observed phenomena associated with individual neutron star systems or neutron star populations find explanations in models in which the neutron star crust plays an important role. We review recent work examining the sensitivity to the slope of the symmetry energy $L$ of such models, and constraints extracted on $L$ from confronting them with observations. We focus on six sets of observations and proposed explanations: (i) The cooling rate of the neutron star in Cassiopeia A, confronting cooling models which include enhanced cooling in the nuclear pasta regions of the inner crust, (ii) the upper limit of the observed periods of young X-ray pulsars, confronting models of magnetic field decay in the crust caused by the high resistivity of the nuclear pasta layer, (iii) glitches from the Vela pulsar, confronting the paradigm that they arise due to a sudden re-coupling of the crustal neutron superfluid to the crustal lattice after a period during which they were decoupled due to vortex pinning, (iv) The frequencies of quasi-periodic oscillations in the X-ray tail of light curves from giant flares from soft gamma-ray repeaters, confronting models of torsional crust oscillations, (v) the upper limit on the frequency to which millisecond pulsars can be spun-up due to accretion from a binary companion, confronting models of the r-mode instability arising above a threshold frequency determined in part by the viscous dissipation timescale at the crust-core boundary, and (vi) the observations of precursor electromagnetic flares a few seconds before short gamma-ray bursts, confronting a model of crust shattering caused by resonant excitation of a crustal oscillation mode by the tidal gravitational field of a companion neutron star just before merger.
The symmetry energy and its density dependence are pivotal for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars. Recently, PREX-II reported a value of $0.283pm0.071$ fm for the neutron-skin thickness of $^{208}$Pb, $R_{rm skin}^{^{208}text{Pb}}$, implying a symmetry-energy slope parameter $L$ of $106pm37$ MeV, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representation based on Gaussian processes to constrain the symmetry energy $S_0$, $L$, and $R_{rm skin}^{^{208}text{Pb}}$ directly from observations of neutron stars with minimal modeling assumptions. The resulting astrophysical constraints from heavy pulsar masses, LIGO/Virgo, and NICER favor smaller values of the neutron skin and $L$, as well as negative symmetry incompressibilities. Combining astrophysical data with chiral effective field theory ($chi$EFT) and PREX-II constraints yields $S_0 = 33.0^{+2.0}_{-1.8}$ MeV, $L=53^{+13}_{-15}$ MeV, and $R_{rm skin}^{^{208}text{Pb}} = 0.17^{+0.04}_{-0.04}$ fm. We also examine the consistency of several individual $chi$EFT calculations with astrophysical observations and terrestrial experiments. We find that there is only mild tension between $chi$EFT, astrophysical data, and PREX-IIs $R_mathrm{skin}^{^{208}mathrm{Pb}}$ measurement ($p$-value $= 12.3%$) and that there is excellent agreement between $chi$EFT, astrophysical data, and other nuclear experiments.
Recently, the radius of neutron star (NS) PSR J0740+6620 was measured by NICER and an updated measurement of neutron skin thickness of ${}^{208}$Pb ($R_{rm skin}^{208}$) was reported by the PREX-II experiment. These new measurements can help us better understand the unknown equation of state (EoS) of dense matter. In this work, we adopt a hybrid parameterization method, which incorporates the nuclear empirical parameterization and some widely used phenomenological parameterizations, to analyze the results of nuclear experiments and astrophysical observations. With the joint Bayesian analysis of GW170817, PSR J0030+0451, and PSR J0740+6620, the parameters that characterize the ultra dense matter EoS are constrained. We find that the slope parameter $L$ is approximately constrained to $70_{-18}^{+21}$ MeV, which predicts $R_{rm skin}^{208}=0.204^{+0.030}_{-0.026},{rm fm}$ by using the universal relation between $R_{rm skin}^{208}$ and $L$. And the bulk properties of canonical $1.4,M_odot$ NS (e.g., $R_{1.4}$ and $Lambda_{1.4}$) as well as the pressure ($P_{2rho_{rm sat}}$) at two times the nuclear saturation density are well constrained by the data, i.e., $R_{1.4}$, $Lambda_{1.4}$, and $P_{2rho_{rm sat}}$ are approximately constrained to $12.3pm0.7$ km, $330_{-100}^{+140}$, and $4.1_{-1.2}^{+1.5}times10^{34},{rm dyn,cm^{-2}}$, respectively. Besides, we find that the Bayes evidences of the hybrid star and normal NS assumptions are comparable, which indicates that current observation data are compatible with quarkyonic matter existing in the core of massive star. Finally, in the case of normal NS assumption, we obtain a constraint for the maximum mass of nonrotating NS $M_{rm TOV}=2.30^{+0.30}_{-0.18}$ $M_odot$. All of the uncertainties reported above are for 68.3% credible levels.
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.
The neutron skin thickness $Delta r_{rm{np}}$ of heavy nuclei is essentially determined by the symmetry energy density slope $L({rho })$ at $rho_c = 0.11/0.16rho_0$ ($rho_0$ is nuclear saturation density), roughly corresponding to the average density of finite nuclei. The PREX collaboration recently reported a model-independent extraction of $Delta r^{208}_{rm{np}} = 0.29 pm 0.07$ fm for the $Delta r_{rm{np}}$ of $^{208}$Pb, which suggests a rather stiff symmetry energy $E_{rm{sym}}({rho })$ with $L({rho_c }) ge 55$ MeV. We demonstrate that the $E_{rm{sym}}({rho })$ cannot be too stiff and $L({rho_c }) le 73$ MeV is necessary to be compatible with (1) the ground-state properties and giant monopole resonances of finite nuclei, (2) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions, (3) the largest neutron star (NS) mass reported so far for PSR J0740+6620, (4) the NS tidal deformability extracted from gravitational wave signal GW170817 and (5) the mass-radius of PSR J0030+045 measured simultaneously by NICER. This allow us to obtain $55 le L({rho_c }) le 73$ MeV and $0.22 le Delta r^{208}_{rm{np}} le 0.27$ fm, and further $E_{rm{sym}}({rho_0 }) = 34.5 pm 1.5$ MeV, $L({rho_0 }) = 85.5 pm 22.2$ MeV, and $E_{rm{sym}}({2rho_0 }) = 63.9 pm 14.8$ MeV. A number of critical implications on nuclear physics and astrophysics are discussed.
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