RELATIVISTIC MEAN FIELD DESCRIPTION OF EXOTIC PHASES IN NEUTRON STAR

Abstract

Neutron stars (NS) are ideal astrophysical laboratories, which have a strong appeal to be a probe for understanding many areas of physics. NS are the perfect example for the high isospin and high density matter and provide us with a robust testing ground for nuclear models aimed at unified description of finite nuclei and infinite matter. Among the variety of nuclear models capable of such wider applicability, the relativistic mean field (RMF) model has been chosen for the study in this thesis. To achieve such a unified approach, it is important to extend the RMF model, either with higher order couplings or with density dependent couplings. We study how these extended versions of RMF models, which are successful in the finite nuclear regime, are capable of explaining the properties of NS. Major emphasis is laid on the consequences of considering the presence of exotic matter like that of antikaons and hyperons, in the core of NS. The study of such exotic matter in the NS core acquired impetus recently due to the new observation of the pulsar J1614-2230 with mass (1.97±0.04) solar mass (M ). This observation has such a strong impact mainly due to the ruling out of: (i) many of the standard and successful equation of state (EoS) by then (for e.g. PAL6, FSUGold) which were yielding softer EoS and hence lower mass, and (ii) most of the EoS involving exotic matter such as kaon condensates or hyperons (for e.g. GM3, GS1) which were believed to be in the core of NS. Soon, these claims were played down by J.M. Lattimer by stating vii viii “To rule out these exotic models fully you also need to know the radius of the star”. He also added that it will be easy to tweak the parameters, to bring back the exotic particles and/or to reproduce the mass. This tweaking cannot be arbitrary due to several established constraints for the symmetry energy, EoS and finite nuclear properties. Many of the recent works were in this direction where few more EoS were introduced and in several models the parameters were adjusted, to reproduce the 2M NS. However, most of these approaches ignored the presence of exotic particles in the core of the NS. This issue also is addressed in this thesis, with many of the results focussed on explaining the 2M NS. Whether a precision observation of radius of most massive NS can confirm/rule-out exotic cores in NS, is also analysed. The role of extensions to the RMF models on the EoS at densities lower than the saturation density of finite nuclei is also explored. These EoS at sub-saturation density governs the phase transitions associated to pasta structures in the crust of neutron stars and are analysed in this work. The thesis is planned to have nine chapters with the first chapter of introduction to the basics, second chapter comprising the core formalism and chapters 3 to 8 pertaining to our results and discussions. A more detailed breakup of the thesis is given below: Chapter 1: This chapter carries a general introduction about the NS and the present status of its observables, mainly the mass, radius and cooling rate. The different possible phases in the structure of the NS like the pasta phases in the crust and the phases of pions, kaons, hyperons and quarks in the core are discussed. The details of the quark matter EoS are listed in the case of MIT bag model and the color flavored locked phase also is discussed. The inconsistencies in nuclear models at high density and high isospin are listed down. The nuclear models can be refined with constraints for EoS through heavy ion collision experiments and NS observations which are outlined. The several links between properties of finite nuclei and NS are also discussed. The details of linking the EoS and NS structure through the TOV equations are presented in this chapter which ends with a list of thesis goals. Chapter 2: Here we start the discussion with the simple version of Quantum Hadroix dynamics i.e. the σ −ω model and also discuss the calculation details. This discussion is gradually built up to the recent versions of the RMF models. In the recent years, a number of effective interactions of meson baryon couplings has been developed out of which four class of parameters are important: 1. Standard nonlinear interactions (NL1, NL3, etc.), 2. Density dependent interactions (DDME1, DDME2, etc.), 3. Interactions with a few additional higher order couplings (FSUGold, IUFSU, etc.) to constrain selected observables, and 4. Effective field theory motivated interactions with several higher order couplings (G1, G2, etc). These effective interactions are adjusted to reproduce various properties of finite nuclei. In this chapter, we discuss all the above-mentioned models, their parameters and details of calculation. Chapter 3: The extensions of RMF models are known to have a strong impact on the high density regime. Here we explore their role on the EoS at densities lower than the saturation density of finite nuclei which govern the phase transitions associated to pasta structures in the crust of neutron stars. We find that, with lower proton fractions, the higher order couplings can play a role in modifying the EoS at sub-saturation densities and hence the pasta structures. We observe that it is more appropriate to link the differences in EoS (and hence the occurrence of pasta structures) to the symmetry energy (and hence the neutron skin thickness). Chapter 4: In this chapter we discuss the role of higher order couplings in conjunction with kaon condensation using recent versions of relativistic mean field models. Our results show that the higher order couplings play a significant role at higher densities where kaons dominate the behavior of the equation of state. We compare our results with other interactions (NLl, NL3, G1 and FSUGold) and show that the new couplings bring down the mass of neutron star (NS), which is further reduced in the presence of kaons to yield results consistent with present observational constraints. We show that the composition of NS varies with the parameter sets. Chapter 5: Here we extend our earlier investigation with condensation of both the antikaons (K− and ˉK0). We find that the onset of condensation of K− and ˉK 0 highly depends not only on the strength of optical potential but also on the new couplings. Presence of x antikaons leads to a softer equation of state and makes the neutron star core as symmetric and lepton deficient matter. We show that these effects strongly influence the mass-radius relation as well as the composition of neutron star. We also show that the recently observed 1.97±.04 M NS can be explained in three ways: (i) A stiffer EoS with both antikaons, (ii) a relatively softer EoS with K− and (iii) a softer EoS without antikaons. Chapter 6: Extending the RMF models either with higher order couplings or with density dependent couplings has been proved to be successful in explaining several properties of finite nuclei, infinite matter and NS in a unified way. Here, we compare how these two extensions fair while explaining the NS without and with antikaons. Even for a very soft EoS, we find that there is a strong possibility of antikaons to be condensed. We find an exception for correlation between NS radius and density dependence of symmetry energy, which gets restored when we introduce antikaons. The implication of the precisely measured 2M NS on our results, is discussed with four sets of interactions which cover all four combinations of stiff/soft symmetry energy and EoS. Chapter 7: Here we extend our approach with the inclusion of all hyperons in the baryon octet and compare the nucleon (N), nucleon-antikaon (NK), nucleon-hyperons (NH), and NKH phases in NS matter. We find that there is a strong interplay between antikaons and hyperons affecting each others influence in the NS properties. Though this approach seems to be better and inclusive, the outcome is sensitive to the hyperon-nucleon coupling constants which are poorly known. Despite this aspect, we find that both the hyperons and the antikaons influence the properties of NS, even in the extended RMF models. Chapter 8: In this chapter, we examine the sensitivity of the radius of the most massive pulsar J1614-2230 with 1.97±0.04 M to the details of its core. With our calculations and analysis, here we show that for the most massive neutron star, with a precise observation of its radius, it may be possible to ascertain the presence of exotic cores. Chapter 9: This chapter comprises an overall summary of the thesis work and few conclusions are presented along with future plans.