Researches On Equation Of State Of Ultra-dense Matter And Population Properties Of Compact Binary Coalescing Systems

What are the states of matter at exceedingly high density?How do compact binary coalescing systems(CBCs)form or evolve?These two important scientific questions remain to be solved in the era of gravitational-wave(GW)astronomy.The equation of state(EOS)of ultra-dense matter holds the key to solving the first problem.However,at supranuclear densities,both theoretical calculations and terrestrial experiments encounter bottlenecks in EOS studies.Neutron stars(NSs)provide astrophysical laboratories for us to learn the EOS at ultra-high density.While the population properties of CBCs offer essential clues to solving the second problem.With the increase in GW detections,we will have a large opportunity to reveal the formation and evolution mechanisms of CBCs.Since NSs,EOS,and GWs play important roles in most of our works,I shall first outline the NS history,the research backgrounds of EOS,the methods for studying EOS,and the observation data of NSs that can be used to constrain EOS,and then introduce the description,the generation,the detection,and the data analysis of GWs.Recently,NS observations have led to significant progress in constraining EOS,benefiting from two breakthroughs,one is the mass and tidal deformability measurements of the landmark event GW170817 originating from the merger of two NSs,and the other is the precise mass-radius measurements of two NSs made by NICER(Neutron star Interior Composition ExploreR).However,it is still not clear whether deconfined quark matter exists in NSs(or their merger remnants)or where/when the potential hadron-quark phase transition happens.Previous studies about the nature of this transition were carried out based on various state-of-the-art theories for both the hadronic and quarkyonic phases,but most of them used the traditional forward-modeling approach rather than Bayesian analysis.Usually,it is difficult to quantify the uncertainties of model parameters and the evidence for presenting phase transition involved in forwardmodeling methods.Meanwhile,it is rather challenging to mimic well all kinds of EOS models in the whole density range with a specific parametrization alone.Therefore,we propose a new phenomenological EOS model that adopts different parametrization approaches in different density ranges.And we jointly constrain the EOS using some reliable measurements of NSs within the Bayesian statistical framework.We find that current observation data are still not informative enough to support/rule out phase transition due to the comparable pieces of evidence for models with and without phase transition.However,the bulk properties of the canonical 1.4M☉NS and the pressure at around two times nuclear saturation density(ρsat)are well constrained by the data.Moreover,strong phase transition at low densities is disfavored,and the 1σ lower bound of transition density is constrained to 1.84ρsat.Besides,we also study the symmetry energy of nuclear matter and compare the neutron skin thickness(Rskin208)obtained from multimessenger data of NSs and that from PREX-Ⅱ(Lead Radius EXperiment).We find that the slope parameter L is approximately constrained to 70-18+21 MeV,which predicts Rskin208=0.204-0.026+0.0.030 fm by using the universal relation between Rskin208 and L.This result is much smaller than the PREX-Ⅱmeasurement but slightly mitigates the tension between measurements of PREX-Ⅱ and other nuclear experiments.In the case of normal NS assumption,we obtain a constraint for the maximum mass of nonrotating NS MTOV=2.30-0.18+0.30 M☉.Based on this result and the current observational and theoretical knowledge about the NS population and its EOS,we find that a binary black hole(BBH)merger scenario for GW 190814 is more plausible.All of the uncertainties reported above are for 68.3%credible levels.In the third chapter,I mainly focus on the applications of EOS.The mass measurements of isolated neutron stars(INSs)are much more challenging than those of NSs in binary neutron stars(BNSs).Benefiting from the recent significant progress made on constraining the EOS of NSs,we propose a novel method to estimate the masses of the INSs with measured gravitational redshifts.We apply our method to RX J 1856.5-3754,RX J0720.4-3125,and RBS 1223,three members of "The Magnificent Seven"(M7),and estimate their masses to be 1.24-0.29+0.29 M☉,1.23-0.05+0.10 M☉,and 1.08-0.11+0.20M☉(68.3%credible interval),respectively.Our results suggest no evidence for experiencing significant accretion of these isolated objects and can trace their birth masses.The post-merger GW radiation of the remnant formed in the BNS coalescence is expected to carry fundamental information on the EOS of the ultra-dense matter as well as the fate of the remnant.Though such signals have not been directly measured yet,the interest in catching them with the upgraded second-generation GW detectors is growing.Significant progress has been achieved in the post-merger gravitational radiation numerical simulations.We estimate the radiated GW energy in the post-merger phase using some simulation results.We find that the EOSs constrained by current observations are in favor of strong post-merger GW radiation.The prominent post-merger gravitational radiation of GW170817-like events is expected to be detectable by advanced LIGO/Virgo(aLIGO/AdV)detectors in the fifth observing run.In the fourth chapter,I shall investigate the population properties of CBCs.Recently,aLIGO/AdV have completed their third observing run.The detected CBCs are largely increased and have enabled us to find some substructures that were not discernible before in the mass spectrum of BBHs.Based on the data of GWTC-2,we perform hierarchical Bayesian analysis and examine whether the mass distribution has a sharp cutoff for primary BH masses below 65M☉,as predicted in the(pulsational)pair-instability supernova model.We construct two empirical mass functions and find that both models can reasonably fit the data.An excess and a sharp drop of the mass spectrum are found at～33M☉ and～50M☉ respectively,suggesting that the stellar evolution scenarios can explain the majority of the observed BHs.On the other hand,the very massive subpopulation,which accounts for at most several percent of the total,may be formed through hierarchical mergers or other processes.With more events being detected in the future,statistical analyses would be essential to probe whether the population properties of merging neutron star-black hole(NSBH)systems are significantly different from those of BBH or BNS systems.Therefore,we investigate the prospect of measuring the mass function of BHs that are merging with NSs.In the presence of a low mass gap,both the mass gap and power-law index(a)of the black hole mass function can be well measured;thus,we can reveal where the a is different for BBH and NSBH systems(if the misclassification of BBH into NSBH is negligible).In a binary system,the gravitational potential of the primary BH may play an important role in enhancing the fallback accretion onto the lighter compact object newly formed in the second supernova explosion.As a result,the final masses of the binary compact objects would be correlated.Interestingly,by analyzing the mass distribution of four GW events,characterized by both a small mass ratio and a low mass(≤5M☉)of the light component,we find tentative evidence for a mass correlation among the objects.This result suggests that the fallback accretion scenario may naturally explain the origin of GW 190814.In the last chapter,I will summarize my dissertation and look into the future.