| Neutron Star(NS)is the natural laboratory of studying the cold dense matter,where the condition is hard to achieve in terrestrial experiments.We use the pressure-density relations under the zero-temperature approximation to describe the properties of the matter in NS,i.e.the equation of state(EoS).At the low density regions((?)1.1ρsat,where the ρsat is the nuclear saturation density),the chiral effective field theory(χEFT)puts on a tight constraint on the EoS using its state-of-the-art calculation results.While at the super high density regions(μ>2.6GeV of ρ(?)40ρsat,where μ is the chemical potential and p is the rest mass density),the state-of-the-art results of perturbative quantum chromodynamics(pQCD)are able to influence the high density region of the EoS via the microscopic stability condition and the causality condition,i.e.,0<cs2<c2,where cs is the sound speed in NS,and c is the speed of light in vacuum.However,in the middle region the above theories are not valid anymore,the current theoretical EoSs are different with each others.The most common way is to use the parameterized phenomenological models to describe the EoSs,and using the Bayesian inference to infer the parameters and the corresponding EoS properties given observation data.The purpose of this thesis is to develop a new nonparametric representation of the NS EoS,and apply it on the study of constraining the EoS.Therefore,we firstly introduce the history of NS theories,basic structure of NS,and the current observations of NS mass and radius.On September 14,2015 we directly detected the gravitational wave(GW)from a binary black hole merger,it’s the beginning of the GW astronomy.2 years later,on August 17,2017 the first binary neutron star merger GW event was detected.Different from black holes(BHs),the matter distributions of NSs can influence the phase of the GW,so it’s the great opportunity to study the NS EoS by GW.We introduce the generation,propagation,detection,and the data analysis of GW in Chapter 1.With the continuous increase of observation data,the amount of data available to us is increasing,which makes machine learning/deep learning methods applied to big data analysis more and more important in astronomical research.Since we use the technologies related to neural networks in the following chapters,we briefly introduce some basic knowledge about machine learning and neural networks in Chapter 2.In Chapter 3,we propose a nonparametric representation of EoS via a feed-forward neural network(FFNN)for the first time.As an universal function approximator,the single layer FFNN with a sigmoid activation function is proven to be able to fit any continues real functions,which makes us to consider it as a nonparametric model to represent the NS EoS.Compared with the parameterized models,the nonparametric models don’t rely on the specific choice of the parametric form of the model,thus it’s less model dependent and has larger functional space,with which we can represent more extreme EoSs.After validating the model’s capability of fitting the theoretical EoSs and recovering the injected parameters,we perform the Bayesian inference to the EoS with the current observation data,i.e.,GW170817 and PSR J0030+0451.We find that for a canonical 1.4M⊙ NS,the radius is constrained to be R1.4=11.83-1.08+1.25km,and the tidal deformability is constrained to be Λ1.4=323-165+334(the error range in the abstract is 90%,unless otherwise specified)。The state of strongly interacting matter at extremely high density is still one of the outstanding problems.How the baryon-quark matter phase transition occurs and whether there is quark matter in NSs need to be solved urgently.Therefore,in Chapter 4,we enhance the original nonparametric method,so that our nonparametric method’s prior space is large enough to include the general types of physical-motivated EoSs,which can be used to study the quark matter in the NSs.It is found that a sizable quark matter core(≥10-3M⊙)is plausible(≥90%probability)for the very massive NS with a gravitational mass above about 0.97MTOV.We also find that the sound speed inρ≥2ρsat could approach to zero only near the center of NS with M≈MTOV and hence does not support the presence of the strong first-order phase transition in the low-mass NSs.Besides,we obtain that the maximum gravitational mass of a non-rotating NS is MTOV=2.18-0.13+0.27M⊙.Although the nonparametric method described above has shown its abilities by various works,the large amount of the parameters(the number of parameters of the above nonparametric model is 31)does increase the computational overhead.In deep learning,the deep generative model variational auto-encoder(VAE)is widely used on the dimensionality reduction tasks.Therefore,in Chapter 5,we first generate 1 000000 EoSs as a training set,and then use the VAE to study the feature representation of these EoSs.When the loss function has been converged by using the gradient decent,we get a welltrained generative model of the NS EoS.In this model,we can use only 4 parameters to represent the EoSs instead of 31,which maintains the nonparameteric properties(larger functional space than parameterized models).We find that the model after dimension reduction by the VAE has been greatly speeded up during the calculations,and can get the same results as before.As the second neutron star merger event,the GW190425 has very different properties.Its total mass is far larger than that of the known binary neutron star systems identified in the Galaxy.For the absence of the electromagnetic counterpart,the gravitational wave data analysis isn’t able to rule out the possibility that the primary/secondary component of GW190425 is a BH.Therefore,in chapter 6,we study the probability of the NS-BH origin of the GW190425.We assume that if the mass of a star is larger than the 1σ lower limit of the mass measurement of the PSR J0740+6620,i.e.,2.04M⊙,which has considered the rotational effects of NS,～0.01 M⊙,it can be considered as a BH.We use the Bayesian inference to reanalyze the gravitational wave data of the GW 190425 under the above BH assumption,and we find that the mass and the dimensionless spin parameter of BH are MBH=2.40-0.32+0.36M⊙ and χBH=0.141-0.064+0.067,respectively.The mass and tidal deformability of NS are MNS=1.15-0.13+0.15M⊙ and ANS=1.4-1.2+3.8×103,respectively.The above results are consistent with current observations,which means that the GW190425 is consistent with being an NS-BH merger event.If confirmed,this gravitational wave event would be the first mass gap event and the first known NS-BH merger gravitational wave event. |
