Maximum mass of neutron stars

Abstract

We determine the structure of neutron stars within a Brueckner-Hartree-Fock approach based on realistic nucleon-nucleon, nucleon-hyperon, and hyperon-hyperon interactions. Our results indicate rather low maximum masses below 1.4 solar masses. This feature is insensitive to the nucleonic part of the EOS due to a strong compensation mechanism caused by the appearance of hyperons and represents thus strong evidence for the presence of nonbaryonic "quark" matter in the interior of heavy stars. The only way to obtain information on the structure and properties of baryonic matter at extreme densities of several times normal nuclear matter density ρ 0 ≈ 0.17 fm −3 seems to be the theoretical modelling of neutron stars, the unique environment where such densities are actually reached in nature, and the subsequent confrontation with observational data. Any given equation of state (EOS) of baryonic matter determines uniquely the mass-radius relation of neutron star sequences and in particular the maximum mass a neutron star can achieve before collapsing into a black hole.Most theoretical investigations performed so far point to an important feature of high-density β-stable matter, namely that hyperons will appear at densities of about 2, . . . , 3 ρ 0 and strongly soften the EOS. The main consequence is a substantial reduction of the maximum mass [1]. This seems to be an inevitable feature of any approach taking into account the hyperons, caused simply by the availability of additional degrees of freedom of the matter at high density. Any theoretical study of neutron stars without allowing for the presence of hyperons is therefore unrealistic.Evidently it is then important to carry out microscopic calculations as precisely as possible in order to make reliable predictions for the maximum mass of a neutron star composed of baryonic matter and the eventual confrontation with observational data. In this work we report on recent results following this motivation. We try to present strong evidence that the maximum mass of baryonic neutron stars is very low and that therefore neutron stars with larger masses (above ca. 1.5 solar masses) must necessarily contain quark matter.Our theoretical framework is the nonrelativistic BruecknerHartree-Fock (BHF) approach based on microscopic nucleonnucleon (NN), nucleon-hyperon (NY), and hyperon-hyperon (YY) potentials that are fitted to scattering phase shifts, where possible. Nucleonic three-body forces (TBF) are included in order to (slighty) shift the saturation point of purely nucleonic matter to the empirical value.It has been demonstrated that the theoretical basis of the BHF method, the hole-line expansion, is well founded: the nuclear EOS can be calculated with good accuracy in the BHF two hole-line approximation with the continuous choice for the single-particle potential, since the results in this scheme are quite close to the full convergent calculations which include also the three hole-line contribution [2]. Due to these facts, combined with the absence of adjustable parameter...

Soft nuclear equation-of-state from heavy-ion data and implications for compact stars

“…Realistic parameter sets should have a U N below the KaoS constraint up to densities of n ∼ (2 − 3) n 0 . The TM1 [61] parametrization as well as the BruecknerHartree-Fock approximation (BHF) [62][63][64][65] fulfill this requirement. For a RMF model with n 0 = 0.17 fm −3 and K 0 = 220 MeV, we arrive at m * /m = (0.53 − 0.65) for n ∼ (2 − 3) n 0 while for K 0 = 250 MeV we obtain m * /m = (0.54 − 0.67) for the same density range.…”

Variational Approach to Neutron Star Matter with Hyperons

“…2 shows the Λ fraction x Λ and the Σ − fraction x Σ − as functions of the baryon number density n B . For all four models of the odd-state ΛΛ interaction, Λ is the first hyperon to appear in NS matter and the critical number density is 0.42 fm −3 , which corresponds to the critical mass density ρ c = 7.4 × 10 14 g/cm 3 as shown in Fig. 1.…”

“…Figure 1 shows the gravitational masses of NSs with the four different odd-state ΛΛ interactions as functions of the central mass density ρ m : Also shown are the masses of NSs calculated with the EOS of pure nucleon matter without hyperons (without Y). The masses of NSs with the abovementioned four hyperon interactions are smaller than those for pure nucleon matter at ρ m higher than the critical mass density ρ c = 7.4 × 10 14 g/cm 3 (vertical dotted line), i.e., hyperons appear in NS matter at ρ m ≥ ρ c . This result shows that the hyperon mixing reduces the NS mass, as reported in the studies based on other many-body techniques [3][4][5].…”

“…The masses of NSs with the abovementioned four hyperon interactions are smaller than those for pure nucleon matter at ρ m higher than the critical mass density ρ c = 7.4 × 10 14 g/cm 3 (vertical dotted line), i.e., hyperons appear in NS matter at ρ m ≥ ρ c . This result shows that the hyperon mixing reduces the NS mass, as reported in the studies based on other many-body techniques [3][4][5]. Figure 1 also shows that the NS mass increases monotonically as the odd-state component of the ΛΛ interaction becomes more repulsive, i.e., from Type 1 to 4.…”

“…In particular, these heavy NSs are difficult to explain when hyperon mixing in NSs is considered. To investigate the hyperon mixing, some EOSs of nuclear matter including hyperons are constructed based on the microscopic many-body calculations starting from the bare baryon interactions [3][4][5]. However, uncertainties in hyperon-nucleon (Y N) and hyperon-hyperon (YY) interactions are large, as compared with the nucleon-nucleon (NN) interaction.…”