Elsevier

Physics Reports

Volume 462, Issue 1, June 2008, Pages 1-20
Physics Reports

Recent developments on kaon condensation and its astrophysical implications

https://doi.org/10.1016/j.physrep.2008.03.002Get rights and content

Abstract

We discuss three different ways to arrive at kaon condensation at nc3n0 where n0 is nuclear matter density: (1) Fluctuating around the n=0 vacuum in chiral perturbation theory, (2) fluctuating around nVM near the chiral restoration density nχ where the vector manifestation of hidden local symmetry is reached and (3) fluctuating around the Fermi liquid fixed point at n0. They all share one common theoretical basis, “hidden local symmetry”. We argue that when the critical density nc<nχ is reached in a neutron star, the electrons turn into K mesons, which go into an s-wave Bose condensate. This reduces the pressure substantially and the neutron star goes into a black hole. Next we develop the argument that the collapse of a neutron star into a black hole takes place for a star of M1.5M. This means that Supernova 1987A had a black hole as result. We also show that two neutron stars in a binary have to be within 4% of each other in mass, for neutron stars sufficiently massive that they escape helium shell burning. For those that are so light that they do have helium shell burning, after a small correction for this, they must be within 4% of each other in mass. Observations support the proximity in mass inside of a neutron star binary. The result of strangeness condensation is that there are 5 times more low-mass black-hole, neutron-star binaries than double neutron-star binaries although the former are difficult to observe.

Introduction

While the phase structure of hadronic matter at high temperature both below and above the chiral phase transition temperature Tχ is being mapped out by laboratory experiments with invaluable help from lattice QCD, the situation with high density is vastly different. There is little information about matter above the nuclear matter density n00.16fm3 from laboratory experiments and there is practically no guidance from QCD proper since lattice–the only non-perturbative QCD tool available–cannot handle high density and the reliable perturbative QCD approach can access density regime only at asymptotic density where such novel phenomena like color-flavor-locked superconductivity can take place. To theorists’ disappointments, though, this density regime may be totally irrelevant to nature. We have a complicated landscape of phases theoretically predicted near and above a chiral restoration nχ which is as rich as the phase structure of water but they are all based on models, the reliability of which is uncertain given the paucity of experimental supports and lack of reliable theoretical control. Consequently the plethora of different scenarios for dense stellar systems such as neutron stars, black holes etc. available in the literature offer little guidance for understanding compact star physics.

The aim of this paper is to exploit a systematic effective field theory framework from three different vantage points to describe with some confidence the phase structure of dense matter crucially relevant to the formation of stable compact stars and its implications on the population of neutron stars and light-mass black holes. These approaches, particularly the second and the third, rely on one common strategy that hadronic systems under extreme conditions can be accessed reliably by hidden local symmetry [1] that incorporates the scaling property of chiral symmetry [2]. Our reasoning will be backed by detailed analysis of astrophysical observations.

This paper consists of two parts, one on an important phase change in hadronic physics and the other on collapse to black holes in astrophysics. Our aim is to bridge these seemingly disparate branches of physical phenomena. In the first part, we discuss recent developments on the most likely phase transition in hadronic matter, namely, kaon condensation, as density increases beyond the nuclear matter density to 3n0. We will develop the thesis that this is the first–and perhaps the last–crucial phase change at high density that matters for the fate of compact stars, leaving wide-open the possibility of other forms of higher-density phases involving quark matter etc. In the second part, we give compelling arguments why astrophysical observations strongly support that neutron stars of mass greater than 1.5M (where M is the solar mass) cannot be stable, as a consequence of which any compact star more massive than the maximum stable mass must be in the form of a black hole. These two developments will then be joined to arrive at the conclusion that kaon condensation at 3n0 implies 5 times more low-mass black-hole, neutron-star binaries than double neutron-star binaries.

Section snippets

Kaon condensation

Although QCD cannot provide, at present, useful and quantitative information for hadronic interactions at high density relevant to the physics of compact stars, there are three vantage points at which we have available reliable effective field theory tools to work with. The first is the matter-free T=n=0 vacuum about which fluctuations can be described by effective chiral field theory. Here there is a wealth of experimental data to guide model building and extrapolating beyond the normal matter

A scenario for a large number of low-mass black holes in the galaxy

This was the title of a paper written by G.E. Brown and H.A. Bethe in W.K. Kellogg Radiation Laboratory [37]. Since that time, much improvements on the calculations have been made, the most important one of which being the expanding about the VM fixed point of hidden local symmetry. And furthermore more observational data have been accumulated.

In this second half of the paper, we would like to present a chain of astrophysical observations to link the kaon condensation in hadronic matter

Conclusions

We have been able to arrive at the strangeness condensation phase transition critical point nc3n0 from three different starting points, the first from the zero-density vacuum, the second from the vector manifestation fixed point and the third from the Landau Fermi-liquid fixed point. In the last two cases, the estimate was made more reliable by arguments based on renormalization group flow which made all of the quantities whose behavior with density was unknown rotated out. In particular in

Acknowledgments

G.E.B. was supported in part by the US Department of Energy under Grant No. DE-FG02-88ER40388. C.H.L. was supported by Creative Research Initiatives (MEMS Space Telescope) of MOST/KOSEF.

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