1 Astrophysical Constraints on Dense Matter in Neutron Stars
3
the radii of neutron stars and show that most of them suffer severely from
systematic errors. In Sect. 1.5 we explore what can be learned from cooling of
neutron stars, and the difficulties in getting clean measurements of temperatures.
In Sect. 1.6 we investigate the highly promising constraints that could be obtained
from the detection of gravitational waves from neutron star–neutron star or neutron
star–black hole systems. We summarize our conclusions in Sect. 1.7. For other
recent reviews of equation of state constraints from neutron star observations, see
[27, 101, 116, 117, 129, 165, 171, 199, 206, 234].
1.2 Expectations from Nuclear Theory
Any observations of neutron stars bearing on the properties of high-density matter
must be put into the context of existing nuclear theory. This theory, which relies
primarily on laboratory measurements of matter at nuclear density that has approximately equal numbers of protons and neutrons, must be extrapolated significantly
to the asymmetric matter at far higher density in the cores of neutron stars. We also
note that the inferred macroscopic properties of neutron stars depend on the nature
of strong gravity as well as on the properties of dense matter (e.g., [183]), but for
this review we will assume the correctness of general relativity.
In this section we give a brief overview of current thinking about dense matter.
We begin with simple arguments motivating the zero-temperature approximation
for the core matter and giving the basics of degenerate matter. We then address a
commonly-asked question: given that the fundamental theory of quantum chromodynamics (QCD) exists, why can we not simply employ computer calculations (e.g.,
using lattice gauge theory) to determine the state of matter at high densities? Given
that in fact such calculations are not practical, we explore the freedom that exists in
principle to construct models of high-density matter; the fundamental point is that
because the densities are well above what is measurable in the laboratory, one could
always imagine, in the context of a model, adding terms that are negligible at nuclear
density or for symmetric matter but important when the matter is a few times denser
and significantly asymmetric. After discussing some example classes of models, we
survey current constraints from laboratory experiments and future prospects. We
conclude with a discussion of how one would map an idealized future data set of
masses, radii, temperatures, etc. of neutron stars onto the equation of state of cold
dense matter.
1.2.1 The Basics: Dense Matter and Neutron Stars
Consider a set of identical fermions (e.g., electrons or neutrons) of mass m and
number density n. The linear space available to each fermion is thus Δx ∼ n −1/3 ,
and the uncertainty principle states that the uncertainty in momentum (and hence
the minimum momentum) is given by ΔpΔx ∼ ¯
h and thus p min ∼ ¯
hn 1/3 , where
3
the radii of neutron stars and show that most of them suffer severely from
systematic errors. In Sect. 1.5 we explore what can be learned from cooling of
neutron stars, and the difficulties in getting clean measurements of temperatures.
In Sect. 1.6 we investigate the highly promising constraints that could be obtained
from the detection of gravitational waves from neutron star–neutron star or neutron
star–black hole systems. We summarize our conclusions in Sect. 1.7. For other
recent reviews of equation of state constraints from neutron star observations, see
[27, 101, 116, 117, 129, 165, 171, 199, 206, 234].
1.2 Expectations from Nuclear Theory
Any observations of neutron stars bearing on the properties of high-density matter
must be put into the context of existing nuclear theory. This theory, which relies
primarily on laboratory measurements of matter at nuclear density that has approximately equal numbers of protons and neutrons, must be extrapolated significantly
to the asymmetric matter at far higher density in the cores of neutron stars. We also
note that the inferred macroscopic properties of neutron stars depend on the nature
of strong gravity as well as on the properties of dense matter (e.g., [183]), but for
this review we will assume the correctness of general relativity.
In this section we give a brief overview of current thinking about dense matter.
We begin with simple arguments motivating the zero-temperature approximation
for the core matter and giving the basics of degenerate matter. We then address a
commonly-asked question: given that the fundamental theory of quantum chromodynamics (QCD) exists, why can we not simply employ computer calculations (e.g.,
using lattice gauge theory) to determine the state of matter at high densities? Given
that in fact such calculations are not practical, we explore the freedom that exists in
principle to construct models of high-density matter; the fundamental point is that
because the densities are well above what is measurable in the laboratory, one could
always imagine, in the context of a model, adding terms that are negligible at nuclear
density or for symmetric matter but important when the matter is a few times denser
and significantly asymmetric. After discussing some example classes of models, we
survey current constraints from laboratory experiments and future prospects. We
conclude with a discussion of how one would map an idealized future data set of
masses, radii, temperatures, etc. of neutron stars onto the equation of state of cold
dense matter.
1.2.1 The Basics: Dense Matter and Neutron Stars
Consider a set of identical fermions (e.g., electrons or neutrons) of mass m and
number density n. The linear space available to each fermion is thus Δx ∼ n −1/3 ,
and the uncertainty principle states that the uncertainty in momentum (and hence
the minimum momentum) is given by ΔpΔx ∼ ¯
h and thus p min ∼ ¯
hn 1/3 , where