28
M. C. Miller
for some perspectives on these oscillations). Unfortunately, the data are insufficient
to make clear identifications. For example, the candidate torsional modes for these
two soft gamma-ray repeaters skip many modes that would have been expected to
be seen. In addition, the theory for these oscillations is not settled. Nonetheless, as
data and models progress mode identifications may become clearer, and if they do
then they will provide a powerful and complementary set of constraints.
In general, the methods discussed in this section have uncertainties that are
dominated by systematics. As a result, future progress depends on both better
observations and better models. For example, there is a recent set of magnetohydrodynamic simulations that aim to reproduce kHz QPO phenomenology in accreting
weakly magnetic neutron stars [36, 119, 120, 139, 140, 189–192]. These simulations
may ultimately result in solid understanding of kHz QPOs that could be used to
interpret observations. The simulations are extremely challenging, however, and
may take many years to get to the point of full reliability. Some of the apparently
disparate constraints may eventually be coupled through the recently discovered “ILove-Q” relations between the moment of inertia I, Love number, and rotational
quadrupole moment Q [238], although the important issues of systematics must be
solved first.
1.5 Cooling of Neutron Stars
As noted in Sect. 1.2, cooling processes are sensitive to different aspects of
the equation of state than are the maximum mass and the mass-radius relation.
This in principle means that observations of cooling neutron stars can give us a
complementary tool with which to constrain the properties of dense matter. In fact,
current data are broadly consistent with the dense matter in neutron stars not having
significant contributions from exotic phases (modulo some complications we shall
discuss), but unfortunately as we will see this is a very blunt tool and there is plenty
of room for exotic matter.
X-rays from cooling neutron stars were originally proposed in the mid-1960s
[62] as one of the few ways that these stars could be detected. In this section we
will focus on cooling theory and observations that bear on the matter at the cores
of neutron stars. We will thus not discuss, e.g., the cooling of transiently accreting
neutron stars (see [172, 239] for recent reviews) that return to quiescence after a
years-long outburst has raised the crust out of thermal equilibrium with the core,
because their cooling curves depend primarily on processes in the crust.
Broadly speaking, after a neutron star forms in a supernova (where at birth its
temperature is roughly the virial temperature T vir ∼ GMm n /(Rk) ∼ 10 12 K),
the star goes through a phase of duration ∼10 4−6 yr in which its cooling is
dominated by neutrino losses from the core. After this point the star cools mainly by
photon luminosity from the surface, where the energy from the core is transported
conductively until the density is low enough that radiative processes take over (this
typically occurs in the outer crust). The temperature of a neutron star at a given
M. C. Miller
for some perspectives on these oscillations). Unfortunately, the data are insufficient
to make clear identifications. For example, the candidate torsional modes for these
two soft gamma-ray repeaters skip many modes that would have been expected to
be seen. In addition, the theory for these oscillations is not settled. Nonetheless, as
data and models progress mode identifications may become clearer, and if they do
then they will provide a powerful and complementary set of constraints.
In general, the methods discussed in this section have uncertainties that are
dominated by systematics. As a result, future progress depends on both better
observations and better models. For example, there is a recent set of magnetohydrodynamic simulations that aim to reproduce kHz QPO phenomenology in accreting
weakly magnetic neutron stars [36, 119, 120, 139, 140, 189–192]. These simulations
may ultimately result in solid understanding of kHz QPOs that could be used to
interpret observations. The simulations are extremely challenging, however, and
may take many years to get to the point of full reliability. Some of the apparently
disparate constraints may eventually be coupled through the recently discovered “ILove-Q” relations between the moment of inertia I, Love number, and rotational
quadrupole moment Q [238], although the important issues of systematics must be
solved first.
1.5 Cooling of Neutron Stars
As noted in Sect. 1.2, cooling processes are sensitive to different aspects of
the equation of state than are the maximum mass and the mass-radius relation.
This in principle means that observations of cooling neutron stars can give us a
complementary tool with which to constrain the properties of dense matter. In fact,
current data are broadly consistent with the dense matter in neutron stars not having
significant contributions from exotic phases (modulo some complications we shall
discuss), but unfortunately as we will see this is a very blunt tool and there is plenty
of room for exotic matter.
X-rays from cooling neutron stars were originally proposed in the mid-1960s
[62] as one of the few ways that these stars could be detected. In this section we
will focus on cooling theory and observations that bear on the matter at the cores
of neutron stars. We will thus not discuss, e.g., the cooling of transiently accreting
neutron stars (see [172, 239] for recent reviews) that return to quiescence after a
years-long outburst has raised the crust out of thermal equilibrium with the core,
because their cooling curves depend primarily on processes in the crust.
Broadly speaking, after a neutron star forms in a supernova (where at birth its
temperature is roughly the virial temperature T vir ∼ GMm n /(Rk) ∼ 10 12 K),
the star goes through a phase of duration ∼10 4−6 yr in which its cooling is
dominated by neutrino losses from the core. After this point the star cools mainly by
photon luminosity from the surface, where the energy from the core is transported
conductively until the density is low enough that radiative processes take over (this
typically occurs in the outer crust). The temperature of a neutron star at a given