Neutron Stars at the Crossroads of Fundamental Physics

I. Organizers

Jeremy Heyl University of British Columbia
Vicky Kaspi McGill University
Feryal Özel University of Arizona
Krishna Rajagopal Massachusetts Institute of Technology
Chris Thompson University of Toronto, CITA
Marten van Kerkwijk University of Toronto

II. Location: UBC 9-13 August 2005

III. Objectives, Activities and Target Audience

A. A short overview of the subject area:

Neutron stars provide a laboratory to verify our understanding of nature at the extreme. The intense magnetic fields of neutron stars exceed those produced on Earth a billion-fold, and the densities and pressures dwarf the realm of Earth-bound matter by a factor of a trillion or more. Neutron stars provide a unique opportunity to extrapolate and verify our theories of matter, energy and their interaction.

We might learn the gross properties of neutron stars such as their mass and radius definitively from observations of the thermal radiation from their surfaces. The details of their cooling history and kinematics may probe the quark-gluon phase transition, and the understanding the dynamics of material and light near their surfaces can verify QED and general relativity. The physics of neutron stars naturally attracts researchers over a wide range of disciplines from radio astronomy to lattice quantum-chromodynamics (QCD).

In recent years our understanding of neutron stars is increasing by leaps and bounds. The recent launch of several X-ray telescopes and the dramatic upgrades of several ground-based facilities has opened a new era of discovery for neutron stars and has deepened our understanding of the physical processes important near and within these objects. Meanwhile on a theoretical front, QCD calculations, strong-field QED and neutron-star atmospheres are beginning to address the observed properties of these objects ab initio.

On the observational front, recent discoveries have provided both new breakthroughs as well as surprising new mysteries, all of which have major relevance to answering basic physical questions. The launches in the past few years of Chandra and XMM have permitted the first precision measurements of neutron star temperatures for quantitative comparison with cooling models, a classic way of constraining the equation of state (EOS). Similarly spectral determination of stellar radii offer tantalizing promise of new quantitative EOS constraints.

Neutron star atmospheres provide us with a window into the dense interiors and strong magnetic fields of these compact objects. All the photons we receive from the neutron star interiors are processed and modified by their atmospheres. It is, therefore, crucial to understand the physical properties of these outermost layers in order to interpret observations and connect them to predictions of the QCD calculations for the neutron star interiors.

Understanding the spectra of the radiation from their surfaces turns out to have its own very interesting physical implications. Many of the spectra resemble black bodies uncannily closely, which is completely unexpected. The very recently claimed detection of spectral lines in some objects suggest strong magnetic fields play a large role. This is providing a huge impetus to studies of radiative transfer, conduction, and behavior of matter in strong magnetic fields. With inferred magnetic field strengths over the critical QED limit, very interesting QED effects become important. Vacuum polarization and vacuum resonance mode conversion likely affect the observed spectra. Hydrogen will be partly neutral even at the 1 million degrees typically encountered, as it is is much more strongly bound in strong fields; indeed, even `molecular' chains may be present. The physical understanding and detailed calculations of binding energies, energy levels, transition probabilities, radiative transfer, etc., are all extremely challenging in these conditions, but are required to compare with the new, excellent observations.

A number of unique physical processes take place in the strongly magnetized plasma that makes up the neutron star atmosphere. For magnetic fields as high as a petagauss, the Landau energy of the electron is larger than any other energy in the system, such as the electron Fermi energy and its rest mass. This magnetic confinement renders the medium birefringent and leads to a highly anisotropic interaction between photons and electrons. Moreover, the vacuum itself is polarized and further modifies the propagation of photons via resonant, polarization-mode changing interactions with virtual pairs.

The strong anisotropy and photon-energy dependence of all these interactions presents a mathematical and computational challenge in treating this multi-dimensional, polarized radiative transfer problem. In recent years, new numerical methods have been developed to address these issues. Moreover, there are currently a number of attempts that diverge from a more standard analysis based on the normal modes of photon propagation and try to cast the differential equations in more tractable forms. Such progress has led to the first detailed models of magnetized neutron star atmospheres in idealized configurations. Comparison of these calculations with the high-quality X-Ray observations from new satellites has already yielded the most accurate measurements of the magnetic field strengths of some neutron stars and has provided strong constraints on their masses and radii.

Even after the photons leave the surface of the neutron star, they probe physics in an otherwise uncharted realm, because the vacuum surrounding the neutron star is birefringent in the presence of the ultra-strong magnetic field. One consequence is that hard X-ray photons can split in two or merge together; another is that the polarization of a photon (regardless of its energy) is not constant as it travels away from the neutron star; a third is that single gamma-rays can convert to bound pairs of electrons and positrons. This workshop will focus on the effects of these QED processes on the X-ray spectra of neutron stars observed in quiescence: in particular on the observability of narrow line features in the thermal radiation from their surfaces; and their ability to generate energetic bunches of relativistic particles that are manifested as pulsed electromagnetic radiation.

New major observational evidence in support of the existence of these strongly magnetized neutron stars (with magnetic fields stronger than a teragauss), or "magnetars," further buoys hopes of using these objects as unique laboratories for testing extreme QED. Timing measurements as well as the recent discovery of infrared variability in magnetar candidates may provide crucial pieces of the puzzle of the emission mechanism. On the other hand, the discovery of apparently high-magnetic field conventional neutron stars, which show no evidence for magnetar type behavior, is an interesting observational challenge to the magnetar model.

More broadly, entire classes of neutron stars are still very poorly understood: the so-called "isolated neutron stars" may represent the tip of the iceberg of old, dead Galactic neutron stars shining due to residual heat, nearly dead magnetars also still hot but much younger, or neutron stars accreting from the interstellar medium. Completely mysterious sources, like the central source in the famous supernova remnant Cas A, represent another to be determined new physical manifestation of neutron stars, be they quiescent magnetars or ultra low magnetic field young objects.

Beneath the atmosphere lies the one of the fundamental goals of the study of neutron stars, understanding the forces that hold nuclei and nucleons together. Quantum chromodynamics (QCD) is the theory of quarks, and therefore must describe neutrons, nuclei and the interior of neutron stars. However, obtaining predictions from QCD for any of these systems is difficult: QCD is the one example we know of in nature of a field theory with no fundamental small parameter. It has a natural length scale, of order a femtometer (fm), and physics at that length scale is nonperturbative and hard to calculate. Recently, theorists have realized that QCD simplifies enormously in the high-density limit, in which matter is squeezed until the spacing between quarks is orders of magnitude smaller than a fm. In this limit, quarks near their (very large) Fermi surfaces form Cooper pairs. The resulting material has bizarre properties: it is a superfluid and a "color superconductor," meaning that it expels QCD-magnetic fields, but it admits an ordinary looking magnetic field, and the associated photon propagates freely through this asymptotically dense material, as in a transparent insulator. Most important from the theoretical point of view, the long wavelength excitations of this material, those with fm length scales where QCD is difficult, are simple enough to be understood analytically. The nontrivial excitations are all at short wavelengths, where QCD itself is tractable. So, any physical property of quark matter is calculable, by dint of sufficient effort, at asymptotically high densities. All of the standard bogeymen of QCD (e.g. confinement and chiral symmetry breaking) are either absent or tractable.

With such a solid foundation upon which to build, why, then, does understanding the physical properties of the extraordinarily dense matter deep within neutron stars remain a profound challenge to quantum field theory? The problem is that to a QCD theorist, even though neutron star cores are the densest matter in the universe they are, frustratingly, not dense enough. The spacing between quarks is on the order of 0.5 to 1 fm, meaning that it is not clear whether the quarks are free or remain correlated in squeezed but recognizable neutrons. At these densities, many questions about the properties of neutron stars remain unanswerable by ab initio methods. Theorists have a handful of hypotheses, based upon different possible answers to the question of what happens to the well-understood but asymptotically dense quark matter as the density is reduced. To make progress, contact with observation is crucial. QCD theorists are therefore striving to turn their hypotheses into predictions of specific heats, neutrino mean emissivities and mean free paths, equations of state, pinning of superfluid vortices and more, which can in turn be used by astrophysical theorists to make predictions for observable phenomena like pulsar glitches, neutron star radii, neutron star temperatures, vibrational modes of neutron stars, neutrino emission from seconds old neutron stars, and gravity wave emission from neutron stars in collision.

The traditional approach to the theory of neutron star matter is complementary to that above: instead of working downward in density from a well understood starting point at asymptotically high densities, one starts with empirical knowledge of ordinary nuclear matter, based upon decades of experiments on finite nuclei and traditional nuclear many body theory. The traditional approach is crucial to understanding the crust and outer layers of a neutron star, while beginning from high density and working down is primarily aimed at understanding the core.

These approaches are complementary in another sense: both are prerequisites to understanding the equation of state. From a purely theoretical point of view, the one calculational method that could in principle provide precise answers at less than asymptotic densities, allowing a unified description from nuclear density all the way up, is lattice QCD, in which spacetime is discretized in a finite sized box and the QCD path integral is evaluated. All conventional algorithms for evaluating the resulting of-order-billion dimensional integrals rely on importance sampling, which is only possible when the integrand is positive definite. QCD at nonzero density represents a grand challenge to computational QCD: the "fermion sign problem" makes the integrand complex, meaning that when formulated in the standard way the path integral involves cancellations among contributions that are individually exponentially larger than the answer. A number of lattice gauge theorists have recently made some progress in reformulating lattice QCD to make it more tractable, so far either at temperatures that are too high to be of interest or in simplified models that lack important features of QCD. The challenge of doing ab initio calculations of the properties of neutron star interiors motivates some of the most theoretically innovative work on the computational QCD frontier.

B. Objectives

The time is ripe to gather people whose research impacts our understanding of neutron stars. Because the study of the physics of neutron stars encompasses a wide range of physics, it is unusual to bring together a stimulating mixture of young researchers and established figures from the various disciplines to present their latest results and to develop collaborations.

The workshop will address both the recent observational and theoretical breakthroughs and the areas where great progress may be imminent. Specifically, the participants will discuss the latest calculational approaches to high-density QCD, non-pertubative QED, neutron-star atmospheres, structure and dynamics. We will also contrast the state-of-the-art theoretical results with our ever-growing observational understanding of neutron stars.

Although successful in accounting for the general properties of the observed X-Ray spectra of isolated neutron stars, current atmosphere models fail to explain the lack of spectral features and the radiation at other energy. The models rely on a number of simplifications imposed mostly by computational difficulties. For example, the energy change in photon-electron scattering has been neglected, bound-free and bound-bound transitions have either been omitted or minimally included, and the magnetic field geometry has been restricted to simple configurations. One of the goals of this meeting is to address the uncertainties in our interpretation of observations arising from these limitations. More importantly, the discussions will focus on the prospects for developing new numerical methods that will relax the above assumptions and produce more complete models of neutron star atmospheres.

Several outstanding calculations must be completed before we understand the implications of X-ray observations of magnetars for their interior physics. Matter immersed in an intense magnetic field (much stronger than the QED value of 44 teragauss) is believed to condense into long molecular chains aligned with the field. In particular, detailed calculations of electronic energy levels of isolated atoms and atomic chains are still incomplete, as are calculations of the strength of the binding between chains and the transport of heat and electricity along them. These calculations are also essential ingredients into the calculation of detailed atmosphere models used to interpret observations of spectral features in cooling neutron stars, which are now being discovered by X-ray telescopes.

Even before neutron stars were discovered, it was recognized that their interiors would become superfluid through pairing of nucleons. The glitching behavior of rapidly rotating radio pulsars is generally ascribed to the presence of a pinned superfluid in their rigid crusts. One of the goals of this workshop is to stimulate a more precise understanding of the hydrodynamic behavior of a nuclear superfluid in a rotating neutron star, and the physical processes underlying neutron star timing behavior. A large fraction of the liquid core is thought eventually to become a superfluid, but the observational constraints on its properties are still poorly developed. The core is also generally believed to be a Type II superconductor; the interaction between superfluid vortices and magnetic fluxoids is also still poorly understood, but has important implications for magnetic field transport and some types of timing behavior such as precession. Calculations of the strength of proton/neutron pairing in nucleon matter are fundamental to our understanding of neutron star behavior, as they strongly influence the rate of neutrino emission and the thermal evolution of isolated neutron stars; the bulk transport properties of nuclear matter; and the decay of magnetic fields -- all of which have observable consequences. One of the goals of this workshop is to examine how the results of these calculations are constrained by observations of radio pulsars and magnetars.

Most neutron stars appear to be formed in nature within a narrow range of masses, 1.35-1.45 times the mass of the sun. The maximum mass of a neutron star could however exceed this range by as much as 50 percent. One of the most intriguing avenues for measuring the equation of state of dense matter at high temperatures is to search for transient flashes of neutrino emission from newborn neutron stars, using underground detectors such as SNO. Some fraction of these objects are generally expected to collapse to form black holes under the weight of infalling matter. The observational signature of these events in neutrino detectors, and the detailed implications for the equation of state will be one subject of this workshop.

C. Activities

The workshop will be devoted to the discussion of recent advances in the theory of nuclear matter in neutron stars, the astrophysical theory and observations of neutron stars. The program will consist of talks through the morning and more informal break-out sessions in the afternoons to foster interaction. We hope to encourage attendees from the various sub-disciplines participate and contribute throughout the four-day intensive workshop.

D. Target Audience:

Students, postdoctoral scholars and more senior researchers who are currently performing active research in the theory and observation of neutron stars

III. Diffusion and sharing of scientific knowledge

If progress in QCD is to inform our understanding of neutron star interiors, and progress in neutron star observation is to inform our understanding of QCD matter at less-than-asymptotic density, it is crucial that QCD theorists, neutron star theorists and neutron star observers understand each other's successes and outstanding obstacles. Many workshops bring two out of three of these communities together. Our purpose is to bring people from all three together, with our selection of participants biased toward those who will be good at explaining the issues they face to the other two communities. Between now and 2005, we expect significant progress in all three communities, as all currently have significant forward momentum. Summer 2005 should be a perfect time to gather, cross-fertilize, and stimulate ideas for what comes next that reach across sub-disciplinary boundaries.