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Impearls: Magnetars and Pulsars: The Physics of Neutron Stars

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Earthdate 2004-05-29

The Physics of Neutron Stars

Continuing review of the Science series on pulsars, in the article “The Physics of Neutron Stars,” J. M. Lattimer and M. Prakash reveal some of the mind-boggling physics employed by neutron stars (the physical core of pulsars). 2

Neutron stars may exhibit conditions and phenomena not observed elsewhere, such as hyperon-dominated matter, deconfined quark matter, superfluidity and superconductivity with critical temperatures near 1010 kelvin, opaqueness to neutrinos, and magnetic fields in excess of 1013 Gauss.  […]

The term “neutron star” as generally used today refers to a star with a mass M on the order of 1.5 solar masses (M[Sun]), a radius R of ∼12 km, and a central density nc as high as 5 to 10 times the nuclear equilibrium density n0 ≅ 0.16 fm−3 of neutrons and protons found in laboratory nuclei.  A neutron star is thus one of the densest forms of matter in the observable universe.  Although neutrons dominate the nucleonic component of neutron stars, some protons (and enough electrons and muons to neutralize the matter) exist.  At supranuclear densities, exotica such as strangeness-bearing baryons, condensed mesons (pion or kaon), or even deconfined quarks may appear.  Fermions, whether in the form of hadrons or deconfined quarks, are expected to also exhibit superfluidity and/or superconductivity.

Neutron stars encompass “normal” stars, with hadronic matter exteriors in which the surface pressure and baryon density vanish (the interior may contain any or a combination of exotic particles permitted by the physics of strong interactions), and “strange quark matter” (SQM) stars.  An SQM star could have either a bare quark-matter surface with vanishing pressure but a large, supranuclear density, or a thin layer of normal matter supported by Coulomb forces above the quark surface.  The name “SQM star” originates from the conjecture that quark matter with up, down, and strange quarks (the charm, bottom, and top quarks are too massive to appear inside neutron stars) might have a greater binding energy per baryon at zero pressure than iron nuclei have.  If true, such matter is the ultimate ground state of matter.  Normal matter is then metastable, and compressed to sufficiently high density, it would spontaneously convert to deconfined quark matter.  Unlike normal stars, SQM stars are self-bound, not requiring gravity to hold them together.  It is generally assumed that pulsars and other observed neutron stars are normal neutron stars.  If SQM stars have a bare quark surface, calculations suggest that photon emission from SQM stars occurs primarily in the energy range 30 keV < E < 500 keV.

After a discussion of how neutron stars form (fascinating, with an illuminating diagram), Lattimer and Prakash go on to discuss a proto-neutron star's possible collapse into a black hole.

The proto-neutron star, in some cases, might not survive its early evolution, collapsing instead into a black hole.  This could occur in two different ways.  First, proto-neutron stars accrete mass that has fallen through the shock.  This accretion terminates when the shock lifts off, but not before the star's mass has exceeded its maximum mass.  It would then collapse and its neutrino signal would abruptly cease.  If this does not occur, a second mode of black hole creation is possible.  A proto-neutron star's maximum mass is enhanced relative to a cold star by its extra leptons and thermal energy.  Therefore, following accretion, the proto-neutron star could have a mass below its maximum mass, but still greater than that of a cold star.  If so, collapse to a black hole would occur on a diffusion time of 10 to 20 s, longer than in the first case.  Perhaps such a scenario could explain the enigma of SN 1987A.  The 10-s duration of the neutrino signal confirmed the birth and early survival of a proto-neutron star, yet there is no evidence that a neutron star exists in this supernova's remnant.  The remnant's observed luminosity is fully accounted for by radioactivity in the ejected matter, meaning that any contribution from magnetic dipole radiation, expected from a rotating magnetized neutron star, is very small.  Either there is presently no neutron star, or its spin rate or magnetic field is substantially smaller than those of typical pulsars.  A delayed collapse scenario could account for these observations.

Lattimer and Prakash proceed to discuss neutron stars' internal structure and composition (also including an illuminating diagram).

A neutron star has five major regions: the inner and outer cores, the crust, the envelope, and the atmosphere.  The atmosphere and envelope contain a negligible amount of mass, but the atmosphere plays an important role in shaping the emergent photon spectrum, and the envelope crucially influences the transport and release of thermal energy from the star's surface.  The crust, extending about 1 to 2 km below the surface, primarily contains nuclei.  The dominant nuclei in the crust vary with density, and range from 56Fe for matter with densities less than about 106 g cm−3 to nuclei with A ∼ 200 but x ∼ (0.1 to 0.2) near the core-crust interface at nn0⁄3.  Such extremely neutron-rich nuclei are not observed in the laboratory, but rare-isotope accelerators hope to create some of them.

Within the crust, at densities above the neutron drip density 4 × 1011 g cm−3 where the neutron chemical potential (the energy required to remove a neutron from the filled sea of degenerate fermions) is zero, neutrons leak out of nuclei.  At the highest densities in the crust, more of the matter resides in the neutron fluid than in nuclei.  At the core-crust interface, nuclei are so closely packed that they are almost touching.  At somewhat lower densities, the nuclear lattice can turn insideout and form a lattice of voids, which is eventually squeezed out at densities near n0.  If so, beginning at about 0.1 n0, there could be a continuous change of the dimensionality of matter from three-dimensional (3D) nuclei (meatballs), to 2D cylindrical nuclei (spaghetti), to 1D slabs of nuclei interlaid with planar voids (lasagna), to 2D cylindrical voids (ziti), to 3D voids (ravioli, or Swiss cheese) before an eventual transition to uniform nucleonic matter (sauce).  This series of transitions is known as the nuclear pasta.

For temperatures less than 0.1 MeV, the neutron fluid in the crust probably forms a 1S0 superfluid.  Such a superfluid would alter the specific heat and the neutrino emissivities of the crust, thereby affecting how neutron stars cool.  The superfluid would also form a reservoir of angular momentum that, being loosely coupled to the crust, could cause pulsar glitch phenomena.

The core constitutes up to 99% of the mass of the star.  The outer core consists of a soup of nucleons, electrons, and muons.  The neutrons could form a 3P2 superfluid and the protons a 1S0 superconductor within the outer core.  In the inner core, exotic particles such as strangeness-bearing hyperons and/or Bose condensates (pions or kaons) may become abundant.  It is possible that a transition to a mixed phase of hadronic and deconfined quark matter develops, even if strange quark matter is not the ultimate ground state of matter.  Delineating the phase structure of dense cold quark matter has yielded novel states of matter, including color-superconducting phases with and without condensed mesons.

Lattimer and Prakash end their review with a discussion of future prospects in neutron star and pulsar physics.

A new generation of neutrino observatories also hold great potential for studies of proto-neutron star evolution and neutron star structure.  Neutrino observations of supernovae, validated by the serendipitous observations of SN 1987A, which yielded about 20 neutrinos, should detect thousands of neutrinos from a galactic supernova.  This could yield neutron star binding energies to a few percent accuracy and provide estimates of their masses, radii, and interior compositions, as well as details of neutrino opacities in dense matter.  Neutrino fluxes from proto-neutron stars with and without exotica (hyperons, Bose condensates, and quarks) have been investigated […].

Gravitational radiation is expected from asymmetric spinning compact objects, from mergers involving neutron stars and black holes, and from gravitational-collapse supernovae.  Depending on the internal viscous forces in rotating neutron stars, gravitational radiation could drive an instability in r-modes of nonradial pulsations to grow on a time scale of tens of seconds.  Mergers can be observed to great distances.  Detectors due to begin operation over the next decade, including LIGO (Laser Interferometer Gravitational-Wave Observatory), VIRGO (Italian-French Laser Interferometer Collaboration), GEO600 (British-German Cooperation for Gravity Wave Experiment), and TAMA (Japanese Interferometric Gravitational-Wave Project), could see up to hundreds of mergers per year.  Binary mergers can yield important information, including the masses and mass-to-radius ratios of the binary's components and possibly details of their inspiraling orbits.

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