ScienceWeek

SCIENCEWEEK

ScienceWeek
January 10, 2003
Vol. 7 Number 2

An Online Digest of Research in the Sciences

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The father of the arrow is the thought:
How do I expand my reach?
-- Paul Klee (1879-1940)

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Section 1

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Thematic Issue: Neutron Stars

1. Introduction
2. On the Birth and Life of Neutron Stars
3. On Neutron Stars
4. Neutron Stars and the Fluid Properties of Hot Atomic Nuclei
5. On the Equation of State of Dense Matter
6. Neutron Stars and Relativistic Jets

Notices and Subscription Information

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Section 2

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1. INTRODUCTION.

In this century, astronomy and astrophysics have contributed
greatly to what might be called the "Hall of Wonders", the
gallery of real-world spellbinding objects. Perhaps the two most
outstanding contributions to this gallery are black holes and
neutron stars. Black holes, born of the death of super-massive
stars, are in this century the most spectacular astronomical
objects known; neutron stars, born of the death of merely massive
stars, are not far behind on any gauge of the extraordinary. A
neutron star is an extremely dense and compact star that has
undergone gravitational collapse to such an extent that much of
the material has been compressed into neutrons. Such stars were
theoretically postulated in the 1930s, but it was not until 1967
that their existence was actually confirmed by observations. It
is also thought that gamma-ray bursts may have neutron star
origins. Models of the structure of neutron stars have been
derived from study of the sudden changes in pulsar spin rates
("glitches").

ON THE PURSUIT OF SCIENCE.

"The pursuit of science has often been compared to the scaling of
mountains, high and not so high. But who amongst us can hope,
even in imagination, to scale the Everest and reach its summit
when the sky is blue and the air is still, and in the stillness
of the air survey the entire Himalayan range in the dazzling
white of the snow stretching to infinity? None of us can hope for
a comparable vision of nature and of the universe around us. But
there is nothing mean or lowly in standing in the valley below
and awaiting the Sun to rise over Kinchinjunga."
--  Subrahmanyan Chandrasekhar (1910-1995) (Nobel Prize in
Physics 1983)

ON THE CHANDRASEKHAR LIMIT.

"In 1928 an Indian graduate student, Subrahmanyan Chandrasekhar
[1910-1995], set sail for England to study at Cambridge with the
British astronomer Sir Arthur Eddington [1882-1944], an expert on
general relativity... During his voyage from India, Chandrasekhar
worked out how big a star could be and still support itself
against its own gravity after it had used up all its fuel. The
idea was this: When the star becomes small, the matter particles
get very near each other, and so according to the Pauli exclusion
principle, they must have very different velocities. This makes
them move away from each other and so tends to make the star
expand. A star can therefore maintain itself at a constant radius
by a balance between the attraction of gravity and the repulsion
that arises from the exclusion principle, just as earlier in its
life gravity was balanced by the heat. Chandrasekhar realized,
however, that there is a limit to the repulsion that the
exclusion principle can provide. The theory of relativity limits
the maximum difference in the velocities of the matter particles
in the star to the speed of light. This means that when the star
got sufficiently dense, the repulsion caused by the exclusion
principle would be less than the attraction of gravity.
Chandrasekhar calculated that a cold star of more than about one
and a half times the mass of the sun would not be able to support
itself against its own gravity. (This mass is now known as the
Chandrasekhar limit.) A similar discovery was made about the same
time by the Russian scientist  Lev Davidovich Landau [1908-
1968]." (Note #1).

Stephen W. Hawking: A Brief History of Time. Bantam Press 1988,
p.83.

Note #1: Chandrasekhar limit: The remnant mass after the blow-off
during the terminal stage of the life of a star determines the
ultimate fate of the star. If the remnant mass is less than 1.44
solar masses (the Chandrasekhar limit for a star with no hydrogen
content), the star collapses into a white dwarf. If the remnant
mass is greater than 1.44 solar masses, depending on the remnant
mass, the star collapses into either a neutron star or a black
hole.

ON MASSIVE STARS, NEUTRON STARS, AND PULSARS.

"The fate of lower-mass stars is to cease fusion after using
their available supply of helium, then to eject their outer
layers quietly, with the cores left to cool slowly as white
dwarfs. Stars more massive than a few solar masses experience
more phases at the ends of their lives, going through one nuclear
fuel after another to battle the crush of gravity. After the
star's helium is exhausted, the core contracts and heats again,
and the outer layers expand... In very massive stars, carbon may
first ignite; for sufficiently massive stars, increasingly heavy
elements are subsequently burned, fusing all the way to iron. The
star becomes a gigantic cosmic onion, consisting of concentric
shells in which increasingly heavier elements are fused. The
final fusion product is iron...

"A star with an iron core must seek an equilibrium with gravity
that does not require further expenditure of energy. Smaller
stars could find their final equilibrium in electron degeneracy.
However, for any object with a mass greater than 1.4 times the
solar mass, the pressure from even electron degeneracy is not
sufficient to support the star against its own weight. In 1930,
Subramaynyan Chandrasekhar realized that in order to provide the
incredible pressures required to maintain more massive stars, the
electrons supplying that support would have to move at greater
than the speed of light, which was known from the special theory
of relativity to be an impossibility. Thus special relativity
demands an upper mass limit, today called the "Chandrasekhar
limit". If the dying star fails to eject enough of its matter to
allow its collapsing core to drop below this limit, the electrons
cannot supply the necessary pressure. But if electron degeneracy
pressure falls short, the star does not just slowly contract. It
collapses catastrophically, sending a shock wave into its outer
layers and blowing them off in a single cataclysmic explosion
called a "supernova"...

"A supernova which arises from the collapse of a massive star is
designated by astronomers as Type II. (This name suggests that
there must be another type of supernova, the Type I supernova.
The Type I supernova originates from the explosion of a white
dwarf in a binary system.)...

"Although a great deal of the star is blown out into interstellar
space by a Type II supernova, some fraction is probably left
behind in a core remnant. If the mass of the remnant still
exceeds the Chandrasekhar limit, what can the star do? It cannot
settle down as a white dwarf star; so what remains? As the star
collapses to greater and greater compaction, the electrons are
squeezed into the atomic nuclei themselves, where they are forced
to merge into the protons, forming neutrons. The neutrons, which
are much more massive than electrons, can themselves exert a
degeneracy pressure known as "neutron degeneracy pressure". The
entire star is compressed essentially to the density of an atomic
nucleus, but composed only of neutrons. This massive neutron
nucleus is known as a "neutron star". A neutron star is
astonishingly compact; if an object with the mass of the Sun were
to collapse completely to a neutron star, its radius would be
only about 10 km, roughly the size of a typical large city on
Earth. The neutron star is a remarkable object. Its existence was
predicted as early as 1934 by Fritz Zwicky and Walter Baade,
although their suggestion was ignored for decades; a neutron star
seemed too bizarre to consider. This attitude changed in 1967
when the first pulsar was detected. A pulsar emits highly
regular, energetic bursts of electromagnetic radiation, generally
as radio waves. The pulses from the first pulsar were so regular
that the discoverers, Jocelyn Bell and Anthony Hewish at
Cambridge University, first thought they had received signals
from another civilization! No familiar astronomical process was
known at the time that could produce electromagnetic bursts of
such sharpness and regularity, at such a rapid rate. Ordinary
oscillations would be inadequate to explain the signal. As more
and more pulsars were observed, however, the mystery slowly
yielded. Thomas Gold first suggested that pulsars might be
associated with the exotic neutron star. Subsequent observations
have borne this idea out; no other mechanism is remotely
plausible to explain the properties of pulsars."

J.F. Hawley and K.A. Holcomb: Foundations of Modern Cosmology.
Oxford University Press 1998, p.132.

NEUTRON STARS: RELATIVITY'S LIMITING ROLE

"For the most part, the effects of general relativity in stars
are very small. The characteristic measure of the size of
relativistic effects in bodies is the quantity GM/Rc2, where M
and R are the mass and radius of the body. For the Sun, this
factor is 10^(-5), while for a white-dwarf star it is 10^(-3),
both small corrections to the overall structure. One of the few
stellar situations in which general relativity was found to have
a qualitative effect was supermassive stars, with masses of
between 1000 and 10^(9) solar masses, once proposed as possible
models for quasars. It turned out, however, that these stars were
on the dividing line between stability and instability to
collapse according to Newtonian theory, and so the general
relativistic effects, though only of order 10^(-4), were enough
to make such stars unstable, and make them unattractive as
candidates for quasars.

"The one material stellar object for which general relativity is
important is the neutron star. (The black hole is, of course,
another object in which general relativity is crucial, but since
the matter in a black hole has fallen across the "event horizon",
it is not a "material" body in the normal sense...)

"The factor GM/Rc2 for a neutron star can be as large as 0.3, so
general relativity can introduce sizable corrections to the
structure of the body. Furthermore, general relativity introduces
important upper bounds on the masses and rotation rates of
neutron stars that are observationally relevant.

"Neutron stars were first suggested as theoretical possibilities
by Walter Baade and Fritz Zwicky in the 1930s as the end product
of the gravitational collapse in the interior of a supernova
explosion. The collapsed star is so highly condensed by
gravitational forces that atomic electrons are crushed together
with the nuclear protons to form neutrons, and the density of the
matter is raised above nuclear densities... Under such
conditions, the neutrons become "degenerate", a state in which
their behavior is governed by the Pauli exclusion principle of
quantum mechanics which prevents any two neutrons from occupying
the same region of space in the same state (the same principle
applied to electrons in atoms leads to the shell structure
evident in the periodic table of the elements). A typical neutron
star model has a mass of one solar mass, and a radius of about 10
km.

"However, neutron stars remained just theoretical possibilities
until the discovery of pulsars in 1967 and their subsequent
interpretation as rotating neutron stars. Since that time, much
effort has been directed toward calculating detailed neutron-star
models, with particular interest in masses, moments of inertia,
internal structure, and oscillations. These quantities are
important in understanding both the steady changes and the
discontinuous jumps ("glitches") in the observed periods of
pulses from pulsars. The principal uncertainty in these
calculations is not general relativity; the equations of
relativistic stellar structure are well known and relatively
simple to implement on the computer. Rather the uncertainty is in
the equation of state of matter above nuclear densities, for
which there is virtually no experimental information. In fact,
some theorists regard pulsar observations and neutron-star models
as a way to test various candidate equations of state.

Clifford Will: in: Paul Davies (ed.): The New Physics. Cambridge
University Press 1989, p.23.

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2. ON THE BIRTH AND LIFE OF NEUTRON STARS.

Joshua N. Winn (Massachusetts Institute of Technology, US)
presents a review of current research on neutron stars, the
author making the following points:

1) Perhaps one problem with the "jaw-dropping" statistics
concerning pulsars is that the statistics are too extreme. Using
Earthly analogies, it is difficult to comprehend an entity with a
density of 10^(14) grams per cubic centimeter [*Note #1] in a
gravitational field that produces an acceleration of free fall
(g) 600 billion times that produced at the surface of Earth. It
is even more difficult to visualize such a dense city-size object
"as it spins furiously, squirting plasma (ionized gases) from
electric arcs near the poles of its inconceivable magnetic field
and swirling up a superfluid of neutrons in its interior." But
after 30 years of research, enough is known about pulsars to
reconstruct the outlines of their existences.

2) The newborn neutron star, produced by a dead massive star,
possesses four salient characteristics: a) a fast rotation rate,
typically 50 times per second; b) a directed velocity in excess
of 1000 kilometers per second that may be caused by violent
asymmetry in the supernova explosion of the parent star; c)
extreme temperature due to the small radiative surface area
(e.g., temperatures of 100,000 to 1 million degrees kelvin; d) an
immense magnetic field, typically a million times stronger than
that of the Earth. (The author notes: "It is easier to write the
figure 10^(12) gauss than to ponder its zeros.")

3) A spinning magnet generates voltages, as was demonstrated by
Michael Faraday in 1831, and a neutron star is a gargantuan
spinning magnet, the resultant voltage tearing electrons,
positrons, and ions from its surface and flinging them outward
into space along the magnetic field lines. This is the so-called
"pulsar wind", whose effects can observed in the turbulence of
gas clouds associated with supernova, the so-called "pulsar-wind
nebula."

4) A second consequence of the intense magnetic field of the
spinning neutron star is the pulsation of the pulsar. The
magnetic poles of neutron stars emit narrow beams of radiation in
addition to the pulsar-wind, and since the magnetic axis is
offset from the spin axis, the beams execute an oscillation in
space observed from Earth as a pulsing of radiation. The
pulsation rate of neutron stars declines with their age, and the
pulse period (P) and the "spin-down rate" ("P-dot"; the time-
derivative of P) are at present the two most important
observables concerning pulsars. A plot or P-dot versus P of the
approximately 700 pulsars that have been identified has been
useful in research on these objects in the same way that the
*Hertzsprung-Russell diagram, plotting luminosity versus
temperature, has been useful in understanding the general
evolution of ordinary stars.

5) Most pulsars slow down at a steady rate, but a few pulsars
exhibit slight and sudden "glitches" in their periods, and these
glitches have been used as the basis for studying the structure
of pulsars. It is presently believed that glitches probably
originate beneath the thin crust of a pulsar, in a dense mantle
of heavy nuclei permeated by a *superfluid of neutrons, and that
the *angular momentum of the superfluid is broken up into
discrete quantized vortices which migrate outward to the crust as
the neutron spin-rate decreases. It is believed the migrations
and surface eruptions of superfluid quantum vortices (which
transfer angular momentum to the crust) cause the sudden changes
in spin-rate which are observed as "glitches" in pulsar behavior
[*Note #2].

Sky & Telescope July 1999

Text Notes:

... ... *Note #1: At such a density, the entire human species
could exist as an object the size of small marble -- with the
total mass of the entire human species retained: i.e., the marble
would weigh approximately 10^(14) grams.

... ... *Hertzsprung-Russell diagram: The Hertzsprung-Russell
diagram is a plot of stellar absolute magnitude against spectral
type (luminosity vs. temperature), and is one of the most useful
diagrammatic aids in astrophysics. The course of a star's
evolution can be traced as a particular path in the H-R diagram,
with the paths of various types of stars showing significant
differences.

... ... *superfluid: In general, a "superfluid" is a fluid that
flows without any resistance (i.e., zero viscosity).

... ... *angular momentum: The momentum of a body by virtue of
its rotation and/or orbital revolution. It is a conserved
quantity, and as a consequence a body spins faster as it becomes
smaller.

... ... *Note #2: A quantum vortex is a type of flow pattern
exhibited by superfluids under certain experimental conditions,
e.g., liquid helium in a rotating container. The term "vortex"
designates the familiar whirlpool pattern where the fluid moves
circularly around a central line and the velocity decreases in
inverse proportion to the distance from the center. A superfluid
is considered to be characterized by a macroscopic quantum-
mechanical wave function that locks the superfluid into a
*coherent state. This forces certain mathematical constraints on
the wave function, so that for a superfluid in a rotating
container, the system (the wave equation for the system) produces
a lattice of quantized vortex lines, each line the axis of a
microscopic vortex, with the entire array of vortex lines
rotating rigidly with the container. The essential idea is that
when superfluid helium is in a rotating container, the
mathematics of the system wave function are such that a set of
discrete microscopic vortex states are produced by each
particular set of boundary conditions, and these microscopic
vortex states are experimentally observable [*Note #3]. In short,
the result is a system where the "quantum world" becomes visible
on a macroscopic scale.

... ... *coherent state: In quantum physics, coherence is matter
of locking of phase differences between wave functions. The wave
functions of two or more particles are said to be coherent if the
phase difference between their wave functions remains constant.
In general, a perfectly coherent system of particles can be
described by a single macroscopic wave function.

... ... *Note #3: Below a certain rotation speed threshold, no
vortices exist, and the superfluid remains at rest while the
container rotates (the Landau state). At the threshold speed, the
first vortex appears and corresponds to the first excited
rotational state of the system. If the container continues to
accelerate, additional quantized vortices appear, and at any
given speed the vortices form a regular array that rotates with
the vessel.

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3. ON NEUTRON STARS

During the terminal stages of the evolution of a star, part of
the mass of the star is blown off and lost. If the remnant mass
is between 1.4 and 2 to 3 solar-masses, the star will collapse
into a neutron star, a body with a radius of only 10 to 15
kilometers, but with a core so dense that its component protons
and electrons have merged into neutrons. The average density of a
neutron star is 10^(15) grams per cubic centimeter and the weight
of an object on the surface of a neutron star would be 10^(11)
times its weight on the surface of the Earth. Neutron stars
apparently have an outer shell of iron, but it is iron like no
Earth iron, an iron of 4 orders of magnitude greater density.
Theory predicts that a neutron star should rotate very rapidly,
be extremely hot, and have an intense magnetic field. *Pulsars,
sources of pulsed radio energy, are evidently spinning neutron
stars which emit beams of radiation from their magnetic poles. A
few pulsars have been found in *binary systems, and the empirical
estimated masses of the pulsars are consistent with the masses
predicted by neutron star models.

L. Bildsten and T. Strohmayer (2 installations, US) present a
review of current research concerning neutron stars, the authors
making the following points:

1) With a density comparable to that of an atomic nucleus, a
neutron star provides an extreme environment for fast and violent
phenomena. Matter orbiting a neutron star can have a period as
short as a millisecond. When such matter crashes into the star
(i.e., is "accreted" by the star), such matter can be moving at
one-third the speed of light. In general, because their behavior
can vary over readily observable timescales, neutron stars can be
rich sources of information about nuclear physics, general
relativity, and astrophysics.

2) Though relatively elusive, neutron stars have been detected
and studied over a broad range of electromagnetic frequencies,
from radio frequencies to *gamma rays. To date, astronomers have
identified more than 1000 of the estimated 10^(8) neutron stars
in our galaxy. New orbiting astronomical satellites have produced
recent rapid growth in our knowledge of these objects, with much
of the progress occurring in our understanding of neutron stars
that undergo sudden large energy releases.

3) Although most neutron stars have been discovered as radio
pulsars, only a small fraction of the radiated energy of a
neutron star (typically approximately 10^(-5)) is expected to be
radio emission energy. Most of the energy instead departs as
photons with energies above 10^(8) *electronvolts.

4) The precise timing of radio pulsars has yielded astonishing
astronomical discoveries, such as multiple Earth-mass planets
orbiting a neutron star, and the direct confirmation of the loss
of orbital angular momentum due to gravitational radiation in a
double neutron star binary system (for which Russell Hulse and
Joseph Taylor received the 1993 Nobel Prize in Physics). The
brightest accreting neutron stars reside in binary systems and
accrete matter from their companions. These accreting neutron
stars typically have luminosities more than a thousand times that
of the Sun.

5) There is every reason to believe that new classes of neutron
stars will be discovered by continued observations from the
currently orbiting satellites combined with the international
fleet of new x-ray and gamma-ray satellites planned for launch
during the next two years.

Physics Today February 1999

Text Notes:

... ... *Pulsars: Pulsars were originally discovered at radio
wavelengths, but there are optical, gamma-ray, and x-ray pulsars,
and some of the gamma-ray pulsars are extremely powerful gamma-
ray emitters.

... ... *binary systems: Binary stars are a pair of stars
revolving around a common center of mass under the influence of
their mutual gravitational attraction, and apparently the
majority of stars in the Universe are binaries and not singlets.
In some cases the binary system is resolvable into two
components, and in other cases the presence of a second star is
inferred by perturbations in the motion or emitted radiation of
the first star. If the binaries are close enough, they may share
stellar material, and this results in a particular kind of
stellar evolution.

... ... *gamma rays: Gamma rays are radiation of high energy,
from about 10^(5) *electronvolts to more than 10^(14)
electronvolts -- radiation with the shortest wavelengths and
highest frequencies, the gamma ray region of the electromagnetic
spectrum merging into the adjacent lower energy x-ray region.

... ... *electronvolts: An  electronvolt is defined as the energy
acquired by an electron falling freely through a potential
difference of one volt, and is equal to 1.6022 x 10^(-19) joule.

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4. NEUTRON STARS AND THE FLUID PROPERTIES OF HOT ATOMIC NUCLEI

Viola and Kwiatkowski (Indiana University Bloomington, US), in a
review of a current experimental approach to understanding the
dynamics of neutron star structure, make the following points:

1) During the catastrophic collapse of stellar material in the
core of a star destined to become a neutron star, gaseous nuclear
matter is believed to condense to the liquid phase. A giant
nucleus, or neutron star, is formed in this nuclear phase
transition.

2) In order to understand the formation of neutron stars and
black holes, it is essential to know the conditions under which
nuclear matter changes from the gas phase to the liquid phase.
These conditions are expressed, both for nuclear matter and for
ordinary matter, in terms of an equation of state  -- the
thermodynamic equation that describes the phase behavior of a
substance as a function of temperature, pressure, and
composition.

3) In the case of the neutron star, the only accessible approach
is to study the reverse process, the expansion and vaporization
of heavy atomic nuclei, which approach a neutron star's density
and, in the intranuclear domain, share many of its fluid
properties.

4) The authors review their work using ISiS (the Indiana Silicon
Sphere detector), an apparatus designed to study fragments
ejected from an atomic nucleus after the nucleus is "boiled" by
the energy of a light-ion collision in a particle accelerator. In
the "soft explosions" analyzed by
ISiS, the nucleus vaporizes. By measuring the charges,
velocities, and flight paths of nuclear fragments, ISiS has
provided evidence that atomic nuclei indeed behave like droplets
of a liquid that expand as they are heated until they reach a
boiling point of approximately 10^(11) degrees Kelvin.

5) Various tests distinguish between the extremes of boiling and
shattering. For example, a signature of phase transition (in this
case, boiling) is that fragments are emitted randomly in all
directions, rather than preferentially emitted in the direction
of the incident projectile.

6) Essentially, the result of these experiments is that a class
of collision events has been observed that exhibits many
characteristics expected for a phase transition in nuclear
matter. The major task is now to make a quantitative connection
between the data and nuclear compressibility, in particular the
nuclear compressibility of the core of neutron stars and black
holes.

American Scientist October 1998

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5. ON THE EQUATION OF STATE OF DENSE MATTER.

The nucleon-nucleon interaction is generally attractive at
nucleon-nucleon separations of (r) = 1 to 2 fm (1 ž 10^(-13) cm
to 2 ž 10^(-13) cm) but becomes repulsive at small separations (<
0.5 fm), making nuclear matter difficult to compress. As a
consequence, most stable nuclei are at approximately the same
"saturation" density [ p(0)~ 2.7 x 10^(14) grams per cubic
centimer] in their interiors, and higher densities do not occur
naturally on Earth. Matter at densities of up to  p = 9 x p(0)
may be present in the interiors of neutron stars (1), and matter
at densities up to about p = 4 x p(0) may be present in the core
collapse of type II supernovae (2). The relationship between
pressure, density, and temperature described by the equation of
state (EOS) of dense matter governs the compression achieved in
supernovae and neutron stars, as well as their internal structure
and many other basic properties (1-5). Models that extrapolate
the EOS from the properties of nuclei near their normal density
and from nucleon-nucleon scattering are commonly exploited to
study such dense systems (1,3-5). Consequently, it is important
to test these extrapolations with laboratory measurements of
high-density matter.

2) Nuclear collisions provide the only means to compress nuclear
matter to high density within a laboratory environment. The
pressures that result from the high densities achieved during
such collisions strongly influence the motion of ejected matter
and provide the sensitivity to the EOS that is needed for its
determination. Full equilibrium is often not achieved in nuclear
collisions. Therefore, it is necessary to study experimental
observables that are associated with the motions of the ejected
matter and to describe them theoretically with a dynamical
theory.

3) To relate the experimental observables to the EOS and the
other microscopic sources of pressure, the authors apply a model
formulated within relativistic Landau theory, which includes both
stable and excited (delta, N*) nucleons (that is, baryons) as
well as pions. The model describes the motion of these particles
by predicting the time evolution of the (Wigner) one-body phase
space distribution functions f(r,p,t) for these particles using a
set of Boltzmann equations.

4) In summary: Nuclear collisions can compress nuclear matter to
densities achieved within neutron stars and within core-collapse
supernovae. These dense states of matter exist momentarily before
expanding. The authors report they analyzed the flow of matter to
extract pressures in excess of 10^(34) pascals, the highest
recorded under laboratory-controlled conditions. Using these
analyses, the authors rule out strongly repulsive nuclear
equations of state from relativistic mean field theory and weakly
repulsive equations of state with phase transitions at densities
less than three times that of stable nuclei, but not equations of
state softened at higher densities because of a transformation to
quark matter. The authors suggest that investigations of the
asymmetry term of the EOS are important to complement their
constraints on the symmetric nuclear matter EOS. Both
measurements relevant to the asymmetry term and improved
constraints on the EOS for symmetric matter appear feasible; they
can provide the experimental basis for constraining the
properties of dense neutron-rich matter and dense astrophysical
objects such as neutron stars.

References (abridged):

1. J. M. Lattimer and M. Prakash, Astrophys. J. 550, 426 (2001).

2. H. A. Bethe, Rev. Mod. Phys. 62, 801 (1990).

3. A. Akmal, V. R. Pandharipande, D. G. Ravenhall, Phys. Rev. C
58, 1804 (1998).

4. M. Prakash, T. L. Ainsworth, J. M. Lattimer, Phys. Rev. Lett.
61, 2518 (1988).

5. N. K. Glendenning, F. Weber, S. A. Moszkowski, Phys. Rev. C
45, 844 (1992).

Science 2002 298:1592

Related Background Brief:

NEUTRON STAR STRUCTURE AND THE EQUATION OF STATE. The authors
consider the structure of neutron stars from theoretical and
observational perspectives. The authors demonstrate an important
aspect of neutron star structure: the neutron star radius is
primarily determined by the behavior of the pressure of matter in
the vicinity of nuclear matter equilibrium density. In the event
that extreme softening does not occur at these densities, the
radius is virtually independent of the mass and is determined by
the magnitude of the pressure. For equations of state with
extreme softening or those that are self-bound, the radius is
more sensitive to the mass. The authors suggest their results
demonstrate that in the absence of extreme softening, a
measurement of the radius of a neutron star more accurate than
about 1 km will usefully constrain the equation of state. The
authors also demonstrate that the pressure near nuclear matter
density is primarily a function of the density dependence of the
nuclear symmetry energy, while the nuclear incompressibility and
skewness parameters play secondary roles. In addition, the
authors demonstrate that the moment of inertia and the binding
energy of neutron stars, for a large class of equations of state,
are nearly universal functions of the star's compactness. The
authors suggest these features can be understood by considering
two analytic, yet realistic, solutions of Einstein's equations,
by, respectively, Buchdahl and Tolman. The authors deduce useful
approximations for the fraction of the moment of inertia residing
in the crust, which is a function of the stellar compactness and,
in addition, the pressure at the core-crust interface. J.M.
Lattimer and M. Prakash: Astrophys. J. 2001 550:426.

Related Background Brief:

SUPERNOVA MECHANISMS AND THE EQUATION OF STATE. Supernovae of
Type II occur at the end of the evolution of massive stars. The
phenomenon begins when the iron core of the star exceeds a
Chandrasekhar mass. The collapse of that core under gravity is
well understood and takes a fraction of a second. To understand
the phenomenon, a detailed knowledge of the equation of state at
the relevant densities and temperatures is required. After
collapse, the shock wave moves outward, but probably does not
succeed in expelling the mass of the star. The most likely
mechanism to do so is the absorption of neutrinos from the core
by the material at medium distances. Observations and theory
connected with supernova SN 1987A are discussed by the author, as
are the conditions just before collapse and the emission of
neutrinos by the collapsed core. Revs Mod Phys 1990 62:801.

Related Background Brief:

EQUATION OF STATE OF NUCLEON MATTER AND NEUTRON STAR STRUCTURE.
Properties of dense nucleon matter and the structure of neutron
stars were studied by the authors using variational chain
summation methods and the new Argonne vip two-nucleon
interaction, which provides an excellent fit to all of the
nucleon-nucleon scattering data in the Nijmegen database. The
neutron star gravitational mass limit obtained with this
interaction is 1.67M. Boost corrections to the two-nucleon
interaction, which give the leading relativistic effect of order
(upsilon/c)(2), as well as three-nucleon interactions, are also
included in the nuclear Hamiltonian. Their successive addition
increases the mass limit to 1.80 and 2.20 M. Hamiltonians
including a three-nucleon interaction predict a transition in
neutron star matter to a phase with neutral pion condensation at
a baryon number density similar to 0.2 fm(-3). Neutron stars
predicted by these Hamiltonians have a layer with a thickness on
the order of tens of meters, over which the density changes
rapidly from that of the normal to the condensed phase. The
material in this thin layer is a mixture of the two phases. The
authors also investigated the possibility of dense nucleon matter
having an admixture of quark matter, described using the bag
model equation of state. Neutron stars of 1.4M. do not appear to
have quark matter admixtures in their cores. However, the
heaviest stars are predicted to have cores consisting of a quark
and nucleon matter mixture. Stars with pure quark matter in their
cores are found to be unstable. The authors also consider the
possibility that matter is maximally incompressible above an
assumed density, and show that realistic models of nuclear forces
limit the maximum mass of neutron stars to be below 2.5M. The
effects of the phase transitions on the composition of neutron
star matter and its adiabatic index Gamma are discussed. A. Akmal
et al: Phys Rev C-Nuclear Physics 1998 58:1804.

Related Background Brief:

NEGATIVE POISSON'S RATIOS FOR EXTREME STATES OF MATTER. [The term
"Poisson's ratio" refers to the ratio of the lateral strain to
the longitudinal strain in a stretched rod.] Negative Poisson's
ratios are predicted for body-centered-cubic phases that likely
exist in white dwarf cores and neutron star outer crusts, as well
as those found for vacuum-like ion crystals, plasma dust
crystals, and colloidal crystals (including certain virus
crystals). The existence of this counterintuitive property, which
means that a material laterally expands when stretched, is
experimentally demonstrated for very low density crystals of
trapped ions. At very high densities, the large predicted
negative and positive Poisson's ratios might be important for
understanding the asteroseismology of neutron stars and white
dwarfs and the effect of stellar stresses on nuclear reaction
rates. Giant Poisson's ratios are both predicted and observed for
highly strained coulombic photonic crystals, suggesting possible
applications of large, tunable Poisson's ratios for photonic
crystal devices. R.H. Baughman et al: Science 2000 288:2018.

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6. NEUTRON STARS AND RELATIVISTIC JETS.

In this context, a "jet" is a long thin linear feature of bright
emission extending from a compact object. Jets are very common at
radio wavelengths, but have also been observed in optical and x-
ray emissions. A "relativistic jet" is a jet moving at close to
the speed of light.

A "Kerr black hole" has angular momentum but no charge (i.e., a
rotating black hole with no charge).

In general, an "Alfven wave" is a disturbance transmitted through
a plasma (a fully ionized gas)  in the presence of a magnetic
field. The direction of propagation is parallel to the mean
magnetic field, with the plasma particles vibrating at right
angles to this direction. The speed of propagation, the "Alfven
speed", depends on the magnetic field strength and plasma
density. Such waves are a type of magnetohydrodynamic wave, and
they have been directly observed in solar wind high-speed streams
from the Sun and in planetary magnetospheres.

The boundary of a black hole is called the "event horizon" (black
hole horizon), because any event within the boundary is invisible
outside, the invisibility resulting from the fact that no
radiation can escape to be detected.

Some galaxies are known to have very "active" central regions
from which enormous amounts of energy are emitted each second,
and it is believed that these "active galactic nuclei" are
probably powered by accretion of matter into a supermassive black
hole of 10^(6) to 10^(9) solar-masses. Astronomers have recently
discovered that many active galactic nuclei eject clouds of
ionized gas with velocities of up to 10 percent of the speed of
light over a wide range of angles, in contrast to the previously
known collimated jets. These mass outflows are considered to be
intriguing because they provide information about the dynamical
forces (such as radiation and wind pressure) near an active
supermassive black hole.

Quasars (quasi-stellar objects) are extremely luminous sources
radiating energy over the entire spectrum from x-rays to radio
waves, and which are apparently the oldest and most distant
objects in the universe. They are believed to involve massive
black holes. Microquasars are quasars of apparent stellar mass.

Gamma ray bursts are intense flashes of gamma rays detected at
energies up to 10^(6) electronvolts. They were discovered by US
Air Force satellites in 1967 but not declassified until 1973. The
detection of these bursts averages about 1 per day, and
measurements indicate the distribution of bursts is isotropic,
i.e., they are uniformly distributed across the sky. The current
consensus is that gamma ray bursts are produced by the merger of
two neutron stars, and up to this point, the bursts that have
been noted apparently originate outside our own galaxy.

MAGNETOHYDRODYNAMIC PRODUCTION OF RELATIVISTIC JETS.

D.L. Meier et al (California Institute of Technology, US) discuss
relativistic jets, the authors making the following points:

1) A jet is a tightly collimated stream of fluid, gas, or plasma.
It typically carries kinetic and internal energy and linear
momentum, and if it is set spinning about its direction of motion
by some means, it can carry angular momentum as well. A
relativistic jet is one whose speed approaches the universally
constant speed of light c = 299,792.5 km per second. At such
velocities, Einstein's theory of relativity becomes important.
The kinetic energy of motion (and possibly the internal thermal
and magnetic energy as well) adds mass to the jet, equal to
E(kinetic)/c^(2), making it more difficult to accelerate. Also,
as seen by viewers at rest, time slows down in the moving jet
material, and any light or radio emission from the jet tends to
be radiated in the direction of flow, not isotropically, as would
be the case if the flow velocity were subrelativistic. Because c
is a maximum speed limit and because conditions become more
extreme as it is approached, the Lorentz factor is often used to
characterize the speed, rather than the velocity.

2) Relativistic jets are common in the astrophysical environment.
The extragalactic radio sources such as radio galaxies and
quasars produce by far the largest and most energetic jets in the
universe, although they do not produce the fastest ones nor those
with the highest instantaneous powers.(1) The less luminous ones
appear as giant elliptical radio galaxies, and the most luminous
appear as radio quasars. Often, the twin jets are pointed at a
large angle to our line of sight, allowing the full extent of the
radio source powered by the jet -- up to a few megaparsecs in
size -- to be seen. In a few sources, however, one of the jets
points nearly directly toward Earth and the other points nearly
directly away. The approaching jet therefore appears to be
substantially Doppler brightened, and the receding one may be so
Doppler dimmed that it is difficult or impossible to detect.

3) In summary: A number of astronomical systems have been
discovered that generate collimated flows of plasma with
velocities close to the speed of light. In all cases, the central
object is probably a neutron star or black hole and is either
accreting material from other stars or is in the initial violent
stages of formation. Supercomputer simulations of the production
of relativistic jets have been based on a magnetohydrodynamic
model, in which differential rotation in the system creates a
magnetic coil that simultaneously expels and pinches some of the
infalling material. The model may explain the basic features of
observed jets, including their speed and amount of collimation,
and some of the details in the behavior and statistics of
different jet-producing sources.(2-5)

References (abridged):

1. R. C. Vermeulen, IAU Symp. 175, 57 (1996).

2. J. A. Biretta, W. B. Sparks, F. Macchetto, Astrophys. J. 520,
621 (1999).

3. F. Macchetto, et al., Astrophys. J. 489, 579 (1997).

4. I. F. Mirabel and L. F. Rodriguez, Annu. Rev. Astron.
Astrophys. 37, 409 (1999).

5. B. Margon, Annu. Rev. Astron. Astrophys. 22, 507 (1984).

Science 2001 291:84

Related Background:

SOURCES OF RELATIVISTIC JETS IN THE GALAXY.

I. F. Mirabel and L. F. Rodr¡guez (Centre d'Etudes de Saclay, FR)
discuss relativistic jets, the authors making the following
points:

1) While the first evidence of jet-like features emanating from
the nuclei of galaxies goes back to the discovery by Curtis
(1918) of the optical jet from the elliptical galaxy M87 in the
Virgo cluster, the finding that jets can also be produced in
smaller scale by binary stellar systems is much more recent. The
detection by Margon et al (1979) of large, periodic Doppler
drifts in the optical lines of SS 433 resulted in the proposition
of a kinematic model (Fabian & Rees 1979; Milgrom 1979)
consisting of two precessing jets of collimated matter with
velocity of 0.26c. High angular radio imaging as a function of
time showed the presence of outflowing radio jets and fully
confirmed the kinematic model (Spencer 1979; Gilmore & Seaquist
1980; Gilmore et al 1981; Hjellming & Johnston 1981). The early
history of SS 433 has been reviewed by Margon (1984).

2) Since the detection of Sco X-1 at radio wavelengths (Ables
1969), some X-ray binaries had been known to be strong, time-
variable non-thermal emitters. Ejection of synchrotron-emitting
clouds was suspected from those days, but the actual confirmation
of radio jets came only with the observations of SS 433. At
present, there are about 200 known galactic X-ray binaries (van
Paradijs 1995), of which about 10 percent are radio-loud
(Hjellming & Han 1995). Of these radio-emitting X ray binaries,
10 have shown evidence of relativistic jets of synchrotron
emission.

3) In the last years it has become clear that collimated ejecta
can be produced in several stellar environments when an accretion
disk is present. Jets with terminal velocities in the order of a
few hundred to a few thousand km per sec are now known to emanate
from objects as diverse as very young stars (Reipurth & Bertout
1997), nuclei of planetary nebulae (L¢pez 1997), and accreting
white dwarfs that appear as supersoft X-ray sources (Motch 1998,
Cowley et al 1998). These types of stellar jets have, however,
non-relativistic velocities (~100 10000 km per sec) and their
associated emission is dominantly thermal (i.e. free-free
continuum emission in the radio as well as characteristic near-
IR, optical and UV lines). Interestingly, in all known types of
jet sources a disk is believed to be present.

4) In summary: Black holes of stellar mass and neutron stars in
binary systems are first detected as hard X-ray sources using
high-energy space telescopes. Relativistic jets in some of these
compact sources are found by means of multiwavelength
observations with ground-based telescopes. The X-ray emission
probes the inner accretion disk and immediate surroundings of the
compact object, whereas the synchrotron emission from the jets is
observed in the radio and infrared bands, and in the future could
be detected at even shorter wavelengths. Black-hole X-ray
binaries with relativistic jets mimic, on a much smaller scale,
many of the phenomena seen in quasars and are thus called
microquasars. Because of their proximity, their study opens the
way for a better understanding of the relativistic jets seen
elsewhere in the Universe. From the observation of two-sided
moving jets it is inferred that the ejecta in microquasars move
with relativistic speeds similar to those believed to be present
in quasars. The simultaneous multiwavelength approach to
microquasars reveals in short timescales the close connection
between instabilities in the accretion disk seen in the X-rays,
and the ejection of relativistic clouds of plasma observed as
synchrotron emission at longer wavelengths. Besides contributing
to a deeper understanding of accretion disks and jets,
microquasars may serve in the future to determine the distances
of jet sources using constraints from special relativity, and the
spin of black holes using general relativity.

Annu. Rev. Astron. Astrophys. 1999 37:409.

Related Background:

BLACK HOLES, MAGNETIC FIELDS, AND RELATIVISTIC JETS

1) S. Koide et al (Toyama University, JP) discuss black holes,
the authors making the following points:

1) Relativistic jets have now been discovered in several
different classes of astrophysical objects, including active
galactic nuclei, microquasars, and gamma ray bursts. A rapidly
spinning black hole may exist at the center of each of these
objects, and energetic reactions that occur near the hole may be
responsible for the jets. One of the most promising processes for
producing relativistic jets is the extraction of rotational
energy from a spinning (Kerr) black hole. One method of
extraction is the "Penrose process", which uses fission of a
particle near the black hole to extract the black hole rotational
energy. However, this process may not be applicable to most
astrophysical objects, because the particle fission must occur
near the black hole, and the relative velocity of the particles
produced by the fission should be near the speed of light. On the
other hand, Blandford and Znajek (1977) demonstrated that a
large-scale magnetic field around a Kerr black hole also could
extract rotational energy. They assumed a magnetic force-free
condition, which corresponds to an extremely strong magnetic
field or an extremely low inertia plasma case.

2) The authors report that using numerical simulations, they
modeled the general relativistic magnetohydrodynamic behavior of
a plasma flowing into a rapidly rotating black hole in a large-
scale magnetic field. The results demonstrate that a torsional
Alfven wave is generated by the rotational dragging of space near
the black hole. The wave transports energy along the magnetic
field lines outward, causing the total energy of the plasma near
the hole to decrease to negative values. When this negative
energy plasma enters the black hole horizon, the rotational
energy of the black hole decreases. Through this process, the
energy of the spinning black hole is extracted magnetically, and
this process may be applicable to the formation of relativistic
jets.

Science 2002 295:1688

References (abridged):

1. T. J. Pearson, et al., Nature 290, 365 (1981)

2. J. A. Biretta, W. B. Sparks, F. Macchetto, Astrophys. J. 520,
621 (1999)

3. I. F. Mirabel and L. F. Rodriguez, Nature 371, 46 (1994)

4. S. J. Tingay, et al., Nature 374, 141 (1995)

5. S. R. Kulkarni, et al., Nature 398, 389 (1999)

Related background:

PLASMA JETS IN ACTIVE GALACTIC NUCLEI

A.P. Lobanov and J.A. Zensus (Max Planck Institute for Radio
Astronomy Bonn, DE) discuss plasma jets in active galactic
nuclei. One of the most intriguing features observed in active
galactic nuclei is highly collimated and relativistic plasma
outflows (jets) that originate in the immediate vicinity of the
center of activity and propagate at distances of up to several
megaparsecs (1 parsec = 3.26 light years). Observations of jets
in active galactic nuclei probe the behavior of extremely
relativistic matter in the Universe and provide a unique and
remote "laboratory" for studying the most powerful cosmic
phenomena such as supermassive black holes and extragalactic
accretion disks. The quasar 3C273 is one of the closest and most
luminous and best studied active galactic nuclei, with a
prominent relativistic outflow observed in the x-ray, optical,
and radio wave bands. The relativistic jet observed in this
quasar is one-sided, with no signs of emission on the counterjet
side at dynamic ranges of up to 16,000:1. This is evidence for
strong relativistic boosting in an intrinsically double-sided
outflow powered by an accretion disk around a black hole. The
enhanced emission features (jet components) identified in the jet
on scales of up to approximately 20 milli-arc seconds are moving
at apparent speeds exceeding the speed of light by factors of 5
to 8. These jet components may result from the flares observed in
this quasar in the optical and radio wavelengths and also reflect
the precession of the jet axis. The structure and kinematics of
such outflows are typically explained in terms of shock waves and
Kelvin-Helmholtz instability.

Science 2001 294:128

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