I gave a rather speculative argument about
why general relativity might suggest close in
planets might plunge into the neutron stars but I
found an article that states that neutron stars should
not have stable orbits close in and in fact the orbits
should be quantized:

Discovery Of 'Cosmic Chords' May Support Prediction Of Einstein's
Theory
http://www.sciencedaily.com/releases...0422070245.htm

All in the Timing.(neutron star oscillations)
Science News, Nov 14, 1998, by Ron Cowen
"According to Newton's theory of gravity, gas can
orbit a compact star at any distance. But according to
general relativity, it a star is massive enough and
dense enough, it will warp space-time so strongly that
the region just outside the star cannot possess a
stable, circular orbit. Gas circling any closer than a
certain minimum distance is doomed to crash onto the
star's surface. This minimum distance is known as the
innermost stable orbit."
http://www.findarticles.com/cf_dls/m...le.jhtml?term=

If so, then if the orbits of the observed "hot Jupiters" are outside
the stability zones for the neutron star we should EXPECT these
planets to plunge into their parent stars after they go supernova.

c.f.:
The Music of the (Neutron) Spheres
by John G. Cramer
Alternate View Column AV-92
"In the Nov-92 issue of Analog in a column called "Centrifugal Forces
and Black Holes", I discussed a newly- realized aspect of general
relativity as applied to intense gravity fields. For circular
trajectories close enough around a black hole, the centrifugal force
works backwards, pointing inward instead of outward, and there are no
stable orbits. This black hole situation is an extreme case, but
Frederick Lamb and his co-workers at the University of Illinois have
applied similar ideas to the intense gravity fields and highly curved
space near neutron stars. They find that when the field is strong
enough, the space curvature predicted by general relativity reduces
the centrifugal force to the point where orbital stability is
destroyed. For any neutron star there is a minimum-diameter stable
orbit, and no stable orbits exist at smaller orbital diameters. An
object with a trajectory within the minimum orbit will spiral into the
gravity well and never emerge."
http://www.npl.washington.edu/AV/altvw92.html


Bob Clark





(Robert Clark) wrote in message . com...
I prefer to think of them as billiard balls:


************************************************** ***************************
From: Robert Clark )
Subject: Neutron star kicks, a proposal.
Newsgroups: sci.astro, sci.physics, sci.physics.relativity
Date: 2000/07/25

...
So the proposal for the origin of neutron star kicks:
since I had been considering the possibility that the origin of pulsar
radio pulses may be due to orbiting planets, I thought they may also be
the origin of the high speeds seen in some neutron stars after their
supernova explosions:

Forum: sci.astro
Subject: How neutron stars get their kicks: Cornell researcher poses
rocket theory (Forwarded)
Date: 06/08/2000
Author: Andrew Yee
http://x59.deja.com/getdoc.xp?AN=632820756

The speeds observed are quite high in some cases, in the range of
hundreds of kilometers per second. Since we know that pulsars have
planets, perhaps the high speeds are due to collisions of the planets
with the neutron star. In the example cited by Lazio these were Earth-
sized planets. However, I'm imagining the Jovian sized planets
frequently observed about Sun-like stars. Indeed in many of these cases
they turn out to be 'Hot Jupiters', Jovian-sized planets orbiting quite
close in to their stars:

Stars May Be Eating 'Hot Jupiters'
http://www.space.com/scienceastronom...ts_991022.html

Death stars
It looks as if most suns make a meal of their planets\0
New Scientist, 23 October, 1999
http://www.newscientist.com/ns/19991...wsstory12.html


So we need a mechanism to explain why these planets rush into their
parent stars after the supernova. Doug Lin of the University of
California, Santa Cruz suggests that most planets this close in have
unstable orbits due to the surrounding gas and dust of the star:

Exploring New Worlds
Scientists puzzle over extrasolar planets
Science News, August 8, 1998
http://sciencenews.org/sn_arc98/8_8_98/bob1.htm

However, this is a case that takes place over millions of years. In
the case of the supernovae we would want this to take place over a much
shorter time period (hours? days?)
After the supernova explosion there is an expanding shell of gas from
the stars outer layers. This would be moving at high speed. It should
be moving radially out from the star. A satellite can be made to decay
in its orbit by giving it a velocity push against its direction of
motion in orbit. But if the planet has a circular orbit, the gas shell
would tend to move it radially outward. However, one feature of the
Jovian size planets so far discovered is that they usually have very
eccentric orbits. In such a case a radially expanding shell would have
a velocity component along the direction of motion of the satellite in
its orbit at most points of the orbit. But at some points this would
tend to speed up the planet and at other points to slow it down. It is
possible that if the planet passed through the gas cloud several times
the result would be to slow it down.
For an expanding supernova gas shell does some remnant of the gas
remain around the star after the explosion? If so then the planet
continuing to orbit around the star through this surrounding gas would
tend to cause the orbital decay of the planet.
However, I'm considering another underlying cause of the decay of the
orbiting planet. That is that the collapse of the star itself causes
the rapid spiraling-in of near orbiting planets into the star. In
Newtonian physics the gravitational effects on an orbiting planet when
the star collapsed from a 1 million kilometer diameter to a 10
kilometer diameter would be the same since the gravitational force is
concentrated at the center. However, this is no longer the case in
general relativity with extremely strong fields such as with a neutron
star.
This is an effect in general relativity called "frame dragging". It
has been verified with Earth satellites and with some black hole
systems:

Earth drags space-time as it rotates
http://exosci.com/news/50.html

RXTE Observes Space-Time Distortion!
http://heasarc.gsfc.nasa.gov/docs/xt...over_1197.html

In the descriptions I've seen so far, only the precession of the orbit
of a satellite is described. However, from the mathematical similarity
of the equations of general relativity to those of motion through a
material medium we might also expect there to be a force produced that
drags the satellite in toward the parent body. This is an effect in
fluid dynamics known as the "Magnus effect":

The Magnus Effect
http://www.b-bop.com/mak/magnus.html

Physics of Sports Lecture 18:
Reynolds Number, Drag Coefficient, and Turbulence
http://courses.washington.edu/phys208/notes/lect18.html

Some papers describing the analogy between general relativity and
motion through a medium a

"The optical-mechanical analogy in general relativity: New methods for
the paths of light and of the planets"
American Journal of Physics, November 1996, V. 64, no. 11, p. 1404-1415

"On the gravitational field acting as an optical medium"
General Relativity and Gravitation, v. 2, p. 347-357, 1971.

Exploiting this analogy fully, we might also expect there would be a
force tending to drag the satellite downwards due to the large mass of
the star rapidly contracting down as it collapsed into a neutron star.

A plsar recently observed by Chandra may support the planetary impact
model for the neutron star kicks:

Chandra Catches Shooting Neutron Star
http://www.space.com/scienceastronom...la_000607.html

It shows twin jets shooting out from the pulsar forward and rearward
aligned with the direction of motion of the pulsar. This could be due
to the explosive energy released on impact for the rearward jet. For
the forward jet, it is known that solar eruptions on one side of the
Sun are accompanied by magnetic disruptions on the opposite side, which
can also cause flares. Also, it has been observed that large lunar
impact areas are accompanied by magnetic anomalies on the opposite side
of the Moon from the impact area (such a similarity supports the idea
that at least some solar eruptions are due to cometary or asteroidal
impacts.)

How to distinguish between the impact model and the asymmetric
supernova model? If the velocity imparted to the star is due to the
outer layers exploding outward asymmetrically then the velocity kick
should occur immediately with the supernova explosion. If it is due to
a planetary impact however then it should take some time for the
planets orbit to degrade fully. I don't know if the time scale for this
is hours, days or years. Perhaps in a case such as supernova SN1987A
where the neutrino emission was observed first it could be determined
the time between the explosion and the time of the velocity kick.
Also when the planet is quite close to the neutron star it should be
moving at relativistic speeds. Such a Jovian size body spiraling into
the intense magnetic field of the neutron star at a significant
fraction of the speed of light should be an intense source of
synchrotron radiation. There are continuous observations of synchrotron
radiation from pusars. But this should be for the brief time when the
planet is quite close in to the star then should be accompanied by
great release of radiation on impact. Since one of the hypothesized
explanations of the mysterious gamma ray bursts is a collision of two
neutron stars it is conceivable that some of these are due to these
planetary impacts, especially for planets on the order of 10 to 100
Jovian masses, about 1/100th to 1/10th solar mass.

A rough estimate for the speed of the planet on impact can be obtained
from the equation mV^2/2 = GMm/R, so V = sqrt(2GM/R), M the star mass,
m the planet mass, R the radial distance, G the gravitational constant,
G = 6.67 x 10^(-11) m^3/s^2 x kg. If the planet maintained its size
until impact at about the radial size of Jupiter, then the distance R
would be about 1.4x10^8 meters. With a neutron star mass of one solar
mass, M = 2x10^30 kg, V = 1400 km/sec. However, it is likely that the
planet will pass through the Roche limit of the star, where the planet
will begin to break up. Then the radial distance could be on the order
of the size of the neutron star 10 to 30 km. Using a radial distance of
20 km, V = 110,000 km/sec. For a planet at 10 Jovian masses, 1/100th of
a solar mass, this could result in a velocity imparted to the star of
1100 km/sec, within the order of magnitude of the velocities observed
for the neutron star kicks.


--
_______________________________________________

"In order for a scientific revolution to occur,
most scientists have to be wrong."
-- Bob Clark
_______________________________________________

************************************************** **************************


Andrew Yee wrote in message m...
Max-Planck-Institut für Astrophysik
Garching, Germany

October 16th, 2003

Neutron Stars as Cannonballs
Hans-Thomas Janka, Konstantinos Kifonidis, Ewald Müller, Leonhard Scheck, Tomek
Plewa

Scientists at the Max-Planck-Institute for Astrophysics in Garching and the
University of Chicago have substantiated an explanation for the high space
velocities of observed pulsars. Their computer models confirm the likely
connection with asymmetries during supernova explosions.

Stars with more than ten times the mass of our Sun end their lives in
spectacularly powerful supernova explosions. While the major part of the stellar
gas is violently ejected, the core of the star collapses by its own gravity to
form a neutron star. The latter has a mass of roughly 1.5 times the Sun, but its
diameter is only about 20 kilometers. The matter in its interior is therefore
more dense than in atomic nuclei.

Some of the known neutron stars are found inside the gaseous remnants of past
supernova explosions. The most famous example is the 'pulsar' within the Crab
Nebula (Fig.1). Because it spins around its axis about 33 times per second, we
receive on Earth characteristic, regular pulses. Such rotating neutron stars
were therefore named pulsars. Other neutron stars, however, move away from the
site of their formation with very high speed (Fig.2). Typical velocities are
several hundred kilometers per second, but some pulsars propagate through
interstellar space with more than 1000 kilometers per second (Fig.3). This is
much faster than the motion of ordinary stars in our Galaxy. Therefore many
neutron stars can escape from the gravitational pull of the Milky Way.

The orgin of the pulsar motions has long been a mystery. There is, however, no
lack of ideas, partly invoking very speculative or exotic physics phenomena. A
connection with observed anisotropies of supernova explosions had so far not
been demonstrated convincingly.

A team of scientists at the Max-Planck-Institute for Astrophysics in Garching
and the ASCI Flash Center of the University of Chicago has now discovered a
simple and natural cause for such a connection. In computer simulations the team
found that stochastic, little perturbations in the star can amplify to huge
anisotropies by the rapid growth of fluid instablities during the launch of the
explosion (Fig.4, movies). The explosion shock wave and the ejected matter
therefore develop global deformation and the neutron star can be kicked to very
high velocities of several hundred kilometers per second within just a second
(Fig.5).

For the first time the computer models allow one to understand the measured
pulsar motions without making use of additional assumptions. Interestingly, the
results seem to support a theory which has been favored for a long time to
explain the beginning of the supernova explosion (see "How do Massive Stars
Explode?", http://www.mpa-garching.mpg.de/HIGHL...ght0102_e.html)
but which could so far not be confirmed by detailed numerical simulations (see
"Supernova Simulations Still Defy Explosions",
http://www.mpa-garching.mpg.de/HIGHL...t0306_e.html): The
explosion is caused by the action of neutrinos. These neutral, weakly
interacting elementary particles are radiated by the hot neutron star in huge
numbers. They heat the gas in the stellar interior and create the pressure by
which the explosion is started. This heating leads to violent buoyancy (see
movies) until the expansion of the stellar gas occurs in a generically
anisotropic manner. The mechanism of the explosion, the observed asymmetries of
supernovae, and the pulsar proper motions are therefore all linked to one effect.

Publication:

L. Scheck, T. Plewa, H.-Th. Janka, K. Kifonidis, and E. Müller: "Pulsar Recoil
by Large-Scale Anisotropies in Supernova Explosions", astro-ph/0307352, Phys.
Rev. Lett., submitted

[NOTE: Images and movies supporting this release are available at
http://www.mpa-garching.mpg.de/mpa/r...003-10-en.html
]

There is a problem with the unstable orbits argument.
In looking up the reference for the black hole case,
the minimal radius is 1.5 times that of the
Schwarzschild radius, which for a solar size black
hole is on the order of 10's of kilometers:

Centrifugal Forces and Black Holes
by John G. Cramer
http://www.npl.washington.edu/AV/altvw55.html

For a neutron star it should be approximately the same
thing. But the "hot Jupiters" would still be orbiting
their parent stars at least at the million kilometer
range. So the minimal stable orbit argument would not
work. Also, I was assuming that GR implies the orbits
are stable at quantized distances. But you'll notice
the article on the quasi-periodic oscillations in the
pulsar pulses only says the x-ray bursts occur at
quantized frequency intervals. It does not
specifically attribute this to quantized orbital
distances; only the highest frequency oscillation is
attributed to a minimal stable orbit distance.


Bob Clark


(Robert Clark) wrote in message . com...
I gave a rather speculative argument about
why general relativity might suggest close in
planets might plunge into the neutron stars but I
found an article that states that neutron stars should
not have stable orbits close in and in fact the orbits
should be quantized:

Discovery Of 'Cosmic Chords' May Support Prediction Of Einstein's
Theory
http://www.sciencedaily.com/releases...0422070245.htm

All in the Timing.(neutron star oscillations)
Science News, Nov 14, 1998, by Ron Cowen
"According to Newton's theory of gravity, gas can
orbit a compact star at any distance. But according to
general relativity, it a star is massive enough and
dense enough, it will warp space-time so strongly that
the region just outside the star cannot possess a
stable, circular orbit. Gas circling any closer than a
certain minimum distance is doomed to crash onto the
star's surface. This minimum distance is known as the
innermost stable orbit."
http://www.findarticles.com/cf_dls/m...le.jhtml?term=

If so, then if the orbits of the observed "hot Jupiters" are outside
the stability zones for the neutron star we should EXPECT these
planets to plunge into their parent stars after they go supernova.

c.f.:
The Music of the (Neutron) Spheres
by John G. Cramer
Alternate View Column AV-92
"In the Nov-92 issue of Analog in a column called "Centrifugal Forces
and Black Holes", I discussed a newly- realized aspect of general
relativity as applied to intense gravity fields. For circular
trajectories close enough around a black hole, the centrifugal force
works backwards, pointing inward instead of outward, and there are no
stable orbits. This black hole situation is an extreme case, but
Frederick Lamb and his co-workers at the University of Illinois have
applied similar ideas to the intense gravity fields and highly curved
space near neutron stars. They find that when the field is strong
enough, the space curvature predicted by general relativity reduces
the centrifugal force to the point where orbital stability is
destroyed. For any neutron star there is a minimum-diameter stable
orbit, and no stable orbits exist at smaller orbital diameters. An
object with a trajectory within the minimum orbit will spiral into the
gravity well and never emerge."
http://www.npl.washington.edu/AV/altvw92.html


Bob Clark





(Robert Clark) wrote in message . com...
I prefer to think of them as billiard balls:


************************************************** ***************************
From: Robert Clark )
Subject: Neutron star kicks, a proposal.
Newsgroups: sci.astro, sci.physics, sci.physics.relativity
Date: 2000/07/25

...
So the proposal for the origin of neutron star kicks:
since I had been considering the possibility that the origin of pulsar
radio pulses may be due to orbiting planets, I thought they may also be
the origin of the high speeds seen in some neutron stars after their
supernova explosions:

Forum: sci.astro
Subject: How neutron stars get their kicks: Cornell researcher poses
rocket theory (Forwarded)
Date: 06/08/2000
Author: Andrew Yee
http://x59.deja.com/getdoc.xp?AN=632820756

The speeds observed are quite high in some cases, in the range of
hundreds of kilometers per second. Since we know that pulsars have
planets, perhaps the high speeds are due to collisions of the planets
with the neutron star. In the example cited by Lazio these were Earth-
sized planets. However, I'm imagining the Jovian sized planets
frequently observed about Sun-like stars. Indeed in many of these cases
they turn out to be 'Hot Jupiters', Jovian-sized planets orbiting quite
close in to their stars:

Stars May Be Eating 'Hot Jupiters'
http://www.space.com/scienceastronom...ts_991022.html

Death stars
It looks as if most suns make a meal of their planets
New Scientist, 23 October, 1999
http://www.newscientist.com/ns/19991...wsstory12.html


So we need a mechanism to explain why these planets rush into their
parent stars after the supernova. Doug Lin of the University of
California, Santa Cruz suggests that most planets this close in have
unstable orbits due to the surrounding gas and dust of the star:

Exploring New Worlds
Scientists puzzle over extrasolar planets
Science News, August 8, 1998
http://sciencenews.org/sn_arc98/8_8_98/bob1.htm
...