Newsgroups: sci.physics.plasma
From: fcrary@benji.Colorado.EDU (Frank Crary)
Organization: University of Colorado, Boulder
Subject: Re: Can Gravity be Induced?

In article <39riii$5l9@mojo.eng.umd.edu>,
Christoph Keller <keller@noao.edu> wrote:
>> Where are the abundant neutrinos that are supposed to radiate from our
>> sun's core?

>Well, we see a lot of neutrinos. The latest observations of low-energy
>neutrinos see also neutrinos from the proton-proton process. This is a
>very nice confirmation of the fusion theory. It is true that even these
>measurements see less photons than you would expect from current theoretical
>solar models, but we do see A LOT OF NEUTRINOS. There are theories that
>conform to the standard model of particle physics and that can explain
>the reduced number of neutrinos observed with fusion in the solar core.

There is also a more direct explanation, although it isn't
quite as popular (probably because it would be very
difficult to prove.) A basic fact of heat conduction is
that short-term variations are averaged out away from
the heat source (i.e. if the period of the variations
is shorter than the time scale for heat conduction.)
Every day examples of this can be seen, for example,
in terrestrial caves: The time scale for heat to
be conducted through several meters of rock is over
a year. As a result, the daily and seasonal variations
in sunlight get averaged out before they reach the
depth of a typical cave and caves tend to have a
constant temperature all year long. In the case of the
sun, it takes hundreds of years (a few thousand, possibly:
I don't remember the figure exactly) for heat to
be conducted from the core to the solar surface.
So the surface temperature of the sun (what we see)
depends on the _average_ amount of heat produced
in the core. Fusion at the core could vary on
timescales of decades without producing noticeable
variation at the sun's surface. Neutrinos, on the
other hand, pass through the sun in a matter of
minutes: They reflect the current, rather than
the average fusion rate. So it is entirely possible
that fusion in the sun's core varies with time, on
a scale of decades. If we happened to be looking
during a time of minimal fusion, we would see
far fewer neutrinos than we would expect, based on
the observed, average energy output. Nor would
this imply periodic variations in solar energy
output: The process of heat conduction would
average out these decade-long variations reached
the observable regions of the sun.

>> Why does the neutrino count drop during sunspot activity?

>The measurements exist only for slightly more than one solar cycle. The
>statistical evidence is rather low and the correlation seen might just be
>due to chance.

It's also worth noting that many, obviously irrelevant things
correlate with the solar cycle. The number of Republicans
in the Unites States Senate correlates very well. The
problem with such correlations is the long time scales.
You need to do your statistics over many cycles to
get a meaningful result. If you average over a mere
century (say ten solar cycles), you would still get
correlations with _anything_ that varied on a time
scale of 10 to 12 years.

>> How does the Sun transfer heat to the Corona without violating the Laws
>> of thermodynamics?

>Current theories on coronal heating rely on various forms of non-thermal
>heating process, most of them involving magnetic fields. Let me just remark
>that there are many theories around that can explain many facts about the
>corona. It is presently, however, not clear, which theory is correct.

As well as the non-thermal heating processes, it is also possible
that the corona is simply not as hot as it looks. This is
actually a good exercise for students of plasma physics.
"Temperature" is really the average kinetic energy of the
particles. But often, the average doesn't mean much.
Fluid mechanics, as well as the solar observations of the
corona, assume that the particles are in a maxwellian
distribution: A single population well-described by the
average. But many space plasmas are not so easily
described. Often the particles are in a much more complex
distribution. Now observations of the corona's temperature
are based on a particular sort of weighted average
(weighted by collision cross-sections and the emissions
they excite) while heat transfer equations are based
on a different, weighted average (based on the
kinetic energy transferred by collisions). If the
particles were in a simple, maxwellian distribution,
these two averages would be the same. But if the
particles aren't in such an idealized state, then the
tow sorts of averages might be very different:
"Temperature", for the purposes of observed, emitted
light might be quite different from "temperature"
for the purposes of heat conduction.

>> If the Sun is a contracted ball of gas, why is its rotation rate so
>> slow?

>Again magnetic fields play an important role in breaking down and removing
>angular momentum from a star. Current theories can indeed explain the
>rotation rates of a large amount of stars.

Almost all stars, in fact. If you assume that a star's
rotation is proportional to its magnetic field (a very
rough approximation of the very uncertain dynamo effect),
then the solar wind from a young, low-mass star would
rapidly carry away angular momentum and slow down the
star's rotation. Above a critical mass, however, the
star's gravity cuts off the solar wind, creating
what is often called a "solar breeze": A very low
velocity flow, carrying away little mass or angular
momentum. Above another, critical mass, the star's
luminosity is so great that photon pressure
becomes significant and strong solar winds
develop, but ones that carry away relatively little
angular momentum and which do not really slow the
star's rotation. These models (applications of the
Webber-Davis solar wind model, if you care) therefore
predict slow rotation from low mass stars, rapid
rotation from more massive stars and strong solar
winds and rapid rotation from the most massive stars.
This trend, as well as the lower cut off mass, matches
almost all observations. The few exceptions are
probably cases where, for some reason, the very
simple, assumed dynamo model does not apply.

>> The fusion reaction is matter in a plasma state. Rotation creates a
>> dynamo effect producing a magnetic field which unifies the plasma, which

>Rotation cannot produce magnetic fields.

While I agree with many of your earlier remarks, this is not
correct. The essence of a dynamo is the creation of
a magnetic field drawing the required energy from
rotational motion. Even in the absence of an initial
magnetic field, a dynamo is unstable and would produce
a strong magnetic field from even the most trivial
disturbance. Rotation in a plasma can, under the
right conditions, produce a magnetic field. Rotation
alone, however, is certainly not enough.

Frank Crary
CU Boulder