My theory in http://arxiv.org/abs/gr-qc/0602022 says NO to the
temperature estimate for the dark matter. OK now I remember yes, they
use the VIRIAL THEOREM v^2 ~ GM/R
(v/c)^2 ~ (Gravity Radius)/(Radius) is VIRIAL THEOREM
kT ~Mv^2 ~ GM^2/R
In my ZPE theory however
GM/R^3 = c^2/\
(Gravity Radius)/R^3 ~ /\
Gravity Radius of Sun ~ 10^5 cm
Gravity Radius of Dark Matter Blob ~ 10^12 cm.
1 light year ~ 10^18 cm
1000 light years ~ 10^21 cm
/\ ~ 10^12/(10^21)^3 ~ 10^12/10^63 ~ 10^-51 cm^-2
i.e. vacuum radius of positive curvature ~ 10^26 cm for the attractive
dark matter blob.
The repulsive dark energy vacuum radius of negative curvature is ~ 10^28
cm ~ Hubble radius
Therefore, the dark matter blob negative ZPE energy density on 10^3
light year scale is ~ 10^4 larger (in absolute value) than the positive
dark energy ZPE density on scale of 10^10 light years.
The Virial Theorem
The virial theorem states that, for a stable, self-gravitating,
spherical distribution of equal mass objects (stars, galaxies, etc), the
total kinetic energy of the objects is equal to minus 1/2 times the
total gravitational potential energy. In other words, the potential
energy must equal the kinetic energy, within a factor of two.
Suppose that we have a gravitationally bound system that consists of N
individual objects (stars, galaxies, globular clusters, etc.) that have
the same mass m and some average velocity v. The overall system has a
mass Mtot = N.m and a radius Rtot.
The kinetic energy of each object is K.E.(object) = 1/2 m v2
while the kinetic energy of the total system is K.E.(system) = 1/2 m N
v2 = 1/2 Mtot v2
where v2 is the mean of the squares of v. The gravitational potential
energy of the system can be written as:
<unknown.gif>
We usually assume that all of the orbits travel on similar orbits that
are isotropic, that is, are not flattened in any way and have no
preferential direction; we say these are random orbits. The virial
theorem then requires that the kinetic energy equals one half the
potential energy, that is:
K.E. = - 1/2 P.E.
<unknown.gif>
v^2 ~ GM/R
kT ~Mv^2 = GM^2/R
Therefore, we can estimate the Virial Mass of a system if we can observe:
The true overall extent of the system Rtot
The mean square of the velocities of the individual objects that
comprise the system
If the motions are not random/isotropic, the virial theorem still
applies, but its form changes a bit. Similarly, since our system is made
up of many objects, we can gain some insight by seeing how the orbital
velocities vary with radius from the center outward.
For example, in a spiral galaxy, the dominant motion of the stars in the
disk is circular rotation in the plane of the disk. The variation in the
orbital velocities with radius V(r) is called the rotation curve.
http://astrosun2.astro.cornell.edu/academics/courses/astro201/vt.htm
On Feb 14, 2006, at 9:51 AM, Jack Sarfatti wrote:
Until I see details of what they assume about how they deduce the
"temperature" I can't say. I am sure this will be discussed next week at
UCLA Conference where I will be.
They have 3 10^7 solar masses in a sphere of diameter 1000 light years.
In my model the energy density is ~ (c^4/G)|/\|
So I would simply compute /\ from their measured density.
For dark matter this is negative ZPE energy density with positive
pressure at w = -1, so /\ < 0.
On Feb 13, 2006, at 2:12 PM, Jack Sarfatti wrote:
Yes, but I think I see the flaw. They are assuming the particles are on
mass shell. They have not even considered that it may be zero point
energy gravitating with positive pressure. I am far from convinced.
Maybe they will be at UCLA next week.
On Feb 13, 2006, at 2:00 PM, Gary S. Bekkum wrote:
This could be critical for your theory:
http://news.bbc.co.uk/2/hi/science/nature/4679220.stm
....the Cambridge team has provided new information with its detailed
study of 12 dwarf galaxies that skirt the edge of our own Milky Way.
Using the biggest telescopes in the world, including the Very Large
Telescope facility in Chile, the group has made detailed 3D maps of the
galaxies, using the movement of their stars to "trace" the impression of
the dark matter among them and weigh it very precisely.
With the aid of 7,000 separate measurements, the researchers have been
able to establish that the galaxies contain about 400 times the amount
of dark matter as they do normal matter.
"The distribution of dark matter bears no relationship to anything you
will have read in the literature up to now," explained Professor Gilmore.
If this 'temperature' for the dark matter is correct, then it has huge
implications for direct searches for these mysterious particles
Prof Bob Nichol
Institute of Cosmology and Gravitation, Portsmouth
"It comes in a 'magic volume' which happens to correspond to an amount
which is 30 million times the mass of the Sun.
"It looks like you cannot ever pack it smaller than about 300 parsecs -
1,000 light-years; this stuff will not let you. That tells you a speed
actually - about 9km/s - at which the dark matter particles are moving
because they are moving too fast to be compressed into a smaller scale.
"These are the first properties other than existence that we've been
able determine."
----- Original Message -----
From: Jack Sarfatti
To: Gary S. Bekkum
Sent: Monday, February 13, 2006 3:56 PM
Subject: Re: NEWS - Dark matter moving at a speedy 9 kilometres per second
too busy
On Feb 13, 2006, at 1:49 PM, Gary S. Bekkum wrote:
Check out BBC audio at right on this page:
http://news.bbc.co.uk/2/hi/science/nature/4679220.stm
----- Original Message -----
From: Jack Sarfatti
To: Gary S. Bekkum ; Lubos Motl
Cc: Dr. Eric Davis ; Hal Puthoff ; Tim Ventura ; David M Mcmahon ; Mark
Pesses ; Ronald Pandolfi ; Creon Levit ; S-P Sirag ; Waldyr Jr. ; Keay
Davidson ; Tony Smith ; carlos castro ; Eric Davis ; Hal P ; Paul Zielinski
Sent: Monday, February 13, 2006 3:35 PM
Subject: Re: NEWS - Dark matter moving at a speedy 9 kilometres per second
I will probably learn more about this next week at the UCLA Dark Matter
meeting. This could be a crucial test of my theory. They could be
misinterpreting their data. In my theory there are no dark matter
particles on mass shell. Dark matter is simply negative zero point
energy with positive pressure and w = -1 since it's isotropic out in
free space. If anisotropic it will change w, e.g. the Casimir plates
example. How do they measure that temperature?
On Feb 13, 2006, at 1:14 PM, Gary S. Bekkum wrote:
"The results were surprising. Aside from their speed, the researchers
calculated the smallest clump of dark matter that could exist, 1000
light-years across.These results imply that dark matter is hotter than
predicted, meaning that what astronomers call 'cold' dark matter may not
be so cold after all. At 10,000°C it's still cool by astronomical
standards. But it's warm enough to solve two problems that have plagued
standard models of how galaxies form: that there are too few dwarf
galaxies and why dark matter has not concentrated in the centre of
galaxies."
http://www.abc.net.au/science/news/stories/s1567144.htm
Dark matter sure is a fast mover
Marilyn Head
ABC Science Online
Monday, 13 February 2006
The galaxy cluster Abell 2029 is composed of thousands of galaxies,
shown in this xray image, and an amount of dark matter equivalent to
more than a hundred trillion Suns (Image: NASA/CXC/UCI/A Lewis et al)
Dark matter particles are zooming around the universe a million times
faster than anyone predicted, UK astronomers say.
They've calculated that this mysterious substance, which governs how
stars and galaxies move, is moving at a speedy 9 kilometres per second.
The University of Cambridge researchers have also worked out how dark
matter likes to clump together and surprising details of how hot it is,
data essential in modelling how galaxies form.
A preliminary report is available on arXiv, the online website operated
by Cornell University.
Dark matter is mysterious because it doesn't emit radiation, making it
difficult to spot. Indeed, no-one has detected it and not all scientists
are convinced it exists.
"The best evidence for dark matter is that there are stars in our sky,"
says Professor Gilmore, director of the Institute of Astronomy at
Cambridge, which made the latest calculations.
"Without it they'd be flying off into space."
Dark matter is the mass needed to hold stars in their given places as
they move around galaxies; the faster they move the more mass is needed.
"Kepler and Newton were able to weigh the Sun just by knowing where
Earth was and how fast it was moving," says Gilmore.
"We did the same thing, only in three dimensions, finding the 'weight'
of dark matter by measuring the place and speed of a very large number
stars in several dwarf galaxies orbiting the Milky Way."
Hanging out in clumps
The results were surprising. Aside from their speed, the researchers
calculated the smallest clump of dark matter that could exist, 1000
light-years across.
These results imply that dark matter is hotter than predicted, meaning
that what astronomers call 'cold' dark matter may not be so cold after all.
At 10,000°C it's still cool by astronomical standards. But it's warm
enough to solve two problems that have plagued standard models of how
galaxies form: that there are too few dwarf galaxies and why dark matter
has not concentrated in the centre of galaxies.
Gilmore says he was initially wary of the results, which together seemed
too simple to be plausible.
The discovery of a super-dim galaxy by Dr Beth Willman from New York
University, gave the team an opportunity to successfully test its
predictions.
.
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