Tuesday, February 14, 2006

Dark Matter Data
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

kT ~Mv^2 ~ GM^2/R

In my ZPE theory however

GM/R^3 = c^2/
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:

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.

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.

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:

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

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.