Missing Mass, Galaxy Ageing, Supernova Redshift, MOND and Pioneer (was: character sets)

[[Mod. note -- I have taken the liberty of changing the Subject:
header in 2 ways:
1. The usenet standard for changing subject from X to Y is
Subject: Y (was: X)
with "(" and ")" parentheses; somehow this thread managed to get
"[" and "]" square brackets instead, which will confuse some
threaded newsreaders.
2. Since we're back to discussing astronomy, not character sets, I've
made Y=astronomy and X=character sets. This way newsreaders are
more likely to abbreviate the thread in a way which suggests astronomy...
-- jt]]

In article , Charles Francis
writes:

I got to the square red shift law on theoretical grounds, by looking at
how I could used teleparallel displacement to get a consistent
mathematical model. But from the point of view of the paper discussed
here I am happy to treat it as phenomenological. It appears to me that
it actually does give a better match with data than the linear law
derived from parallel transport of light.

Segal sang the praises of a "quadratic Hubble law" for years, claiming
it was a better fit to the data. As many have pointed out, this is not
the case. (His model fails on many other grounds as well.) What
concrete data are better fit by your law than with the standard one?

In message , Phillip Helbig---
remove CLOTHES to reply writes
In article , Charles
Francis writes:

I got to the square red shift law on theoretical grounds, by looking at
how I could used teleparallel displacement to get a consistent
mathematical model. But from the point of view of the paper discussed
here I am happy to treat it as phenomenological. It appears to me that
it actually does give a better match with data than the linear law
derived from parallel transport of light.

Segal sang the praises of a "quadratic Hubble law" for years, claiming
it was a better fit to the data. As many have pointed out, this is not
the case. (His model fails on many other grounds as well.)

Yes. But I am talking about quite a different square law. As I
understand Segal had redshift proportional to the square of distance. I
have redshift proportional to the square of the expansion parameter

1 + z = (a_0/a(t))^2

To first order this is linear in distance

1+z = 1 + 2 r adot / a

So I have for Hubble's constant

H = 2 adot / a

Thus I have it that the universe is expanding at half the currently
accepted rate. It follows immediately that it is twice as old, and
requires a quarter of the critical density for closure

What concrete data are better fit by your law than with the standard
one?

Missing mass is probably not concrete data, but I think there is some
from the observation of galaxies and EROs at z=1.4 and greater,

C. R. Mullis, P. Rosati, G. Lamer, H. Boehringer, A. Schwope, P.
Schuecker, R. Fassbender, 2005, Discovery of an X-ray-Luminous Galaxy
Cluster at z=1.4, ApJ Letters, 623, L85-L88, astro-ph/0503004.

Doherty M., Bunker A. J., Ellis R. S., McCarthy P. J., 2005, MNRAS, 361
525-549.

According to Doherty, the most up to date semi-analytic hierarchical
models (e.g. Somerville R. S. et. al., 2004, ApJ, 600, L135.) have great
difficulty in reproducing the observed high space density of massive
galaxies with red colours and evolved stellar populations. This suggests
that the universe at these red shifts is much more mature than has been
thought, giving a high level of support for the square red shift law.
Observations of objects at even higher redshifts will conclusively
distinguish between the models.

I have calculated the redshift magnitude relation to first order in z
for zero cosmological constant. I get

m ~ 5log z + 1.086(1.5 - 0.125Omega)z

Where I have multiplied the value of Omega by 4, so as to keep Omega=1
as critical density. Using the critical density Omega=1 this is the same
plot as the standard one with Omega = 0.41 and Omega_Lambda = 0.59. I
have estimated that for z=1 the second order correction is close to 0.1,
which brings the figures quite remarkably close to the standard
concordance model. Really though I need to adapt the computer programs
used to analyse supernova data to get better figures, and I don't know
how I can go about doing that.

I have two other results, for MOND and Pioneer, which don't directly
test the square law, but the relationship between them does. Expansion
is always detectable in Doppler measurements and this is detected by
Pioneer. I get a blue shift equivalent to an acceleration -Hc, in
agreement with observation. But I also get no classical acceleration,
this is just an anomalous shift. I think this is concrete evidence of
the model (but not of the square law), since there is no other
explanation. Potentially it should be possible to measure the position
of a spacecraft by both Doppler and ranging, which would establish or
falsify my conclusion.

I understand that there is a planned mission which will precisely
determine the direction of the acceleration. It is a concrete prediction
that this will be toward the earth, not the sun, nor along the spin
axis, nor in the direction of motion.

Likewise I have it that MOND is not really a change to newtonian
dynamics, but essentially an optical effect due to cosmological
redshift. To calculate it I have to observe that an effect of the square
redshift law is that the coordinates used to calculate the wave function
are stretched by a factor of two in the radial and time direction and by
a factor 1/2 in the orthogonal direction (although 4pi in a circle is
suggestive of the behaviour of the phase of a Fermion, I have not
explored this). This means that in coordinates with an origin at the
centre of a galaxy the orthoganal component the pioneer acceleration is
Hc/4. I get 3 more factors of two when writing down acceleration, ending
up with an inward component Hc/32

The redshift is interpreted as being due to the motion of a body in
orbit about G with orbital velocity v_p. Then

v_p^2 / x = Hc/32 or v_p = root(Hcx/32). 3.3.2

This simulated velocity, v_p, is independent of galactic mass and would
appear in Minkowski coordinates with an origin at any point in space. If
the true orbital velocity of the star S due to gravity is vg then the
observed orbital velocity is

v = v_g + v_p = root(GM/x) + root(Hcx/32) 3.3.3

3.3.3 recognises that, since the alteration to redshift is an optical
effect, it is correct to add velocities, not accelerations as would be
the case for a dynamical law. Then the apparent acceleration toward G is

v^2/x = GM/x^2 + root(GMHc/8)/x + Hc/32 3.3.4

The first term in 3.4.4 is the acceleration due to gravity. The last is
simply the component of Pioneer acceleration toward G, and appears also
in the absence of a source of gravity. This leaves an unmodelled
acceleration equivalent to a redshift due to velocity,

v^2 = root(GMHc/8) 3.3.5
,
in precise agreement with MOND, the phenomenological law proposed by
Milgrom (1994) which retains Newton's square law for accelerations
xdoubledot a_M for some constant a_M, but replaces it with

xdoubledot = - (GMa_M)^1/2 /x for xdoubledot a_M
3.3.6

and gives a good match with data. The best fit value of a_M from
observations on thousands of stars is 1x10^-8 cm s-2 in precise
agreement with a_M = Hc/8 using the value 8x10^-8 cm s-2 found from the
observations on Pioneer.


Regards

--
Charles Francis