No Errors in Stolmar's Cosmic Background Model – answer to Ned Wright

[NW: Stolmar's cosmological model uses a tired light redshift. The Earth is located in the center of a uniform density sphere of stars extending out to some maximum radius R_max which is about 7 or 8 Hubble radii. The redshift factor 1+z is exponential with distance,]

Z = 2^(t/Hd) – 1 where Hd = 4.234 billion years Hubble wavelength doubling time.

[NW: and thus reaches a few thousand at the edge of the sphere. Starlight redshifted by this factor of a few thousand provides the cosmic background.]

All the stars radiating within that region with frequency, which arrives in the range of 0-600 GHz after redshift are calculated!

[NW: However, this model does not agree with the observations and must be rejected: ]

Typical Ned Wright preconception. Indeed the Stolmar model agrees with the observations and should be accepted as correct fundamental physics representation.

The spectrum is correct

[NW: In his CMB page on 27 July 2001 Stolmar gave the following equation for the solid angle covered by stars in a shell with radii between R_- and R₊,

where A is the area of a star and n is the number density of stars. Stolmar gave this equation for the energy in the background radiation:

where the index j is the frequency in GHz. It is hard to determine exactly what is meant by this equation, since it appears to give the odd combination of energy density per unit wavelength divided by the frequency, but Stolmar also gave the equation for a blackbody:

which can be used to normalize the previous equation. Now Stolmar also assumes (1+z) = exp(HR/c).]

If you compare the two - and know something about radiative heat transfer - you can see that the two equations represent the energy transferred from the source to the observer in both cases. The shells are represented with their respective total radiating and not blocked surfaces of stars, the radiated wavelengths are calculated back from the observed, because at each
frequency only the arriving at that frequency radiation is calculated. The energy also decreased by the (1+z) tired light energy loss, this is what causes the (1+z)^4 power.

[NW: If I take the limit of infinitesimally small shells in radius, I get a normalized integral for the specific intensity of the CBR which is

where y = H R/c, f is the frequency in Hz, and I_f is in [erg/cm²/sec/sr/Hz].]

Instead of understanding my equation, an erratic integral is introduced and some allegations made based on that. It is simply wrong.

[NW: Stolmar prefers to use the doubling time of photon wavelengths, H_d, instead of the Hubble constant H, but these parameters are related by H = ln(2)/H_d. This formula has three free parameters: Anc/H determines the overall intensity scaling, T_* determines the frequency scaling, and y_max determines the shape of the spectrum. Note that Anc/H is the optical depth per Hubble radius and it is very small in Stolmar's model so the use of the optically thin approximation here is appropriate.]

There is indeed fundamental difference between Ned’s representation and mine. In short, his is wrong, my is correct. I represent the stars with a uniform temperature and sum the correct intensities of radiation, arriving here at the frequency of the microwave range from the different redshift shells. Ned simply don’t understand that you have to accumulate the intensities from the sources, coming at the frequencies observed and generated at the frequencies resulting from the Hubble redshift.

[NW: Also note that Stolmar assumes that all of the power emitted by the stars at redshift z reaches us, but with an apparent temperature redshifted to T_*/(1+z).]

Simply not true. I calculate all the stars at the input defined temperature, but I limit the calculation only to the frequencies, which we are observing here in the microwave range, by 1 GHz frequency steps. I reduce the intensity by the (1+z), I define the calculated wavelength by the same ratio – obviously, where it had to be originated to arrive here at that frequency. Also, the solid angle of a z redshift shell already contains the correction for the blocking effect by the inner layers.

[NW: Normally in tired light models one allows for the loss of photon energy by a factor of (1+z) which would change the (1+z)⁴ = exp(4y) in the above equations to (1+z)³ = exp(3y).]

Wrong again: the (1+z)^4 is already a reduced by that factor intensity!

[NW: The only set of these parameters that agree with the FIRAS data on the CMB is y_max < 0.00005, T_* = T_o = 2.725 K, and Anc/H = y_max^-1. In this case the optical depth per Hubble radius is high so one has an opaque isothermal source: a blackbody.[

Indicating that a realistic star density and star temperature model together with the tired light cause of Hubble redshift could very well be the source of CMBR.

[NW: But real stars are not blackbodies, so even this limit will not actually work.]

They are close enough to black bodies – and the mixture of stars in one shell results in a very smooth Plank curve in a tired light cosmology. It should be simple enough to understand that the closer may absorb what was an emission farther away and fill-up as well the volleys of absorptions.

[NW: When y_max is not infinitesimal, one gets a Rayleigh-Jeans low frequency tail rising to a peak corresponding approximately to a graybody with temperature exp(-y_max)T_*, a Wien high frequency tail corresponding approximately to a graybody with temperature T_*, and an I_f proportional to f^-1 behavior between these two tails. The low frequency tail can approximate a blackbody for an appropriate choice of Anc/H. But this model can not simultaneously fit the data both above and below the peak unless y_max is infinitesimal.]

Please note that relates only to Ned’s erratic model, I calculate the correct intensities at the input defined temperatures.

[NW: The examples given by Stolmar are extremely inconsistent with the FIRAS data on the CMB, as shown in Figure 1. Stolmar's comment about this discrepancy is "The higher calculated values on the right from the peak require closer examination of the reported processing of CMBR data". In other words, blame the data for not agreeing with his theory. However, these data have been confirmed by a separate experiment: see Gush, Halpern & Wishnow (1990, PRL, 65, 537).]

http://arxiv.org/abs/astro-ph/0106412 contains an interesting table on the last page, called Zodi fitting. The author is Ned, the meaning is about the same: when you are leaving only a fraction of the observed value as the significant value you have to be careful concluding that it perfectly fit to the Plank curve. I stand for my theoretical value. Will show more results in the future.

[ Figure 1: Stolmar's model with T_* = 4000 and R_max = 99 Glyr, which deviates from the FIRAS data by up to 13,000 standard deviations. This value of R_max and H_d = 8.468 Glyr give y_max = 8.1 while my best match to Stolmar's curve is with y_max = 7.7. In this plot I use values read from Stolmar's graph. However, Stolmar recently changed H_d and has not updated these figures. ]]

The results from my calculations fit very well to the observed CMB, the higher then the Plank curve values on the right side of the peak is a fact, shown on the Figure 2 by Ned. It could be concluded - even before evaluating the screened values with the interstellar materials blocking effect - that the Hd = 4.234 billion years tired light Hubble wavelength doubling constant value is good, and the so called cosmic microwave background is a remnant of surrounding us stars normal radiation, red-shifted to these wavelengths. The 3K CMB intensity is shown for quantitative representation of the theoretical and experimental intensity fit.

[NW: Since Stolmar's cosmology career on sci.astro started with the announcement of the DIRBE far IR background, it is interesting to plot his model on a much wider frequency range and compare not just to the CMB but also to the IR and optical backgrounds. ]

And the source of the IR background now is accepted that a result of normal stellar radiation redshifted, as I stated.

[NW: This is shown in Figure 2. The long I_f proportional to f^-1 section becomes a constant when one plots f I_f , and this behavior is quite contrary to the data, both the detections and the upper limits.]

Figure 2: Stolmar's model compared to FIRAS, DIRBE, HST, groundbased and far UV measurements of the cosmic background. Since Stolmar's graphs do not extend to such short wavelengths, I have evaluated my integral version of his equations numerically. Green curve: Stolmar's model. Black curve, FIRAS BB fit. Black IR points: Hauser et al. (1998) on the CIRB. Red points: Wright et al. (2000, 2001) on the CIRB. Magenta upper limits from lack of TeV gamma-ray absorption. Blue points: Bernstein et al. (2001) on the optical background. Black optical and UV points: Toller; Dube et al.; and Hurwitz et al. ]

Another typical lie of Ned: it could be seen on my graph above that the green line could not possibly represent my results! At around 0.6 THz the value should be near ½ of the peak even by the old graph!

The solid black line is the Planck curve for the 2.723 K. The measurement points do not follow the curve after the peak, but show a significantly higher intensity – exactly like my calculation does!

Stars do not last 100 billion years – and they don’t have to, just live their normal cycle !

[NW: The stars at the edge of the sphere that produce the peak of the CMB are radiating at a time that is 7 or 8 Hubbles times ago. That is nearly 100 billion years, and only very low mass red dwarfs last that long.]

Even in a big bang hoax type Universe the source is located in the past, there is no connection between the age of an individual star! Yes the observed radiation had to travel z=1000-3000 value producing time, which is t = 4.234 *ln(z+1)/ln(2) 40 to 50 billion light years. I feel a major confusion here! May be Ned thinks that the star now also has to be there if we are seeing it?!

[NW: But low mass M dwarfs produce very little radiation, and Stolmar's model requires a lot of radiation. On 24 July 2001 Stolmar changed his H to 160 km/sec/Mpc, which alleviates this problem but disagrees with the data on the Hubble constant.]

Which is??? So, my theoretical Hubble constant value is in the middle of Hubble’s original and the current – adjusted to eliminate the age contradiction, heavily undersized around 50 – values. Is there a problem with that? It makes sense!

The new value of the Hubble wavelength doubling time constant Hd = 4.234 billion years got an interesting collaborating evidence: http://www.eso.org/outreach/press-rel/pr-1998/pr-14-98.html "NGC 1232 is located 20o south of the celestial equator, in the constellation Eridanus (The River). The distance is about 100 million light-years, but the excellent optical quality of the VLT and FORS allows us to see an incredible wealth of details. At the indicated distance, the edge of the field shown in PR Photo 37d/98 corresponds to about 200,000 lightyears, or about twice the size of the Milky Way galaxy."

The incredible detail could be compared to some of Halton Arp findings. He featured it on the back cover of the book _Quasars, Redshifts and Controversies_.

First, the cute little spiral to the left, NGC 1232A. It's so typical of companion galaxies (like the Magellanic Clouds to our own Milky Way) that it was listed as "same redshift" as NGC 1232 without even bothering to take a spectrum. When someone finally got around to measuring the redshift, what a shock! It was 4776 km/sec higher than the redshift of the main galaxy.

But even more amazing is the cute little knot at the top -- NGC 1232B. Here's the story, in Arp's words, from _Quasars, Redshifts and Controversies_, pg 89. "Purely out of curiosity, and fully expecting an HII (gaseous emission) region at the redshift of the main galaxy, I took its spectrum. [...]
The spectrum showed a redshift of over 28,000 km/sec (almost one-tenth the velocity of light), far exceeding the mere 1,776 km/sec of the main galaxy."
http://www.eso.org/outreach/press-rel/pr-1998/phot-37d-98-preview.jpg

Now let's do the little calculation using my exponential Hubble law with the new value for the constant:
t = 4,234 * ln(z+1)/ln(2) is the distance in million light years. For the NGC1232 v=1776 km/s results a distance of 36 million light years! But it means that this galaxy is about the same size as the Milky Way! Now the "companion galaxy" v = 6552 km/s and D = 132 million light years. It's interesting! The size ratio corresponds to the calculated distance ratio, so the size range again close to the Milky Way!

How about that cute little dot at 12 o'clock from the center of NGC1232?! v = 28,000 km/s D = 545 mly or about 4 times farther away than the NGC1232A - which is also about right comparing to the size!
Now we see three Milky Way size galaxies at the right distances, calculated from the exponential Hubble redshift vs. distance law with the constant value, very close to Hubble's original...

We must be in the center of the Universe – our view of the Universe is centered on us(!)

[NW: If we are not in the center of the Universe, a large dipole anisotropy is produced that has the spectrum of a graybody at temperature T_*/exp(y_max). The observed dipole anisotropy has a different spectrum. Thus we must be nearly exactly in the center of the sphere of stars. A rough analysis of the FIRAS dipole anisotropy spectrum suggests that we must be centered within Stolmar's sphere of stars to within 1 part in 100,000 of R_max_, which means that the Milky Way could be the center, but the center of mass of the Local Group could not. Having the sphere of stars centered on the Local Supercluster is completely ruled out.]

I give-up! This speculation I simply cannot follow – because it is so stupid. First of all, I pointed out that the superimposed Doppler caused dipole corresponding to our motion relative to the background could be superimposed only on a tired light caused Hubble redshift and could not be superimposed on a Doppler caused redshift! If someone don’t understand it, should ask questions about the geometry and heat transfer but it should be obvious.