New Developments 2004

Update On Dark Matter Results (November, 2004)

One of the most fundamental predictions of the Self-Similar Cosmological Paradigm (SSCP) is that the Stellar Scale is dominated by a very large population of ultracompact objects (black holes and neutron stars) that are self-similar to the unbound subatomic particles and fully ionized nuclei that dominate the Atomic Scale.  The well documented, but still enigmatic, Dark Matter that constitutes at least 90% of the mass in galaxies is consistent with this general prediction.  More specifically, the SSCP predicts that most of the Dark Matter mass is contributed by two populations of black holes with masses of either 0.15M¤ (the larger population) or 0.58M¤ (a considerably smaller population).

 The MACHO survey was the most comprehensive experiment to date for determining whether stellar-mass objects played a role in the galactic Dark Matter.  The bottom-line results1 of that experiment are that 8% to 50% of the galactic Dark Matter is comprised by previously unknown stellar-mass objects that emit very little radiation and have masses in the range 0.15M¤ to 0.9M¤.  These exciting results were quite surprising to astrophysicists, but are consistent with SSCP predictions.

Now a separate microlensing experiment, the VATT/Columbia survey1, which targets a different galaxy (M31, our neighboring Andromeda galaxy) has reported similar results.  A very large population of previously unknown stellar-mass objects appears to constitute 16% to 59% of that galaxy’s Dark Matter.  The masses of these Dark Matter objects are estimated to fall within the range of 0.02M¤ to 1.5M¤, again consistent with SSCP predictions.

The authors of the most recent study conclude that because two different experiments using two different galaxies give very similar results, the discovered population of stellar-mass Dark Matter objects is “likely to be a universal phenomenon.”  They also comment: “Perhaps the most surprising conclusion drawn from the MACHO data is that the lenses lie in a mass range occupied by stellar objects and are well above … the brown dwarf/stellar boundary”.  Primordial black holes are pointed out as a candidate class of objects because they emit little radiation and do not violate baryonic constraints.

From the SSCP standpoint, these results are very encouraging.  Moreover, another research team using the ESO’s Integral satellite and conducting a different experiment on diffuse gamma rays has also found evidence for a large, and previously unknown, population of black holes and neutron stars.2,3  In cases where members of this population occur within clouds of gas and dust, they accrete enough matter to emit a “soft” gamma ray glow that has been detected.  A census of the size of this population of ultracompacts is underway.  The SSCP proposes that this population belongs to the same huge class of Dark Matter objects already identified by the MACHO and VATT/Columbia microlensing experiments. 


  1. Uglesich, R.R., et al, Astrophysical Journal 612, 877-893, 2004.
  2. White, N., Nature 428, 264-265, 2004.
  3. Lebrun, F., et al, Nature 428, 293-296, 2004.

Gamma Ray Bursts and the SSCP (November 2004)

For several decades scientists have been mystified by huge bursts of very high energy gamma rays coming from enigmatic sources. The bursts appear to come at random times and from random directions. They have not been linked to previously identified precursors and their distribution is global, with most occurring at large distances rather than being confined to our own galaxy. Time scales for the burst phase of the GRBs range from ~ 0.03 sec to ~ 900 sec and there appears to be a bimodal distribution of short and long bursts. It is possible that the Self-Similar Cosmological Paradigm can shed light on the enigma of GRBs.

According to the Principle of Cosmological Self-Similarity any phenomenon on the Stellar Scale of the infinite cosmological hierarchy will have a self-similar analogue on the Atomic Scale.  The natural candidate for the Atomic Scale counterpart to GRBs would be subatomic phenomena such as e-e+ annihilation and the decay of radioactive isotopes, since these phenomena involve very high energies and emission of gamma rays.  Table I shows a representative set of subatomic phenomena, giving the type of event, the gamma ray energy emitted and the predicted energy output for a Stellar Scale counterpart.  The latter is calculated by the following method.  Since the dimensions of energy are ML2/T2, the self-similar scaling factor predicted by the SSCP is L3.174 » 1.7 x 1056, where L » 5.2 x 1017.  The total energies observed for GRB events fall mainly within the 1050 ergs to 1051 ergs range, which is in agreement with the expected values calculated according to the scaling rules of the SSCP.


Atomic Scale Event Total Energy In Gamma
Atomic to Stellar Scaling
Factor (See Papers #1 and #2)
Predicted Energy For
Stellar Scale Analogue
e-e+ annihilation 1.022 Mev
L3.174 » 1.7 x 1056
2.78 x 1050 ergs
7Be decay 0.477 Mev
» 1.7 x 1056
1.30 x 1050 ergs
10C decay 0.72 Mev
» 1.7 x 1056
1.96 x 1050 ergs
14C decay 5.30 Mev
» 1.7 x 1056
1.44 x 1051 ergs
16N decay 6.13 Mev
» 1.7 x 1056
1.67 x 1051 ergs
19O decay 0.20 Mev
» 1.7 x 1056
5.44 x 1049 ergs
20O decay 1.06 Mev
» 1.7 x 1056
2.88 x 1050 ergs
Typical nuclear de-excitations 0.01 Mev to
7.0 Mev
» 1.7 x 1056
2.72 x 1048 ergs to
1.87 x 1051 ergs


The SSCP explanation for the GRB phenomena is that galaxies contain vast populations of ultracompact Dark Matter objects in the form of black holes and neutron stars.  They are the self-similar Stellar Scale analogues of subatomic particles and fully ionized atomic nuclei.  It is the interactions, “decay” and de-excitation of these objects that are proposed for the origins of GRBs.  Perhaps the reason that astrophysicists have found it so difficult to solve the enigma of GRBs is that they have searched for one class of objects and a single mechanism to explain what may in fact be a more heterogeneous set of related phenomena, as happens with Atomic Scale nuclear activity.

 The SSCP predicts that the short duration GRBs will have a distinct total energy peak at » 3 x 1050 ergs that is self-similar to the total energy peak for e-e+ annihilation at 1.022 Mev (or » 1.6 x 10-6 ergs).  In general, the distribution of total energies for the GRBs should mimic the range and peak locations that are found for the most common Atomic Scale nuclear events when scaled up by the SSCP’s self-similar transformation factor for energies or masses: » 1.7 x 1056.

Preferred Stellar Masses At Predicted SSCP Values (August 2004)

The SSCP predicts that stars should have preferred masses at 0.145M, 0.29M, 0.44M, 0.58M, 0.87M, 1.02M, 1.16M and 1.31M. Peaks occur at multiples of the fundamental proton analogue mass of 0.145M, except for a highly diagnostic gap at the n=5 multiple (0.73M, see Paper #6).

White dwarf stars are proposed to be self-similar analogues to 4He+ ions with the remaining electron in the lowest energy state, and far lesser numbers of more massive systems in the same He+-like state. Therefore we expect the mass function (MF) for white dwarfs to have a very small peak at  0.44M (3He+), a dominant peak at  0.58M, a conspicuous gap at 0.73M and peaks of decreasing size at  0.87M1.02M1.16M and  1.31M.

In Paper #6 of the “Papers” section of this website, the mass function for white dwarfs in the mass range of 0.3M - 1.0Mwas shown to conform to our expectations, especially the main peak at 0.58M, the gap at  0.73M and the secondary peak at  0.87M. A recent sampling of the high-mass end (0.8M– 1.3M) of the white dwarf MF (M. Nalezyty and J. Madej, Astronomy & Astrophysics, 420, 507-513, 2004) appears to increase the agreement between observed white dwarf masses and SSCP predictions. The graph shown above has been created by grafting the new high mass results onto the 0.30M– 0.80M portion of Figure 3 in Paper #6. Admittedly this grafting of different samples might cause some grumbling on technical grounds, but if we are only testing for qualitative features and a first approximation quantitative agreement with the SSCP predictions, then I think this is scientifically permissible.

The results are fairly impressive. Given the limited size of the combined sample (267 stars) and the somewhat limited accuracy of stellar mass estimates, the agreement between predictions and observations is quite strong, and the overall signature of the MF is unique. An interesting question is: why do white dwarf samples regularly display the signature features predicted by the SSCP, while samples of main sequence stars are much more ambiguous, often possessing some of the peaks but not others? Does this merely reflect differing levels of uncertainties in mass estimates for the different classes of stars? Is a more subtle explanation required? Is the true degree of Cosmological Self-Similarity between the Atomic and Stellar Scales fairly high, as indicated by the white dwarf results, or considerably lower, as suggested by available mass estimates for main sequence stars? An accurate mass function for the galactic dark matter would provide an unambiguous answer.

Follow-Up On The RECONS Stellar Mass Data (July, 2004)

Improved stellar mass data from the RECONS Project (see “New Development” December 2003) are now available and have been analyzed. Unfortunately the results are still ambiguous. The predicted gap at »0.73M¤, and the expected peaks at 0.10M¤– 0.15M¤, 0.55M¤– 0.60M¤ and 0.84M¤– 0.90M¤ are in evidence, but there is much less discreteness than anticipated. At this point it is difficult to determine which of several possible causes of this ambiguity apply here.

However, a sample that does show the predicted signature mass function has been identified and is shown above.