The Origin of Dark Matter

The nature of dark matter is evident from the similar spatial distribution of dark matter and photons

Dark matter: In the vicinity of galaxies, the observed strength of the gravitational field is much larger than to be expected based on Newtonian or Einsteinian gravity. In addition it has an unexpected spatial distribution.

Present-day physics assumes a yet unknown type of particle which does not have any interactions except via gravity. But the intensified search for them over the past decades has not yielded the faintest result. And even if a particle were found, there is no explanation for the very specific distribution of these particles.

However, this spatial distribution is itself a strong indication of the nature of dark matter. It is a striking fact that the distribution is identical to that of photons in those areas, a fact which is at present not in the focus of the physical investigations.

The conclusion that photons themselves are the origin of the observations yields correct results - even quantitatively correct results. However, this requires a modification of the laws of gravity in the way that gravitation is not caused by mass or energy.

This assumption may be felt to be shocking but is not in conflict with observation.


1 The manifestations of dark matter

1.1 Rotation of stars and galaxies

This phenomenon of increased gravity was first observed in connection with the fast rotation of galaxies in clusters. Other well investigated cases are single stars orbiting a galaxy. The stars in the outer regions of galaxies orbit the center too quickly. In addition, the dependence of their speed on the distance from the center of the galaxy does not follow Newton's law but displays a flat shape (see figure 1 for the galaxy NGC 3198).

Figure 1: The galaxy NGC 3198

This flat shape of the curve is striking. For an explanation we have to conclude, if we follow Newton's law of gravity, that the dark matter causing this behavior has a spatial distribution of 1/r2 in the outer region of the galaxy (where r is the distance to the center of the galaxy). And this observed motion has let physicists to conclude that there is a huge amount of invisible matter. So the physical matter known to us should only account for a small partion - around 1/6 - of the matter in the universe, while the rest is completely unknown up to now. - This portion of 1/6 is however not observed but consequence of a specific cosmological model.

1.2 Gravitational lensing in Abell 2261

Gravitational lensing is also stronger than can be explained by the masses of the lensing objects, which in general are also galaxies.

The huge galaxy cluster "Abell" A2261 has been thoroughly investigated with regard to gravitational lensing [1]. The results not only indicate a stronger gravitational field than the Newtonian prediction, but have also revealed details of the distribution of dark matter. Figure 2 shows that at the far end, which is free of baryonic matter, the distributon of dark matter also follows the slope 1/r2.

Figure 2: The strength of gravity in the vicinity of Abell 2261

1.3 The bullet cluster

In this situation, two galaxies have passed each other. Their distribution after the passage shows the dark matter moving in front of both clusters (figure 3). This is surprising since the assumed heavy dark matter particles should not move faster than normal baryonic matter.



   
Figure 3: The bullet cluster: The blue colour indicates dark matter
 

1.4 Renzo's rule

Renzo's rule refers to the observation that those parts of a galaxy having a reduced luminosity display a reduced gravitational field. This can be detected in orbiting stars whose path is modified when passing along such a region.

This conflicts with the general physical understanding that dark matter should not cause any correlation beween the luminosity and the shape of rotation curves.


1.5 Fast formation building

In the cosmological development of the universe, the growth of clusters forming stars and galaxies has been faster than can be explained by baryonic matter. Again, the conclusion is that there must have been more gravitational than visible matter around to cause this rate of growth.

 


2   Current theories of dark matter

As mentioned above, today's physics predominantly assumes that there is a currently unknown type of particle which interacts with matter only through gravity. There are two problems with this approach

  1. Despite a series of intensive searches during the past decades, not the faintest indication has been found for the existence of such types of particle
  2. Even if such particle existed, there is no detailed explanation as to why the distribution of these particles should be as observed. Particularly the rotation curves at galaxies, which provide a very strong quantiative indication of this spatial distribution, do not seem understandable from this approach.


Apart from this assumption of unknown particles, another theory has been proposed by the name MOND ("Modified Newtonian Dynamics"). It assumes that Newton's law of gravity changes from the 1/r2 rule to a rule 1/r at a certain distance from the gravitational source - equivalently at a certain weak field. This is able to describe the shape of the rotation curve for galaxies having a specific radius given by this theory.

The weakness of this theory is
  1. There are no physical arguments for such a law of gravity
  2. The transition from 1/r2 to 1/r has to be adapted and can only fit for certain specific radii
  3. This approach does not explain the other manifestations of dark matter phenomena.

 


 

3  The photon solution

The assumption that photons are the originators of dark matter phenomena explains all observations. In the special case of the rotation curves it yields even quantitative results.

3.1 Quantitative results for galaxy NGC 3198

We can use the case of stars orbiting a galaxy like NGC 3198 (figure 1)to show that the assumption of photons as the particles of the dark matter has a quantitative proof.

We will check here the hypothesis that every elementary particle contributes to the gravitationl field to the same degree independent of its mass.

For this we make the following assumptions:
  • the proton and the neutron are composed of 3 elementary particles (i.e. quarks) and the electron is 1 elementary particle
  • the photon is taken to be composed of 2 elementary particles ("half-photons"). - Historically, Louis de Broglie once found it appropriate to understand it in this way.
     

Based on this assumptions and on published data, the galaxy NGC 3198 contains within a radius 5 kpc (kiloparsecs)

  • a number of 3×1067 elementary particles. On the other hand
  • a number of 4.4×1067 photons, so 8.5 "half-photons", as can be concluded from its luminosity.
 

These two counts are suitable numbers in terms of the available accuracy for his radius of 5 kpc. Looking at the graphical presentation (figure 1) we see that at the radius of the core of the galaxy both particle types contribute to this degree to the gravitational field, whereas outside of it the photons dominate over the baryonic one in the way that is visible from the flat shape of the rotation curves.

 


An exact numerical evaluation is given in the appendix for the galaxy NGC 3198. This calculation appears to be obvious proof that the assumption of photons as particles of dark matter is supported by the rotation curves.

3.2 Renzo's rule from the perspective of the photonic gravity

In areas of low luminosity, the gravitational field is diminished, as is apparent through the deflection of orbiting stars. This is a direct indication that light is the cause of gravity.

3.3 Fast formation building from the perspective of the photonic gravity

If photons cause a gravitational field, then their existence everywhere explains a higher speed of formation building than expected. And this fact also explains the phenomenon that is otherwise not understood: dark matter contributes considerably to the building of formations, i.e. objects; but it does not become part of these objects.
 

4  Einstein's near-solution

In 1911, Einstein attempted a new approach to gravitation. He published a paper [2] in which he started to draw conclusions from the fact that the speed of light is reduced in a gravitational field. He deduced this reduction by considering the energetic state of a light-like particle moving in a field. That seemed plausible, however it is not correct. It seems that Einstein has noticed that the results he was achieving were unphysical, and therefore ceased pursuing this path and returned to Newton's understanding which related gravity to mass or - with respect to his theory of special relativity - to energy.

It is possible to continue along the path followed initially by Einstein. His error with respect to the dependency of the speed of light on gravity has to be avoided, and our present understanding of particle physics will also be used. We know that the reduction in the sspeed of light c depends on the direction of a light-like particle with respect to the source of gravity. From this, a functional model can be deduced which treats gravity as a universal feature of an elementary particle which does not depend on mass or energy. This results easily in the conclusion that dark matter and photons have similar properties.

This model also achieves all the same results as Einstein's GRT, however much more easily, without resorting to Riemannian geometry and without special assumptions about space and time.

 


5 Conclusion

The analysis of the observations show quite clearly that dark matter is made up of photons. The qualitative as well as the quantiative data do not allow for another explanation.

The price to pay is that we have to modify our theories about gravitation, Newton's as well as Einstein's.

 

6  References

[1] CLASH: Precise new constraints on the mass profile of the galaxy cluster A2261; The Astrophysical Journal 757(1):22 (2012). .

[2] A. Einstein (1911): Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes. [On the Influence of Gravitation on the Propagation of Light]. Annalen der Physik, 340, 898-908.

 

NOTE:

The concept of mass-independent gravitation was first presented at the Spring Conference of the German Physical Society (Deutsche Physikalische Gesellschaft) on 5 March 2005 in Berlin by Albrecht Giese.

Comments are welcome.


(Note: This page is also available as a pdf-file .)

2024-07-04

 



Appendix

Dark matter determined by photonic gravity in galaxy GNC 3198

1) The quantity of solar photons by the solar spectrum


At first the determination of the overall rate of photons emitted by the sun by weighing of the solar energy spectrum:

The energy peak of the solar spectrum is at 0.55 μm. However the averaged energy of the photons is lower because photons of a longer wavelength in the tail of the spectrum have a lower energy. So there must be more photons in that region to deliver the energy of the spectrum at that value. The weighted energy of the photons over the spectrum range was integrated. The average weighted energy is then
Eph_avrg = 1.6 eV = 2.56×10-19 J. - This means an averaged wavelength of 0.790 μm.

Rate of photons from the sun:

The energy emission of the sun is Esun = 3.8×1026 W = 3.8×1010 J/s.

The rate of photons from the sun is then
Rtph,sun = Esun / Eph_avrg = 3.8×1026 [J/s] / 2.56×10-19 [J] = 1.48×1045 s-1.
 


2) The quantity of photons around NGC 3198.

The photon rate from NGC 3198:

The galaxy contains Nsun =5×1010 suns assuming that the sun represents the stars here in the average.
So the rate of photons from the galaxy is: Rtph_galx = Nsun× Rtph_sun = 5×1010 ×1.48×1045 [s[-1 = 7.4×1055 [s-1].

Now the number of photons Nph_galx present around the galaxy is given by the rate of photons Rtph_galx times the residence time Tresi in the volume under consideration,which is a sphere of radius r.
Tresi = r/c = r/(3×108)s.
Nph_galx = Rtph_galx × Tresi = 7.4×1055 ×r /(3* 108).
Nph_galx = r × 2.5 × 1047.

 


3) Gravitational contribution of the photons.

Here we use the assumption that every elementary particle contributes equally to the gravitational field, so also the photons.

We compare this contribution with the classical contribution of an average atom and relate it to the number of elementary particles in the atom. For this determination we use the Cu atom, which is average with respect to the relation of neutrons to protons and electrons; and also because this material was used for the precise determination of the gravitational constant.

Mass of the Cu atom: mCu = 105.2 × 10-27 kg.
The Cu-Atom contains 221 elementary particles (64×3 quarks in the nucleus und 29 electrons in the shell.) So the average mass of an elementary particle is: m = 105.2 × 10-27/221 kg = 0.476 × 10-27 kg.

It is (according to de Broglie) assumed here that the photon consists of 2 elementary particles. One argument is that it has twice the spin of a fermion. So a photons consisting of 2 elementary particles has an "equivalent gravitational mass" of M°ph = 2 × 0.476 × 10-27 kg = 0.952 × 10-27 kg.

 


4) The gravitational field around NGC 3198 caused by the photons.

Next the equivalent mass M°ph_galx of all photons in the given range r around the galaxy:
From Nph_galx = r × 2.5×1047 we get
M°ph_galx = Nph_galx × M°ph = r ×2.5 ×1047×0.952×10-27 kg = r × 2.38×1020 kg.


Now the gravitational acceleration using the gravitational constant G:
agrav = G × M°ph_galx /r2 = 6.67×10-11 × r × 2.38 × 1020 / r2 [m2/s2] = 1.59×1010 / r [m2/s2]

agrav× r = 1.59 × 1010 m2/s2.

The gravitational acceleration agrav must be equal the rotational acceleration arot:

agrav ! = arot

=> arot × r = 1.59×1010 m2/s2.

With arot = v2 / r
=> v2 = r × arot = 1.59×1010 [m2/s2] ,

v = 1.26 × 105 m/s = 126 km/s,

which is shown in the diagram below.

The result deviates from the measurement by -12%.

Please note that the speed does not depend on the radius.

 


Figure A.1:

Rotation curve of the galaxy NGC 3198 for photonic dark matter

 
  This is a pretty perfect match given the accuracy of the galaxy data.