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Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


Plasma Redshift, Dark Matter and Rotational Velocities of Galaxies Ari Brynjolfsson

Applied Radiation Industries, 7 Bridle Path, Wayland, MA 01778, USA

Abstract Great many experiments confirm the newly discovered and theoretically deduced plasmaredshift cross-section and the associated heating in the coronas of the Sun, stars, galaxies, and quasars. The experiments show that the intergalactic plasma has an average electron density Ne = 2 · 10−4 cm−3 with an average per particle temperature of 2.7 · 106 K. These densities and temperatures predict the observed cosmological redshift, the observed magnitude-redshift relation for SN Ia, the observed cosmic microwave background (CMB) and the cosmic X-ray background. There is no need for big-bang, inflation, expansion, accelerated expansion, dark energy, dark matter, nor cosmic time dilation, only basic physics in an infinite, everlasting world. In this paper we show how the dense intergalactic plasma (more than 1200 times denser than that assumed in the big-bang cosmology) leaks into the gravitational depressions and increases the Galactic mass from 9 · 1010 solar masses at 8 kpc to 2 · 1012 at 250 kpc, resulting in flat rotation. The same applies to other galaxies, galaxy clusters, and gravitational lenses.

Keywords: Cosmology, cosmological redshift, plasma redshift, cosmic evolution, dark energy, dark matter, rotational velocities of galaxies, black hole. PACS: 52.25.Os, 52.40.-w, 98.80.Es



Plasma redshift is theoretically deduced from conventional axioms of physics. Great many experiments confirm it. I have failed to find any experiment or observation that contradicts it. The conventional deduction of the Compton scattering assumes that the force on charge e of the electron is D ·e instead of E ·e, where E = D/ε is the electrical field, D the displacement field, ε the dielectric constant. The conventional deduction of the Compton scattering assumes thus that ε = 1. In ordinary laboratory plasma this approximation is permissible, because all the low quantum mechanical energy levels are occupied and do not affect the dielectric constant. But in the sparse hot coronas of stars and in the hot intergalactic plasma this approximation, ε = 1, is not permissible. When we then take the dielectric constant properly into account, we get in sparse hot plasmas in addition to the conventional Compton scattering cross section, two new cross sections, namely the plasmaredshift cross-section, and the Raman-scattering cross-section on plasma frequency. These two new cross sections are fundamental and a key to proper understanding of cosmology; see reference [1]. In thermodynamic equilibrium, the redshifts and the blue shifts, produced by Raman scattering on the plasma frequency cancel each other. The concurrent angular scattering adds some fussiness comparable to that observed. The plasma redshift has much greater consequences. It explains most of the redshifts of the solar Fraunhofer lines, and the cosmological redshift. The energy the photons lose in the plasma redshift is transferred to the plasma. This explains the hot coronas of the Sun, the stars, and the quasars; and it explains the hot plasma of intergalactic space with an average per particle temperature of 2.7 · 106 K and an average density of (Ne )avg ≈ 2 · 10−4 cm−3 . ∗ Corresponding


Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


In the plasma-redshift cosmology, the distances are given by the relation: R = (c/H0 ) · ln(1 + z), where H0 is the Hubble constant; see Eq. (50) in [1]. In the Big-Bang cosmology the distances are approximated by a rather complicated integral, which depends on the Dark-Energy parameter, the Dark-Matter parameter and the Curvature parameter, which are adjusted to fit the experiments. Supernova researchers don’t recognize the reduction in light intensity caused by the Doppler effect on the electrons in the intergalactic plasma. Instead they assume that the cosmic time-dilation reduces the intensity, (although the experiments indicate that there is no cosmic time dilation, when the Malmquist bias is taken properly into account). This false cosmic time dilation accounts for only 50 % of the needed reduction. The remaining about 50 % and the effects of intrinsic redshifts are partially explained as due to hypothetical increase in the expansion rate. In the Big Bang cosmology the surface brightness decreases with the 1/(1 + z)4 , while the plasma redshift cosmology predicts decrease with 1/(1 + z)3 consistent with observations. The big-bang cosmologists usually set the proton density equal to Np ≈ ρ/mp = 1.124 · 10−5 Ωh2 −3 cm . For a baryonic density of Ω = 0.04 and h = H0 /100 = 0.60, we get Np ≈ 1.62 · 10−7 cm−3 . In plasma redshift cosmology, the intergalactic medium is thus about 1200 times denser than that surmised in the Big-Bang cosmology. In plasma redshift cosmology, the temperatures and densities of the intergalactic plasma are not uniform but vary very significantly. In plasma-redshift cosmology, we have large very hot ”bubbles” of hot low-density plasma surrounded by colder higher density ”web” of plasma at the surface of the hot ”bubbles”. The galaxies are usually a part of the colder plasma ”web”. In plasma redshift cosmology some of this dense plasma leaks into the gravitational depression created by the galaxies and the galaxy clusters, as we explain in sections 3 to 6. Plasma redshift cosmology, which explains the cosmological redshift, the cosmic microwave background, the X-ray background and much more (without the Big Bang, Inflation, Dark Energy, Dark Matter, Black Holes, or Cosmic Time Dilation), is thus radically different from the Big-Bang cosmology.


Brief Overview of Plasma-Redshift Cosmology

For helping the reader to understand the high-density coronas that supplant the need for Dark Matter, we will briefly review the plasma-redshift cosmology.


Plasma-redshift, cut-off wavelength, CMB, and H0

Plasma redshift z is deduced from the corrected dynamical equations and is given by: (see [1]) ln (1 + z) = 3.326 · 10


ZR Ne dx +

γi − γ0 , ξω



where the first term on the right side is the electron density (Ne ) integral from the source to the observer. The second term, the line-width term, is insignificant in cosmological redshifts, but important for small redshifts in the Sun and the stars. It is especially important when the pressure in the line forming elements is high; such as in the dwarf stars and black hole candidates (BHCs). Eq. (1) is valid only when the following plasma-redshift cut-off equation is valid:   T B2 √ λ0.5 ≤ 3.185 · 10−6 1 + 1.3 · 105 cm, (2) Ne Ne All units are in cgs units; that is, the magnetic field B in Gauss, electron density Ne in cm−3 , and the temperature in units of K. In the Sun the cut-off wavelength, λ0.5 ≈ 5 · 10−5 cm, is at the densities, temperatures, and magnetic fields found in the middle of the transition zone to the solar corona. Table 1 of [1] gives more exact values for the predicted cut-off. For λ ≤ λ0.5 , the plasma-redshift cross-section is independent of wavelength λ. This accounts for the beautiful blackbody spectrum of the CMB with blackbody temperature TCM B given by −2 4 aTCM , B = 3kTe N dyne cm


Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


where a = 7.566 · 10−15 dyne cm−2 K−4 , N ≈ NH + NHe + Ne ≈ 1.917Ne cm−3 , and Te = 2.7 · 106 , is the average temperature of the electrons; see Appendix C1.7 0f [1]. In spite of the large temperature and density variations, the pressure p/k ∝ Te N is nearly constant, and the temperature, TCM B , given by Eq. (3) is well defined and about constant. This explains also the small fluctuations in TCM B . In intergalactic space the densities are usually so low and the temperatures so high that the 21.1 cm photons are fully redshifted. However, in the coldest regions of intergalactic space, and in the coronas of stars, galaxies, and quasars, the cut-off wavelength, λ0.5 , is less than the 21.1 cm. This line is then redshifted less than the optical lines. This is consistent with observations. In quasars, the redshifts of 21.1 cm lines are usually not even recognized as coming from the quasars, because most of the redshifts of optical lines from quasars are intrinsic plasma redshifts. These smaller observed redshifts of the 21.1 cm line are an independent confirmation of the plasma redshift theory. The Hubble constant is in plasma-redshift cosmology given by; see Eq. (49) of [1] H0 = 3.076 · 105 · (Ne )avg km s−1 Mpc−1 ,


where the average electron density is (Ne )avg in cm−3 . The coronas of the emitting galaxy and the Milky Way increase (Ne )avg and increase thereby the value of H0 . In the big-bang cosmology all increases in value of H0 at small z indicate that the expansion of the universe is accelerating.


Heating of the coronas of galaxies

Plasma-redshift heating dominates the heating of the solar corona, and is the main cause for the steep temperature increase in the transition zone to the corona; see sections 5.1 and 5.2 in [1]. The plasma-redshift heating increases the diamagnetic moments in the plasma and thereby reduces and destroys the magnetic field lines. The reconnection of the field lines is a consequence of this destruction of the field by the heating, and not the cause of the heating and the destruction of the field, as often claimed; see Appendix B of [1]. Before the discovery of the plasma redshift heating, the steep increase of the temperature in the transition zone, the high temperature (2.2 million K) corona, and the destruction (or the reconnection) of the magnetic field lines could not be explained properly. The observed temperatures at each height in the solar corona match those predicted by the plasma redshift heating. This is still another strong confirmation of the plasma-redshift theory. The evaluation of the observed heating of the Milky Way’s corona showed that the plasmaredshift heating of direct light from the Galaxy was not enough to heat the dense corona observed by Pettini et al. [2]. For understanding the heating of the Galactic corona, it is necessary to take into account, not only the heating by the plasma redshift of light emitted by our Milky Way Galaxy, but also the heating by the intense X-rays from the intergalactic plasma; see section 5.7 in [1]. Only a small fraction of the photon energy emitted by our Galaxy is directly absorbed by our Galactic corona. The photon energy that escapes the galaxy is absorbed in the plasma-redshift in the intergalactic plasma. On the average, most of this plasma-redshift heating forms X-rays, which return the energy back to the galaxies. The X-rays are mainly absorbed in low temperature parts of the coronal plasma. Even after all this absorption, the coronal temperatures are relatively low. Plasma redshift may, however, heat some of the filaments to million K temperatures, while outside the filaments the average temperatures are lower and densities higher. The prevailing low temperatures and high densities in the coronas of galaxies partially prevent plasma redshift of the λ = 21.1 cm wavelength light, because 21.1 cm exceeds the cut-off wavelength λ0.5 given by Eq. (3). Optical lines, on the other hand, are usually both plasma redshifted and Doppler shifted in the Galactic corona. It is then usually more difficult to interpret the shifts of these lines. Often used method, when determining the rotational velocities is to fold (reflect) these measurements around the center point of the galaxy. This complication is the reason that the researchers, when measuring the rotational velocities, usually prefer to use the 21.1 cm line.

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies



Interpretation of observed redshifts

Big-bang cosmologists usually deny the intrinsic redshifts, such as the plasma redshifts. The cosmological redshifts and even redshifts of quasars are assumed to be due to Doppler redshifts. These misinterpretations in turn lead to the Big Bang, the Cosmic Inflation, Dark Energy, and Dark Matter. The plasma redshifts of the different lines of a quasar vary, because the depth of line formation varies. The lines formed in the photosphere below the cut-off zone have the largest redshifts. Lines with high ionization potentials, which are formed at the high temperatures above the cut-off zone, such as, O III 5007, Ne V 3426, Fe X 6375, and Fe XIV 5303, are observed to have smaller average redshifts in accordance with predictions of the plasma-redshift theory. These high-excitation lines are often broadened, because they are formed over extended range above the cut-off zone, see Eq. (2) above. The broad absorption lines of (BAL) quasars are thus formed above the cut-off zone. Because they are formed slightly higher, they have smaller average redshifts than the lines formed deeper or below the plasma-redshift cut-off. In some cases the center-limb effect may also broaden the lines, especially those with small pressure shifts. All these observations, which have defied reasonable explanations, are consistent with predictions of the plasma-redshift theory. Usually, the high-redshift quasars do not have any 21.1 cm line, because the plasma-redshift cutoff in the corona, prevents their plasma redshift. This line is redshifted in the intergalactic space, where the densities are lower and the temperatures higher. The redshifts of the 21.1 cm line are then more indicative of the quasars’ actual distances. Usually, however, the redshift of the 21.1 cm line is much lower than that of the optical lines, and is not even recognized as coming from a quasar, because its redshift is much smaller compared with that of the optical lines. Most intrinsic redshifts of stars and galaxies are also misinterpreted by big-bang cosmologists as entirely due to Doppler shifts and gravitational redshifts. O and B stars with relatively large corona usually have relatively large redshifts. Star-bust galaxies with huge corona (and therefore large intrinsic redshifts) are surmised to be relatively distant objects. As mentioned at the end of subsection 2.1, the accelerated expansion is partially due failure to recognize intrinsic redshifts. A supernova, such as SN 1987A, will initially have white light as it expands rapidly. Lines from supernovas should usually be blue shifted due to the expansion of the light emitting layers. However, if plasma redshift causes absorption between the star and the observer, the absorption lines are redshifted independent of the velocity of the white light emission background. Pettini et al. [2] observed a redshifted broad absorption line Fe X 6374.51 ˚ A in the spectra from SN 1987A in the Large Magellanic Cloud (LMC). It is reasonable, as they did, to interpret this as caused by an absorption in Galactic corona. The redshift stretched from about 210 to 365 km s−1 . Knowing the plasma redshift, this explanation becomes even more reasonable.


Weightlessness of photons

Plasma redshift and Raman scattering on the plasma frequency are an undeniable consequence of the conventional axioms of physics. No new physical assumptions have been made. However, the weightlessness of photon in a local system of reference is not a consequence of the conventional axioms of physics. It contradicts the equivalence principle of gravitational and inertial mass in conventional physics. But it is an experimental fact. I discovered this fact when I compared the predicted plasma redshift with the great many measured redshift of the solar photons. I found that the plasma redshift fully and systematically explained the observed redshift of the solar Fraunhofer lines, without any gravitational redshift. When confronted with this surprising contradiction to conventional theory, it became clear to me that we have been wrong all along about the photons weight. Einstein is right that the gravitational time dilation results in gravitational redshift of all frequencies of atoms and photons in the Sun, as seen by a distant observer on Earth. This has been proven in many experiments. But Einstein made an additional assumption. He contended that the photons would retain this gravitationally redshifted frequency as they moved from the Sun to the Earth. Reading Einstein’s original articles, it became clear to me that Einstein was thinking in terms of classical physics. He made arguments like: ”Equally many waves must arrive on Earth as leave the Sun.” No such a statement follows

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


when using quantum mechanics. Without any gravitational redshift, the solar redshifts measured on Earth agree with the predictions of the plasma redshift theory. Therefore, the gravitational redshifts of photons in the Sun must be reversed when the photons move to the Earth. The frequencies of photons behave just like the frequencies of atoms. When the atoms move from the Sun to the Earth, their gravitationally redshifted frequencies in the Sun are reversed, and the solar atoms when they arrive on Earth, will have the same frequencies as the atoms that have been on Earth all along. The comparison of the observed and predicted plasma redshift indicated that the photons frequencies behave the same way as the frequencies of atoms. I then analyzed the many experiments that have been assumed to prove photons’ weights. To my surprise, I discovered then that all the experiments had been incorrectly designed and interpreted. No conclusion about the photon’s weight could be derived from any of the experiments, because it was impossible for the photons to change their frequencies as they moved to different elevation. For example, in the experiments by Pound, Rebka, and Snider, [3] and [4], it takes the photons 22.5/(3 · 108 ) s = 75 nanoseconds to move from the basement to the top floor, while the uncertainty principle in quantum mechanics requires a minimum time of 19 000 nanoseconds for the photons to change their frequency. The atomic nuclei (the clocks) at the basement and on the top floor had plenty of time to change their frequencies; see [5]. None of the experiments therefore contradict the fact that, given the time, the photons reverse their gravitational redshift when moving from the Sun to the Earth. This applies to short wavelength photons. The long-wavelength photons (such as microwaves) when emitted from the position of the Earth, however, have too long a wavelength to be able to change their frequencies. Photons with λ = 13 cm, when traveling outwards from the position of Earth, such as the photons used in Pioneer 10 and 11 experiments, may need about 10 AU to reverse their small redshift, about z = 10−6 . However, there is a major difference between frequencies of atoms and photons. We must lift the atoms from the Sun to the Earth. The energy transferred to the atoms equals the blue shift of their frequencies. But we do not lift the photons. The gravitational field must lift the photons; or it must repel the photons as they move from the Sun to the Earth, as seen by an observer on Earth. Similarly, all the many well-executed experiments do not tell us anything about the constancy of a solar photon’s frequency, when it moves from the Sun to the Earth. The uncertainty principle in quantum mechanics was not taken properly into account in the design and interpretation of the experiments. The fact that the photons are weightless in the local system of reference or repelled in a distance system of reference together with plasma-redshift cross-section leads to radically different (and beautiful) cosmology. It leads to eternal renewal of old star matter to primordial matter in objects that are usually thought to be black holes or super-massive black holes. We designate them as black hole candidates (BHC) and (SMBHC), because in fact there are no BHs and no SMBHs. (There are those who contend that the formation of a black hole follows from theory of general relativity (TGR). But that is nonsense. TGR becomes invalid as we approach the classical singularity and can’t predict anything in or beyond the singularity.) The weightlessness of photons also eliminates the need for Einstein’s Λ, because in distant system of reference the photons are repelled. The repulsive Λ is replaced by repulsive photons. The more matter is gravitationally attracted and concentrates in BHCs, the more matter is transformed into photons, which are repelled. This is all self regulating. The big-bang cosmologists, on the other hand, had to balance not an elephant but the whole Universe on the tip of a needle. This also explains why we can have so high densities in the Universe. We should realize that at the densities of intergalactic space, the plasma-redshift cross section is many orders of magnitude (often about million times) larger than the free-free emission and absorption usually surmised. This all changes the explanations of a long series of phenomena, including the CMB and CXB. For this reason the big-bang cosmologists, who do not know about plasma redshift, often have difficulties in believing in the new cosmology. In reference [5], I analyze the different experiments. I show that this change in the equivalence principle does not destroy the ”Theory of General Relativity” (TGR), but makes it more beautiful. The inclusion of quantum mechanical effects modifies the theory radically. I am inclined to call it the ”Modified Theory of General Relativity” (MTGR).

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies



Bubble Universe

The temperature of the intergalactic plasma varies significantly. This variation is caused by imbalance between the plasma-redshift heating, which is proportional to Ne , and the X-ray cooling, which is usually proportional to Ne2 . In a low-density volume (a bubble), the heating dominates, and expands the ”bubble”, which decreases the density further. On the other hand, the colder high-density volumes at the surface of the bubble shrink, because the cooling dominates the heating. This imbalance increases until other processes take over. In the hot areas the heat conduction κ ≈ 10−6 T 5/2


increases steeply with the temperature and moves the heat from the center of the ”bubble” to the colder periphery. The X-rays will be absorbed mainly in the cold parts. We end up with huge ”bubbles” (often with diameters on the order of Mpc) filled with hot (about 30 million K) plasma surrounded by colder plasma (about 0.3 million K) at the intersections between the ”bubbles”. The galaxies are formed mainly in the densest regions containing the colder plasma. These structures of hot ”bubbles” surrounded by a web of colder plasma match the observations. Without the plasma redshift these structures in space could not be understood. The heating imbalances created by the plasma redshift are often more powerful than the gravitational forces in creating galaxies. The plasma-redshift imbalances also create the solar flares, which (aided by magnetic fields) are initiated in and below the solar chromosphere; see section 5.5 in [1].


Effect of magnetic and electrical forces

The magnetic repulsion of the diamagnetic moments created by ions and electrons in a divergent magnetic field at a point P due to their velocity vP ⊥ perpendicular to the magnetic field is often significant. Eq. (B10) in Appendix B2 of [1] shows that this magnetic repulsion force is given by FP =

n mvP2 ⊥ , 2 RP


where n is the measure of the divergence of the field at Rp . For example, n = 2 in case of a radial magnetic field, and n = 3 in case of a magnetic dipole field. FP is the main force driving the solar wind. The cosmological magnetic fields are created almost exclusively by the imbalance between diamagnetic moments and the fields. The energy density of the magnetic field is often on the order of the kinetic energy density of the particles, (see section 5.7.2 and Appendix B2 of [1]. Plasma redshift transfers some of the photon energy to the electrons, which in sparse plasma get very hot, because the energy transfers from the hot electrons to the positive ions is slow in a sparse plasma. The hot electrons diffuse then outwards and create an electrical field that pulls the positive particles outwards. Together with the Eq. (6), the plasma redshift heating pushes the ions (the solar wind) outwards from the Sun. These forces are in play in the coronas of stars and galaxies.


Densities in the Corona of the Milky Way Galaxy

In plasma-redshift cosmology, the baryonic density, (Ne )avg ≈ 2 · 10−4 cm−3 , in intergalactic space is about 1000 times higher than the density in Big-Bang cosmology. The average temperature is Tavg ≈ 2.7 · 106 K. These densities and temperatures result in the observed cosmic X-ray background (CXB) and the observed CMB; see Appendix C of [1]. The Universe, which renews itself in the black hole candidates (BHCs) and supermassive black hole candidates (SMBHCs) is quasi static and ever lasting. The coronal and interstellar densities are then also much greater than those predicted by the Big-Bang cosmology, because the plasma from intergalactic space will leak into the depression of low gravitational potential in and around the galaxies and fill them with plasma. We will in the following discuss different estimates of the densities.

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies



Conventional density estimates

Lyman Spitzer Jr. [6] was one of the first to suggest that our Milky Way had a hot corona. Lines from highly ionized and excited states of atoms indicated to him that the densities in the galactic corona were significant. Most of such lines are formed in the hot filaments with relatively low density. These hot filaments are interspersed with colder filaments, which cause significant dilution. Spitzer observed also extended coronas around hot stars. These coronas extended far beyond the Str¨omgren radii of the stars. Not knowing about plasma redshift, he could not find any good way to heat the coronal plasma. He suggested that the hot corona from supernovas drifted into the Galactic corona and supplied the needed energy. He did not know about the hot and dense intergalactic plasma. His density estimates for the Galactic corona were low by more than a factor of 20. Using the bright SN 1987A in the LMC, Pettini et al. [2] obtained a good spectrum; see subsection 2.2 above. They observed an absorption trough of Fe X 6374.51 line, which indicated a column density N (H)H ≥ 3.2 · 1021 cm−2 . When averaged over a distance of about 50 kpc from the solar system to the Large Magellanic Cloud (LMC), the absorption of the Fe X 6374.51 ˚ A line indicates an average density over 50 kpc of (N (H)avg50 ≥ 0.0242 cm−3 . Plasma-redshift heating of the corona by Galactic light is not adequate; see section 5.7 of [1]. It is essential to take the intense X-ray heating from intergalactic space into account. The X-rays from the intergalactic plasma with a large spread in the temperature, usually between 0.3 and 30 million K, and an average temperature Tavg = 2.7 · 106 K, corresponding to 1.5 · kT ≈ 349 eV, are effective in stripping iron atoms (through Auger effects and direct photoelectric effects) of their electrons to form Fe X (≈ 235 eV) in the corona and its transition zone. If we with Pettini et al. [2] assume that the ionization is collision controlled, the plasma temperature will be on the order of 106 K. However, the ionization is largely controlled by X-rays. The coronal plasma temperature could then be much lower. As shown by Lyndon-Bell [7] and Bertschinger [8], the densities should decrease roughly as ρ ∝ 1/R2 , where R is the distance from the Galactic center. This follows from the assumption that mass is falling down and diffusing through the galaxy at a nearly uniform speed. This applies also in a quasi-static universe when about equal mass is streaming outwards. This can be modified at small and large distances from the Galactic center as suggested, for example, by Navarro, Frenk and White [9]; see also: Navarro et al. [10]. Low in the corona and in the transition zone to the Galactic corona, the temperatures are relatively low and the plasma may not be fully ionized. Higher in the corona the temperatures will increase slightly, but closer to the LMC, the temperatures may fall slightly.


Density from the Fe X-line measurements

We assume that the number density of H atoms towards SN 1987A in the LMC decreases roughly as NH ≈ a/R2 for distances 15 ≤ R ≤ 45 kpc from the center. From the measurement of Pettini et al. [2] we get then when integrating from R1 to R2 kpc that ZR2 N (H)avg · 50 kpc ≈ 0.0242 · 50 kpc = 1.21 kpc ≤

a · dr, r2


a 1.21 kpc · (R1 R2 ) where N (H) = 2 cm−3 and a ≥ , r R2 − R1


where the average number density 0.0242 cm−3 over a distance of 50 kpc is obtained from the measurements of Pettini et al. [2], and where r and R are the Galactocentric distances. The hot corona with the Fe X ions may stretch, not over 50 kpc, but from about R1 = 15 kpc to about R2 = 40 kpc, or it may stretch from R1 = 15 kpc to about R2 = 45 kpc, while outside these ranges the Fe X fractions are significantly lower. In these examples, we have that (N (H))15−40 kpc =

a 1.2 · (15 · 40) 29 = = 2 cm−3 R2 (40 − 15) · R2 R



Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies (N (H))15−45 kpc =

a 1.2 · (15 · 45) 27.2 = = 2 cm−3 , respectively R2 (45 − 15) · R2 R

8 .

In the fully ionized plasma, the total particle density is N ≈ Ne + NHe + NH = (1.2 + 0.1 + 1) NH = 2.3 · NH . When the high temperature regions stretch from R1 = 15 kpc to R2 = 40 kpc and from R1 = 15 kpc to R2 = 45 kpc, we get then by extrapolation that at R = 8 kpc N = 29 · 2.3/64 = 1.0 cm−3 and 27.2 · (2.3)/64 = 0.98 cm−3 , respectively. At a position of about 8 kpc from the Galactic center, the temperatures are usually lower than at distances R1 ≥ 15 kpc. The actual density at 8 kpc could then be much greater. The temperature is unstable, because when X-rays (mostly from intergalactic space) and ultraviolet photons have supplied most of the ionization energy, the plasma-redshift heating can easily increase rather abruptly the temperature to about 106 K (confer the steep transition zone to the solar corona). This in turn causes significant density variations. These predictions help us explain the high and low temperature regions often observed beyond the heliopause (the point where the interstellar pressure equals the solar wind pressure). Only plasma redshift gives a simple physical explanation of these observations.


Density from the Boltzmann distribution

A different approach is obtained when we consider the density as being determined by Boltzmann distribution. Plasma-redshift cosmology shows that the average density in intergalactic space is about Ne ≈ 2·10−4 cm−3 , which is about 1000 times the baryonic density in the Big-Bang cosmology. The plasma-redshift cosmology leads then to much greater densities in the Galactic corona and in the intracluster medium than the densities usually deduced in the Big-Bang cosmology. At a Galactocentric distance of R = 8 kpc, the gravitational potential of the proton mass mp is Egrpot = G MR mp /R = 8.0978 · 10−10 erg, or about 505.4 eV, and vp ≈ 220 km s−1 −1

where G = 6.673·10−8 cm3 g s−2 is Newton’s gravitational constant, MR = 9·1010 ·M is the mass inside R ≈ 8 kpc, and M = 1.99 · 1033 g is the solar mass. The gravitational potential of higher atomic numbers is still greater. The concentration of helium and of higher atomic numbers must therefore increase towards the center. However, several mixing processes inhibit this separation. If the Galaxy did not rotate and was free of electrical and magnetic fields, the inward gravitational flow of matter would be isotropic. However, accumulation of the stars and dust in the plane of the galaxy is a fact. This distribution is a consequence of the galactic rotation. The rotation reduces the inward gravitational flow component perpendicular to the axis. The diamagnetic moments of positively and negatively charged particles are both pushed outwards, when the field decreases outwards; see Eq. (B10) in Appendix B2 of [1]. Also, the electron temperature is slightly higher than the temperature of the positive nuclei. The electrons will therefore move outwards ahead of the positive ions. Both the magnetic and the electrical fields will therefore slow the gravitational influx and speed up the outward flux of charged baryons. In the first approximation, we assume an average temperature in the Galactic corona is about TG = 9 · 105 K, corresponding to kTG = 1.24 · 10−10 erg, or about 77.5 eV. We get then that the gravitational potential difference alone creates a Boltzmann density factor of exp(Egrpot /kTG ) = exp(505.4/77.5) = exp 6.52 = 680. When the temperature in intergalactic space decreases from TIG ≈ 2.7·106 K to TG ≈ 0.9·105 K close to the top of the corona of the Galaxy, the electron density increases by a factor of about 3(=2.7/0.9), or from Ne ≈ 2 · 10−4 cm−3 to Ne ≈ 6 · 10−4 cm−3 . The density of the corona of the Galaxy at 8 kpc from the center is then Ne ≈ 680 · 0.0006 = 0.41. When we then equate NH ≈ 0.41 cm−3 , we get when multiplying it by 82 = 64 that a ≈ 0.41 · 64 = 26.2 or that a 26.2 NH = 2 ≈ 2 cm−3 . (9) R R This crude density estimate is independent, but comparable to those in Eq. (8) that are derived from the experiments of Pettini et al. [2]. The coronal temperatures vary greatly. The value of TG = 9·105 K takes into account that high temperatures in this case have greater weight. We also have inputs of both X-ray heating and the plasma redshift heating. The average temperature of TG = 9.0 · 105 K is therefore only a crude estimate and makes the uncertainty in the determination of a in Eq. (9)

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


large. A better determination of a requires better knowledge of the distribution of the heat inputs and preferably direct measurements, such as those by Pettini et al. (1989).


Density from the pressure in the heliopause

The pressure in the Galaxy at the location of our solar system is usually estimated by extrapolating from solar wind pressure and heliospheric pressure to the interstellar pressure at the heliopause, which is usually estimated to be between 110 and 230 AU. At the position of Earth, the protonnumber density is about Np ≈ 6 cm−3 and the outwards directed proton velocity is v ≈ 5 · 107 cm s−1 . These numbers vary with time and position. For example, the Ulysses experiments show that the velocity is higher outside the equatorial regions. Usually, it is about v ≈ 7.5 · 107 cm s−1 , while the proton-number density may be slightly lower than 6. Disregarding the electrons and the thermal heat, but including 10 % helium, we get that the outwards directed kinetic energy density in erg cm−3 at 1 AU is about Ekin 1 AU = (1/2)ρv 2 ≈ (1/2) · (6 · 1.4 · 1.67 · 10−24 ) · (5 · 107 )2 = 1.76 · 10−8 erg cm−3 .


The outward directed pressure is then p = 2ρ · v 2 = 7.04 · 10−8 dyne cm−2 . Close to the heliopause at about 150 AU the pressure is smaller. Disregarding the influx from interstellar space, it is about 1/R2 = 1/1502 of that at 1 AU. We get then that the pressure at the heliopause at R = 150 AU is about: php = 7.04 · 10−8 /1502 = 3.1 · 10−12 dyne cm−2 . (11) For R ≥ 1 AU, the X-ray cooling and the plasma-redshift heating are small. The pressure in Eq. (12) may then be equated with the thermal pressure p = kT N. We get then at 150 AU that the p/k = (T N )150 AU ≈ 3.1 · 10−12 /k = 22 700 K cm−3 .


In the literature the corresponding values p/k around the solar system are often in this range, but usually slightly smaller. For example, the extreme UV and X-ray emission measurements by Bowyer et al. (1995) and Bergh¨ ofer et al. (1998), result in T N ≈ 16 500 K cm−3 . From Eq. (8), we get that N = 2.3NH = 2.3 · 29/R2 ≈ 66.7/R2 cm−3 . For R = 8 kpc, we have then that N = 66.7/64 = 1.04 cm−3 . From Eq. (12), we derive then that the corresponding temperature at 8 kpc from the galactic center is about T ≈ 22 700/1.04 = 22 000 K. This indicates that high-energy X-rays from intergalactic space producing Fe X through Auger processes are important, and that the Fe X is usually formed high in the Galactic corona. The electron density estimates from the observations of Pettini et al. are then higher than if we assumed that the line was formed over the entire 50 kpc range. The 21 cm line appears rather strong from the region around the Sun. This indicates that the temperature is often much lower, maybe 2200 K. At 8 kpc, the density would then be more than about 10 times higher. In the plasma-redshift heated bubbles, the temperature could be much higher.


Galactic Mass

The mass of the Galaxy consists of: I stars, black hole candidates (BHC), planets, interstellar dust and grains; and of II the coronal and interstellar plasma and of neutral clouds. The solar system with mass m rotates with velocity v around the Galactic center. We assume that the centrifugal force is equal to the gravitational attraction, or m · v 2 /R = m · GMR /R2 , where MR is the Galactic Mass inside the Galactocentric distance R. From this, we derive that at 8 kpc p the rotational velocity for the solar system is v8 = GM8 /R = 2.2 · 107 cm s−1 = 220 km s−1 , corresponding to a mass M8 = 9 · 1010 · M , where the solar mass M = 1.99 · 1033 g.

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


The rotation decreases the material flow perpendicular to the rotational axis. The main fall of mass into the galaxy is therefore along lines perpendicular to the plane of the galaxy. The gravitational fall increases the temperature of the plasma, which is therefore transparent, but contains more mass than is usually assumed. The falling mass collects in the plane of the galaxy. In the Big-Bang cosmology, the total Galactic mass inside R has usually been assumed to consist mainly of masses listed under item I, while the interstellar masses identified under item II above have been estimated to be much smaller. In Big-Bang cosmology, these low estimates of item II masses follow from the extremely low mass densities and low temperatures in intergalactic space. In plasma-redshift cosmology, on the other hand, the plasma densities in intergalactic space are more than 1000 times higher, or an average Ne ≈ 2 · 10−4 cm−3 , and the average temperature about 2.7 · 106 K, which correspond to p/k ≈ (2.3/1.2) · (2 · 10−4 ) · (2.7 · 106 ) = 1000 cm−3 K. The intergalactic plasma leaks into the gravitational depression formed by the Galaxies and causes high densities in the corona and in the interstellar space. This coronal plasma which is denser than that usually assumed makes both the gravitational potential depression and the plasma it contains more isotropic than that usually surmised in the Big-Bang cosmology. If the proton’s number density, Np = a/R2 , at R is given by Eqs. (8), and if we have 10 % helium, then the mass density is about ρ/R2 = 1.4 · 1.67 · 10−24 · a/R2 . Eqs. (8) correspond then to ρ29 /R2 = 29 · 1.4 · 1.6726 · 10−24 = 6.74 · 10−23 /R2

g cm−5


where R is in kpc. Assuming isotropic corona, we get from Eq. (8) that the mass, M , inside R1 is M29 (R1 ) = 9 · 10


Z · M + 8


M · 6.74 · 10−23 · (3.086 · 1021 )3 · 4πR2 · dR. 1.99 · 1033 · R2


and when integrating, we get M29 (R1 ) = 9 · 1010 · M + 1.25 · 1010 · (R1 − 8) · M


In this crude approximation the masses M29 (R1 ) increase linearly outward with R1 . Table 1. The masses M29 and the rotational velocities v29 versus Galactocentric distance R R1 → 8 kpc 25 kpc 50 kpc 100 kpc 200 kpc M29 (R1 ) 9 · 1010 · M 30.3 · 1010 · M 61.5 · 1010 · M 124 · 1010 · M 249 · 1010 · M

v29 km/s 220 228 230 231 232 Table 1 shows that the masses of the interstellar plasma and interstellar clouds are likely to account for the mass needed to make the rotational velocity curves flat. This is reasonable when we realize that in plasma-redshift cosmology the intergalactic plasma is about 1000 times denser and the temperature much higher than that in Big-Bang cosmology. In this evaluation, we have not considered many details, such as the spiral structures of the Galaxy, and the density perturbations created by structures, such as, the Small and Large Magellanic Clouds (SMC) and (LMC). We also have not made detailed analyses of the stellar (item I) masses. Nor have we taken into account that the coronal temperature is likely to increase outwards and decrease thereby the mass density. An outward increasing temperature would reduce the outward increase in mass. When R1 approaches the hot plasma ”bubble” in intergalactic space, the temperature will increase rather abruptly and mark a cut-off for increase in mass with R1 . For R1 less or equal to about 5 kpc the gravitational heating and other forms of heating (including plasmaredshift) will reduce the density of the interstellar matter, and make the mass of stars, BHCs and SMBHCs more dominant. We have not included effects of magnetic and electrical fields. Magnetic fields are created by the diamagnetic moments. The diamagnetic moments (which strangely are usually disregarded by astrophysicists) are most important. The diamagnetic moments coalesce to form huge domains, see Appendix B and section 5.3.3 in [1], which account for the magnetic field of the Earth, Sun, stars,

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


black hole candidates, and of intergalactic space. The energy density in the magnetic field is usually on the order of the kinetic energy density of the charged particles in the plasma. In addition to the usual electrical fields between charged particles, we have that the plasmaredshift heating transfers energy from the photons to the plasma electrons, which then transfer that energy to the protons. This last mentioned energy transfer is slow and causes the electrons to be significantly hotter than the positively charged particles. The electrons diffuse then outwards and create a collective electrical field over huge distances, which then drag the positive ions outwards and thus counteract the gravitational field. These many factors require more detailed research and analysis. In spite of the many details not considered, there is no well-founded reason to introduce Dark Matter. With our limited knowledge, the coronal plasma appears to able to account for the flat rotational curves. A similar density distribution is expected in other galaxies. In galaxy clusters the coronal density will increase the mass of the clusters significantly. We have also that the high densities of the intracluster plasma increase the plasma redshifts of the galaxies in the back of the clusters. This increases the redshift differences between the galaxies in the front and the back of the clusters. For example, the Virgo cluster with about 1500 member galaxies within a radius of about 2.2 Mpc from its center may easily have an average intracluster hot plasma density of 10 times the average intergalactic density, or Ne ≈ 2 · 10−3 cm−3 . The plasma redshift over a distance of 2.2 Mpc is then about z ≈ 3.326 · 10−25 · 2 · 10−3 · 2.2 · 3.08 · 102 4 = 0.045. This redshift corresponds radial velocity of about vr = 1350 km s−1 , which is about that observed. The increased plasma densities and temperatures also predict increased X-ray emission consistent with that observed. In accordance with Eq. (3), the CMB in the direction of Virgo cluster should also increase slightly, as observed.


Conclusion: Plasma-redshift Cosmology Has No Need for Dark Matter

Plasma-redshift cosmology makes it clear that intergalactic space is filled with relatively hot (Tavg = 2.7 · 106 K) and dense ((Ne )avg ≈ 2 · 10−4 cm−3 ) plasma, corresponding to p/k ≈ 1000 cm−3 . The heating by the plasma redshift (that is, the transfer of a fraction of the photon energy to the plasma) is a first order process in the density, Ne , while the cooling by the X-ray emission (and many other cooling processes) is a second (or higher) order processes. This leads to temperature instabilities, see subsection 2.5 above, with hot ”bubbles” that may reach more than 30 · 106 K surrounded by colder plasma with temperature that decrease steeply to T < 0.3 · 106 K. The galaxies and galaxy clusters are formed in these colder (and denser) regions at the surface of the hot ”bubbles”. The colder plasma surrounding the galaxies invariably falls into the gravitational depression formed by the galaxies. This in turn increases the depth of the gravitational potentials until the Boltzmann thermal distribution causes equally many particles to move outwards as move inwards. We have shown that in case of the Milky Way the coronal densities derived from the measurements of Pettini et al. [2] and the estimates of the pressure in the heliopause confirm the densities needed to explain the observed rotational velocities in the Milky Way. The general arguments apply not only to the Milky Way, but to all galaxies, galaxy clusters and gravitational lenses. This increases significantly (as Table 1 shows) the mass of the galaxies and the galaxy clusters. Some of the lensing effect may be caused by the dielectric constant in the plasma. The higher plasma densities in and around the galaxies increase also the intrinsic plasma redshifts in accordance with Eq. (1) provided Eq. (2) is fulfilled, especially within the galaxy clusters. This can be checked experimentally. We will then find that the galaxies in the back of the clusters have relatively large plasma-redshifts. I have not checked this systematically; but the observations reported in Figure 8 of [13] shows that the members of Centaurus (close to the Great Attractor) have larger redshifts than other galaxies, when plotted against the Tully-Fisher distances. This is consistent with greater plasma density in this region, which in turn is consistent with the observed slightly higher CMB intensity in this direction. In case of the CMB, this is a small effect, because the increased absorption and emission partially compensate each other. Also, the absorption and emission lengths of the microwave radiation are very large or about 5000 Mpc. We should be

Ari Brynjolfsson: Plasma Redshift, Dark Matter, and Rotational Velocities of Galaxies


able to confirm these predictions by measuring the distances from the Cepheid variables, and by measuring the distance from the redshifts. We find thus that in plasma-redshift cosmology there appears to be no need or reason for introduction of Dark Matter.

References [1] Brynjolfsson, A.; Redshift of photons penetrating a hot plasma; arXiv:astro-ph/0401420 v3 [2] Pettini, M., Stathakis, R., Dâ&#x20AC;&#x2122;Odorico, S., Molaro, P., Vladilo, G., Million degree gas in the Galactic Halo and the Large Magellanic Cloud II. The line of sight to supernova 1987A ApJ. 340 (1989) 256-264 [3] Pound, R. V., Rebka, G. A. Jr. Phys. Rev. Lett. 3 (1959) 439; ibd 3 (1959) 554; ibd. 4 (1960) 337 [4] Pound, R. V., Snider, J. L. Phys. Rev. Lett. 13 (1964) 539 [5] Brynjolfsson, A.; Weightlessness of photons: A quantum effect; arXiv:astro-ph/0408312 v3 17 Feb 2006 [6] Spitzer, Lyman Jr., On the Possible Interstellar Galactic Corona, Ap.J. 124 (1956) 20-34 [7] Lyndon-Bell, D., Statistical mechanics of violent relaxation in stellar systems (M.N.R.A.S. 136 (1967) 101-121 [8] Bertschinger, E., Self-similar secondary infall and accretion in an Einstein-De Sitter Universe, ApJS, 58 (1985) 39-66 [9] Navarro, J. F., Frenk, C. S., and White, S. D. M. The structure of Cold Dark Matter Halos, ApJ., 462 (1996) 563-575; arXiv:astro-ph/9508025 [10] Navarro, J. F., Ludlow, A., Springel, V., Wang, J., Vogelsberger, M., White, S. D. M., Jenkins, A., Frenk, C. S., and Helmi, A., The diversity and similarity of cold dark matter halos (submitted to MNRAS); arXiv:astro-ph/0810.1522. [11] Bowyer, S., Lieu, R., Sidher, S. D., Lampton, M., Knude, J. , Nature, 375 (1995) 212-214 [12] Bergh¨ ofer, T. W., Bowyer, S., Lieu, R., Knude, J. , Ap. J, 500 (1998) 838 [13] Mould, J. R, Staveley-Smith, L., Schommer, R. A., Bothun, G. D., Hall, P J., Han, M. S., Huchra, J. P., Roth, J., Walsh, W., Wright, A. E. The velocity field of clusters of Galaxies within 100 Megaparsecs. I. Southern clusters, ApJ, 383 (1991) 467-486

Plasma Redshift, Dark Matter and Rotational Velocities of Galaxies_APSMay2toMay52009