Welcome to Cosmology and Thermodynamics

The Sun is Electrically Positively Charged. 

     I invite readers to study carefully the basis for the hypothesis that the Sun is electrically positively charged;  there are nine reasons given below based on firm observational evidence. 

    The two diagrams below are the Maxwell-Boltzmann distributions curves for velocities of electrons and protons at 1.1 million degrees Kelvin, which is the approximate  temperature of the outer Sun.  See how these velocities compare with the velocity of escape.
 
 
 
 
     The velocity of escape from the Sun is 617000 m s-1 and it can be seen that almost all the electrons exceed this speed and virtually no protons do.  Superficially this leads to the conclusion that the Sun would lose all its electrons and none of its protons.  Obviously this does not happen.  Therefore there must be a mechanism for holding back most of the electrons.  It is deduced that the Sun is positively charged. 

     The Solar Wind now comes into the picture which must be neutral overall, otherwise the Earth, which is bathed in the Solar Wind, would acquire an electric charge over a period of time.  Therefore the net positive charge which holds back the electrons must also repel a small proportion of protons from the Sun into space. 

     The consequences of this hypothesis are far-reaching.  It leads to the logical conclusion that all hot stars have a positive charge and that this is balanced by a net negative charge in the interstellar space in a galaxy.

     The next step in the reasoning is that there are attractive electrical forces between these stars and the bulk of the galaxy and that these attractive forces account for the pattern of velocities of stars in orbit in a galaxy (the so-called ‘flat rotation curve’).  It follows that there is no need for a “missing mass” to provide a gravitational force for this velocity pattern;  this is also called “dark matter”.   

     It is this “flat rotation curve” which is the cause of the frequent assertion that there must be “dark matter” or a “missing mass”. 

     But is this “flat rotation curve” genuine?  See the diagram below - the velocities of the orbits of stars in the Milky Way.  Actually there is no smooth curve.   

The point is that if the concept of “missing mass” were valid then the orbital velocities of the stars would be on a smooth curve in the way that the velocities of the planets lie on a smooth curve.

     The diagram above demonstrates a powerful argument which supports this new hypothesis, namely that I predicted that stars which are not hot enough to have an ionized corona should not be positively charged and therefore they should have orbital velocities in the galaxy below the so-called flat rotation curve. I then found data showing that this is in fact the case.

      This data was found in the reports by Fuchs, Jahreiss and Wielen (1999).  They ‘determined reliable space velocities of 560 nearby subdwarfs’, i.e. nearby to the Sun.  The variation in their velocities is so wide that there is no way they could be accommodated on a ‘flat curve’. 

     Reiteration; - unattached brown dwarfs, which are marked red in the diagram, have rotation velocities below the other stars;  the explanation is that they are not hot enough to eject electrons and therefore they do not have a net positive charge.
 
 
 

     Before listing the observational evidence in favour of the new hypothesis I will outline the results of some calculations.  

     The Sun is a plasma and the nature of an electrostatically charged plasma is quite different from other electrostatically charged bodies.  There are observations that positively charged oxygen ions, O5+ , in the corona are accelerated radially away from the Sun with even greater velocity than protons, and these data provide a means of estimating the charge on the Sun (This calculation is not given here). 

     In the chromosphere the protons must be accelerated to 6.2x105 m s-1 which is the velocity of escape. 

     The excess positive charge on the Sun is in the order of  6.6 x1022 C. 

     The mass of the Sun is 2 x 1030  kg, which is equivalent to 1.2 x 1057 protons and electrons in almost equal balanced proportions.

     The excess positive charge of 6.6 x 1022 Coulombs is equivalent to 

4.1 x 1041  protons.

 

     Therefore the incremental excess number of protons over electrons is in the ratio

        4.1 x 1041  :  1.2 x 1057 

      i.e.   one in 3 x 1015 .

      Therefore it is not surprising that this extremely small excess positive charge has not yet been detected by astronomers.

Considerations for the Galaxy.

     We now make the reasonable assumption that when the galaxy first formed, it was electrically neutral, i.e. there were equal numbers of protons  and  electrons.   The  same  assumption  applies  to the birth  of stars such as the Sun.  If the Sun now has a net positive charge of  6.6 x 1022 Coulombs  then it has lost that amount of negative electrons to interstellar space.   Since there are believed to be in the region of  1.5 x 1011  stars in our galaxy, this suggests that the space in the galaxy contains in the order of 1034  Coulombs of surplus electrons. 

     The model of our galaxy now develops in this way;  the stars have a small positive charge - and this includes the stars in the central bulge;  it follows that the negative electrons are attracted to some extent towards the centre of the galaxy, i.e. there is an electric field which decreases from the centre outwards.  There is a small attractive force between this negative electric field and the stars circulating in the galaxy.  The hypothesis is put forward here that it is this attractive force which is causing the characteristic star velocities in a galaxy and this velocity effect is NOT caused by the gravitational force of the ‘missing mass’.  

     Observations in favour of the new hypothesis as against the theory of missing mass.

 (1)  In the corona of the Sun, oxygen ions, O5+ , are accelerated radially away from the Sun faster than protons, (Kohl et al. (1998) and Aschwanden et al. (2001)).  Since oxygen ions are 16 times heavier than protons, this unexpected phenomenon cannot be explained by simple diffusion.  The natural explanation is that that the oxygen ions with the higher positive charge are being accelerated by a positive electric field. 

 

     See the diagram below.
 
 

(2)  Taylor and Cordes (1993) have studied the distribution of electrons in interstellar space in our galaxy.  Because electrons repel each other, we might expect this distribution to be widely dispersed spherically but this is not the case.  Electrons keep closely to the disk and are concentrated in the central bulge of the galaxy and in the spiral arms where most of the stars are concentrated.  The diagrams of Taylor and Cordes are quite clear on this point.  This observation presents a strong argument in favour of the new hypothesis  because there is the easy explanation, that the negative electrons are attracted to positively charged stars.

     Weisberg et al (1995) confirm the electron densities of Taylor and Cordes.

 (3)  As has been stated above, the central idea in this new hypothesis is that the orbits of stars are governed to some extent by the positive electric charge on stars.  By the same reasoning, positively charged ions in interstellar space would also be expected to have non-Keplerian orbits whereas neutral atoms and molecules would have Keplerian orbits.  But most interstellar clouds are mixtures of ions and neutral particles and it will be explained below how these interact.

     In this hypothesis we would expect that a cloud of ionized gas would move faster than a cloud of un-ionized gas, and this has actually been observed in NGC 4214 (Wilcots and Thurow, 2001).  Wilcots and Thurow give a different explanation from the one proffered here, - but then they were not looking for the possibility that there might be an attractive force between the ionized cloud and a net negative charge towards the centre of the galaxy NGC 4214. 

     This effect has also been observed in NGC 891 (Swaters, Sancisi and van der Hulst 1997).  They report that there is neutral hydrogen in a halo up to 5 kpc from the plane of the disk and the rotation of this hydrogen is 25 to 100 km s-1  slower than the gas in the plane.

 (4)  There are exceptions to the observations of Section (3).  There is observational evidence that the interstellar medium in our own galaxy contains neutral hydrogen atoms,  helium atoms,  electrons,  protons  (H II) and other positively charged ions such as He+ and Si+ (Wood and Linsky, 1997) and H3+  (Geballe, 2006).   Now if we pursue the logic of the present hypothesis, that the space towards the centre of the galaxy contains a slight excess of negative charge, it might be expected that the positive ions such as protons would exhibit a higher rotational velocity than neutral atoms because of the electric attraction towards the centre of the galaxy.  In some cases they do (3).  But Wood and Linsky have pointed out that there is probably continual charge exchange between the neutral atoms and the ionized atoms; for example the ion N2H+ has been detected in our Galaxy and one origin is probably the equilibrium,

      H3+ + N2 N2H+ + H2    (Bergin et al. 2001).

Another way in which this N2H+ ion could be produced is the direct action of a proton on a nitrogen molecule.   Therefore in this gas mixture a distinctive velocity pattern for the ionized atoms separate from the neutral atoms would not be observed.

(5)  Pont et al (1997) report a study of the rotational curve of the Milky Way using cepheids as tracers.  For the galactic radii 6 to 16 kpc the results show widely scattered rotational velocities, - hardly a ‘flat curve’, - but there is a clear trend that H II regions (protons) are rotating faster than cepheids.  This can be explained if the cepheids, which are comparatively cool stars, have lost part of the positive charge which they had originally. 

     The point here is that in a hot star such as the Sun, there is an equilibrium created by its positive charge such that there is a balance between ejecting some protons and holding back the fast moving electrons.  When a star cools down the equilibrium will be re-adjusted;  relatively fewer electrons need to be held back and more protons will be repelled until there is a lower net positive charge on the star.

 (6)   Kent (1986) presented rotational velocity diagrams for 37 galaxies and Sanders and Verheijen (1998) give velocity diagrams for 6 galaxies.  There is substantial variation in the shapes of these velocity profiles;  some of these are ‘flat’ curves and some are not.  We would not expect that degree of variation for a universally distributed ‘missing mass’.

(7)   Brand and Blitz (1993) have studied the velocity field in the outer Galaxy.  Most of the objects observed are nebulae of positively charged hydrogen or of neutral hydrogen.  Their Figure 3 shows ‘Circular velocity as a function of galactocentric distance’.  There is a wide scatter of velocities from 165 km s-1  to 345 km s-1 but they have chosen to draw an almost horizontal smooth curve through these scattered points.  In spite of this scatter, there is a clear trend for the regions with H+ ions having greater velocities than neutral hydrogen.

     Kulkarni, Blitz and Heiles (1982) also present data with a wide scatter of rotational velocities.  This wide variation in orbital velocities cannot be explained in terms of the gravitational attraction of a ‘missing mass’ but it can be explained by the hypothesis that different nebulae or different stars have different positive charges.  

     An important point is that it is quite possible for different stars to have evolved with different positive charges, therefore there will be different forces of attraction between the stars and the electric charge in the bulk of the galaxy.  This feature would cause a different orbital velocities,  i.e. the scatter of orbital velocities is not a problem for the new hypothesis.

(8)  Fich, Blitz and Stark (1989) have studied ‘The Rotational Curve of the Milky Way to 2RO’.   They found that the curve is not strictly flat.  First there is a wide scatter of observational points;  this has already been found in other studies and has been discussed above.

     Second, there is a ‘dip’ in the curve at the radius of 10 kpc ‘primarily from objects in the Perseus arm’.  Fich et al did not find an explanation for this anomaly but one is presented here.

     The Perseus arm contains a lower electron density than the other spiral arms in the Milky Way (see Taylor and Cordes, 1993) and the Perseus arm is between 9 and 10 kpc from the centre of the Milky Way.  Therefore hydrogen ions at 10 kpc just beyond the Perseus arm will be subjected to a lower attractive force than hydrogen ions in other parts of the Milky Way and therefore they will have a lower orbital velocity, which is exactly what is observed, namely this ‘dip’. 

 

(9)   Another fact which is in favour of the new hypothesis is that galaxies display a weak magnetic field.  This is what we should expect in a galaxy with positively charged stars moving in orbits.  It is possible that the attraction between galaxies in clusters (currently attributed to the missing mass) is partly due to magnetic forces.

 (10)  Eddington’s Errors.

     It has been objected that the possibility that the Sun is positively charged has been studied previously by Eddington (1926 and 1959) and by Mestel (1999) and they showed that the effect is infinitesimal.

     Mestel simply copies the result of Eddington without going through the reasoning.  Eddington’s book of 1959 is identical with the first edition of 1926 and his analysis of the velocities of ions in the Sun is flawed. 

     First he takes the Maxwell-Boltzmann equation for velocity distribution of ions and integrates it over all velocities.  But we are not concerned with all velocities, we are concerned with velocities greater than the escape velocity from the Sun, which Eddington never mentions

     Second, Eddington uses the Maxwell-Boltzmann equation to calculate densities of ions, but the Maxwell-Boltzmann distribution of velocities is independent of the density of fluids, therefore this is an inappropriate application of that equation. 

     Thirdly, as has been shown above, there is a considerable amount of evidence that oxygen ions (O5+ ) are being accelerated outwards more than protons.  (Antonucci, Dodero and Giordano 2000, and Kohl et al 1998, Aschwanden et al. 2001).  Now, how can that come about?  As has been pointed out above, oxygen ions are 16 times heavier than protons so the natural explanation is that the high positive charge is the cause of that acceleration, i.e. the Sun must have an effective positive charge.

     The velocities of the oxygen ions and protons are “strongly anisotropic”, (Kohl et al. 1998) i.e. the velocities radially outwards are more than the velocities in other directions;  this is not consistent with Eddington’s findings, and the high acceleration of oxygen ions is contrary to his results.

     Finally it should be pointed out that the Solar Wind was not known in 1926, so Eddington did not extend his analysis to the concept that ions would actually leave the Sun in substantial quantities. 

A Criticism.

     It might be argued against this hypothesis that the Sun could not retain a steady state of positive charge simultaneously with producing a neutral Solar Wind.  The system is in a state of dynamic equilibrium.  Suppose a mass ejection threw out an extra quantity of positive ions, then the net charge on the Sun would decrease;  but it is this net charge which holds back electrons;  therefore a temporary decrease in positive charge would release more electrons because their velocities are greater than the velocity of escape.

     The state of the Sun would then revert to its previous steady state. 

     The Solar Wind might well have fluctuations in its electrical charge, but on balance it remains neutral.  Indeed it is these fluctuations which are known to affect adversely the electrical systems on Earth.  

 

Final Discussion and Conclusion

     The “received wisdom” about the missing mass is expressed in the paper ‘Baryonic Dark Matter’ by B. Carr (1994) :-  

 

     ‘The evidence for dark matter on all scales from star clusters to the Universe itself has built up steadily over the last 50 years.  Although the strength of evidence on different scales varies considerably, there is now little doubt that only a small fraction of the mass of the Universe is in visible form.

     ‘The best evidence for dark matter in galaxies comes from the rotation curves from spirals.’ 

 

     Then again, Blitz (1995) describes the evidence of dark matter from the measurement of flat galaxy rotation curves as ‘compelling’. 

     I have shown that the evidence for dark matter is far from “compelling” in view of the fact that brown dwarfs and cepheids do not fit the flat rotation curves, and furthermore the rotation velocities display a wide scatter which is inconsistent with the theory. 

 

      The evidence for the new hypothesis is overwhelming, namely that the Sun and other hot stars are electrically positively charged, that galaxies contain zones of electrons and that the electrical attraction between these opposite charges explains nature of the rotation velocities of stars and brown dwarfs in the Milky Way.

     This explains why scientists have been looking for “dark matter” for 50 years in vain!!

References.

Antonucci E., Dodero M.A., Giordano S., 2000,  Fast Solar Wind Velocity in a Polar Coronal Hole During Solar Minimum, Solar Physics,  197,  115.  Aschwanden, M.J. et al. 2001,  The New Solar Corona, ARA&A,  39,  175. 

Bergin E.A. et al. 2001, Aug. 10, Molecular Excitation and Differential Gas-Phase Depletions in the IC 5146 Dark Cloud,  ApJ,  557,  209,  mentions N2H+

Blitz L. 1995, Dark Matter in the Milky Way, Conference Proceedings of the American Institute of Physics. 

Brand J., Blitz L., 1993, The Velocity Field of the outer Galaxy, A&A,  275, 67. 

Burstein D., Rubin V.C., 1985,  ApJ, 297, 423.   

Carr, B. 1994,  Baryonic Dark Matter, ARA&A,  32,  531. 

Eddington A.S., 1959,  The Internal Composition of the Stars, first edition 1926, p. 272, Cambridge University Press.

Fich M., Blitz L., Stark A.A., 1989, July 1,  The Rotation Curve of the Milky Way to 2RO , ApJ,  342,  272.  

Fuchs B., Jahreiss H., Wielen R., 1999,  Kinematics of Nearby Subdwarfs, Ap&SS,  265,  175.   

 

Geballe T., 2006,  H3+  Toward and Within the Galactic Center, Discussion Meeting at the Royal Society London,  ‘Physics, Chemistry and Astronomy of H3+ ‘ and other references therein.

Kent S.M., 1986 June, Dark Matter in Spiral Galaxies, I, Galaxies with Optical Rotation Curves, AJ,  91, No. 6,  1301. 

Kohl J.L. et al. 1998, July 1, UVCS/SOHO Empirical Determinations of Anisotropic Velocity Distributions in the Solar Corona, ApJ,  501,  L127. 

Kulkarni S.R., Blitz L. and Heiles C., 1982, Aug. 15,  Atomic Hydrogen in the Outer Milky Way, ApJ, 259,  L63.

Mestel L.  1999,  Stellar Magnetism,  p. 183.

Pont F. et al. 1997,  Rotation of the Outer Disc from Classical Cepheids, A&A,  318,  412. 

Sanders R.H., Verheijen M.A.W., 1998, Aug. 10, Rotation Curves of Ursa Major Galaxies in the Context of Modified Newtonian Dynamics, ApJ, 503,  97.

Swaters R.A., Sancisi R., van der Hulst J.M., 1997, The HI Halo of NGC 891, ApJ,  491, 140.

Taylor J.H., Cordes J.M., 1993, July 10, Pulsar Distances and the Galactic Distribution of Free Electrons, ApJ.  411, 674.  

Weisberg J.M. et al. 1995, July 1, Neutral Hydrogen Absorption Measurements of Four Distant Pulsars and the Electron Density in the Inner Galaxy, ApJ,  447, 204.   

Wilcots E.M., Thurow J.C., 2001, July 10, WIYN Integral Field Unit Study of the Kinematics of the Ionized Gas in NGC 4214, ApJ,  555,  758.  

Wood B.E., Linsky J.L.,  1977, Jan. 1, A New Measurement of the Electron Density in the Local Interstellar Medium, ApJ,  474,  L39. 

  

     The following textbooks give information on electric phenomena in plasmas and these provided the basis for the calculations on the electrical charge on the Sun.

Bittencourt J.A., 2004, Fundamentals of Plasma Physics, p. 8, 3rd Edition, Springer, New York. 

Dendy R.O. 1993, Plasma Physics, An Introductory Course, Cambridge University Press.

The Feynman Lectures,  Addison-Wesley Publishing Company, 1963,  Vol. II, Ch. 7.

Thyagaraja A. Lectures on Plasma Physics,  2002 Dec., UKAEA, Culham Science Centre,  p. 4.

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