Electrostatic Effects in Planetary and Stellar Atmospheres

Trevor Turton, trevor@turton.co.za
© Trevor Turton 1990-2004.

This paper has been superceded by a newer version.

Abstract

This paper conjectures about the behavior of charged particles in the Earth's upper atmosphere. These particles arise primarily from the irradiation of atmospheric gases by ultraviolet rays from the Sun. It is suggested that many of the electrons freed in this process rise to form an electron atmosphere at very high altitude, that some return to the Earth's surface along geomagnetic lines of force, and that their recombination with positive ions in the polar atmospheres releases light energy, contributing to the Aurorae Borealis and Australis.

It is further suggested that the positive ions created in the upper atmosphere gradually drift downwards to Earth, recombining at or near its surface with a return stream of negative charge flowing through the Earth from the polar regions. This ion flow may play a large role in the massive electrical discharges that often accompany thunderstorms. The paper addresses the similar behavior of electrons and positive ions in other planetary atmospheres, and also that of our Sun. The behavior of electrons and positive ions within gas and dust clouds surrounding young stars and planetary nebulae is discussed, and also that in accretion disks surrounding massive stars, neutron stars, and quasars.

Charged Particles in the Earth's Atmosphere

There are a large number of charged particles in the Earth's upper atmosphere. These arise primarily as a consequence of the ultraviolet components of the Sun's radiational energy impinging upon the gas particles in the upper atmosphere. Ionized oxygen molecules recombine to form ozone (O3) molecules. These are present in sufficient quantity in the stratosphere to have given rise to the term ozone layer.

During the daylight hours when solar irradiation occurs, a very large number of molecules become ionized. This leads to a large number of positively charged gas molecules and free electrons in the stratosphere. There is of course a very strong attraction between the positively charged ions and the negatively charged electrons, which in the fullness of time would result in the recombination of these particles. However this recombination does not complete immediately, since the great majority of the particles are uncharged gas molecules. Charged particles collide with and rebound from uncharged particles in the same way as uncharged particles interact amongst themselves. Electrons, being much lighter, will tend to rebound with greater velocity.

Where two charged particles do approach one another, electrostatic forces will come into play. Particles with the same charge will repel one another. The combined momentum and kinetic energy of the particles will be preserved in each such interaction, which therefore approximate to well enough to the elastic collision of ideal gas particles. Particles with opposite charge will attract one another, causing them to accelerate towards one another, but their initial velocities must be taken into account. Unless these are very small, or their initial trajectories would have brought them into very close proximity, then they will not collide. Once again the particles' momentum and kinetic energy will be preserved in each such interaction, which therefore approximates to well enough to the elastic collision of ideal gas particles.

Electron Gas

While the electrons remain in an uncombined state in the upper atmosphere, they behave very much as particles in an ideal gas do, if one ignores the effects of magnetic fields upon them. The electrons have very small masses compared to those of the particles with which they interact. The mass of an electron is about 10-28 grams, whereas that of a nitrogen molecule is 10-24 grams. As a result of the collisions between electrons and the uncharged particles in the stratosphere, the electrons will tend to acquire large velocities relative to the other more massive particles with which they interact so that on average the particles of different sizes have the same kinetic energy. The average velocity v of a gas particle of mass m in a gas at temperature T is given by:

v = (kT/m)0.5     {1}

where k is Boltzmann's constant. At an altitude of 30km in the Earth's atmosphere the temperature is about 220oK. We can therefore predict that free electrons at this altitude will have an average velocity of about 40km/sec as a consequence of their thermal energy. This velocity is way in excess of the escape velocity of the Earth's gravitational field, some 11km/sec at the Earth's surface. If gravitational forces were the only ones that needed to be considered then we could predict that free electrons in the stratosphere would escape from the Earth's gravitational field into the surrounding vacuum of space in considerable quantities. Gravitational forces are not however the only ones acting on the electron gas. We also need to take into account the effects of electrostatic and electromagnetic forces upon them.

Electromagnetic forces

The Earth has a considerable magnetic field of its own. This corresponds quite well to the field that would be produced by a magnetic dipole at the centre of the Earth, inclined about 11o from the Earth's axis of rotation. This field's strength is about 5 x 10-5 Tesla at the Earth's surface in the vicinity of the equator. Free electrons in the stratosphere would tend to follow helical paths along geomagnetic lines of force. As they do so, they will collide with uncharged particles and interact with other charged particles as described before. After each such interaction, the velocity of the free electron involved will be changed in both magnitude and direction. The geomagnetic field will once again constrain it to follow a new helical path about a magnetic line of force. This line may be at a higher or lower altitude than its prior one. Those electrons that diffuse downwards will tend to recombine with positively charged ions, but those that diffuse upwards will eventually reach an altitude where there are insufficient positively charged ions for them to recombine with, since the positively charged ions are constrained by the Earth's gravitational field to lower altitudes. The electrons that attain higher altitudes will persist, interact with one another, and some will continue to diffuse upwards.

Electrostatic Forces

If a steady stream of electrons escaped from the Earth's gravitational field into outer space then the Earth as a whole would gradually accumulate a net positive charge. As this charge built up, it would exercise an increasing attractive force upon the free electrons within the stratosphere. Eventually this force it would reach such a magnitude that it would prevent all but the most energetic electrons from escaping from the Earth. This net outflow would be balanced by the net inflow of electrons garnered from the Solar wind. The inflow would be constrained by the Earth's magnetic field to enter the atmosphere at the magnetic poles.

Layers of Charge within the Ionosphere

During each day a new assembly of electrons is freed from the upper atmosphere by the Sun's radiation. A pulse of electron gas will rise into the ionosphere. During the night that follows, relatively few electrons will be freed. The distribution of negative charge within the ionosphere should reflect its genesis. Alternate layers of greater and lesser negative charge should be observable. These may correspond to the Kennelly-Heaviside Layers.

Recombination Luminescence

Atmospheric ionization takes place most abundantly at the region of the Earth currently facing the Sun most directly. Once freed electrons have risen to the ionosphere, their mutual repulsion will force them to disperse. Electrostatic and electromagnetic forces hinder dispersion upwards into space, and hence the main path of dispersion will be laterally along lines of geomagnetic force. As the electrons disperse in this way, they will reach the polar regions where the lines of force converge through the Earth's upper atmosphere into its crust. Here the electrons will be brought back into contact with atmospheric gas molecules. The convergence of the geomagnetic lines of force will result in a high concentration of returning electrons in the polar region.

The presence of a substantial negative charge in the atmosphere above the Earth's magnetic poles will induce a corresponding positive charge on the Earth's surface in these areas, since the Earth is, approximately speaking, a large spherical conductor. The normal passage of airflow over the Earth's surface will pick up positive charge. Electrostatic attraction will cause these positively charged particles and the negatively charged electrons to approach and combine in the atmosphere. Some of energy gained by this recombination will be released in the form of visible light. This effect may be a major contributor to the Aurora Borealis during the northern winters, and the Aurora Australis during the southern winters. The same effects will hold at the opposite (summer) pole each season, but the high level of illumination due to the sun's continuous presence under these conditions would mask the visual effects.

Lightning

The migration of electrons from the equatorial and temperate regions of the Earth's atmosphere would result in a net residue of positively charged ions in the atmosphere above these regions. The presence of a substantial positive charge above portions of the Earth's surface would induce a corresponding negative charge to form on its surface in these areas. This local negative charge would attract the positive ions, which would diffuse down through the atmosphere to the Earth's surface, where they would be neutralized by the negative charge. The dense packing and violent thermal agitation of air molecules in the Earth's lower atmosphere would retard the downward flow of positively charged ions. If the air as a whole were relatively still, one would expect an even gradient of charge distribution to be set up, with a strong positive charge at higher altitudes, and a strong negative charge at the Earth's surface. However the Earth's atmosphere is never completely still, because of the solar energy that it gains each day. Warmed air rises, cooler air moves in behind it.

This large-scale movement of air masses will distort the even gradient of charge distribution in the atmosphere. Rising hot air will introduce negative charge into the upper atmosphere, while descending cool air will introduce positive charge into the lower atmosphere. Where two such disparately charged air masses happen to be adjacent to one another, a much higher potential gradient will be established than would be the case in still air. Air is normally an excellent insulator, but if the electric potential gradient becomes high enough then an electric discharge will take place through the air - the familiar lightning bolt.

In the tropics the warming effects of the sun on the Earth's surface are at their maximum, and the upward motion of warm air most pronounced. Towering cumulus clouds with their heads in the stratosphere are a common occurrence. Given the charge gradient already existing between the stratosphere and the Earth, these formations act as natural van der Graaf generators of gigantic size. Negative charge is taken up from the Earth's surface to high altitudes very rapidly, and a great deal of electric discharge activity results.

Similar but less well-known phenomenon called elves, sprites, and blue jets accompany the large-scale movement of charge between the tops of thunderstorms and the ionosphere [1].

Other Planetary Atmospheres

The patterns of ionization and net the migration of electrons from tropical to polar regions should take place on any planet that has an atmosphere. The planet's distance from its sun will affect the strength of the incident ultraviolet radiation and hence the rate at which ionization takes place.

The Sun's Atmosphere

The conditions that prevail in the Sun's atmosphere are very different from those of any planet. The Sun radiates huge quantities of energy from its surface, and this radiation is fairly evenly distributed across its surface. Within the Sun's chromosphere the temperature is about 1,000,000oK. All molecules are dissociated into individual atoms, and all atoms are ionized. Using equation {1} we find that electrons within the Sun's chromosphere will have an average velocity of about 2,700km/sec as a consequence of their thermal energy. This velocity is way in excess of the escape velocity of the Sun's gravitational field, some 618km/sec. If gravitational forces were the only ones that needed to be considered then we could predict that free electrons in the chromosphere would escape from the Sun's gravitational field into the surrounding vacuum of space in considerable quantities. But the loss of electrons in this way would cause the Sun to acquire a net positive charge that would grow to the point where it prevented the further escape of electrons.

Electrons that diffuse above the chromosphere would tend to follow helical paths along the lines of the Sun's magnetic field to the Sun's magnetic poles. They would of course interact with one another, and the more energetic would disperse to ever higher altitudes. There should therefore be a steady migration of electrons above all parts of the Sun's surface to its magnetic poles. This would have to be compensated for by a return flow of electrons from the magnetic poles to all parts of the Sun's surface, and/or a contra-flow of positive ions to the poles. But the very high temperature and violent thermal agitation of the Sun's substance would impede the flow of charge. Over time, very large potential differences could build up across the Sun's surface in a north-south direction. These may be relieved periodically by massive flows of charged material from one place on the surface to another.

The steady net loss of electrons from the Sun should result in an accumulation of positive charge on the Sun. The electrostatic attraction that this would exercise would tend to reduce the outflow of electrons, but not prevent it entirely. Periodically, the chance accumulations of net positive charge in some areas may increase to the point where the electrostatic repulsion of ionized Hydrogen exceeds the Sun's gravitational attraction. Positive charge may erupt from the Sun, seeking to escape. Occasionally such a large amount of positive charge may accumulate within a region that when the material ejects from the Sun's surface, it overcomes the Sun's gravitational and magnetic bonds and escapes into space. Events such as these are observed periodically, and are known as Coronal Mass Ejections (CMEs) [2].

Accretion Disks around Young Stars

A lot of star formation takes place within regions of space that contain large concentrations of gas and dust. The stars that form in such regions attract neighboring gas and dust that typically forms an accretion disk swirling around the star. Matter is drawn from the inner edge of such a disk onto the surface of the star.

New stars tend to emit large amounts of ultraviolet radiation. This would ionize the gas (mostly Hydrogen) within the accretion disk. As in planetary atmospheres, electrons freed in this way would tend to behave as gas particles, and individual electrons would acquire much higher velocities than the gas and dust particles. The electron gas would tend to "boil off" from the accretion disk, leaving it with a net positive charge. As material from the disk accretes onto the star's surface, so the star itself will accumulate a positive charge on its spinning surface. This may contribute to the establishment of the star's magnetic field. Eventually the excess positive charge on the star coupled with the excess positive charge in the inner regions of the accretion disk may become so large that it repels protons (ionized Hydrogen atoms) in the accretion disk more strongly than the star's gravitational force attracts them. Protons in the inner edge of the accretion disk would flee from the system. They would be constrained to flee along the lines of the star's magnetic field, eventually to fan out from the star's magnetic poles.

Planetary Nebulae

When the cores of stars of moderate size run out of Hydrogen to fuel their nuclear reactions, they expand to become red giants. Our Sun will one day expand to approximately the Earth's orbit. The surface temperature of red giants is "only" about 3,500oK, but this is still more than enough to ionize the gas in its atmosphere. The gravitational field at the red giant's surface is greatly reduced on account of its distance from the center; so free electrons are able to escape. This leaves the star with a net positive charge. The strong convection currents that carry heat from the star's core will distribute this charge throughout its volume. The rotation of this charge will give rise to a magnetic field with its poles aligned with the star's axis of rotation. This field will retard the escape of electrons, as will the star's growing net positive charge.

When the red giant no longer has enough Hydrogen to fuel its burning, its core collapses. The greatly increased temperature and pressure at the center causes the fusion of Helium and heavier elements into yet heavier elements, which releases bursts of energy that blow off almost all of the red giant's layers, leaving an extremely dense core that becomes an intensely hot white dwarf or neutron star, with a temperature of about 25,000oK. The white dwarf may have the mass of our Sun but only the diameter of the Earth, and its rotational period is typically measured in milliseconds. The excess positive charge that it still carries is thus spun round at very high speed, leading to a very intense magnetic field.

The outer layers of the red giant expand to form a planetary nebula. If gravitational forces were the only ones that shaped this expansion then one would expect a spherically symmetric bubble to emerge. In practice, planetary nebulae are considerably more complex [3]. They are usually elongated, and often comprise two overlapping bubbles of more or less equal size with widely separated centers, sometimes with a third, smaller bubble centered on the white dwarf. The high temperature of the white dwarf results in intense ultraviolet radiation that ionizes the expanding gas bubbles.

If we take the magnetic field of the star into consideration, and also the fact that its atmosphere is ionized, then the characteristic shape of planetary nebulae may be explained by assuming that when the central core explodes, the motion of the ionized material that is expelled in any direction other than along the star's magnetic poles will be retarded and redirected by the magnetic field. This will create some backpressure, and much of the material will be ejected in the directions of the two magnetic poles where it does not have to cross the magnetic field. As this material clears the magnetic field, it will be free to expand, and its net positive charge will ensure that it does. Hence two bubbles evolve. Whatever Hydrogen remains in the Red Giant's atmosphere will be most rapidly accelerated by the electrostatic repulsion, and will form the largest bubble. Heavier elements which may not be fully ionized and which carry neutron ballast will be accelerated less, and hence form smaller bubbles.

The heaviest elements in the red giant's atmosphere may well have a high enough mass to charge ratio to pass right through the star's magnetic field, albeit with reduced velocity. They, together with the lighter elements that they drag with them, could account for the third, smaller bubble that is centered on the remnant white dwarf. Some elongation of this bubble in the polar direction may be expected.

Accretion Disks around Neutron Stars

Where an accretion disk forms around a neutron star (sometimes material drawn from a close binary partner that is undergoing an expansionary phase) the same sort of phenomena as described for Harbig-Haro objects above should occur - material should be ejected along the poles of the star's magnetic field. An extra development should arise from the fact that as material collides with the surface of a neutron star, it does so with such high velocity that gamma rays are emitted. When these strike material in the surrounding accretion disk, some electron and positron pairs will be created. Some of these will recombine to liberate energy again, but a portion of the positrons will escape. Given their extremely high positive charge to mass ratio, they will be impelled to flee from the positively charged neutron star with very high velocities. As with fleeing protons, they will be constrained to flee along the lines of the neutron star's magnetic fields.

Accretion Disks around Black Holes

Observations suggest that there are probably extremely massive gravitationally collapsed stars (black holes) at the centers of some, perhaps most galaxies - including our own. There is usually a high concentration of gas and dust at the hubs of galaxies, so a black hole in this location would be accompanied by a large accretion disk. The regime that obtains in this situation would be similar in many ways to one in which a neutron star is surrounded by an accretion disk, but on a much larger scale. Matter on the inner edge of the accretion disk is dragged into the black hole's event horizon at speeds almost equal to that of light. The extremely high velocity gives rise to frictional heating, with the emission of ultraviolet and even gamma rays. As before, electron gas will tend to boil off from the accretion disk giving it and the black hole which it circles a strong positive charge. The rapidly rotating positively charged accretion disk will create a strong magnetic field, roughly toroidal in shape. Positrons will be formed by collisions between gamma rays and material in the accretion disk. These, together with protons, will be accelerated at relativistic speeds from the poles of the magnetic field.

Given the strong repulsion that positrons and protons have for one another, one would expect the jets of ejecta to fan out as they leave the immediate vicinity of the black hole and its accretion disk. However, a stream of positive charge creates its own surrounding tubular magnetic field. As these jets of positive charges penetrate far out into space, they will attract electrons from surrounding space, and also impact on the gas and dust that happens to lie in their path with such energy that they will knock its electrons free. Electrons will flow into the jets. They will of course be strongly attracted to the positrons and protons within it, but recombination will not be immediate because of the relativistic speeds of the positrons and protons. Some recombination will certainly occur, and this will give rise to a charge gradient, with more positive charge near the black hole and accretion disk from which the jet originates. Once within the jet, electrons will tend to flow towards the region of greater charge. They will thus move in the opposite direction to the positive charge. The magnetic field that results from this counter-flow of electrons will reinforce the one created by the flow of positive charge. This field would tend to "pinch" the positive and negative charges together. The fact that the positive charge is interpenetrated by some negative charge will somewhat reduce the electrostatic repulsion experienced by the positive charges. Taken together, these two effects may be enough to complete the "pinch" effect. Instead of diverging, the jets of positrons and protons will act as self-collimating beams, penetrating perhaps hundreds of light years out into space. Huge jets that conform to this general description have been observed emerging from some quasars, which are assumed to be generated by huge black holes sucking in surrounding material at the centers of galaxies.

References

  1. "Blue Jets May Link Thunderstorms to the Ionosphere", Scientific American 2002-03-14, http://www.sciam.com/print_version.cfm?articleID=0000E922-F54A-1CCF-B4A8809EC588EEDF
  2. "Coronal Mass Ejections", http://science.nasa.gov/ssl/pad/solar/cmes.htm
  3. "The Extraordinary Deaths of Ordinary Stars", Scientific America, July 2004 issue.