Friday, 16 February 2018

The Sunspot Delusion



Lies, Damned Lies and Statistical Mechanics - 4

The Story So Far:

The three previous blogs explained how the Sun came to be a hydrogen shell with a fusion zone supporting it by thermal pressure from below while the weight of the coronal constituents bears down on it from above. Also how the photosphere and lower corona, squeezed by gravitational pressure, have their temperatures (i.e. kinetic energies) kept low by the Pauli Exclusion Principle. The solar spectrum is then manufactured by the progress of Compton collisions through the photosphere and corona. This left us with puzzles about the nature of sunspots and the presence of elements heavier than hydrogen in the corona, bar those in the protostellar cloud that arrived late on the scene.

The delusion is that sunspots are said to be dark because “they are colder material than the super bright solar surface”. However, if that was the case, there would be a point above the surface where the sunspot outflows reached the same temperature as the photosphere and this would be visible. It seems more likely that sunspots are hotter than the photosphere. Also, why is there all that electromagnetic activity? And why do pairs of sunspots often form?

Magma Plumes on Earth

In some senses, the interior of the Earth is a structural analogue of the Sun’s interior. Think of the Hydrogen shell mimicking Earth’s crust and the internal plasma matching the Earth’s magma (molten rock, or lava beneath the crust). Then there is helioseismology. While Earth’s seismic shocks are transmitted through magma, they originate in the crust. So where do the Sun’s shocks originate?

You may be familiar with the volcanic hotspots on Earth, which arise where plumes of magma burst through the Earth’s crust, often with dramatic effect, building new islands in the Pacific or creating enormous volcanic structures like the Yellowstone caldera.

Plasma Plumes

Deep in the solar interior, much violent fusion is going on, which probably rises and falls in its intensity, occasionally building so much pressure that it bursts upwards, in the form of a plume, and breaks through the photosphere. It is also possible that stray asteroids puncture the Sun’s surface, allowing some of the plasma to escape. (Is it just a co-incidence that the solar cycle corresponds with Jupiter’s orbital period? Jupiter’s gravitational field acts as a magnet to re-focus the more eccentric small orbiting bodies)

Ions, travelling, are, in effect, electric currents. The positive ions work like a reverse direction current. So since antiparallel currents repel each other, whilst parallel currents attract each other, the two streams of positive and negative ions tend to separate streams that can become twin plumes, then each plume follows its own path along a radius out to the photosphere. Hence twin sunspots are observed. Once at the surface, the plasma from below merges with that from above, but at the point of outflow, the opposing magnetic fields, generated by the plumes create substantial magnetic fields that use the other plasma as conduits.

One might wonder why the hydrogen shell below the photosphere doesn’t disintegrate, but volcanoes on Earth don’t have this effect on Earth’s crust.

Heavy Elements in the Corona

These plasma plumes may be bringing helium and other elements from the solar centre to the corona, accounting for some of the non-hydrogen lines in the solar spectrum.

This is part 4 of my solution to the Solar temperature and heat transfer problem and completes the set.

Monday, 5 February 2018

The Solar Spectrum Delusion



Lies, Damned Lies and Statistical Mechanics - 3

Recapitulation

The earlier blogs in this series explained how quantum mechanics determines the matter phases of the hydrogen in the Sun and the inability of densely packed atoms to absorb heat due to the Pauli Exclusion Principle. Re-examining the star formation process in this light reveals how fusion is possible in cold hydrogen if it is sufficiently densely packed and under sufficiently high gravitational pressure. These conditions would be extremely difficult, if not impossible, to replicate in Earth-bound laboratories. (Having said that, any facility that stores very cold, or liquid, hydrogen under pressure needs to beware.) It was concluded that the physical structure of a star consists of the following main shells/zones in sequence from the centre (heavy elements e.g. fusion products at the centre), fusion, solid, liquid, gas and plasma. The granular appearance of the photosphere is owed to the boiling surface of the liquid. Effects similar to the majority of solar prominences can be seen above vigorously boiling water.

We now turn to the matter of how these revelations affect the solar spectrum.

It is widely stated that orbital electrons can only jump quantum levels if photons of exactly the correct energy collide with them. This is not correct. If sufficiently high energy photons are present, Compton scattering can occur in which an exchange of energy occurs. If the electron is boosted by an inexact energy match, the excess energy is re-emitted.

There is no black body here. Radiation emitted by the hydrogen fusion zone occupies four distinct wavelengths in the gamma region. In the hydrogen shell, where the atoms are too tightly packed, no absorption is possible. As the pressure eases slightly, Compton collisions occur semi-productively. Electrons may initially absorb energy and jump to a higher energy level, but the pressure forces them back again, emitting hydrogen Balmer line radiation as they do so. The overall effect on the photon compliment is shown in the diagram:


In the above event diagram, time runs left to right. Vertical bars mark the occurrence of events. The black path shows the progress of the status of an electron with time while the red paths represent those of photons. The first event represents the collision between photon and electron, at which the electron gains energy at the expense of the incoming photon. The second event represents the electron rebounding to its original energy level and in doing so emitting a new photon. Effectively the collision has resulted in splitting the original photon into two, and the original spectrum has been altered so that one high energy line has been dimmed, and two new emission lines have appeared.

The directions of travel of the photons are also changed so that photons are now much more likely to undergo collisions amongst themselves, resulting in a spread of wavelengths either side of their original values, due to energy/momentum swapping amongst the photons. This gives rise to a pronounced bump around most of the Balmer region, in the spectrograph. Looking at Jack Martin’s Book “A Spectroscopic Atlas of Bright Stars” the Hydrogen Balmer bulge is plain to see in many of the spectrographs.

As the atom density decreases further, longer term absorption can occur, and it is at this stage that the earlier hydrogen emissions can be absorbed, giving the characteristic absorption spike in the spectrograph. Further rebounds can still occur at the lower levels. It is not necessary for the incoming photon to exactly match the energy required for an electron quantum jump, as long as it has sufficient energy for a productive collision to occur.

This process repeats progressively throughout the height of the corona, and beyond, until the matter and photons are too sparse to collide. The original photon energies are therefore progressively reduced through several energy levels. Similar effects are experienced by the atoms of any other elements that may be present in the above-surface medium.

Thus, the solar spectrum is constructed. Observed absorption lines at higher energies are, in some cases, due to absence, or lower rates, of emissions, leading potentially to false identification of elements in the corona. Since the Sun will have formed from a cloud of mixed gas and dust there are probably several trace elements, other than hydrogen, in the corona however one should always look at forbidden lines with suspicion.

Given that each successive shell, working outwards, is hotter than its inner neighbour, convection does not occur anywhere in the Sun.

Another source of real elements, other than hydrogen, in the corona may be sunspots, which are discussed in the next blog.

This is one component of my solution to the solar heat transfer problem.

Friday, 26 January 2018

The Stellar Formation and Structure Delusions



Lies, Damned Lies and Statistical Mechanics - 2

(Aimed at a broad readership)

The key to the solar structure lies in the way quantum mechanics controls the stellar formation process.

First, some history: In 1902 James Jeans published his theory of instability of a gas cloud that was sufficiently dense and cold. If it is cold enough and dense enough, gravity can overcome thermal pressure and cause the cloud to collapse and become a star. Such a collapsing cloud, it was thought, would become increasingly hot at the centre, due to increasing pressure, until hot enough to initiate fusion. Consequently a hot gaseous sphere would result, with plasma at the centre and cooling to gas at its extremities. However this theoretical structure does not concur with the evidence of solar measurements. When the (verified) data disagrees with the theory, the theory must be wrong.

Physics has moved on, including the discovery of quantum mechanics, and will always move on, so we need to re-evaluate in that light.

Quantum mechanics (recapitulation) tells us that the electron in a hydrogen atom inhabits a cloudy region surrounding its nucleus, referred to as a “probability distribution”, whose radius depends on the electron’s quantum energy level – the higher the energy: the larger the radius. The Uncertainty Principle, in the guise of Pauli’s Exclusion Principle, says that two electrons of the same quantum energy configuration cannot occupy the same “system”, or in this case probability distribution. When you try to compress atoms into very high density, this principle causes a force between the atoms known as electron degeneracy pressure. It has the effect of restricting the size of the electron cloud surrounding each atom’s nucleus, rather like squeezing soft rubber balls together, to the point where the atoms behave increasingly like solid spheres. 

This degeneracy pressure prevents densely packed atoms absorbing more energy, because, otherwise, the size of the individual electron clouds would have to increase and breech the Pauli Exclusion Principle by overlapping each other. Hence, at high density, constrained by externally imposed pressure, atoms cannot have their temperatures increased. Indeed they can even become colder.

During stellar formation, gravitational pressure (which is like Earth’s atmospheric and oceanic pressures) puts more of a squeeze on the centre as the protostar continues to grow, in mass and size, due to the incoming gas/dust from the remainder of the protostellar cloud. Gravitational potential energy possessed by the cloud constituents prior to the collapse gets converted to kinetic energy as it falls in and when the incoming matter reaches the protostar some of this energy is converted to heat on the outside of the protostar. This heat cannot permeate to the inner regions due to the Pauli Exclusion Principle being invoked by the density and pressure as stated above.

With much earlier beginnings: In 1611, Kepler had conjectured that identical solid spheres could not be packed together more densely than to 74% of the total enclosing volume. This idea was supported by Gauss but only proven (computationally) in 1998 and accepted as a theorem in 2014. (You thought Peter Higgs had a long wait?!) Now, if this principle is extended to densely packed atoms, it can be seen that at 74% packing density, the atoms are unable to move in relation to each other meaning that the matter is solid. The packing density has to be reduced to about 50% to permit full fluidity and around 25% to allow gas formation (my informed estimates). (Matter can still be solid at lower densities and similarly for liquids; it’s the maxima that are important in this case.)

The radii of hydrogen atoms at different energy levels can be readily calculated and applying the principles above we can determine the relation between atom energy, density and phase of matter. The maximum possible density of hydrogen is found to be 1029 atoms per cubic metre and only if it is cold. Anything hotter, at that density, or denser than that isn’t hydrogen.

So the pre-stellar sphere, prior to fusion initiation, has a cold solid centre but as it gets less dense away from the centre it can get hotter and, as it does so, goes through the phases from solid to liquid to gas. This structure is, of course, completely opposite to the conventional model but it complies with the measured data. But that is before it has fired up.

Crunch time!

Pressure is the same thing as energy density. This can be derived, from the ideal gas equation of state, and, also, the physical dimensions of these measures are identical. In order for two hydrogen atoms to fuse, some force or pressure is needed to overcome the electrostatic repulsion between the two positively charged nuclei. This is called the Coulomb barrier and the energy needed to overcome it is calculated by Gamow’s theorem. If therefore, at the centre of the star, the pressure divided by the atomic density (giving the energy per atom) exceeds the Gamow energy (and, of course, electron degeneracy pressure) we can have fusion. Clearly there is a critical mass that must be present for fusion to initiate and new versions of the Jeans’ equations are being sought on this new basis. This critical mass for fusion start-up is irrespective of the eventual mass of the complete star.

Initially, fusion may be started before the star is sufficiently massive to maintain the central gravitational pressure against the outward thermal pressure caused by the fusion. So there can be some false starts before continuous fusion gets under way. Once fusion has been established it starts eating away the surrounding solid hydrogen from the inside. Heat is borne from the centre to the exterior by radiation, heating the outer layers progressively, as permitted by the Pauli Exclusion Principle and as stated in my previous blog (The Photosphere Delusion). In the biggest stars, the fusion-capable region is correspondingly bigger so the rate of fusion is higher than for smaller stars, making them hotter and brighter, which is confirmed by observations. Brown dwarfs may be objects that had insufficient mass for fusion to initiate and their observed radiation comes from the hot matter at their outer regions (gravitational potential energy converted to heat as described earlier) as they cool.

Consequently, the resulting star has fusion at the centre surrounded by a solid shell followed by a liquid layer, gas, and then plasma. The densities of the solar structure from the photosphere outward have been measured repeatedly and the inner areas are too dense to be gaseous, let alone plasma. The granulation evident on the solar “surface” is vigorously boiling liquid hydrogen.

In a mature star, fusion products, i.e. denser elements fall to the innermost centre of the star. During hydrogen fusion helium atoms are produced. Helium atoms are slightly smaller that hydrogen and are equivalent to four hydrogen atoms in content and mass. So the mass density of helium is much higher than that of hydrogen. Consequently, hydrogen fusion creates material that can reach higher densities (both mass and number density), making room, as it were, for further fusion to occur. The hydrogen shell surrounding the fusion zone is kept in place by the balance between internal thermal and radiation pressures and external gravitational pressure, which also accounts for its spherical shape. The star will eventually die when this balance is lost, either by implosion or explosion, depending on which pressure wins.

The stellar structure described here is inevitable from the measured data.

There are still more delusions to deal with including the solar spectrum itself (next blog) and sunspots.

This is one component of my solution to the solar heat transfer problem.

Thursday, 18 January 2018

The Photosphere Delusion



Lies, Damned Lies and Statistical Mechanics

(Aimed at a broad readership)

We have a problem with the Sun. The temperatures don’t seem to add up. Whereas the middle and periphery are immensely hot the intervening, visible, surface, known as the photosphere, is relatively cool. This set-up does not accord with the laws of thermodynamics. So what’s wrong?

First, some history: it has been known, for some time, that the apparent temperature of the solar surface is around 6kK (6 kilo Kelvin or 6000 Kelvin. If you’re not used to Kelvins, a temperature change of 1 Kelvin is the same as a change of 1 degree Celsius and 0 Kelvin, or “absolute zero”, is equal to -272.8 degrees Celsius). It was Arthur Stanley Eddington who deduced that the source of the Sun’s energy must be hydrogen fusion, because no other form of energy generation could account for the amount of energy output and the length of time for which it has been “burning”. Experiences on Earth suggest that hydrogen fusion requires a temperature of more than 20 MK (20 MegaKelvin or 20,000,000 Kelvin) for its initiation. This level of concentrated energy is necessary to overcome the electrostatic repulsion between two hydrogen nuclei, known as the Coulomb barrier and calculated by Gamow’s theorem. The heat produced by such fusion is immense, as witnessed in hydrogen bomb explosions, with temperatures around 100MK.  Naturally, it was assumed that the Sun was entirely comprised of a ball of superheated plasma that cooled towards its periphery. So then, how does all this energy NOT heat up the photosphere to more than 6kK? The presumption was that the dense layers of hydrogen beneath the photosphere must be optically opaque so radiation must be giving way to convection as the heat transport mechanism. (Radiation warms up atoms by a process known as Compton Scattering.) Convection is a slow process and, therefore, would not be passing energy through fast enough to heat up the atoms. Then, when the temperatures and densities of the solar corona were measured for the first time, in the 1970s, it was a complete surprise that the coronal periphery was at around 5MK. (Temperatures and other coronal characteristics have been confirmed by extensive further analysis since then, using increasingly sophisticated satellite-based instruments.) How could this be?

Something "unknown" is going on here. It was known that considerable electromagnetic activity goes on in the corona, so extensive efforts have been made, without universally accepted result, to explain how this activity could explain the energy transfer from the centre to the corona and drive the solar wind. (The relevant science is known as magnetohydrodynamics or MHD for short.)

At this point, consider that the definition of temperature arises from the study of thermodynamics and statistical mechanics, based largely on heat engines, experiences with smelting metals and Earth-bound laboratory experiments. But the environment on the Sun is different from Earth’s in two significant ways: much higher ranges of both gravity and radiation. (For which reason I call the laws of thermodynamics “the steam engine laws”. Anyone who can cook an omelette can cook a feast?)

Whichever way you look at it, the solar surface should be hotter than is apparent, being heated either by the central fusion or even by the hot outer corona. Logically, something is preventing the atoms in the photosphere getting and/or appearing “hotter” and the effective “temperature” must be different from that defined by statistical mechanics.

In statistical mechanics, temperature is representative of the kinetic energy of the molecules (or, in this case, atoms), observable as the atoms/molecules “jiggling about”: the hotter they get, the more they jiggle.

The temperature of the photosphere is obtained by means of spectroscopy from which we can measure the kinetic energy of the atoms, but also we get an overall radiation profile from which we can use Wien’s Displacement Law to derive a temperature. Both agree on the temperature of about 6kK. But could this agreement just be a coincidence? Remember that we see the solar surface through the corona, which itself intervenes, actively, between ourselves and the photosphere. The plot thickens.

Now for some clues.

Quantum mechanics tells us that the electron in a hydrogen atom inhabits a cloudy region surrounding its nucleus, referred to as a “probability distribution”, whose radius depends on the electron’s quantum energy level – the higher the energy: the larger the radius. The Uncertainty Principle, in the guise of Pauli’s Exclusion Principle, says that two electrons of the same quantum energy configuration cannot occupy the same “system” or, in this case, probability distribution. When external forces try to compress atoms into very high density, this principle causes a force between the atoms known as electron degeneracy pressure. It has the effect of restricting the size of the electron cloud surrounding each atom’s nucleus, rather like squeezing soft rubber balls together, to the point where the atoms behave increasingly like solid spheres as they become more compressed. 

This degeneracy pressure prevents densely packed atoms absorbing more energy, because, otherwise, the size of the electron clouds would have to increase and breech the Pauli Exclusion Principle by overlapping each other. Hence, at high density, constrained by externally imposed pressure, atoms cannot have their temperatures increased, regardless of how much radiation energy is present.

It is also known that the hydrogen atom is 99.99999% empty space, plenty of room for radiation photons to pass through, so the opacity idea (mentioned in the second paragraph at the beginning of the blog) seems flawed.

We can now put forward a proposition.

The photosphere and the regions immediately above and beneath it, constrained by gravitational pressure (the same thing as atmospheric pressure on Earth but augmented by the reaction from ejecting the solar wind), are being maintained at sufficient density to limit the absorption of radiation emitted by the solar core, whilst being transparent to radiation due to the “emptiness” of these atoms.
Consequently the kinetic energy of the atoms is not representative of the total energy present and the apparent temperature is inaccurate. The rate of absorption of radiant energy increases as the density reduces, with growing height above the photosphere, hence resulting in the increase in temperature with height.

Since the radiation is largely absorbed before leaving the corona, or in driving the solar wind, it is not observable in the solar spectrum. The correct temperature of the photosphere is, therefore, not directly deducible from the solar spectrum, but must be calculated from the total energy flux (including the energy of the solar wind) exiting the corona. An alternative would be to calculate the considerable radiation pressure necessary to balance the difference between the gravitational and thermal pressures, at the photosphere, and calculate the equivalent temperature of that. The correct temperature is probably in the region of 75 MK. (Precise calculations are complicated, involving factors not discussed here, are ongoing and are still subject to extensive cross-checking).



This is not the whole story, there are other delusions: the internal structure of the Sun is another. This is just one component of my proposed solution to the solar heat transfer problem.