The UpHeatingDownCooling Gravity theory of the sun's coronal heat. With the Maths...
An Explanation for some of the Heating of the Sun’s corona
(That should also be seen on other stars).
The Mystery
As everyone knows, the further you move away from something very hot, the cooler things should get. That’s how heat/radiation and thermodynamics works. The sun however (and possibly most other stars) seems to defy that rule. The temperature at the surface of the sun is up to 10,000 kelvin, but in the further out corona the temperatures appear to be in excess of 1 million kelvin (deduced from the degree of ionization of the atoms in the atmosphere – as detected from spectral lines). https://www.nasa.gov/feature/goddard/2018/nasa-s-parker-solar-probe-and-the-curious-case-of-the-hot-corona).
In the sun’s case, the strong gravity (30 times more at the surface than the Earth’s) and extreme pressure at the surface are a further reason why, as you move further away, things should get cooler. Things should progressively cool toward the background temperature of space, the cosmic microwave background’s near zero of 3 kelvin.
Proposed magnetic based explanations of Alfven waves, nanoflares and various forms of heat injection from the sun to its corona are being considered, but may not sum up to something sufficient to explain the heat problem (and in themselves require some explanations for their power). Likewise the sheer power of the outflowing solar (and stellar) winds and coronal mass ejections seems difficult to explain, given the power of the sun’s gravity.
Further observations
Recent observations show evidence for cool clumps and atoms within the corona (again mysterious given the surrounding heat/high temperature) and a variation in temperature between different materials/atoms and ions in the corona.
Considering all this, I propose an explanation that refers to basic physics (so it may apply to all hot stars) and is not dependent on the circumstantial characteristics of the sun.
The Up-Heating/Down-Cooling Gravity Theory
Comprises three parts:-
1 Mass
Presently, we do not yet know what determines the rest mass of a particle. I propose that if we see the particle as a bundle of contained wave energy, then its mass can be a measure of the frequency or speed of its contained waves.
2 General Relativity
According to GR, when an object or particle leaves (goes up from) a gravity field then there should be two relativistic effects. One is that its mass should decrease and the other is that its speed of time should increase. However, according to the description of mass as a bundle of wavy energy these two effects would be contradictory. The speeding up of its waves should increase its mass and not decrease it as required by GR.
3 Quantum Physics and the Uncertainty Principle
A solution to this problem is enabled by the uncertainty principle, which says the exact position of a particle cannot be determined. Instead of the contained waves in the particle speeding up (making it more massive when it should be less) the uncertainty principle allows the (uncertain) position of the particle to be speeding up/changing faster. In effect this means the particle becomes hotter rather than more massive. By the same reasoning, any particle going down, toward the strengthening gravity field, should experience a cooling effect.
This heating or cooling will occur continuously as the particle moves up or down through a changing strength gravity field. Note, this heat is not initially obtained through particle collisions /transference of kinetic energy - it is making a particle shake or vibrate rather than move around faster - but when the particle touches other particles then the vibration would be converted to normal kinetic energy/heat.
The Maths - Calculating the Heat and Temperature
The first step is to calculate the delta increase in mass ( Δm) that would occur from the speeding up due to reduced gravitational time dilation. (Since the mass must decrease according to GR then this supposed increase in mass must become the energy/heat. One can use the same basic equation used for (approximate) gravitational redshift to determine the delta increase.
Δm = G M / c² R (G = gravitational constant, M= mass (of the sun) R = radius (of the sun)
The second step is to use Einstein’s famous mass to energy equation to calculate the energy in Joules that the delta increase must become.
E = m c² (Small c = speed of light constant)
Combining the two equations we get a simple equation for the energy given to the ascending particle.
E = G M / R
This is the energy given to a particle, or amount of mass, moving up in the gravity field of an object of mass M, from a radius of R to a distance of infinity.
When you have worked out the energy/heat in joules given to the rising mass, you can work out the temperature it may acquire (in a closed system) from the specific heat capacity of the substance the mass consists of. There is a great range of heat capacity values. Hydrogen has a high heat capacity – so it takes a lot of heat to raise its temperature. You thus divide the energy, E, by the heat capacity value, (capital C) to calculate the rise in temperature ΔT.
The final simple equation then is
ΔT = G M /R C
Returning to the sun as our neighbourly example here’s what happens to (1kg of) iron according to the equation.
Gravity constant G = 6.674×10−11 N·kg–2·m2.
Mass M (of the sun) = 1.989 × 10^30 kg
Radius of the sun = 695,508 km
Heat capacity C (of 1kg Iron) = 450
Using these numbers we get a ΔT of 424187000 k. (over 420 million degrees).
The heat capacity of Hydrogen changes with temperature but starts at about 30 times more than iron, therefore would make 30 times less temperature, about 14 million degrees.
These seem high values, and to be true to the theory they should be higher still because the original calculated (Δm) mass increase was the difference to an unchanging mass, but GR requires the mass to decrease relativistically, so the Δm value, and thus the calculable ΔT temperatures, should be doubled.
Of course these high temperature values do not directly translate into a calculation for what the corona’s temperature should be. We consider that whatever is heating the corona has to have the power to overcome the familiar thermodynamics that say the corona should be getting cooler the further away from the sun, and given that, these high temperature calculations may be on target.
Coolers
Here is a list of factors that moderate the calculable temperatures of the corona.
1 The specific heat capacity of the elements and ions may rise with temperature.
2 Ionization and phase transitions use heat energy.
3 According to the theory, any material that is going (back) down towards the sun /star will be cooled and this matter, along with the atmospheric matter that is overall not rising or falling (not being heated) will absorb some of the heat of (or cool) the uprising matter that it interacts with.
4 Adiabatic cooling will occur.
Adiabatic cooling occurs when a quantity of gas (moles) is rapidly given a greater space to occupy, and that proportionately decreases the pressure and temperature.
Note that according to the theory, the rate at which the uprising/outflowing material is heated diminishes with distance, in an inversely proportional fashion (1/R). By contrast the rate at which adiabatic cooling occurs will be proportional to the new space occupied, which increases cubically with distance (R³). This means that beyond a certain range an adiabatic cooling effect will outpace the heating from the gravity field.
Adiabatic cooling also occurs when the cooling/expansion is doing work. In the theory we have hot material that goes up, further heated by going up, leading to further expansion and going up, so the material is accelerated away into an up/outflow. This becomes the solar wind. Heat is effectively channelled into movement in a direction, upward and outward, so the heat is converting to a work, the generation of the solar wind.
Testing the Theory
There are a number of observations that can test the theory. Firstly it should be clear that this theory does not displace other theories that consider the heat of the corona to be caused by events originating from the sun. Rather it adds some necessary power and explanation to those ideas and observations. The heat and power of nanoflares, coronal mass ejections, waves or anything that goes up against the strong gravity is supported by this theory.
The theory/observation that magnetic loops of material – that may break and release heat /energy into the corona - is also supported, as this heating could cause of the breaking of the magnetic loops in the first place.
Observations of material that is ejected and then falls back down into the sun may show a rapid heating /expansion on the way up and cooling/contraction on the way down. This would show up in a shape. Where we would normally see a parabolic arch, the heating at the high part would inflate it to make balloon up and out more in shape. I believe we see that. We also see a general acceleration of material away from the surface of the sun, supporting the theory.
And then we can analyse the constituents, looking for cooling material (going down) amongst the warming material (going up) and the temperatures of the various constituents to see how they agree with a general heating or cooling effect applied to various specific heat capacities.
Credibility of the Theory
At this time, as the author of the theory, I would not say whether I believe it is correct (further evidence / observations will help to decide) but I will say what I think is special about it.
If it is thought that gravity / (general) relativity and quantum physics are distinct laws of physics that govern different facets of the universe, then here we have a physical phenomenon where they overlap and where one, general relativity, necessitates the existence of the other, quantum physics.
Mark James Bridger
26th August 2018
