The Mindblowing Physics of the Sun

THE MINDBLOWING PHYSICS OF THE SUN

PRITHVIR P. JHAVERI, DUKE UNIVERSITY 2019

Abstract

This paper was written with the purpose of exposing my Professor Hubert Bray[*], and the rest of my class[**], to aspects of the sun that they might not be aware of. If bananaswere to replace the hydrogen present in the sun could thesame average surface and coretemperature be maintained? Could a certain solar activity in the distant future contribute to the destruction of the earth? Are solar minimums as predictable as we think they are?Does the sun’s history support the theory of evolution?How big is the sun, in reality?

Introduction

The claim that the sun would remain as hot as it is today if its hydrogen content was replaced by bananas was exploredand supported using Gay – Lussacs’ Law. On further investigation it was noted that the nuclear fusion reactions that take place in the sun’s core actually dispute this claim in the long term.

The theory that the earth will, at some point in time in the distant future, be consumed by the ever expanding sun was proved using nuclear reactions, specifically the triple alpha process in which helium is converted to carbon.

The unpredictability of existing space and data technologies in detecting x class solar flares was touched upon. It was concluded that no matter how advanced our technological systems maybe, there is still a lot that is unknown. The faint young sun paradox was dealt with in a three-fold manner. The solution involved the greenhouse gas hypothesis, the idea of a reduction in radiogenic activity, and the reduction in the moons distance from the earth that lead to a decrease in tidal heating.The suns actual volume was computed, and found to be not as large as expected. In fact, the conclusion might be extremely surprising to most.

Could bananas work?If the sun were made of bananas it would be probably still be as hot.

Within the core of the sun, temperatures soars at about 15000000K. While pressures soar at about 340 billion times that on earth. It’s important to note that the soaring temperature is actually a result of the soaring pressure. Closed surfaces get heated when lots of fluid (in this case- gas) is forced inside them. The pressure increases the temperature. This is a direct application of Gay- Lussacs’ Temperature - Volume Law which states that “At a fixed volume, the temperature and pressure of a gas are directly proportional to each other.”

Below is the equation for Gay- Lussacs’ Law followed by a graph demonstrating it.

T1= Initial Temperature (Kelvin - K)

P1= Initial Pressure (atm or mmHg)

T2= Final Temperature (Kelvin - K)

P2= Final Pressure (atm or mmHg)

Now, it’s important to note that because of this intense pressure and temperature,nuclear reactions are constantly taking place in the sun’s core. These nuclear reactions complete a cycle of renewing the heat and pressure that actually cause them. The main reaction that takes place in the sun is the fusion of hydrogen to form helium. The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos (which changes two of the protons into neutrons), and energy. The reaction is shown in the diagram below.

Furthermore, if the sun was not primarily composed of Hydrogen, the fusion reaction that keeps it going would not get underway: so a banana sun would would cool down rapidly from it’s initial heat.

Even if the sun were to cool downinstantaneously, it would take the people on earth 8 minutes to realize this. Light travels at a speed of 3 x 10^8 m/s and the distance between the sun and the earth is 1.5 x 10^11 m/s. Assuming there is no acceleration of the velocity of this light,

Time taken = (1.5 x 10^11) / (3 x 10^8) s

= (0.5 x 10^3) s

~ 8 minutes 20 seconds.

It’s interesting, however, to wonder whether the high potassium content in bananas could possibly contribute to the nuclear reaction in some way, owing to potassium and hydrogen’s proximity in the periodic table, and their highly similar chemical nature.

The Death of the Earth: There are many theories floating around that speak of the ultimate destruction of the earth. Most of these stem, in some way or another, from the activities of the sun. The most popular theory is that at some point in the distant future, the sun will consume the earth. The sun is believed to have been burning for about 5 billion years. It is supposed to be “middle aged”. I.e. it has burnt up half the hydrogen present in its core. Therefore, its life expectancy is postulated to be around 5 billion more years. When all the hydrogen in the core is used up, nuclear reactions will stop there, but they will continue in a shell around the core. The core will contract (since it is not generating energy) and as it contracts it will heat up. Eventually it will get hot enough to start burning helium into carbon.

This is called the triple- alpha process. Here, three Helium- 4 nuclei (alpha particles) are converted to carbon.

4He2 + 4He28Be4 (-91.8 KeV)

8Be4 + 4He2 12C6 (+7.367 MeV)

While the core is contracting, the helium burning aroundit in the outer layers will heat up and then expand, and then cool. The Sun, as a whole, will gradually expand. At some point in time it will become what is called a Red Giant[*] and its radius will be large enough to envelop the Earth.

Unpredictability of solar minimums

Approximately every 10 years, solar activity increases to a maximum. Sunspots (temporary phenomena on the photosphere of the sun that appear visibly as dark spots compared to surrounding regions that correspond to concentrations of magnetic field flux that inhibit convection and result in reduced surface temperature compared to the surrounding photosphere) appear at different locations all over the sun, and unsystematically explode. Large clouds of gas known as “Coronary Mass Ejections” (largebursts of gas and magnetic field arising from the solar corona[*]) spread throughout the solar system. These CMEs actually contribute to the Auroras seen in northern countries like Greenland and Iceland etc. In fact, in a solar maximum between 2000 and 2001, people as far south as Mexico and Florida claimed to witness auroras. As dangerous as these solar maximums are to radio and electrical activity on earth, they are predictable. We know when to expect them and thus take the necessary precautions to deal with them.

Recently, there has been discussion that solar minimums are a whole different ball game. Solar Physicist David Hathaway of the NASA Marshall Space Flight Center believes that solar activity never stops. “Not even during a solar minimum.” Hathaway counted the number of X- class solar flares each month during the last three solar cycles of the 20th century as seen in the diagram below. An X-class solar flare is the most powerful solar flare with Peak Flux Range at 100-800 picometre of > 10-4 Watts/metre2. The result was that there was at least one X class flare in each of the last three solar minima.

What this tells us is that no matter how advanced our space technology detecting systems are[1], we still have a long way to go. Space travel is still extraordinarily dangerous. Astronauts have to always be on the look out for X- Class solar flares, even in periods of so called solar minima. Space travel is planned in ways that reduce the amount of predicted interaction between the travel path and CMEs. However, there will always be that sense of unpredictability.

Faint young sun paradox

During the Archean period (3.8 – 2.5 billion years ago), the sun was supposed to be only 75% as bright as it is today. Given the radius of the earth’s orbit around the sun, there is no way that the sun would’ve been able to provide the same energy to maintain a temperature conducive to liquid water on earth. The temperature would’ve been way too low and water would be frozen. Obviously, life would not have been able to develop the way that it did. There is no way that that temperature would be able to support of the theory of evolution.

Here lies the contradiction. Geologists believe that the earth has remained at a constant temperature throughout its development. Furthermore, the primary species prevalent during this period, the Archaea, are not just extremophilic microbes. Many of them cannot survive in harsh conditions. In fact, the Archeans that are present in our gut today are similar to the ones that were present in that period- they needed salinity, oxygen levels, and temperature akin to what is present today. With the given amount of resources and knowledge available, scientists attempt to understand and solve the paradox. There are three basic hypotheses.

1.The Greenhouse Hypothesis: the general consensus is that the young earth contained larger amounts of greenhouse gases in the atmosphere than that are present today. The atmosphere was able to trap enough heat to compensate for the smaller quantity of solar heat energy reaching it.Carbon dioxide concentrations may have been higher because there was no bacterial photosynthesis to reduce the gas to carbon and oxygen. Methane, a very active greenhouse gas that reacts with oxygen to produce carbon dioxide and water vapor, may have been more prevalent as well. Most importantly, it was proposed that Carbonyl Sulfide (OCS) was present in the Archean atmosphere. Carbonyl sulfide is an efficient greenhouse gas and the scientists estimate that the additional greenhouse effect would have been sufficient to prevent Earth from freezing over.

2.The Radiogenic Hypothesis: There is mass belief that any attempts to explain the faint young sun paradox must take into account the radiogenic contributions. Whenever radioactive isotopes spontaneously decay, heat energy is released as a byproduct. In the past, the geothermal release of decay heat, emitted from the decay of the isotopes potassium-40, uranium-235 and uranium-238, and thorium-232 was believed to be considerably greater than it is today. As shown in the diagram below.

3.Tidal Heating: (also known as tidal working) occurs through the tidal friction processes- orbital and rotational energy are dissipated as heat in either the surface ocean or interior of a planet or satellite.We calculate the quantity of tidal heating using this formula:

Where = mean density of the satellite. I.e. the moon;

- the fifth power of the average angular speed of the satellite;

- the fourth power of the radius of the orbit of satellite around the planet whose tidal heating we’re calculating;

- the eccentricity of the orbit;

- the shear modulus;

Q - a dimensionless dissipation factor;

The Moon was much closer to the Earth billions of years ago. Since the fourth power of the radius of the satellites orbit is directly proportional to the tidal heating, one would assume that the tidal heating was less. However, reduction in the radius also implies greater angular velocity. And, since tidal heating is proportional to the fifth power of the angular velocity[*], tidal heating was actually greater in the Archean period, which offset the lack of heat from the sun and thus enabled life to develop on earth.

How big is the sun actually?

The sun weighs about 1.989 × 10^30 kg. The entire solar system has a combined mass of 1.993 x 10^30 kg. This means that the sun contributes 1.989/ 1.993 or 99.8 % of the entire solar system.Furthermore, the sun occupies 1.41×10^18 km3 of space, which is 1,300,000 times that of the Earth.

In fact, its shape is possibly the closest perfect natural sphere known to man.

The truth is that these are known facts, and most people interested in the study of the universe could tell you this.

However, what people forget is that atoms are 99.9999999999999 per cent empty space. If you forced all the atoms together, removing the space between them, crushing them down so the all those vast empty spaces were compressed, a single teaspoon or sugar cube of the resulting mass would weigh five billion tons; about ten times the weight of all the humans who are currently alive.

In the same way, the sun would have a volume of:

= 1.41 * 10^18 - (99.9999999999999 / 100 * 1.41 * 10^18)

~1410 km3.

In theory, if we could some how squeeze together all the atoms that contribute the sun, we could fit all these atoms inside less than half the volume of Lake Michigan (the 5th largest lake in the world) with a volume of 4918 km3.

In conclusion, the sun is truly a mind-blowing natural phenomenon. And, we need to understand and accept the fact that despite all that we know so far about the universe, there is still a long, long way to go.

References:

1. Kasting, J.F.; Ackerman, T.P. (1986). "Climatic Consequences of Very High Carbon Dioxide Levels in the Earth's Early Atmosphere".Science234(4782): 1383–1385.doi:10.1126/science.11539665.PMID11539665.
2. "DOE looks again at inertial fusion as potential clean-energy source", David Kramer,Physics Today, March 2011, p 26
3. S. Atzeni, J. Meyer-ter-Vehn (2004). Chapter 1: "Nuclear fusion reactions". The Physics of Inertial Fusion. University of Oxford Press.ISBN 978-0-19-856264-1
4. Ueno, Y.; Johnson, M. S.; Danielache, S. O.; Eskebjerg, C.; Pandey, A.; Yoshida, N. (August 2009). "Geological sulfur isotopes indicate elevated OCS in the Archean atmosphere, solving faint young sun paradox Ueno, Y.; Johnson, M. S.; Danielache, S. O.; Eskebjerg, C.; Pandey, A.; Yoshida, N.". Proceedings of the National Academy of Sciences 106 (35): 14784–14789. Bibcode:2009PNAS..10614784U. doi:10.1073/pnas.0903518106.
5. Schröder, K.-P.; Connon Smith, Robert (2008), "Distant future of the Sun and Earth revisited", Monthly Notices of the Royal Astronomical Society 386 (1): 155–163, arXiv:0801.4031, Bibcode:2008MNRAS.386..155S, doi:10.1111/j.1365-2966.2008.13022.x
6. Shultis, J.K. and Faw, R.E. (2002). Fundamentals of nuclear science and engineering. CRC Press. p. 151. ISBN 0-8247-0834-2.
7. Appenzeller; Harwit; Kippenhahn; Strittmatter; Trimble, eds. (1998). Astrophysics Library (3rd ed.). New York: Springer. ISBN.
8. Ostlie, D.A. & Carroll, B.W. (2007). An Introduction to Modern Stellar Astrophysics. Addison Wesley, San Francisco. ISBN 0-8053-0348-0.
9. "Sunspots". NOAA. Retrieved 22 February 2013.
10. Sagan, C.; Mullen, G. (1972). "Earth and Mars: Evolution of Atmospheres and Surface Temperatures". Science 177 (4043): 52–56. Bibcode:1972Sci...177...52S. doi:10.1126/science.177.4043.52. PMID 17756316.
11. Czechowski, L., 2006, Parameterized model of convection driven by tidal and radiogenic heating, Adv. Space Res, 38, 4, 788-793
12. Peale, S.J. Tidally induced volcanism. Celest. Mech. & Dyn. Astr. 87, 129–155, 2003.
13. Walker, James C. G. (June 1985). "Carbon dioxide on the early earth" (PDF). Origins of Life and Evolution of the Biosphere 16 (2): 117–127. Bibcode:1985OLEB...16..117W. doi:10.1007/BF01809466. Retrieved 2010-01-30.
14. Pavlov, Alexander A.; Kasting, James F.; Brown, Lisa L.; Rages, Kathy A.; Freedman, Richard (May 2000). "Greenhouse warming by CH4 in the atmosphere of early Earth". Journal of Geophysical Research 105 (E5): 11981–11990.
15. Arevalo Jr, R., McDonough, W. F., & Luong, M. (2009). The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution. Earth and Planetary Science Letters, 278(3), 361–369

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[*]Hubert Bray is a Professor of Mathematics and Physics at Duke University

[**]The class is a seminar on introductory astrophysics called Math 89S at Duke University

[*] a very large star of high luminosity and low surface temperature. Red giants are thought to be in a late stage of evolution when no hydrogen remains in the core to fuel nuclear fusion.

[*] A corona (Latin, 'crown') is an aura of plasma that surrounds the sun and other celestial bodies. The Sun's corona extends millions of kilometers into space and is most easily seen during a total solar eclipse

[1]Here’s an example of how advanced our space detecting systems can be

[*]angular velocity (w) = linear velocity(v) / radius of circular path (r)