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The Life Of A Star

Updated: Jul 5, 2022

Stars were one of the very first majestic celestial beings to be born in the early universe and are warehouses for the synthesis of elements. Every element heavier than hydrogen was once synthesized in a star. As Neil Degrasse Tyson said, “The atoms of our bodies are traceable to stars that manufactured them in their cores and exploded these enriched ingredients across our galaxy, billions of years ago ... And we are atomically connected to all atoms in the universe. We are not figuratively, but literally, stardust.”


So, let’s talk about the different stages of evolution in the life of a star, from its origin in molecular gas clouds to its retirement.


One of the most active sites of star formation is the Orion Nebula, a molecular gas cloud in the Orion constellation. A small perturbation or turbulence in a giant molecular gas cloud creates over-densities, which lead to gravitational collapse of the cloud forming a dense ball called the protostar [1], a very young star that is still gathering mass from its parent cloud. The proto-stellar phase is the earliest one in the process of stellar evolution.

An active site of star formation, the Orion Nebula (Credit: NASA) and an artist illustration of an accreting protostar. (https://planetfacts.org/protostar/)


The time it takes for a protostar to be formed out of the molecular cloud, under the influence of gravitational attraction is called the free-fall time, and it depends on the initial density of the cloud [2]. The heat generated in the ball due to gravitational pressure is initially released back into the molecular cloud, but as density increases, the outer layers of the ball become increasingly opaque, trapping the heat in its core [3].


Not every molecular cloud will collapse into a protostar. The criteria that determine whether a cloud will collapse into a protostar or not is called the Jeans instability, named after the English physicist Sir James Hopwood Jeans. In his analysis of the stability of a spherical nebula, Jeans showed that for the molecular cloud to be stable, the gas needs to be in a hydrostatic equilibrium, which means that the internal gas pressure should be equivalent to the gravitational pressure of the cloud [4]. A cloud of small enough mass and volume remains stable, but once it passes a critical mass and length, which he defined as Jeans mass and Jeans length, respectively, the cloud will begin to contract unless some other force is able to counter the gravitational collapse. With advancements in the understanding of pre-stellar evolution, astrophysicists debated on the Jeans Instability and its mathematical derivability. They named it the “Jeans Swindle,” and the Jeans instability equations continue to be analyzed as new findings come to light [5, 6, 7].

Diagram showing the evolution of the protostar from its initial collapse to the main sequence where stars live most of their lives. (https://astronomy.swin.edu.au/cosmos/z/Zero+Age+Main+Sequence)


Once a gas cloud takes the form of a protostar, the different stages of its evolution can easily be visualized using the Hertzsprung-Russell diagram (H-R diagram) [8], a graph with the absolute magnitude or luminosity, which is the light emitted by the star, at the y-axis and the temperature of the star at the x-axis. The temperature increases from right to left and the luminosity increases from bottom to top. A newborn star starts its journey from the bottom of the graph, with low temperature and luminosity. A star’s luminosity depends on the radius and temperature of the star. A lower temperature implies a larger radius, and vice versa [9].

Hertzsprung-Russell diagram showing the entire life cycle of a star. (https://www.universetoday.com/39974/hertzsprung-russell-diagram/)


The protostar continues to contract but much more slowly, during which it follows the Hayashi track downwards, as described by Professor Chushiro Hayashi in 1916 [10]. The protostar becomes several times less luminous while staying at roughly the same surface temperature until either of two circumstances occur. One, a radiative zone develops, after which stars greater than 0.5 times the mass of our Sun follow the Henyey track, as described by astronomer Louis G. Henyey and his colleagues in 1955 [11]. Second, a nuclear fusion begins, which marks the star’s entry into the main sequence. Henyey showed that protostars can remain in radiative equilibrium throughout a small period of its contraction as it enters the main sequence.

Hayashi track. (Credit: Pearson Education, https://home.strw.leidenuniv.nl/~nielsen/SSE17/lectures/Stellar_lecture_8-1.pdf). Forbidden Zone. (https://lweb.cfa.harvard.edu/COMPLETE/learn/protostars/protostar.html)


There is a so-called “Forbidden zone” towards the right of the Hayashi track, where no star can remain in a hydrostatic equilibrium and will try to move towards the left to become stable. The developments in understanding the pre-main-sequence stages of evolution are described in [12].


When the pressure and temperature at the star’s core are high enough for nuclear fusion to begin, the star finally enters the main sequence and is then called a zero-age main-sequence star. After this time the star enters a phase of stellar evolution that is quite stable, and steadily processes hydrogen into higher elements. Without differences in initial chemical composition or in rotational velocity, all the stars would originate from exactly this unique line. As the stars evolve, they adjust to the increase in the helium-to-hydrogen ratio in their cores and gradually move away from the zero-age main sequence [13].


A star spends most of its lifetime as part of a strip in the H-R Diagram called the Main Sequence. The mass, chemical composition, and age of the star determine its position on this strip. The star is said to be in Hydrostatic Equilibrium when the inward gravitational pressure is cancelled out by the outward thermal pressure from the nuclear energy generated in the core.

Visual example of hydrostatic equilibrium within the Sun. (Credit: woodahl.physics.iupui.edu)


The smallest theoretical mass for a star to support nuclear fusion in its core is around 0.08 solar masses [14]. Brown dwarfs are substellar objects that have a mass between the most massive gas giant planets and the least massive stars; they have a mass approximately 13 to 80 times that of Jupiter. Unlike main sequence stars, brown dwarfs do not acquire enough mass to trigger sustained nuclear fusion of ordinary hydrogen (1H) into helium in their cores. For this reason, brown dwarfs are sometimes referred to as failed stars. They are, however, thought to fuse deuterium (2H) and lithium (7Li) if their mass is more than 65 times that of Jupiter. This is what gives brown dwarfs their faint glow [15].

An artist illustration of a brown dwarf. (Credit: NASA/JPL-Caltech)


The main source of nuclear energy for a main-sequence star is produced by the hydrogen burning in its core at temperatures greater than 10^8 K or 10 million degrees Celsius. Hydrogen atoms fuse together to make helium, releasing huge amounts of energy in the process. This is also known as “rp-process” or rapid proton capture process [16]. The smallest stars only convert hydrogen into helium. In medium-sized stars like our Sun, when the hydrogen becomes depleted late in their lives, they can convert helium into oxygen and carbon.


A star is not a static object; there is a continuous churning of material in its interior. Due to temperature difference between the core and outer layers of a star, the two modes for transporting this energy are radiation and convection. The radiation zone is where energy is transported by radiation and is stable against convection or very little mixing of the plasma. In the convection zone, the energy is transported by the bulk movement of plasma, with hotter material rising to the surface and cooler material descending to the outer envelope of the inner layers [17].

An artist illustration of the different layers of the interiors of a star like our Sun. (Credit: Kelvinsong - Own work, CC BY-SA 3.0)


In massive stars with a mass greater than 10 times that of the Sun, an alternate process of helium generation is via the Carbon-Nitrogen-Oxygen (CNO) cycle. The rate of energy generation by the CNO cycle is very sensitive to temperature, so the fusion is highly concentrated at the core. Consequently, there is a high temperature gradient in the core region, which results in a convection zone for more efficient energy transport. This mixing of material around the core removes the helium ash from the hydrogen-burning region, allowing more of the hydrogen in the star to be consumed during the main-sequence lifetime. The outer regions of a massive star transport energy by radiation, with little or no convection. Unlike the proton-proton reaction, which consumes all its constituents, the CNO cycle is a catalytic cycle. In the CNO cycle, four protons fuse, using carbon, nitrogen, and oxygen isotopes as catalysts, each of which is consumed at a single step of the CNO cycle and is regenerated in a later step [18].

Hydrogen burning (https://www.forbes.com/sites/startswithabang/2017/09/05/the-suns-energy-doesnt-come-from-fusing-hydrogen-into-helium-mostly/?sh=1d00185f70f9) and the Carbon-Nitrogen-Oxygen cycle. (Credit: Borb - Own work based on: Fusion in the Sun)


The life span of a star depends on how massive it is. For our Sun, it could be around 10 billion years. The more massive a star, the shorter its life span as its nuclear material gets used up at a much higher rate than an average star. After using up most of the hydrogen fuel at its core, the star leaves the main sequence. This is referred to as the Turn Off Point for a star, which is a knee shaped curve at the top of the main sequence. At this stage, hydrogen is no longer the primary nuclear fuel in a star, and we can say that the star is officially retired from the main sequence.

Turn off point. (Credit: Brooks/Cole Thomson Learning)


Red dwarfs are another kind of peculiar stars. They are by far the most common type of stars in the Milky Way, but because of their low luminosity, individual red dwarfs cannot be easily observed [19]. The coolest red dwarfs have a surface temperature of around 2,000 K, and the smallest ones have radii of around 9% and masses about 7.5% that of the Sun.

An artist illustration of a red dwarf star. (https://www.spaceanswers.com/deep-space/red-dwarfs-the-fascinating-stars-that-live-for-trillions-of-years/)


Red dwarfs remain convective over most of their lives; they continue to burn hydrogen in their core for trillions of years. They do not experience red giant phases in their old age, which is why they are exceptions; they don’t have a turning point, but they slowly lose their luminosity and temperature and turn into blue dwarfs and then into white dwarfs. This also makes them one of the longest living stars in the Universe [20]. According to an article by Phil Plat of SYFY on red dwarfs, there are speculated to be around at least 100 billion red dwarf stars in the Milky Way alone [21].


Many processes in the evolutionary stages of a star are still a mystery, such as the stages of pre-main-sequence evolution, the hydrogen and helium burning processes in the outer envelopes, the different processes related to convection and mixing of nuclear material, and how different levels of initial mass and metallicities affect its evolution. These are all highly active and crucial subjects of research to better understand stellar evolution.



References


[1] McKee, C.F. and Ostriker, E.C., 2007. Theory of star formation. Annu. Rev. Astron. Astrophys., 45, pp.565-687.


[2] Stellar Structure and Evolution Kippenhahn, Rudolf; Weigert, Alfred. Springer-Verlag, 1994, 3rd Ed. p.257 ISBN 3-540-58013-1


[3] Hayashi, C., 1966. Evolution of protostars. Annual Review of Astronomy and Astrophysics, 4 (1), pp.171-192.


[4] Jeans, J.H., 1902. I. The stability of a spherical nebula. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 199 (312-320), pp.1-53.


[5] Falco, M., Hansen, S.H., Wojtak, R. and Mamon, G.A., 2013. Why does the Jeans Swindle work?. Monthly Notices of the Royal Astronomical Society: Letters, 431 (1), pp.L6-L9.


[6] Ershkovich, A.I., 2011. The" Jeans Swindle": the end of a myth?. arXiv preprint arXiv:1108.5519.


[7] Kremer, G.M., 2021. Jeans instability in an expanding universe with dissipation. arXiv preprint arXiv:2108.08068.


[8] Chiosi, C., Bertelli, G. and Bressan, A., 1992. New developments in understanding the HR diagram. Annual review of astronomy and astrophysics, 30 (1), pp.235-285.


[9] Myers, P.C., Adams, F.C., Chen, H. and Schaff, E., 1998. Evolution of the bolometric temperature and luminosity of young stellar objects. The Astrophysical Journal, 492(2), p.703.


[10] Hayashi, Chushiro (1961). "Stellar evolution in early phases of gravitational contraction". Publications of the Astronomical Society of Japan. 13: 450–452.


[11] Henyey, L. G.; Lelevier, R.; Levée, R. D. (1955). "The Early Phases of Stellar Evolution". Publications of the Astronomical Society of the Pacific. 67 (396): 154–160


[12] Palla, F., 2012, September. 1961–2011: Fifty years of Hayashi tracks. In AIP Conference Proceedings (Vol. 1480, No. 1, pp. 22-29). American Institute of Physics.


[13] Mengel, J.G., Sweigart, A.V., Demarque, P. and Gross, P.G., 1979. Stellar evolution from the zero-age main sequence. The Astrophysical Journal Supplement Series, 40, pp.733-791.


[14] Pinochet, J. (2019) “Brown dwarfs and the minimum mass of stars”, Physics Education. IOP Publishing, 54 (5), bl 055021.492


[15] Spiegel, D.S., Burrows, A. and Milsom, J.A., 2011. The deuterium-burning mass limit for brown dwarfs and giant planets. The Astrophysical Journal, 727 (1), p.57.


[16] Wallace, R.K. and Woosley, S.E., 1981. Explosive hydrogen burning. The Astrophysical Journal Supplement Series, 45, pp.389-420.


[17] Schwarzschild, M., 1961. Convection in Stars. The Astrophysical Journal, 134, p.1.


[18] Farrell, E., Groh, J., Meynet, G. and Eldridge, J.J., 2021. Understanding the evolution of massive stars. arXiv preprint arXiv:2109.02488.


[19] Henry, T.J., Kirkpatrick, J.D. and Simons, D.A., 1994. The solar neighborhood, 1: Standard spectral types (K5-M8) for northern dwarfs within eight parsecs. The Astronomical Journal, 108, pp.1437-1444.


[20] Adams, F.C., Laughlin, G. and Graves, G.J., 2004, December. Red dwarfs and the end of the main sequence. In Revista Mexicana de Astronomia y Astrofisica Conference Series (Vol. 22, pp. 46-49).


[21] Phil Plait (2019) Red dwarfs: tiny, faint, and loaded with planets [Online]. Available at: https://www.syfy.com/syfy-wire/red-dwarfs-tiny-faint-and-loaded-with-planets (Accessed: 12 December 2021)


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