Stellar evolution is a specialist area of astrophysics concerned with the aging of different masses of stars, and their ultimate fates. It is generally approached using analysis of complex stellar models, see e,g.
But we confine attention here to gross properties and how they are assessed using the tool of the Hertzsprung -Russell (H-R) diagram, one example of which is shown above. This particular diagram shows an "evolutionary track" for our own star, the Sun. That is, an extended lifetime path from stellar birth to its death as a white dwarf.
In the diagram there are two “quality dimensions”- displayed on the vertical axis and on the horizontal. In this case, the “Absolute magnitude” value (M) on the vertical represents a measure of absolute brightness and doubles as an index for what we call Luminosity (L).. In terms of absolute magnitude the lower the value, the greater the brightness. The scale is also logarithmic, so that a star of (-10) say will always be 100 times brighter than a star of (-5). So five magnitudes difference in M corresponds to 100 times brightness ratio. Thus, every single magnitude arithmetic difference will be a ratio of 2.512 times.
The other quality dimension is the horizontal axis which is labeled in capital letters associated with the spectral class. In terms of this lettering, class O stars are always the hottest, and class M the coolest. Thus, we have also can double the spectral class as a temperature scale (top of diagram). Within this representation framework all the key domains - star colors, star ages, star distances, star energy use, can be integrated and depicted in their relations if one can interpret the quality axis properly and use them in specific ways.
Stellar ages enter via the position a star’s evolutionary track (makes with a band called “the Main Sequence” – with the latter being the superposed domain for all stable stars. On the main sequence we have what is called a pressure-gravity balance so the star is maintained in a state of equilibrium.
dP/dr = - G M(r) r / r2
So that the outward (radiation) gas pressure(P) is balanced by the inner directed gravitational pull from the star's layers. Another equation makes use of the fact that a star’s luminosity is produced through the consumption of its own mass. This may be expressed mathematically as:
dL/dM = e
where e denotes the rate of energy generation. For the proton-proton cycle (for stars like the Sun- and designed for cgs units!):
e= 2.5 x 106 (r X2).· (106 /T)2/3 exp[-33.8(106 /T)1/3]
The faster the rate of energy generation the more rapid the star's evolution.
In the case of the proton-proton cycle we are looking at the steady depletion of the Sun's hydrogen fuel. When only ten percent hydrogen remains (X= 0.10, Y = 0.87 for fractional abundances, say), the Sun is no longer able to generate sufficient energy from its core nuclear reactions to balance the weight of overlying layers. According to a well-known physical principle (the virial theorem), the Sun’s core must contract. The contraction converts gravitational potential energy into thermal (heat) energy that heats the core.[1] By now, hydrogen burning has moved to a peripheral shell around the core, and is ignited by the core heating process.
The ignition creates radiation pressure that forces the outer shells, layers to expand. This same radiation, however, is now emitted from a much larger surface area. The result of this combination of circumstances is that the Sun becomes a Red Giant.
The details and theoretical consistency of such diagrams are generally checked by plotting brightness (on the stellar magnitude scale) and spectral index or color index (B-V)[2] for a variety of open star clusters, such as the Pleiades.
Going back to the H-R diagram, the dot on the Main Sequence indicates roughly where the Sun is currently in its evolution. As can be seen, its path to the Red Giant (R)region remains ahead of it, as does its subsequent collapse to a compressed white dwarf star, with the track veering down and to the left.
In the case of a star much more massive than the Sun (say more than ten times the solar mass), pre-Main Sequence collapse also occurs within an interstellar gas and dust cloud, but the Main Sequence is joined at a higher position, corresponding to greater luminosity. Astronomers have determined a basic empirical relation for mass and luminosity to be:
L = (M’/M) 3.5
That is, the luminosity is proportional to the mass raised to the 3.5 power. What this also means is that the massive star initiates its Main Sequence lifetime at higher temperatures, including higher core temperatures. In most applications the equation is used in a ratio form, say for comparing one star's mass with the Sun's (as a standard). Then we would have:
L’/L = (M’/M) 3.5
Or Log (L’/L) = 3.5 Log (M’/M)
where L, M refer to solar luminosity and mass values and L', M' to stellar values. The equation enables us to infer the actual brightness of a main sequence star based on its mass, and also to compare stellar luminosities (intrinsic brightnesses) and deduce other stellar properties such as mass and radius.
As an illustration, say that we observe the intrinsic brightness (luminosity) of Regulus to be greater than the Sun's by a factor 120. Then we can find the approximate mass of Regulus.
Here: L'/L = 120 so Log (120) = 3.5 Log (M'/ M)
and we are seeking to find M' in terms of M.
Log (120) = 2.079 = 3.5 Log (M'/ M)
Or:
0.594 = Log (M'/M)
Taking antilogs of each side:
3.93 = (M'/M) or M' = 3.93 M
So Regulus is approximately 4 times the mass of the Sun.
0.594 = Log (M'/M)
Taking antilogs of each side:
3.93 = (M'/M) or M' = 3.93 M
So Regulus is approximately 4 times the mass of the Sun.
This means, of course, that it will evolve more rapidly given the increased mass.
In massive stars, fusion reactions are much more diverse than in the Sun because a far more diverse range of heavier elements is produced. A key transition point occurs after carbon is formed in the core, and reaches a critical density and temperature to detonate. The resulting deflagration, which includes the core separating from exploding outer layers, turns the star into an instant nuclear factory. Nickel and iron are formed as well as lighter elements in the shells including: magnesium, sulphur, silicon, manganese, chromium and a host of lesser atomic weight elements such as oxygen and nitrogen.
If the star survives carbon detonation, its end is still heralded by formation of nickel-iron in the core. The nuclear reactions become endothermic, absorbing energy instead of generating it. This means the star’s radiation, gas pressure supporting the outer layers is radically decreased. Collapse of the layers occurs, with oxygen ignited in one of them precipitating the spectacular explosion we call a supernova. One of the most recent significant events was designated 1987A, in The Large Magellanic Cloud. Gamma ray line radiation from the decay of Cobalt 56 (Co 56)was detected in this event[3], indicating that indeed it had been precipitated by formation of an unstable Nickel (Ni 56)core.
In such cosmic cataclysms the star's outer layers explode into space, while its core collapses to form a neutron star or black hole. It is the outer layers - containing magnesium, silicon, sulphur and especially carbon, expelled into space that set the stage for the future evolution of life on other worlds.
What is the importance of stellar evolution then? Just this: that biological life forms cannot arise unless the fundamental element for life - carbon, has been first manufactured in stars[4]. It also shows that the stars themselves evolve at different rates, the more massive stars at faster rates than the less massive (like the Sun). The role of massive stars, therefore, is to expedite elemental production and evolution by making available more complex elements -the building blocks for planets as well as life, on a more rapid time scale than would otherwise be possible.
Creationists contend that all stars were ‘created’ by some divine fiat in the past. However, this is refuted by the observational, astronomical evidence. The fact is that embryonic stars can be detected right now with infrared telescopes, as well as the Hubble Space Telescope, collapsing out of interstellar dust and gas analogous to phases 1 and 2 of the evolutionary track in the H-R diagram for the Sun. Some of these T Tauri stars are in the well-known Orion Nebula about 1600 light years away. On an H-R diagram like that shown for the Sun, these embryo stars would be on the track approaching the Main Sequence.
What is the importance of stellar evolution then? Just this: that biological life forms cannot arise unless the fundamental element for life - carbon, has been first manufactured in stars[4]. It also shows that the stars themselves evolve at different rates, the more massive stars at faster rates than the less massive (like the Sun). The role of massive stars, therefore, is to expedite elemental production and evolution by making available more complex elements -the building blocks for planets as well as life, on a more rapid time scale than would otherwise be possible.
Creationists contend that all stars were ‘created’ by some divine fiat in the past. However, this is refuted by the observational, astronomical evidence. The fact is that embryonic stars can be detected right now with infrared telescopes, as well as the Hubble Space Telescope, collapsing out of interstellar dust and gas analogous to phases 1 and 2 of the evolutionary track in the H-R diagram for the Sun. Some of these T Tauri stars are in the well-known Orion Nebula about 1600 light years away. On an H-R diagram like that shown for the Sun, these embryo stars would be on the track approaching the Main Sequence.
The T Tauri and other observations clearly demonstrate that creationism can’t be valid. If it were, no new stars should be forming. This is only one contradiction arising when the scrolls of unscientific nomads are accepted too literally. Another example is the Genesis account that Earth was formed before the Sun (the "light to rule the day"). Logically, however, the Sun had to form before any planets, since vegetation can’t exist without benefit of photosynthesis - which depends on sunlight. Also, it’s impossible for a planet to exist by definition without a Sun to revolve around! Planets require a massive object to provide the centripetal acceleration to enable them to remain in orbit.
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[1] According to the virial theorem: 2K + W = 0 for any spherical system in equilibrium, where K is the gas kinetic energy (K = 3/2(y-1)U) and W is the gravitational potential energy. From this one can obtain the binding (or total) energy of a star as: E(S)= K + W. Combining the two equations, E(S) = W/ 2 = -K. Thus, the total energy of the star is negative and equal to half the gravitational potential energy, or the negative of the gas kinetic. Hence, if E(S) decreases, K increases, but W decreases, i.e. contraction.
[2] The (B-V) index uses the difference in apparent magnitudes between the blue spectral region and the violet (m_B – m_V).
[3] Arnett, D. and Bazan, G.: Nucleosynthesis in Stars: Some Recent Developments, in Science, Vol. 276, 30 May, 1997, p. 1359.
[4] The primary elements formed in the immediate aftermath of the Big Bang were hydrogen and helium. So, in the ‘beginning’, there was really nothing – no building blocks from which life could emerge. This had to await the first stars.
[2] The (B-V) index uses the difference in apparent magnitudes between the blue spectral region and the violet (m_B – m_V).
[3] Arnett, D. and Bazan, G.: Nucleosynthesis in Stars: Some Recent Developments, in Science, Vol. 276, 30 May, 1997, p. 1359.
[4] The primary elements formed in the immediate aftermath of the Big Bang were hydrogen and helium. So, in the ‘beginning’, there was really nothing – no building blocks from which life could emerge. This had to await the first stars.
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