[3.0] Stellar Mechanics & Evolution (1)

v3.3.0 / chapter 3 of 10 / 01 jan 18 / greg goebel

* Stars are born, live, and die. This chapter and the next discusses the evolution of stars, with this chapter focusing on their birth, the evolution of small and medium-sized stars, and why some stars pulsate on a regular basis.

star birth clouds in Eagle Nebula



* Modern astronomy traces the origin of the Universe to an instant about 14 billion years ago in the explosive Big Bang. At the first moments of the Big Bang, the entire Universe was small, very hot, and very dense. As it expanded, it cooled, and particles, then eventually hydrogen, some helium, and a trace of lithium congealed out of the fireball. Eventually this primordial matter collapsed into stars and systems of stars, the galaxies. The galaxies are continuing to expand outward in space.

The stars performed nuclear fusion reactions in their cores, creating "metal" elements such as carbon and oxygen heavier than helium. Big stars live short lives, and they eventually exploded, seeding space with constituents of new stars and the heavier elements needed to create rocky planets and biological organisms. Star formation continues today, though clearly at a much lower overall rate than existed in the first generation of star formation.

* The hydrogen and helium created in the Big Bang and the much smaller concentrations of "metals" created by stars afterward are now scattered through space. Most of the material is still hydrogen, existing as an exceedingly thin gas known as the "interstellar medium". Light and radiation from stars breaks up molecules and so most of the interstellar medium is in the form of monatomic hydrogen.

Our Milky Way Galaxy is a great pinwheel structure with spiral arms. These arms are created by a wave of gravitational forces passing around the spiral, and cause the interstellar medium to collect into much denser clouds of gases and dust, increasingly bound by their own gravitational force. These clouds become dense enough to block out light and other radiation that heat them up and cause them to disperse. Molecules can also form inside such cold dark clouds, and so they are known as "molecular clouds".

Molecular clouds can be huge, hundreds of light-years across, and despite the fact that they are still pretty good vacuums by Earthly standards, they can be very opaque. In its early days a molecular cloud is very dark, blocking out stars beyond them and cloaking their interiors. Such "dark nebulas" appear as a simple black void in space. The most prominent of these quiescent dark nebulas is the "Coal Sack", which appears in the skies of the Southern Hemisphere as a region distinctly empty of stars.

Until the 1980s, much more was known about the origin of the Universe in the Big Bang than was known about the origins of star systems in molecular clouds. Molecular clouds can be observed at millimeter wavelengths, between the microwave radio and the infrared bands. Trace gases such as carbon monoxide and carbon monosulfide have prominent spectral lines in the millimeter wavelengths, and in the past few decades millimeter-wave observatories have revealed a great deal about the events inside of molecular clouds.

A molecular cloud can remain stable and dark for millions of years, but it will eventually begin to collapse into itself under its own gravity. Hydrogen, the predominant element in such molecular clouds, tends to gather into masses known as "molecular cores" or "dense cores". These dense cores are a few light months across and are only at about 10 degrees Kelvin. The dense cores are normally stabilized against further collapse by processes that are not very well understood. For reasons which are also not very well understood, possibly the influence of a shock wave from a supernova, the dense core then begins to collapse further. As the core collapses, some gas flows will fall in directly, while others that had a tangential velocity component will be gradually draw into a spiral disk of material, with a hot dense "protostar" forming in the center.

Magnetic forces set up by the disk of swirling material focus material pouring out of the center of the disk into two energetic and opposed "jets" from the poles of the forming protostar. The jets can be several light-years long. The heated gas in the jets can clump into knots, or accumulate where the front of a jet plows into the molecular cloud, forming a "hot spot".

These hot spots once created a degree of confusion. They were independently observed by an American astronomer named George H. Herbig (1920:2013) and a Mexican astronomer named Guillermo Haro (1913:1988) in the early 1950s, and were known as "Herbig-Haro objects" as a result. They were thought to be stars in the process of formation for about two decades, until observations in the 1970s and early 1980s demonstrated the Herbig-Haro objects were associated with outward flows from a central protostar.

In any case, the central protostar grows hotter and brighter from the energy of its collapse. Such protostars grow large and very luminous, even though nuclear reactions haven't started. They still cannot be seen with optical telescopes, though an infrared telescope can detect the hot mass forming inside the dark nebula.

When the protostar reaches a total mass of a few tenths that of our own Sun, its core temperature climbs to about 1 million degrees Kelvin and fusion begins. However, this initial fusion reaction is based on the fusion of deuterium, not hydrogen. Normal hydrogen has a nucleus consisting of a single proton. Deuterium, also known as "heavy hydrogen", is a hydrogen isotope that has a nucleus of a proton and a neutron. About one deuterium nucleus was created in the Big Bang for every 50,000 hydrogen nuclei. As hydrogen-bomb developers learned, deuterium undergoes fusion at lower temperatures than hydrogen, and so deuterium fusion begins first. As the hydrogen-bomb developers also knew, deuterium fusion liberates plenty of energy. Deuterium fusion takes place in the core of the protostar, and the energy released cannot simply shine away through the upper layers of the protostar. Instead, the energy creates "convection currents" through the protostar's upper layers, with a vertical flow of material feeding more deuterium into the core.

Deuterium burning makes the protostar swell. A protostar with the mass of our Sun will have a diameter five times greater than that of our Sun. The enhanced energy production also contributes to a strong "stellar wind" that drives back matter falling towards the protostar, incidentally shutting off the polar jets as the mass flow into the protostar falls off. While the exact mechanisms that produce the wind are not well understood, it is clear that the winds drive away the molecular cloud and the newborn star becomes visible. The disk around the star similar begins to accumulate into planets.

The newborn star is called a "pre-main-sequence" star. It is extremely bright, though not from deuterium burning since by this time most of the reactive and relatively scarce deuterium has been burned up. The pre-main sequence star glows brightly from the thermal energy produced by the gravitational collapse that formed it. On the HR diagram, pre-main sequence stars occupy their own region in the upper left "hot and bright" corner. As mentioned earlier, such young stars are unsurprisingly unstable and are often irregular variables. They also have strong stellar winds.

These objects don't remain off the main sequence for very long. Gravitational collapse continues after the end of deuterium burning until the core temperature reaches about 10 million degrees Kelvin and normal hydrogen fusion begins. Four protons fuse into a helium nucleus, or "alpha particle", which consists of two protons and two neutrons, and incidentally emit two positive electrons or "positrons", two insubstantial neutrinos, and energy.

There are a number of different ways hydrogen fusion can take place. The simplest is the "proton-proton (PP) chain" reaction:

   proton + proton -> H2 + positron + neutrino
   H2 + proton     -> He3 + gamma_ray
   He3 + He3       -> He4 + proton + proton

The term "H2" means a deuterium nucleus, with a neutron and a proton, while "He3" means a helium isotope with two protons and a neutron, and "He4" means a normal helium nucleus with two protons and two neutrons. In the first generation of stars, when no "metals" were present, this was the only possible hydrogen fusion reaction. In stars where traces of heavier elements were present, hydrogen fusion could also proceed by alternate paths.

There are two alternate paths that have low probability of occurrence and are of little importance, one involving the synthesis of beryllium and then lithium, followed by the breakdown of lithium into two helium nuclei; the other involving the synthesis of beryllium and then boron, followed by the breakdown of boron into two helium nuclei. However, another alternate path, known as the "carbon-nitrogen-oxygen (CNO) cycle", is very important:

   C12 + proton -> N13 + gamma_ray
   N13          -> C13 + positron + neutrino
   C13 + proton -> N14 + gamma_ray
   N14 + proton -> O15 + gamma_ray
   O15          -> N15 + positron + neutrino
   N15 + proton -> C12 + He4

This reaction also has some low-probability alternate paths that will not be described here. In any case, the PP chain predominates at the lower end of the fusion temperature range, while the CNO cycle predominates at the higher end of the fusion temperature range. The CNO cycle releases slightly less energy than the PP chain.

* Once hydrogen fusion begins, the radius of the star falls, and the star enters the main sequence. The path that the adolescent star took through the HR diagram from its emergence as a protostar to its graduation to the main sequence is known as the "Hayashi track", after Japanese astrophysicist Chushiro Hayashi (1920:2010), who investigated pre-main sequence stars in the 1960s. Our own Sun spent about 30 million years on the Hayashi track, a short time in the cosmic scheme of things.

In any case, as stars form in a molecular clouds they gradually evaporate the cloud around them, emerging in the form of a brilliant, compact "open" star cluster. The nearby Orion Nebula is a neat example of this process in action, and in fact one of the Orion Nebula's stars is believed to have only begun fusion reactions a few thousand years ago. This particular star can only be detected in the infrared at present, but it should emerge in due time.

star-forming region in NGC3063

Eventually the cloud will dissipate, leaving only a bright star cluster. Since such open star clusters are relatively small in mass, they are only loosely bound by gravity and the random motions of their stars cause them to gradually dissipate. The neat pattern of stars in the core of the Orion Nebula, the Trapezium, is a very young star cluster, while the Pleiades are somewhat older, having mostly emerged from their nebular nest, and the "Hyades", the "horns" of the constellation Taurus, have spread apart somewhat. Incidentally, although the Pleiades is surrounded by a nebula that gives it its beautiful shimmering appearance, that nebula is not a remnant of the one that gave rise to the star cluster; the star cluster actually collided with a separate nebula, or rather two of them.

The dynamics of protostar creation in molecular clouds seem to often lead to the formation of binary or multiple systems. The precise mechanisms that cause this to happen are not well understood.



* The path a star takes once it enters the main sequence depends strongly on its mass. Small stars continue hydrogen burning at a low rate, living very long lives as red dwarfs, eventually exhausting their hydrogen fuel and simply fading away into darkness. Astronomers believe they will end up as burned-out cinders known as "black dwarfs", but given how long red dwarfs live there are few, if any, black dwarfs in existence in the current era.

Long before red dwarfs fade out, the larger stars live out their life cycles. The bigger a star is, the faster it burns up its hydrogen, but large stars have further options for energy production.

As a star ages, it accumulates helium in its core as "ash" from hydrogen fusion, and hydrogen fusion continues in a shell around that core. This hydrogen-burning shell continues to grow larger as the core grows larger, and the star correspondingly grows larger and brighter, as its larger surface area allows it to emit more light.

A star the size of our Sun will burn hydrogen for about 10 billion years. Once the star burns up its hydrogen, it begins to collapse in on itself. The pressure and temperature in the helium core rise until at a temperature of 100 million degrees Kelvin, helium begins to undergo fusion itself. The core shrinks, becoming hotter, to dump the heat into the outer layers of the star -- which causes them to expand monstrously, resulting in a red giant star. Despite the greater energy output at the core, the red giant is relatively cool because the energy is being dispersed over a much greater surface area -- double the radius of a sphere and the surface area goes up by a factor of four. However, the increase in energy and surface area also results in an increase in overall luminosity. The pressure of radiation due to the increased luminosity tends to increase the amount of mass lost to the "stellar wind", with the loss rate increasing with the mass of the star.

The red giant has helium fusion in progress at its core, with hydrogen fusion continuing in a growing shell around the core. Although hydrogen fusion had been understood in general terms by Arthur Stanley Eddington and its details clarified by Gamow and others, it wasn't until the 1950s that fusion processes beyond those of hydrogen fusion were understood, the critical document being a 1957 paper by the astrophysicists Geoffrey Burbidge (1925:2010), his wife Margaret Burbidge (born 1919), Willy Fowler (1911:1995), and Fred Hoyle (1915:2001). Fowler would share the 1983 Nobel prize with Subrahmanyan Chandrasekhar for his investigations of stellar astrophysics.

The original obstacle in figuring out helium fusion was that it was known that an atomic nucleus with an atomic number of five -- two protons and three neutrons, three protons and two neutrons, or whatever -- is completely unstable. It can't exist, it can't be formed, and so helium fusion could not operate by simply adding another neutron or proton to a helium nucleus.

What actually happens in helium fusion is that three helium nuclei collide, creating a carbon nucleus. That's the simple explanation. The collision of the three helium nuclei actually has a very low probability of happening at once, and so in the majority of cases two helium nuclei collide to form a transient beryllium-8 nucleus, which then absorbs another helium nucleus to form carbon.

From a physicist's point of view, this is still something of a freak occurrence, since beryllium-8 breaks down in 10E-19 second; it's so unstable that the impact of a third helium nucleus would seem likely to simply break it apart again. However, the merging of three helium nuclei forms a "carbon resonance" that energetically makes it easier for the three to stay together than fall apart, permitting the formation of a carbon nucleus. Even this series of events has a very low probability, but at high enough temperatures the number of collisions is so great that it happens on a regular basis. The carbon resonance is regarded as fortunate, since if it didn't happen, synthesis of the elements would be hard-pressed to get through the beryllium-8 bottleneck.

Another helium nucleus can collide with the carbon nucleus, producing an oxygen nucleus. These reactions can be summarized in a simplified form as follows:

   He4 + He4 + He4 -> C12 + gamma_ray
   He4 + C12       -> O16 + gamma_ray

This sequence of reactions accounts for the fact that carbon and oxygen are relatively common in the Universe. Lithium, beryllium, and boron have smaller nuclei than carbon, but they are not heavily produced by stars and are much less common than carbon.

Hoyle provided the vital insight into this process, and his rival and friend George Gamow decided to write a parody of the book of Genesis in his honor:


In the excitement of counting, [the Lord] missed calling for mass five and so, naturally no heavier elements could have been formed. God was very much disappointed, and wanted first to contract the Universe again, and to start all over from the beginning. But it would be much too simple. Thus, being almighty, God decided to correct His mistake in a most improbable way. And God said: "Let there be Hoyle." And there was Hoyle. And God looked at Hoyle ... And told him to make heavy elements any way he pleased.


* A star about the size of our Sun will live as a red giant for a few hundred million years, a short time by cosmic standards. As it ages, its core burning gets hotter and hotter, increasing the radiation pressure and driving off its outer layers, forming an expanding shell of gas, a "planetary nebula", mentioned earlier. As the star ultimately fizzles out, its remains shrink into a superdense white dwarf.

Planetary nebulas are common but faint and hard to see. The nearby "Helix Nebula (NGC 7293)", covers an area of the sky as big as the full Moon, but it is completely invisible to the naked eye. Planetary nebulas may grow to several light-years in size before they dissipate. Their age can be calculated from the size of the nebula and its rate of expansion, and their ages have been measured to in a few thousands to a few tens of thousands of years. Planetary nebulas are a very short-lived phenomenon in cosmic terms.

The "Ring Nebula (M57)" in the constellation Lyra, discovered in 1779, is regarded as something of an archetype of planetary nebulas. The Ring Nebula is about 1,000 to 2,000 light years away and is hundreds of times bigger than our solar system. It appears as a neat ring with a central star and what appears a faint surrounding halo of gas. The central star ionizes the atoms in the nebula, stripping the electrons off the atoms, and when they recombine, they emit light, causing the nebula to glow. Interestingly, the central star of a planetary nebula always seems to have a mass of about 0.6 Suns, no matter how big the precursor star was.

Spectral analysis of the light from a planetary nebula shows it to generally match the composition of an older star, consisting of about 70% hydrogen, 28% helium, and the rest various "metals", particularly carbon, nitrogen, and oxygen. That implies that the nebula includes materials from the very core of the star. Since planetary nebulas do not seem to be created by explosive events, this hints at strong convection processes in old stars.

The neat ringlike appearance of the Ring Nebula suggests that the entire nebula is in the form of a sphere around the dying central star, appearing as a ring due to higher density of gaseous as seen through the edge of the sphere. However, analysis shows that the edge of the ring is much brighter compared to the interior regions than it should be if that were the case. The appearance of the Ring Nebula also changes depending on the wavelengths in which it is observed, and it has variously been modeled as a sphere, a ring, a torus, an ellipsoid, and an hourglass shape.

In fact, different planetary nebulas can have wildly different appearances, as thoroughly confirmed by spectacular images obtained in the late 1990s by the US National Aeronautics & Space Administration's (NASA) orbiting Hubble Space Telescope -- named after the American astronomer Edwin Powell Hubble (1889:1953), with more said about Hubble later. Some planetary nebulas clearly have an hourglass shape, due to stellar emission confined to particular planes or poles, possibly by dust clouds around the equator of the host star; the effect of stellar or substellar companions in the star system; or interactions with a dense interstellar medium. Whether planetary nebulas have a wide variety of structures, or whether we are simply observing a common structure from different angles, is not known. They do often have clearly irregular features due to instabilities in the star producing them.

The Hubble images seem to show that planetary nebulas are structured into several irregularly spaced layers, implying that the star creates the nebula in a "fits and starts" fashion, and the images also have provided new details on lumps of gas associated with such nebulas, known as "fast, low-ionization emission regions (FLIERs)".

Hourglass Nebula

* The Sun will end in such a fashion. The Sun is now about 4.5 billion years old, a little less than half of its lifetime as a hydrogen-burning star. The Universe had been around for 10 billion years before the creation of the Sun, and our Sun incorporates "metals" created by earlier generations of stars. It is a measure of the relative scarcity of such heavier elements that the Sun is still mostly hydrogen, some helium, and traces of everything else.

In the beginning, when the Sun entered the main sequence, it was only 70% as luminous as it is now. In 1.1 billion years, the expansion of its hydrogen-burning shell will make it 10% more luminous than it is know. It will be 2.2 times more luminous 6.5 billion years from now, just before it exhausts its hydrogen fuel. With the end of hydrogen burning, the Sun will leave the main sequence and become a red giant star, expanding in another 1.3 billion years to 170 times its current diameter, engulfing Mercury. It will then shrink and remain stable for about 120 million years, and then expand again to the diameter of the current orbit of the Earth.

The Earth will not be engulfed. By this time, the Sun will have shed considerable mass, and the Earth will be in an orbit with a diameter 1.7 times wider than now. However, the red giant Sun will be 5,200 times more luminous, and the Earth will have a surface temperature of about 1,600 degrees Kelvin, reducing it to a ball of red-hot molten rock.

The Sun will only remain a red giant for a few million years. It will then shed its outer layers, creating a planetary nebula, and shrivel into a small, dense, hot white dwarf. The planets will be frozen and barren.



* One of the puzzles of stellar evolution are the pulsating variable stars. The vast majority of stars are stable, with such oscillations damped out. Why do a few of them pulsate?

Analysis of pulsating stars shows that the oscillations do not occur in the star's interior, but are confined to the outer layers. The outer layers contract and heat, then expand and cool. As the outer layers contract, the rising temperature leads to full ionization of helium atoms, stripping them of both electrons, which are absorb excess energy being pumped into them by the contraction. This energy is not radiated away into space, instead being absorbed in the layer where the ionization takes place. This forces the outer layers to expand and cool. As they cool, electrons recombine with helium nuclei, and the cycle starts over again.

This process is dependent on the star's temperature. In a cool star, the ionized helium layer is so deep that it cannot move the mass of stellar material above it. In a hot star, the ionized helium layer is so close to the surface that oscillations are not set up. In practice, this means that only stars within a certain limited range of temperatures pulsate. The average value of this range of temperatures decreases as the size of the star increases, forming a narrow and linear "instability strip" on the HR diagram.

HR diagram / pulsating stars

This also means that variability is not necessarily associated with any particular phase in a star's life, or its composition. If a star becomes hot enough relative to its size, its outer layers pulsate, no matter what is going on in the star's core.

Since the instability strip is narrow, variability tends to be short-lived on the cosmic time scale. In fact, in the 1960s, the pulsating variable RU Camelopardis surprised astronomers by suddenly ending its pulsations. It has sputtered momentarily into pulsations again, but so far has always stopped.

The behavior of Polaris also suggests the transient nature of instability, if in a subtler fashion. Its four-day period lengthens by 8 seconds every year, and though its brightness changed by 15% over the course of its period a century ago, the variation is only 2% now, suggesting that it may stop pulsating in the relatively near future. It is also 15% brighter now than it was a century ago -- and if the measurements of Ptolemy are anywhere near valid, about twice as bright as it was two millennia ago.