Thursday, October 13, 2016

Supernovae PART 2: Low Mass Stars

For Supernovae PART 1: Introduction, click here.

Brown Dwarf Stars

The smallest mass that can form into a star is a brown dwarf.

A brown dwarf forms from a protostar mass less than 0.08 M (M = one solar mass or 2 x 1030 kg). This mass is on the edge between being a star and being a planet.

What distinguishes a brown dwarf as a star is its formation. Unlike a planet formed from the protoplanetary disk material around a star, a brown dwarf is formed in the manner described in PART 1. In this case, however, the star's core is too small to have sufficient pressure and heat to ignite the fusion of hydrogen into helium. Fusion does ignite, though. If the mass is at least 0.0125 M (about 13 times the mass of Jupiter), it will trigger the fusion of deuterium into helium, at least temporarily. Deuterium is a stable less abundant isotope of hydrogen that contains a proton as well as a neutron in its nucleus. This fusion reaction requires a lower ignition temperature - roughly 1 x 106 K compared to 4 x 106 K required for hydrogen fusion. This means that 0.0125 M is the smallest possible protostar mass that can evolve into a main-sequence star. Even a large-end brown dwarf will only shine very briefly and dimly. It will eventually cool and die gradually and peacefully into an inert mass. At first only theoretical objects, since the 1990's hundreds of brown dwarfs have been identified by infrared surveys. Almost impossible to see in visible light, the cores of brown dwarfs are compressed enough to emit heat, and that heat gives them away even long after deuterium fusion has fizzled out.

Red Dwarf Stars

A slightly higher mass protostar evolves into a red dwarf star. With a mass between about 0.08 M and 0.50 M, these stars are massive enough to fuse hydrogen into helium through the proton-proton chain reaction. An artist's conception of a typical red dwarf star is shown below right. Though called "red" dwarfs, the surface temperature of these stars means that they would look orange at close range.

Courtesy NASA
Red dwarfs with a mass less than 0.35 M are fully convective, and this makes them uniquely long-lived stars. The helium produced during fusion mixes throughout the star rather than building up in the core as it does with most larger stars. This means that a red dwarf makes thorough use of its hydrogen fuel. It evolves very slowly and maintains a constant luminosity for up to trillions of years before it leaves the main-sequence stage of its life. In main-sequence phase these stars are very dim, emitting between 1/10,000th up to 1/10th of the Sun's luminosity. Although red dwarfs are by far the most common stars in the universe, making up about 75% of all stars, they are difficult to observe. Only very young red dwarfs currently exist. After all, the universe is only 13.8 billion years old. Eventually a red dwarf will fuse all of its hydrogen into helium, end its main-sequence phase, and evolve into a helium white dwarf.

White Dwarf Stellar Remnants

A white dwarf is a stellar remnant. These stars cannot form directly in a nebular cloud. They are denser than any main-sequence star because they are composed of atomic nuclei packed together in a sea of free electrons rather than ordinary atomic matter. Intense force is needed to squeeze atomic matter into such a state. About 97% of the stars in the Milky Way, all stars too small to end up as neutron stars or black holes - from red dwarfs to stars ten times more massive than our Sun - will end up as white dwarfs. When a red dwarf burns up most of its hydrogen fuel, fusion begins to taper off. As the outward pressure from fusion decreases, the star (almost all helium by this time) is overcome by gravitational pressure. Electrons are forced down into orbitals closer and closer to the nuclei, similar to the kind of compression that happens when matter cools off but this case is unique. Even though the matter is compressed, thermal (outward) pressure decreases rather than increases as it normally would because atoms can't move around freely. This means that the core continues to contract. There is a limit to how close electrons can get, however. More than one electron cannot occupy the same quantum state in matter, according to the Pauli exclusion principle. This generates a counter pressure against further collapse. It is called electron degeneracy pressure because, as electrons are forced into lowest possible orbitals, they themselves move faster and faster, generating their own pressure. The helium nuclei at this point can no longer hold onto their electrons so a sea of free fast electrons forms, embedded with helium nuclei. Because it is not in an ordinary atomic state, electron degenerate matter cannot cool off like ordinary matter does. The star will continue to shine white-hot for billions of years and it will only very gradually cool to an inert black dwarf. Heat slowly diffuses outward from its degenerate inner core to a thin outer layer of non-degenerate atomic matter. This thin layer of matter is able to radiate the heat into space, emitted as light, first blue-white, then yellow, orange, and finally red. The brief animation below shows what this process would look like over time.

The heat loss is very inefficient and that is why white dwarfs cool very slowly. Although white dwarf stars on their own die very slowly and peacefully like this, white dwarf relationships with other stars or stellar remnants end badly in explosions called Type 1a Supernovae. They will be explored in PART 3.


Protostars with masses between 0.50 M and 10 M are mid-size stars. These stars are destined to undergo a red giant phase at the end of their main-sequence phase, before they end as white dwarfs. Unlike smaller red dwarf stars, these stars are not significantly convective, The plasma doesn't mix much so a shell of hydrogen remains unburned around the core as it undergoes fusion. Smaller mid-size stars like the Sun utilize the proton-proton chain reaction to fuse hydrogen into helium. With increasing stellar mass, another fusion chain reaction called the CNO cycle becomes the more efficient reaction, fusing hydrogen into helium at higher core temperatures. Whereas proton-proton chain fusion ignites at about 4 x 106 K, the CNO fusion reaction becomes self-maintaining at about 15 x 106 K. There are various reaction paths available, where carbon, oxygen and nitrogen (products of helium fusion) function as catalysts. Stars over 1.8 M almost exclusively utilize to the CNO cycle.

Mid-size stars go through a more complex evolution than smaller red dwarfs. During any star's main-sequence phase, the core is a spherical fusion reaction that maintains hydrostatic equilibrium between outward radiation pressure and inward gravitational pressure. The smaller the star's mass, the longer it will stay in equilibrium as a main-sequence star. Fusion reactions take place at a slower pace in general and increased convection stirs new reactants into the core. The Hertzsprung-Russell diagram (below) plots stars based on luminosity versus surface temperature. This diagram, created in 1910, led to major theoretical developments in stellar physics, well before stellar fusion was understood to be the reaction mechanism in stars (discovered in the 1930's by Hans Bethe). The diagram has evolved since then as theory evolved. It is still one of the most useful tools astronomers have to study stellar evolution. It highlights a number of important trends, the most obvious one being that luminosity tends to increase with surface temperature. You can also see that a star's colour is an indication of its surface temperature. A star's mass determines its position on the main sequence. More massive stars are hotter and brighter than less massive stars. Though shown incorrectly as pale yellow in this case, the Sun is a white (white-hot) star of luminosity 1 (solar unit). It is located in the middle of the down-sloping central spine of the main sequence.

Image created by the European Southern Observatory; original source here.
Our Sun, at 1 M (solar mass), is an example of a mid-size star. The photo below left shows you what the Sun looks like in visible light through a filter.

Geoff Elston; Society for Popular Astronomy:Wikipedia
Its position is currently on the main sequence but it will move across the diagram as it evolves. The Sun will exist as a main-sequence star, fusing hydrogen into helium for a total of 10 billion years. In another 4.5 billion years, its core's hydrogen fuel will be almost entirely fused. At that point, like a victim shot in the saloon of an over-acted Western, the Sun will begin a dramatic and complex series of death throes. The core will start to collapse under its own weight as dwindling outward pressure from hydrogen fusion no longer sustains its volume. The core will heat up under increasing pressure and eventually this process will cause the Sun to expand into a red giant (see the bubble attached to the right of the main sequence in the Hertzsprung-Russell diagram). This change happens because the core has gotten so hot that hydrogen in the shell around the core starts fuse causing the shell to expand. The Sun's surface temperature will cool from white to reddish-orange as it balloons outward to a radius about 200 times its current size (the H-R diagram is not to scale). Despite its cooler surface temperature, it will be almost 3000 times more luminous than it is now because it will be so huge. Its luminosity will increase as it ascends the short red giant branch as the rate of hydrogen fusion in the outer core shell layer increases. The diagram below puts the change in size (200X) into perspective.

Oona Räisänen (User:Mysid), User:Mrsanitazier;Wikipedia 
Having left its main-sequence phase, the Sun will arrive at a new but shorter-lived equilibrium, perhaps lasting hundreds of million of years. It will now occupy the tip of the red giant branch (RGB), the bubble on the Hertzsprung-Russell (H-R) diagram above. As the Sun continues to fuse hydrogen in the thick shell around its core via the CNO cycle, the helium in the core builds up mass. During the last million years or so of the RGB phase, the Sun will lose about 20% of its mass as rapid hydrogen fusion ejects gas from the outermost layers. As hydrogen is used up and fusion slows down, gravity dominates over fusion pressure. Core pressure meanwhile builds as new helium is deposited around it. Gravity squeezes the helium atoms into an electron degenerate state. In stars up to about 2 M, the RGB phase will end abruptly when the inert degenerate helium core reaches the ignition temperature (about 108 K) for fusion into carbon and oxygen using the triple alpha process. Much of the core helium will fuse simultaneously in a violent but invisible process called a helium flash. It will all take only a few minutes because the core is mostly degenerate. Degenerate matter has no opportunity to expand and dissipate the fusion heat. The reaction rate increases into a runaway state, in which a positive feedback loop further increases the reaction rate. All this takes place in an electron sea that is a perfect conductor of heat. The electrons transfer the energy of the fusion reaction throughout the core almost at once, so runaway fusion takes place across it simultaneously. If light could stream away from the Sun at this point, it would exhibit a flash so bright it would be about 1011 times brighter than it is now, about as bright as the entire Milky Way, but it won't be able to. Energetic photons produced by the flash will be absorbed by the Sun's now extremely thick and dense outer envelope of plasma instead.

The force of the run-away helium flash will blast the core nuclei and electrons apart, allowing them to reorganize as ordinary atoms. The core will quickly expand to dissipate the reaction heat. Triple alpha fusion will continue at a now steady rate as the Sun enters an even briefer third stable period, lasting about 100 million years, on the horizontal branch. This branch is not shown in the H-R diagram above. If you scroll downward you will see an evolution graph specific for the Sun. The horizontal branch is a dotted line band. By this time, about 40% of the Sun's total mass is helium and 6% is carbon.

When the helium starts to dwindle, the core will contract further under gravitational pressure and the Sun will expand once again as it resorts to fusing the remaining hydrogen and helium in its outer layers. It will now reach a new stability as an asymptotic giant star, reddish orange, and about 2000 times more luminous than it is now. In another 30 million years, it will begin to eject its outer layers of mass through a series of thermal pulses, each one lasting about 100,000 years, where the core temperature wobbles slightly, causing significant changes in the fusion rate. The ejected outer envelopes of gases will form a planetary nebula around a core remnant that has recompressed into the degenerate matter of a carbon/oxygen white dwarf, containing about half the Sun's current mass squeezed down to the size of Earth. Starting out bluish white hot and about 100 times more luminous than the Sun is now, it will very, very gradually fade into a black dwarf.

The life of the Sun is illustrated in more general terms below, where changes in size are shown to scale. The Sun started out as a relatively small star formed from a molecular cloud. It will spend most of its life as a stable white star until its core begins to run out of hydrogen fuel. It will expand to 200 times its former size into a red giant star. Eventually its outer layers of material will blow away leaving behind an Earth-sized white dwarf (tiny white dot) in the center of a planetary nebula.

ESO/S. Steinhofel;Wikipedia
The graph below tracks the evolution of a 1M star like the Sun.

Though complex and dramatic, the death of a star like our Sun is a mild event by astronomical standards. When our Sun leaves the main sequence, planetary orbits will probably be disturbed by powerful solar wind gusts and the innermost rocky planets will be engulfed as the Sun expands to a red giant. Still, there is some evidence that Earth, though scorched, sterilized and possibly engulfed by hot plasma at some point, might survive physically intact to eventually orbit the Sun's white dwarf remnant.

For all mid-sized stars the evolutionary scenario is similar with some exceptions. Stars slightly smaller than our Sun also evolve into red giants but their cores don't have enough mass to ignite helium fusion. They don't reach the tip of the red giant branch shown above, and there is no helium flash. Instead, these stars move directly into a state that more resembles the post- AGB (asymptotic giant branch) top horizontal line in the graph above, except that they are less luminous. Like the Sun, they eventually blow off their outer layers to form a planetary nebula, leaving behind, in this case, a helium white dwarf. In stars more massive than our Sun, between 2.25 M and 10 M, the core is large enough and dense enough to reach the fusion ignition temperature of helium before it has a chance to contract into a degenerate state. This eliminates the helium flash from their life cycle for a different reason. Like the Sun, these more massive stars expand into red giants as the outer layers of the star cool and become opaque to radiation. However, those layers of gases are even thicker in these more massive stars. They effectively hold in the heat and cause the hydrogen shell around the core to further heat up and expand to form much larger stars, often called super-AGB stars, which tend to evolve further along the horizontal branch than Sun-like stars do. They can become very unstable pulsating stars that can shine yellow, white or even blue-hot. The particular evolutionary path of the star depends on its heavy element content (called metallicity in astronomy) and helium content to start with. The contribution of these elements, in turn, depends on the composition of the molecular cloud in which the star formed. The lines are dotted in the graph above because these horizontal evolutionary paths are still being modeled. The cores of these more massive stars eventually become degenerate and hot enough to fuse carbon into larger nuclei. Some of these stars might ignite a carbon flash analogous to the helium flash of smaller stars. If the original star is between 8 M and 10 M, it will most likely form an initially blue-hot white dwarf surrounded by a planetary nebula, much like less massive mid-range stars, with the exception that the white dwarf will be made of oxygen, neon and magnesium, all of which are products of carbon fusion.

As we've seen here, low mass (small and medium sized) stars die in a step-by-step process that, though violent, is not explosive. At around 8 M in some cases, stars have enough mass to go out spectacularly and these supernovae can vary considerably. Some massive stars buck the trend and don't explode at at all. It all depends on the high-energy physics of matter deep within their cores, next.

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