# Why do massive stars not undergo a helium flash

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I understand that for low-mass stars the helium flash occurs due to their degenerate helium cores. Thus the answer to this question is probably that more massive stars do not have a degenerate core, but I do not understand why they wouldn't. Due to their increased mass, I'd assume their central pressure is even higher, so surely their cores should also be degenerate?

After H burning has finished, the he mass of the He core gradually increases, as does its density and temperature.

Low-mass stars have denser cores when they reach a temperature at which He is ignited. The density is high enough that the electrons in the core are degenerate. In such conditions the heat from the nuclear reactions goes almost exclusively into raising the temperature of the He ions, but almost none goes to the degenerate electrons which have a very low heat capacity, yet dominate the pressure. This leads to a runaway increase in the nuclear fusion rate.

In higher mass stars the core is less dense when it reaches the He ignition temperature. This temperature is almost exactly the same as the ignition temperature for lower mass stars because of the very strong temperature dependence of the triple alpha reaction. The level of degeneracy depends on the ratio of density to temperature (it does not directly depend on the pressure).

At the lower densities in the higher mass stars, the electrons are not degenerate when He ignites and the heat capacity of the electron gas is higher than the ions (because there are more electrons than ions). In this case the heat from the nuclear reactions can effectively raise the pressure, doing work which expands the core and regulates the nuclear reaction rate.

Massive stars do not undergo helium flash because they have core temperatures high enough to prevent the helium core from becoming electron-degenerate. Check here for some more information.

Therefore, the star can burn helium in a smooth transition, instead of undergoing helium flash. In more details, the massive star's core heats up past the helium burning threshold, preventing a degenerate helium core from forming. I hope this helps.

More massive stars indeed have higher pressures, but what's key is that they also have higher temperatures. After leaving the main sequence, they reach core temperatures of a few times $$sim10^8$$ Kelvin while their densities remain at something like $$sim10^4$$ g cm$$^{-3}$$ - which, you can check, is within the nondegenerate regime. Therefore, helium fusion begins comparatively gently, rather than with the explosion helium flash characteristic of evolved Sun-like stars.

Central density tends to decrease with increasing mass, and central temperature tends to increase with increasing mass. It's not surprising that there's a mass cutoff above which temperature clearly wins out, at around $$1.5M_{odot}$$-ish; similarly, it's not surprising that there's a mass cutoff below which a star will never reach core temperatures required for helium fusion.

## Why do massive stars die?

*Some notes before we start:
The word, 'Massive' in astronomy is regarding the total mass of the subject. So when it is said that a star is Massive, it's not referring to size, but to the mass of it. Although mass and size correlate to some degree.

Every star fuses hydrogen into helium in its core when it is first born. Stars similar to our sun, stars that get to be around the size of Jupiter called Red Dwarfs and Supermassive stars that are usually hundreds of times more massive than our sun all undergo this first stage of the nuclear reaction.

The more massive a star is, the higher temperature its core reaches and the faster it burns through its nuclear fuel.
As a star's supply of hydrogen to fuse runs out, it begins to contract and the temperature increases. If the star gets dense and hot enough, it will start to fuse heavier elements.

Sun-like stars, once hydrogen burning completes, will get hot and dense enough to fuse helium into carbon, but that's the most that star this(sun) size will get to accomplish. To enter the next stage of the nuclear reaction, a star eight or more times more massive than our sun is required.

Now we're getting into Carbon Fusion
Sun-like stars would expel their outer layers as a planetary nebula and contract into a white dwarf. And the Red dwarfs that never even make it to burning helium would contract down to a white dwarf as well.
But the more massive stars give a cataclysmic show.

Often, especially in the lower-mass end of the spectrum (

20 solar masses and under), the core temperature steadily rises and fusion goes onto heavier elements: Burning carbon to oxygen and/or neon, and then even burning magnesium, silicon, and sulfur, which reaches a climax in a core of iron, cobalt, and nickel.

Since fusing these elements would use more energy than it produces, the core implodes and collapses into a supernova form. After the supernova, one of two permanent outcomes occur. Either the newly dead supermassive star becomes a neutron star, it becomes a black hole.

## 101 clouds of gas: Where do massive stars begin?

Astronomy students sorted through 101 clouds of gas to find those that may be in the first phases of forming massive stars.

“There’s still a pretty open question in astronomy when it comes to massive star formation,” says Jenny Calahan, a recent graduate of the University of Arizona. “How do stars weighing more than eight solar masses form from clouds of dust and gas?”

Astronomers understand this process for stars the size of our sun. Particles in clouds are attracted to each other and begin to clump together. Gravity takes hold and the gases flow to the center of the cloud as it collapses. Over millions of years, the gas is put under so much pressure that it begins to burn, and the star is born when nuclear fusion finally begins in the core of the compressed gas.

Theories about how much gas and time it takes to make a star like our sun can be proven through observations, because each stage of a sun-like star’s life—from the collapse of gas clouds into a pre-stellar core to the star’s expansion into a red giant and collapse into a white dwarf—are observable throughout the galaxy.

But astronomers have yet to understand how stars more than eight times the mass of our sun form. Stars of this size explode into supernovae at the end of their lives, leaving behind black holes or neutron stars.

### Two theories

“There are a few theories for massive star formation that work in simulations, but we haven’t seen those initial conditions out in the wild universe,” Calahan says.

One theory is the formation of massive cores, says Yancy Shirley, associate professor in the astronomy department. The massive cores are dense collections of gas several times larger than the star they create. For massive stars, the cores must be at least 30 times the mass of our sun.

“People are having trouble finding objects like that,” Shirley says.

The other theory is that multiple low-mass cores form within a gas clump. The low-mass cores grow as they compete for material in the clump, and eventually, one of the cores grows large enough to form a massive star.

“This is the debate: which of these two pictures is more correct, or is it some combination of the two?” Shirley says.

### Find the right ‘clumps’

The first step in answering the question is identifying the earliest phase of star formation, so Calahan, with Shirley’s guidance, set out to find clumps showing signs of collapsing gas motion, called “inflow.”

Calahan selected 101 subjects from a list of more than 2,000 huge, cold, and seemingly starless clouds of gas called starless clump candidates, or SCCs.

Though astronomers have studied SCCs in the past, many of them focused on the brightest and most massive objects. Calahan’s study was unique in that it was a blind survey.

Ranging in size from a few hundred times the mass of our sun to a few thousand solar masses, the SCCs Calahan selected are a representative sample of all gas clouds that have the potential to form massive stars.

Using the Arizona Radio Observatory’s 12-meter radio telescope at the university’s Steward Observatory on Kitt Peak, Calahan detected and tracked radio waves emitted by the molecular gas oxomethylium (HCO+), which emits a specific radio wavelength.

Once Shirley and students use the telescope to identify objects of special interest, like collapsing SCCs, they then study the clumps of interest using ALMA, which can peer deeper into the gas and find stars or other objects that cannot be seen with the 12-meter telescope.

Oxomethylium, one of the more abundant ion molecules in space, is a highly reactive ion that would not survive in our Earth’s atmosphere. When oxomethylium moves towards an observer, the wavelengths are compressed when the gas moves away from an observer, the wavelengths are stretched.

##### How cosmic winds stop stars from forming

By analyzing the wavelengths, Calahan identified six SCCs that showed the telltale signs of collapse, suggesting that gas collapse happens quickly, accounting for only 6 percent of the formation process of massive stars.

“One side is falling away from us and one side is falling towards us,” Calahan says.

“The way we’re using it right now is as a pathfinder,” Shirley says. He and the undergraduates use the 12-meter telescope to conduct surveys that identify objects of special interest, like collapsing SCC’s. These clumps of interest are then further studied using ALMA, which can peer deeper into the gas and find stars or other objects that cannot be seen with the 12-meter telescope.

## Ask Ethan: Why Were The First Stars Much Larger Than Even Today's Biggest Ones?

An artist's conception of what the Universe might look like as it forms stars for the first time. . [+] Stars might reach many hundreds or even a thousand solar masses, and could lead to the relatively fast formation of a black hole of the mass the earliest quasars are known to possess.

Place enough mass together in one place, give gravity enough time to contract and collapse it, and you'll eventually get a star. Get a large enough cloud of matter together, and you'll get a huge cluster of new stars, with a wide variety of masses, colors, and temperatures to them. Yet, if we look to the earliest times, we fully expect to find that the most massive stars from back then were far larger and heavier than any we find today. Why is that? Steve Harvey wants to know, asking:

I do not understand why a star's metallicity has an impact on its size. Why? I am asking this because in one of your articles, you were saying that in the beginning of the universe, stars with mass almost 1000 [times] the sun's mass probably existed because they were almost 100% hydrogen and helium.

It's a tough pill to swallow, because the only thing that's changed appreciably, from then until now, is the elements that make up these stars.

At the photosphere, we can observe the properties, elements, and spectral features present at the . [+] outermost layers of the Sun. The very first stars may not have had the same elements our Sun did, as they only had the Big Bang to create their building blocks, rather than also having previous generations of stars.

NASA’s Solar Dynamics Observatory / GSFC

If we look at a star like our Sun, we can find evidence for a whole slew of elements that span the periodic table. In the outer layers of a star, you can see what elements are present by their absorption features. When electrons, in atoms, see a slew of incoming photons, they can only interact with the ones that have a specific amount of energy, corresponding to the energy levels that cause atomic transitions for that particular element. In the Sun, alone, there are scores of elements.

The visible light spectrum of the Sun, which helps us understand not only its temperature and . [+] ionization, but the abundances of the elements present. The long, thick lines are hydrogen and helium, but every other line is from a heavy element that must have been created in a previous-generation star, rather than the hot Big Bang.

Nigel Sharp, NOAO / National Solar Observatory at Kitt Peak / AURA / NSF

But while the Sun was born with approximately 70% hydrogen, 28% helium, and 1-2% of all the heavier elements combined, the very first stars should have been hydrogen and helium exclusively, to better than the 99.9999999% level. This is because the only way we form those heavier elements is through nuclear fusion, which happens pretty much exclusively in two ways in the Universe:

1. In the first few minutes following the Big Bang, and
2. In the cores of stars and stellar remnants.

When the Universe first formed protons and neutrons, it fused them into heavier elements: hydrogen, deuterium, helium-3, helium-4, and a tiny, trace amount of lithium-7.

The predicted abundances of helium-4, deuterium, helium-3 and lithium-7 as predicted by Big Bang . [+] Nucleosynthesis, with observations shown in the red circles. The Universe is 75-76% hydrogen, 24-25% helium, a little bit of deuterium and helium-3, and a trace amount of lithium. The first stars in the Universe will be made of this combination of elements nothing more.

Everything else? It was made subsequently, many millions or even billions of years later. This means that the very first stars would have had practically no heavy elements at all: just hydrogen and helium alone, in about a 75%/25% split (by mass).

Over time, we expect that the interstellar medium, which is where the gas that gives rise to stars originates, gets more and more enriched by new generations of stars that live-and-die, with the heaviest-mass stars dying first. The ratio of these heavier-than-helium elements to the pure hydrogen (or hydrogen-and-helium combined, depending on who's doing the measuring) is known as metallicity, because astronomers call all elements that aren't hydrogen or helium "metals."

The Eagle Nebula, famed for its ongoing star formation, contains a large number of Bok globules, or . [+] dark nebulae, which have not yet evaporated and are working to collapse and form new stars before they disappear entirely. The stars that form first compete with all the other clumps of matter to accrete the star-forming gaseous material before it evaporates away.

In our modern Universe, when new stars form, they form with a wide variety of masses: from about 0.08% the mass of the Sun up to about 260-300 times the Sun's mass. The lower limit is set by the threshold for where you can ignite true hydrogen fusion, because you need that much mass and a temperature of about 4 million K to start fusing hydrogen into helium. But the upper limit is a little trickier.

Sure, you need a lot of mass and massive material to build the largest stars, but there are plenty of star-forming regions of the Universe that have a huge amount of mass. Just in the Large Magellanic Cloud, for example, right here in our local group, we have the star forming region 30 Doradus in the Tarantula Nebula. With a total mass of around 400,000 Suns, it houses some of the most massive, hottest, bluest young stars in the known Universe.

The star forming region 30 Doradus, in the Tarantula Nebula in one of the Milky Way's satellite . [+] galaxies, contains the largest, highest-mass stars known to humanity. The largest, R136a1, is approximately 260 times the Sun's mass the light from these hot, new, bright stars is predominantly blue, however.

NASA, ESA, and E. Sabbi (ESA/STScI) Acknowledgment: R. O’Connell (University of Virginia) and the Wide Field Camera 3 Science Oversight Committee

But even these cap out at about 250-260 solar masses. The reason for this is that forming a star is a race between three competing processes:

1. Gravity, which works to pull everything into whatever overdense regions are present, with the initially densest regions growing the fastest.
2. Radiation pressure, which comes from the collapsing matter, nuclear fusion, and existing stars, which work to blow off the matter that could continue to fall in.
3. And radiative cooling, which comes from the proto-star's ability to radiate this energy away, allowing the star to cool itself and accrue more mass in shorter time periods.

Stars only have a limited amount of time to gain mass before the star-forming material is blown away. So the key to forming a super-massive star is getting extremely massive as fast as possible.

The star-forming region NGC 2174 showcases the nebulosity, the neutral matter and the presence of . [+] external elements as the gas evaporates.

NASA, ESA, and the Hubble Heritage Team (STScI/AURA), and J. Hester

Gravity works the same in the modern Universe as it did in the early Universe. Same with radiation pressure: you form stars, matter collapses, nuclear fusion occurs, etc., and this doesn't really depend very much on whether you have lots of heavy elements or none at all.

But that third component — the ability of a proto-star to cool itself — is what's different for metal-free stars versus metal-rich ones. The basic difference is that heavier elements, with more protons and neutrons in their nuclei, can absorb, radiate, and carry away more energy than light elements alone. Put simply, more metals means more cooling at a faster rate.

An illustration of the first stars turning on in the Universe. Without metals to cool down the . [+] stars, only the largest clumps within a large-mass cloud can become stars.

So why, then, would the earliest, metal-free stars be allowed to be heavier than the stars we form today? It seems counterintuitive, but the reason is because metals, and heavy elements, are more efficient at cooling and forming dust-nucleation sites. Without them, there are fewer ways to cool the gas that forms these stars down. Instead of radiative cooling from a wide variety of elements, as well as from dust grains, we only have hydrogen molecules (H2), which are already pretty rare, and electron cooling.

For gas to cool and form stars, you need the cooling timescale to be smaller than the dynamical (collapse) timescale. This means you need larger masses to collapse and form stars, and these both represent rarer density fluctuations and mean that smaller regions, which produce lower-mass stars, can't collapse at all.

An illustration of CR7, the first galaxy detected that was thought to house Population III stars: . [+] the first stars ever formed in the Universe. JWST will reveal actual images of this galaxy and others like it.

In the early Universe, it's only very large clouds of gas that can collapse to form stars at all only these extremely massive clumps have the ability to do it. But the more massive your clump is, the easier it is to form more massive stars, and accrue more and more matter. Gravity is like a runaway train, where the more mass it accumulates early on, the faster it grows to accumulate even more mass. Without large numbers of small clumps, and rather smaller numbers of large clumps, it's expected that the typical mass of stars, rather than the 0.4 solar masses we see today, will be more like 10 solar masses, on average, in the earliest stages.

An artist's conception of what the Universe might look like as it forms stars for the first time. As . [+] they shine and merge, radiation will be emitted, both electromagnetic and gravitational.

NASA/ESA/ESO/Wolfram Freudling et al. (STECF)

In other words, the "average" first star is 25 times more massive than the "average" new star formed today, because it formed from larger clumps of gas that we'll ever see in the modern Universe!

Since there are smaller numbers of stars, but they have higher masses on average, we expect the entire mass distribution to be shifted. We even have a different name for it: modern mass distributions follow the Salpeter mass distribution, but the first stars are thought to follow what's called a top-heavy initial mass function.

The first stars and galaxies in the Universe will be surrounded by neutral atoms of (mostly) . [+] hydrogen gas, which absorbs the starlight. Without metals to cool them down or radiate energy away, only large-mass clumps in the heaviest-mass regions can form stars.

Nicole Rager Fuller / National Science Foundation

The larger your star-forming region, the more mass gets locked up in heavier, higher-mass stars. Without heavy metals, you don't have dust to cool your clumps down, which means the smaller clumps get washed out and don't form. It's only the largest clumps in the largest clusters that have a chance, and that leads to ultra-massive stars that have less competition for accumulating mass than even the most massive stars today have. It isn't merely the presence or absence of heavy elements that leads to more massive stars directly, but the fact that metal-free stars can only form in extremely massive regions at all, and that those regions will be dominated by the most massive, fastest-growing clumps inside them.

That's why we think that among the very first stars, they may have reached or exceeded 1,000 solar masses at the extremes. If you ever wondered how we got such large, supermassive black holes so fast, the very first, metal-free generations of star may be the answer to that puzzle, too!

## Why do massive stars not undergo a helium flash - Astronomy

All the helium in the Universe has been created by the fusion of hydrogen nuclei, either in the early Universe (a minute after the Big Bang) or in stars.

What happens to the Helium? Most stars, after converting a significant portion of their hydrogen to helium undergo an internal change. The internal core collapses, and heats up, until it is hot enough to fuse helium into larger atoms, for instance, by combining three helium atoms into carbon. At this same time, some helium will fuse with that carbon to produce oxygen. Outside the core, in what's called the envelope, there is still enough hydrogen to fuse into more helium. But the core begins fusing heavier nuclei. This, by the way, is the transition from a 'normal' star like our Sun to a Red Giant.

After the red giant phase, the Sun will lose its outer layers leaving behind its helium-rich core (called white dwarf), which will gradually cool over the lifetime of the Universe. In stars more massive than the Sun, after the red giant phase. it becomes essentially a free-for-all for creating heavier and heavier atoms. As soon as the helium in the core runs out, the star collapses again, heats up, and starts fusing carbon and oxygen into larger atoms. If the star is massive enough, this keeps happening until iron is fused. At which point a hotter core still won't lead to fusion. The star collapses, becomes unstable, and POW. Explodes, forming a supernovae and neutron star (or black hole).

#### David Bernat

David received his PhD in Physics in 2011. He studies extrasolar planets, brown dwarfs, and theoretical cosmology.

## A 40-Year-old problem in Astrophysics is Finally Solved.

As many of us know that Stars — our Sun included — contain mostly Hydrogen and Helium. And Stars creates energy by nuclear fusion — Hydrogen atoms fuse together at high temperature and pressure — while another product is also Helium.

Two different isotopes of Hydrogen, Deuterium — Hydrogen with one proton and one neutron — and Tritium — Hydrogen with one proton and two neutrons — undergo nuclear fusion at high heat — 15.7 million kelvin — and pressure — 25.33 trillion KiloPascals — and release out enormous amounts of energy —17.58 MeV — with a Helium atom and a neutron.

If one ton of deuterium were to be consumed through the fusion reaction with tritium, the energy released would be 8.4 × 10²⁰ joules. This can be compared with the energy content of one ton of coal — namely, 2.9 × 10¹⁰ joules. In other words, one ton of deuterium has the energy equivalent of approximately 29 billion tons of coal.

Variety of other nuclear fusion reaction also happen such has Hydrogen-Hydrogen, and also Deuterium-Deuterium fusion reactions also occur. Now we wonder would Helium and Hydrogen undergo nuclear fusion to produce Lithium in the Star?

F ifty years ago Ann Merchant Boesgaard found one of the first Lithium rich star. The star had more Lithium in it compared to other stars and meteorites.

Stars, as per the known mechanism of evolution, actually destroy Lithium as they evolve into a Red Giant. They destroy the Lithium via low temperature Nuclear Burning.

There were numerous theories which theorized ways of why stars were Lithium rich. One popular theory was Planet Engulfment theory. For example, a Earth-like planet may increase the star’s lithium content when their plunge into the star’s atmosphere when the star becomes a Red Giant.

Planets are known to have more Lithium than their stars, for an example take our Sun and Earth. Earth has more Lithium than the Sun.

But evidence was found to contradict this. Some stars were found to be Lithium-rich. Here are a few papers on the observation of such stars:

## Why do massive stars not undergo a helium flash - Astronomy

Stars and planets are traditionally differentiated based on two properties:

(i) Whether or not they undergo nuclear reactions that burn hydrogen in their cores. Stars do this planets don't. In order to have high enough temperatures in the core to burn hydrogen, an object needs to have a mass of at least 75 or so times that of Jupiter. Anything more massive than that is automatically considered a star.

(ii) The way they form. Stars form when a cloud of gas, out in a nebula or other region of interstellar space, collapses under the influence of gravity. Planets, on the other hand, form when material in the disk around a pre-existing star begins to condense around rock/ice cores. You can have situations where the entire planet is almost completely rock/ice/water (such as the Earth), or situations where a large amount of gas is subsequently attracted to the rock/ice core (such as Jupiter, Saturn, etc.).

There is actually some ambiguity in the above definitions, mainly because of the existence of objects called "brown dwarfs". Brown dwarfs are too small to burn hydrogen, so they can't be considered stars, but most of them seem to form in the same way that stars do, often out on their own in a cloud of interstellar gas, so they can't really be considered planets either. The question then becomes, where is the boundary between a planet and a brown dwarf? What if you have an object that is, say, thirty times the mass of Jupiter but is located near a star? Is it a planet or a brown dwarf? Astronomers don't generally know the formation mechanism in that case, whether the object formed along with the star from condensing gas or whether it has a rock/ice core at its center like a planet.

Because of this problem, a lot of people in recent years have advocated a new, simpler distinction between planets, brown dwarfs and stars which doesn't include the formation process in it. Under this scenario, the boundary between brown dwarfs and stars is still around 75 times the mass of Jupiter, as above, but the boundary between brown dwarfs and planets is set at around 13 times the mass of Jupiter, since that is the mass at which objects reach high enough central temperatures to burn deuterium (an isotope of hydrogen which undergoes nuclear burning at lower temperatures than regular hydrogen does).

#### Dave Rothstein

Dave is a former graduate student and postdoctoral researcher at Cornell who used infrared and X-ray observations and theoretical computer models to study accreting black holes in our Galaxy. He also did most of the development for the former version of the site.

## How Stars Work

As we mentioned before, stars are large balls of gases. New stars form from large, cold (10 degrees Kelvin) clouds of dust and gas (mostly hydrogen) that lie between existing stars in a galaxy.

1. Usually, some type of gravity disturbance happens to the cloud such as the passage of a nearby star or the shock wave from an exploding supernova.
2. The disturbance causes clumps to form inside the cloud.
3. The clumps collapse inward drawing gas inward by gravity.
4. The collapsing clump compresses and heats up.
5. The collapsing clump begins to rotate and flatten out into a disc.
6. The disc continues to rotate faster, draw more gas and dust inward, and heat up.
7. After about a million years or so, a small, hot (1500 degrees Kelvin), dense core forms in the disc's center called a protostar.
8. As gas and dust continue to fall inward in the disc, they give up energy to the protostar, which heats up more
9. When the temperature of the protostar reaches about 7 million degrees Kelvin, hydrogen begins tofuseto make helium and release energy.
10. Material continues to fall into the young star for millions of years because the collapse due to gravity is greater than the outward pressure exerted by nuclear fusion. Therefore, the protostar's internal temperature increases.
11. If sufficient mass (0.1 solar mass or greater) collapses into the protostar and the temperature gets hot enough for sustained fusion, then the protostar has a massive release of gas in the form of a jet called a bipolar flow. If the mass is not sufficient, the star will not form, but instead become a brown dwarf.
12. The bipolar flow clears away gas and dust from the young star. Some of this gas and dust may later collect to form planets.

The young star is now stable in that the outward pressure from hydrogen fusion balances the inward pull of gravity. The star enters the main sequence where it lies on the main sequence depends upon its mass.

Now that the star is stable, it has the same parts as our sun:

• core - where the nuclear fusion reactions occur
• radiative zone - where photons carry energy away from the core
• convective zone - where convection currents carry energy toward the surface

However, the interior may vary with respect to the location of the layers. Stars like the Sun and those less massive than the sun have the layers in the order described above. Stars that are several times more massive than the sun have convective layers deep in their cores and radiative outer layers. In contrast, stars that are intermediate between the sun and the most massive stars may only have a radiative layer.

### Life on the Main Sequence

Stars on the main sequence burn by fusing hydrogen into helium. Large stars tend to have higher core temperatures than smaller stars. Therefore, large stars burn the hydrogen fuel in the core quickly, whereas, small stars burn it more slowly. The length of time that they spend on the main sequence depends upon how quickly the hydrogen gets used up. Therefore, massive stars have shorter lifetimes (the sun will burn for approximately 10 billion years). What happens once the hydrogen in the core is gone depends upon the mass of the star.

## Why do massive stars not undergo a helium flash - Astronomy

The short answer is that because changes (whether gradual shrinking or contraction) in a star's core where fusion is occuring (or perhaps no longer occuring!) must result in changes throughout the rest of the star, including its surface.

So what's happening in the hydrogen fusing core of a main sequence star?

Well, 4 hydrogen nuclei are being fused into a single helium nucleus many times per second (emphasis on many), releasing energy that ends up replacing that energy lost at the surface of star we call star light - luckily, there are a lot of hydrogen nuclei available for fusion. But what impact does that have? There are two that we've discussed.

1) Gas pressure depends upon number density of gas particles exerting the pressure and the temperature of the gas. If every time a helium nucleus is formed, 4 hydrogen nuclei (and additionally 2 electrons) disappear, then gradually the number density of gas particles will drop and unless something happens gas pressure within the core will fall out of equilibrium with gravity.

2) Over substantial fractions of the main sequence life span, the "fuel" hydrogen is being converted to helium within the star's core, and helium doesn't (yet) contribute any energy from fusion to the star. i.e., the fuel tank will eventually run dry. When that occurs, relatively rapid changes will ensue.

So what's a star's core to do?

First things, first - the star's core must deal with the pressure-gravity problem. Gravity gets a slight advantage as the number of particles there drops due to fusion, and very gradually the core shrinks*. That is, gravity does work on the core, heating it - gravitational potential energy is converted into thermal energy of the gas as it shrinks. Another way to think of it is this: the smaller the core becomes, the stronger gravity becomes (masses are closer together), and so to get back into pressure-gravity equilibrium the core's gas pressure exerted must be even higher than before. With a (slightly) higher temperature (recall that Pgas is proportional to n x T, where n is the number density of gas particles and T is the temperature), the greater pressure is again able to balance the stronger gravity. But the process of fusion continually albeit gradually reduces the number of particles within the core, and so this very gradual core shrinkage is inevitable.

But wait a minute, higher temperatures in the core mean that more energy is released from hydrogen fusion. Generally speaking, that extra energy generated by the core translates into (1) making the star's envelope larger and cooler and (2) raising the star's surface luminosity (other subtle effects may play a role and can alter the outcome in detail, but we won't pay any attention to these). Why does (1) occur? Because when you dump energy into a normal gas (in this case the star's envelope), the pressure that gas exerts increases. In very small, gradual steps gas pressure in the envelope exceeds gravity, and so the envelope expands very gradually - reacting to the gradual increase in energy dumped into it from the core below. By doing work against gravity, the envelope (and so the surface) ultimately cools to re-establish pressure-gravity balance. But keep in mind that these changes are relatively minor while the star is on the main sequence much larger changes are in store as its core runs out of hydrogen "fuel".

A general rule of thumb is that as the core becomes smaller and hotter, the envelope becomes larger and cooler (and vice versa!), for reasons just discussed. And so generally speaking, stars evolve from the main sequence over toward the upper right quadrant of the H-R diagram, eventually becoming giant or supergiant stars. As stars age away from the main sequence, their cores continue to fuse lighter elements into heavier ones (releasing energy), first within a central core, then in a shell surrounding that central core. The "ashes" of one fusion stage become the "fuel" for the next stage, assuming a sufficiently high temperature is attained to allow fusion to occur (recall that heavier elements have more protons and so are more repulsive to each other due to the electromagnetic force). While the central core is contracting, because it hasn't yet reached a sufficiently high temperature to begin the next stage of fusion, the resulting changes are relatively rapid. But after fusion begins again in the central core, the changes are much more subtle and over relatively longer spans of time. Each successive stage of central core fusion has a shorter duration than the previous one, mainly because the net energy released per full reaction becomes less and less as the heavier elements are fused.

Here are the major stages of central core fusion, with their major products, their "ignition temperatures", and the approximate minimum mass star that will go through that stage of fusion:
4H --> He about 10 million K 0.08Msun
3He --> Carbon (C), then He + C --> O (oxygen) 100 million K 0.5Msun or so
Carbon fusion: Neon, Magnesium 600 million K or so about 6Msun
Oxygen fusion: Silicon, Sulfur 1 billion K or so 8Msun
Silicon fusion: Iron 3 billion K 10Msun

What determines whether or not the ever-heavier elements that are produced in one stage will fuse in next stage? It is a race between density and temperature in a core that becomes ever smaller under the force of gravity. For if gravity can compress the core to become sufficiently hot to fuse that next element, it will do so and that next stage of fusion will occur. But if the core becomes too dense before the "ignition" temperature for that element is reached, another source of pressure will step in and halt the core's contraction. In that event, the core can become no hotter, and so the next stage in fusion cannot occur, signaling the end of the star's life. What is this source of pressure that occurs at very high densities?

Electron Degeneracy Pressure. This exotic form of pressure generated by the free electrons will begin to dominate over normal gas pressure in stellar interiors when the densities exceed 1 10,000 g/cm 3 (recall that water has a density of 1 in these units). This pressure has nothing to do with the fact that electrons have like charges, but rather it becomes important when electrons are confined to lie very near to one another and yet are compelled to avoid one another (this same property explains why/how electrons that are bound to atoms arrange themselves in "orbital" shells). Electron degeneracy pressure depends on the electron number density (as n 5/3 ), and does not depend on the temperature of the gas. Once established, this pressure will eventually halt any gravitational contraction 2 . Why is this important? Because if the electrons in a star's core become degenerate before the "ignition" temperature of the next stage of fusion is reached, that next stage of fusion will never begin, and the star will soon die, ultimately ejecting its envelope in a planetary nebula with the core (supported by electron degeneracy pressure) becoming a white dwarf. It is also this pressure that sets in to keep objects less massive than 8% of the Sun's mass from ever becoming stars, since their cores will then never become hot enough to sustain full hydrogen fusion.

Finally , consider stars with masses exceeding 10 times the mass of our Sun. They are able to fuse elements all the way up through iron, with a series of successive shells (or zones) of lighter element fusion surrounding an iron core (like layers in an onion). Once an iron core forms, catastrophic doom awaits that star - for fusion involving iron removes energy from the environment. What happens next can be summed up in this way. The above fact combined with the extreme conditions of temperature (billions Kelvin) and density ultimately result in a complete gravitational collapse of the iron core. For a variety of reasons 3 , the increasing temperature and density actually push pressure further away from its required equilibrium with gravity to prevent a collapse. The net result is that in a fraction of 1 second of time, an iron core about the size of the Earth and a bit over 1 solar mass collapses to a ball of neutrons about the size of Kalamazoo. The rest of the core (fusing the lighter elements in successive shells) also begins falling inward, although the star's envelope remains totally oblivious to what's happening inside. Neutron degeneracy pressure 4 suddenly halts the collapse of the innermost neutron core, which then rebounds a bit like a suddenly released compressed rubber ball, sending out a shock wave that plows through the surrounding zones where fusion is still occuring. The shock wave compresses and heats these zones, the energy released from fusion becomes explosive and the star suddenly explodes as a supernova - the star's envelope is driven away at thousands of km/s (how this happens in detail is an active area of research). At peak luminosity, a supernova emits several to 10 billion solar luminosities of light, and then slowly fades with time. Ultimately, the luminous and the kinetic energies of the exploding star, plus the energy carried away by the zillions of neutrinos formed in the explosive fusion reactions is paid by the gravitational potential energy released in the collapse of the iron core. What remains of the collapsed core is expected to be a neutron star, as long as its mass lies below 2-3 solar masses. Neutron stars are indeed observed in the centers of violently expanding supernova gas shells.

*This shrinking of the star's core converting hydrogen into helium is much more gradual than gravitational contraction, the latter eventually taking place when hydrogen is exhausted in the central-most region of the core composed of helium.
1
More precisely, this critical density depends upon the temperature of the gas, proportional to (T/10 8 ) 3/2 .
2 More precisely, this pressure can support at most about 1.4 solar masses of material, depending on its composition and other details, called the Chandrasekhar limit. More massive objects initially supported by this pressure must collapse under gravity.
3 Details, details. As the temperature exceeds several billion Kelvin, Wien's law of thermal radiators (blackbodies) tell us that energetic gamma rays are numerous, and some of these have sufficient energies to break apart the iron nuclei all the way back down to protons. This process removes energy from the core (it's essentially fusion run in reverse!), robbing the iron core of pressure needed to support itself. Soon thereafter the extreme densities and temperatures now present allow the free electrons to begin combining with protons to create neutrons, robbing the iron core of virtually all remaining pressure support. Very rapid ("free fall") collapse ensues - with the matter reaching infall velocities of up to 70,000 km/s! As usual, don't worry about the details.
4 Neutron degeneracy pressure is similar in nature to electron degeneracy pressure, except it involves the much more massive neutron and so is much more powerful. It too has a limiting mass it can support, lying somewhere between 2-3 solar masses. The reason for the uncertainty is because inside a neutron star the densities soar to such high values (greater than 100 million - 1 billion tons per cm 3 ) that the neutrons themselves "fall apart" (or rather this matter changes phase, as ice melts to liquid water), and we don't yet understand the nature of this form of matter. Neutron stars more massive than this limit must collapse, and the result is probably a black hole - something so dense that light cannot escape from it.

Kirk Korista
Professor of Astronomy
Department of Physics
Western Michigan University