Starscontinued

Notes compiled by

Paul WoodwardDepartment of AstronomyUniversity of Minnesota

We now begin looking at stars by tracing their lives, beginning with their formation out of huge interstellar gas clouds and ending with their expulsion of their outer envelopes or simply with an explosion.

This subject is covered in your textbook in Chapter 17.

You should review that chapter thoroughly.

When discussing the formation of the solar system, we already talked quite a lot about the early stages of the star formation process, going from a large cloud of interstellar gas to a protostar surrounded by a protoplanetary disk.

Therefore we will skip that part of the story here.

Fig. 16.3 Artist’s concept of a collapsing stellar disk.

The bipolar jets emanating from compact objects at the centers of rotating disks of gas, as shown on the previous slide, seem to be a common feature of all such systems, big and small.

We will encounter them again when we discuss double star systems, and yet again when we discuss the nuclei of galaxies.

This is a feature of astronomy, we find again and again close similarities in the behavior of systems that differ in scale by factors as large as a thousand or even a million. The key point is that these systems do not differ in any fundamental aspects other than sheer scale.

In the early 2000s these bipolar jets were identified as a mechanism for removing angular momentum from a collapsing disk, allowing the central stellar object to form.

If we think about the glob of a larger gas cloud that collapses to form a single star, we can distinguish 4 stages of this contraction process under gravity, once this glob has contracted sufficiently to establish its distinct identity. We consider its collapse beginning after it has become opaque to radiation, so that it makes sense to talk about its “surface,” the surface region from which light can escape into space.

1. First, the surface temperature of the gas cloud is very low, but its surface area is very large. As it contracts, liberating gravitational potential energy as heat, this heat is radiated away into space very efficiently. The luminosity of the gas cloud is therefore very high, perhaps as much as 100 times as high as it will be once the star reaches the main sequence and begins burning hydrogen in its core. However, this radiation, because of the low surface temperature of the cloud, will appear mostly in the infrared.

2. Second, as the gas cloud continues to collapse, radiating into space essentially all of the heat generated from gravitational potential energy release, its surface temperature warms only slightly. However, as the collapse proceeds, the surface area of the cloud is diminished, so that its luminosity is diminished accordingly. This stage lasts only a few million years (for a protostar of about one solar mass).

3. Third, release of gravitational potential energy, together with the reduced radiating surface area, cause the interior of the protostar to heat steadily. In this third stage the core temperature exceeds a few million degrees K, so that hydrogen fusion to form helium begins in the center and significantly slows the continuing collapse of the protostar. Continued shrinkage and continued heating give slight increases in the luminosity over about 10 million years (for a one solar mass protostar).

4. Fourth, shrinkage of the protostar and increase of the rate of fusion in its core continue for a few tens of millions of years until the fusion rate finally establishes gravitational equilibrium, and the star is said to be on the main sequence.

For whatever it is worth, we can plot such a protostellarevolutionary track on the H-R diagram.

Stars of different masses of course follow different tracks on the diagram, but they all follow the same 4 stages of protostellarevolution outlined above.

Fig. 16.6Life tracks

from protostar to main

sequence star for stars of different masses.

You may remember that we said previously that the H-R diagram for the Pleiades cluster indicates that the cluster is about 60 million years old.

You may also remember that this determination was made from the main sequence turn-off point.

There were some stars in the cluster on the main sequence, and some more massive stars had already begun to move off to the right of the main sequence.

However, the least luminous stars in the cluster, the lowest mass stars, were mostly located a bit above the main sequence.

Now you can understand that these low-mass stars have not yet reached the main sequence for the Pleiades cluster. The previous slide indicates that only stars of about one solar mass or more have had time to reach the main sequence by now.

From observing star clusters, we can roughly determine the relative frequencies of formation of main sequence stars of different masses.

This initial mass function, as it is called, strongly favors low-mass stars.

For every star formed between 10 and 100 solar masses, we find roughly 10 stars between 2 and 10 solar masses, and a few hundred stars below half a solar mass.

We have never conclusively seen any star of greater than about 100 solar masses.

It is believed, as the British astronomer Eddington pointed out, that a star of such great mass would generate so much energy in its core that the outward streaming radiation would tear it apart. (People still argue about this.)

We are not sure where the star formation story ends on the low mass end of the scale.

As very low mass protostars (say, below 0.08 solar masses) contract under gravity, we believe that a bizarre physical phenomenon called degeneracy pressure would halt the collapse before efficient, self-sustaining hydrogen fusion could begin in the core.

Such low mass stars fill the gap between stars and planets.

It is not clear whether Jupiter-sized objects form individually from collapsing gas clouds, without being planets forming within the protostellar disks of larger objects.

Such a “star,” or “brown dwarf,” with 0.05 solar masses, Gliese 229B, was discovered orbiting a “real” star, Gliese 229A in 1995.

The brown dwarf Gliese 229B.This object was detected with a 1.5 m telescope on the ground (left) but the Hubble Space

Telescope provided a much sharper image (right). The small companion, Gliese 229B, has a mass of only 20 to 50 times that of Jupiter. Gliese 229B is the companion of an ordinary

star, but it has a luminosity of only 2 to 4 millionths that of the sun. Its spectrum resembles that of Jupiter. It has a lot of methane and a surface temperature of 600ºC to 700ºC.

Early models of the contraction of protostars to form main sequence stars were based upon rough scenarios like the one we have just outlined.

The Japanese astronomer Hyashi built models assuming this sort of “quasi-static” evolution, that is, a slow progress through a series of physical states each of which was very nearly in equilibrium.

Unfortunately, life is not this simple.

First Karl-Heinz Winkler, working in Germany, and later Frank Shu, at Berkeley, worked out detailed models for the formation of single solar mass stars that we now think are basically correct.

These models reveal that the protostar is not in equilibrium, but instead its surface is marked by an extremely strong shock front, in which infalling gas from the surrounding cloud is suddenly decelerated upon striking the surface of the protostar.

It is from this shock front that a huge amount of kinetic energy from the infalling gas, just converted into heat in the shock, is radiated into space.

The dynamics of this situation determines much of the internal structure of the protostar. The loss of huge amounts of heat of condensation from the shock, essentially before that energy can become incorporated into the protostar, greatly affects the course of such a protostar’s development.

These models, of course, did not include rotation or magnetic field affects, which still remain to be treated properly in such work.

These theoretical studies have led us to the conclusion that the internal structures of main sequence stars of different masses are dramatically different.

High mass stars generate nuclear energy prodigiously in their cores.

They produce so much energy so rapidly that “conduction” by radiation diffusion cannot transport it outward fast enough. Instead, we believe that their cores are fully convective. Nevertheless, outside their cores, where the gas is still very hot and ionized, radiation diffusion works well in carrying the energy all the way out to the surface.

Medium mass stars like our Sun transport liberated nuclear energy outward from their cores by radiation diffusion. In a layer near the surface, the gas becomes too opaque for efficient radiation diffusion, and convection takes over.

Low mass stars are believed to be convective from their surfaces right down to their cores.

Such stars with fast rotation rates can produce very powerful flares as a result of the winding up of their magnetic fields by their deep convection zones.

Proxima Centauri is such a “flare star.”

Low mass stars gradually burn their core hydrogen, reducing the number of independent particles (four protons are replaced by a single helium nucleus) in their cores.

In this process, their cores shrink, and they grow gradually a bit more luminous (the sun is thought to have increased in luminosity by perhaps 30% over the 4.7 billion years of the Earth’s history to date).

In the Sun, hydrogen nuclei are combined to produce helium nuclei (and extra energy in various forms).

Because helium nuclei usually have two protons and two neutrons, we have to combine four hydrogen nuclei (protons) to get one helium nucleus.

This is incredibly unlikely to happen in a single event.

Instead, it proceeds in stages, each involving only the collision of two particles.

The previous slide illustrates the primary nuclear reaction chain in the Sun.

It provides about 86% of the Sun’s energy.

Together with the alternate (second) reaction chain on the next slide, which involves berylium and lithium as intermediate products, these two reaction sequences produce 98.5% of the Sun’s energy.

The remainder of the Sun’s energy is produced by the CNO-cycle, the third reaction chain (on the next slide) involving carbon, nitrogen, and oxygen.

These alternate reaction chains are included here for correctness, but all you need concern yourself with is understanding the primary chain shown on the previous slide.

Do not memorize these nuclear reactions. They are given here for completeness and to satisfy the curious.

Now let’s consider what happens to a star like the Sun when it runs out of hydrogen fuel in its core.

It’s subsequent evolution is called the “red giant phenomenon,” and it is one of the early triumphs of computational science.

It was stellar evolution models that made us understand that red giant stars are not separate sorts of objects that have always been that way since their formation. These computer models, which take stars from one equilibrium state to the next, in which the nuclear makeup is slightly altered by the star’s burning, were the only way that we were able to figure out that red giant stars are just the evolved states of main sequence stars.

When hydrogen is exhausted in the core of a star like the Sun, the inert helium there does not generate further nuclear energy, so it contracts under the crushing weight of the gas above it.

The contraction of the helium core releases gravitational potential energy, so it actually heats up.

The layers above the core, which still contain unburnt hydrogen, contract and heat up as well.

The layer of hydrogen just above the helium core becomes so hot that it begins to burn, and this process actually generates more nuclear energy than the core hydrogen burning did when the star was on the main sequence.

The star can eventually increase in luminosity by up to 4 orders of magnitude. This process takes about a billion years, for a star like the Sun, and longer for less massive stars.

In order to radiate all this luminosity into space, the layers above the hydrogen burning shell expand enormously (by about a factor of 100 in radius) and become fully convective.

The now far greater surface area produces the much greater luminosity, ironically, at a somewhat reduced surface temperature.

The star has thus become a red giant.

As newly produced helium adds to the mass of the inert core, its greater gravity causes it to shrink still further.

The hydrogen burning shell shrinks along with the core, growing hotter and denser.

This makes the hydrogen burning rate increase in the shell, which increases the star’s luminosity still further.

This vicious cycle feeds upon itself until the temperature in the helium core reaches about 100 million degrees K, at which point helium nuclei can fuse in the core to produce carbon.

The process by which the core of a star can get hotter, rather than cooler, once its source of nuclear heat generation ceases is a bit odd, but we can understand it as follows.

We begin when nuclear reactions are continually generating heat in the core.

This heat produces pressure, which supports the core against gravity at its present radius.

The heat generation is balanced by escape of heat due to radiation, conduction, or convection from the surface region of the core. So the pressure, the gravity, and the radius of the core remain constant.

Now suppose that the nuclear reactions shut off from lack of further fuel.

The escape of heat does not shut off.

The escaping heat would cause the core to cool off, if only its gravity and its radius were to remain constant, as before.

But the escape of heat causes a reduction of the pressure supporting the core, so that it contracts under its gravity.

We can think of this contraction as generating ordered inward motion, which has an associated kinetic energy derived from the liberation of gravitational potential energy.

We can also think of the inward moving material as colliding with other material moving inward and toward it, so that the kinetic energy of the ordered motion is transformed into kinetic energy of disordered motion, which we call heat.

This additional heat will raise the pressure of the gas.

If the pressure rises enough, the collapse will stop, or at least pause or slow, since heat continues to escape from the surface.

How much added pressure does it take to arrest the collapse?You might think that all we have to do is to replace the heat

energy that escaped from the surface of the core with heat energy generated in the collapse from release of gravitational potential energy.

But this cannot be true, since the collapse makes the core smaller.The core’s mass is still the same, but now its smaller size means

that its gravity is stronger.This in turn means that we need more pressure than before in

order to support it at this smaller size.Therefore, if the collapse is slowed and nearly stopped, we know

that the pressure must be higher than before.In fact, the temperature, which is proportional to the ratio of the

pressure to the density, must be higher to counter the stronger gravity at this smaller core radius.

Once hydrogen fusion ignites in a shell around the core, it eventually burns much more brightly than the hydrogen burning in the star’s core.

We can understand this also.The energy generation rate we had with core hydrogen burning had to be sufficient to

provide enough pressure to hold up all the material overlying the core against the crush of gravity. It had to do this while matching the rate at which energy was escaping from the star through its surface.

Now the energy generated in the hydrogen burning shell must still support all this overlying material, but that material weighs more than before, because the core region has shrunk while its mass remained the same, and therefore Newton’s law of gravity says that the weight of material of a fixed mass located just above this core must be larger than before by a factor equal to the ratio of the square of the old radius of the core to the square of the new one.

As the core grows progressively smaller, with more and more inert helium added to it, the strength of gravity just above it increases also, and therefore the hydrogen burning shell burns more and more vigorously to hold up the outer layers of gas above it.

At each stage of this process, the hydrogen burning shell burns just strongly enough to essentially halt the shrinkage of the star.

If it did not do so, the inner region would shrink further, heat up further, and the hydrogen reaction rate would then necessarily increase, stopping or reversing the shrinkage.

However, there cannot be a true steady state of this burning process, because through this burning, the inert helium core must grow ever more massive.

Because the helium cannot yet burn at these temperatures in the core at this stage, as its mass increases, and 4 hydrogen atoms generating pressure are continually replaced by only 1 helium atom generating pressure, this core must continue to shrink.

The continual, slow shrinkage of the helium core slowly causes the conditions under which the hydrogen shell burning occurs. The result is that the gravity there is constantly increasing, and the hydrogen must burn ever more vigorously to maintain a nearly stationary state of the star.

Because helium nuclei have twice the charge of hydrogen nuclei, they repel each other more strongly.

They must therefore be moving faster in order to strike each other hard enough to overcome this repulsion and form beryllium. (The beryllium would split back into two helium nuclei, but under the conditions in a helium burning stellar core another helium nucleus can come along before this happens, so that a stable carbon nucleus can be created.)

Helium fusion in a red giant star ignites suddenly, in what is called a helium flash.

When the helium first ignites, the core is supported by degeneracy pressure, and its total pressure does not increase much as its temperature, and the helium fusion rate, shoot up.

After the helium flash, the core does expand against gravity, expanding and cooling the hydrogen burning shell.

Degeneracy pressure is a concept that will pop up again and again in our discussions of stellar evolution.

It can be understood, at least qualitatively, by the following analogy.

Think about a room.Now put a whole lot of billiard balls into the room. Just pour

them in until they fill up, say, a quarter of the room’s volume.They will be in the lower quarter of the room.If you try to squeeze them so that they take up less volume, you

will probably be unable to do so (let’s say that you can’t squeeze hard enough to pulverize them, so that all the little spaces between them can be filled with the powder produced).

The billiard balls now act like helium gas exerting degeneracy pressure. The billiard balls are touching. You can’t get them any closer to each other no matter how hard you push.

Now let’s put some energy into this system of billiard balls by picking them up and throwing them every which way.

Let’s imagine that we can do this somehow without getting hit, although the billiard balls will all hit each other.

The billiard balls have a lot more kinetic energy of disordered motion than before. They are a lot hotter.

And they must now take up a lot more room.If you were to turn a winch and pull the ceiling of the room

downward, you could make the billiard balls take up less roomBut this would take a lot of work, because the billiard balls would

be hitting the ceiling pretty hard, especially as the volume available to them got closer and closer to a quarter of the original room volume (when they would all be touching once again).

Without crushing the billiard balls, you could not make them take up less volume than a quarter of the original room.

Degeneracy pressure is like the force of resistance that the billiard balls exert when they are all touching and you try to squeeze them into a smaller volume.

Normal gas pressure is like the force that the billiard balls exert against the ceiling of the room as you lower it with your winch against the force of their bouncing off of it.

Normal gas pressure is strong, but you can overcome it if you press hard enough, and you can make the gas squeeze into a smaller volume.

Degeneracy pressure is stronger, in the sense that you cannot overcome it and squeeze the material into a smaller volume unless you squeeze so hard that the material changes its fundamental nature. An example of such a change is when the particles of the material fuse into different particles that take up less space. This is like pulverizing the billiard balls, or like combining protons with electrons in a star to form neutrons, which take up dramatically less space, believe it or not.

Fig. 16.10a Core structure of a helium-burning star.

Fig. 16.10b Relative sizes of a low-mass star as a main-sequence star, a red giant, and as a helium-burning star.

It turns out that the helium burning cores of all low-mass stars fuse helium into carbon at about the same rate. Therefore these stars all have about the same luminosity.

However, these stars can have different masses, based upon how much mass they started out with and how much mass they lost in stellar winds during their red giant phases.

Stars that lost more mass end up with smaller radii and higher surface temperatures.

These helium burning stars therefore occupy a horizontal branchin the H-R diagram of a star cluster.

The core helium of a low-mass helium-burning star runs out in about a hundred million years.

Once helium is exhausted in the core, the core again shrinks and heats up, helium begins burning in a shell around this core, and hydrogen continues burning in a shell around the helium region.

Once again the luminosity increases to new heights as the core size shrinks, and the outer layers of the star puff up again to a greater extent than ever.

Computer models show that the helium burning in the shell spikes upward every few thousand years in a series of thermal pulses.

For a one solar mass star, this stage can last less than a million years.

In order to ignite carbon in the core of such a star, the temperature must rise to about 600 million degrees K.

For low-mass stars, degeneracy pressure halts the shrinkage of the core before this very high temperature can be reached.

Such stars have huge stellar winds, and during the thermal pulses, carbon can be dredged up from the core and brought to the surface and into the wind by convection.

Red giants with high carbon concentrations in their atmospheres are called carbon stars.

Such carbon in the stellar wind can form dust grains, because of the very low surface temperatures of these stars.

During the final stages of the evolution of a low-mass star, the wind from the star becomes very great.

Ultimately, all the mass of the envelope surrounding the inert, degenerate carbon core is ejected to form a nebula, which is set aglow by the ultraviolet radiation of the cooling, but still very hot core.

This luminous nebula is called a planetary nebula.

The degenerate carbon core is called a white dwarf.

The textbook discusses what humans might do 5 billion years hence, when the Sun begins to become a subgiant, and the rest. This discussion is interesting enough to warrant reading, once. But 5 billion years is a long time.

The next slide summarizes the life story of a low-mass star, before we go on to look at some planetary nebulae.

In between the helium burning shell and the hydrogen burning shell above it is a region containing a mixture of helium from hydrogen burning and also carbon from the burning of helium.

In the last stages of the star’s life as a giant (as an AGB star), before it expels its outer hydrogen-rich envelope, the helium shell burns intermittently in a series of “helium shell flashes” at intervals of about a thousand years. These brief (2-year) flashes mix carbon from helium burning into the layers above the helium-free core of carbon and oxygen.

When the helium shell flashes into action, the hydrogen shell is lifted upward by the greatly increased pressure generated by helium burning, and hydrogen burning ceases. After the flash, as hydrogen begins burning again, the products of helium burning (mainly carbon) are “dredged up” by the convection of the outer envelope and carried to the surface of the star.

Once the carbon gets to the surface of the star, where the temperature is relatively low, it can condense to form dust grains.

These dark dust grains absorb the light coming out from the interior of the star and are pushed outward by this radiation pressure to create a strong stellar wind that carries off a portion of the outer layer of gases.

This process repeats with each successive helium shell flash, until eventually all the outer material of the star is expelled, and the inner core of carbon and oxygen remains.

We call this exposed carbon/oxygen core a white dwarf, because its surface is “white hot” and its radius is tiny (comparable to the radius of the earth).

Although carbon is the main product of helium burning in the star, other reactions also occur.

When hydrogen gets mixed in with the carbon above the helium burning shell, it can fuse with the carbon to form radioactive nitrogen.

This nitrogen-13 decays to form carbon-13, and this becomes a source of neutrons that get added to heavy elements that exist in trace quantities in this region of the star. Over time, exposure to these neutrons builds ever heavier elements, including such very heavy elements as lead.

All these trace constituents of the gas in the region get dredged up by the envelope convection, carried to the stellar surface, and expelled into the surrounding interstellar environment.

From there, they can become incorporated in a later generation of stars and/or planets.

The Owl Nebula, on the following slide, gives an idea why these nebulae, formed by mass ejections from dying stars, are called planetary nebulae – with poor telescopes they look like planets.

Planetary Nebula, the “Owl” in Ursa Major (NGC 3587)

Planetary Nebula, Abell 39,

a textbook example; 6 light years across,

7000 light yearsdistant

A small collection of Hubble Space Telescope images of planetary nebulae is shown on the next few slides. The mass of gas ejected from a star in this manner can be up to 75% of the total.

The first of these planetary nebulae, the Stingray Nebula, is so young that only 20 years ago its gas was not hot enough to emit light. However, the temperature of the central star has increased rapidly, so we will be able to witness the formation of this planetary nebula, a process that may take only 100 years or so.

The ultraviolet light from the central white dwarf star causes the surrounding nebula to glow.

Because Henize 1357 is 18,000 light-years away, only the Hubble Space Telescope can resolve its structure.

The central star is in a binary system, and its companion could be responsible for the dense ring of gas surrounding the star that has shaped the nebula, making the ejected gas form two bubbles.

The Stingray Nebula, or Henize 1357,HST image.

The Egg Nebula, CRL 2688, is likely to have first appeared a few hundred years ago.

The arc structures in this nebula, visible on the next slide, have been interpreted as shells of gas ejected previously by the central star at intervals of perhaps 100 to 500 years (could these have been the periodic helium flashes predicted by stellar evolution models?).

In the infrared (shown on the second slide), there is a dumbbell structure of molecular hydrogen. Matter streams out along the polar axis at 100 km/sec and collides with previously ejected gas moving at only 20 km/sec.

The matter in the two polar streams darkens the centers of the two cones of visible light from the central star.

The Egg Nebula, CRL 2688

The Hourglass Nebula, MyCn18, discovered by Margaret Mayall and Annie Cannon, at first fits the standard model of planetary nebula formation.

The idea is that matter is ejected from the central star in wind-like flows that are episodic, and that grow faster and faster.

We believe that the earlier ejected matter is denser at the equator than at the poles, and that it therefore channels the new, more rapidly ejected gas into an hourglass shape.

The Hourglass Nebula shows this structure beautifully, with the walls of the hourglass showing detailed structure that may either be related to the episodes of the earlier, slower winds or to the interaction of an energetic stream of gas with the walls of this channel.

The Hourglass Nebula is at a distance of 8,000 light-years.

Hubble Space

Telescope image of

the Hourglass Nebula,

MyCn 18.

“Snowplow” model of planetary Nebula

Internal structure of main sequence star and helium burning star

Internal structure of one solar mass star in second red giant stage

Internal structure of star – 15 solar mass in late second red giant stage

The ultimate fate of a star depends mainly upon the mass that it had when it was on the main sequence, burning hydrogen to form helium in its core.