The Sun and Stars.

The Sun and Stars

THIS WEEK Chapters 11, 12, 13 Review Tuesday, April 12
Exam #2 Thursday, April 14 Assigned question due Today: Question 3 from Chapter 12.

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Why does this produce energy? Before: the mass of 4 protons is 4 proton masses. After: the mass of 2 protons and 2 neutrons is 3.97 proton masses. Einstein: E = mc2. The missing mass went into energy! 4H ---> 1He + energy

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Image from Nick Strobel’s Astronomy Notes (

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Extremely high temperatures and densities are needed! Images from Nick Strobel’s Astronomy Notes (

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Extremely high temperatures and densities are needed! The temperature is about 8,000,000K at the core of the Sun.

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). The details are a bit complex: Image from Nick Strobel’s Astronomy Notes (

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). The details are a bit complex: In the Sun, 6 hydrogen nuclei are involved in a sequence that produces two hydrogen nuclei and one helium nucleus. This is the proton-proton chain. In more massive stars, a carbon nucleus is involved as a catalyst. This is the CNO cycle.

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Why doesn’t the Sun blow up like a bomb?

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Why doesn’t the Sun blow up like a bomb? There is a natural “thermostat” in the core.

Controlled Fusion in the Sun
First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature. Rate ~ (temperature)4 for p-p chain. Rate ~ (temperature)15 for the CNO cycle. Small changes in the temperature lead to large changes in the fusion rate. Suppose the fusion rate inside the Sun increased: The increased energy heats the core and expands the star. But the expansion cools the core, lowering the fusion rate. The lower rate allows the core to shrink back to where it was before.

Models of the Solar Interior
The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities: Temperature Pressure Mass density

The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities: Temperature Pressure Mass density The relationship between these three quantities is called the equation of state.

Ideal Gas For a fixed volume, a hotter gas exerts a higher pressure:
Image from Nick Strobel’s Astronomy Notes (

Hydrostatic Equilibrium
The Sun does not collapse on itself, nor does it expand rapidly.

The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance: Image from Nick Strobel’s Astronomy Notes (

The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun. Image from Nick Strobel’s Astronomy Notes (

The pieces so far: Energy generation (nuclear fusion). Ideal gas law (relation between temperature, pressure, and volume. Hydrostatic equilibrium (gravity balances pressure). Continuity of mass (smooth distribution throughout the star). Continuity of energy (amount entering the bottom of a layer is equal to the amount leaving the top). Energy transport (how energy is moved from the core to the surface).

Solve these equations on a computer: Compute the temperature and density at any layer, at any time. Compute the size and luminosity of the star as a function of the initial mass. Etc……. It is possible to explain the temperature-luminosity diagrams of clusters (among other things).

Odds and Ends Why does L vary like (mass)4? E.g., why is an O-star about 10,000 times more luminous than the Sun when its mass is only 20 times the solar mass?

Odds and Ends Why does L vary like (mass)4? E.g., why is an O-star about 10,000 times more luminous than the Sun when its mass is only 20 times the solar mass? More massive stars need hotter interiors to be stable. The increased temperature leads to large increase in energy generation (the rate varies like (temperature)15.) Image from Nick Strobel’s Astronomy Notes (

Odds and Ends Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass?

Odds and Ends Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? At the high end, the pressure rises rapidly with mass, and is stronger than gravity when the mass gets near 100 solar masses.

Odds and Ends Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? At the high end, the pressure rises rapidly with mass, and is stronger than gravity when the mass gets near 100 solar masses. The star is no longer stable!

Odds and Ends Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? At the low end, the core temperature does not get high enough to fuse hydrogen since the gravitational force is relatively weak.

Odds and Ends Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? At the low end, the core temperature does not get high enough to fuse hydrogen since the gravitational force is relatively weak. “Brown dwarfs” are such low-mass objects.

Temperature-Luminosity Diagrams
Most of the stars are in the “main sequence”. We can understand these stars pretty well. Image from Nick Strobel’s Astronomy Notes (

Most of the stars are in the “main sequence”. We can understand these stars pretty well. What about these “giants” and “white dwarfs”? Image from Nick Strobel’s Astronomy Notes (

Most of the stars are in the “main sequence”. We can understand these stars pretty well. What about these “giants” and “white dwarfs”? These are stars in a much later stage of evolution… Image from Nick Strobel’s Astronomy Notes (

Stellar Evolution and the Life Cycles of the Stars

Stellar Evolution There are several distinct phases in the life cycle of a star. The evolutionary path depends on the initial mass of the star.

Stellar Evolution There are several distinct phases in the life cycle of a star. The evolutionary path depends on the initial mass of the star. Although there is a continuous range of masses, we often talk about “lightweight” stars (masses similar to the Sun) and “heavyweight” stars (masses about about 10 solar masses).

Stellar Evolution

Stellar Evolution The basic steps are: Gas cloud Main sequence
Red giant Rapid mass loss (planetary nebula or supernova explosion) Remnant

Stellar Evolution The basic steps are:
Gas cloud Main sequence Red giant Rapid mass loss (planetary nebula or supernova explosion) Remnant The length of time spent in each stage, and the details of what happens at the end depend on the initial mass.

Star Formation The starting point is a giant molecular cloud. The gas is relatively dense and cool, and usually contains dust.

Star Formation The starting point is a giant molecular cloud. The gas is relatively dense and cool, and usually contains dust. A typical cloud is several light years across, and can contain up to one million solar masses of material.

Star Formation The starting point is a giant molecular cloud. The gas is relatively dense and cool, and usually contains dust. A typical cloud is several light years across, and can contain up to one million solar masses of material. Thousands of clouds are known.

Side Bar: Observing Clouds
Ways to see gas:

Ways to see gas: By “reflection” of a nearby light source. Blue light reflects better than red light, so “reflection nebulae” tend to look blue.

Ways to see gas: By “reflection” of a nearby light source. Blue light reflects better than red light, so “reflection nebulae” tend to look blue. By “emission” at discrete wavelengths. A common example is emission in the Balmer-alpha line of hydrogen, which appears red.

Ways to see dust:

Ways to see dust: If the dust is “warm” (a few hundred degrees K) then it will emit light in the long-wavelength infrared region or in the short-wavelength radio.

Ways to see dust: If the dust is “warm” (a few hundred degrees K) then it will emit light in the long-wavelength infrared region or in the short-wavelength radio. Dust will absorb light: blue visible light is highly absorbed; red visible light is less absorbed, and infrared light suffers from relatively little absorption.

Ways to see dust: If the dust is “warm” (a few hundred degrees K) then it will emit light in the long-wavelength infrared region or in the short-wavelength radio. Dust will absorb light: blue visible light is highly absorbed; red visible light is less absorbed, and infrared light suffers from relatively little absorption. Dust causes “reddening”.

Giant Molecular Clouds
This nebula is in the sword of Orion. It is about 29 light years across and 1500 light years away. Dark regions are apparent (obscuration by dust), as well as regions of glowing gas (heated by a nearby hot star) Image from Nick Strobel’s Astronomy Notes (

Giant Molecular Clouds
This nebula is in the belt of Orion. Dark dust lanes and also glowing gas are evident.

The Protostar A giant molecular cloud is in rough hydrostatic equilibrium: gravity balances internal pressure.

The Protostar A giant molecular cloud is in rough hydrostatic equilibrium: gravity balances internal pressure. An external disturbance can cause the cloud to collapse:

The Protostar A giant molecular cloud is in rough hydrostatic equilibrium: gravity balances internal pressure. An external disturbance can cause the cloud to collapse: The material collapses to a rotating disk, and friction drives material into the center, where it builds up. The central object heats up as the cloud collapses. Eventually, the temperature gets hot enough for nuclear fusion to occur.

The Protostar An external disturbance can cause the cloud to collapse:
The material collapses to a rotating disk, and friction drives material into the center, where it builds up. The central object heats up as the cloud collapses. Eventually, the temperature gets hot enough for nuclear fusion to occur. We are left with a newly born star surrounded by a disk of material.

The Protostar Protostars with dusty disks are common in the Orion nebula.

The Protostar Infrared observations often reveal hundreds of newly-formed stars embedded in molecular clouds.

The Protostar Newly-formed hot stars can alter their environment.
Image from Nick Strobel’s Astronomy Notes (

The Protostar A collapsing cloud can form hundreds of stars.

The Protostar A collapsing cloud can form hundreds of stars.
Stars with small masses (less than a solar mass) are much more common than massive stars (stars more than about 15 to 20 solar masses).

The Protostar A collapsing cloud can form hundreds of stars.
Stars with small masses (less than a solar mass) are much more common than massive stars (stars more than about 15 to 20 solar masses). The highest mass stars are very hot and luminous, and can alter the cloud environment.

The Main Sequence A star that is fusing hydrogen to helium in its core is said to be on the main sequence.

The Main Sequence A star that is fusing hydrogen to helium in its core is said to be on the main sequence. A star spends most of its “life” on the main sequence; the time spent is roughly proportional to 1/M3, where M is the initial mass.

After the Main Sequence
On the main sequence, the star is in hydrostatic equilibrium where internal pressure supports the star against gravitational collapse.

On the main sequence, the star is in hydrostatic equilibrium where internal pressure supports the star against gravitational collapse. Nuclear fusion (hydrogen to helium) is the energy source.

On the main sequence, the star is in hydrostatic equilibrium where internal pressure supports the star against gravitational collapse. Nuclear fusion (hydrogen to helium) is the energy source. What happens when all of the hydrogen in the core is converted to helium?

On the main sequence, the star is in hydrostatic equilibrium where internal pressure supports the star against gravitational collapse. Nuclear fusion (hydrogen to helium) is the energy source. What happens when all of the hydrogen in the core is converted to helium? The details depend on the initial mass of the star…

After the Main Sequence: Low Mass
After the core hydrogen is used up, internal pressure can no longer support the core, so it starts to collapse. This releases energy, and additional hydrogen can fuse outside the core.

After the core hydrogen is used up, internal pressure can no longer support the core, so it starts to collapse. This releases energy, and additional hydrogen can fuse outside the core. The excess energy causes the outer layers of the star to expand by a factor of 10 or more.

After the core hydrogen is used up, internal pressure can no longer support the core, so it starts to collapse. This releases energy, and additional hydrogen can fuse outside the core. The excess energy causes the outer layers of the star to expand by a factor of 10 or more. The star will be large and cool: these are the red giants seen in the temperature-luminosity diagram.

The red giants are stars that just finished up fusing hydrogen in their cores. Image from Nick Strobel’s Astronomy Notes (

Some red giants are as large as the orbit of Jupiter! Image from Nick Strobel’s Astronomy Notes (

The excess energy causes the outer layers of the star to expand by a factor of 10 or more. The star will be large and cool: these are the red giants seen in the temperature-luminosity diagram.

The excess energy causes the outer layers of the star to expand by a factor of 10 or more. The star will be large and cool: these are the red giants seen in the temperature-luminosity diagram. The core continues to collapse, and helium can fuse into carbon for a short time. The star expands further.

The excess energy causes the outer layers of the star to expand by a factor of 10 or more. The star will be large and cool: these are the red giants seen in the temperature-luminosity diagram. The core continues to collapse, and helium can fuse into carbon for a short time. The star expands further. The outer layers eventually may be ejected to form a “planetary nebula”.

Planetary Nebulae These objects resembled planets in crude telescopes, hence the name “planetary nebula.” They are basically bubbles of glowing gas.

Planetary Nebulae They are basically bubbles of glowing gas.
The ring shape is a result of the viewing geometry. Image from Nick Strobel’s Astronomy Notes (

Planetary Nebulae The red light is the Balmer alpha line of hydrogen, and the green line is due to oxygen. Image from Nick Strobel’s Astronomy Notes (

Planetary Nebulae This HST image shows freshly ejected material interacting with previously ejected material. Image from Nick Strobel’s Astronomy Notes (

Planetary Nebulae The outer layers of the star are ejected, thereby returning material to the interstellar medium.

Planetary Nebulae The outer layers of the star are ejected, thereby returning material to the interstellar medium. What about the core?

The Remnant: Low Mass After all of the helium in the core is used up, a low mass star cannot get hot enough to go to the next step of carbon fusion.

The Remnant: Low Mass After all of the helium in the core is used up, a low mass star cannot get hot enough to go to the next step of carbon fusion. There is no more energy source to support the core, so it collapses.

The Remnant: Low Mass After all of the helium in the core is used up, a low mass star cannot get hot enough to go to the next step of carbon fusion. There is no more energy source to support the core, so it collapses. To what?

Degenerate Matter Eventually, the gas becomes supercompressed so that the particles are touching. The the gas is said to be degenerate, and acts more like a solid. For a star with an initial mass of less than about 8 solar masses, the final object has a radius of only about 1% of the solar radius, and is extremely hot (and therefore blue).

Degenerate Matter Eventually, the gas becomes supercompressed so that the particles are touching. The the gas is said to be degenerate, and acts more like a solid. For a star with an initial mass of less than about 8 solar masses, the final object has a radius of only about 1% of the solar radius, and is extremely hot (and therefore blue). These are white dwarfs.

The red giants are stars that just finished up fusing hydrogen in their cores. The white dwarfs are the left over cores of red giants that have shed their mass in planetary nebulae. Image from Nick Strobel’s Astronomy Notes (

White Dwarfs White dwarfs are supported by “electron degeneracy pressure”, which is explained by quantum mechanics: basically no two electrons can occupy the same space. The density can be 106 times that of water. A higher mass white dwarf has a smaller radius than a lower mass white dwarf. The maximum allowed mass is 1.4 solar masses.

After the Main Sequence: High Mass
A massive star (more than about 10 to 15 solar masses) will use up its core hydrogen relatively quickly. The core will collapse.

A massive star (more than about 10 to 15 solar masses) will use up its core hydrogen relatively quickly. The core will collapse. The core heats up, and helium is fused into carbon. After this, carbon and helium can fuse into oxygen since the high mass gives rise to very high temperatures.

A massive star (more than about 10 to 15 solar masses) will use up its core hydrogen relatively quickly. The core will collapse. The core heats up, and helium is fused into carbon. After this, carbon and helium can fuse into oxygen since the high mass gives rise to very high temperatures. Eventually elements up to iron are formed in successive stages.

Eventually elements up to iron are formed in successive stages. Iron fusion does not produce energy, so there is no energy source to halt the gravitational collapse.

Eventually elements up to iron are formed in successive stages. Iron fusion does not produce energy, so there is no energy source to halt the gravitational collapse. If the initial mass of the star is more than about 8 solar masses, the core will be too massive to form a white dwarf, since at that stage the gravity is stronger than the electron degeneracy pressure.

Eventually elements up to iron are formed in successive stages. Iron fusion does not produce energy, so there is no energy source to halt the gravitational collapse. If the initial mass of the star is more than about 8 solar masses, the core will be too massive to form a white dwarf, since at that stage the gravity is stronger than the electron degeneracy pressure. The collapse continues.

If the initial mass of the star is more than about 8 solar masses, the core will be too massive to form a white dwarf, since at that stage the gravity is stronger than the electron degeneracy pressure. The collapse continues. Protons and electrons are fused to form neutrons and neutrinos. The core collapses to a very tiny size, liberating a huge amount of energy. The outer layers are blown off in a supernova explosion.

Supernovae A supernova can be a billion times brighter than the Sun at its peak.

Supernovae Material is returned to the interstellar medium, to be recycled in the next generation of stars. Owing to the high temperatures, lots of exotic nuclear reactions occur, resulting in the production of various elements. All of the elements past helium were produced in supernovae.

Supernovae Material is returned to the interstellar medium, to be recycled in the next generation of stars. Owing to the high temperatures, lots of exotic nuclear reactions occur, resulting in the production of various elements. All of the elements past helium were produced in supernovae. Most of the atoms in your body came from a massive star!

The Remnant: High Mass What happened to the core?

The Remnant: High Mass What happened to the core?
Gravity overcame the electron degeneracy pressure, so the collapse continued. Protons and electrons form neutrons, and the gas is compressed so that the neutrons become degenerate (i.e. they are basically touching). The resulting remnant has a radius of about 10 km, and a typical mass of 1.4 solar masses. This is a neutron star.

Neutron Stars Neutron stars have roughly 1.4 times the mass of the Sun packed into an object with a radius of only 10 km.

Neutron Stars The best model for a radio pulsar is a rapidly rotating neutron star with a strong magnetic field.

Neutron Stars The spinning neutron star acts like a “light house”, leading to pulsed radiation being observed on Earth.

Where it Stops For large masses (initial mass greater than about 30 solar masses): The core ends up with a substantially more than 1.4 solar masses. The temperature gets hot enough to fuse elements all the way up to iron. The fusion of iron takes energy rather than liberating it. The core collapses, but it is too massive to be supported by electron degeneracy pressure and neutron degeneracy pressure.

Where it Stops For large masses (initial mass greater than about 30 solar masses): The core ends up with a substantially more than 1.4 solar masses. The temperature gets hot enough to fuse elements all the way up to iron. The fusion of iron takes energy rather than liberating it. The core collapses, but it is too massive to be supported by electron degeneracy pressure and neutron degeneracy pressure. No known force can halt the collapse, and the core collapses to a point.

Where it Stops For large masses (initial mass greater than about 30 solar masses): The core ends up with a substantially more than 1.4 solar masses. The temperature gets hot enough to fuse elements all the way up to iron. The fusion of iron takes energy rather than liberating it. The core collapses, but it is too massive to be supported by electron degeneracy pressure and neutron degeneracy pressure. No known force can halt the collapse, and the core collapses to a point. A black hole is born.

A Black Hole A black hole is an object with a gravitational field so strong that nothing, not even light, can escape. Newton’s gravitational theory no longer accurately describes gravity, one must use Einstein’s more complex theory.

A Black Hole A black hole is an object with a gravitational field so strong that nothing, not even light, can escape. Newton’s gravitational theory no longer accurately describes gravity, one must use Einstein’s more complex theory. The matter is compressed to a single point (called the singularity). There is no physical surface.

Detecting a Black Hole If light cannot escape from a black hole, how do we detect them?

Detecting a Black Hole If light cannot escape from a black hole, how do we detect them? By looking at material close to the black hole, before it disappears…

Detecting a Black Hole If the black hole is close to another star, it can pull material off that star. As the matter falls into the black hole, it gets very hot, and emits X-rays.

Detecting a Black Hole To look for a black hole, look for a binary system where a star is orbiting an optically dark companion that is a source of X-rays.

Detecting a Black Hole To look for a black hole, look for a binary system where a star is orbiting an optically dark companion that is a source of X-rays. 18 such systems are currently known.

The Sun and Stars.

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