Astronomy

A. Dayle Hancock

adhancock@wm.eduSmall 239

Office hours: MTWR 10-11am

http:// physics.wm.edu/~hancock/171/

Stellar Evolution

Main Sequence star changes during nuclear fusionWhat happens when the fuel runs outOld stars and second stage fusionH-R diagrams for star cluster in the later stages of evolutionTwo kinds of stellar populationsPulsating older starsHow stars in binary systems evolve differently

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Life on the Main Sequence

A main sequence star is a star that has a core which is 'burning' hydrogen by nuclear fusion. It is in hydrostatic equilibrium (the outward pressure of the fusion core is balanced by the inward pull of gravity). Stars on the main sequence have a main sequence lifetime. For the Sun this is about 12 billion years. A newly formed main sequence star is called a zero-age main sequence star. Over their lifetime on the main sequence, stars undergo changes as the hydrogen fuel is 'burned' in the star's core. As we have seen, new main sequence stars start with 74% hydrogen, 25% helium and 1% heavy elements.

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The Sun is almost ½ way through its lifetime. The graphs show the composition of the Sun as a function of distance from the center. 4.5 billion years ago the Sun had 75% hydrogen at the center but now is about 35%. The helium was originally at 25% but is now 65% of the mass at the center.

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Life on the Main Sequence

As 4 H are converted into 1 He in the core, the number of nuclei in the core is reduced and the core shrinks. This increases the temperature and density in the core. As the core shrinks,

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outer layers of the Sun expand and shine more brightly. Because the core is hotter and denser more fusion occurs. The increased energy causes the increased luminosity. Over the last 4.56 billion year the Sun has become 40% more luminous and the radius has increased by 6%.

Life on the Main Sequence

For small mass stars (0.08 to 0.4 Mⵙ the situation is different. This spectral class M stars are called red dwarfs. They are small and are 'red' because of their low temperature. They account for 85% of all stars. In red dwarf stars, convection cells extend into the core and move helium out of the core and hydrogen into the core.

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Life on the Main Sequence

Over the lifetime of a red dwarf, the star converts all of its hydrogen to helium. Since a red dwarf is small the fusion process is slower. Calculations indicate red dwarfs live for hundreds of billions of years. This is longer than the age of the universe. No red dwarf has ever converted all of its hydrogen into helium.

Lifetimes of Main Sequence Stars The lifetime of a main sequence star depends on its mass. Massive stars are more luminous and have short life times Less massive stars are less luminous and have longer lifetime.

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t∝1

M 2.5

The relationship between mass and lifetime is given by:

where M is the mass in Mⵙ and t is given in Sun lifetimes of 1.2 x 1010 years.

Red Giants

A star <0.4 Mⵙ will eventually (100s of billions of years) will use all of its hydrogen and become a ball of helium. A star >0.4 Mⵙ like the Sun will become a red giant. After the core hydrogen is used up, fusion continues in the hydrogen-rich shell outside of the core (shell hydrogen fusion).

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The burnt-out core will heat up from gravitational contraction. This increases the shell hydrogen burning. The helium falls into the core which contract more and heat up further. The core of a 1 Mⵙ star will contract to 1/3 its original size. The outer shells expands as the shell hydrogen fusion 'eats' its way outward into the surrounding material. The luminosity increase due to the larger size.

The surface temperature of the red giant drops. The core (mainly helium) increases from 15 million degrees to ~100 million degrees. Because of the large size, the gravity is weaker in the out regions. Mass escapes from the star. As much as 10-7 Mⵙ per year can escape. This compares to a 1 Mⵙ star like the Sun of 10-14 Mⵙ per year.

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Red Giants

The distant Future of the Solar System

The Sun's luminosity will continue to increase. In 1.3 billion years, the temperature of the Earth will increase to 50oC. In 3 ½ billion years the temperature of Earth will be higher than the boiling point of water. The Earth will become uninhabitable. After another 7 billion years the Sun will finish converting hydrogen to helium in its core and the sun will move off of the main sequence and become a red giant. After 700 million years the Sun will have expanded to a radius of 1 AU with a surface temperature of 3500 K. Mercury, Venus and Earth will be vaporized inside of the Sun. The Jovian planets will lose their outer atmospheres leaving only their tiny rocky cores.

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Fusion of Helium into Carbon and Oxygen

A young red giant star (>0.4 Mⵙ ) has a helium core with no thermonuclear reactions. Shell hydrogen fusion is the source of the red giant's energy. When the helium core (helium ash) become highly compressed and hot

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(100 million degrees), helium fusion can take place:

4He + 4He → 8Be

8Be (beryllium) is very unstable with a half life of 7 x 10-17 s. Because the helium core is so dense and hot, there is a significant possibility the 8Be will collide with another 4He. This then produced 12C through the triple alpha process:

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Fusion of Helium into Carbon and Oxygen

8Be + 4He → 12C + γWhere the γ is a high energy gamma ray photon. The process can continue with:

12C + 4He → 16O+ γ

Helium Flash and Electron Degeneracy

For stars with > 0.4 Mⵙ and < 2-3 Mⵙ helium fusion begins suddenly in what is called the helium flash. At the density and temperature of the helium core, the material is ionized into nuclei and electrons. The electrons are so tightly compressed they obey the Pauli exclusion principle. The Pauli exclusion principle state two fermion particles can not be in the same energy state. Just before the helium fusion begins theelectrons are so densely packed they exert a strong force to resist further compression known as degenerate electron pressure. As the helium fusion begins this heats the core but the core can not expand and cool which causes the helium fusion to proceed quickly – the helium flash. Eventually the electrons become so hot they are no longer degenerate and the core can expand.

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Continued Evolution of a Red Giant

After the helium flash, the stars luminosity decreases because of core expands and reduces the hydrogen shell fusion. Temperature and luminosity drops. The outer layers contract leaving a star with less luminosity, smaller and with a higher surface temperature. For a 1 Mⵙ star, helium fusion

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only last for about 108 years compared to its 12 billion years on the main sequence.

H-R Diagrams and Red Giant Evolution

This zero age main sequence (ZAMS) H-R diagram shows what various mass stars do when they the have exhausted the hydrogen in their cores and leave the main sequence at the dashed line. High mass stars move quickly from left to right maintaining their luminosity as their temperature decrease. After helium core fusion begins their luminosity peaks. For lower mass stars, helium core fusion starts with a helium flash and the luminosity decreases.

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These H-R diagrams show the evolution of stars which start in the same star cluster. Stars of different masses all begin in the cluster as protostars. Th more massive stars approach the main sequence faster than the smaller stars.

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Clusters and Stellar Evolution

After 3 million years most of the massive stars are main sequence stars. After 30 million years some of the massive starts have used up their hydrogen and are red giants while the less massive stars are approaching the main sequence. After 66 million years more of the main sequence stars have become red giants. 16

Clusters and Stellar Evolution

After 100 million years, many stars > 1 Mⵙ have ended hydrogen core fusion and have moved to become red giants. After 4.5 billion years, only the smaller stars remain on the main sequence.

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Clusters and Stellar Evolution

These two open star clusters have different ages. The lower cluster (NGC 2158) has no blue stars which indicates it contains only smaller stars and stars that have become red giants and is much older. The M35 cluster has many blue stars and is much younger (150 million years).

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Real Clusters

This globular cluster contains a few hundred million stars in a region only 20 pc across. Globular clusters are old because they contain no high mass main sequence stars. This globular cluster contains red giants and horizontal branch stars with helium fusion and shell hydrogen fusion.

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Clusters and Stellar Evolution

The age of a star cluster can be found from the turn off point. The turn off point is where there are no more high mass main sequence stars. The lower down the turn off point, the older the cluster.

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Measuring the Age of Clusters

Star clusters show the difference between the oldest and youngest stars. Population I stars have strong absorption line for metals. Population II stars show very weak absorption lines of metals. The early universe contained only H and He and very small amounts of metals. Population II stars formed out of this material and are the oldest stars. Second generation population II stars formed from nebula with fusion produced metals and are younger stars. The Sun and solar system formed from material with 12C, 16O etc. produced by helium fusion in ancient stars. 21

Population I and II stars.

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Pulsating Stars

Some stars pulsate. Their intensity will change over long or short periods of time. The image show the variation in the long period variable star Mira. At its maximum luminosity,

Mira is 100 times a bright as when it at its minimum. Mira's period is 332 days. It has a surface temperature of 3500 K.Long period variables have luminosities of 10 – 10,000 Lⵙ. The radius also increases with its luminosity. The details of a long period variable are not completely understood. Note: the image just shows brightness, not radius.

Pulsating stars are located in the upper right of a H-R diagram. Cepheid variables (named after δ Celhei) have shorter periods of days to months. Cepheids are located in the instability strip where main sequence stars are becoming red giants. This is the region where helium fusion has started. As the star passes through this region its brightness varies periodically.

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Cepheid Variable Stars

δ Celhei was discovered in 1784 and pulsates with a period of 5.4 days (top image). In 1894 Doppler shifting of its spectrum showed the surface of the surface was expanding at maximum brightness and contracting at minimum brightness over the same 5.4 day period.

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Cepheid Variable Stars

When δ Celhei is at its maximum brightness, the surface temperature is at a maximum. At its maximum brightness diameter is expanding.

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Cepheid Variable Stars

What makes a Cepheid variable star pulsate? Eddington suggested that Cepheids pulsate because they are more opaque when compressed. This increases the temperature because of trapped heat energy and the star expands. As it expands, the heat can escape, the internal pressure drops and the star collapses. In the 1960s, John Cox showed that helium was the cause. Normally un-ionized helium is transparent to radiation. In certain outer layers of the Cepheid, compression ionizes the helium instead of just heating it. When the helium becomes ionized it becomes opaque to radiation. This traps the radiation causing the star to expand. As this outer layer expands, it cools and the helium becomes transparent and releases the heat. The stars surface then falls inward.

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Cepheid Variable Stars

Cepheids have luminosities of 102-104 Lⵙ. Plotting the luminosity of a Cepheid vs the Cepheid's period on a log log plot show the period is related to the luminosity. Measuring the period gives the luminosity and knowing the luminosity determines the distance using the inverse square law. With such large luminosities, Cepheid can be used to measure distances to stars millions of pc away even stars in distant galaxies. 27

Cepheid Variable Stars

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RR Lyrea Variables. Low mass stars do not become variable states. The third type of variable star is the RR Lyrea. These stars have periods of less than a day and luminosities of ~100 Lⵙ. The region on the H-R diagram instability strip for RR Lyrea stars is a segment of the horizontal branch. These are Population II stars and are often found in globular clusters. They have been used to determine distances of stars in the Milky Way in the same way Cepheids are used to find distances to stars in other galaxies.

Binary systems can effect stellar evolution. In a binary system where the stars are far apart, both stars are nearly perfect sphere. In a close binary, the mathematical surface which defines the gravitational domain of each star is call the Roche surface. Tidal forces can distort the stars surface in a close binary. The Lagrangian point is where the two Roche surfaces touch in a close binary. Gravity and rotational forces balance at the Lagrangian point. In a semi-detached binary, one star fills its Roche lobe (surface). 29

Mass transfer in Binary Systems

In a contact binary system, both stars fill their Roche lobe. Mass can flow from either star into the other star across the Lagrangian point.

If both stars are so close they overfill their Roche lobe (overcontact binary), the stars can share their outer atmospheres.

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Mass transfer in Binary Systems

If the binary systems orbital plane is edge-on from our viewpoint, eclipses of the stars can be seen. In the case of the semi-detached binary Algol system, the variation in intensity is because of the more luminous main sequence star eclipsing the larger red giant.

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Observation of Mass transfer

In the β Lyrea semi-detached binary system, the less massive β Lyrea fills its Roche lobe but the more massive binary companion is enveloped in an accretion disk of gas being captured by β Lyrea. Eventually, the detached star will fill its Roche lobe and they system will become an over-contact binary system.

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Observation of Mass transfer

W Ursae Majois is an example of an over contact binary system where the two star share a common outer atmosphere.

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Observation of Mass transfer