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ASTRO 101

Principles of Astronomy

Instructor: Jerome A. Orosz (rhymes with “ boris ” ) Contact: • Telephone: 594-7118 • E-mail: [email protected]

• WWW: http://mintaka.sdsu.edu/faculty/orosz/web/ • Office: Physics 241, hours T TH 3:30-5:00

Homework/Announcements • Chapter 9 homework due April 23: Question 13 (Draw an H-R Diagram …) • Chapter 10 homework due April 30: Question 15 (Explain how and why the turnoff point on the H-R diagram of a cluster is related to the cluster’s age.)

• Stellar Evolution.

Stellar Evolution • Observational aspects – Observations of clusters of stars • Theory – Outline of steps from birth to death

Stellar Groupings • To understand how stars evolve, one must study groups of stars since an individual star takes a

very long time

to change.

Stellar Groupings • To understand how stars evolve, one must study groups of stars since an individual star takes a

very long time

to change.

• One must choose samples of stars

very carefully

to avoid bias and to eliminate “ variables ” .

Stellar Groupings • One way to get around sample biases is to study groups of stars bound by gravity . Why?

1 The distance across a group is relatively small, which means the stars in the group have roughly the same distance from us . This in turn means that ratios in apparent brightness are the same as the ratios of intrinsic luminosities .

Stellar Groupings • One way to get around sample biases is to study groups of stars bound by gravity . Why?

2 The groups are loosely bound, meaning that the stars must have formed together , rather than being “ captured ” after formation.

Stellar Groupings • One way to get around sample biases is to study groups of stars bound by gravity . Why?

2 The groups are loosely bound, meaning that the stars must have formed together , rather than being “ captured ” after formation. This means the stars in the group all have the same age and the same chemical composition .

Star Clusters • Star clusters can be roughly classified based on how “ tight ” they are.

 “ Open ” clusters are less compact, and generally have relatively small numbers of stars (a few hundred).

Star Clusters • Star clusters can be roughly classified based on how “ tight ” they are.

 “ Globular ” clusters are more compact, and generally have relatively large numbers of stars (a few hundred thousand).

Star Clusters • The physical size of a cluster is only a few dozen light years, compared to typical distances of several hundred or a few thousand light years.

Star Clusters • The physical size of a cluster is only a few dozen light years, compared to typical distances of several hundred or a few thousand light years. All of the cluster stars have the same distance from us to an accuracy of a few percent. • You can plot the apparent brightness instead of the intrinsic luminosity on the temperature-luminosity diagram.

Star Clusters • Here is a plot of

apparent magnitude

vs. the color. No pattern is seen since each star is at a different distance.

Figure from Michael Richmond ( http://spiff.rit.edu/classes/phys230/phys230.html

)

Star Clusters • Here is a plot of luminosity (expressed as

absolute magnitude)

vs. the color. A clear pattern is seen since the luminosity is a physical property.

Figure from Michael Richmond ( http://spiff.rit.edu/classes/phys230/phys230.html

)

Star Clusters • Here is a plot of luminosity (expressed as

absolute magnitude)

vs. the color. A clear pattern is seen since the luminosity is a physical property.

Comparing Stellar Properties • Sometimes in order to understand how stars work, it is useful to compare two or more stars.

• Note you can sometimes compare properties without knowing the actual values, as in species.

” “ The female rabbit of this species is larger than the male rabbit of the same • A simple question to ask is “ Which star is more luminous than the others?

”

Comparing Stellar Properties • This large-area photograph shows the constellations of Orion, Canis Major, Canis Minor Taurus, and a few others. • Which star is more luminous: Rigel or Sirius

Comparing Stellar Properties

Comparing Stellar Properties • Looking up the distances, we find • Rigel – d = 240 pc – L = 66,000 L o • Sirius – d = 2.64 pc – L = 25.4 L o • The ratio of the fluxes is not the ratio of the luminosities since the distances are different.

Comparing Stellar Properties

Comparing Stellar Properties • A cluster is a group of stars bound by their own gravity. The size of the cluster is small compared to its distance from Earth.

• Which star is more luminous: Star A or Star B

Comparing Stellar Properties

Comparing Stellar Properties • Comparing the apparent brightnesses does not help if the stars have different distances. Figure from Michael Richmond ( http://spiff.rit.edu/classes/phys230/phys230.html

)

Comparing Stellar Properties • • Comparing the apparent brightnesses of stars in a cluster

does

help since each star in that cluster has the same distance from the Earth. The distance is still needed to compute the actual luminosities, and not just the relative ones.

Figure from Michael Richmond ( http://spiff.rit.edu/classes/phys230/phys230.html

)

Star Clusters • Let ’ s plot the stars from several different clusters on the diagram and draw “ tracks clean it up… ” where the stars are to Figure from Michael Richmond ( http://spiff.rit.edu/classes/phys230/phys230.html

)

Star Clusters • The “ sequences (within certain bounds).

” occupied by cluster stars changes from cluster to cluster

Star Clusters • The “ sequences (within certain ” occupied by cluster stars changes from cluster to cluster bounds). WHY????

• This is related to the life cycles of stars.

The Life Cycles of Stars • To understand why different star clusters have different tracks in the temperature luminosity diagram, we must return to a result found from eclipsing binaries…

Mass-Luminosity Relation • The luminosity of a star is related to its mass: L ~ M p , where p is almost 4.

Mass-Luminosity Relation • The luminosity of a star represents the amount of energy emitted per second. There must be a source of this energy, and it cannot last forever.

• The amount of “ fuel ” to its initial mass.

a star has is proportional

Mass-Luminosity Relation • The luminosity of a star represents the amount of energy emitted per second. There must be a source of this energy, and it cannot last forever.

• The amount of “ fuel ” its initial mass.

a star has is proportional to • The length of time the fuel can be spent is equal to the amount of fuel divided by the consumption rate.

Mass-Luminosity Relation • The luminosity of a star represents the amount of energy emitted per second. There must be a source of this energy, and it cannot last forever.

• The amount of “ fuel ” its initial mass.

a star has is proportional to • The length of time the fuel can be spent is equal to the amount of fuel divided by the consumption rate.

• Age ~ mass/luminosity

Mass-Luminosity Relation • The luminosity of a star represents the amount of energy emitted per second. There must be a source of this energy, and it cannot last forever.

• The amount of “ fuel ” its initial mass.

a star has is proportional to • The length of time the fuel can be spent is equal to the amount of fuel divided by the consumption rate.

• Age ~ mass/luminosity = mass/(mass) 4 =1/(mass) 3

Mass-Age Relation • Age ~ 1/(mass) 3 ( “ age ” main sequence, “ mass ” means time on the means initial mass).

• More massive stars “ drops by a factor of 8.

die ” much more quickly than less massive stars. For example, double the mass, and the age

Mass-Age Relation • Age ~ 1/(mass) 3 ( “ age ” main sequence, “ mass ” means time on the means initial mass).

• More massive stars “ drops by a factor of 8.

die ” much more quickly than less massive stars. For example, double the mass, and the age • On the main sequence, O and B stars (the bluest ones) are the most massive. Their lifetimes are relatively short.

Mass-Age Relation • Detailed computations show:

Star Clusters • Large radii • Small radii • High mass (main sequence) • Low mass (main sequence)

Star Clusters • The “ sequences (within certain bounds).

” occupied by cluster stars changes from cluster to cluster

Star Clusters • Some clusters have “ lost ” only the bluest main sequence stars.

• Others have lost main sequence stars down to type F.

Star Clusters • Some clusters have “ lost ” only the bluest main sequence stars.

• Others have lost main sequence stars down to type F.

• The differences in the tracks are due to age differences of the clusters!

Star Clusters • Here is an animation showing how a cluster ages: http://spiff.rit.edu/classes/phys230/lectures/clusters/hr_anim_slow.gif

Star Clusters • Here is a temperature luminosity diagram for the Hyades cluster.

• This one is relatively young.

Star Clusters • Here are the temperature luminosity diagrams for a three clusters.

• These diagrams and others can be used to make a “ movie ” on how stars evolve.

Star Clusters • Here is a schematic diagram showing a cluster age from zero years (formation) to several billion years.

Stellar Evolution • Observational aspects – Observations of clusters of stars • Theory – Outline of steps from birth to death

Stellar Models

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, there are 4 ranges of masses that capture all of the interesting features.

Stellar Evolution

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 .

Points to Remember: • How to counter gravity: – Heat pressure from nuclear fusion in the core (no mass limit) • Gas pressure proportional to the temperature.

– Electron “ degeneracy ” solar masses) pressure (mass limit 1.4 – Neutron “ degeneracy ” masses) pressure (mass limit 3 solar • Stars experience rapid mass loss near the end of their “ lives ” , so the final mass can be much less than the initial mass.

Points to Remember: • Sources of energy: – Nuclear fusion: • needs very high temperatures • about 0.7% efficiency for hydrogen into helium.

– Gravitational “ accretion ” energy: • Drop matter from a high “ potential ” • About 10% efficient when falling onto massive bodies with very small radii.

Stellar Evolution

Star Formation • The starting point is a contains dust.

giant molecular cloud

. The gas is relatively dense and cool, and usually • 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:  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.

Side Bar: Observing Clouds • 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 belt of Orion. Dark dust lanes and also glowing gas are evident.

Giant Molecular Clouds • Interstellar dust makes stars appear redder.

Giant Molecular Clouds • This images shows dust obscuration, an emission nebula, and a reflection nebula.

Giant Molecular Clouds • Inside many nebula one finds very dense cores called Bok globules that are ready to collapse…

Gravity and Angular Momentum • There are two important concepts to keep in mind when considering the fate of giant molecular clouds: – Gravity: pulls things together – Angular momentum: a measure of the spin of an object or a collection of objects.

Gravity • There are giant clouds of gas and dust in the galaxy. They are roughly in equilibrium, where gas pressure balances gravity.

• Sometimes, an external disturbance can cause parts of the cloud to move closer together. In this case, the gravitational force may be stronger than the pressure force.

Gravity • Sometimes, an external disturbance can cause parts of the cloud to move closer together. In this case, the gravitational force may be stronger than the pressure force.

• As more matter is pulled in, the gravitational force increases, resulting in a runaway collapse.

Angular Momentum • Angular momentum is a measure of the spin of an object. It depends on the

mass

that is spinning, on the

distance

from the rotation axis, and on the

rate of spin

• I = (mass) .

(radius) .

(spin rate) • The angular momentum in a system stays fixed, unless acted on by an outside force.

Conservation of Angular Momentum • An ice skater demonstrates the conservation of angular momentum: • Arms held in: high rate of spin.

• Arms extended: low rate of spin.

• I = (mass) .

(radius) .

(spin rate) (angular momentum and mass are fixed here)

Conservation of Angular Momentum • If an interstellar cloud has some net rotation, then it cannot collapse to a point. Instead, the cloud collapses into a disk that is perpendicular to the rotation axis.

Condensation Theory • An interstellar cloud collapsed to a disk. Friction in the disk drives matter inward and outward (conserving angular momentum).

• Planets may eventually form in the disk.

Condensation Theory Image from Nick Strobel ’ s Astronomy Notes ( http://www.astromynotes.com

)

The Protostar • This diagram shows the steps as computed using a computer model.

The Protostar • This diagram shows how a star “ moves ” through the temperature-luminosity diagram as it forms.

The Protostar • High mass stars simply get bluer, whereas the lower mass stars contract and become dimmer.

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.

Young Star Systems • There is strong evidence for a disk surrounding the star Beta Pictoris.

Young Star Systems • Many stars in the Orion nebula are surrounded by disks of material.

Young Star Systems • 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.

Young Star Systems • Infrared images are useful since the infrared light penetrates deeper into the dark clouds, allowing one to see what is inside. Often one sees young stars.

Young Star Systems • Infrared observations often reveal hundreds of newly-formed stars embedded in molecular clouds.

• In this particular case, many of the stars have not arrived on the main sequence.

Young Star Systems • Newly-formed hot stars can alter their environment.

Hubble Anniversary

Star Formation Summary

Stellar Evolution

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 to 1/M 3 “ life ” on the main sequence; the time spent is roughly proportional , where M is the initial mass.

Hydrostatic Equilibrium • The Sun (and other stars) does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun.

• The energy from fusion in the core ultimately provides the pressure needed to stabilize the star.

Stellar Evolution

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

Nuclear fusion (hydrogen to helium) is the energy

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

Nuclear fusion (hydrogen to helium) is the energy • What happens when all of the hydrogen in the core is converted to helium?

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

Nuclear fusion (hydrogen to helium) is the energy • 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 • Stars with masses between 0.1 and 0.4 solar masses convert their entire mass into helium.

• This can take hundreds of billions of years or more.

After the Main Sequence • Stars with masses between 0.1 and 0.4 solar masses convert their entire mass into helium.

• Stars with higher mass don cores… ’ t mix new fuel into their

Points to Remember: • Sources of energy: – Nuclear fusion: • needs very high temperatures • about 0.7% efficiency for hydrogen into helium.

– Gravitational “ accretion ” energy: • Drop matter from a high “ potential ” • About 10% efficient when falling onto massive bodies with very small radii.

• After a stage of nuclear fusion is complete in a stellar core, it will collapse and get hotter.

More Nuclear Fusion • •

Fusion

of elements lighter than iron can release energy (leads to higher BE ’ s).

Fission

of elements heaver than iron can release energy (leads to higher BE ’ s).

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 Sun ’ s core is about 15,000,000 K).

Images from Nick Strobel ’ s Astronomy Notes ( http://www.astronomynotes.com

)

• The 4 “ Forces ” of Nature Both gravity and the electromagnetic force are “ inverse square ” forces where the strength of the force depends on 1/d 2 .

– F grav = product of masses divided by distance squared.

– F elec = product of charges divided by distance squared. Higher concentrations of (like) charges need stronger forces to bring them together (recall like charges repel).

More Nuclear Fusion •

Fusion

of elements lighter than iron can release energy (leads to higher BE ’ s).

• As you fuse heavier elements up to iron,

higher and higher temperatures are needed

since more and more electrical charge repulsion needs to be overcome.

– Hydrogen nuclei have 1 proton each temperature ~ 10,000,000 K – Helium nuclei have 2 protons each temperature ~ 100,000,000 K – Carbon nuclei have 6 protons each temperature ~ 700,000,000 K – …..

• After each stage of fusion is complete, the core collapses and heats up.

• More mass in the core --> higher core temperature --> fusion of heavier elements … • For a given core mass, there is a limit to how hot it can become.

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.

• The excess energy causes the outer layers of the star to expand by a factor of 10 or more.

• 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: diagram.

these are the red giants seen in the temperature-luminosity

After the Main Sequence: Low Mass • The red giants are stars that just finished up fusing hydrogen in their cores.

Image from Nick Strobel ’ s Astronomy Notes ( http://www.astronomynotes.com

)

After the Main Sequence: Low Mass • Some red giants are as large as the orbit of Jupiter!

Image from Nick Strobel ’ s Astronomy Notes ( http://www.astronomynotes.com

)

After the Main Sequence: Low Mass • Some red giants are as large as the orbit of Jupiter!

• The Sun will reach approximately to the orbit of the Earth

After the Main Sequence: Low Mass • 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: diagram.

these are the red giants seen in the temperature-luminosity

After the Main Sequence: Low Mass • 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: diagram.

these are the red giants seen in the temperature-luminosity • The core continues to collapse, and helium can fuse into carbon for a short time. The star expands further.

After the Main Sequence: Low Mass • Helium fusion starts in a “ shell ” around the core, then after a “ helium flash the core.

” the helium fusion starts in

After the Main Sequence: Low Mass • Helium fusion starts in a “ shell ” around the core, then after a “ helium flash the core.

” the helium fusion starts in

In Brief: Evolution of Close Binaries • The evolution of stars in a close binary can be drastically altered. In many cases, one star transfers mass to the other, thereby changing its evolution.

In Brief: Evolution of Close Binaries • In Algol and in many other similar systems, the the main sequence. Shouldn ’

less

massive star is a red giant, and the higher mass star is on t the higher mass star have evolved first?

In Brief: Evolution of Close Binaries • In Algol and in many other similar systems, the the main sequence. Shouldn ’

less

massive star is a red giant, and the higher mass star is on t the higher mass star have evolved first? Mass transfer messed things up…

In Brief: Evolution of Close Binaries • In eclipses can only be explained by the presence of an “ b Lyrae and other similar systems, the shapes of the accretion disk ” around one of the stars. Mass transfer is taking place in these systems.

In Brief: Evolution of Close Binaries • In W Ursae Majoris and other similar systems, the two stars apparently share a common atmosphere. When one eclipse ends, the other begins.

After the Main Sequence: Low Mass • As core hydrogen fusion stops, low mass stars become more luminous and red (e.g. cooler), higher mass stars tend to just get redder while keeping the same luminosity.

• In all cases, the star gets larger in size.

• The “ deaths ” of stars.

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ASTRO 101

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