Ast 309N (47760) 1

Agenda for Ast 309N, Sep. 27

• Quiz 3• The role of stellar mass• Ages of star clusters• Exam 1, Thurs. Oct. 4 Study guide out on 9/28• Next topic: brown dwarfs and extrasolar planets

9/27/12

This image of the central part of the globularcluster Omega Centauri was taken with theHubble Space Telescope. Let’s organize thestars according to their observed properties.

After sorting the stars by color (left to right)and brightness (top to bottom), we have a

Hertzsprung-Russell (HR) Diagram!

Measuring Masses from Binary Stars

• In Ast 301, you should have learned aboutNewton’s form of Kepler’s Third Law:

!

P2= 4" 2

G(M1+M2)a 3 OR M1+M2=

4" 2

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• A more convenient form, derived by scaling by theSun-Earth system, we have:

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=a/A.U."

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Ast 309N (47760)9/27/12

The Mass-Luminosity Relation

By compiling results frommany binary stars, it wasdiscovered that there is arelationship betweenmass and luminosity.

But note: this holdsonly for stars on theMain Sequence.

Ast 309N (47760)9/27/12

The Main Sequence is a sequence in mass

Ast 309N (47760)9/27/12

It’s a fairly commonmisconception thatstars evolve by movingalong (e.g. down) theMain Sequence; this isnot the case.

In fact, each point onthe Main Sequence isoccupied by stars of aspecific initial mass.

• All Main sequence stars fuseH ! He in their cores.

• Larger masses exert greaterweight (force) at center

• Requires higher centralpressure to balance this

• Result: faster rate of nuclearfusion reactions

" Luminosity increasesstrongly with mass.

Why is there a Mass-Luminosity Relation?

Ast 309N (47760)9/27/12

L varies as mass cubed,or L ! M3

Corollary: The Mass-Lifetime Relation

The “lifetime” is the total length of a time (e.g. years)a star can stay on the Main Sequence, fusing Hydrogen.

The amount of fuel is proportional to MIt is used up at a rate proportional to L ! M3

How long does it last? M/L = M/M3 = 1/M2

• High-mass stars burn fuel like a bus!• Low-mass stars burn fuel like a compact car!• The Sun will last 1010 years = 10 billion yrs.

Ast 309N (47760)9/27/12

•

The mass of a stardetermines its spectraltype, luminosity, andlifetime while on theMain Sequence.

High-mass stars

Low-mass stars

The lowest-massstars, 0.8 M! orbelow, have lifetimesgreater than 13.7billion years, the ageof the Universe. Sosuch stars formedlong ago are still onthe Main Sequence.

The Mass-Lifetime Relation

Ast 309N (47760)9/27/12

Summary: Main-Sequence Stars

High Mass:

High Luminosity Short-Lived Large Radius Hot surface (blue)

Low Mass:

Low Luminosity Long-Lived Small Radius Cool Surface (red)

Ast 309N (47760)9/27/12

• Stars that have finished fusing Hydrogen to Helium in theircores are no longer on the Main Sequence.

• Stars tend to become larger and cooler (giants andsupergiants) after exhausting their core hydrogen.

• Later on, most stars end up as small, hot white dwarfsafter fusion has ceased and the outer layers are expelled.

What are the non-Main Sequence stars?

9/27/12

Non-Main Sequence stars: Giants & Dwarfs

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Star Clusters: stars of all possible masses,all formed at the same place and time

A few thousand loosely packedstars, usually relatively young

Open Clusters Globular Clusters

Up to a million or so stars tightlybound by gravity, usually very old

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The Hyades: A Young Star Cluster

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http://bdaugherty.tripod.com/gcseAstronomy/images/HRcluster.jpg

Using HR Diagrams to Find Cluster Ages

9/27/12

• At first, there are starsof all masses on thecluster’s Main Sequence• The most massive stars“die off” first• As time passes, lower-mass stars begin to moveoff the Main Sequence• Find this “turn-off”point: the cluster’s age isequal to the MainSequence lifetime of starsat the turn-off.

Main-sequenceturnoff

The Main Sequence “Turn-off” Point

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Animation ofstars “peelingoff” the MainSequence, astimes passes

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Star clusters ofdifferent ages havedifferent turn-offpoints; younger onesstill have high-massMain Sequence stars,for older clusters,more of the M.S. has“peeled off.”

Determining the Ages of Star Clusters

9/27/12 Ast 309N (47760)

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HR Diagrams of Old Star Clusters

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Indicated regions: Main Sequence (MS),subgiant branch (SGB), red giant branch (RGB),horizontal branch (HB), white dwarfs (WD)

MS

SGB

RGBHB

WD