# 9. Properties Of Stars

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Astronomy 110: SURVEY OF ASTRONOMY9. Properties of Stars1. Distances & other parameters2. The Hertzsprung-Russell diagram3. Star clusters & stellar evolution

Distance measurements are critical to understandingstellar properties. Stars span an enormous range ofluminosity, temperature, and size, and these parametersare profoundly related to each other. Studying clustersof stars born at the same time provides clues to thelives of stars.

1. DISTANCES & OTHER PARAMETERSa. The Scale of the Solar Systemb. How Far to the Stars?c. Luminosity and Brightness

The Scale of the Solar SystemKepler and later astronomers made good scale modelsof the Solar System, but they didn’t know its true size.a (AU)0.3870.7231.0001.5245.2039.537P (yr)0.2410.6151.0001.88111.85729.424To find the value of one AU, a measurement of theactual distance (in km) to any planet would suffice.SPlanetMercuryVenusEarthMarsJupiterSaturn

Parallax Method: TheoryObserve P from points 1, 2 separated by baseline, b.D1b2θPθto distant starSuppose that from point 1 the planet lines up with adistant star, while from point 2 the angle between theplanet and star is θ.

Parallax Method: TheoryHow many triangles?N 360 θDCircumferenceC of big circle?C360 θbθPθbRadius of big circle?D1 360 2π θbThat’s the distance to P!C

The Distance to MarsOn October 1, 1672, Mars lined upwith a bright star:Paris (Europe)Cayenne (South America)Wikipedia: Giovanni CassiniMars was then 0.43 AU from Earth. Cassini used theknown distance between the two observing points andthe measured parallax angle to find this distance in km:DMars6.0 107 km1 AU1.38 108 km

Measuring the AU1. Transits of Venus: 1761, 1769, 1874, 1882— inconclusive due to effects of atmosphere2. Observations of Mars: 18771 AU 81.49 10km3. Observations of Eros: 19301 AU 1.4960 108 km4. Radar measurements: 1958 and since1 AU 81.49597871 10km

How Far to the Stars?We need a much largerbaseline to measurestellar distances! TheEarth’s orbit gives abaseline ofb 2 AUDecJune

Stellar ParallaxOver the course of ayear, nearby stars seemto move in small ovalsas a result of Earth’smotion about the Sun.Parallax of a Nearby Star

Stellar ParallaxOver the course of ayear, nearby stars seemto move in small ovalsas a result of Earth’smotion about the Sun.

Parallax CalculationsThe parallax anglep is half the total shift:1 360 D 2π p AUStars are far away, sop is measured in arcsec (1 1 /3600).Define a new distanceunit, the parsec (pc):1 pc 360 36002πAU Dec2pJuneDpAU133.09 10 kmD1 pcp

1. Suppose star B is twice as far away as star A.A. Star B has 4 times the parallax angle of star A.B. Star B has 2 times the parallax angle of star A.C. Both stars have the same parallax angle.D. Star A has 2 times the parallax angle of star B.E. Star A has 4 times the parallax angle of star B.

2. If we could measure stellar parallaxesfrom Mars instead of Earth, would nearbystars move in ovals which areA. the same size as seen from Earth,because the stars are just about asfar from Mars.B. larger than seen from Earth, becauseMars has a larger orbit.C. smaller than seen from Earth, becauseMars is a smaller planet.

NearestKnown StarsMost too dimto see withouta telescope!3.50 pc 11.4 ly3.50 pc 11.4 ly3.22 pc 10.5 ly3.65 pc 11.9 ly2.63 pc 8.6 ly1.32 pc 4.3 ly3.62 pc 11.8 lyWikipedia: Nearest stars

A Stellar Distance Scale1. Distances on Earth are determined by surveyingtechniques.2. Parallax measurements at two points on Earth yielddistances to other planets (now checked by radar).3. These distances set the scale for the Solar System,and fix our distance to the Sun: 1 AU 1.496 108 km.4. Parallax measurements at two (or more) points onEarth’s orbit yield distances to nearby stars.At each step, known distances areused to find unknown distances.

3. Suppose we found an error in our calculation of theAU, and the correct value was 10% larger. How wouldthis change our values for stellar distances?A. Stellar distances would be unchanged.B. Stellar distances would increase by 10%.C. Stellar distances would decrease by 10%.

Luminosity and BrightnessAbsolute Luminosity (L)is the energy a star radiatesper unit time.L 3.8 1026 wattApparent Brightness (B)is the energy received perunit time and unit area.B 1366 watt / m2

Brightness: Inverse-Square LawEnergy conservation impliesthat the same luminositypasses through each sphere.Sphere of radius D has areaA 4πD2Thus, brightness is inverselyproportional to (distance)2:LLB A 4πD2

The Sun and αCen ComparedαCen appears much fainter:αCen is much further away:Bα 2.8 10-8 watt / m2Dα 1.32 pc 4.1 1016 mB 1366 watt / m2D 1 AU 1.49 1011 mWhat about their luminosities?Lα Bα (4πDα2) 5.9 1026 wattL B (4πD 2) 3.8 1026 wattαCen is about 50% more luminous than the Sun!

4. How would αCen’s apparent brightness change if itwas 3 times further away?A. It would be 1/3 as bright.B. It would be 1/6 as bright.C. It would be 1/9 as bright.D. It would appear the same.E. It would be 3 times as bright.

Neighbors of the SunA few nearby stars are more luminous than the Sun, butmost are much less luminous; of the 150 nearest stars:10100Numberof Stars411014αCen: 1.5 L 0.1125τCet: 0.46 L 0.010.1210.0010.01570.00010.00129From (L ) To (L )ExamplesVega: 50 L

DISTANCES & OTHER PARAMETERS: REVIEW1. Parallax equation: (a) number oftriangles, (b) circumference of circle,(c) radius of circle.1 360 D 2πbDbθPθ2. Brightness and luminosity:— brightness is what we observe; it has units ofenergy per unit time per unit area.— luminosity is what a star puts out; it has units ofenergy per unit time.

2. THE HERTZSPRUNG-RUSSELL DIAGRAMa. Interpreting Stellar Spectrab. The Main Sequencec. Beyond the Main Sequence

Stars have different luminosities and colors.— luminous stars may be red or blue— dim stars are generally redSWEEPS ACS/WFC Color Composite

Types of Spectra: ReviewBlack Body Spectrum

Black-Body (Thermal) RadiationAny opaque object(black body) with atemperature T 0 Kemits light (radiation).As the temperaturegoes up, this light getsbrighter and bluer.Relationship Between Temperature and Luminosity

Properties of Thermal Radiation Higher temperaturemore light at all wavelengths Higher temperaturepeak shifts towards blue

Types of Spectra: ReviewBlack Body SpectrumEmission SpectrumBlack Body Absorption Spectrum

Spectral Lines: ReviewEach electron orbit has adefinite energy level.In hydrogen, orbit n has energy1En 1 - 2 13.6 eVnwhere an eV is an energy unit.()To jump from orbit to orbittakes a photon with exactlythe right amount of energy.n 13.6 eVn 613.2 eVn 513.1 eVn 412.8 eVn 312.1 eV2.9 eV2.6 eV1.9 eV434 nm486 nm656 nmn 210.2 eV

Stellar SpectraIn stars, the lower photosphere produces a black-bodyspectrum, while cooler gas above creates dark lines.Black Body Absorption SpectrumTextStars exhibit a tremendous variety of spectra — why?Stellar Spectra

Interpreting Stellar SpectraStars have different spectra almost entirely because theyhave different surface temperatures!Stellar Spectra and TemperaturesComposition plays a minor role — almost all stars aremostly hydrogen and helium, just like the Sun.

Spectral TypesHydrogenT 30000 KOOldT 20000 KBBreadT 9000 KAAndT 6800 KFFruitT 5500 KGGetT 4200 KKKindaT 3500 ide

Spectral TypesHydrogenT 30000 KMost H atomsare ionized.T 20000 KMost H atomsat n 2 level.T 9000 KT 6800 KT 5500 KMost H atomsat n 1 level.T 4200 KT 3500 KIonizedCalciumTitaniumOxideSodiumTitaniumOxide

Plotting the HR DiagramThe HR diagram showssurface temperature onthe horizontal axis andluminosity on thevertical axis.

The Main SequenceMost stars in the Sun’sneighborhood fall alonga roughly diagonal lineon an HR diagram.This line is called themain sequence.

Nature of the Main SequenceAll main-sequence starsproduce energy in thesame way as the Sun, byfusing hydrogen to formhelium in their cores.A star’s place along themain sequence is fixedby its mass.

Measuring Stellar Masses: ReviewFor any two masses M and m orbiting each other,Newton’s version of Kepler’s Law III states:2Pa3 24πmG(M m)MWikipedia: Kepler’s LawsThis provides a way of ‘weighing’ stars — we observe apair of stars orbiting each other (a double-star) andsolve this equation to get their masses.

Stellar Lifetimes Along the Main SequenceThe main sequence isalso a sequence of lifetimes.High-mass stars musthave hotter cores tobalance gravity, so theyuse up hydrogen faster.

The Main Sequence: SummaryMass is the key property of a main-sequence star: otherbasic properties are all determined by mass.Low MassHigh Masslow luminosityhigh luminositylow temperaturehigh temperaturelong lifetimeshort lifetime

Giants and SupergiantsSome stars are not partof the main sequence;they are relatively coolbut very luminous.These stars must haveenormous radii to giveoff so much energy.

White DwarfsOther stars are hot butvery dim.These stars must havetiny radii to give off solittle energy.

THE H-R DIAGRAM: SUMMARYa. Interpreting Stellar Spectra— spectra differ mostlybecause of temperature.b. The Main Sequence— on the main sequence,stars are arranged by mass.c. Beyond the Main Sequence— giants and dwarfs havevery different radii.

Main Sequence Lifetimes 1 M star:L L — lifetime: T 1010 yr4 L10Mstar:L 10 10 fuel; use at 104 rateT (10/104) T 107 yr 0.1 M star:L 0.003 L 0.1 fuel; use at 0.003 rateT (0.1/0.003) T 3 1011 yr

3. STAR CLUSTERS & STELLAR EVOLUTIONa. Nature of Star Clustersb. Cluster HR Diagramsc. Cluster Distances

Nature of Star ClustersOpen clustersGlobular clusters

Two Types of Clusters1. Globular Clusters— old, ‘metal’-poor stars— contain 105 to 106 stars— found in halo of Milky Way2. Open Clusters— young, ‘metal’-rich stars— contain 100 to 104 stars— found in disk of Milky Way

Cluster FormationStar clusters form in massiveinterstellar gas clouds.— cloud well-mixed— rapid formationstars have similar compositionstars have similar agesStar Cluster R136 Bursts Out

Star Cluster DynamicsClusters are held together by mutual gravity of stars.Simulated Star ClusterHigh-mass cluster stars tend to form pairs and ejectsmaller stars. This eventually disrupts open clusters.

Cluster HR DiagramsAll the stars in a clusterhave the same age, so HRdiagrams for cluster starstell us about: cluster ages stellar evolution cluster distancesThe Pleiades (M45)

Evolution of HR DiagramsHigh-mass stars burn out first; low-mass stars die later.So as a cluster ages, themain sequence ‘burnsdown’ in order.lifetime: 107 yrlifetime: 108 yrlifetime: 109 yrlifetime: 1010 yr(Note: this animation alsoshows stars after theyleave the main sequence.)Using the H-R Diagram to Determine the Age of a Star Cluster

Evolution of HR DiagramsHigh-mass stars burn out first; low-mass stars die later.So as a cluster ages, themain sequence ‘burnsdown’ in order.Instead of plotting stars,we represent them witha line of constant age.Using the H-R Diagram to Determine the Age of a Star Cluster

The Pleiades: A Young ClusterUsing the H-R Diagram to Determine the Age of a Star ClusterPleiades and Stardust

M67: An Older ClusterUsing the H-R Diagram to Determine the Age of a Star ClusterStar Cluster Messier 67

Cluster HR Diagrams ComparedGlobular Cluster M4Clusters have a range of ages; giant and dwarf starsappear at different stages of cluster aging process.

A Cluster Distance Scale1. Parallax measurements at two (or more) points onEarth’s orbit yield distances to nearby stars.2. Nearby stars are used to measure luminosity of mainsequence.3. Main sequence luminosity is used to get distance toHyades & Pleiades (also checked by parallax).4. Improved main sequence luminosities yield distancesto other clusters throughout galaxy (and beyond!).At each step, known distances areused to find unknown distances.

1. Suppose star B is twice as far away as star A. A. Star B has 4 times the parallax angle of star A. B. Star B has 2 times the parallax angle of star A. C. Both stars have the same parallax angle. D.Star A has 2 times the parallax angle of star B. E. Star A has 4 times the parallax angle of star B.

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