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.
Cluster Distances106Pleiades105All stars in a cluster areat the same distance.Main seq. in Hyadesappears 9 brighterthan in Pleiades; why?104103apparent brightnessPlot apparent brightnessinstead of luminosity.Hyades1021010.110-210-310-4Pleiades are 3 moredistant than Hyades!10-53000010000surface temperature3000
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.
CONTENTS 2 Introduction 4 Rising Stars in Artist Management 8 Rising Stars in Orchestra Leadership 13 Rising Stars in Presenting 18 Rising Stars in Communications/Public Affairs 22 Adventuresome Programming. Rising Stars in Education 28 Rising Stars in Radio and Recording 32
DCEPS stars; CW (W Virginis), CWA and CWB stars 128 7.4 RR (RR Lyrae), RR(B), RRAB, and RRC stars 131 8 Lessregularsingle-starvariables 133 8.1 M (Mira) stars 133 8.2 SR (semi-regular variable); SRA; SRB; SRC; SRD; and SRS stars 137 8.3 A naked-eye hypergiant variable star 141 8.4 L (slow irregular variable); LB and LC stars 143
1 Class 4 : Basic properties of stars Distance to stars Parallax method for determining distance Definition of the “parsec” Flux, luminosity, magnitude and color HR diagrams I : The distance to the stars The distance to any astronomical object is the most basic parameter we want to
6.5.3 Neutron stars and white dwarfs 294 6.5.4 A variety of neutron star models 296 6.5.5 Maximum masses of neutron stars 297 6.5.6 The nature of the maximum mass of neutron stars 298 6.5.7 The upper bound on the maximum mass 301 6.5.8 Low-mass neutron stars and the minimum mass 302 6.6 Radii and surface redshifts 303 6.6.1 Circumferential .
Ben: So today, Bethany, we’re talking about neutron stars. David: Well, neutron stars are these incredibly dense dead stars. They’re formed after a large star has collapsed when it runs out of fuel and, um, these neutron stars are incredibly, incredibly dense.
To receive a four or five-star rating, you must first meet all items in sections I through X. Then you may select from the items in the “Extra Points” section to earn enough points for four or five stars. Center Programs 4 stars: 35-55 points 5 stars: 56-79 points Family Child Care (FCC) 4 stars: 30-45 points 5 stars: 46-64 points
OurStory: Exploring the Sky See the Stars Parent Guide, page 2 of 2 CHALLENGE WORDS astronomy: the science of the stars, planets, sun, moon, and sky constellation: a pattern of stars, like connect-the-dot pictures planetarium: a room that uses lights to show stars, planets, and the sky telescope: a tool for vi
Keystone STARS Program Manual I. About Keystone STARS Keystone STARS is a program of Pennsylvania's Office of Child Development and Early Learning (OCDEL). Keystone STARS has four primary goals: To improve the quality of early care and education; To support early care and education providers in meeting their quality improvement goals;