1How big are stars?How do we know?Interferometry• Stars are simply too far away toeasily measure their diameters!– Atmospheric blurring and telescopeeffects smear out the light• Can combine the light from two ormore telescopes to pick out moredetail – this is called interferometry– Two telescopes separated by adistance of 300 meters have almostthe same resolution as a singletelescope 300 m across!2Measuring Temperature usingWein’s Law!nmK109.26"#=T1901, Annie Jump Cannon > spectral classification3The Stefan-Boltzmann Law• The Stefan-Boltzmann Law links astar’s temperature to the amount oflight the star emits– Hotter stars emit more!– Larger stars emit more!• A star’s luminosity is then related toboth a star’s size and a star’stemperature• We need an organizational tool tokeep all of this straight…! flux ="T4Flux is energy / unit areaWhere, σ= 5.67×10−8 W·m-2·K-4! L = flux • Area ="T4• 4#r2A convenient tool for organizing stars• In the previous unit, we saw thatstars have different temperatures,and that a star’s luminositydepends on its temperature anddiameter• The Hertzsprung-Russelldiagram lets us look for trends inthis relationship.4The H-R Diagram• A star’s location on the HRdiagram is given by its temperature(x-axis) and luminosity (y-axis)• We see that many stars are locatedon a diagonal line running fromcool, dim stars to hot bright stars– The Main Sequence• Other stars are cooler and moreluminous than main sequence stars– Must have large diameters– (Red and Blue) Giant stars• Some stars are hotter, yet lessluminous than main sequence stars– Must have small diameters– White Dwarf stars5The Family of StarsHertzsprung—Russell diagram(1910)1. temps (= colors = spect type) OBAFGKM2. luminositiesNOTICE:same T  bright or faint ?!3. same temp , diff Lum different radii !!!L = σT4 4πR2Stars come in all sizes…• A star’s location on the HR diagram isgiven by its temperature (x-axis) andluminosity (y-axis)• We see that many stars are located on adiagonal line running from cool, dimstars to hot bright stars– The Main Sequence• Other stars are cooler and moreluminous than main sequence stars– Must have large diameters– (Red and Blue) Giant stars• Some stars are hotter, yet less luminousthan main sequence stars– Must have small diameters– White Dwarf stars• So what’s going on here?6The Mass-Luminosity Relation• Some of these stars arebinaries.• Newtons formulation ofKeplers 3rd law > Mass!– Low mass mainsequence stars tend to becooler and dimmer– High mass mainsequence stars tend to behotter and brighter• The Mass-LuminosityRelation: Massive stars burn brighter!5.3ML !The Mass-Luminosity RelationB0.. B1… B9larger number, cooler star.7Most of the brightest stars in the sky are a) relatively hot main-sequence stars that are relatively close to the Sun. b) relatively cool giant stars that are relatively close to the Sun. c) relatively cool main-sequence stars that are relatively far from the Sun. d) relatively cool main-sequence stars that are relatively close to the Sun. e) giant stars and relatively hot main sequence stars.The Types of Binary Stars• Many stars are found orbitinganother star. These star systemsare called binary stars.• Three types:– If we can see from pictures takenover time that the stars areorbiting each other, the system isa visual binary– If the stars are so close together(or distant from Earth) that theirspectra blur together, the systemis called a spectroscopic binary– If the stars are oriented edge-onto the Sun, one star willperiodically eclipse the other starin the system. These are calledeclipsing binaries8Measuring Stellar Masses withBinary StarsNote that this technique only gives us the combined mass of the two stars…How do we know the distance?Using the Doppler Shift to detect binarysystems• As a star in a binary system moves away from us, itsspectrum is shifted towards red wavelengths. As itmoves toward us again, the spectrum is shifted towardthe blue wavelengths• This Doppler Shift allows us to detect some binaries!9Using eclipsing binary systems to measurestellar diametersMassive stars burn brighter10•Oh! Be A Fine Girl/Guy, Kiss Me•Officially, Bill Always Felt Guilty Kissing Monica•Oh Big And Ferocious Gorilla, Kill My RoommateNow, Sir.•Only Big Astronomy Federal Grants Keep Money.Research Needs Support!•Only Bored Astronomers Find Gratification KnowingMnemonics•Only Boys Advocating Feminism Get KissedMeaningfully•Oh Boy An F-Grade Kills Me•Oven Baked Ants Fried Gently Keep Moist•Only Boring Astronomers Find Gratification KnowingMnemonics Like TheseO B A F G K