1Exam #2 ReviewThe Sun• The Sun is a huge ball ofgas at the center of thesolar system– 100 times Earth diameter,300,000 earth mass– 1 million Earths would fitinside it!– Releases the equivalentof 100 billion atomicbombs every second!– 1366 watts/square meterat Earth– 15 Tera watts in 62 sq mi• Exists thanks to adelicate balance ofgravity and pressureLooks “quiet in the visible”2Knowledge of interior based on models which fit observables:•Mass•Radius•Luminosity•Surface Temperature•Image details: granules, spicules, corona, chromosphereThe Photosphere• The photosphereis the visible“surface” of ourstar– Not really asurface, as theSun is gaseousthroughout– Photosphere isonly 500 km thick– Averagetemperature is5780 K3Energy Transport in the Sun• Just below the photosphere is the convection zone.– Energy is transported from deeper in the Sun by convection, inpatterns similar to those found in a pot of boiling water (hot gas rises,dumps its energy into the photosphere, and then sinks)• Energy in the convection zone comes from the radiative zone.– Energy from the core is transported outward by radiation– Takes more than 100,000 years for a single photon to escape theSun!The Solar Atmosphere• Regions of the Sun abovethe photosphere are calledthe Sun’s atmosphere• Just above the photospherelies the chromosphere– Usually invisible, but canbe seen during eclipses• Above the chromosphere isthe corona– Extremely hightemperatures (more than1 million K!)– Rapidly expanding gasforms the solar wind.4The Ideal Gas LawPressure = Constant × Temperature × DensityThe Sun’s Energy• The Sun’s energy comes from fusion – the merging ofhydrogen nuclei into helium• The reaction releases only a little bit of energy, but ithappens a lot!• A hydrogen nucleus has less mass than the four protons(hydrogen nuclei) that fuse• This difference in mass is converted into energy:E = m×c2The Proton-ProtonChain5Sunspots• Sunspots are highlylocalized cool regions inthe photosphere of theSun– Discovered by Galileo– Can be many timeslarger than the Earth!– They contain intensemagnetic fields.Solar FlaresCoronal Mass Ejection6The Aurora• When CME materialreaches the Earth, itgets funneled byEarth’s magnetic fieldand collides withionospheric particles,close to the poles• The collision excitesionospheric oxygen,nitrogenand whichcauses it to emit aphoton• We see these emittedphotons as theaurora, or NorthernLights7Measuring theDistance toAstronomicalObjects usingparallaxJust a littleTrigonometry…1 parsec = 206265 AU8Moving Stars• The positions of stars are notfixed relative to Earth– They move around the center ofthe galaxy, just as Earth does.– This motion of stars through thesky (independent of the Earth’srotation or orbit) is called propermotion– Over time, the constellations willchange shape!• The speed of a star’s motiontoward or away from the Sun iscalled its radial velocityThe Inverse-SquareLaw• A star emits light in all directions,like a light bulb. We see thephotons that are heading in ourdirection• As you move away from the star,fewer and fewer photons areheading directly for us, so the starseems to dim – its brightnessdecreases.• The brightness decreases withthe square of the distance fromthe star– If you move twice as far fromthe star, the brightness goesdown by a factor of 22, or 4!• Luminosity stays the same – thetotal number of photons leavinga sphere surrounding the star isconstant.9You see this every day!• More distant streetlights appeardimmer than ones closer to us.• It works the same with stars!• If we know the total energy output ofa star (luminosity), and we can countthe number of photons we receivefrom that star (brightness), we cancalculate its distance• Some types of stars have a knownluminosity, and we can use thisstandard candle to calculate thedistance to the neighborhoods thesestars live in.BLd!4=MeasuringTemperature usingWein’s Law!nmK109.26"#=T10The Stefan-BoltzmannLaw• The Stefan-Boltzmann Law linksa star’s temperature to theamount of light the star emits– Hotter stars emit more!– Larger stars emit more!• A star’s luminosity is thenrelated to both a star’s size anda star’s temperature• We need an organizational toolto keep 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#r2Photons in StellarAtmospheres• Photons have a difficult time moving through a star’s atmosphere• If the photon has the right energy, it will be absorbed by an atom and raisean electron to a higher energy level• Creates absorption spectra, a unique “fingerprint” for the star’s composition.The strength of this spectra is determined by the star’s temperature.111- variation in H linestrengths….“Spectral types” based on H lines strength:ABCDEF…Classify:1901, Annie Jump Cannon > spectral classification12Spectral Classification• Spectral classificationsystem– Arranges starclassifications bytemperature• Hotter stars are Otype• Cooler stars are Mtype• New Types: L and T– Cooler than M• From hottest to coldest, they areO-B-A-F-G-K-M– Mnemonics: “Oh, Be A FineGirl/Guy, Kiss Me– Or: Only Bad Astronomers ForgetGenerally Known MnemonicsA convenient tool fororganizing stars• In the previous unit, we sawthat stars have differenttemperatures, and that astar’s luminosity depends onits temperature and diameter• The Hertzsprung-Russelldiagram lets us look fortrends in this relationship.13Stars come in allsizes…• A star’s location on the HR diagramis 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 stars• So what’s going on here?The Mass-LuminosityRelation14Stars come in allsizes…• L vs T! b =L4"d2b=brightness,d=distanceaway! T =2.9 "106K # nm$Stellar Evolution on theMain Sequence15The Main-SequenceLifetime of a Star• The length of time a star spends fusing hydrogen into helium iscalled its main sequence lifetime– Stars spend most of their lives on the main sequence– Lifetime