Chapter 11 Surveying the Stars How luminous are stars? The brightness of a star depends on both distance and luminosity Luminosity: Amount of power a star radiates (energy per second=Watts) Apparent brightness: Amount of starlight that reaches Earth (energy per second per square meter) (not much) Thought Question These two stars have about the same luminosity -- which one appears brighter? A. Alpha Centauri B. The Sun Luminosity passing through each sphere is the same Area of sphere: 4π (radius)2 Divide luminosity by area to get brightness The relationship between apparent brightness and luminosity depends on distance: Apparent Brightness = Luminosity 4π (distance)2 We can determine a star’s luminosity if we can measure its distance and apparent brightness: Luminosity = 4π (distance)2 x (Brightness) Note that there is a huge range in stellar luminosities Proxima Centauri = 0.0006 Lsun Betelgeuse = 38,000 Lsun Thought Question How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. B. C. D. It would be only 1/3 as bright It would be only 1/6 as bright It would be only 1/9 as bright It would be three times brighter Parallax and distance. p = parallax angle in arcseconds d (in parsecs) = 1/p 1parsec= 3.26 light years Parallax and distance. • Nearest Star: Alpha Centauri • distance = 4.3 light years • (since 1 parsec = 3.26 light years) • Distance (d) in parsecs = 4.3/3.26 = 1.32 • What is the parallax of this star? • • d=1/p hence p=1/d (in parsecs) p for nearest star is 0.76 arcseconds • All other stars will have a parallax angle smaller than 0.76 arcseconds Laws of Thermal Radiation hotter brighter, cooler dimmer hotter bluer, cooler redder Hottest stars: blue~50,000 K Coolest stars: Red~3,000 K (Sun’s surface is 5,800 K) An aside on “computers” • In the old days an “Astronomical Computer” was not a machine, but a person….often a woman. • These were the people who calculated positions and analyzed the photographic plates • Women did most of the work in compiling these huge stellar catalogues. An aside on “computers” • • • What the “computers” did was sift through literally 100’s of thousands of stellar spectra. Established a classification scheme based on Hydrogen lines…. The types were alphabetical….letters were assigned in declining strength of the H-lines Stellar Classification • • • Like most early classification systems, they got it wrong initially Today we arrange spectral classes by temperature Wien’s Law: The hotter the object, the bluer the radiation it emits, and the more total energy is emitted. Stellar Classification • The hottest stars turned out to be (of course) the bluest. • Also the level of heat determined what sorts elements would be prominent in the star’s spectrum • For example only the hottest stars can ionize helium • Only the coolest stars can have molecules Remembering Spectral Types (Hottest) O B A F G K M (Coolest) • Oh, Be A Fine Girl/Guy, Kiss Me • Only Boys Accepting Feminism Get Kissed Meaningfully A star’s full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star): I II III IV V - supergiant - bright giant - giant - subgiant - main sequence Examples: Sun - G2 V Sirius - A1 V Proxima Centauri - M5.5 V Betelgeuse - M2 I Star Types Now we know temperature, luminosity, and Distance……what about mass? Newton shows the way…… We measure mass using gravity Direct mass measurements are possible only for stars in binary star systems p = period a = average separation 4π2 p2 = a3 G (M1 + M2) Most massive stars: 100 MSun Least massive stars: 0.08 MSun (MSun is the mass of the Sun) Stellar Properties Review Luminosity: from brightness and distance 10-4 LSun - 106 LSun Temperature: from color and spectral type 3,000 K - 50,000 K Mass: from period (p) and average separation (a) of binary-star orbit 0.08 MSun - 100 MSun Core pressure and temperature of a highermass star need to be larger in order to balance gravity Higher core temperature boosts fusion rate, leading to larger luminosity Mass & Lifetime Sun’s life expectancy: 10 billion years Until core hydrogen (10% of total) is used up Life expectancy of 10 MSun star: 10 times as much fuel, uses it 104 times as fast 10 million years ~ 10 billion years x 10 / 104 Life expectancy of 0.1 MSun star: 0.1 times as much fuel, uses it 0.01 times as fast 100 billion years ~ 10 billion years x 0.1 / 0.01 Stellar Evolution • Stars are like people in that they are born, grow up, mature, and die. • A star’s mass determines what life path it will take. • The HertzsprungRussel Diagram is a roadmap for following stellar evolution. Luminosity An H-R diagram plots the luminosity and temperature of stars Temperature High-Mass Stars Normal hydrogenburning stars reside on the main sequence of the H-R diagram Low-Mass Stars H-R diagram depicts: Temperature Color Spectral Type Luminosity Radius *Mass *Lifespan *Age C Luminosity B Which star is the most luminous? D A Temperature C Luminosity B Which star has the largest radius? D A Temperature C Luminosity B D A Temperature Which star is the main sequence star? C Luminosity B Which star is the hottest? D A Temperature C Luminosity B D A E Temperature Which of these stars will have changed the least 10 billion years from now? Main-Sequence Star Summary High Mass: High Luminosity Short-Lived Large Radius Blue Low Mass: Low Luminosity Long-Lived Small Radius Red Open cluster: A few thousand loosely packed stars Globular cluster: Up to a million or more stars in a dense ball bound together by gravity How do we measure the age of a star cluster? Pleiades: no stars with life expectancy of less than 100 million years Main-sequence turnoff Mainsequence turnoff point of a cluster tells us its age Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old