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How luminous are stars? Luminosity passing through each sphere is the same Luminosity: Amount of power a star radiates (energy per second=Watts) Area of sphere: 4π (radius)2 Apparent brightness: Amount of starlight that reaches Earth Divide luminosity by area to get brightness (energy per second per square meter) The brightness of a star depends on both distance and luminosity So how far are these stars? The relationship between apparent brightness and luminosity depends on distance: 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) 1 Parallax is the apparent shift in position of a nearby object against a background of more distant objects Most luminous stars: 106 LSun Least luminous stars: p (arcsec) = 1/d(AU) How hot are stars? Every object emits thermal radiation with a spectrum that depends on its temperature 10-4 LSun Shift is measurable for nearest stars only (LSun is luminosity of Sun) Laws of Thermal Radiation 1) Hotter objects emit more light at all wavelengths 2) Hotter objects tend to emit light at shorter wavelengths and higher frequencies 2 Hottest stars: 50,000 K 106 K 105 K Coolest stars: 3,000 K (Sun’s surface is 5,800 K) 104 K Ionized Gas (Plasma) 103 K Neutral Gas 102 K Molecules 10 K Solid Level of ionization also reveals a star’s temperature Lines in a star’s spectrum correspond to a spectral type that reveals its temperature (Hottest) O B A F G K M (Coolest) This is a high-resolution spectrum of one star. Absorption lines in star’s spectrum tell us ionization level 3 Remembering Spectral Types (Hottest) O B A F G K M (Coolest) • Oh, Be A Fine Girl, Kiss Me • Only Boys Accepting Feminism Get Kissed Meaningfully Thought Question Thought Question Which kind of star is hottest? A. B. C. D. M star F star A star K star How massive are stars? Which kind of star is hottest? A. B. C. D. M star F star A star K star The orbit of a binary star system depends on strength of gravity 4 The Center of Mass Binary Stars More than 50% of all stars in our Milky Way are not single stars, but belong to binaries: center of mass = balance point of the system. Pairs or multiple systems of stars which orbit their common center of mass. Both masses equal => center of mass is in the middle, rA = rB. The more unequal the masses are, the more it shifts toward the more massive star. If we can measure and understand their orbital motion, we can estimate the stellar masses. Isaac Newton We measure mass using gravity Direct mass measurements are possible only for stars in binary star systems p2 = aAU3 ____ MA + MB = Py2 4π2 G (M1 + M2) p = period a3 a = average separation Need 2 out of 3 observables to measure mass: v 1) Orbital Period (p) 2) Orbital Separation (a or r=radius) 3) Orbital Velocity (v) For circular orbits, v = 2πr / p r M Usually we don’t know inclination, so mass estimate is uncertain: (M1 + M2) = (a’/sin i)3/P2 (MA and MB in units of solar masses) 5 Types of Binary Star Systems Visual Binary • Visual Binary • Eclipsing Binary • Spectroscopic Binary About half of all stars are in binary systems Visual Binaries We can directly observe the orbital motions of these stars Eclipsing Binary The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly. We can measure periodic eclipses 6 Eclipsing Binaries Usually, inclination angle of binary systems is unknown Eclipsing Binaries Peculiar “double-dip” light curve → uncertainty in mass estimates. Special case: Eclipsing Binaries Here, we know that we are looking at the system edge-on! Example: VW Cephei Eclipsing Binaries Spectroscopic Binary Example: Algol in the constellation of Perseus From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane. We determine the orbit by measuring Doppler shifts 7 Spectroscopic Binaries Spectroscopic Binaries Typical sequence of spectra from a spectroscopic binary system Time The approaching star produces blueshifted lines; the receding star produces redshifted lines in the spectrum. Doppler shift → Measurement of radial velocities → Estimate of separation a → Estimate of masses 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 (0.08 MSun) 10-4 LSun - 106 LSun (100 MSun) Temperature: from color and spectral type (0.08 MSun) 3,000 K - 50,000 K (100 MSun) Mass: from period (p) and average separation (a) of binary-star orbit 0.08 MSun - 100 MSun 8 Luminosity What is a HertzsprungRussell Diagram? The Mass-Luminosity Relation More massive stars are more luminous. An H-R diagram plots the luminosity and temperature of stars L ~ M3.5 Temperature Why is a star’s mass its most important property? Main-Sequence Star Summary Core pressure and temperature of a higher-mass star need to be larger in order to balance gravity High Mass: Higher core temperature boosts fusion rate, leading to larger luminosity Low Mass: High Luminosity Short-Lived Large Radius Blue Low Luminosity Long-Lived Small Radius Red 9 High-Mass Stars Mass & Lifetime Most stars reside on the Main Sequence. Until core hydrogen (10% of total) is used up These stars are burning hydrogen in their cores. Sun’s life expectancy: 10 billion years 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: Low-Mass Stars 0.1 times as much fuel, uses it 0.01 times as fast 100 billion years ~ 10 billion years x 0.1 / 0.01 Stars with low temperature and high luminosity must have large radius Luminosity H-R diagram depicts: Temperature Color The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T4); hotter stars are brighter. But brightness also increases with size: A B Spectral Type Star B will be brighter than star A. Luminosity Radius *Mass *Lifespan Absolute brightness is proportional to radius squared, L ~ R2. Quantitatively: L = 4 π R2 σ T4 *Age Temperature Surface area of the star Surface flux due to a blackbody spectrum 10 Ia Bright Supergiants Ia Luminosity Classes Luminosity effects on the width of spectral lines Ib II Ib Supergiants II Bright Giants III Giants III IV Same spectral type, but different luminosity IV Subgiants V Lower gravity near the surfaces of giants V Main-Sequence Stars ⇒ smaller pressure ⇒ smaller effect of pressure broadening ⇒ narrower lines C D A Temperature C B Which star is the hottest? Luminosity Luminosity B Which star is the most luminous? D A Temperature 11 C D A Which star has the largest radius? D A Temperature Temperature A A Which star is most like our Sun? D Luminosity D Luminosity C B Which star is a main-sequence star? Luminosity Luminosity B B B C Temperature Which of these stars will have changed the least 10 billion years from now? C Temperature 12 A Luminosity D B Which of these stars can be no more than 10 million years old? Surveys of Stars Ideal situation: Determine properties of all stars within a certain volume. Problem: C Fainter stars are hard to observe; we might be biased towards the more luminous stars. Temperature A Census of the Stars Faint, red dwarfs (low mass) are the most common stars. Bright, hot, blue main-sequence stars (high-mass) are very rare. Giants and supergiants are extremely rare. 13 What are the two types of star clusters? Open cluster: A few thousand loosely packed stars How do we measure the age of a star cluster? Massive blue stars die first, followed by white, yellow, orange, and red stars Main-sequence turnoff Pleiades Globular cluster: Up to a million or more stars in a dense ball bound together by gravity Main -sequence turnoff point of a cluster tells us its age Pleiades now has no stars with life expectancy less than around 100 million years 14 Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old Sets minimum age for the Universe! 15