Distances to Stars. The Trigonometric Parallax. Chapter 8: The Family of Stars. We already know how to determine a star s

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1 We already know how to determine a tar urface temperature chemical compoition urface denity Chapter 8: The Family of Star In thi chapter, we will learn how we can determine it ditance luminoity radiu ma and how all the different type of tar make up the big family of tar. Ditance to Star The Trigonometric Parallax d in parec (pc) p in arc econd 1 d= p Example: Nearet tar, α Centauri, ha a parallax of p = 0.76 arc econd d = 1/p = 1.3 pc = 4.3 LY With ground-baed telecope, we can meaure parallaxe p 0.02 arc ec => d 50 pc Trigonometric Parallax: Star appear lightly hifted from different poition of Earth on it orbit 1 pc = 3.26 LY Thi method doe not work for tar farther away than 50 pc. The farther away the tar i (larger d), the maller the parallax angle p. 1

2 Intrinic Brightne / Abolute Viual Magnitude The more ditant a light ource i, the fainter it appear. The ame amount of light fall onto a maller area at ditance 1 than at ditance 2 => maller apparent brightne. Area increae a quare of ditance => apparent brightne decreae a invere of ditance quared Intrinic Brightne The flux received from the light i proportional to it intrinic brightne or luminoity (L) and inverely proportional to the quare of the ditance (d): Star A F ~ L d 2 Star B Both tar may appear equally bright, although tar A i intrinically much brighter than tar B. Earth Ditance and Intrinic Brightne Rigel appear 1.28 time brighter than Betelgeue, Betelgeue The Size (Radiu) of a Star We already know: flux increae with urface temperature (~ T 4 ); hotter tar are brighter. But brightne alo increae with ize: But Rigel i 1.6 time further away than Betelgeue Thu, Rigel i actually (intrinically) 1.28*(1.6) 2 = 3.3 time brighter than Betelgeue. Rigel A B Star B will be brighter than tar A. Abolute brightne i proportional to radiu quared, L ~ R 2. Quantitatively: L = 4 π R 2 σ T 4 Surface area of the tar Surface flux due to a blackbody pectrum 2

3 Example: Polari ha jut about the ame pectral type (and thu urface temperature) a our un, but it i 10,000 time brighter than our un. Thu, Polari i 100 time larger than the un. Thi caue it luminoity to be = 10,000 time more than our un. Organizing the Family of Star: The Hertzprung-Ruell Diagram Abolute mag. or We know: Star have different temperature, different luminoitie, and different ize. To bring ome order into that zoo of different type of tar: organize them in a diagram of Luminoity veru Temperature (or pectral type) Luminoity Hertzprung-Ruell Diagram Temperature Spectral type: O B A F G K M The Hertzprung Ruell Diagram The Hertzprung-Ruell Diagram (II) Mot tar are found along the main equence Star pend mot of their active life time on the Main Sequence. Same temp., but fainter Dwarf Same temperature, but much brighter than MS tar Mut be much larger Giant Star 3

4 Mae of Star in the HertzprungRuell Diagram The higher a tar ma, the more luminou (brighter) it i: L ~ M3.5 tlife ~ M-2.5 Sun: ~ 10 billion yr. 10 Mun: ~ 30 million yr. 0.1 Mun: ~ 3 trillion yr. Hi gh The Ma-Luminoity Relation More maive tar are more luminou. m a e L ~ M3.5 M a e ma Low High-ma tar have much horter live than low-ma tar: Mae in unit of olar mae Mae are meaured from tudie of binary tar 50% of tar are binarie What are the mot common tar? Ideal ituation: Determine propertie of all tar within a certain volume. Problem: Fainter tar are hard to oberve; we might be biaed toward the more luminou tar. 4

5 Faint, red dwarf (low ma) are the mot common tar. A Cenu of the Star Bonu Quetion Why do more maive tar evolve fater? Bright, hot, blue main-equence tar (highma) are very rare. Giant and upergiant are extremely rare. 5