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The Nature of the Stars Orion from +7.0 to 2.0 mag sky 量離量亮度度兩亮度度度量 http://www.darksky.org/infoshts/is120.html 亮度 (brightness) 來亮度度離 (apparent magnitude) 來亮度亮數例 1 2 亮 19 30 亮 1 6 亮 100-26.8 亮度 2.51 狼 -1.5 女 0.0 裸見 6 參 0.4 見 5000~6000 2000~3000 1010,000 力 2 兩亮度 Q1: 亮度 Q2: 狼 -1.5 Sirius B 亮度狼亮度狼 B Q3: 7 mm 12 Q4: 12 兩亮度 3 1 兩 Q1: 亮度 A: (2.512) 2 (2.5) 2 6.25 6 times fainter Q2: 狼 -1.5 Sirius B 亮度狼狼 B A: 100 times of flux 5 mag difference, so 10,000 times fainter 10 mag larger, Sirius B has m = -1.5 + 10 = 8.5 mag Q3: 7 mm 12 A: naked eye limit = 6 mag, so 12 mag is (2.5) 6 250 times fainter telescope aperture should be > 7 mm x 16 = 110 mm Q4: 12 兩亮度 31 兩 A: b 1 /b 2 = 3/1, so (b 1 +b 2 )/b 2 =4/1, m 1+2 m 2 =2.5 log ¼ -1.5 m 2 = 12 + 1.5 = 13.5 mag; likewise m 1 = 12 + 0.3 = 12.3 mag 1

來亮度參獵狼參獵參獵獵 = Orion 獵 = Orionis = Ori 離便度離 10 pc 1 pc = 3.26 ly 年 d= 10 pc (m) (M, absolute magnitude) derivation 離 11 AU 1 Note: m = M when d =10 pc Q: m = -27 (M) Q: m = -27 (M) Luminosity (1 L ) A: m = -27 mag, and d = 1 AU = (206265) -1 pc 5 log d 5-31.6, M 4.6 mag Q: (Epsilon) Eridani is 3.23 pc from Earth. As seen from Earth, the star appears only 6.73 x 10-13 as bright as then Sun. Estimate the luminosity of Eridani compared with that of the Sun. A: L/L = (d/d ) 2 (b/b ) 3.23 pc = 3.23 x 206265 AU/pc = 6.66 x 10 5 AU L/L = (6.66 x 10 5 ) 2 (6.73 x 10-13 ) = 0.30 Number of stars in 1000 pc 3 Stars like the Sun (L=1 L ) are relatively common. Very luminous stars are quite rare. Absolute magnitude Low-luminosity stars are common. 2

Inverse-Square Law b: apparent brightness, in W/m 2 L: a star s luminosity, in W d: distance to the star, in meters For the Sun, This is called the Earth s Solar Constant. (parallax) 離離不來 Distance Determination by Parallax 例亮狼年 (annual parallax) 0.38 狼離 2.6 pc 8.6 年度利 parallax < 1 kpc 離 d (pc) =1/p (arcsec) AU 更度離來亮度度度力力狀力 vs 力輻度量例 X 藍輻率輻度率輻例藍量力度力度度度 3

濾 (e.g., UBV 量亮度, 例藍 (blue) 綠 (visual) 亮度輻兩率輻度 VB 兩亮度度 Orionis Tauri 量例 Annie Jump Cannon 類 19 Harvard College Observatory 女類度度類 A B, C, 來度度若度列 O-B-A-F-G-K-MO 度 30,000~50,000M 2500~4000 度 G 度 Oh, Be A Fine Guy/Girl, Kiss Me! 4

不度不度不度度 III 離 III 兩 L Red 1300-2500 Neutral potassium, rubidium, Brown dwarf Teide 1 and cesium, and metal hydrides T Red < 1300 Strong neutral possisium, and Brown dwarf Gliese 229B some water 5

http://en.wikipedia.org/wiki/stellar_classification HD: Henry Draper Catalogue 輻便 Q: Betelgeuse (Alpha Orionis) is 60,000 times more luminous than the Sun and has a surface temperature of 3500 K. What is its radius? A: R/R = (5800 K/3500 K) 2 (6 x 10 4 ) 1/2 = 670 The Sun s radius is 6.96 x 10 8 km, so R Betelgeuse ~ 3 AU! This is beyond the orbit of Mars in the solar system. 度度 Hertzsprung-Russell diagram 羅 1911 by Ejnar Hertzsprung (Danmark) & 1913 by Henry Norris Russell (USA) 度度 H-R diagram --- An astronomer s tool of the trade H-R diagram 90 狀度度 O B A F G K M Spectral type (main sequence) 度度讀羅 H-R diagram 羅 (main-sequence stars) 羅度度亮 (red giants) (red supergiants) HR 度度 (white dwarfs) 6

L = luminosity radiation per unit area total surface area T = surface temperature = Boltzmann const. R = stellar radius 度度例 5800K 度力 luminosity class 行力量來不力了 50 年 50 年兩料離離 < 1 kpc 類類 (O, B, A, F, G, K, M) + 度類 (I, II, III, IV, V) 離度類來 (spectroscopic parallax) 量度量量力量力量度度 (binary) 來量 Animations --- http://www.astronomy.ohio-state.edu/~pogge/ast162/movies/ 類 optical doubles (apparent binaries) 兩度 visual binaries 兩量兩 M 量 a AU P 年例 4 AU 2.5 年兩量 7

(zeta) Ursae Majoris is a binary system separated by ~0.01. (cont.) spectroscopic binaries 兩量兩兩 2MASSSW J074625+2000321 is a binary system separated by ~1/3, observed respectively by the HST, VLT, Keck I, and Gemini North. (cont.) eclipsing binaries 兩量兩 8

量度 (mass-luminosity relation; ) Roughly L ~ M 3.5 9