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The Family of Stars Please press “1” to test your transmitter. The Family of Stars We already know how to determine a star’s • surface temperature • chemical composition Now, see how we can determine its • distance • luminosity • radius • mass and how all the different types of stars make up the big family of stars. Distances of Stars d in parsec (pc) p in arc seconds 1 d = __ p Trigonometric Parallax: Star appears slightly shifted from different positions of the Earth on its orbit The further away the star is (larger d), the smaller the parallax angle p. 1 pc = 3.26 LY The Trigonometric Parallax Example: Nearest star, a Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 pc = 4.3 LY With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 pc This method does not work for stars further away than 50 pc. Sirius, the brightest star in the sky, has a trigonometric parallax of p = 0.385 arc seconds. What is its distance from Earth? 1. 2. 3. 4. 5. 0.385 pc 0.80 light years 1.255 pc 2.60 light years 8.47 light years The method of trigonometric parallaxes (from ground based telescopes) allows us to measure distances … 1. 2. 3. 4. 5. only to objects in our solar system. only to stars in our solar neighborhood within the Milky Way. to stars throughout the entire Milky Way. to stars and galaxies throughout the Local Group. even to other clusters of galaxies. Intrinsic Brightness / Absolute Magnitude The further away a light is, the fainter it appears. Intrinsic Brightness / Absolute Magnitude (II) More quantitatively: The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): L __ F~ 2 d The stars A and B have the same intrinsic luminosity, but A is 5 times further away from Earth than B. Then: Star A 1. 2. 3. 4. 5. Star B Both stars will appear equally bright. A will appear 5 times brighter than B. B will appear 5 times brighter than A. A will appear 25 times brighter than B. B will appear 25 times brighter than A. Earth Distance and Intrinsic Brightness Example: Magn. Diff. Intensity Ratio 1 2.512 2 2.512*2.512 = (2.512)2 = 6.31 … … 5 (2.512)5 = 100 For a magnitude difference of 0.41 – 0.14 = 0.27, we found: Rigel appears 1.28 times brighter than Betelgeuze But Rigel and Betelgeuze may be at quite different distances from us! Betelgeuze App. Magn. mV = 0.41 Rigel App. Magn. mV = 0.14 Absolute Magnitude To characterize a star’s intrinsic brightness, define Absolute Magnitude (MV): Absolute Magnitude = Magnitude that a star would have if it were at a distance of 10 pc. If we know a star’s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes. Absolute Magnitude (II) Betelgeuze Rigel mV 0.41 0.14 MV -5.5 -6.8 d 152 pc 244 pc Betelgeuze Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512)1.3 = 3.3 Rigel is actually 3.3 times brighter than Betelgeuze! Rigel 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 Star B will be brighter than star A. Specifically: Absolute brightness is proportional to radius (R) squared, L ~ R2. Example: Both Spica B and Sirius B are B-type stars, but Sirius B is a white dwarf star, with a radius ~ 560 times smaller than Spica B. Thus, since L ~ R2, Sirius B is intrinsically 5602 ≈ 320,000 times fainter than Spica B. Polaris has just about the same spectral type (and surface temperature) as our sun, but it is 10,000 times brighter. Thus, Polaris’ radius is … the sun’s radius. 1. 2. 3. 4. 5. the same as 100 times larger than 100 times smaller than 10,000 times larger than 10,000 times smaller than Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity Luminosity versus Temperature (or spectral type) Hertzsprung-Russell Diagram Spectral type: O Temperature B A F G K M The Hertzsprung Russell Diagram The Hertzsprung-Russell Diagram (II) Same temperature, but much brighter than MS stars → Must be much larger → Giant Stars Radii of Stars in the Hertzsprung-Russell Diagram Rigel Betelgeuze Polaris Sun 100 times smaller than the sun Ia Bright Supergiants Ia Luminosity Classes Ib Ib Supergiants II II Bright Giants III Giants III IV IV Subgiants V V Main-Sequence Stars Examples: • Our Sun: G2 star on the Main Sequence: G2V • Polaris: G2 star with Supergiant luminosity: G2Ib