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Chapter 11: Stars 03/09/09 Habbal Astro110-01 Lecture 20 1 Fundamental Properties of Stars • Luminosity • Surface Temperature • Mass 03/09/09 Habbal Astro110-01 Lecture 20 2 The brightness of a star depends on both its distance and luminosity 03/09/09 Habbal Astro110-01 Lecture 20 3 Luminosity: Amount of power a star radiates. Expressed in units of energy per second (e.g. Watts) Apparent brightness: Amount of starlight that reaches Earth Expressed in energy per second per surface area (e.g. Watts/sq. meter). 03/09/09 Habbal Astro110-01 Lecture 20 4 Relationship between luminosity and apparent brightness • Luminosity passing through each imaginary sphere is the same. • Area of sphere = 4π (radius)2 • Divide luminosity by area to get brightness. 03/09/09 Habbal Astro110-01 Lecture 20 5 Relationship between luminosity and apparent brightness Brightness = Luminosity 4π (distance)2 This is the inverse square law for light. Can use this to determine a star’s luminosity: Luminosity = 4π (distance)2 x (Brightness) 03/09/09 Habbal Astro110-01 Lecture 20 6 QUESTION: How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. B. C. D. 03/09/09 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 Habbal Astro110-01 Lecture 20 7 QUESTION: How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. B. C. D. 03/09/09 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 Habbal Astro110-01 Lecture 20 8 • We observe the apparent brightness of stars. • To determine the luminosities (total energy output per second), we need to know the distances to stars. • How do we measure the distances to stars? 03/09/09 Habbal Astro110-01 Lecture 20 9 Parallax = apparent motion of an object relative to the background due to change in viewing positions. More distant stars have smaller parallaxes. 03/09/09 10 Units of stellar distances • d = 1/p (for very small angles p) • 1 parsec is distance when parallax angle (p) is measured in arcseconds • 1 parsec = 3.26 light years Example: a star with p = 1/10 arcsec, is d = 10 parsecs away, or 32.6 light years away. 03/09/09 11 Parallax Parallax is the apparent shift in position of a nearby object against a background of more distant objects. 03/09/09 12 Parallaxes of the nearest stars Apparent positions of the nearest stars shift by about an arcsecond as Earth orbits the Sun. 03/09/09 13 Parallax Angle as a Function of Distance Parallax angle is directly proportional to distance. More distant stars have smaller parallaxes. 03/09/09 14 Measuring Parallax Angle Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star. 03/09/09 15 There is a large spread in stellar luminosities. Use the luminosity of the Sun LSun as a reference Most luminous stars: ~106 LSun Least luminous stars: ~10-4 LSun (Lsun = Sun’s luminosity) Factor of 10 billion spread. 03/09/09 Habbal Astro110-01 Lecture 20 16 How hot are the stars? • Every object emits thermal radiation: Hotter objects emit more light at shorter wavelengths (bluer colors). • So by measuring the colors of stars, we can determine their surface temperature. 03/09/09 Habbal Astro110-01 Lecture 20 17 Measuring a star’s surface T • Astronomers measure the surface temperature because the interior temperature can only be inferred from models. • Surface T is easier to measure than its luminosity because it does not depend on distance. 03/09/09 Habbal Astro110-01 Lecture 20 18 Two Properties of Thermal Radiation Hotter objects emit more light at all wavelengths per unit area. Hotter objects emit photons with a higher average energy (bluer). Relative intensity per unit area • • 03/09/09 Habbal Astro110-01 Lecture 20 19 Hottest stars: 50,000 K Coolest stars: 3,000 K The Sun: 5,800 K. 03/09/09 Habbal Astro110-01 Lecture 20 (All these temperatures refer to the star’s surface.) 20 Luminosity of an object depends both on its size and temperature • An object of fixed size grows more luminous as temperature rises. • An object of fixed temperature grows more luminous as it gets bigger. 03/09/09 Habbal Astro110-01 Lecture 20 21 The types of absorption lines in a star’s spectrum also tell us about its temperature. (Hot interior emits a continuous spectrum, which is partly absorbed by the cool outer layers.) 03/09/09 Habbal Astro110-01 Lecture 20 22 106 K 105 K 104 K Ionized Gas (Plasma) 103 K Neutral Gas 102 K Molecules 10 K Solid 03/09/09 Habbal Astro110-01 Lecture 20 The level of ionization depends on a star’s surface temperature. Therefore, stars of different temperatures will show different absorption lines in their spectra. 23 Spectral type = classification of stellar spectra based on the absorption lines (hence, another way of determining stellar temperature) Examples O Rigel B Sirius A Polaris F Sun, Alpha Centauri A G Arcturus K Betelgeuse, Proxima M Centauri Stars of Orion’s Belt 03/09/09 Habbal Astro110-01 Lecture 20 30,000 K 20,000 K 10,000 K 7,000 K 6,000 K 4,000 K 3,000 K 24 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” • Spectral classes are further broken down into sub-classes, numbered from 0 to 9 (warmer to cooler). For example, the Sun is a G2 star, meaning it is warmer than a G5 star. 03/09/09 Habbal Astro110-01 Lecture 20 25 QUESTION: Which kind of star is hottest? A. B. C. D. 03/09/09 M star F star A star K star Habbal Astro110-01 Lecture 20 26 QUESTION: Which kind of star is hottest? A. B. C. D. M star F star A star K star “Oh, Be A Fine Girl, Kiss Me” 03/09/09 Habbal Astro110-01 Lecture 20 27 Pioneers of Stellar Classification Annie Jump Cannon and the “calculators” at Harvard laid the foundation of modern stellar classification. 03/09/09 Habbal Astro110-01 Lecture 20 28 Pioneers of Stellar Classification Williamina Fleming (1857-1911) classified stellar spectra according to the strength of their hydrogen lines: A strongest, B slightly weaker, and O for the weakest. She classified more than 10,000 stars, which Pickering published in 1890. Annie Jump Cannon joined Pickering’s group in 1896. Building on the work of Fleming and Antonia Maury, she realized that the spectral classes fell into a natural order – but not the alphabetical order determined by hydrogen lines alone. She also found that some of the original classes overlapped others and could be eliminated. She discovered that the natural sequence was OBAFGKM. She added subdivisions by number. Jump Cannon personally classified 400,000 stars. In 1925, Cecilia Payne-Gaposchkin showed that the differences in spectral lines from star to star reflected changes in the ionization of the emitting atom. She published her findings in her doctoral thesis. 03/09/09 Habbal Astro110-01 Lecture 20 29 How do we determine the masses of stars? Use binary stars (pairs of stars held together by gravity). About ~1/2 of all stars are binaries. Relative sky positions of Sirius A & B over 70 years 03/09/09 Habbal Astro110-01 Lecture 20 30 We measure mass using gravity (Newton’s version of Kepler’s Third Law). Direct mass measurements are possible only for stars in binary star systems 3 a p p22= = a3 G (M(M + M+M ) 2) 2 4π2 G 1 4π Isaac Newton 03/09/09 1 2 p = period a = average separation M1, M2 = mass of the 2 stars We measure the binary’s period and separation to get the sum of the stellar masses. Habbal Astro110-01 Lecture 20 31 03/09/09 Habbal Astro110-01 Lecture 20 32