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Measuring the Stars How big are stars? How far away are they? How bright are they? How hot? How old, and how long do they live? What is their chemical composition? How are they moving? Are they isolated or in clusters? By answering these questions, we not only learn about stars, but about the structure and evolution of galaxies they live in, and the Universe. How Far Away are the Stars? Earth-baseline parallax useful in Solar System Parallax demo Earth-orbit parallax - useful for nearest stars New distance unit: the parsec (pc). Using Earth-orbit parallax, if a star has a parallactic angle of 1", it is 1 pc away. Remember 1" (arcsecond) = 1/60 arcmin = 1/3600 degrees If the angle is 0.5", the distance is 2 pc. 1 Distance (pc) = Parallactic angle (arcsec) Closest star to Sun is Proxima Centauri. Parallactic angle is 0.7”, so distance is 1.3 pc. 1 pc = 3.3 light years = 3.1 x 10 18 cm = 206,000 AU 1 kiloparsec (kpc) = 1000 pc 1 Megaparsec (Mpc) = 10 6 pc The Solar Neighborhood Nearest star to the Sun: Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex Model of distances: • Sun is a marble, Earth is a grain of sand orbiting 1 m away. • Nearest star is another marble 270 km away. • Solar system extends about 50 m from the Sun; rest of distance to nearest star is basically empty. Earth-orbit parallax using ground-based optical telescopes is good for stars within 30 pc (1000 or so). Tiny volume of Milky Way galaxy. Other methods later. Our nearest stellar neighbors Star Motion Barnard’s Star (top) has the largest proper motion of any – proper motion is the actual shift of the star in the sky, after correcting for parallax. The pictures (a) were taken 22 years apart. (b) shows the actual motion of the Alpha Centauri complex. Clicker Question: Suppose we observe a star with an annual parallax of 600 milliarcseconds, what is its distance in parsecs? A: 100 parsecs B: 1.7 parsecs C: 0.1 parsecs D: 0.01 parsecs Question 2 The angle of stellar parallax for a star gets larger as the a) distance to the star increases. b) size of the star increases. c) size of the telescope increases. d) length of the baseline increases. e) wavelength of light increases. Question 2 The angle of stellar parallax for a star gets larger as the a) distance to the star increases. b) size of the star increases. c) size of the telescope increases. d) length of the baseline increases. e) wavelength of light increases. Astronomers typically make observations of nearby stars 6 months apart, making the baseline distance equal to 2 AU (Astronomical Units). How Luminous are Stars? Remember, luminosity of the Sun is LSun = 4 x10 33 erg/s (amount of energy put out every second in form of radiation). Luminosity also called “absolute brightness”. How bright a star appears to us is the “apparent brightness”, which depends on its luminosity and distance from us: apparent brightness luminosity (distance) 2 So we can determine luminosity if apparent brightness and distance are measured: luminosity apparent brightness x (distance) 2 This is an example of the inverse square law. apparent brightness luminosity (distance) 2 Luminosity and Apparent Brightness Therefore, two stars that appear equally bright might be a closer, dimmer star and a farther, brighter one. Luminosity and Apparent Brightness Apparent luminosity is measured using a magnitude scale, which is related to our perception. It is a logarithmic scale; a change of 5 in magnitude corresponds to a change of a factor of 100 in apparent brightness. It is also inverted – larger magnitudes are dimmer. Stellar Temperatures The color of a star is indicative of its temperature. Red stars are relatively cool, whereas blue ones are hotter. Stellar Temperatures The radiation from stars is blackbody radiation; as the blackbody curve is not symmetric, observations at two wavelengths are enough to define the temperature. Spectral Classes Strange lettering scheme is a historical accident. Spectral Class Surface Temperature O B A F G K M 30,000 K 20,000 K 10,000 K 7000 K 6000 K 4000 K 3000 K Examples Rigel Vega, Sirius Sun Betelgeuse Further subdivision: BO - B9, GO - G9, etc. GO hotter than G9. Sun is a G2. Classification of Stars Through Spectroscopy Ionized helium. Requires extreme UV photons. Only hottest stars produce many of these. Remember: stellar spectra show black-body radiation and absorption lines. Pattern of absorption lines depends on temperature (mainly) and chemical composition. Spectra give most accurate info on these as well as: density in atmosphere gravity at surface velocity of star towards or from us Stellar Temperatures The different spectral classes have distinctive absorption lines. Stellar Sizes A few very large, very close stars can be imaged directly; this is Betelgeuse. Stellar Sizes - Indirect Method Almost all stars too far away to measure their radii directly. Need indirect method. For blackbodies, use Stefan's Law: Energy radiated per cm2 of area on surface every second (T = temperature at star’s surface) T4 And: Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2) So: Luminosity (temperature) 4 x (surface area) Determine luminosity from apparent brightness and distance, determine temperature from spectrum (black-body curve or spectral lines), then find surface area, Surface area Luminosity / (temperature) 4 then find radius (sphere surface area is 4 R2) The Wide Range of Stellar Sizes How Massive are Stars? 1. Binary Stars. Orbital period depends on masses of two stars and their separation. 2. Theory of stellar structure and evolution. Tells how spectrum and color of star depend on mass. Relationship of Luminosity, Size, and Temperature Burner and Boiling Spaghetti Analogy Which burner will cook the pot of spaghetti faster? A. The one on the left B. The one on the right C. Neither, both will cook the spaghetti in the same amount of time Relationship of Luminosity, Size, and Temperature Luminosity α radius2 x temperature4 The Hertzsprung–Russell Diagram The H–R diagram plots stellar luminosity against surface temperature. This is an H–R diagram of a few prominent stars. Building the Hertzsprung-Russell (H-R) Diagram Which is larger, S or T? => A.) S B.) T C.) same size D.) can’t tell Building the Hertzsprung-Russell (H-R) Diagram Which is larger, S or X? => A.) S B.) X C.) same size D.) can’t tell Summary of Chapter 10 • Distance to nearest stars can be measured by parallax. • Apparent brightness is as observed from Earth; depends on distance and absolute luminosity. • Spectral classes correspond to different surface temperatures. • Stellar size is related to luminosity and temperature. Summary of Chapter 10, cont. • H–R diagram is plot of luminosity vs. temperature; most stars lie on main sequence. • Distance ladder can be extended using spectroscopic parallax. • Masses of stars in binary systems can be measured. • Mass determines where star lies on main sequence.