Properties of Stars
Distances Parallax ( Triangulation ): - observe object from two separate points - use orbit of the Earth (1 AU) - measure angular shift of object - angle depends on distance to object more distant objects = smaller parallax angle p * Measuring distances to stars: http://sci2.esa.int/interactive/media/flashes/2_1_1.htm http://css-tricks.com/examples/starrynight/ Other examples of parallax: http://muffi.pl/en/, http://www.noleath.com/noleath/ http://www.intacto10years.com/index_start.php Distance (d): - if parallax angle measured in arcsec ( ) d = 1/p d = distance in parsecs New Unit of Distance: : Parsec 1 pc = the distance when angle is exactly 1 ( = 3.26 light years or 206265 AU s) Practical limit: 0.01 from ground telescopes 0.001 from space (Hipparcos) Baseline (1 AU) Parallax Angle (p) p * Distance (d)
Luminosity and Brightness Luminosity (L): - total energy output of an object Brightness (b): - amount of energy received by observer - depends on luminosity and distance Magnitude Scale to describe brightness - developed by Hipparchus (190 120 B.C) Brightest stars = 1 st Magnitude ½ as bright stars = 2 nd Magnitude Faintest stars = 6 th Magnitude BUT, Scale is backwards Brighter stars smaller magnitude Fainter stars larger magnitude http://www.london2012.com/weightlifting/event/men-56kg/index.html Response of human eye What we see as twice (2 times) as bright 100 Watt 250 Watt = 2.512 times as much energy! Apparent Magnitude (m) - measure of how bright object appears - depends on luminosity and distance Oooh! Bright stars!!
Absolute Magnitude (M) - how bright star would appear IF the distance to star is exactly 10 parsecs - depends only on luminosity Spectral Classification Classification of stars into spectral types This one s not so bright. Spectral Types: determined by temperature This one is REALLY bright!! 10 pc Relation between M, m, and distance m M = 5 log d - 5 Brightness (m) Distance (d) Luminosity (M) O, B, A, F, G, K, M hottest coolest Oh, Be A Fine Girl/Guy Kiss Me! Subdivisions of Spectral Types: 0-9, F8, F9, G0, G1, G2,, G8, G9, K0, K1, hotter > > > > > > > cooler
Diameters of Stars - cannot be determined directly from observations http://www.noao.edu/image_gallery/html/im0649.html Our Sun: Surface Temperature: 5778 K (= 5500 o C or 9940 o F) Spectral Type: G2 Spectral Lines Spectral Type Temperature
But, can be found from luminosity, temperature. Temp amount of E per square meter (flux) Lum. total energy output from entire surface Energy from each m 2 X number of m 2 = Total Energy output Properties of Stars - Examples (1) Two stars with the same temperature, different diameters. A. 5000 K B. 5000 K Which has the higher luminosity? where: L = ( 4 π R 2 ) X ( σ T 4 ) Stefan - Boltzmann Law R = radius of star (size), σ = Stef-Boltz Constant (2) Two stars with the same diameter, different temperatures. A. 5000 K B. 10000 K Temperature Size (Radius) Luminosity Which has the higher luminosity? (3) Two stars with the same luminosity, different temperatures. A. B. 5000 K 10000 K Which star is larger?
Stefan Boltzmann Law with money (1) Two sheets (stars) with the same denomination (temperature), different size (diameters). A. B. 1 dollar bills 1 dollar bills Which has the higher total value $ (luminosity)? (2) Two sheets (stars) with the same size (diameter), different denominations (temperatures). The Hertzsprung Russell Diagram Henry N. Russell, Ejnar Hertzsprung -made a simple plot of stars -M vs. Spectral Type -to see if properties are related RESULTS: The H-R Diagram most important correlation between stellar properties discovered to date (Mihalas & Binney, Galactic Astronomy) High L A. B. 1 dollar bills 20 dollar bills Which has the higher total value $ (luminosity)? Luminosity or M (3) Two sheets (stars) with the same total value $ (luminosity), different denomination (temperatures). Low L A. B. 1 dollar bills 20 dollar bills Which sheet (star) has a larger size (diameter)? High T Low T Temperature or Spectral Type or Color
Groups on the HR diagram: - Main Sequence - Red Giants - White Dwarfs - Supergiants In general: (90% of all stars) Hotter stars are more luminous Main Sequence But, some stars are cool & very luminous some stars are hot with low luminosity
Luminosity Class - separate groups on HR diagram Luminosity Class Type of Star I Supergiant II Bright Giant III Red Giant IV Subgiant V Main Sequence
Mass of Stars Use binary star systems - two stars that orbit around each other Finding mass of stars: - depends on orbital properties - size of orbit, time to complete orbit (period) - depends on center of mass (balance point) Two equal mass stars: Center of mass exactly in the middle Two unequal mass stars: Example: Total Mass: 6 M Based on CM: if M 1 = M 2 What are M 1, M 2? Based on CM: if M 1 = 2M 2 What are M 1, M 2? Size of Orbit + Period of orbit MASS + Center of Mass Center of mass closer to more massive star http://csep10.phys.utk.edu/guidry/java/binary/binary.html http://astro.unl.edu/naap/ebs/animations/ebs.html Mass Luminosity Relation - developed by studying binary stars - can be applied to all Main Sequence stars - but not to other stars L related to (mass) 3
Stellar Models based on: Hydrostatic Equilibrium Thermal Equilibrium Heat Transport Russell - Vogt Theorem: - all the properties of a star are uniquely determined by: Mass Chemical Composition Difference between stars along the main sequence: Difference in Mass Difference between main sequence and other groups: Difference in Composition