Pr P ope p rti t es s of o f St S a t rs

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1 Properties of Stars

2 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: Other examples of parallax: 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 AU s) Practical limit: 0.01 from ground telescopes from space (Hipparcos) Baseline (1 AU) Parallax Angle (p) p * Distance (d)

3 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 ( 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 Response of human eye What we see as twice (2 times) as bright 100 Watt 250 Watt = times as much energy! Apparent Magnitude (m) - measure of how bright object appears - depends on luminosity and distance Oooh! Bright stars!!

4 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

5 Diameters of Stars - cannot be determined directly from observations Our Sun: Surface Temperature: 5778 K (= 5500 o C or 9940 o F) Spectral Type: G2 Spectral Lines Spectral Type Temperature

6 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 K B 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 K B K Temperature Size (Radius) Luminosity Which has the higher luminosity? (3) Two stars with the same luminosity, different temperatures. A. B K K Which star is larger?

7 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

8 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

9 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

10 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 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

11 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

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