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Download Introduction to Stars: Their Properties
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Learning goals: Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star. Define brightness (see text), apparent magnitude, absolute magnitude. Describe the methods used to determine the temperature, luminosity, and radius of a star. 1 Questions: Which stars are the brightest? Which stars are putting out the most watts? (luminosity = energy per second) NEED TO KNOW: Distances The most fundamental and accurate (within a certain range) means of finding distances is measuring the parallaxes of stars. 2 PARSEC: Parallax ARc SECond A star having a parallax of 1 arc second is 1 parsec away 1 parsec (pc) = 3.26 light years 1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc Baseline is 1 Astronomical Unit Small angle formula for distance in AU’s: 3 Works accurately for stars within about 200 pc (Hipparchos satellite) Biggest problem: measuring the miniscule shift of a star against more distant stars parallax 0.75 arcseconds 1 distance = 1.3 pc 4.3 ly 0.75 parallax 0.15 arcseconds 1 distance = __?__ 6.7 pc __?__ 22 ly 0.15 parallax 0.0015 arcseconds 1 distance = __?__ 667 pc __?__ 2170lyly 0.0015 •Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star. 4 Using SIMBAD to find the parallaxes of the stars of Exercise 2 41 Cygni data (partial) QuickTime™ and a decompressor are needed to see this picture. Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc seconds Distance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly 5 Every 5 magnitudes difference means 100 x difference in brightness One magnitude difference QuickTime™ and a decompressor are needed to see this picture. is 2.512 times in brightness. (2.5125 = 100) • Define brightness, apparent magnitude, absolute magnitude 6 Using SIMBAD to find necessary measured (observed) quantities 41 Cygni data (partial) QuickTime™ and a decompressor are needed to see this picture. V = apparent magnitude through “visual” filter Think of it as mv . UV QuickTime™ and a decompressor are needed to see this picture. IR 7 Work on star table -- SIMBAD Search Star ID 41 Cygni Spectral Type F5 Iab 52 Cygni G9.5 III 69 Cygni B0 Ib xi Cygni K4.5 Ib-II Surface Temp. (K) App . Mag Paralla x (mas) Dist. (pc) Abs . Mag Lstar/Lsun Rstar/Rsun 6,900 4.02 4.24 4,800 4.23 16.22 26,000 5.94 3,900 3.72 0.36 3.87 8 QuickTime™ and a decompressor are needed to see this picture. 9 Solar data QuickTime™ and a decompressor are needed to see this picture. 10 Absolute magnitude is the apparent magnitude a star would have m M 5log10 (d pc ) 5 if its distance = 10 parsecs. M m 5log10 (d pc ) 5 Relates luminosities by “placing” stars on common scale. Smaller the absolute magnitude number, the more luminous the star. 41 Cygni dpc = 236 parsecs mv = 4.016 M v mv 5log 10 (d pc ) 5 M v 4.016 5log 10 (236) 5 M v 4.016 5(2.37) 5 2.8 What does the answer tell you? • Define apparent magnitude, absolute magnitude 11 52 Cygni parallax _____ arcseconds distance = 1 ______ parallax m M 5log10 (d pc ) 5 M m 5log10 (d pc ) 5 12 Relationship between absolute magnitude and luminosity - bring in the Sun! 41 Cygni’s calculations Lstar M Sun M star 2.5log 10 LSun M Sun M star Lstar log 10 2.5 LSun M Sun M star 10 M Sun M star 10 2.5 2.5 10 L log10 star L Sun Lstar LSun M Sun M star Lstar 2.5 10 LSun 4.74 (2.8) Lstar 2.5 10 1070 LSun Lstar 1070LSun 13 52 Cygni M Sun M star Lstar 2.5 10 ________ LSun 14 Luminosity Depends on •Size (radius, R) •Temperature L 4 R 2 T 4 L 4 R 2 T 4 2 4 Lstar 4 Rstar Tstar 2 LSun 4 RSun TSun4 2 4 Rstar 2 Tstar 4 Lstar 4 Rstar Tstar 2 4 LSun 4 RSun TSun RSun TSun Lstar TSun 4 Rstar 2 LSun Tstar RSun 41 Cygni 2 2 1070 R T L 5770 star Sun star 4 2 Rstar Lstar TSun TSun Lstar R T L 6440 1 Sun star Sun RSun LSun Tstar Tstar LSun Rstar 26 or Rstar 26RSun RSun • Describe the methods used to determine temperature, luminosity, radius 15 52 Cygni Rstar RSun TSun 2 Lstar Tstar LSun Rstar _______ RSun 16 Work on star table -- SIMBAD Search Star ID 41 Cygni Spectral Type F5 Iab 52 Cygni G9.5 III 69 Cygni B0 Ib xi Cygni K4.5 Ib-II Surface Temp. (K) App . Mag Paralla x (mas) Dist. (pc) Abs . Mag Lstar/Lsun Rstar/Rsun 6,900 4.02 4.24 4,800 4.23 16.22 26,000 5.94 3,900 3.72 0.36 3.87 17