PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Work on star table -- SIMBAD SearchSlide 9Solar dataSlide 1152 CygniRelationship between absolute magnitude and luminosity - bring in the Sun! 41 Cygni’s calculationsSlide 14LuminositySlide 16Slide 171QuickTime™ and a decompressorare needed to see this picture. 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.Learning goals:Learning goals:2Questions:Questions:Which stars are the brightest?Which stars are putting out the most watts? (luminosity = energy per second)NEED TO KNOW:NEED TO KNOW:DistancesThe most fundamental and accurate (within a certain range) means of finding distances is measuring the parallaxes of stars.3PARSEC: Parallax ARc SECondA star having a parallax of 1 arc second is 1 parsec away1 parsec (pc) = 3.26 light years1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc Baseline is 1 Astronomical UnitSmall angle formula for distance in AU’s:4 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 arcsecondsdistance = 10.75=1.3 pc = 4.3 ly€ parallax = 0.15 arcsecondsdistance = 10.15= __?__ pc = __?__ ly€ parallax = 0.0015 arcsecondsdistance = 10.0015= __?__ pc = __?__ ly6.7 22667 2170 ly•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.5Using SIMBAD to find the parallaxes of the stars of Exercise 2QuickTime™ and a decompressorare needed to see this picture.41 Cygni data (partial)Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc secondsDistance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly6 Every 5 magnitudes difference means 100 x difference in brightness One magnitude difference is 2.512 times in brightness.(2.5125 = 100)QuickTime™ and a decompressorare needed to see this picture.• Define brightness, apparent magnitude, absolute magnitude7Using SIMBAD to find necessary measured (observed) quantitiesQuickTime™ and a decompressorare needed to see this picture.41 Cygni data (partial)V = apparent magnitude through “visual” filterThink of it as mv .QuickTime™ and a decompressorare needed to see this picture.UVIR8Work on star table -- Work on star table -- SIMBAD SearchSIMBAD SearchStar ID Spectral Type Surface Temp. (K) App. Mag Parallax (mas) Dist. (pc) Abs. Mag Lstar/Lsun Rstar/Rsun 41 Cygni 52 Cygni 69 Cygni xi Cygni F5 Iab4.02 4.246,900G9.5 III4.23 16.224,800B0 Ib5.94 0.3626,000K4.5 Ib-II3.72 3.873,9009QuickTime™ and a decompressorare needed to see this picture.10Solar dataSolar dataQuickTime™ and a decompressorare needed to see this picture.11Absolute magnitude is the apparent magnitude a star would have if its distance = 10 parsecs.Relates luminosities by “placing” stars on common scale.Smaller the absolute magnitude number, the more luminous the star.€ m − M = 5log10(dpc) − 5M = m − 5log10(dpc) + 5• Define apparent magnitude, absolute magnitude41 Cygni dpc = 236 parsecsmv = 4.016€ Mv= mv− 5log10(dpc) + 5Mv= 4.016 − 5log10(236) + 5Mv= 4.016 − 5(2.37) + 5 = −2.8What does the answer tell you?12€ m − M = 5log10(dpc) − 5M = m − 5log10(dpc) + 552 Cygni52 Cygni€ parallax = _____ arcsecondsdistance = 1parallax= ______13Relationship between absolute magnitude and luminosity Relationship between absolute magnitude and luminosity - bring in the Sun! 41 Cygni’s calculations- bring in the Sun! 41 Cygni’s calculations€ MSun− Mstar= 2.5log10LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟MSun− Mstar( )2.5= log10LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟10MSun−Mstar( )2.5=10log10LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟10MSun−Mstar( )2.5=LstarLSunLstarLSun=10MSun−Mstar( )2.5LstarLSun=104.74 −(−2.8)( )2.5=1070€ Lstar=1070LSun1452 Cygni52 Cygni€ LstarLSun=10MSun−Mstar( )2.5= ________15Depends on•Size (radius, R)•Temperature€ L = 4πR2( ) σT4• Describe the methods used to determine temperature, luminosity, radius€ L = 4πR2( ) σT4Lstar= 4πRstar2( ) σTstar4LSun= 4πRSun2( ) σTSun4LstarLSun=4πRstar24πRSun2σTstar4σTSun4=RstarRSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2TstarTSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟4LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟TSunTstar ⎛ ⎝ ⎜ ⎞ ⎠ ⎟4=RstarRSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2RstarRSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟=LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟TSunTstar ⎛ ⎝ ⎜ ⎞ ⎠ ⎟4=TSunTstar ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟LuminosityLuminosity€ RstarRSun=TSunTstar ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟=57706440 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟210701 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟RstarRSun= 26 or Rstar= 26RSun41 Cygni1652 Cygni52 Cygni€ RstarRSun=TSunTstar ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟=RstarRSun= _______17Work on star table -- Work on star table -- SIMBAD SearchSIMBAD SearchStar ID Spectral Type Surface Temp. (K) App. Mag Parallax (mas) Dist. (pc) Abs. Mag Lstar/Lsun Rstar/Rsun 41 Cygni 52 Cygni 69 Cygni xi Cygni F5 Iab4.02 4.246,900G9.5 III4.23 16.224,800B0 Ib5.94 0.3626,000K4.5 Ib-II3.72
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