112http://stardate.org/radio/program/delta-lyrae3 Explain what is meant by the parallax of a star, how wemeasure it and use it to find the distance to a star.Define arc second, parsec. Define brightness, apparent magnitude, absolute magnitude.Describe the methods used to determine the temperature,luminosity, and radius of a star.Learning Learning goals:goals:24Questions:Questions:Which stars are the brightest?Which stars are putting out the mostwatts? (luminosity = energy persecond)NEED TO KNOW:NEED TO KNOW:DistancesThe most fundamental andaccurate (within a certain range)means of finding distances ismeasuring the parallaxes of stars.5You already know about the parallax effect:•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.Demonstrating parallaxParallax of Stars6Define arc secondHow many degrees in a circle?How many arc minutes in a degree?How many arc seconds in an arc minute?How many arc seconds in a degree?How many arc seconds in a circle?__?__ radians = 360 degrees1 radian = 57.3 degreesHow many arc seconds in 1 radian?360, 60, 60, 3600; 1,296,000; 2 pi; 206,265 arc sec/rad37PARSEC: 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:• Define arc second, parsec8 Works accurately for stars within about200 pc (Hipparchos satellite) Biggest problem: measuring the minisculeshift 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.9•Explain what is meant by the parallax of a star, how we measureit and use it to find the distance to a star.410Using SIMBAD to find the parallaxes of the stars of Exercise 241 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 ly11Inverse square law for lightInverse square law for lightp. 49412How the star looks to US HERE ON EARTH.10 times farther away100 Watt 1000 Watt1 Watts! 1000times farther away2 x farther away, 1/4 as bright 3 x farther away, 1/9 as bright• Define brightness, apparent magnitude, absolute magnitude! apparent brightness = L4"D2513 Every 5 magnitudesdifference means 100 xdifference in brightness One magnitude differenceis 2.512 times in brightness.(2.5125 = 100)• Define brightness, apparent magnitude, absolute magnitude14When you see only “magnitude,” that means APPARENT magnitude.1. The magnitude (m) of star A is 1, the magnitude (m) of star B is6. How many times brighter is A than B?a) 5 b) 10 c) 100 d) 10002. m of star C is 12, m of star D is 2: How many times brighter isstar D than star C? (Or, equally stated, how many times dimmeris star C than star D?)a) 10 b) 24 c) 100 d) 10,0003. The Sun is the brightest star in the sky, with an apparentmagnitude of about -26.5 Sirius is next in line, with an apparentmagnitude of -1.5; how many times brighter is the Sun thanSirius?a) 25 b) 28 c) 100,000 d) 10,000,000,00015Using SIMBAD to find the apparent magnitudes of the starsof Exercise 241 Cygni data (partial)V = apparent magnitude through “visual” filterThink of it as mv .UVIR616Absolute magnitude is the apparent magnitude a star would haveif its distance = 10 parsecs.Relates luminosities by “placing” stars on common scale.Smaller the absolute magnitude number, the more luminous thestar.! m " M = 5log10( dpc) " 5M = m " 5log10( dpc) + 5• Define brightness, 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?17Define brightness, apparent and absolute magnitudeDefine brightness, apparent and absolute magnitude18Supergiant IBright-Giant IIGiant IIISub-Giant IVMain Sequence Star (dwarf) VWe estimate the luminosityof a star by measuring howbroad the absorption lines arein its spectrum.At a given temperature, theless luminous stars haveatoms colliding a lot morethan in the giant stars.• Describe the methods used to determine temperature, luminosity, radius719LuminosityHighLowTemperatureHighLow20Using SIMBAD to find the parallaxes of the stars of Exercise 241 Cygni data (partial)F5 Iab21The H-RThe H-RDiagramDiagram! L = 4"R2( ) #T4822Relationship between absolute magnitude and luminosityRelationship between absolute magnitude and luminosity- bring in the Sun!- bring in the Sun!! 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= 1070 LSun23Depends on•Size (radius, R)•Temperature! L = 4"R2( ) #T4• Describe the methods used to determine temperature, luminosity, radius! L = 4"R2( ) #T4Lstar= 4"Rstar2( ) #Tstar4LSun= 4"RSun2( ) #TSun4LstarLSun=4"Rstar24"RSun2#Tstar4#TSun4=RstarRSun$ % & ' ( ) 2TstarTSun$ % & ' ( ) 4LstarLSun$ % & ' ( ) TSunTstar$ % & ' ( ) 4=RstarRSun$ % & ' ( ) 2RstarRSun$ % & ' ( ) =LstarLSun$ % & ' ( ) TSunTstar$ % & ' ( ) 4=TSunTstar$ % & ' ( ) 2LstarLSun$ % & ' ( ) LuminosityLuminosity! RstarRSun=TSunTstar" # $ % & ' 2LstarLSun" # $ % & ' =57706440" # $ % & ' 210701" # $ % & ' RstarRSun= 26 or Rstar= 26RSun24The H-RThe
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