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1 http://stardate.org/radio/program/delta-lyrae 2 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 arc second, parsec. Define brightness, apparent magnitude, absolute magnitude. Describe the methods used to determine the temperature, luminosity, and radius of a star. 3 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. 4 You already know about the parallax effect: Demonstrating parallax Parallax of Stars •Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star. 5 Define arc second How 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 degrees 1 radian = 57.3 degrees How many arc seconds in 1 radian? 360, 60, 60, 3600; 1,296,000; 2 pi; 206,265 arc sec/rad 6 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: • Define arc second, parsec 7 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. 8 •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 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 10 Inverse square law for light p. 494 QuickTime™ and a decompressor are needed to see this picture. 11 How the star looks to US HERE ON EARTH. L apparent brightness = 4 D2 1000 times farther away 100 Watt 1000 Watt Qui ckTime™ and a decompressor are needed to see thi s pi cture. 1 Watts 10 times farther away Qui ckTime™ and a decompressor are needed to see thi s pi cture. Qui ckTime™ and a decompressor are needed to see thi s pi cture. Qui ckTime™ and a decompressor are needed to see thi s pi cture. 2 x farther away, 1/4 as bright 3 x farther away, 1/9 as bright • Define brightness, apparent magnitude, absolute magnitude 12 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 13 When you see only “magnitude,” that means APPARENT magnitude. 1. The magnitude (m) of star A is 1, the magnitude (m) of star B is 6. How many times brighter is A than B? a) 5 b) 10 c) 100 d) 1000 2. m of star C is 12, m of star D is 2: How many times brighter is star D than star C? (Or, equally stated, how many times dimmer is star C than star D?) a) 10 b) 24 c) 100 d) 10,000 3. The Sun is the brightest star in the sky, with an apparent magnitude of about -26.5 Sirius is next in line, with an apparent magnitude of -1.5; how many times brighter is the Sun than Sirius? a) 25 b) 28 c) 100,000 d) 10,000,000,000 14 Using SIMBAD to find the apparent magnitudes of the stars of Exercise 2 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 15 Absolute magnitude is the apparent magnitude a star would have if its distance = 10 parsecs. m M 5log10 (d pc ) 5 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 brightness, apparent magnitude, absolute magnitude 16 Define brightness, apparent and absolute magnitude 17 Supergiant Bright-Giant Giant Sub-Giant Main Sequence Star (dwarf) I II III IV V We estimate the luminosity of a star by measuring how broad the absorption lines are in its spectrum. At a given temperature, the less luminous stars have atoms colliding a lot more than in the giant stars. • Describe the methods used to determine temperature, luminosity, radius 18 Luminosity High Low High Temperature Low19 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. F5 Iab 20 The H-R Diagram L 4 R 2 T 4 21 Relationship between absolute magnitude and luminosity - bring in the Sun! 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 22 Depends on •Size (radius, R) •Temperature Luminosity L 4 R 2 T 4 L 4 R 2 T 4 2 4 Lstar 4 Rstar Tstar 2 LSun 4 RSun TSun4 Lstar 4 R LSun 4 R 2 star 2 Sun T T 4 star 4 Sun Rstar 2 Tstar 4 R Sun TSun Lstar TSun 4 Rstar 2 L T R Sun star Sun Rstar Lstar TSun 4 TSun 2 Lstar R L T T L Sun Sun star star Sun 2 2 Rstar TSun Lstar 5770 1070 RSun Tstar LSun 6440 1 Rstar 26 or Rstar 26RSun RSun • Describe the methods used to determine temperature, luminosity, radius 23 The H-R Diagram 24