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How Far to a Star ? Astronomical Distances Astronomical Distances

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How Far to a Star ? Astronomical Distances Astronomical Distances How far to a Star ? Astronomical Distances • distance = speed x time - Fundamental problem ….. • light speed c = 3 ´ 10 5 km/s - How far away is a point of light ? • 0.002 s Edinburgh-St.Andrews . Is it a 100-watt light bulb ? • 0.1 s Earth circumference . A star as bright as the Sun ? . A galaxy of 10 11 stars ? • 1.2 s Earth-Moon distance - Brightness alone is not enough. • 8 min Sun-Earth - How to measure astronomical distances ? • 40 min Jupiter • 5 hr Pluto Stars & Elementary Astrophysics: Introduction Press F1 for Help 1 Stars & Elementary Astrophysics: Introduction Press F1 for Help 2 Astronomical Distances Parallax • 4.3 yr nearest star (Proxima Centauri) geometrical method • 25,000 yr centre of our Milky Way Galaxy p = parallax angle • nearest big galaxy a = 1 Astronomical Unit 2 6 yr (1 AU) = radius of Earth’s . ´ 10 (Andromeda, Messier 31, M31) orbit around the Sun. • nearest cluster of galaxies 5´10 7 yr . (Virgo cluster) p a = d tan p • 10 edge of visible part of Universe » 10 yr d a » d p (small angle p) . (The Big Bang) a d » p Stars & Elementary Astrophysics: Introduction Press F1 for Help 3 Stars & Elementary Astrophysics: Introduction Press F1 for Help 4 a The Parsec -new distance unit Stellar Parallaxes are tiny Example: p a 1 arcsec ( 1") d p = = • Bessel (1838) First parallax: a 1 AU 3600 " 180 ° 61 Cygni p = 0.29 arcsec Þ d = = ´ ´ p 1" 1° p radian d = 1/0.29 = 3.42 pc • also in 1838: Henderson (á Centauri) = 206265 AU Fast Method: . Struve (Vega) 16 = 3.1´10 m • The nearest star (beyond the Sun) d = 1/p = 3.26 light yr Proxima Centauri p = 0².76 , d = 1.31 pc. For p in arcsec = 1 parsec (1 pc) and d in parsec Stars & Elementary Astrophysics: Introduction Press F1 for Help 5 Stars & Elementary Astrophysics: Introduction Press F1 for Help 6 Limits of Parallax The Distance Ladder • Different methods • Ground-based CCDs 0.05” 20 pc • for different supernovae • Hubble Telescope 0.01” 100 pc • distances • Hipparcos (all sky) 0.005” 200 pc • cepheid variables Today: Nearby Stars Only • stars • 2015: GAIA (whole galaxy) 10,000 pc • PARALLAX IS THE FOUNDATION FOR ALL OTHER METHODS Stars & Elementary Astrophysics: Introduction Press F1 for Help 7 Stars & Elementary Astrophysics: Introduction Press F1 for Help 8 Inverse Square Law Luminosity, Flux energy Luminosity L = time Units: Joule / sec = Watt (e.g. 100 W light bulb) Solar luminosity: 26 L sun = 3.8´10 W energy Flux F = time´ area Units: Watts / square metre 2 Sun viewed from Earth: F sun = 1380 W/m Stars & Elementary Astrophysics: Introduction Press F1 for Help 9 Stars & Elementary Astrophysics: Introduction Press F1 for Help 10 Inverse Square Law http://concam.net Continuous sky images. fish-eye lens + CCD. d area of sphere = 4p 2 d 7 observatories L Sky from Australia: Magellenic Clouds L F = 2 Flux viewed from distance d : 4pd Milky Way centre Stars & Elementary Astrophysics: Introduction Press F1 for Help 11 Stars & Elementary Astrophysics: Introduction Press F1 for Help 12 Magnitudes Apparent Magnitude • Hipparcos (2nd century BC) (measures apparent brightness) stars visible by eye: • Pogson (1856) 1st mag = brightest . apparent magnitude: 6th mag = faintest • Herschel (1780s) 1st mag stars are m = -2.5log( F / F 0) 100 times brighter than 6th mag stars. -(m /2.5) F = F 0 ´10 • 1800s -- eye responds to flux ratios true flux 1 : 10 : 100 F 0 = flux of 0 mag star (Vega) perceived 1 : 2 : 3 Stars & Elementary Astrophysics: Introduction Press F1 for Help 13 Stars & Elementary Astrophysics: Introduction Press F1 for Help 14 Naked Eye Stars Magnitude Difference (measures brightness ratio) • brightest: Sirius (mag -1.5) • bright mag -1 1 star m1- m2 = -2.5 log( F1/ F2 ) . 0 3 m1 > m 2 F 1 < F 2 . 1 11 m1 - m 2 F 2 / F 1 . 2 40 5 100 . 3 150 10 104 . 4 500 1 5100 @ 2.512 . 5 1600 0.1 » 1.1 (10%) faint mag 6 4800 stars 0.01 » 1.01 (1%) Stars & Elementary Astrophysics: Introduction Press F1 for Help 15 Stars & Elementary Astrophysics: Introduction Press F1 for Help 16 Apparent Magnitude Absolute Magnitude (measures true brightness) • m = apparent mag at distance d. • Sun m = -26.8 25mag= 1010 • M = aparent mag at 10 pc. • full moon -12.5 2 d • venus -4 F (10 pc ) = F (d ) ´ ( 10 pc ) • Sirius -1.5 30 mag= 12 • Vega 0.0 10 M = - 2.5 log ( F (10 pc ) / F 0 ) • faintest galaxies = m - 5 log ( d / 10 pc ) detected by HST +30 • d known (e.g. parallax) for nearby stars. Stars & Elementary Astrophysics: Introduction Press F1 for Help 17 Stars & Elementary Astrophysics: Introduction Press F1 for Help 18 Absolute Magnitude Distance Modulus • m = apparent mag at true distance d. (measures distance) • M = aparent mag at 10 pc. • d known (parallax) for nearby stars • star (pc) m M d m - M = 5 log d /10 pc • Vega 0.0 +0.5 8.1 ( ) • Sirius -1.5 +1.4 2.7 = 5 log ( d / pc )- 5 • Sun -26.8 +4.5 1/206265 • Which star is truly brighter? Stars & Elementary Astrophysics: Introduction Press F1 for Help 19 Stars & Elementary Astrophysics: Introduction Press F1 for Help 20 Electromagnetic Radiation Thermal (Blackbody) radiation (EMR) • EMR = Light (of any wavelength) • • speed of light in vacuum (slower in air, glass,…) Characterised by temperature T. c = 3´108 m /s furnace temperature T • wave properties (interference,diffraction) . frequency = speed / wavelength small hole . Hz = cycles/s = (m/s) / m f = c / l • particle properties (photons) blackbody radiation . discovery by Planck (1900) E = h f light reaches equilibrium . photon energy : with hot walls of furnace. h = Planck’s constant (6.6x10^(-34) Joule/Hz) Stars & Elementary Astrophysics: Introduction Press F1 for Help 21 Stars & Elementary Astrophysics: Introduction Press F1 for Help 22 Stellar Spectra Blackbody Spectra Planck function (1900) • Resemble blackbody spectra • temperature T at star surface B(l,T ) • (hotter interior invisible) hot 1. Peak shifts 2. Area increases photon escapes First clue to quantum mechanics To Earth cool photon trapped in gas near star surface wavelength l Stars & Elementary Astrophysics: Introduction Press F1 for Help 23 Stars & Elementary Astrophysics: Introduction Press F1 for Help 24 Wien’s Law Star Colours T = constant l max cool hot » 0.003 m K 4 æ l max ö æ10 K ö ç ÷ » ç ÷ è 300 nm ø è T ø Stars & Elementary Astrophysics: Introduction Press F1 for Help 25 Stars & Elementary Astrophysics: Introduction Press F1 for Help 26 Wien’s Law in action B(l,T ) Blackbody Flux Area increases with T. • Sun: 6000 K, 500 nm T » lmax » 4 – intensity peak at visible wavelength B( T ) = s T – looks yellow or white to us l • hot star: T = 12000 K, l » 250 nm max energy W æ W ö – ultraviolet peak, looks blue units : = ç ÷ ( K4 ) time area m2 m2K4 • cool star: T = 3000 K, lmax » 1000 nm è ø – infrared peak, looks very red Stefan Boltzmann constant s = 5.7 ´ 10 - 8 W m - 2 K - 4 Stars & Elementary Astrophysics: Introduction Press F1 for Help 27 Stars & Elementary Astrophysics: Introduction Press F1 for Help 28 Review Review magnitudes : m = -2.5 log ( F / F 0 ) temperature : T M = m -5 log ( d /10 pc) flux at star surface : B(T) = s T4 light speed : c = 3´108 m / s radius : R area : 4p R2 frequency: f = c / l 2 4 photonenergy : E = h f luminosity : L = 4p R s T 2 4 R,T distance : area : 4 æ l max ö æ10 K ö d p d blackbody peak: ç ÷ » ç ÷ è300 nm ø è T ø luminosity : L = 4p d2 F flux : B(T) = s T 4 d 2 L 4æ R ö flux : F = =s T ç ÷ 4p d2 è d ø Stars & Elementary Astrophysics: Introduction Press F1 for Help 29 StarsF & Elementary Astrophysics: Introduction Press F1 for Help 30 White Dwarf vs Red Giant log L = 2 log R + 4 log T + const (Earth-sized star) bright 100 R1 = 0.01Rsun R 2 = Rsun T1 =30,000 K T2 = 3,000 K R/Rsun 2 4 100 æ L1 ö æ R 1 ö æ T 1 ö log L ç ÷ = ç ÷ ç ÷ 10 è L 2 ø è R 2 ø è T 2 ø . 1 = -8 ´ 4 = - 4 0.1 10 10 10 0.01 faint L = 4p R 2 s T 4 hot cool log L = log( 4ps ) + 2 log R + 4 log T log T Stars & Elementary Astrophysics: Introduction Press F1 for Help 31 Stars & Elementary Astrophysics: Introduction Press F1 for Help 32 Our Sun’s Future How a Star works Nuclear furnace H --> He --> C, N, O, … Fe R/Rsun Hot gas pushes out. Gravity pulls in. 100 log Force: Force: L 10 k T M 2 ~ ~ G M F out F in 2 1 m R R 0.1 0.01 G M m log T T ~ » 2´ 10 7 K Sun’s Core Temperature: k R Stars & Elementary Astrophysics: Introduction Press F1 for Help 33 Stars & Elementary Astrophysics: Introduction Press F1 for Help 34 Our Sun’s Future Planetary NebulaNebulae (PN) (PN) He --> C,N,O,... envelope ejects envelope expands (Planetary Nebula) (red giant) He core H --> He Ashes cool 75% H, 25% He (made in the Big Bang) (white dwarf) Stars & Elementary Astrophysics: Introduction Press F1 for Help 35 Stars & Elementary Astrophysics: Introduction Press F1 for Help 36 Dumbell Nebula (M27) Egg Nebula (polarised) Dumbell Nebula (M27) Egg Nebula (polarised) Stars & Elementary Astrophysics: Introduction Press F1 for Help 37 Stars & Elementary Astrophysics: Introduction Press F1 for Help 38 NGC 3132 NGC 3132 Hourglass Hourglass Stars & Elementary Astrophysics: Introduction Press F1 for Help 39 Stars & Elementary Astrophysics: Introduction Press F1 for Help 40 Spirograph Spirograph Ring (M57) Ring (M57) Death of a Star, Stars & Elementary Astrophysics: Introduction Press F1 for Help 41 BirthStars & Elementaryof a Astrophysics: White Introduction Dwarf Press F1 for Help 42 Broadband Photometry SpectrumVega Spectrum of Vega bandpass filters B V B B(l,T) U R Flux ratios I U e.g.
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