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
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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
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• 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
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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
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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%)
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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?
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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
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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
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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
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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
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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
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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)
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NGC 3132 NGC 3132 Hourglass Hourglass
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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. F(B)/F(V) V change with l 300 500 700 nm temperature T. R measure flux in each bandpass I F(U) F(B) F(V) F(R) F(I)
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Sun-likeSpectrum Spectrum of Sun Colour Indices æ F(V ) ö apparentmag : 2.5 log ç ÷ V = mV = - ç ÷ è F 0 (V)ø absolute mag: 5log /10 pc B V M V = mV - ( d ) R (and similarlyfor U , B, R, I, etc.)
U I colour index :
æ F(B) F0 (B) ö B -V = -2.5 logç ÷ è F(V) F0 (V) ø (and similarlyfor U-B , V-R, R-I, etc.)
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Hertzsprung-Russell Theory Observation (or H-R) Diagram flux apparent mag Bright F U, B,V ,... luminosity absolute mag M V L M V = V - 5log( d /10pc) temperature colour index T B - V Faint Blue Red hot B -V cool Stars & Elementary Astrophysics: Introduction Press F1 for Help 47 Stars & Elementary Astrophysics: Introduction Press F1 for Help 48 Globular Cluster (M55) H-R Diagram Most stars are born in Star Clusters. Same red giants distance, age
white dwarfs
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Kirchhoff’s laws Spectral Analysis 3 types of spectra
– light is dispersed into a spectrum blackbody using a diffraction grating (or prism) in a spectrograph gas cloud 3. Continuous + absorption-line spectrum – Fraunhofer (1815) first extensive study of prism the Sun - identified about 600 dark lines
– Fraunhofer lines - strongest named A,B,... 2. Emission-line spectrum (+ weak continuum) 1. Continuous spectrum
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Kirchhoff’s laws Vega - absorption lines A hot opaque body, e.g. a hot dense gas, produces a continuous spectrum, e.g. a “black-body” spectrum. A hot transparent gas emits an emission-line spectrum , bright spectral lines, sometimes with a faint continuous spectrum. A cool transparent gas in front of a continuous spectrum source produces an absorption-line spectrum - a series of dark spectral lines. (Kirchoff and Bunsen laboratory experiments, 1850s) SS Cygni - emission lines
Stars & Elementary Astrophysics: Introduction Press F1 for Help 53 Stars & Elementary Astrophysics: Introduction Press F1 for Help 54 Kirchoff’s Laws Spectral Fingerprints absorption lines – Each element / molecule absorbs and emits only certain specific wavelengths of light. hot opaque interior, cool transparent atmosphere – Spectral lines are diagnostic of the chemical composition and – physical conditions (temperature, pressure)
hot transparent gas (accretion disc) emission lines
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Atoms and Ions Atoms and Ions • atoms: nucleus (protons + neutrons) + electrons • Examples: – Hydrogen ( H ) ( 1 proton ) + 1 electron mass charge – H II ( 1p ) charge +1 proton 1 +1 neutron 1 0 – Helium (He) ( 2p + 2n ) + 2 e- 0 electron 1/1836 -1 – He II ( 2p + 2n ) + 1 e- +1 – He III ( 2p + 2n ) +2 atom - neutral : equal numbers of protons (+ve) and electrons (-ve) – Oxygen (O) ( 8p + 8n ) + 8 e- 0 ion - ionised : electrons removed, – OIII ( 8p + 8n ) + 6 e- +2 positive net charge – OVI ( 8p + 8n ) + 3 e- +5
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Atomic Energy Levels Atomic Transitions e.g. Hydrogen: bound-free free-free 2 bound-bound e I ¥ E n = - = - ¥ 2 3 rn n 3 2 E1 = -13 .6 eV 2
E ¥ = 0 photon n=1 n=1 I = 13.6eV = Ionisation Potential absorption ionisation recombination e = protoncharge emission r = size of electron orbit Stars & Elementary Astrophysics: Introduction Press F1 for Help 59 Stars & Elementary Astrophysics: Introduction Press F1 for Help 60 Energy Conservation bound-bound • Energy change associated with each transition is free-free h c E =h f = ( h is Planck's constant) l h c higher E ® higher frequency (shorter wavelength) + E1 = E2 photon is absorbed/emitted l
h c 1 2 bound-free + m 1 • energy changes are very small v l1 2 – measured in ELECTRON VOLTS (eV) 1 eV = 1.602 ´ 10-19 J h c 1 2 = + m v 2 h c 1 2 l 2 2 + E1 = E¥ + mv l 2
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• Example: Lyman Series – H atom ¥ • (see handout: energy level diagram) 3 – Energy difference between the ground state (n=1) 2 and the first excited state (n=2) : æ 1 1 ö E = E2 - E1 = I ´ç - ÷ = (13.6 eV)(0.75)=10.2eV è12 22 ø n=1 h c (6.626´10-34 J s)(3´108 m/s)(109 nm/m) l= = -19 Lyman a b g L ¥ E (10.2 eV)(1.602´10 J/eV) = 121.6 nm in UV part of spectrum 91 .2 nm Lyman a line (La) Lyman continuum photons ionise H from the ground state.
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Balmer Series Balmer absorption and emission lines ¥ 3 2 H¥ Hb Balmer Ha Hb H¥ Ha 656.3 nm 364 nm n=1
Balmer continuum photons ionise from n=2
Stars & Elementary Astrophysics: Introduction Press F1 for Help 65 Stars & Elementary Astrophysics: Introduction Press F1 for Help 66 Rydberg formula 1 æ 1 1 ö = R ç 2 - 2 ÷ • Hydrogen is simplest. l è n l nu ø 1 7 -1 = 91.2 nm • Multi-electron atoms have more - Rydberg constant R = 1.097 ´ 10 m R complicated energy-levels. nl - principal quantum number of lower level n - " " " of upper level • ions with 1 electron are like Hydrogen u but with larger Ionisation Potential due LYMAN series n = 1 n 2, 3, 4 … UV l u = to higher charge of nucleus BALMER 2 3, 4, 5 … visible PASCHEN 3 4, 5 … near IR BRACKETT 4 5, 6 … IR PFUND 5 6, 7 … IR
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Line Strengths and Widths Equivalent Width
Measures line strength, NOT line width. Ca II Fe I, II E.W. = width of rectangle with same area as line. Units: nm 1
He Hd 0 Same width, different equivalent width. each line has different strength (quantum mechanics)
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Doppler (1843) Doppler Shift for sound.. Doppler Shift l=l0 -1 • Example: v = 200 km s , l0 = 500 nm -1 l
mv2 random motions » kT 2 of atoms
Typical redshift: z ~ 1 High redshift: z > 5, UV light shifts to red wavelengths l0 Stars & Elementary Astrophysics: Introduction Press F1 for Help 73 Stars & Elementary Astrophysics: Introduction Press F1 for Help 74
Rotational Broadening Pressure Broadening Energy levels shift when particles are nearby
high pressure gas l0 Stars & Elementary Astrophysics: Introduction Press F1 for Help 75 Stars & Elementary Astrophysics: Introduction Press F1 for Help 76
Zeeman Shift Quantum Uncertainty Energy levels shift and split in Magnetic field “fuzzy” energy levels short visit -> uncertain E
DE Dt » h -15 magnetic field h = 4.1´10 eV sec
Stars & Elementary Astrophysics: Introduction Press F1 for Help 77 Stars & Elementary Astrophysics: Introduction Press F1 for Help 78 Spectral Types Why spectra differ
O Spectral Types • Line strengths (EW ratios) M change mainly due to SURFACE TEMPERATURE A (hot-> high ionisation and excitation cool-> neutral atoms and molecules) • Some line widths and ratios change G with LUMINOSITY G A • Very little range of abundances M O B V (74% H + 24% He 2% everything else) Stars & Elementary Astrophysics: Introduction Press F1 for Help 79 Stars & Elementary Astrophysics: Introduction Press F1 for Help 80
Spectral Classification – 1890s first photographic spectra – 1918-24 Henry Draper Catalogue • handout: "spectral classes" of ~ 225,300 stars !!! – spectral classes provide a "short-hand" (star names HD 35311, HD 209458, etc) description of the appearance of a stellar – original classification: spectrum. A,B,… R,S from simple to complex lines – many letters later dropped or merged. – 1920s photometry (colour indices) revealed correct temperature sequence – confirmed by atomic physics – 1940s Morgan & Keenan (MK spectral types) Stars & Elementary Astrophysics: Introduction Press F1 for Help 81 Stars & Elementary Astrophysics: Introduction Press F1 for Help 82
Spectral Types Spectral Types hot cool hot cool O B A F G K M O B A F G K M Girl Girl ( Oh! Be A Fine Guy, Kiss Me! ) ( Oh! Be A Fine Guy, Kiss Me! ) ( "early-type" "late-type" ) ( "early-type" "late-type" ) – sub-class 0 - 9 e.g. B0, B9, G2 – sub-class 0 - 9 e.g. B0, B9, G2
(N R S ( No Romeo, Scram ))
Stars & Elementary Astrophysics: Introduction Press F1 for Help 83 Stars & Elementary Astrophysics: Introduction Press F1 for Help 84 ¬ one example of a luminosity criterion: Luminosity Classes
• H lines of Balmer series are affected strongly by pressure broadening ¬ – main-sequence V most common – subgiants IV • pressure gradient µ surface gravity of star g – red giants common GM III g = ¬ R 2 – bright giants II rare (M = mass, R = radius, G = gravitational constant) – supergiants Ia,b very rare • dwarf star, small R, large g Þ broadened H lines (blue to red) • giant star, large R (~100´), small g Þ narrow H lines – white dwarfs DA quite common • (handout: spectra showing luminosity effects) – DB,DO
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MK Spectral Types Review • Multicolour Photometry – Sun G2 e.g. V – Use filters (e.g. U B V R I ) Vega A0 V – measure : ( , , ) . Betelgeuse M2 Iab flux densities fB fV ... Rigel B8 Ia – apparent magnitudes : (B, V, …) Aldebaran K5 III – colour indices :
(B - V ) = - 2 .5 log [ f B f V ]+ constant – absolute magnitudes (d from parallax):
M V = V - 5 log( d /10 pc )
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Bolometric Magnitude Spectral Types
Mbol = absolute bolometric magnitude total flux over the entire spectrum. O B.C. vs Spectral Type M
gives MV gives M bol A
F
l G G Difficult to measure M . A bol O Easy to measure M . M V B V Stars & Elementary Astrophysics: Introduction Press F1 for Help 89 Stars & Elementary Astrophysics: Introduction Press F1 for Help 90 Bolometric Corrections Calibrations
• B.C. = Mbol - M < 0 to make star brighter. V • Calibrations of colour indices, temperatures, • Sun: M = 4.83, B.C. = -0.14 M = 4.69 V bol absolute visual magnitude (M ), and • F0 B.C. = 0 (most optical) V V (less precise) spectral types . O5V = -3.8 (mostly UV – very well defined for most main-sequence M8V = -4.0 mostly IR) stars (5,000 £ T £ 30,000 K) L -0.4 çæ M - (sun) ÷ö – less so for hotter O stars (> 40,000 K) =10 è bol M bol ø L(sun) – and cooler M stars (< 2,500 K) æ L ö (handout: example of relevant calibrations) (sun) 2.5 log M bol -M bol = - ç ÷ è L(sun) ø Stars & Elementary Astrophysics: Introduction Press F1 for Help 91 Stars & Elementary Astrophysics: Introduction Press F1 for Help 92
• The Hertzsprung-Russell (HR) Diagram Theory vs Observations – first presented independently by H (1911) • Alternative versions of the H-R diagram: and R (1913) to show links between observations spectral types (or colours) of stars and theory absolute magnitudes Luminosity – now recognised as one of the most L Mv or important diagrams for all astronomy, M because of its importance for bol understanding the evolution (ageing) of stars colour index (e.g. B-V) • (handout: HR diagram) Temperature T or Spectral Type
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Stellar Radii Typical Radii • To calculate R: 2 4 L = 4pR sT • Solar radius: Rsun=7x10^5 km • Observe: . parallax p --> distance d=1/p. main-sequence stars: . spectral type or colour index --> T R ~ 0.1 - 10 Rsun . apparent magnitude, e.g. V. giants: R ~ up to 100 Rsun
V - MV = 5log ( d /10 pc) Mbol =MV +B.C. supergiants: red: R ~up to 1000 Rsun blue: R ~20-50 Mbol -M bol(sun) =-2.5 log( L/ L(sun) ) white dwarfs: R ~ 0.01 Rsun • Not highly accurate (10-50%)
Stars & Elementary Astrophysics: Introduction Press F1 for Help 95 Stars & Elementary Astrophysics: Introduction Press F1 for Help 96 Accurate Radii Binary Stars -- two stars in mutual gravitational attraction, • Most accurate radii (<1%) from orbiting their common centre of mass . ECLIPSING BINARY STARS and (for nearby stars) -- only source of empirical masses for stars . INTERFEROMETRY -- accurate sizes, shapes, temperatures, and (for a few stars) luminosities (hence distances) . LUNAR OCCULTATIONS. • Accurate R improves T via 1 æ L ö 4 T = ç ÷ è 4pR2sø • if distance (hence L) also known. Stars & Elementary Astrophysics: Introduction Press F1 for Help 97 Stars & Elementary Astrophysics: Introduction Press F1 for Help 98
Centre of Mass Orbit Velocities primary star secondary star V 2 a a m1 m2 a1 a2 a1 a2 V1
a1 m1 = a2 m2 P = orbit period
a1 m2 a2 m1 2 = = V 1 a1 m2 p a = = V 1+V 2 = a m1 + m2 a m1 + m2 V 2 a2 m1 P
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EllipticalElliptical Orbits Orbits Visual binary
Model binary binary1
Stars & Elementary Astrophysics: Introduction Press F1 for Help 101 Stars & Elementary Astrophysics: Introduction Press F1 for Help 102 Types of Binaries Spectroscopic binary • visual binary
• spectroscopic binary . SB1 SB2 lines from 1 or 2 stars
• eclipsing binary
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Eclipsing binary Proximity Effects Star sizes from timing
ellipsoidal variations
heating effects
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Types of Binaries Binary Star with Accretion Disc
detached
semi-detached
contact
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Orbital Phase
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Velocity curvesVelocity for curve binary stars
K1
K2 redder Radial Velocity
bluer
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Orbit inclination To measure masses: - visual i = 0 for face-on orbit – radial velocity and light variations - spectroscopic - eclipsing degrees for edge-on orbit i = 90 1 velocity 2 2 3 4 + 4 Doppler shifts measure C of M 3 1 orbital ´ 1 phase 3 . K = V sin i 4 (time) 2 - 2
1 4 radial velocity curves
Stars & Elementary Astrophysics: Introduction Press F1 for Help 113 Stars & Elementary Astrophysics: Introduction Press F1 for Help 114 Masses • Analysis of RV curves gives Observe: K1 = V1sin i "minimum masses" P = sin i 3 3 K 2 V 2 (M1 sin i ), (M2 sin i ) Calculate masses: and projected sizes of orbits m1 K 2 = 2p a sin i = (K 1+ K 2) P m2 K1 (a1 sini ), (a2 sini) Kepler’s Law: 2 3 æ m1 + m2 öæ P ö æ a ö ç ÷ç ÷ = ç ÷ è M sun øè yr ø è AU ø
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• Analysis of light curves • Hence, for eclipsing, spectroscopic of eclipsing binaries gives binaries, we obtain: – orbital inclination i – masses and – radii of both stars, M1 M2 relative to the size of the orbit – radii R1 and R2
– luminosities L1 and L2 • (if T or T known) æ r1ö æ r2 ö 1 2 ç ÷, ç ÷ è a ø è a ø
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– used as tests of theoretical models of • Empirical MASS-LUMINOSITY stars HR Diagram relationship for main-sequence stars: 4 high mass . L µ M i.e. 4 main sequence L é M ù for 0.4 10 L = ê ú Msun < M < Msun Lsun ëMsun û low mass see log M vs.log L plots (handout) T
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Mass-Luminosity for Main Sequence Star Lifetimes • Energy supply: 2 E = DM c (Joules) • Rate of burning: L µ 4 (W = Joule/s) • Lifetime: M E DM c2 DM M c2 Slope = +4 t ~ = = L L M L 4 -3 L µ M 10 æ DM / M ö æ M ö ~ 10 yr ç ÷ ç ÷ 0.0015 sun 4 è ø è M ø L æ M ö @ ç ÷ Lsun è Msun ø • Stars burn for a long time. • Big stars burn out faster. Stars & Elementary Astrophysics: Introduction Press F1 for Help 123 Stars & Elementary Astrophysics: Introduction Press F1 for Help 124
The Celestial Sphere Celestial Pole N
5. THE MOTIONS OF STARS IN SPACE Celestial Equator
S Stars & Elementary Astrophysics: Introduction Press F1 for Help 125 Stars & Elementary Astrophysics: Introduction Press F1 for Help 126 Star Coordinates N Declination ( Dec, d ) (Degrees North) d
W E a Right Ascension (RA, a ) (Hours East ) (24 hours = 360 degrees) S Stars & Elementary Astrophysics: Introduction Press F1 for Help 127 Stars & Elementary Astrophysics: Introduction Press F1 for Help 128
v Star Velocities d vd star star vr vr
va va
observer observer 3 velocity components - in line-of-sight (radial direction) (mutually perpendicular) -1 RADIAL VELOCITY vr (km s )
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vd vd star star vr vr
va va
observer observer
- 2 components perpendicular to the va and vd are the components of vt line of sight in the directions of increasing -1 TRANSVERSE VELOCITY vt (km s ) RIGHT ASCENSION (a) and 2 2 DECLINATION (d) on the sky. V t = Va +Vd
Stars & Elementary Astrophysics: Introduction Press F1 for Help 131 Stars & Elementary Astrophysics: Introduction Press F1 for Help 132 Proper Motions tiny • v - from Doppler shift of spectral lines r Speeds of stars orbiting the Galaxy • , - projected onto the sky va vd v ~ 250 km s-1 – we can measure only angular • but distances are in parsecs - changes over time, 1 pc = 3 ´ 1013 km called PROPER MOTION • thus proper motions are small . m ( arcsec yr-1 ) m (< 0.1 arcsec yr-1) – Two components of m are
ma cos d, md – (see handout …)
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d • Fast caclulation: m Vt
small angle Vt =4.74m d
V t = m d -1 -1 • ONLY for in km s-1, m (arcsec yr )´d (pc) æ 3´1015 km pc ö V t = ´ç ÷ ç 7 -1 ÷ m in arcsec yr-1, 206,265 (arcsec/radian) è 3´10 s yr ø d in parsecs
2 2 m= (macosd) +md
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Astrometry Satellites v d • HIPPARCOS (1997) star vr • Accurate parallax and proper motion
va for bright stars (V < 9) 10-3 arcsec yr -1 observer • stars to 200 pc • SPACE MOTION = velocity vector • GAIA planned ESA (2012 ...) • parallax -5 arcsec speed 2 2 10 V = V + V r t • proper motion 10-6 arcsec yr -1 + direction specified by va, vd, vr • distances and motions . of stars throughout the Galaxy Stars & Elementary Astrophysics: Introduction Press F1 for Help 137 Stars & Elementary Astrophysics: Introduction Press F1 for Help 138 Star Cluster at the Galactic Centre Stars orbiting VLT (Very Large the Black Hole Telescope) D=8m, one of 4, in Chile. Adaptive Optics (corrects for seeing) Infrared light (to see through the intervening dust) 0.05 pc 206265 arcsec ´ 8500 pc radian Stars & Elementary Astrophysics: Introduction Press F1 for Help 139 Stars & =Elementary1.2 arcsec Astrophysics: Introduction Press F1 for Help 140
Star Motions at the Galactic Centre
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Black Hole at the Galactic Centre THE END • From the proper motions, measure sizes and periods of the star orbits. • Kepler’s law : 3 - 2 M æ a ö æ P ö = ç ÷ ç ÷ M sun è AU ø è yr ø • the black hole mass
6 M » 3´10 M sun
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