R. Kippenhahn & A. Weigert: Stellar Structure and Evolution. Clayton: Principles of stellar Evolution and Nucleosythesis

Transcription

1 Physics of Stars Prof. Dr. Ulrich Heber, Prof. Dr. Horst Drechsel Wintersemester 2013/14 1. Introduction 1 1 Recommended textbooks 1 2 B.W. Carroll & D.A. Ostlie: An Introduction to Modern Astrophysics D. Prialnik: An Introduction to the Theory of Stellar Structure and Evolution Hansen & Kawaler: Stellar Interiors Ryan & Norton: Stellar Evolution and Nucleosynthesis R. Kippenhahn & A. Weigert: Stellar Structure and Evolution (comprehensive work, but aiming at researchers in this field) Clayton: Principles of stellar Evolution and Nucleosythesis (comprehensive work with emphasis on nuclear physics ) John Lattanzio s stellar evolution tutorial: Introduction 1 Outline 1 3 Fundamental properties of stars Stellar structure equations: Continuity equation conservation of mass, momentum and energy energy transport Properties of stellar material Equation of state opacities energy generation Computation of stellar models The main sequence The structure of the sun, solar neutrinos Introduction 2

2 Outline 1 4 post main-sequence evolution low-mass stars(initial mass 8 M ) massive stars (initial mass>8 M ) Supernovae & γ-ray bursts End stages of stellar evolution Evolution of binary stars Stellar Pulsations Variable stars Introduction 3 Stellar physics = applied physics 1 5 Physics needed to model the structure and evolution of stars, e.g.: plasma physics gas-radiation interaction: atomic physics thermonuclear energy production: nuclear physics neutrino production: particle physics equation of state: thermodynamics convective energy transport: hydrodynamics radiative energy transport: physics of radiation... Introduction 4 Fundamental stellar properties 1 6 distance mass M radius R luminosityl=energy output per time (effective) temperature Teff chemical abundances Introduction 5 Magnitudes 1 7 First classification of stars: Stars of magnitude 1 : brightest (visible) stars Stars of magnitude 6 : faintest (visible) stars Hipparchus (?? 127 BC) Introduction 6

3 Magnitudes 1 8 Pogson (1865): Eye sensitivity is logarithmic, such that A brightness difference of 5 magnitudes corresponds to a ratio of 100 in detected flux So, if magnitudes of two stars arem1 andm2, then This means: f1 f2 = 100 (m 2 m1)/5 or log 10 (f1/f2) = m 2 m1 5 log = 2 5 (m 2 m1) m2 m1 = 2.5log 10 (f1/f2) = 2.5log 10 (f2/f1) Note: Larger Magnitude = FAINTER Stars Introduction 7 Luminosity and distance 1 9 Inverse square law links flux fat distancedto fluxf measured at another distance D: F f = L/4πD2 L/4πd = 2 ( d D ) 2 Convention: to describe luminosity of a star, use the absolute magnitude M, defined as magnitude measured at distanced = 10 pc. Therefore, m M = 2.5log(F/f) = 2.5log(d/10 pc) 2 = 5logd 5 m M is called the distance modulus,dis measured in pc. Introduction 8 Distances 1 10 Distances of stars are crucial to derive absolute values of stellar parameters like absolute magnitudemv = V 5 log(d/10pc) or luminosity L. parallax measurement is the only direct method today we can reach an accuracy of 1 milli arcsec, i.e. distances up to a few hundred parsec can be measured with reasonable accuracy (Hipparcos and ground based) This includes some important open clusters like Hyades and Pleiades Introduction 9 Distances 1 11 Best parallax measurements to date: ESA s Hipparcos satellite systematic error of position: 0.1 mas effective distance limit: 1 kpc standard error of proper motion: 1 mas/yr broad band photometry colours: B V, V J magnitude limit: 12 mag complete to mag(see later) Results available at Hipparcos catalogue: objects with milliarcsecond precision. Tycho catalogue: 10 6 stars with mas precision, two-band photometry Introduction 10

4 Blackbody Radiation 1 12 Blackbody radiation Definition: a blackbody is in thermal equilibrium with its surroundings it is a perfect absorber and emitter of radiation a blackbody emits a continuous spectrum whose shape (as a function of wavelength) is defined by its temperature alone Realisation in nature: blackbody very well approximated if photons are frequently absorbed and re-emitted (short free paths) fulfilled in the stellar interior not fulfilled in stellar atmospheres blackbody still a useful first approximation Thermal Radiation 1 Blackbody Radiation 1 13 described by the Planck function Bλ(T) = 2hc2 1 λ 5 exp ( hc λkt) 1 (power per unit area/wavelength interval/solid angle) Integration over all wavelengths and solid angles gives the Stefan-Boltzmann law F = σt 4 Surface flux per unit area. σ = W m 2 K constant. 4 is the Stefan-Boltzmann Thermal Radiation 2 Blackbody Radiation 1 14 Total power radiated by a (stellar) surface is flux surface area: L = 4πR 2 F For a blackbody radiator we can use the Stefan-Boltzmann law to derive a relation between luminosity, radius and surface temperature L = 4πR 2 σt 4 Define the effective temperatureteff of a star as the temperature of a blackbody radiating the same energy/time. L = 4πR 2 σt 4 eff Thermal Radiation 3 Blackbody Radiation 1 15 The wavelength at which the energy output from a blackbody peaks is given by Wien s law λmax T = mk object temperature λmax band Sun 5800 K 500 nm visible earthlings 310 K 10,000 nm infrared Thermal Radiation 4

5 Spectral Classification 1 16 HD He HD HD HD HD 9547 HD BD HD HD HD SAO HD Yale 1755 H β He H α Fe Na TiO MgH TiO TiO HD SAO HD Annie Cannon (around 1890): Stars have different spectra. NOAO Spectral Classification 1 Spectral Classification 1 17 Summary spectral classes as a temperature sequence. O - B - A - F - G - K - M K 3000 K early type late type plus subtypes: B0... B9,A0... A9, etc. Sun is G2. O Ionised Helium B Neutral Helium A Hydrogen Ionised Metals Rel. Strength of Lines F Spectral Class G K Neutral Metals Molecules M Note: early and late has nothing to do with age! Mnemonics: ( O Be A Fine Girl Kiss Me Mid-1995: Two new spectral classes added: L & T Spectral Classification 2 Hertzsprung-Russell diagram 1 18 Several different versions of HR diagrams in use: Original: absolute magnitudes plotted versus spectral types Physical: luminosity versus effective temperature (note: increasing from right to left) Photometric: absolute magnitude versus photometric colour R L, andteff are linked together vial = 4πR 2 σt eff 4 value for all three parameters.. Every point has a unique Hertzsprung-Russell diagram 1 HR diagram theoretical 1 19 Evolutionary track for the Sun in HR diagram The track shows the evolution from the protostar phase down to the main sequence (A) and the later evolution to a red giant (D E) and beyond. Hertzsprung-Russell diagram 2

6 Colours 1 20 Colour temperature Flux ratios in different wavelength bands (e.g. B and R) construct a quantitative colour index (e.g. B R) which reflects the temperature. B R T = 7500 K: high flux inb, lower flux inr FB/FR > 1 T = 4500 K: low flux in B, higher flux in R FB/FR < 1 Hertzsprung-Russell diagram 3 Masses 1 21 Measurement of the orbital motion of visual binary systems Orbits often elliptical. Two possible reasons: 1. eccentric orbite 0 2. inclination of the orbital plane against the line of sighti 0 However, these cases can be distinguished: 1.i = 0;e 0: primary in focal point of secondary orbit 2.i 0;e = 0: primary in centre of secondary motion Fundamental parameters or stars 1 Masses 1 22 α: measured apparent major axis (arcsec) If the distancedis known: a = d sinα sini Kepler s third law: P 2 = 4π2 a 3 M 1+ G(M1+) If orbits are measured absolutely (not only relative to each other) we can use M1/ = a2/a1 to determine values for the individual massesm1 and. This has been done for a total of about a dozen systems. Fundamental parameters or stars 2 Spectroscopic binaries 1 23 Spectroscopic binaries: These systems are relatively close together and the orbital motion can be measured via the Doppler shift of spectral lines. Sometimes both components are visible (SB2), sometimes only one (SB1). In eclipsing SB2 systems the inclination angle can be determined (usually close to i = 90 ) and masses for both components calculated. Fundamental parameters or stars 3

7 Spectroscopic binaries v 2 v r θ For spectroscopic binaries: can only measure radial velocity along line of sight For circular orbit, angle θ on orbit: θ 8 1 θ = ωt whereω = 2π/P. Observed radial velocity: radial velocity Earth vr = vcos(ωt) If orbit has inclination i, then Time vr(t) = vsinicos(ωt) From observation ofvr(t)= vsini. ( velocity amplitude ) Fundamental parameters or stars 4 Spectroscopic binaries 1 25 Double-lined spectra, case SB2 Assume circular orbit (e = 0) K1, K2 velocity half amplitudes of components 1 & 2 P orbital period 2πa 1/2 orbital radii of components 1 & 2 K 1/2 = 2πa 1/2 P sini = a 1/2 sini = P 2π K 1/2 again sin i remains indetermined Fundamental parameters or stars 5 Spectroscopic binaries 1 26 centre of mass law: Kepler s third law: M1 = a 2 a1 = K 2 K1 M1+ = 4π2 GP a 3, 2 a = a1+a2 = P 2π (K 1+ P 2π K 2)/sini = M1+ = 4π2 GP 2 P 3 (2π) 3 (K1+K2) 3 (sini) 3 ( ) = M1+ = P 2πG (K1+K2) 3 (sini) 3 (M1+)(sini) 3 = P 2πG (K 1+K2) 3 = two equations for three unknowns (M1+,sini), sin i can only be determined for eclipsing binaries Fundamental parameters or stars 6 Spectroscopic binaries 1 27 Single-lined spectra, case SB1 (only one spectrum visible): K2 unknown: K2 = K1 M 1 Insert in equation ( ): (M1+)(sini) 3 = P 2πG (K 1+K1 M1 ) 3 Mass functionf(m): (1+ M 1 (1+ M 1 )(sini) 3 = P K3 1 ) 3 2πG f(m) = M 2(sini) 3 (1+ M 1 = P K3 1 M ) 2 2πG 2 Fundamental parameters or stars 7

8 Radii 1 28 Fundamental parameters or stars 8 Radii 1 29 Eclipsing Binaries diametersda anddb: da+db = v(t5 t2) da db = v(t4 t3) = da = v(t5 t2+t4 t3)/2 db = v(t5 t2 t4+t3)/2 requires extremely accurate photometry independent of distance Fundamental parameters or stars 9 Star clusters testbeds of stellar evolution 1 30 NGC 7789 age: 1.5 Gyr Pleiades age: 150 Myr M 67 age: 5 Gyr open clusters Star clusters 1 Stellar clusters testbeds of stellar evolution 1 31 globular clusters M13 age: 12 Gyrs Star clusters 2

9 Stellar clusters testbeds of stellar evolution 1 32 Stars in a stellar cluster were born during one star formation event from one interstellar cloud they all have the same age and initial chemical abundances ( metallicity ) they have the same distance distances can be calibrated with well understood stars Star clusters 3 HR diagram of the globular cluster M Stars not distributed uniformly in HR diagram. Major groupings along main sequence and red giant branch Major groupings indicate slow evolutionary phases, i.e. stable phases of stellar evolution Obviously, certain configurations of stellar material are more stable than others Star clusters 4 HR diagram of the globular cluster M Major evolutionary phases MS: main sequence, H burning in core. Stars leave the MS at the turn-off (TO) RGB: red giant branch, H burning in a shell around He core HB: horizontal branch (red clump in younger populations), He burning in core AGB: asymptotic giant branch, H and He burning shells around C and O core Star clusters 5 Next: Stellar structure equations mass conservation 2. hydrostatic equilibrium 3. energy generation 4. energy transport Stellar structure equations 1