Electromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev

Transcription

1 Electromagnetic Spectra AST443, Lecture 13 Stanimir Metchev

2 Administrative Homework 2: problem 5.4 extension: until Mon, Nov 2 Reading: Bradt, chapter 11 Howell, chapter 6 Tenagra data: see bottom of Assignments & Exams section on course website M11 (B+V), M52 (B+V+R), HD b (R, all data taken) expect M37 (B+V+R) data tonight remaining: Hyades (B+V+R) 2

3 Outline Overview color-magnitude and color-color diagrams spectral classification Electromagnetic spectra optically thin, synchrotron, and blackbody emission electronic line transitions Stellar diagnostics atmospheres: temperature, pressure, abundance binarity 3

4 Color-Magnitude Diagram 4

5 Extinction and Reddening: CCD Legend: arrow: A V = 5 mag extinction solid line: main sequence + giants dotted line: substellar models crosses: known brown dwarfs solid points: brown dwarf candidates A V = 5 mag Metchev et al. (2003) 5

6 OBAFGKM + LT higher ionization potential species 6

7 Color-Magnitude Diagram 7

8 Outline Overview color-magnitude and color-color diagrams spectral classification Electromagnetic spectra optically thin, synchrotron, and blackbody emission electronic line transitions Stellar diagnostics atmospheres: temperature, pressure, abundance binarity 8

9 Radiation (Lecture 12) specific intensity I ν de = I ν dt da dν dω [erg s 1 cm 2 Hz 1 sterad 1 ] or [Jy sterad 1 ] 1 Jy = erg s 1 cm 2 Hz 1 = W m 2 Hz 1 surface brightness of extended sources (independent of distance) spectral flux density S ν S ν = I ν dω [erg s 1 cm 2 Hz 1 ] or [Jy] or [W m 2 Hz 1 ] S λ = S ν c/λ 2 [erg s 1 cm 2 nm 1 ] point sources, integrated light from extended sources flux density F F = S ν dν [erg s 1 cm 2 ] or [W m 2 ] power P P = F da = de / dt [erg s 1 ] or [W] received power: integrated over telescope area luminosity: integrated over area of star conversion to photon counts energy of N photons: Nhν 9

10 Extinction and Optical Depth (Lecture 4) Light passing through a medium can be: transmitted, absorbed, scattered extinction at frequency ν over distance s dl ν (s) = κ ν ρ L ν ds = L dτ ν L ν = L ν,0 e τ = L ν,0 e κρs =L ν,0 e s/l A ν = 2.5 lg (F ν,0 /F ν ) = 2.5 lg(e)τ ν = 0.43τ ν mag medium opacity κ ν [cm 2 g 1 ], density ρ [g cm 3 ] optical depth τ ν = κ ν ρs [unitless] photon mean free path: l ν = (κ ν ρ) 1 = s/τ ν [cm] A V = m V m V,0 10

11 Neutral Atoms and Molecules Are Strong Wavelength-Dependent Absorbers 11

12 Electronic Transitions bound-free free-bound free-free (bremsstrahlung) 12

13 Examples of Continuum Spectra optically thin thermal radiation synchrotron radiation (non-thermal) blackbody (optically thick) thermal radiation 13

14 Optically Thin Bremsstrahlung optical depth << 1 hot plasma: free electrons accelerated in near-collisions with massive ions large accelerarion due to Coulomb force: radiation continuum spectrum: j(",t) # Z 2 n e n i T $1 2 e $h" kt [W m 3 Hz 1 ] Z n e,n i atomic number (charge number) of ions number densities [m 3 ] of electrons, ions spectrum is flat at low (radio) ν (i.e., ~independent of ν) occurrence: x-rays in dentist s tube shocks in supernova remnants stellar coronae (~1,000,000 K) 14

15 Synchrotron Radiation charged electrons spiraling in a B field spiraling motion means acceleration, hence radiation relativistic electrons can emit x-ray to gammaray photons beaming in direction of travel spectrum reflects energy distribution of radiating electrons power law: I = Kν α [W m 2 Hz 1 sterad 1 ] (α < 0) 15

16 Blackbody Radiation (Lecture 4) Planck law specific intensity I(",T) = 2h" 3 c 2 1 e h" kt #1 Wien displacement law T λ max = 0.29 K cm Stefan-Boltzmann law F = σ T 4 energy flux density [erg s 1 cm 2 ] " = 2# 5 k 4 Stellar luminosity power [erg s 1 ] Inverse-square law F(r) = L * / r 2 15c 2 h 3 = 5.67 $10%5 erg cm 2 s 1 K 4 L * = 4"R 2 4 * #T eff 16

17 Blackbody Radiation (Lecture 4) T eff, Sun = 5777 K T λ max = 0.29 K cm 17

18 Examples of Continuum Spectra optically thin thermal radiation synchrotron radiation (non-thermal) blackbody (optically thick) thermal radiation see Fig of Bradt, p

19 Radiative Transfer (again) The optical depth τ λ accounts for interaction between photospheric matter and radiation field. 19

20 Line Radiation & h" = #E $ R 1 2 n % 1 ) ( 2 + ' 1 n 2 * 20

21 Outline Overview color-magnitude and color-color diagrams spectral classification Electromagnetic spectra optically thin, synchrotron, and blackbody emission electronic line transitions Stellar diagnostics atmospheres: temperature, pressure, abundance binarity 21

22 Spectral Lines as Atmospheric Diagnostics chemical content and abundances mostly H and He, but heavier metals (Z > 2) + molecules are important sources of opacity photospheric temperature individual line strength line ratios photospheric pressure non-zero line width surface gravity g, mass M * stellar rotation Doppler broadening dp dr = " GM r# = "g# r 2 equation of hydrostatic equilibrium 22

23 Taking the Stellar Temperature individual line strengths N n " g n e #$ n kt g n statistical weight g n = 2n 2 for hydrogen line ratios N n = g n e # ( $ n #$ m ) kt N m g m 23

24 Taking the Stellar Temperature T eff (Fe II λ5317 / Fe I λ5328) line ratio decreases with decreasing T eff 24

25 Line Profiles Natural line width (Lorentzian [a.k.a, Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 25

26 Stark Effect in Hydrogen if external field is chaotic, the energy levels and their differences are smeared line broadening 26

27 Van der Waals Force: Long-Range Attraction 27

28 Van der Waals Force: Long-Range Attraction 28

29 Line Profiles Natural line width (Lorentzian [a.k.a, Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 I " = 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u /c 29

30 Line Profiles: Rotational Broadening 30

31 Line Profiles I ν profiles normalized to the same total area ν 31

32 Line Profiles Natural line width (Lorentzian [a.k.a, Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body Composite line profile: Lorentzian + Gaussian = Voigt profile # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 I " = 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u /c 32

33 Line Profiles Natural line width (Lorentzian [a.k.a., Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body Composite line profile: Lorentzian + Gaussian = Voigt profile # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 I " = 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u /c 33

34 Example: Pressure Broadening of the Na D Fine Structure Doublet 34

35 Line Profiles: Equivalent Width (EW) EW = " $ 2 ( F ", cont # F ", line ) d" " 1 " $ 2 F ", cont d" " 1 λ 1 λ 2 35

36 Lorentzian Line Profile at Increasing τ simulation for the Hα line profile 36

37 Lorentzian Line Profile at Increasing τ simulation for the Hα line profile saturation at τ > 5 37

38 Lorentzian Line Profile at Increasing τ simulation for the Hα line profile 38

39 Lorentzian vs. Gaussian Line Profiles: Small τ simulation for the Hα line profile 39

40 Lorentzian vs. Gaussian Line Profiles: Large τ simulation for the Hα line profile core more sensitive to Gaussian parts wings more influenced by Lorentzian parts 40

41 Curve of Growth: Dependence of Line Equivalent Width W on Column Density N N integral of number density of absorbing atoms or molecules along line of sight [cm -2 ] for small N, W N linear part of the curve of growth for larger N, W " ln N after the Gaussian core bottoms out flat part of the curve of growth for even larger N, W " N after the absorption by the Lorentzian wings becomes strong square root part of the curve of growth There is a different curve of growth, W(N), for each spectral line 41

42 Universal Curve of Growth the ratio of W to Doppler line width Δλ depends upon the product of N and a line s oscillator strength f in the same way for every spectral line (e.g. Unsöld 1955). " log W # $ % ' &! ( linear W " N flat square root W " ln N W " N "# = # v c = # c 2kT m m: absorber particle mass ( ) log Nf 42

43 Alkali (Na, K) lines in visible spectra of late-l and T dwarfs become saturated! (Kirkpatrick 2005) 43

44 Curve of Growth: Determining Abundances Measure W for a lot of lines (each with distinct, known f) of a number of atomic or ionic species. Plot W/ λ against xnf where: N is the column density of one species x is the relative abundance of the atomic species that gives rise to the line (ratio of number density of that species to the number density of the first species), Adjust x, N, and λ until the points fit the universal curve of growth. Then one knows these three quantities for each species. 44

45 Outline Overview color-magnitude and color-color diagrams spectral classification Electromagnetic spectra optically thin, synchrotron, and blackbody emission electronic line transitions Stellar diagnostics atmospheres: temperature, pressure, abundance binarity 45

46 Spectroscopic Binary (a) (d) (a) double-lined (SB2) spectra of both stars visible (b) (c) (b) (c) (d) single-lined (SB1) only spectrum of brighter star visible (d) 46

47 Example: SB1 47

48 Example: SB2 48

49 Radial Velocity vs. Time for Double-lined SB in a Circular Orbit 49

50 Radial Velocity vs. Time for Doublelined SB in Elliptical Orbit (e = 0.4) 50

51 51 Peg Ab is an SB1! first planet detected around a main-sequence star primary SpT: G2 V M p sin i = 0.47 M Jup (Mayor & Queloz 1995) 51