SISD Training Lectures in Spectroscopy

Transcription

1 SISD Training Lectures in Spectroscopy Anatomy of a Spectrum Visual Spectrum of the Sun

2 Blue Spectrum of the Sun Morphological Features in Spectra λ 2 Line Flux = Fλ dλ λ1 (Units: erg s -1 cm -2 ) Continuum Fit Continuum Emission Lines Absorption Lines

3 Residual Intensity Residual Intensity is the Flux Spectrum Divided by Continuum Fit Line Depth Line Width (Units: A o or km/s) v λ = c λ Equivalent Width: λ 2 W = eq ( 1 rλ ) dλ λ1 (Units :A) o Wide Variety of Continuum Shapes

4 Planck Function «Assumptions Uniform temperature source Source is opaque «Mathematical description B λ 2hc = exp 2 5 / λ ( hc / λkt) 1 Units : Emitting Area erg 2 o s cm A ster h = Planck Constant = erg s c = Speed of Light = cm s -1 k = Boltzmann Constant = erg K -1 λ = Wavelength of Light T = Uniform Temperature ( cm) ( K) Computed Blackbody Spectra 2 5 2hc / λ B = λ exp ( hc / λkt) 1 Rayleigh-Jeans Tail Wien Law

5 Wien Displacement Law «Blackbody peak wavelength inversely proportional to temperature «Find peak wavelength by solving: db λ = 0 where dλ ( 1 e y ) = y 5 where 2hc B = λ exp y = hc kt λ pk 2 5 / λ ( hc / λkt) 1 Numerical solution : y = λ pk T = 029. cm K 4.97 Wien Law: T = 300 K λ pk = 10 µ m T = 3000 K λ pk = 1 µ m T = 30, 000 K λ pk = 0. 1 µ m Stellar Flux Spectra vs. Planck Function

6 Spectral Features due to Hydrogen Laboratory Spectra to Identify Lines

7 Line Identification References «Labelled Spectral Atlases Solar Photosphere, micron (Wallace et al ) Sunspot, micron (Wallace et al ) Arcturus (K1 III), micron (Hinkle et al ) «Printed Line Lists Atomic and Ionic Spectrum Lines Below 2000 A (Kelly 1987) FUV lines in solar spectrum (Sandlin et al. 1986, ApJS, 61, 801) Ultraviolet Multiplet Table (Moore 1950) A Multiplet Table of Astrophysical Interest (Moore 1945) «Electronic Media Kurucz CD-ROM Series ( ) Vienna Atomic Line Database (VALD, Kupka et al. 1999, A&AS, 138) Atomic Data for Resonance Absorption Lines (Morton 1991, ApJS) Definition of Spectral Resolution Intrinsic Thorium Profile Resolution: R = λ or o (Units : A or c λ λ km s -1 ) Observed Profile λ FWHM Resolving Power: λ R = λ (Units : Dimensionless) λ

8 Line Spread Function (LSF, IP, PSF) Intrinsic Profile Line Spread Function (LSF) Observed Profile Resolution vs. Sampling Coverage vs. Redundancy Convo lution Sum of Shifted and Scaled LSFs Nyquist Sampling λ Dispersion = 2R Effect of Resolution and Sampling

9 Opacity «Absorption coefficient: α Fractional decrease in intensity per unit distance travelled I α = I x I = αi x α = n σ ( Units : cm -1 ) n = Number density of Absorbers -3 ( Units : cm ) σ = Cross-sectional Area of Absorber ( Units : cm 2 ) I I+ I Note : σ, α, and Ican be functions of λand x. x Mean Free Path «Approximate path length required to absorb beam. l 1 = = α 1 nσ Electrons locked up In neutral molecules σ << σ T «Example: For electrons: In this room: Absorption coefficient: Mean free path: σ T = cm n Room -3 = cm We can see further than 0.5 km α = σ = cm 1 l = = cm = 0.5 km α n Room T -1

10 Definition of Optical Depth Recall: I = αi x As x 0 this becomes I() x Solving for I gives: I() 0 di I = e = αdx τ It s an optical depth effect where τ( x)= αdx is optical depth. 0 x Optical depth is the number of times light from a source has been diminished by a factor of 1/e = 37%. Optical depth is dimensionless. Optical Depth Examples Examples: 0.1 At τ = 01. intensity has dropped to e = 90% of I0 At τ = 2 3 intensity has dropped to 0.7 e = 50% of I0 3.0 At τ = 30. intensity has dropped to e = 5% of I0 Optically thin means minimal absorption: τ << 1 Optically thick means complete absorption: τ >> 1 How far do we see into a star? To the Depth of Formation, where τ = 2 3 Depth of formation is a strong function of wavelength.

11 Structure of the Solar Atmosphere Behavior or spectrum driven by wavelength dependence of depth of formation Photosphere C IV Fe I Transition Region Visible Depth Of NUV Formation Of Continua FUV Chromosphere Temperature Minimum Spectral Features due to Hydrogen

12 Analysis of Vega Spectrum «Strong Balmer series and Balmer jump (transitions from N = 2) Seeing much higher, cooler, fainter layers in lines Balmer opacity is large in A-type stars. Why? α = nσ «Recall: is an atomic property that is identical for all stars is actually the product of several factors: σ n n = total number density of particles abundance (hydrogen is 90% by number) neutral fraction (~50%, ~100% for Sun) excitation (fraction of hydrogen in N = 2) Excitation of N = 2 must be high. Why? «Relative population in level N: «Excitation fraction: «For hydrogen: 1 Boltzmann Factor (Excitation) f N p N Statistical weight, g = 2N 2 exp p p N = = p + p + p +... U 2 1 E = 0, E = 10.2 ev, E ( E kt) N Boltzmann factor N Partition Function = 12.1 ev,... U 2, since E << kt f N 2 exp( EN kt) N N ( ) f2 4exp 118, 000 T 9 Sun: T = 5770 K f2 = 4e = Vega: T = 10, 000 K f2 = 4e = 3 10 «Vega has 5000 times as much hydrogen in N = 2. «Additional heating increases excitation, but neutral fraction drops.

13 Radiative Transfer di «Recall: = α dx = dτ I di «Transfer Equation: = I + S dτ Absorption Source Function (Emission) «If collisions are more frequent than photon emission: System is in Local Thermodynamic Equilibrium (LTE) Calculate n(x) from T(x) Calculate τ( x) from n(x) and α Local emission (source function) is Planck function: Solve transfer equation for I(x), especially at the surface! «Otherwise system has non-lte (NLTE) characteristics. are interrelated very messy! I, S, τ, n, and T S = B λ Stellar Parameters «Stellar parameters that affect synthetic spectrum Effective temperature (via ionization and excitation) Gravity (high gravity gives broad line wings due to collisions) Abundances or a global metallicity (affects opacity in lines) Magnetic fields (changes wavelength dependence of opacity) Microturbulence and Macroturbulence (Doppler smearing) Rotation (more Doppler smearing) Radial velocity (Doppler shift) «Spectroscopy Made Easy (SME) Fit observations or just synthesize a spectrum Atomic data still a pain Valenti & Piskunov (1996), A&AS, 118, 595

14 Effect of Rotation