sisd training lectures in spectroscopy anatomy of a spectrum jeff valenti · jeff valenti sisd...
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Jeff Valenti
SISD Training Lectures in Spectroscopy
Jeff Valenti
Anatomy of a Spectrum
Jeff Valenti
Visual Spectrum of the Sun
Jeff Valenti
Blue Spectrum of the Sun
Jeff Valenti
Morphological Features in Spectra
EmissionLines
AbsorptionLines
Continuum Fit
Continuum
Line Flux = ∫ λ λλ
λF d
1
2
)cm s erg :(Units -2-1
Jeff Valenti
Residual Intensity
Residual Intensity is the Flux Spectrum Divided by Continuum Fit
Line Width
Lin
e D
epth
km/s) or A :(Unitso
λλ∆=∆
c
v
eqW r d= −( )∫ 1
1
2
λ
λ
λλ
Equivalent Width:
)A :(Unitso
Jeff Valenti
Wide Variety of Continuum Shapes
Jeff Valenti
Planck Function
« Assumptions¥ Uniform temperature source¥ Source is opaque
« Mathematical description
( ) 1/exp/2 52
−=
kThchc
Bλ
λλ
Units : erg
s cm A ster 2 o
Emitting Area
h Planck Constant 6.63 erg s= = × −10 27
c Speed of Light 3.00 cm s-1= = ×1010
k Boltzmann Constant 1.38 erg K-1= = × −10 16
( )cmLight ofh Wavelengt =λ( )K eTemperatur Uniform =T
Jeff Valenti
Computed Blackbody Spectra
WienLaw
( ) 1/exp/2 52
−=
kThc
hcB
λλ
λ
Rayleigh-JeansTail
Jeff Valenti
Wien Displacement Law
« Blackbody peak wavelength inversely proportional to temperature« Find peak wavelength by solving:
( ) 1/exp/2 52
−=
kThchc
Bλ
λλ
0d
d=
λλB
where
( ) ye y =− −15 where kT
hcy
pkλ=
97.4 :solution Numerical =y
λ pk cm KT = 0 29.
Wien Law: T = → =300 10 K mpkλ µT = → =3000 1 K mpkλ µT = → =30 000 0 1, . K mpkλ µ
Jeff Valenti
Stellar Flux Spectra vs. Planck Function
Jeff Valenti
Line Identification References
« Labelled Spectral Atlases¥ Solar Photosphere, 0.36-22 micron (Wallace et al. 1991-1999)¥ Sunspot, 0.39-21 micron (Wallace et al. 1992-2000)¥ Arcturus (K1 III), 0.37-5.3 micron (Hinkle et al. 1995-2000)
« 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 (1993-1999)¥ Vienna Atomic Line Database (VALD, Kupka et al. 1999, A&AS, 138)
http://www.astro.univie.ac.at./~vald/
¥ Atomic Data for Resonance Absorption Lines (Morton 1991, ApJS)http://www.hia.nrc.ca/staff/dcm/atomic_data.html
Jeff Valenti
Definition of Spectral Resolution
IntrinsicThoriumProfile
Observed Profile
FWHM
λ∆
λ
Resolution:
Rc= ∆ ∆λ λλ
or
)s kmor A :(Units 1-o
Resolving Power:
λλ
∆=R
ess)Dimensionl :(Units
Jeff Valenti
Line Spread Function (LSF, IP, PSF)
Intrinsic Profile
Line SpreadFunction (LSF)
Sum of Shiftedand Scaled LSFs
Observed Profile
Nyquist Sampling
R2 Dispersion
λ=
Convo lution
Resolution vs. SamplingCoverage vs. Redundancy
Jeff Valenti
Effect of Resolution and Sampling
Jeff Valenti
Opacity
« Absorption coefficient:¥ Fractional decrease in intensity per unit distance travelled
α
α α=−
↔ = −
∆
∆∆ ∆
I
Ix
I I x
∆x
I I I+ ∆α σ= ( )n Units : cm-1
n = Number density of Absorbers
σ = Cross-sectional Area of Absorber
( )-3cm :Units
( )2cm :Units
Note : , , and can be functions of and .σ α λI x
Jeff Valenti
Mean Free Path
« Approximate path length required to absorb beam.
« Example:¥ For electrons:¥ In this room:
¥ Absorption coefficient:
¥ Mean free path:
l1
n= =
α σ1
σ T2 cm= × −7 10 25
nRoom-3 cm= ×3 1019
α σ= = × −nRoom T-1 cm2 10 5
l = = × =15 104
α cm 0.5 km
Electrons locked upIn neutral molecules
σ σ<< T
We cansee furtherthan 0.5 km
Jeff Valenti
Definition of Optical Depth
Recall: ∆ ∆I I x= −α
As ∆x → 0 this becomesd
dI
Ix= −α
Solving for I gives:( )( )
τ−= e0I
xI
where τ αx x0
x
( ) = ∫ d is optical depth.
Optical depth is the number of times light from a sourcehas been diminished by a factor of 1/e = 37%.
Optical depth is dimensionless.
Its
an o
ptic
al d
epth
eff
ect
Jeff Valenti
Optical Depth Examples
At τ = 0 1. intensity has dropped to0
1.0 of %90e I=−
At τ = 23 intensity has dropped to 0
7.0 of %50e I=−
At τ = 3 0. intensity has dropped to 00.3 of %5e I=−
Examples:
Optically thin means minimal absorption: τ <<1Optically 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.
Jeff Valenti
Structure of the Solar Atmosphere
Chromosphere
Photosphere
Tra
nsit
ion
Reg
ion
Temperature Minimum
Visible
NUV
FUV
DepthOfFormationOf Continua
C IV
Fe I
Behavior or spectrum driven by wavelength dependence of depth of formation
Jeff Valenti
Spectral Features due to Hydrogen
Jeff Valenti
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?
« Recall:¥ is an atomic property that is identical for all stars¥ is actually the product of several factors:
¥ Excitation of N = 2 must be high. Why?
α σ= nσn
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)
Jeff Valenti
Boltzmann Factor (Excitation)
« Relative population in level N:
« Excitation fraction:
« For hydrogen:
¥ Sun:¥ Vega:
« Vega has 5000 times as much hydrogen in N = 2.« Additional heating increases excitation, but neutral fraction drops.
( )kTENpNN
−= exp2 2
Statistical weight, g Boltzmann factor
U
p
ppp
pf NNN
=+++
=...
321Partition Function
... ,Ve 1.12 ,Ve 2.10 ,0321
=== EEE
U E kTN≈ <<2, since f N E kTN N≈ −( )2 exp
f T2 4 118 000≈ −( )exp ,
T f= → = = × −5770 4 6 1029 K e-20.5
T f= → = = × −10 000 4 3 1025, K e-11.8
Jeff Valenti
Radiative Transfer
« Recall:
« Transfer Equation:
« If collisions are more frequent than photon emission:¥ System is in Local Thermodynamic Equilibrium (LTE)¥ Calculate from¥ Calculate from and¥ Local emission (source function) is Planck function:¥ Solve transfer equation for , especially at the surface!
« Otherwise system has non-LTE (NLTE) characteristics.¥ are interrelated — very messy!
τα d dd −=−= xII
SII +−=τd
d
Absorption
Source Function(Emission)
)(xnτ ( )x
)(xT)(xn α
λBS =)(xI
TnSI and ,,,, τ
Jeff Valenti
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