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SISD Training Lectures in Spectroscopy Anatomy of a Spectrum

Jeff Valenti
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Visual Spectrum of the Sun

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Blue Spectrum of the Sun

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Morphological Features in Spectra


Line Flux =



F

1

2

d

Continuum Fit

(Units : erg s-1 cm-2 )
Continuum Emiss ion Lines

Abs orptio n Lines

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Residual Intensity

Residua l Inten sity i s the Flu x Sp ectrum Di vided by Contin uum Fit
Line Depth
(Units: A or km/s)

Line W idth o

v = c

Equiva lent W idth:

W

eq

=





(1 - r )
2



d
o

1

(Units : A )

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Wide Variety of Continuum Shapes

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Planck Function
« Assumptions ¥ Uniform temperature source ¥ Source is opaque « Mathematical description

Emit ting A rea

B =

2hc 2 / 5 exp(hc / kT )- 1

erg o Units : s cm 2 A ster

h = Planck Constant = 6.63 â 10 -27 erg s c = Speed of Light = 3.00 â 1010 cm s-1 k = Boltzmann Constant = 1.38 â 10 -16 erg K

-1

= Wavelength of Light (cm

T = Uniform Temperature

) (K )

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Computed Blackbody Spectra
2hc 2 / 5 exp(hc / kT )- 1

B =

Rayleigh -Jeans Tail

Wien Law

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Wien Displacement Law

« Blackbody peak wavelength inversely proportional to temperature « Find peak wavelength by solving:

dB =0 d

where

B =
y=

2 hc 2 / 5 exp(hc / kT )- 1
hc pk kT

5 1- e

(

-y

)=

y

where

Numerical solution : y = 4.97

Wien Law:

T = 300 K pk = 10 µm T = 3000 K pk = 1 µm
T = 30, 000 K pk = 0.1 µm
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pkT = 029 cm K .

Stellar Flux Spectra vs. Planck Function

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Spectral Features due to Hydrogen

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Laboratory Spectra to Identify Lines

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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 ://w ww .a stro .univ ie .a c.a t./~vald/

¥ Atomic Data for Resonance Absorption Lines (Morton 1991, ApJS)
http ://w ww .hia .nrc.ca /sta f f/dcm /a tom ic_da ta .htm l
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Definition of Spectral Resolution
Intrinsi c Thorium Profile

Resolution:

R = or
o

c

(Units : A or km s-1 )

Resolving Power:

R=
Observed Profile

(Units : Dimensionless)




FW H M



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Line Spread Function (LSF, IP, PSF)
Intrinsic Profile Line Spread Function (LSF)

Observed Profile

Resolution vs. Sa mpl ing Coverage vs. Redu ndan cy

Convo lution Sum of Shifted and Scaled LSFs

Nyquist Sampling
Dispersion =

2R

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Effect of Resolution and Sampling

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Opacity
« Absorption coefficient: ¥ Fractional decrease in intensity per unit distance travelled

I = I x -



I = -Ix
-1

= n
n

(
(Uni
(Units

Units : cm
-3

)

I

I +I

= Num ber densit y of A bsorbers
ts : cm



)

= Cross-sectional Area of Absorber
: cm
2

)

Note : , , and I can be functions of and x.

x
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Mean Free Path

« Approximate path length required to absorb beam.

1 1 l= = n
« Example: ¥ For electrons: T = 7 â 10 -25 cm 2 ¥ In this room: nRoom= 3 â 1019 cm -3 ¥ Absorption coefficient: ¥ Mean free path:

Electrons locked up In neutral molecules

< T <
We can see further than 0.5 km

= n Room T = 2 â 10 -5 cm 1 l = = 5 â 10 4 cm = 0.5 km

-1

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Definition of Optical Depth Recal l: As

I = -Ix
I (x ) =e I (0)
x

x 0 this b ecomes

dI = - dx I
-

Solvi ng f or

I

giv es:

where ( x ) = dx is optical depth.
0



Optical depth is the number of times light from a source has been diminished by a factor of 1/e = 37%. Optical de pth is dimensionless.
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Optical Depth Examples

Exampl es:

. At = 01 in tensity h as dropped to e-0.1 = 90% of I0 -0.7 At = 2 3 in tensity h as dropped to e = 50% of I0 -3.0 . At = 30 in tensity h as dropped to e = 5% of I0
Optically thick means com plete absorption: >> 1 How far do we see into a star? To the Depth of Formation, where Optically thin means m in im al ab sorption: << 1

= 23
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Depth of formati on is a strong functi on of wavele ngth.

It s an optic al depth effec t


Structure of the Solar Atmosphere
Beh avior or s pec trum driv en by w ave len gth dep end enc e o f dep th o f f orm ation

Pho tos phe re
C IV

Fe I

Visible Depth Of NUV Formation Of Continua

Chro mos ph ere

FUV

Temp erature Min imum

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Spectral Features due to Hydrogen

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Transit ion Reg ion


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: = n ¥ is an atomic property that is identical for all stars ¥ n is actually the product of several factors:

n

= total number density of particles â abundance (hydrogen is 90% by number) â neutral fraction (~50%, ~100% for Sun) â excitation (fraction of hydrogen in N = 2)

¥ Excitation of N = 2 must be high. Why?
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Boltzmann Factor (Excitation)
pN = 2 N 2 exp - E
p
N

« Relative population in level N: « Excitation fraction: « For hydrogen:

(

N

kT

)

Statistical weight, g

fN =

p1 + p2 + p3 + ...

=

p

Boltzmann factor

N
Partition Function

U

E1 = 0, E2 = 10.2 eV , E3 = 12.1 eV , ...

U 2, since EN < kT <

f2 4 exp( - 118, 000 T

fN N 2 exp( - EN kT

)

)

¥ Sun: T = 5770 K f2 = 4e -20.5 = 6 â 10 -9 ¥ Vega: T = 10, 000 K f2 = 4e -11.8 = 3 â 10 -5 « Vega has 5000 times as much hydrogen in N = 2. « Additional heating increases excitation, but neutral fraction drops.
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Radiative Transfer
dI = - dx = - d I

« Recall:

Sour ce Fu nc tion (Emissio n)

« Transfer Equation:

dI = -I + S d
Ab sorp tion

« If collisions are more frequent than photon emission: ¥ System is in Local Thermodynamic Equilibrium (LTE) ¥ Calculate n( x) from T ( x ) ¥ Calculate ( x ) from n( x) and ¥ Local emission (source function) is Planck function: S = B ¥ Solve transfer equation for I ( x) , especially at the surface! « Otherwise system has non-LTE (NLTE) characteristics. ¥ I , S , , n, and T are interrelated -- very messy!
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Stellar Parameters

« Stellar parameters that affect synthetic spectrum ¥ E f fective 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
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Effect of Rotation

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