Overview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy · 2009. 2. 23. · Feb 4, 2009 PHY 688, Lecture 5 2 Outline •Review of previous lecture •Stellar atmospheres

Overview of Astronomical ConceptsIII. Stellar Atmospheres; Spectroscopy

PHY 688, Lecture 5Stanimir Metchev

Feb 4, 2009 PHY 688, Lecture 5 2

Outline

• Review of previous lecture

• Stellar atmospheres– spectral lines– line profiles; broadening

• Astronomical spectroscopy and spectral types


Previously in PHY 688…


Internal Equilibrium Equations

• hydrostatic equilibrium

• mass continuity

• conservation of energy

• temperature continuity– depends on mode of energy transport

!

dP

dr= "

GMr#

r2

dMr

dr= 4$r2#

dLr

dr= 4$r2#(% "%& )


Modes of Energy Transport and theTemperature Continuity Equation

• conduction– k: thermal conductivity– important only when photon m.f.p. < electron

m.f.p.• white dwarfs, neutron stars

• radiation– photons absorbed by cooler outer layers– efficient in:

• >1 MSun star envelopes• cores of 0.3–1 MSun stars• all stellar photospheres

• convection– adiabatic exponent γ = CP/CV– important when radiation inefficient:

• interiors of brown dwarfs and <0.3 MSun stars• cores of >1 MSun stars• envelopes of ~1 MSun stars

!

dT

dr= "

1

k

Lr

4#r2

dT

dr= "

3$%Lr

64#r2&T 3

dT

dr= 1"

1

'

(

) *

+

, - T

P

dP

dr


Energy Transport in the Sun


• stars < 0.25MSunfully convective

• all stars have aradiative outerlayer: thephotosphere


Additional Constitutive Equationsand Boundary Conditions

• equation of state• equation of energy

generation• opacity equation

• boundary conditions

P = P (T, ρ, composition)ε = ε (T, ρ, composition)

κ = κ (T, ρ, composition)

r =0: M0 = 0, L0 = 0r = R: MR = M, TR ≈ 0,

PR ≈ 0


A Special Solution to the E.O.S.:Stars as Polytropes

• P ≡ P(ρ) = Kργ, γ = 1+1/nK - constant, n - polytropic index

• Lane-Emden equations:– dimensionless forms of equation of

hydrostatic equilibrium– solutions:

• important polytropes:– n = 3: normal stars– n = 1.5: brown dwarfs, planets, white

dwarfs (all are degenerate objects)– n = 1: neutron stars– n = ∞: isothermal proto-stellar clouds

!

1

" 2

d

d"" 2 d"

d#

$

% &

'

( ) + # n "( ) = 0

# " = 0( ) =1 stellar core

d#

d"

$

% &

'

( ) " = 0

= 0 stellar core

!

P = P0"m+1

, # = #0"m, T = T

0"

Feb 4, 2009 PHY 688, Lecture 5 10

Energy Generation: p-p Chain

Feb 4, 2009 PHY 688, Lecture 5 11

Outline




Feb 4, 2009 PHY 688, Lecture 5 12

Stellar Atmospheres

higherionizationpotentialspecies

Feb 4, 2009 PHY 688, Lecture 5 13

Line Radiation

!

h" = #E $ R1

n1

2%1

n2

2

&

' (

)

* +

Feb 4, 2009 PHY 688, Lecture 5 14

Spectral Lines as Photospheric(≡ 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= "

GMr#

r2

= "g#

Feb 4, 2009 PHY 688, Lecture 5 15

Taking the Stellar Temperature

• individual line strengths

gn – statistical weightgn = 2n2 for hydrogen

• line ratios

!

Nn " gne#$n kT

Nn

Nm

=gn

gme# $n#$m( ) kT

Feb 4, 2009 PHY 688, Lecture 5 16

Taking the Stellar Temperature

• (Fe II λ5317 / Fe I λ5328) line ratio decreases with decreasing Teff

Teff

Feb 4, 2009 PHY 688, Lecture 5 17

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– ∆tcoll < ∆temission ~ 10–9 s– dependent on T, ρ

• Pressure broadening (~ Lorentzian profile)– ∆tinteraction > ∆temission– 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)

!

I" = I0

# /2$

" %"0( )

2

+ # 2/4

# & Lorentzian FWHM

!

" natural =#Ei + #E f

h /2$=1

#ti+1

#t f

" collisional = 2 #tcoll

" pressure % r&n; n = 2,3,4,6

Feb 4, 2009 PHY 688, Lecture 5 18

Stark Effect in Hydrogen

• if external field is chaotic, the energy levels and their differences are smeared →line broadening

Feb 4, 2009 PHY 688, Lecture 5 19

Van der Waals Force:Long-Range Attraction

argon

Feb 4, 2009 PHY 688, Lecture 5 20






– 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

!

I" = I0

# /2$

" %"0( )

2

+ # 2/4

# & Lorentzian FWHM

!

I" =1

2#$e

%" %"

0( )2

2$2

$ &Gaussian FWHM

!

"thermal

= #0

kT

mc2

"rotational

= 2#0u /c

!


h /2$=1

#ti+1

#t f


" pressure % r&n; n = 2,3,4,6

Feb 4, 2009 PHY 688, Lecture 5 21

Line Profiles: Rotational Broadening

Feb 4, 2009 PHY 688, Lecture 5 22

Line Profiles

profiles normalized to the same total area

ν

I ν

Feb 4, 2009 PHY 688, Lecture 5 23








– radiation emitted from a spatially unresolved rotating body• Composite line profile: Lorentzian + Gaussian = Voigt profile

!

I" = I0

# /2$

" %"0( )

2

+ # 2/4

# & Lorentzian FWHM

!

I" =1

2#$e

%" %"

0( )2

2$2

$ &Gaussian FWHM

!

"thermal

= #0

kT

mc2

"rotational

= 2#0u /c

!


h /2$=1

#ti+1

#t f


" pressure % r&n; n = 2,3,4,6

Feb 4, 2009 PHY 688, Lecture 5 24

Line Profiles• Natural line width (Lorentzian [a.k.a., Cauchy] profile)







– radiation emitted from a spatially unresolved rotating body• Composite line profile: Lorentzian + Gaussian = Voigt profile

!

I" = I0

# /2$

" %"0( )

2

+ # 2/4

# & Lorentzian FWHM

!

I" =1

2#$e

%" %"

0( )2

2$2

$ &Gaussian FWHM

!

"thermal

= #0

kT

mc2

"rotational

= 2#0u /c

!


h /2$=1

#ti+1

#t f


" pressure % r&n; n = 2,3,4,6

Feb 4, 2009 PHY 688, Lecture 5 25

Example: Pressure Broadeningof the Na D Fine Structure Doublet

Feb 4, 2009 PHY 688, Lecture 5 26

Line Profiles: Equivalent Width

Feb 4, 2009 PHY 688, Lecture 5 27

Outline




Feb 4, 2009 PHY 688, Lecture 5 28

Astronomical Spectrograph

telescope focus

Feb 4, 2009 PHY 688, Lecture 5 29

SpectroscopicBestiary

Feb 4, 2009 PHY 688, Lecture 5 30

OBAFGKM + LT

higherionizationpotentialspecies

Documents

Overview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy · 2009. 2. 23. · Feb 4, 2009 PHY 688, Lecture 5 2 Outline •Review of previous lecture •Stellar atmospheres