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
Feb 4, 2009 PHY 688, Lecture 5 3
Previously in PHY 688…
Feb 4, 2009 PHY 688, Lecture 5 4
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#(% "%& )
Feb 4, 2009 PHY 688, Lecture 5 5
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
Feb 4, 2009 PHY 688, Lecture 5 6
Energy Transport in the Sun
Feb 4, 2009 PHY 688, Lecture 5 7
• stars < 0.25MSunfully convective
• all stars have aradiative outerlayer: thephotosphere
Feb 4, 2009 PHY 688, Lecture 5 8
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
Feb 4, 2009 PHY 688, Lecture 5 9
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
• Review of previous lecture
• Stellar atmospheres– spectral lines– line profiles; broadening
• Astronomical spectroscopy and spectral types
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$=1
#ti+1
#t f
" collisional = 2 #tcoll
" pressure % r&n; n = 2,3,4,6
Feb 4, 2009 PHY 688, Lecture 5 18
Stark Effect in Hydrogen
• if external field is chaotic, the energy levels and their differences are smeared →line broadening
Feb 4, 2009 PHY 688, Lecture 5 19
Van der Waals Force:Long-Range Attraction
argon
Feb 4, 2009 PHY 688, Lecture 5 20
Line Profiles• Natural line width (Lorentzian [a.k.a, Cauchy] profile)
– Heisenberg uncertainty principle: ∆ν =∆E/h• Collisional broadening (Lorentzian profile)
– collisions interrupt photon emission process– ∆tcoll < ∆temission ~ 10–9 s– dependent on T, ρ
• Pressure broadening (~ Lorentzian profile)– ∆tinteraction > ∆temission– nearby particles shift energy levels of emitting particle
• Stark effect (n = 2, 4)• van der Waals force (n = 6)• dipole coupling between pairs of same species (n = 3)
– dependent mostly on ρ, less on T• Thermal Doppler broadening (Gaussian profile)
– emitting particles have a Maxwellian distribution of velocities• Rotational Doppler broadening (Gaussian profile)
– radiation emitted from a spatially unresolved rotating body
!
I" = I0
# /2$
" %"0( )
2
+ # 2/4
# & Lorentzian FWHM
!
I" =1
2#$e
%" %"
0( )2
2$2
$ &Gaussian FWHM
!
"thermal
= #0
kT
mc2
"rotational
= 2#0u /c
!
" natural =#Ei + #E f
h /2$=1
#ti+1
#t f
" collisional = 2 #tcoll
" pressure % r&n; n = 2,3,4,6
Feb 4, 2009 PHY 688, Lecture 5 21
Line Profiles: Rotational Broadening
Feb 4, 2009 PHY 688, Lecture 5 22
Line Profiles
profiles normalized to the same total area
ν
I ν
Feb 4, 2009 PHY 688, Lecture 5 23
Line Profiles• Natural line width (Lorentzian [a.k.a, Cauchy] profile)
– Heisenberg uncertainty principle: ∆ν =∆E/h• Collisional broadening (Lorentzian profile)
– collisions interrupt photon emission process– ∆tcoll < ∆temission ~ 10–9 s– dependent on T, ρ
• Pressure broadening (~ Lorentzian profile)– ∆tinteraction > ∆temission– nearby particles shift energy levels of emitting particle
• Stark effect (n = 2, 4)• van der Waals force (n = 6)• dipole coupling between pairs of same species (n = 3)
– dependent mostly on ρ, less on T• Thermal Doppler broadening (Gaussian profile)
– emitting particles have a Maxwellian distribution of velocities• Rotational Doppler broadening (Gaussian profile)
– radiation emitted from a spatially unresolved rotating body• Composite line profile: Lorentzian + Gaussian = Voigt profile
!
I" = I0
# /2$
" %"0( )
2
+ # 2/4
# & Lorentzian FWHM
!
I" =1
2#$e
%" %"
0( )2
2$2
$ &Gaussian FWHM
!
"thermal
= #0
kT
mc2
"rotational
= 2#0u /c
!
" natural =#Ei + #E f
h /2$=1
#ti+1
#t f
" collisional = 2 #tcoll
" pressure % r&n; n = 2,3,4,6
Feb 4, 2009 PHY 688, Lecture 5 24
Line Profiles• Natural line width (Lorentzian [a.k.a., Cauchy] profile)
– Heisenberg uncertainty principle: ∆ν =∆E/h• Collisional broadening (Lorentzian profile)
– collisions interrupt photon emission process– ∆tcoll < ∆temission ~ 10–9 s– dependent on T, ρ
• Pressure broadening (~ Lorentzian profile)– ∆tinteraction > ∆temission– nearby particles shift energy levels of emitting particle
• Stark effect (n = 2, 4)• van der Waals force (n = 6)• dipole coupling between pairs of same species (n = 3)
– dependent mostly on ρ, less on T• Thermal Doppler broadening (Gaussian profile)
– emitting particles have a Maxwellian distribution of velocities• Rotational Doppler broadening (Gaussian profile)
– radiation emitted from a spatially unresolved rotating body• Composite line profile: Lorentzian + Gaussian = Voigt profile
!
I" = I0
# /2$
" %"0( )
2
+ # 2/4
# & Lorentzian FWHM
!
I" =1
2#$e
%" %"
0( )2
2$2
$ &Gaussian FWHM
!
"thermal
= #0
kT
mc2
"rotational
= 2#0u /c
!
" 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 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
• Review of previous lecture
• Stellar atmospheres– spectral lines– line profiles; broadening
• Astronomical spectroscopy and spectral types
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