Overview of Astronomical Concepts
IV. Stellar Evolution
PHY 688, Lecture 6
Stanimir Metchev
Outline
• Review of previous lecture
• Stars
–
–
–
–
spectral classification
Hertzsprung-Russell and color-magnitude diagrams
formation
evolution
Feb 6, 2009
PHY 688, Lecture 6
2
Previously in PHY 688…
Feb 6, 2009
PHY 688, Lecture 6
3
On Convection, Radiation, and Lava
Lamps
• wax (+non-flammable solvent) denser
than water at room T, less dense at
higher T
• convection sets in because radiative T
gradient too steep
• if bottom heating is insufficient, excess
heat is merely radiated away, wax does
not expand, and lava lamp does not work
" 1 % T " dP %
" dT %
$ ' > $1( ' $ '
# dr & star # ) & P # dr & star
Feb 6, 2009
PHY 688, Lecture 6
4
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*
dP
GM r #
= " 2 = "g#
dr
r
• stellar rotation
– Doppler broadening
Feb 6, 2009
!
PHY 688, Lecture 6
5
Taking the Stellar Temperature
• individual line strengths
N n " gn e# $ n kT
gn – statistical weight
gn = 2n2 for hydrogen
• line ratios (Saha equation)
N n gn #( $ n # $ m ) kT
=
e
N m gm
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PHY 688, Lecture 6
6
The Actual Saha Equation
• relevant for ionized
species in thermal
equilibrium
N+, ne, N: number
densities of ions,
electrons, neutrals
u+, u: partition functions
!
(i.e., statistical weights)
χion: ionization potential
Feb 6, 2009
N + n e u + 2 -# ion
=
e
3
N
u "
h2
"$
2%m e kT
PHY 688, Lecture 6
kT
(electron thermal de
Broglie wavelength)
7
Taking the Stellar Temperature with
the Saha Equation
Teff
• (Fe II λ5317 / Fe I λ5328) line ratio decreases with decreasing Teff
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8
Iν
Line Profiles
ν
profiles normalized to the same total area
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9
Line Profiles
•
I" = I0
Natural line width (Lorentzian [a.k.a., Cauchy] profile)
– Heisenberg uncertainty principle: ∆ν =∆E/h
•
# & Lorentzian FWHM
Collisional broadening (Lorentzian profile)
– collisions interrupt photon emission process
– ∆tcoll < ∆temission ~ 10–9 s
– dependent on T, ρ
•
#E i + #E f
1
1
" natural =
=
+
h /2$
#t i #t f
Pressure broadening (~ Lorentzian profile)
!
– ∆tinteraction > ∆temission
– nearby particles shift energy levels of emitting particle
" collisional = 2 #t coll
" pressure % r
• 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)
Rotational Doppler broadening (Gaussian profile)
kT
mc 2
"rotational = 2# 0 u /c
"thermal = # 0
Composite line profile: Lorentzian + Gaussian = Voigt profile
Feb 6, 2009
; n = 2,3,4,6
%
1
2
I" =
e 2$
2# $
$ & Gaussian FWHM
– radiation emitted from a spatially unresolved rotating body
•
&n
(" % " 0 ) 2
– emitting particles have a Maxwellian distribution of velocities
•
# /2$
2
(" % " 0 ) + # 2 /4
!
PHY 688, Lecture 6
10
!
Outline
• Review of previous lecture
• Stars
–
–
–
–
spectral classification
Hertzsprung-Russel and color-magnitude diagrams
formation
evolution
Feb 6, 2009
PHY 688, Lecture 6
11
infrared spectra
visible spectra
Spectral Classification: Temperature
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12
Spectral Classification: Temperature
XXX
Weak Ca+
T
1,400–2,500 K
none
Molecules: H2O, hydrides
reddest star-like objects
<1,400 K
none
Molecules: H2O, CH4
Feb 6, 2009
PHY 688, Lecture 6
<0.08
~ 0.1
10–5–10–3
none
~ 0.1
10–6–10–5
none
13
Stellar Classification: Temperature
Sun
stars
(G dwarf) M dwarf
Feb
6, 2009K
5700
~3500 K
brown dwarfs
L dwarf
T dwarf
PHY 688,
~2000
KLecture 6 ~1000 K
planets
Jupiter
160 K
14
Spectral Classification: Luminosity
• luminosity, radius, surface gravity, and surface pressure
are mutually related
– L = 4πR2σTeff4, g = GM/R2, P = ρgl (l is photon m.f.p.)
• define “luminosity spectral class”
V: dwarfs, log g ~ 4.5 [cgs units]
IV: subgiants, log g ~ 3 (approximately as on Earth)
III: giants, log g ~ 1.5
II: (bright) giants, log g ~ 0.5
I: supergiants, log g ~ –0.5
• Sun: G2 V star (Teff = 5777K, log g = 4.43)
Feb 6, 2009
PHY 688, Lecture 6
15
(courtesy: D. Gray)
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PHY 688, Lecture 6
16
Hertzsprung
-Russell
(H-R)
Diagram
• log L vs. log Teff
• main sequence:
– locus of most stars
– bulk of stellar
lifetimes
– L ∝ M3.8
– τMS ≈
1010 yr (M/MSun)–2.8
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PHY 688, Lecture 6
17
ColorMagnitude
Diagram
(CMD)
• proxy for the (TeffL) HertzsprungRussell diagram
• e.g., B–V vs. MV,
J–K vs. MK, etc.
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PHY 688, Lecture 6
18
Star Formation
• molecular clouds:
–
–
–
–
–
n ~ 1000 cm–3
ρ ~ 10–27 g cm–3
M ~ 103–105 MSun
T ~ 10–100 K
r ~ 100 pc
• Jeans mass
– minimum mass for gravitational
collapse
# " & c s3
MJ = % ( 3 2 1 2
$6'G )
Feb 6, 2009
sound speed
3
#
&
# n &+1 2
cs
* (2MSun )%
+1 ( %
3
+3 (
$ 0.2kms ' $ 10 cm '
PHY 688, Lecture 6
19
Relevant Timescales
32
• free fall until hydrostatic
equilibrium is reached
• isothermal (KelvinHelmholtz) contraction
t ff " #
t KH
( R 2)
12
GM
( )
& $ )%1 2
" 35min (
%3 +
' g cm *
0.5GM 2 /R
"%
L
2
M MSun )
(
7
" 2 ,10 yr
( R RSun )(L LSun )
• main-sequence lifetime
– 10% of available hydrogen is
consumed on main sequence
– 0.7% of hydrogen rest mass
turned into energy
Feb 6, 2009
t MS
!
PHY 688, Lecture 6
0.007 , 0.1Mc 2
"
L
M MSun )
(
"
,1010 yr
(L LSun )
20
Star Formation: the H-R Perspective
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PHY 688, Lecture 6
21
Star Formation: the H-R Perspective
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PHY 688, Lecture 6
22
Evolutionary Models of Star and
Brown Dwarf Formation
Feb 6, 2009
PHY 688, Lecture 6
(Baraffe et al. 2002)
23
Post-Main Sequence Evolution
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24
Post-main sequence evolution
• Link to movies at Valdosta State U:
http://www.valdosta.edu/~cbarnbau/astro_demos/ste
llar_evol/home_stellar.html
Feb 6, 2009
PHY 688, Lecture 6
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