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Stellar Evolution
• Hertzsprung-Russell (HR) Diagram: A graph plot
indicating individual stars as points, with stellar luminosity
on the vertical axis & surface temperature (spectral type)
on the horizontal axis
• We can use spectroscopy to determine the spectral type
& luminosity of a star
• Main Sequence (MS): Prominent line of points running
from the upper left to lower right on an HR Diagram;
these stars shine by fusing hydrogen in their core
• For the Main Sequence
! Mass increases from right to left along the MS
! Most stars have low mass
! High-mass stars have short MS lives; low mass
stars have long MS lives
Hertzsprung-Russell Diagram or ColorMagnitude Diagram
Increasing mass
Stars stay on the main sequence most of
Their lives, burning H to He
i.e., Temperature
Spectral Types
Blue
Red
Surface gravity, g, sets the Pressure
Gradient of Atmosphere
g = G M / R2
Emission/Absorption Features
Associated with Different S.T.s
Spectral Sequence
Stellar radii
on HR
Diagram
Luminosity Class
•
•
•
•
•
I = Supergiants
II = Bright Giants
III = Giants
IV = subgiants
V = dwarfs (Main Sequence)
Initial Mass Function • IMF, ! (M) = distribution in mass of freshly formed stars
• Form 1: Salpeter IMF
! (M) " M-2.35
• Form 2: Scalo IMF For M # 0.2 Msun.
! (M) " M-2.45 for M > 10 Msun.
! (M) " M-3.27 for 1 Msun > M > 10 Msun.
! (M) " M-1.83 for M < 0.2Msun.
• I.e., there are lots of low-mass stars & very few high-mass
stars
Different Mass Stars Follow Different
Tracks Along this Diagram
MS masses & lifetimes
Estimating Lifetimes on the Main
Sequence
• Recall that, for the Sun, the H-burning lifetime is
• The more generic expression is
10 MSolar Star – 107 years
2 MSolar Star – 109 years
1 MSolar Star – 1010 years
Stars spend most of their lives on the MS
• For the horizontal branch, the luminosity of a star is LHB
= 50 Lsun
• During a star’s life on the HB, it converts M(He core) =
0.45 Msun into O & C
• About 0.5 of the He " O & the other 0.5 He " C
• Thus,
Pressure
• There are three sources of pressure in a star:
• Normal gas pressure -
• Radiation Pressure
• Electron Degeneracy Pressure
Electron Degeneracy
1) Pauli Exclusion Principle: No two electrons can
have exactly the same set of quantum numbers
2) It is impossible to define the position & momentum of
a particle to an accuracy better than Planck’s
constant, h. I.e., if !x & !px are the uncertainties in
the position & momentum of a particle, respectively,
then
• Pressure arises from the random motions of particles.
Thus, for electrons, even if the temperature is 0 K,
they still have motion resulting from quantum
mechanical effects (& !px different by at least h/!x
such as not to violate the exclusion principle),
especially if #x is small
Electron Degeneracy
• To get an idea of where the pressure expression
comes from, rewrite the idea gas law as
• where vx and px are the mean x velocity & momentum
of electrons, respectively. Thus,
Electron Degeneracy
• Given the condition of charge neutrality, n+ ion per
unit volume with atomic number Z & weight µ and ne
electrons per unit volume
• The density is
• And thus,
Evolutionary Tracks
Life of a Low-Mass Star
1)
2)
3)
4)
5)
6)
7)
Fusion of hydrogen into helium
Core hydrogen ends, star collapses, hydrogen fusion begins in
outer shell
Core continues to collapse, outer shell expands because of
hydrogen fusion, star becomes luminous
Core becomes degenerate (sustained by electron pressure), outer
shell dumps helium ash onto core
Helium flash! Helium fusion (into carbon) begins in core
Core helium fusion ends, eventually leading to both hydrogen &
helium fusion shells & a degenerate carbon core
End results ! outer layers drift away (planetary nebula), leaving a
naked core (white dwarf)
Life Track of 1 Solar Mass Star
Example of a Planetary Nebula
Life Cycle of a Massive Star
1)
2)
3)
4)
Successive episodes of shell fusion occur, leading up
to a degenerate iron core
Iron is unlike other elements in that no energy is
released through fusion or fission
Thus, core continues to accrete iron ash until
degeneracy is finally broken
Supernova may result in part from:
! core bounce associated with collapse into a
neutron star
! release of neutrinos ($) which deposit energy
into the dense outer envelopes of the star
(i.e, p+ + e- ! no + $)
The importance of Iron (Fe)
Nucleus sufficiently small for strong force to
overcome coulomb repulsion
Massive star core near end of life
Time for massive star to go supernova
•
•
1.4 Msun of H " Fe before exploding
So, the mass of a Fe56 ~ 55.5 & H = 1, so, the efficiency is,
•
And thus,
•
If L3 x 103 Lsun, then,
Elements heavier than Fe56
• Are built through the s- & r-processes.
• The slow-process occurs as neutrons bombard &
combine with heavy nuclei at a rate < the time for
beta decay if the isotope formed is unstable
• The rapid-process occurs as neutron bombard &
combine with heavy nuclei at a rate much faster than
the beta decay timescale. Free neutrons exist in large
quantity during a supernova event
Supernova Remnant
More comments on abundances
• H, He, Li, Be, B - primordial ratios
• C, N, O, Fe - stellar nucleosynthesis
• Th, U - stellar nucleosynthesis, but must have formed
very recently
Remnants: condensed matter
• For Mstar < 8 Msolar " white dwarf
Leftover after much mass loss
MWD " 0.55 – 0.6 Msolar
Typical Radius = 107 m (about Earth size)
• For 8 Msolar $ Mstar $ 60 Msolar " neutron star
Optically invisible, but visible as radio pulsars
MNS " 1.4 Msolar
Typical Radius = 104 m (a little taller than Mt Everest)
• For Mstar > 60 Msolar " Black Hole
Optically invisible
MBH > 1.4 Msolar
Radius = 2GM /c2
Remnants: radius - mass relation
• Recall that, for a degenerate (non-relativistic) core,
• And the central pressure of a star is,
• Equating the two gives
• I.e., the volume of degenerate objects like a white
dwarf is inversely proportional to the mass
Remnants: Some numbers - Density
• Density of a white dwarf ~ 106 g cm-3. One
sugarcube-size piece of WD matter would weigh
more than a car
• Density of a neutron star ~ 2x1014 g cm-3. One
sugarcube-size piece of neutron matter would weigh
as much as the total human population of the Earth.
Note that, for a neutron,
I.e., in a neutron star, the neutrons are almost
touching.
Remants: some numbers - escape
velocity
• Escape velocity of a white dwarf -
• Escape velocity of a neutron star -
• Escape velocity of a black holes = c
Remnants: Final observation
• Stars ending their lives as white dwarfs & neutron
stars have their fate determined by quantum
mechanics (degeneracy)
• Stars ending as black holes have their fate
determined by gravity