Mass Statistics
• Add mass for main
sequence to our plot
• Masses vary little
• Model: Stars are the
same: mass determines
rest
• Heavy stars hot,
luminous
1
Mass-Luminosity Relation
• Find approximately
• Borne out by models: Mass
compresses star increasing
rate of fusion
• If amount of Hydrogen
available for fusion is near
constant fraction, big stars run
out sooner
• OB stars are young!
2
Main Sequence Stars
• Stellar modeling matched to data tells us
about how stars work
• Main-Sequence stars fuse Hydrogen to Helium
in core
• Hydrostatic Equilibrium determines rate of
fusion and density profile from mass
3
CNO Chain
• In large stars
core hot and CNO chain
dominates fusion
• Rate rises rapidly with
temperature
4
Size Matters
• Mechanisms of heat
transfer depend on mass
• In small stars, entire
volume convective so all
available to fuse in core
• In large stars, radiation
and convection zones
inverted
5
Expansion by Contraction
• As a main sequence star ages
core enriched in Helium
• Rate of fusion decreases –
temperature and radiation
pressure decrease
• Number of particles decreases –
thermodynamic pressure
decreases
• Core contracts and heats
• Fusing region grows
• Luminosity increases
• Envelope expands
6
• Sun now 25% brighter
than when it formed
• Core now 60% Helium
• Continues to brighten –
heating Earth
• In 1-3Gy could be
uninhabitable?
• Orbit stable out to 1Gy?
Questions
• For 90% of stars we have a good
understanding of how they work
• This comes from careful observation and
detailed modeling
• Where do the rest come from?
• What happens when core is all Helium??
7
Modelling Collapse
• Model a cloud of mass
• Within a few Ky form opaque radiating
photosphere of dust and later H• Photosphere contracts from
to
at constant
fueled
by Kelvin-Helmholtz and deuterium fusion over
600Ky
8
Pre-Main Sequence
• Initial photosphere contracts
at constant T decreasing L
• Rising ionization in center
reduces opacity creating
radiative zone increasing L
• When fusion begins L
decreases initially as core
expands
• In 40My settle down to MS
equilibrium: KH time!
• Larger stars go faster
9
105
106
107
Too Small
• Below
effective
fusion does not occur
•
is a brown dwarf type L,
T, Y
• How Many? 1:1? 1:5?
10
Too Big?
• Models suggest that collapse with
fails as radiation pressure fragments cloud
• Recent record
11
On the Main Sequence
• Hydrogen fusion in core
supports envelope by thermal
and radiation pressure
• Luminosity, surface
temperature determined by
mass, composition, rotation,
close binary partner,
atmospheric and interstellar
effects
• Main Sequence thickened by
variations in these
12
• Over time core contracts and
heats
• Fusion rate increases
• Envelope expands slowly with
little change in temperature
• Evolutionary track turns away
from Main Sequence
Running Out of Gas
• Inner 3% inert Helium
core is isothermal
• Hydrogen fusion in shell
exceeds previous core
luminosity
• Envelope expands and
cools
• Inert core grows
13
Sub-Giant Branch
• In isothermal core pressure
gradient maintained by
density gradient
• If core too large
cannot support outer layers.
• Core collapses rapidly (KH
scale)
• Gravitational energy expands
envelope
• Temperature decreases
• Sub-Giant Branch
14
Red Giant
• Core collapses
• Compression heats shell
increasing luminosity
• Envelope expands and
cools, H- opacity creates
deep convection
• First dredge-up brings
fusion products to
atmosphere
• Mass loss up to 28%
15
Then What?
• Core does not collapse due to
electron degeneracy pressure
• Quantum effect of Pauli
exclusion principle
• Squeezing electrons into small
space requires occupying
higher energy states
• Produces temperatureindependent contribution to
pressure
16
• This is smaller than thermal
pressure in Hydrogen core
today
• In compressed inert Helium
core degeneracy pressure
stops collapse
Helium Core Flash
• When core temperature
reaches 108K Helium fusion via
triple-α process occurs
explosively in degenerate core
• For a few seconds produce
galactic luminosity absorbed in
atmosphere, possibly leading
to mass loss
• Expands shell decreasing
output
• Envelope contracts and heats
17
Horizontal Branch
• Deep convection rises
• Convective core fusing
Helium to Carbon,
Oxygen
• Shell fusing Hydrogen to
Helium
• Core contracts
• Envelope contracting and
heating
18
Early Asymptotic Giant Branch
• Inert CO core collapses to
degeneracy
• Helium fusion in shell
• Hydrogen shell nearly
inactive
• Envelope expands and cools
• Convective envelope
deepens: second dredge-up
• Mass loss in outer layer
19
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•
•
•
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Thermal Pulse AGB
Hydrogen shell reignites
Helium shell flashes intermittently
Flash expands Hydrogen shell,
luminosity drops and envelope
contracts heats
Hydrogen reignition increases
luminosity envelope expands cools
Convection between shells and deep
convective envelope: third dredge-up
and Carbon stars
Rapid mass loss to superwind
s-process neutron capture
nucleosynthesis produces heavier
elements
The End
• Pulses eject envelope
exposing inert degenerate
CO core
• Initially hot core cools
• Expanding envelope
ionized by UV radiation of
white dwarf glows as
ephemeral planetary
nebula
21
M57
22
23
Ghost of Jupiter
(NGC 3242)
Cat’s Eye
24
Hubble 5
25
NGC-2392 (Eskimo)
26
Clusters and the Model
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•
•
•
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Model predicts how clusters will evolve
Massive stars evolve faster
Later stages of evolution rapid
Can find cluster age from Main-Sequence turnoff
Main Sequence Matching leads to distance:
Spectroscopic Parallax and other cluster distance
measures
Does it Work?
• IC 1795 – OB Association
28
• NGC 2264 8My
Older
• Orion Nebula Cluster 12My
29
• M45 130My
• NGC6494 300My
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And Older
• M44 800My
• M67 3.5Gy
31
Oldest
• M13 12Gy
Blue Stragglers
• Some MS stars found
past turnoff point
• Mechanism:
– Mass Transfer in close
binary
– Collision and Merger
• Likely both
32
Populations
• Astronomers distinguished
Population II from Population I
stars based on peculiar motion
• Differ in metallicity: Population
II metal-poor formed early
• Globular Clusters are
Population II
• Population III: Conjectured
first stars – essentially metal
free
33
• Some Giants and
Hypergiants
exhibit regular
periodic change
in luminosity
• Mira (Fabricius
1595) changes
by factor of 100
with period of
332d
• LPV like Mira not
well modelled
34
Variable Stars
Instability Strip
• A nearly vertical region traversed
by most massive stars on HB
• RR Lyrae: PII HB stars with
periods of hours. Luminosity
varies little (!)
• Cepheids (PI) , W Virginis (PII)
periods of days.
35
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•
•
•
•
•
36
Why They Pulse
Cepheids oscillate in size (radial oscillation)
Temperature and luminosity peak during rapid
expansion
Eddington: Compression increases opacity in
layer trapping energy and propelling layer up
where it expands, releases energy
Problem: compression reduces opacity due to
heating
Solution: compression ionizes Helium so less
heating. Expansion reduces ionization – κmechanism
Instability strip has partially ionized Helium at
suitable depth
•
•
•
Why We Care
Leavitt 1908: Period-Luminosity
Relation for SMC cepheids
Luminous cepheids have longer
periods
With calibration in globular clusters
cepheids become standard candles
• Later: W Virginis PLR less
luminous for same period
37
Discovery
• Bessel 1844: Sirius wobbles: a
binary
• Pup hard to find. Clark 1846
• Orbits:
• Surface Gravity
• Spectrum: Very broad
Hydrogen absorption lines
• Estimate:
• Spectrum (Adams 1915):
• No Hydrogen else fusion
38
Degenerate Matter
• White dwarves are the
degenerate cores of
stars with
• Composition is Carbon
Oxygen
• Masses
• Significant mass loss
39
• Chandrasekhar:
• Relativity:
Mass-Radius
40