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The Sun and the Stars
The Sun and the Stars
Dr Matt Burleigh
The Sun and the Stars
Stellar evolution
i) Stellar birth
HST image of The Eagle nebula, a stellar nursery
Stars appear to be born in groups – why?
Dr Matt Burleigh
The Sun and the Stars
Consider giant molecular cloud (H2 region), with mass M, radius R, no. of particles N,
of average mass m, at temperature T
The potential energy of the cloud U, is given by
U  const
GM ( Nm )
R
The total kinetic energy (KE) of the particles in the cloud is,
KE 
3
NkT
2
For collapse, U  KE
GMNm
 NkT
R
So,
 kT 
MJ  
R
 Gm 
Alternatively, this can be written in terms of the
Jeans density, J, where J is given by
æ kT ö 3 1
rJ > ç
÷
è Gm ø pM 2
So for collapse require low temperatures,
and large masses
Where MJ is the Jeans mass
Dr Matt Burleigh
The Sun and the Stars
Molecular cloud (H2 region) collapses under its own self-gravity
(free-fall  internal pressure zero, no collisions)
NB fragmentation likely.
[Exact trigger unknown - possibly density inhomogeneities
shocks (SN), winds etc.]
As cloud collapses, PE converted into KE+ radiation
in roughly equal proportion
Collapse continues provided:
 KE dissipated
 Radiation escapes
If these conditions satisfied, gas remains cool, pressure
remains low, collapsing material is a Protostar
Collapse continues until density of core high enough that
  1, core optically thick.
Radiation trapped, core heats up, collapse stalls.
Hydrostatic equilibrium established. Star is now a
Pre-Main Sequence star
Dr Matt Burleigh
Cloud Collapse
Dr Matt Burleigh
The Sun and the Stars
Stellar birth cont’d
PMS fully convective
Because T low, opacity high, PMS star is fully convective
L~30xLsun
Heat transported rapidly to surface, R is large, therefore
L is large (30xLsun, point B on next page)
PMS contracts slowly, core heats up, but T(sfce)constant
L decreases slowly (point C). As core Temp rises opacity
decreases, radiation becomes increasingly dominant transport
mechanism and moves outward slowly from core.
Once radn transport exceeds convection, sharp kink to left
on H-R diagram (point D)
Eventually T core high enough (few million K) that nuclear
fusion dominates energy production. Hydrostatic equilibrium now
maintained by fusion, star stops contracting. Star is now a
Zero Age Main Sequence Star (ZAMS) E. Star radiative in core,
convective in outer layers.
Takes ~20 million years to reach ZAMS from initial collapse.
PMS slowly contracts
core heats up
opacity drops
radiative transport in core
convection in outer layers
radiative transport dominates
T> few million K
fusion maintains HE
contraction halted
ZAMS star
A solar mass star will spend approx 10 billion years on main sequence
quietly converting H  He in the core via the PP-chain.
Dr Matt Burleigh
The Sun and the Stars
Evolutionary track for a PMS star
A core has developed
B PMS fully convective (L~30xLsun)
C core contracts without change in Tsfce
D radiative transport dominates
E T> few million K (TNR)
contraction halted
ZAMS star
It takes approximately 20 million years from the initial collapse for star to join main sequence
Dr Matt Burleigh
Star Formation
Dr Matt Burleigh
Star Formation
Dr Matt Burleigh
Star Formation
Dr Matt Burleigh
Star Formation
Dr Matt Burleigh
Stellar Lifecycle
Dr Matt Burleigh
The Sun and the Stars
Mass-luminosity relation
Eddington 1924 - for stars on the main sequence, a graph of mass versus luminosity
follows a power-law, with slope   3
L
 M 


Lsun  Msun 

In fact =2.3 for dim red stars, and breaks to =4 for more luminous stars, at a mass of 0.43 Msun.
This break in slope reflects
(i) differences in stellar interiors
(ii) changes in opacity with temperature
Dr Matt Burleigh
The Sun and the Stars
Stellar lifetimes
M-L relationship for main-sequence stars
æ M ö
L
µç
÷
Lsun è Msun ø
3.3
Stellar lifetime depends on its mass M, and the rate at which it consumes fuel,
ie its’ luminosity L.
Therefore a stars lifetime t, relative to the suns lifetime tsun,
æ M ö æ M ö
ç
÷ ç
÷
-2.3
t
è Msun ø è Msun ø æ M ö
=
=
=
ç
÷
tsun æ L ö æ M ö3.3 è Msun ø
ç
÷ ç
è Lsun ø è Msun ÷ø
So, more massive stars have shorter lifetimes!!
Dr Matt Burleigh
The Sun and the Stars
Stellar evolution I – evolution of 1 solar mass star (pop I)
After 10 billion years, most of
Hydrogen in core exhausted
 core mostly He.
Log(L/Lsun)
PN ejected
to WD
during this time, T (core) has increased slightly and
star has expanded slightly, luminosity increases
A-B Once hydrogen in core used up thermonuclear
reactions in core cease. Drop of pressure in core
causes core to contract. Surrounding H is pulled
into core region and raised in temperature. Burning
occurs in H-shell around He core. Burnt H added to
core, whose density increases
B-C Core contracts when too much material has
been added to it. Energy generation in shell
accelerates. Envelope must store more energy,
and so it expands
 radius of star increases, surface temperature
decreases. (moves to right on H-R diagram)
Thermal Pulse begins
4
AGB
E
2
He
Helium Flash
D
C+O
RGB
H
B
0
WD
cooling
4.2
He
C
A
3.8
3.4
Log Teff (K)
Dr Matt Burleigh
The Sun and the Stars
Stellar evolution I – evolution of 1 solar mass star
Log(L/Lsun)
PN ejected
to WD ~0.65Msun
C-D Lower T  higher opacity, energy carried by
convection. Radius of star increases, surface
temperature decreases further. Heat transport
dominated by convection, v efficient. Luminosity
increases rapidly
Thermal Pulse begins
4
AGB
E
2
He
C+O
RGB
star moves up Red Giant Branch – winds remove a
fraction of star’s atmosphere
Core continues to contract
Helium Flash D
H
B
0
WD
cooling
He
C
A
When T reaches 100 million K , Helium burning
occurs (triple-alpha process)
4.2
4
He  4He  8Be  
8
Be  4He12C  
3.8
Lighter elements are rare because they quickly combine with H to produce He nuclei, eg.
3.4
Log Teff (K)
7
Li  1H 2 4 He
Dr Matt Burleigh
The Sun and the Stars
D Heat spreads rapidly through core.
Triple-alpha reaction rate increases due to
increased temperature, increases
energy and hence temperature….
thermal runaway (Helium flash – heat spreads
throughout core in few minutes, 60-80% He burnt
at this stage)
Log(L/Lsun)
PN ejected
to WD
Thermal Pulse begins
4
AGB
E
2
He
Core pressure increases, core expands and cools.
He core burning temporarily ceases
D-E Outer envelope and core contracts under gravity
 luminosity decreases, but surface temperature increases
Star moves down and to left on HR diagram.
When core temperature sufficiently high core helium reignites
E Star burns He in core and H in layer around core (Subgiant)
Helium FlashD
C+O
RGB
H
0
B
WD
cooling
4.2
He
C
A
3.8
3.4
Log Teff (K)
Once core converted to C, core contracts again,
burning layer of He around core, forces star to expand,
star again becomes a giant. Star moves up Asymptotic Giant
Branch (AGB).
Triple alpha-reaction v. sensitive to temperature, star becomes
unstable – thermal pulses.
Dr Matt Burleigh
The Sun and the Stars
Thermal pulses – core contracts, causes burning shell around core to heat up, heats outer layers
which expand and therefore cool, energy generation drops, core contracts…cycle repeats
Thermal pulses (every few thousand years) cause luminosity to vary by up to 50% on timescales
of a few years. Energy transported rapidly to surface by convection
Star develops super wind removing outer layers, exposing core
Wind driven material form Planetary nebula (ionised by core). Core cools as a white dwarf.
Dr Matt Burleigh
Evolutionary phases of a solar mass star, post main-sequence
H-R position
Stage
Physical processes
ZAMS
Core hydrogen burning begins
A
Evolution on mainsequence
Core hydrogen burning ceases; shell
hydrogen burning begins
A-B-C
Evolution off mainsequence
Shell hydrogen burning continues;
convection dominates energy transport
C-D
Red giant
Helium flash occurs; core helium burning
begins
E
Subgiant
Core helium burning continues along with
shell hydrogen burning
Red giant again (AGB)
Thermonuclear reactions then end; shell
helium and hydrogen burning continues
Planetary nebula
Star enters the planetary nebula stage
White dwarf
All thermonuclear reactions stop; slow
cooling
Dr Matt Burleigh
End of Main Sequence
Dr Matt Burleigh
The Sun and the Stars
Example planetary nebulae – note WD at centre of nebulae
Dr Matt Burleigh
Population I Stars





Typical stars are young, in galactic spiral arms where
gas and dust found
Typically reside in open star clusters
~2% of mass elements heavier than H or He (ISM
enriched by supernovae)
If M* a little > M energy generation is by CNO cycle
Sun is population I
Dr Matt Burleigh
Population II Stars





First stars to be formed in Universe
Have only 0.01% heavy elements
Typically found in galactic bulge and globular
clusters
Similar sequence of evolution but occupy different
region of H-R diagram during core He burning
Significant temperature changes, heating and then
cooling
Dr Matt Burleigh