Lec 7
II-8c. Late Stages of
Evolution and Death
(Main Ref.: Lecture notes;
Parts of FK Ch. 19 and 20)
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(i) Introduction
When ~ 10 – 30 % of mass in the central core becomes He,
H-burning cannot catch up with energy lost by radiation,
because temperature outside the He core is too low for Hburning (see Fig. II-41). Then, the only other energy
source is gravitational energy through contraction, and so
the star starts to contract again  End of the long,
relatively stable middle-age era as a main sequence (MS)
star.
What happens, afterward, depends on mass. Life after MS (=
post main sequence) is drastically different for massive
stars ( M ≥ ~ 8 M☉) and less massive stars (M ≤ ~ 4
M☉). We will follow the fate of low mass stars first, then
high mass stars. Then discuss the fate of intermediate
mass stars ( ~ 4 M☉ ≤ M ≤ ~ 8 M☉).
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(ii) Low Mass Stars ( M
≤ 4 M☉) (Main Ref.: Class notes; FK Sec.19-1
to 4, 20-1 to 3; CD photos shown in class)
When the contraction proceeds, both density c and temperature
Tc of the central core increases while the core radius Rc decreases.
Since thermal pressure P is proportional to ~ kT, increased
central Tc means increased core Pc, which pushes up the
surrounding envelope  larger size (i.e. larger stellar
radius R) and lower surface temperature Ts.
Note: This process, of contracting core resulting in increased Tc and
decreased Rc, while decreased Ts and increased R, takes place
repeatedly during subsequent evolutionary stages. Note also, that
in the reverse situation, where the central core expands, decreased
Tc and increaded Rc,will result in increased Ts and decreased R.
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That also takes place repeatedly during the evolution.
As the contraction of the core proceeds further and the core
heats up, and when the central Tc reaches ~108 K, it is
sufficiently high to trigger He burning, where He changes
to carbon C and oxygen O (see FK p. 541). This He
burning is called `triple  process’, because He nuclei are
called  particles, and in this process 3 He nuclei combine
to become one C, etc.
By the time He burning starts, the star gets so large that it is called a
`red giant’. Since the He burning can supply new nuclear energy
source to balance the energy lost by radiation, contraction stops, and
the star (as a red giant (RG) and horizontal branch (HB) star) can
exist as a stable star, with an increasing core of C and O. When the
C/O core grows and its mass gets ~ 20%, however, the temperature
of the core boundary gets less than the critical T required for He
burning. So, again due to lack of sufficient nuclear energy source,
contraction resumes, as AGB (asymptotic giant branch) star.
However, about this time, something very important happens in a
low mass star like the sun – called Electron Degeneracy.
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Electron Degeneracy: Degeneracy takes place when density effect gets
larger than temperature effect. When density gets high enough, QM
(quantum mechanics) becomes important – electrons are `quantized’,
i.e., they can take only discrete energy levels. Then, the Pauli
Exclusion Principle forbids more than two electrons to occupy one
energy level. This causes a tremendous pressure – called
`Degeneracy Pressure’. (See class notes for the details.)
In a low mass star, since it is relatively denser and cooler than
more massive hot stars, the density increase due to
contraction is relatively larger than temperature increase 
the result is that the degeneracy pressure of electrons
overtakes thermal pressure of gas. Once that stage is
reached, the electron degeneracy pressure can support the
gravity and so contraction stops. Then, no more contraction
means no more core temperature increase. Without further
increase of core temperature, no more higher-level nuclear
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reactions to `cook’ heavier elements. What happens then?
The story is rather complicated, due to `Helium flash’, etc. The red
giant, after the intermediate stages such as `Horizontal Branch
(HB) Star, Asymptotic Giant Branch (AGB) Star, Planetary Nebula,
finally ends up as White Dwarf. See Fig. II-62 for the structure of
an AGB star.
Note: From the red giant to the planetary nebula stage, a lot of mass is
lost. This is due to instability, pulsation, etc., during the HB and
AGB stages.
A planetary nebula is clouds of gas ejected from the
central star which are illuminated by the central hot UV
star and shine (like an emission nebula).
Enjoy beautiful photos of planetary nebulae in Fig. II-66 and CD
photos shown in class.
(Study class notes and FK 20 -1 through 3, for the details.)
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Fusion of helium into carbon and oxygen begins at
the center of a red giant
Fig. II-61: Stages in Stellar Evolution
•When the central temperature of a red giant reaches about 100 million K,
helium fusion begins in the core
•This process, also called the triple alpha process, converts helium to carbon
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and oxygen
Fig.II-62: Structure of AGB star.
Evolutionary Track on the HR-Diagram:
Although the evolutionary track of a low mass star on the HR diagram is rather
complicated, most parts again can be explained by the Stefan Boltzman
Law, as done for pre-main sequence stars earlier.
L = 4  R2  T4. Eqn(16)
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(See Fig. II-63, and class notes for the details.)
Fig.II-63: Post MS
evolution of
low stars.
low mass
a MS star:
Lifetime: Lifetime of a
red giant tRG is less
than that of main
sequence stars.
Reason: He burning
releases less energy,
and so it takes less time.
Example: Sun tRG ~ 2 x109 years < ~ 1010 years
for MS.
EX 37: Shell of a ~ circular-shaped planetary
nebula (PN) is observed to expand at velocity
of 20 km/sec. The diameter of the shell is 1
ly. How old is this PN?
Ans: 8333 years. Hint: Useful equation is
t = R/V
Eqn(28)
(See class notes for the details.)
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As stars age and become giant stars, they expand tremendously
and they eject matter into space
EX 38b
EX 38b
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Fig. II-64: Red Giant in M50
Fig. II-65: A Mass Loss Star HD 65750
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EX 39
Fig. II-66: Various Planetary Nebulae
Fig. II-67: Formation Mechanism of some planetary
nebulae
(iii) High Mass Stars (M ≥ ~8M☉)
(Main Ref.: Lecture notes;
FK Sec 20-5,6,7,9,10; CD photos shown in class)
When ~ 30% of central mass becomes He, the temperature
at the boundary of the core gets less than ~107 K required for
H burning, and due to lack of nuclear energy source, the star
starts contracting, and as in low mass stars, the core
temperature and density increases while the envelope expands
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and radius increases. When the central temperature Tc
reaches ~ 108 K that is high enough for He burning (triple 
process), which supplies nuclear energy source and so the
contraction stops. The star can exist as a stable (noncontracting) star for a while while He burning continues and
C/O core increases with time, as it happens in low mass stars.
One difference from the low mass case, however, is that
luminosity at this point (start of He burning) is so high that the
star is a red supergiant, not red giant. Another is that He
burning is stable and He flash does not take place. Since the
energy available from He burning is less than H burning, the
energy source is exhausted quickly. What happens next is
very different from the low mass case.
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Degeneracy never happens in high mass stars! Why?.
Reason: High mass stars are hotter and less dense than low
mass stars. Remember that degeneracy takes place when
density effect overtakes temperature effect.
(see class notes for the details.)
What happens next?
In the absence of degeneracy pressure which prevents further
contraction of the core, the core contraction resumes, releasing further
gravitational energy, and the central temperature Tc increases again.
When Tc reaches 6 x 108 K, C (carbon)-burning starts, which
transforms C to Ne (neon). Eventually the Ne core grows in size, and
the boundary temperature gets too low for C-burning. Then
contraction again resumes.
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. This cycle of nuclear fusion involving heavier and heavier elements
involving higher and higher temperatures and gravitational
contraction in between each nuclear fusion with higher levels
continues – after C-burning, Ne and O burning follow, and finally Si
burning produces heavy elements all the way up to Iron (Fe). During
this process various elements from C to Fe are produced. (See class
notes and FK for further details.)
At this point, the central core is made predominantly of Fe,
surrounded by layers of elements, from lighter to heavier, as you go
from surface to center – looking like an onion (see Fig. II-68). This
core, looking like an onion, is only the size of the earth. However, by
this time the envelope expanded to such a huge degree that the radius
of the entire star is as large as Jupiter’s orbit! The core gets denser,
core temperature gets higher, and timescale of each nuclear fusion
gets shorter as it gets to more advanced stages involving heavier
elements. See Table II-6.
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Note: substantial mass loss takes place during the supergiant stages.
Fig. II-68: Structure of pre-supernova high mass star
Table II-6: Post main sequence evolution of massive star
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EX 40
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Fig. II-69: Mass Loss from a Supergiant Star
Fig. II-70: Turbulence in a Supernova
EX 41
Fig. II-71: Cas A Supernova Renmant
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In 1987 a nearby supernova gave us a close-up look
at the death of a massive star
Fig. II-72: SN 1987A
EX 42
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Supernova Explosion: When the nuclear fusion proceeds all the way to
`cooking’ of Fe, and the onion-like structure with an Fe core is
reached, something drastic happens – a supernova explosion! How
does it happen?
Photodisintegration: By this time the central temperature is so high
that heavy nuclei hit by high energy photons (gamama rays)
disintegrate to He nuclei ( particles)- so, photodisintegration.
Core Collapse: Fusion of light elements up to Fe releases nuclear
energy. However, the reverse, from Fe to He, requires energy input.
The only source of such energy input is gravitational energy. So,
catastrophic core collapse – implosion! Also, in the central core
efficient production of neutrinos takes place. The escaping neutrinos
carry energy – need more energy input  accelerates collapse
further!
Birth of a Neutron Star: When the collapsing core reaches nuclear
density (N = 4 x 1017 kg/m3), the core is predominantly made of
neutrons. These neutrons are degenerate and the degenerate pressure
of neutrons can support the core, and so it gets suddenly very stiff,
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and further contraction stops  birth of a neutron star!
Core Bounce: Due to the sudden stopping of collapse the core bounces
back.
Explosion: The sudden core bounce sends powerful wave of pressure,
which ejects the outer envelopes  supernova explosion! The
ejected envelopes travel fast – when the speed gets faster than the
sound speed shocks form. Shocked ejected material and interstellar
medium emit a lot of light (radio to gamma rays)
 supernova remnants as nebulae, e.g. the Crab Nebula.
See class notes and FK for further details. Enjoy CD photos shown in
class and in Fig. II-71, 72.
Why nuclear fusion stops at Fe? Because `cooking’ of elements
heavier than Fe from Fe requires extra energy. See class notes with
BE/A vs A diagram, for the reason.
Then how are these elements heavier than Fe formed? This
belongs to nuclear physics – beyond the level of ASTR 373. There
are r(rapid)-process, n(neutron)-process, s(slow)-process, etc.,21
through which these very heavy elements are formed.
Note: 10M☉ (main sequence) star: final collapsed core is a ~ 1.4M☉
neutron star. The rest, 8.6M☉, is ejected and becomes an extended
supernova remnant, as the surrounding nebula.
Note: White dwarfs, made from low mass stars, are supported by
degenerate pressure of electrons. Neutron stars are supported by
degenerate pressure of neutrons. Neutron degenerate pressure is
much larger than electron degenerate pressure, since neutron mass is
~2000 times larger than electron mass.
Bith of a Black hole: When original M > ~ 25M☉, even neutron
degenerate pressure cannot support the collapsed core, so the
collapse continues indefinitely
 Birth of a black hole!
See class notes and later sections for further details.
(iv) Intermediate Mass Stars ( 8M☉> M > ~ 4M☉)
(Main
Ref.: Lecture notes)
Hard to calculate evolution of intermediate mass stars due to various
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complications such as instability, mass loss, etc., which become even
more serious than for low mass stars. One thing sure appears to be that in
most cases, due to larger mass and higher temperature involved in the
central core, in these stars nuclear fusions of higher levels can proceed,
before degeneracy stops further gravitational contraction before they go
all the way to creation of an iron core and catastrophic explosion. So
most of them probably will go through the planetary nebula stage and
eventually end up as white dwarfs. However, before the degeneracy sets
in finally in the core, elements heavier than C and O would be
synthesized. So, their core will consist of elements heavier than C and O,
e.g., Mg, Si, but not Fe.
However, some calculations show that some of these stars on the heavier
side, near 8M☉, may manage to become a supernova, but it will be all
explosion, with no collapsed core left. I mean, all matter is ejected.
So far, we covered evolution of isolated stars. The evolution of binary
stars is far more complicated. Due to lack of time I will not cover that
topic, but one section of FK devotes to this topic.
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(v) Late Stages of Stellar Evolution - Summary
Fig. II-73: Pathways of Stellar Evolution
Horizontal branch star
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Fig. II-74: PostMain Sequence
Evolution of Stars
in HR Diagram
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II-8d. Stellar Cluster Evolution (Main Ref.: Lecture notes; FK
18-6,19-4, 20-1)
Star Clusters:
Stellar Association: Youngest, mostly bright, high mass, hot O and
B stars – called O, B associations. Gravitationally unbound,
mostly moving away from each other right after birth. Not many,
extended.
Open Clusters (= Galactic Cluster): Relatively young, high mass,
bright O,B stars. Gravitationally only loosely bound, relatively
young. Not as many and densely populated as globular clusters.
More extended than globular clusters.
Examples: Pleiades, NGC 2264.
Globular Clusters: No bright, high mass hot stars – they have
already evolved away. Brightest stars are red giants. Very old, (1 –
2) x 1010 years, ~ spherical, tightly bound and compact ~ 100 pc.
Many stars ~ 106 stars.
Example: M10
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Enjoy pretty pictures in II-75 and CD photos shown in class!
EX 43
Fig. II-75a: Young Cluster NGC 2264
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EX 44
Fig. II-75b: Open Cluster Pleiades
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EX 45
Fig. II-75c: Globuler Cluster M10
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Fig. II-76: HR Diagram of a Globular Cluster
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Fig. II-77: HR Diagram of Clusters
Cluster Evolution:
Stars in clusters are born at the same time. So, by looking at
and studying carefully the distribution of stars in clusters
on the HR Diagram, you can find the evolution and
approximate age of the cluster! The best way to
demonstrate this is by examples.
See Fig II-78 and class notes for the details.
As a cluster ages, the main sequence is “eaten away” from
the upper left as stars of progressively smaller mass evolve
into red giants
• So, the cluster’s age is equal to the age of the main-seq
uence stars at the turnoff point (the upper end of the
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remaining main sequence)
Fig II-78: the Evolution of a Theoretical Cluster
supergiants
supergiants
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Fig II-78: (conti.)
EX 46: M55: Globular cluster,Very old!. Why?
See Fig. II-79b and class notes.
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Age of Clusters:
How to estimate the age of a cluster from the HR Diagram of the
cluster? Best way to demonstrate is by examples
– see class notes for the details!
EX 47: How old is h &  Persei?
Ans: ~ 107 years
EX 48: How old is M41?
Ans: ~ 2 x 108 years
EX 49: How old is M67?
Ans: ~ 8 x 109 years
EX 50: Roughly how many times older is M3 cluster than
h &  Persei?
Ans: M3 ~ 700 times older.
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Fig II-79a: HR Diagram of Many Stars
Fig II-79b: M55 in HR Diagram
Fig. II-80: Age of Clusters
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