Transcript PHYS3380_110215_bw - The University of Texas at Dallas

PHYS 3380 - Astronomy
The second exam will be next Monday, November 9 at the
regular class time. It is closed book but you may bring in
one 8 1/2 X 11 inch “cheat sheet” with writing on both
sides. It will cover everything I have covered in class up
through last Wednesday’s class (excluding what I
covered on the first exam – i.e., starting with the class on
9/28/15). It will not cover anything from today’s or
Wednesday’s class. The homework solutions up to
assignment #8 are already on line. The solutions to the
homeworks will be on line after Wednesday’s class
PHYS 3380 - Astronomy
The Source of Stellar Energy
Recall from our discussion of the sun:
Stars produce energy by nuclear fusion of hydrogen into helium.
In the sun, this
happens primarily
through the
proton-proton
(PP) chain
PHYS 3380 - Astronomy
The CNO Cycle
In stars slightly more
massive than the sun,
a more powerful
energy generation
mechanism than the
PP chain takes over:
The CNO Cycle.
Highly temperature
dependent
PHYS 3380 - Astronomy
Energy Transport Structure
Inner convective,
outer radiative zone
Inner radiative,
outer convective
zone
CNO cycle dominant
PP chain dominant
PHYS 3380 - Astronomy
Summary: Stellar Structure
Convective Core, radiative
envelope;
Energy generation through
CNO Cycle
Sun
Radiative Core, convective
envelope;
Energy generation through PP
Cycle
Convection and the CNO Cycle
• As a result of the extreme temperature dependence of CNO burning, those
stars that are dominated by CNO fusion have very large values of L/4πr2 in the
core. This results in convective instability and convective energy transport is
extremely efficient.
• Because of the extreme temperature sensitivity of CNO burning, nuclear
reactions in high mass stars are generally confined to a very small region,
much smaller than the size of the convective core.
PHYS 3380 - Astronomy
Schwarzschild criterion
The conditions under which a region of a star is unstable to convection is
expresses by the Schwarzschild criterion:

dT
g

dZ C p
where g is the gravitational acceleration, and Cp is the heat capacity.
A parcel of gas that rises
slightly will find itself in an environment of lower
pressure than the one it came from. As a result, the parcel will expand and cool.
If the rising parcel cools to a lower temperature than its new surroundings, so
that it has a higher density than the surrounding gas, then its lack of buoyancy
will cause it to sink back to where it came from. However, if the temperature
gradient is steep enough (i. e. the temperature changes rapidly with distance
from the center of the star), or if the gas has a very high heat capacity (i. e. its
temperature changes relatively slowly as it expands) then the rising parcel of
gas will remain warmer and less dense than its new surroundings even after
expanding and cooling. Its buoyancy will then cause it to continue to rise. The
region of the star in which this happens is the convection zone.
Convection and Size
•In stars more than 1.3 times the mass of the Sun, the nuclear fusion of
hydrogen into helium occurs via CNO cycle instead of the proton-proton
chain. The CNO process is very temperature sensitive, so the core is very
hot but the temperature falls off rapidly. Therefore, the core region forms a
convection zone that uniformly mixes the hydrogen fuel with the helium
product. The core convection zone of these stars is overlaid by a radiation
zone that is in thermal equilibrium and undergoes little or no mixing.
•In stars of less than about 10 solar masses, the outer envelope of the star
contains a region where partial ionization of hydrogen and helium raises the
heat capacity. The relatively low temperature in this region simultaneously
causes the opacity due to heavier elements to be high enough to produce a
steep temperature gradient. This combination of circumstances produces
an outer convection zone, the top of which is visible in the sun as solar
granulation. Low mass main sequences of stars, such as red dwarfs are
convective throughout and do not contain a radiation zone.
As the stellar mass increases, so does the size of the convective core (due
again to the large increase in ε with temperature). Supermassive stars with
M≈100M would be entirely convective.
PHYS 3380 - Astronomy
Low-Mass Star Evolution
H-burning continues in a shell around the core,
and as T increases, the CNO process can
occur in the shell
As CNO T17 energy generation is concentrated
in the regions of highest T and highest H
content (in shell T ~ 20 x106 K):
This high T causes high P outside the core and the H
envelope expands.
- expansion becomes more pronounced when
>10% of the stellar mass in the He core.
This early expansion terminates the main-sequence
lifetime
Luminosity remains approximately constant - Teff must
decrease, star moves right along the red subgiant
branch.
Subgiant
branch
Solar Composition Change
Theoretical estimates of the
changes in a Sun-like star’s
composition. Hydrogen and
helium abundances are shown (a)
at birth, just as the star arrives on
the main sequence; (b) after five
billion years; and (c) after 10
billion years. At stage (b) only
about five percent of the star’s
total mass has been converted
from hydrogen to helium. The
change speeds up as the nuclear
burning rate increases with time.
PHYS 3380 - Astronomy
Expansion onto the Giant Branch
The shell source slowly burns,
moving through the star, as the
He core grows.
- the star expands and its
surface cools during the
phase of an inactive He core
and a H-burning shell
But the star cannot expand and
cool indefinitely.
The Sun will
expand
beyond
Earth’s orbit.
When the temperature of the
outer layers reach <5000 K the
envelopes become fully
convective. This enables greater
luminosity to be carried by the
outer layers and hence quickly
forces the star (< ~8 M) almost
vertically in the HR diagram - the
star becomes a red giant
PHYS 3380 - Astronomy
Degenerate Matter
Star expands but He core continues to contract
- core is not producing energy - temperature
not high enough for He fusion
- not enough thermal pressure to resist and
balance gravity
- continues to contract until it becomes
degenerate
Gas so dense, lower energy levels filled - only
two electrons per level- Pauli Exclusion Principle
- max occupancy of phase space volume of
phase space cell dxdydzdpxdpydpz=h3
- so in [p,p+dp] 4dpdV/h3 cells each with
max occupancy of 2e- (spin ,)
Resists compression - electrons can not be
packed arbitrarily close together and have small
energies - independent of temperature
Temperature defined mainly by the energy
distribution of the heavy particles (He nuclei) gravitational collapse is resisted by electron
degeneracy pressure.
PHYS 3380 - Astronomy
Red Giant Evolution
H-burning shell
keeps dumping He
onto the core.
4 H → He
He
He-core gets denser
and hotter until the
next stage of nuclear
burning can begin in
the core:
He fusion
through the
“Triple-Alpha
Process”
4He
+ 4He  8Be + 
8Be
+ 4He  12C + 
PHYS 3380 - Astronomy
Helium Fusion
For T~108K, triple- reactions start in the very dense core. They generate
energy, heating core, and KE of He nuclei increases, increasing the energy
production. Energy generation and heating under degenerate conditions core doesn’t expand, reactions go faster, generates more energy, raises
temperature, reactions go faster - leads to runway - the He Flash - core can
generate more energy than an entire galaxy. Stars more than ~3 M don’t
become degenerate - start burning He without He flash.
PHYS 3380 - Astronomy
Red Giant Evolution
(3 solar-mass star)
• Core T rises until core no longer
degenerate - pressure from He
fusion causes core to expand absorbs energy used to support
outer envelope
• Outer layers contract - surface
heats up, luminosity decreases
C,
O
Inactive
He
• Star stabilizes - He burning
period similar to main phase H
burning - luminosity stabilizes but
surfaces heats up
• As a byproduct, some O is
produced:
12C
+ 4He  16O + 
• Inert C and O core created He/H burning shells - outer layers
expand again - surface T
decreases
PHYS 3380 - Astronomy
The Asymptotic Giant Branch
The core will soon consist only of C+O, and
in a similar way to before, the CO-core
grows while a He-burning shell source
develops.
These two shell sources force expansion of
the envelop and the star evolves up the red
giant branch a second time - this is called
the asymptotic giant branch.
For high metallicity stars, the AGB coincides closely with the first
RGB.
For globulars (typical heavy element composition 100 times lower
than solar) they appear separated.
PHYS 3380 - Astronomy
Red Dwarfs
Stars with less
than ~ 0.4 solar
masses are
completely
convective.
Consume H slowly - long lifetimes - longer than the age of
the universe
 Hydrogen and helium remain well mixed throughout the
entire star.
 No phase of shell “burning” with expansion to giant.
Star not hot enough to ignite He burning.
PHYS 3380 - Astronomy
Sunlike Stars
Sunlike stars (~
0.4 – 4 solar
masses) develop
a helium core.
 Expansion to red giant during H burning shell phase
 Ignition of He burning in the He core
 Formation of a degenerate C,O core
PHYS 3380 - Astronomy
Evolution of Massive Stars (> 8 M)
The electrons in their cores do not become degenerate until the final burning stages,
when iron core is reached.
Mass-loss plays an important role in the entire evolution
The luminosity remains approximately constant in spite of internal changes. The
track on the HRD is therefore horizontal - star becomes a supergiant.
For a 15-25M star there is a gradual redwards movement. But for higher mass (or
stars with different initial compositions) the star moves back and forth between low
and high effective temperatures as it burns successively higher mass elements
PHYS 3380 - Astronomy
From He Burning to Core-Collapse
•
•
•
•
•
•
The He burning core is surrounded by a H-burning shell
The triple- process liberates less energy per unit mass than for H-burning
(~10%). Hence the lifetime is shorter, again around 10%
There is no He-flash as densities in the He-core are not high enough for
electron degeneracy.
Star has a core of 12C and 16O, surrounded by He and H burning shells.
The core will again contract and the temperature will rise, allowing C and O
burning to Mg and Si.
This process continues, with
increasing Z, building up heavier and
heavier elements until the iron group
elements of Ni, Fe and Co are
formed. The core is surrounded by a
series of shells at lower T, and lower 
PHYS 3380 - Astronomy
Major Nuclear Burning Processes
Common feature is release of energy by consumption of nuclear fuel. Rates of
energy release vary enormously.
Nuclear
Fuel
Process
Tthreshold
106K
Products
Energy per nucleon (Mev)
H
PP
~4
He
6.55
H
CNO
15
He
6.25
He
3
100
C,O
0.61
C
C+C
600
O,Ne,Ma,Mg
0.54
Ne
Ne+Ne
1000
O,Mg
~0.4
O
O+O
1500
S,P,Si
~0.3
Si
Alpha
3000
Co,Fe,Ni
<0.18
PHYS 3380 - Astronomy
Fusion Into Heavier Elements
Fusion into heavier
elements than C, O:
requires very high
temperatures; occurs only in
very massive stars (more than
8 solar masses).
PHYS 3380 - Astronomy
The Life “Clock” of a Massive Star (> 8 Msun)
Let’s compress a massive star’s life into one day…
H  He
11 12 1
Life on the Main
Sequence
10
9
2
+ Expansion to Red
Giant: 22 h, 24 min.
8
4
3
7
6
5
H burning
H  He
He  C, O
He burning:
(Red Giant
Phase) 1 h, 35
min, 53 s
11 12 1
10
9
2
8
4
3
7
6
5
PHYS 3380 - Astronomy
The Life “Clock” of a Massive Star (2)
H
He
He  C, O
C  Ne, Na, Mg,
O
C burning:
6.99 s
H
HeO
He  C,
11 12 1
2
10
3
9
4
8
7 6 5
C  Ne, Na, Mg, O
Ne  O, Mg
Ne
burning:
6 ms
23:59:59.996
PHYS 3380 - Astronomy
The Life “Clock” of a Massive Star
H
HeO
He  C,
C  Ne, Na, Mg, O
Ne  O, Mg
O  Si, S, P
O burning:
23:59:59.99997
3.97 ms
H
HeO
He  C,
C  Ne, Na, Mg, O
Ne  O, Mg
O  Si, S, P
Si  Fe, Co, Ni
Si burning:
0.03 ms
The final 0.03
msec.
PHYS 3380 - Astronomy
Summary of Post Main-Sequence Evolution of Stars
Supernova
Evolution of 4
- 8 Msun stars
is still
uncertain.
Fusion
proceeds;
formation
of Fe core.
M > 8 Msun
Fusion
stops at
formation of
C,O core.
M < 4 Msun
M < 0.4 Msun
Mass loss in
stellar winds
may reduce
them all to <
4 Msun stars.
Red dwarfs:
He burning
never ignites
PHYS 3380 - Astronomy
Mass Loss From Stars
Stars like our sun are constantly losing mass in a stellar wind
( solar wind).
The more massive the star, the stronger its stellar wind - our
Sun loses mass at 0.001 M per billion years
Large radiation pressure of red giant
drives mass-loss - particles absorb
photons from radiation field accelerated out of the gravitational
potential well.
- observations of red giants
and supergiants are in the
range 10-9 to 10-4 M yr-1
WR 124
PHYS 3380 - Astronomy
Mass-Loss from High Mass Stars
Large amount of evidence now that high
mass stars loose mass through a strong
stellar wind.
• The winds are driven by radiation
pressure - UV photons from a hot, very
luminous star absorbed by the optically
thick outer atmosphere layers.
• atmosphere is optically thick at the
wavelength of many strong UV
transitions (resonance transitions) of
lines of Fe, O, Si, C (and others).
• photons absorbed, imparting
momentum to the gas and driving an
outward wind.
• measured in O and B-stars, and leads
to (terminal) wind velocities of up to
4000 km/s and mass-loss rates of up to
5 x 10-5 M yr-1
Huge effect on massive stellar
evolution - the outer layers are
effectively stripped off the star.
PHYS 3380 - Astronomy
Mass-loss is generally classified into two types of wind:
1. Stellar wind: described by empirical formula, linking mass, radius,
luminosity with simple relation and a constant from observations. Typical
wind rates are of order 10-6 M yr-1

M 1013
L R M0
L0 R0 M
M 0 yr -1
2.A superwind: a stronger wind, leading to stellar ejecta observable in shell
surrounding central star
- periodiceruptions called thermal pulses can eject large amounts of
mass
- triple  process very temperature sensitive ( T30)
- makes He-fusion cell very sensitive to temperature - unstable leads to sudden eruptions that lift outer layers of star and drives gas
from surface
Mass loss can be as much as 10-5 M yr-1 - 8 M star can reduce mass to
3 M in just 500,000 years
Existence of superwind suggested by two independent variables
- the high density observed within the observed shells in stellar ejecta
- relative paucity of very bright stars on the AGB - expected compared to
observed is >10
So superwind causes envelope ejection - cores evolve into C-O white dwarfs.
- Core mass at tip of AGB ~0.6 M - close to mass of most white dwarfs.
PHYS 3380 - Astronomy
Age and Metallicity
Two of the fundamental properties of stars that we can measure –
age and chemical composition
Composition parameterised with
X,Y,Z  mass fraction of H, He and all other elements
e.g. X = 0.747 ; Y = 0.236 ; Z = 0.017
Note – Z often referred to as metallicity
Would like to studies stars of same age and chemical composition
– to keep these parameters constant and determine how models
reproduce the other observables
PHYS 3380 - Astronomy
Evidence for Stellar Evolution: Star Clusters
We observe star clusters
• Stars all at about the same
distance
• Dynamically bound
• Same age
• Same chemical composition
Can contain 103 –106 stars
NGC3603 from Hubble Space Telescope
Have wide range of masses can be used test our
understanding of stellar
evolution.
PHYS 3380 - Astronomy
HR Diagram of a Star Cluster
Stellar clusters large
group of stars born at
same time, age of cluster
will show on HR-diagram
as the upper end, or turnoff of the main-sequence.
We can use this as a tool
(clock) for measuring age
of star clusters. Stars
with lifetimes less than
cluster age, have left
main sequence. Stars
with main-sequence
lifetimes longer than age,
still dwell on mainsequence.
PHYS 3380 - Astronomy
Estimating the Age of a Cluster
The lower on
the MS the
turn-off
point, the
older the
cluster.
PHYS 3380 - Astronomy
Example: HR diagram of the Globular Star Cluster M 55
Horizontal
branch
High-mass stars
evolved onto the
giant branch
Turn-off point
Low-mass stars still
on the main
sequence
PHYS 3380 - Astronomy
Star Clusters
NGC3293 - Open cluster
47 Tuc – Globular cluster
10 - 1000 stars
About 25 pc in diameter
Open, transparent
appearance - stars are not
crowded together
105 - 106 stars
10 - 30 pc in diameter
Nearly spherical and much
closer together than open
clusters
PHYS 3380 - Astronomy
Open Cluster HRD
•MS turn off point varies massively,
faintest is consistent with globulars
•Maximum luminosity of stars can
get to Mv-10
•Very massive stars found in these
clusters
Globular Cluster HRD
•MS turn-off points in similar position.
Giant branch joining MS
•Horizontal branch from giant branch to
above the MS turn-off point
•Horizontal branch often populated only
with variable RR Lyrae stars
PHYS 3380 - Astronomy
Open vs. Globular Clusters
Differences are interpreted due to age – open clusters lie in the disk of the
Milky Way and have large range of ages. The Globulars are all ancient,
with the oldest tracing the earliest stages of the formation of Milky Way (~
12 109 yrs)
Globular clusters are old and
metal poor - produce a horizontal
branch
• Mass-loss dependent on
metallic content - drives
bluewards evolution
Open clusters are metal rich produce a red clump
• More metal rich stars
appear towards red
• Clump stars  extreme red
end of HB
PHYS 3380 - Astronomy
PHYS 3380 - Astronomy
Modelling star clusters
Best way to check stellar evolutionary calculations
is to compare calculated and observed tracks. But
can’t observe stars as they evolve - need to use
star clusters.
Isochrones:
A curve which traces the properties of stars as a
function of mass for a given age.
Be clear about the difference with an evolutionary
track - which shows the properties of a star as a
function of age for a fixed mass.
Isochrones are particularly useful for star clusters all stars born at the same time with the same
composition. Consider stars of different masses
but with the same age . Make a plot of Log(L/L)
vs. LogTeff for an age of 1Gyr. The result is an
isochrone.
Important - When we observe a cluster, we are seeing a “freeze-frame” picture at a
particular age. We see how stars of different masses have evolved up to that fixed
age (this is not equivalent to an evolutionary track).
PHYS 3380 - Astronomy
NGC6231 young cluster
Age~ 6Myrs
47 Tuc : globular cluster. Age=
8-10Gyrs
Pleiades young open cluster
Age~ 100Myrs
NGC188: old open cluster .
Age= 7Gyrs