Transcript Slide 1

HW #13
read 9.4-end
Questions 9.9, 9.13,9.14
Problems 9.7,9.8,9.9,9.11
extra time due next Thursday!
We are proceding to
CHap 10 stellar old age
chap 11 The death of high mass stars
Contraction of Giant Molecular Cloud Cores
Horse
Head
Nebula
• Thermal Energy (pressure)
• Magnetic Fields
• Rotation (angular momentum)
• Turbulence
 External
trigger required to
initiate the collapse of clouds
to form stars.
Sources of Shock Waves
Triggering Star Formation
d) Spiral arms
in galaxies like
our Milky Way:
Spirals’ arms
are probably
rotating shock
wave patterns.
Protostars
Protostars =
pre-birth
state of
stars:
Hydrogen to
Helium fusion
not yet
ignited
Still enshrouded in opaque “cocoons” of dust =>
barely visible in the optical, but bright in the infrared.
Heating By Contraction
As a protostar contracts, it heats up:
ZAMS LINE
From Protostars to Stars
Star emerges
from the
enshrouding
dust cocoon
Ignition of H
 He fusion
processes
Globules
Bok
Globules:
~ 10 to
1000
solar
masses;
Contracting
to form
protostars
Globules (2)
Evaporating Gaseous
Globules (“EGGs”): Newly
forming stars exposed by
the ionizing radiation from
nearby massive stars
The Source of Stellar Energy
QUICKY REVIEW
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
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.
Flow of energy
Stellar Structure
Energy transport
via convection
Sun
Energy transport
via radiation
Energy
generation via
nuclear fusion
Basically the same
structure for all stars
with approx. 1 solar
mass or less.
Temperature, density
and pressure decreasing
Hydrostatic Equilibrium
Gravity, i.e. the
Imagine a star’s
interior composed of
individual shells.
Within each shell, two forces
have to be in equilibrium with
each other:
weight from all
layers above
Outward pressure
from the interior
In building computer simulations of Stars we make
Assumptions as our first approach.
1. The Stars are spheres
2. Temperature, density and composition are spherically
symmetric. IE. They depend only on the distance, r, from the
center.
Consider the shell at radius r with density r(r) then the amount of mass in this shell is
dM = r (r) dV but dV = 4pr2 dr why??? dM = 4pr2 r (r) dr { eq. 9.32b}
dM/dr= 4pr2 r (r) {9.33}=MASS CONTINUITY
r
Furthermore M(r) = 4p
0
r(r’) r’2 dr’ The total mass within a radius r!
Hydrostatic Equilibrium (2)
Outward pressure force must exactly balance the
weight of all layers above everywhere in the star.
This condition uniquely determines the interior
structure of the star.
Consider in dr a cylinder, blown up here!
FB
r
dr
FG
FB the buoyant force is balanced by FG gravitational
Pull of mass within (M(r) )
FB is due to the pressure difference on the cylinder!
Hydrostatic equilibrium FG
+FB =0
P (r+dr)dA
Hydrostatic Equilibrium 3
First, we consider cylinder with mass dm =r (r )dV=r ( r) drdA
From Physics we know F = PA
dP =P(r+dr) –P(r) in the usual calculus manner
P (r)dA
Hence FB =P( r) dA – P(r+dr) dA  FB = -dPdA…..why -? EQ 40
FG =-GM(r) dm /r2= -[GM( r)/r2 ] r ( r) drdA eq 37
Using HE  FG +FB =0 and equations 37 and 40 we get
the equation of Hydrostatic Equilibrium(43)
dP/dr = -[GM (r ) /r2] r ( r)
Example 9.4..assume Sun has constant density r integrate 43 from 0 to R
(solar radius) And Pressure from Pc(at center) to 0 at the surface we get an
estimate for the central pressure in The Sun at 1 x 1016 which is 20 times too
small with more sophisticated models
Check out this problem ..be able to do it..
Energy Transport Structure
Inner convective,
outer radiative
zone
Inner radiative,
outer convective
zone
CNO cycle dominant
PP chain dominant
Building Computer Models
We make various assumptions (hope intelligent) about the nature of the material, how
energy is Created and Transported and use the equilibrium equation to build computer
Models of stable stars.
For example if we assume the star is an ideal gas you may have learned that
PV=nRT conects P, V and T…we use a variation of this
Equation of State for an ideal Gas
namely P = (r/m) kT
Using the Pc from before we can use this equation to estimate Tc for the Sun
See Example 9.5
Energy Transport equations are justified in section 9.4.2
Showing how the temperature varies in a star (dT/dr) for radiation transport is
derived..relating the luminosity L see messy equation 9.53
Also energy generation is discussed
Namely, how does the luminosity change with radius depends on the energy
generated at a given radius e ( r )
Equation 9.55 dL/dr = 4 p r2 r (r ) e (r )
Main Sequence Stars- putting it
all together on a computer
The structure and evolution of a star is determined by
• Hydrostatic equilibrium the laws of • Conservation of mass
• Energy transport
• Conservation of energy
Radiation
Equation 9.53
As dT/dr
Computer model predicts that
a star’s mass (and chemical
composition) completely
determines its properties.
H-R Diagram Main Sequence and beyond
DOC
How long do I have
On the
Main Sequence?
Evolution on the Main Sequence (2)
A star’s life time T ~ energy reservoir / luminosity
Energy
reservoir ~ M
Luminosity
L ~ M3.5
T ~ M/L ~ 1/M2.5
Massive stars
have short
lives!
Evolution off the Main Sequence:
Expansion into a Red Giant
Hydrogen in the core
completely converted
into He:
“Hydrogen burning”
(i.e. fusion of H into He)
ceases in the core.
H burning continues in a
shell around the core.
He Core + H-burning
shell produce more
energy than needed for
pressure support
Expansion and cooling of
the outer layers of the
star  Red
Giant
Expansion onto the Giant Branch
Expansion and
surface cooling during
the phase of an
inactive He core and
a H- burning shell
Sun will expand
beyond Earth’s orbit!
Degenerate Matter
Matter in the He core has
no energy source left.
 Not enough thermal
pressure to resist and
balance gravity
 Matter assumes a
new state, called
degenerate
matter:
Pressure in degenerate
core is due to the fact that
electrons can not be
packed arbitrarily close
together and have small
energies.
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 + g
8Be
+ 4He  12C + g
Helium Fusion
He nuclei can fuse to
build heavier elements:
When pressure and
temperature in the He core
become high enough,
Red Giant Evolution
(5 solar-mass star)
C, O
Inactive He
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).
Summary of Post Main-Sequence
Evolution of Stars
Supernova
Fusion
proceeds;
formation
of Fe core.
M>8
Msun
Evolution of
4 - 8 Msun
stars is still
uncertain.
Mass loss in
stellar winds
may reduce
them all to <
4 Msun stars.
Fusion
stops at
formation of
C,O core.
M<4
Msun
M < 0.4 Msun
Red dwarfs:
He burning
never
ignites
Evidence for Stellar Evolution: Star
Clusters
Stars in a star cluster all have
approximately the same age!
More massive stars evolve more quickly
than less massive ones.
If you put all the stars of a star cluster on a
HR diagram, the most massive stars
(upper left) will be missing!
HR Diagram of a Star Cluster
Example: HR diagram of the star cluster M 55
High-mass stars
evolved onto the
giant branch
Turn-off point
Low-mass stars
still on the main
sequence
Estimating the Age of a Cluster
The lower
on the MS
the turn-off
point, the
older the
cluster.
HW #13
read 9.4-end
Questions 9.9, 9.13,9.14
Problems 9.7,9.8,9.9,9.11
extra time due next Thursday!
We are proceding to
CHap 10 stellar old age
chap 11 The death of high mass stars
marker