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 • Thermal Energy (pressure) • Magnetic Fields • Rotation (angular momentum) • Turbulence External trigger required to initiate the collapse of clouds to form stars.
Horse Head Nebula
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 .
Stellar Structure
Energy transport via convection Energy transport via radiation Energy generation via nuclear fusion Basically the same structure for all stars with approx. 1 solar mass or less. Sun Temperature, density and pressure decreasing
Hydrostatic Equilibrium
Imagine a star’s Gravity, i.e. the weight from all interior composed of layers above individual shells.
Within each shell, two forces have to be in equilibrium with each other: 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 dM/dr= 4
p
r 2
but r
dV = 4
p
r 2 (r) dr
why???
dM = 4
{9.33}=MASS CONTINUITY
r
p
r 2
r
(r) dr
{ eq. 9.32b} Furthermore
M(r) = 4
p
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!
F B r dr F G F B the buoyant force is balanced by F G Pull of mass within (M(r) ) gravitational F B is due to the pressure difference on the cylinder!
Hydrostatic equilibrium F G +F B =0
P (r)dA 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 Hence F B =P( r) dA – P(r+dr) dA
F B = dPdA…..why -? EQ 40 F G =-GM(r) dm /r 2 = -[GM( r)/r 2 ]
r
( r) drdA eq 37 Using HE
F G +F B =0 and equations 37 and 40 we get the equation of Hydrostatic Equilibrium(43) dP/dr = -[GM (r ) /r 2 ]
r
( r) Example 9.4..assume Sun has constant density
r
small with more sophisticated models integrate 43 from 0 to R (solar radius) And Pressure from P c(at center) to 0 at the surface we get an estimate for the central pressure in The Sun at 1 x 10 16 which is 20 times too 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 P c from before we can use this equation to estimate T c 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
r 2
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 ~ M 3.5
T ~ M/L ~ 1/M 2.5
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
4 H → He He
H-burning shell keeps dumping He onto the core.
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”
4 He + 4 He 8 Be + g 8 Be + 4 He 12 C + 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)
Inactive He C, O
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 M sun Fusion stops at formation of C,O core.
M < 4 M sun M < 0.4 M sun Evolution of 4 - 8 M sun stars is still uncertain.
Mass loss in stellar winds may reduce them all to < 4 M sun stars.
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