2. Chapter 17 Homework. Chapter 17:
1. 1 Astr 2310 Thurs. April 17, 2009 Today’s Topics Chapter 16 cont.: The Evolution of Stars
Stellar Evolution cont.
Evolution off the Main Sequence
Chemical Composition and Evolution
H-R Diagrams of Star Clusters
Synthesis of Heavy Elements in Stars
Chapter 17: Star Deaths
White Dwarfs in Binary Stars
Plulsars – Rotating Neutron Stars
Physics of Black Holes
Structure of Spacetime
Observational Evidence for Blackholes
2. 2 Chapter 17 Homework Chapter 17: #1, 3, 4, 13, 20
(Due Tues. April 28)
3. 3 Post Main-Sequence Evolution – High Mass As Hydrogen is exhausted in the cores the stars evolve off the main sequence. Hydrogen shell burning rapidly begins
Star’s envelope rapidly expands
Luminosity remain approx. constant and radius increases rapidly. Star becomes a supergiant.
Helium burning begins when core temp. ~ 108 K.
No core degeneracy so no He flash
Helium rapidly exhausted and Carbon burning begins producing Magnesium
Elements capture He nuclei to build up even numbered nuclei
4. 4 Onion Skin Model for Massive Stars Star develops a multi-shell, “onion-skin” structure.
Heavy elements rapidly built up but little energy released (see curve of binding energy and timescales below)
Massive (1 solar mass) core of Iron is eventually formed.
5. 5 Testing Stellar Evolution via Star Clusters Observations of a variety of star clusters allow comparison of their H-R diagrams
H-R diagrams of most clusters are devoid of massive, hot stars.
Main-sequence lifetime is short for high mass stars
Most massive and hottest stars on the main sequence can be used to age-date a star cluster
Location of evolved stars in H-R diagram can be fit with model evolutionary tracks.
6. 6 Observations of Youngest Star Clusters Young cluster “NGC 2264”
Few million years old
High mass stars have reached main sequence
Lower mass stars are still approaching main sequence
Locus of Deuterium burning
Variable stars known as T Tauri stars
Earlier stages hidden by dust
Infrared observations reveal hot cores (protostars).
Accreting material in rotating disk
Gaseous outflows along poles
7. 7 Observations of Moderately-Young Clusters Praesepe star cluster
Few million years old
Higher mass stars on the main sequence
A few Red Giants present too.
Low mass stars have reached main sequence
Entire main sequence populated
Evidence of young age
Stars rapidly rotating
Strong magnetic fields
High variability of low-mass stars
Note the contamination by stars along the line of sight
8. 8 Observations of Oldest Star Clusters Old cluster “47 Tucanae”
About 12 Billion years old
Stars more massive than the Sun have evolved off the main sequence
Horizontal Branch stars are evident
Asymptotic Giant Branch stars evident as well
Note that the stars at the Tip of the Red Giant Branch are bright but not extremely bright.
Note the accuracy of the stellar models and the age dating.
9. 9 Evolutionary States of Stars in H-R Diagram Evolution state of individual stars can also be evaluated given their location in the H-R diagram
Evolutionary tracks “fit” to a star to estimate mass and age.
Observational properties of these post-main-sequence stars can then provide context to their evolutionary state.
Stellar winds (mass loss, dust production)
Atmospheric compositional differences
(dredge-up of enriched material)
10. 10 Synthesis of Heavy Elements - I As fuel is exhausted the core continues to shrink with a rise in temperature until the next nuclear reaction ignites.
Recall the curve of binding energy
Each new reaction creates heavier elements but the energy produced is more modest (low efficiency)
Reactions must go faster and faster to prevent collapse
Star takes on an “onion-skin” structure with shells of heavier elements fusing and synethsizing heavier elements
11. 11 The Curve of Binding Energy If you keep adding protons to a nucleus?
Coulomb repulsion continues to increase
new proton feels repulsion from all other protons
Strong force attraction reaches limit
new proton can’t feel attraction from protons on far side of a big nucleus
Gain energy only up to point where Coulomb repulsion outweighs strong force attraction.
Most “stable” nucleus is 56Fe (26 protons, 30 neutrons, 56 total)
Release energy by fusion of light nuclei to make heaver ones– up to 56Fe
Release energy by fission of heavy nuclei to make lighter ones – down to 56Fe
12. 12 Synthesis of Heavy Elements - II Nuclear synthesis creates enhancements in the CNO elements
a-capture onto C12 during triple-a produces O16, Ne20
Carbon burning produces Mg24 and Si28
Silicon burning produces Fe56
Iron (Fe56) is also enhanced since it is the most tightly bound nucleus
Higher atomic numbered nuclei need more neutrons to mitigate Coulomb repulsion
Elements heavier than Fe are less tightly bound
Fusion cannot synthesize elements beyond Fe56
Odd-even effect due to only a-particles (He nuclei) being present in these hot environments (sort of):
AGB stars and SN: a-capture onto C12 and higher also produces:
C12, O16, Ne20, Mg24, Si28, S32, Ar36, Ca40 ...
Picture is oversimplified as it ignores neutron capture
Nuclei experience neutron flux in neutron-rich environments
s and r process (slow and rapid neutron capture)
Essential for the “trans-Fe” elements
Burbidge, Burbidge, Fowler and Hoyle (B2FH) described processes
Models can be tested via abundance pattern of very heavy elements
13. 13 Current Elemental Abundances Recall that the abundance of the elements can be modeled with an accurate stellar atmosphere.
Once the temperature and density profile of the atmosphere is specified the Boltzman and Saha equations can be solved
strengths of individual spectral lines modeled to infer abundances
Li, Be, and Boron (light elements) very rare
Triple-a process skips them to form Carbon
a-process creates CNO peak
Odd-even pattern evident
Iron peak evident as well
14. 14 Chapter 17: Star Deaths Moderate-low mass stars produce White Dwarfs
Instabilities during double-shell burning within AGB stars produces tremendous amounts of mass-loss
UV photons ionize surrounding envelope to form planetary nebula
Example of a proto-planetary nebula: Red Rectangle
Envelope eventually fully expelled to reveal hot degenerate core and surrounding ionized nebula
15. 15 Proto-planetary Nebula Red Rectangle
Prototype of proto-planetary nebula
Shells evidence for pulsations expelling stellar envelope
Thick, dusty torus surrounds post-AGB star
Spectroscopy indicates dust and PAH formation
“Rays” probably result of shadowing effects
16. 16 Planetary Nebula Once envelope is expelled the central hot core can ionize surrounding gas (nebula)
Temp. ~ 105 K
Rapid cooling of central star means lifetime of only ~ 104 yrs.
Result will be a White Dwarf
17. 17 Physical Properties of White Dwarfs Chandrasekhar Developed Models for White Dwarfs
Degenerate Equation of State:
P = kr5/3 (non-relativistic gas)
P = kr4/3 (relativistic gas)
Combining with the definition of density (r ~ M/R3) we have:
P ~ r5/3 ~ M5/3/R5
Hydrostatic Equilibrium Requires P ~ M2/R4
M2/R4 ~ M5/3/R5 which yields:
R ~ 1/M1/3
Note that as Mass increases R decreases (Mass-Radius Relation)
Detailed modeling indicates a maximum mass for White Dwarfs:
Chandrasekahar Mass ~ 1.44 Msun
18. 18 Observational Evidence of White Dwarfs White Dwarfs in Nearby Binary System
Sirius and Procyon
Astrometric Orbits yield Masses
MSiriusB = 2.1 x 1030 kg (typically 0.7 Msun)
Temperatures and Luminosities yield Radii
RSiriusB = 5.5 x 105 km (typically 0.01 Rsun ~ Rearth)
Redshifts Inconsistant with Velocity of Primary
Strong Gravitational Redshift!
Consistent with Predictions of General Relativity
19. 19 White Dwarfs in H-R Diagram
20. 20 White Dwarfs in Binary Systems White dwarfs in close binary systems have interesting properties and implications.
The White Dwarf was originally the more massive since it evolved first.
If the companion begins to expand it can fill its Roche lobe and begin to transfer mass onto the White dwarf.
Hot accretion disk can surround White Dwarf
Cataclysmic variable stars
Strong x-ray emission from accretion disk
Accreting White Dwarf can reach Chandrasekhar mass and collapse as a Type-Ia supernova
(no Hydrogen lines in the spectrua)
21. 21 Massive stars produce Neutron Stars
Silicon burning goes very fast as very little energy is produced
Temperature of Fe core rises but no further fusion is possible
Fe56 + g 14 He4 + n
Process absorbs energy instead of producing it.
Core produces burst of neutrinos (n)
Core collapses to density of atomic nucleus!
Energy absorbed results in huge drop in central pressure
Core undergoes free-fall collapse to enormous density
He nuclei and electrons squeezed together to form neutron core:
p + e n
Neutrinos blow off outer layers of star creating type II supernova
If Mcore < 3 Msun the neutron degeneracy can support the core
Result is a neutron star
Inner, dense layers of star’s envelope undergo rapid nuclear fusion due to expanding shock wave
Trans-Fe elements synthesized (r-process)
22. 22 Type II Supernovae - I Enormous explosions in our galaxy and distant galaxies. Chinese record of supernovae include (clockwise from upper left): Vela supernova (~ 4000 BC) and the Crab (1054 AD), more recent examples include those named for Tyco (1572) and Kepler (1604).
23. 23 Type II Supernovae - II Association of historical supernova events with remnants and pulsars
No recent supernovae in our Galaxy
No modern photometric or spectroscopic data available.
Supernovae in distant galaxies provide the only modern data for context and interpretation.
Extensive surveys of extragalactic supernovae have resulted in a wealth of data including:
Luminosities: 109 Lsun
Expansion velocities: V ~ 10,000 km/sec
Heavy element abundances: trans-Fe elements, direct evidence for the r-process
24. 24 Possible Supernovae Precursors Several Galactic stars have been suggested as possible precursors for type-II supernovae. These include r Cass, Eta Caraina (right).
At present there is no reliable way to predict the event.
Such an event could be visible in the daytime sky.
Some have suggested that any corresponding Gamma-ray bust would present a hazard to life on Earth.
25. 25 Physical Properties of Neutron Stars Mass: M ~ 2 Msun
Radius: R ~ 12 km
Density: r ~ 5 x 1017 kg/m3 ~ 4 x 1011 Sun’s
Conservation of angular momentum means enormous rotational velocities (near speed of light)
Magnetic field: B ~ 2 x 1011 Gauss
Surface gravity: g ~ 1011 gearth
Escape velocity: Vesc ~ 30% c
Initial Temp: T ~ 1011 K
Core: superfluid of neutrons and pions
Mantle: superconducting fluid of neutrons and protons
Crust: Iron crust few meters thick
26. 26 Observational Evidence of Neutron Stars: Pulsars Pulsars: Pulsating Stars
Rapid pulses at radio wavelengths, extremely regular
Periods from 1 to few 1000 msec
Lighthouse beaming of synchrotron emission (spiraling e- in strong mag. Field)
Field strengths of ~ 108 Teslas
Deformation into oblate spheroid
Steady period changes indicate spindown
Abrupt period changes suggest crustal shrinkage (quakes!)
27. 27 Crab Pulsar at X-ray Wavelengths Crab pulsar is the nearest, best observed pulsar
P = 0.03 sec.
Much of what we know about neutron stars comes from the Crab
Optical pulses detected by tuning photon counting detector to the radio period.
Pulsar powers the Crab nebula
See movie on class website
28. 28 Observational Evidence for Neutron Stars: Binary Systems Mass of neutron stars can be measured if in binary system.
No mass transfer or x-ray emission
Single line spectroscopic binaries
Only limits for mass of neutron star
If a pulsar then the time delay provides orbital velocity and hence mass
Binary pulsar provides masses for both as well as critical tests of General Relativity
Mass Transfer Systems:
Strong x-ray source due to hot accretion disk
Emission lines from accretion disk (velocity and hence mass)
29. 29 Origin of Black Holes The neutron star equation of state suggests that neutron degeneracy cannot provide sufficient support for M > 4 Msun
Nothing can halt collapse and core collapses to a point mass.
Models imply that stars with M > 20 Msun will likely produce a Black Hole
Amount of mass loss is uncertain and so models are not definitive
30. 30 Physical Properties of Black Holes Cannot be described without General Relativity
General Relativistic solutions:
Schwarzschild: Static, non-rotating Black Hole
Kerr: Rotating Black Hole
Hawking: “Black Holes have no hair.”
Only three numbers describe a Black Hole:
Law of Cosmic Censorship:
Mass, angular momentum, and charge
Event horizon masks singularity
Singularity is surrounded by surface at which the escape velocity reaches speed of lightWithin this volume no light can escape!
R = 2GM/c2 (Schwarzschild radius)
Angular momentum should be huge but it is limited:
Lmax ~ GM2/c (otherwise singularity is exposed)
31. 31 Black Holes in Binary Systems Presence in mass transfer systems can results in strong x-ray emission.
Infalling material acquires enormous kinetic energy (v ~ c)
Candidate Black Hole binary systems now number ~ 50 systems
32. 32 Chapter 17 Homework Chapter 17: #1, 3, 4, 13, 20
(Due Tues. April 28)