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Astr 2310 Thurs. April 17, 2009

Today’s Topics

• Chapter 16 cont.: The Evolution of Stars– Stellar Evolution cont.

• Evolution off the Main Sequence– Massive Star

• Chemical Composition and Evolution

– H-R Diagrams of Star Clusters

– Synthesis of Heavy Elements in Stars

• Chapter 17: Star Deaths– White Dwarfs

• Physical Properties

• Observational Evidence

• White Dwarfs in Binary Stars

– Neutron Stars• Physical Properties

• Plulsars – Rotating Neutron Stars

• Supernovae Connection

– Black Holes• Physics of Black Holes

• Structure of Spacetime

• Observational Evidence for Blackholes

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Chapter 17 Homework

Chapter 17: #1, 3, 4, 13, 20

(Due Tues. April 28)

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Post Main-Sequence Evolution – High Mass

• As Hydrogen is exhausted in thecores the stars evolve off themain sequence. Hydrogen shellburning rapidly begins– Star’s envelope rapidly expands

– Luminosity remain approx.constant and radius increasesrapidly. Star becomes asupergiant.

• Helium burning begins whencore temp. ~ 108 K.– No core degeneracy so no He

flash

– Helium rapidly exhausted andCarbon burning beginsproducing Magnesium

– Elements capture He nuclei tobuild up even numbered nuclei

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Onion Skin Model for Massive Stars

– Star develops amulti-shell,“onion-skin”structure.

– Heavy elementsrapidly built upbut little energyreleased (seecurve of bindingenergy andtimescales below)

– Massive (1 solarmass) core of Ironis eventuallyformed.

Not to scale. A large Hydrogen envelope surrounds core

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Testing Stellar Evolution via Star Clusters

• Observations of a variety of star clustersallow comparison of their H-R diagrams

– H-R diagrams of most clusters are devoid ofmassive, hot stars.

– Main-sequence lifetime is short for highmass stars

– Most massive and hottest stars on the mainsequence can be used to age-date a starcluster

– Location of evolved stars in H-R diagramcan be fit with model evolutionary tracks.

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Observations of Youngest Star Clusters

• Young cluster “NGC 2264”

– Few million years old

• High mass stars have reachedmain sequence

• Lower mass stars are stillapproaching main sequence

– Locus of Deuterium burning

– Variable stars known as TTauri stars

• Earlier stages hidden by dust

– Infrared observations revealhot cores (protostars).

– Accreting material in rotatingdisk

– Gaseous outflows along poles

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Observations of Moderately-Young Clusters

• Praesepe star cluster– Few million years old

• Higher mass stars on the mainsequence

• A few Red Giants present too.

• Low mass stars have reachedmain 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 alongthe line of sight

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Observations of Oldest Star Clusters

• Old cluster “47 Tucanae”

– About 12 Billion years old

• Stars more massive than the Sunhave evolved off the mainsequence

• Horizontal Branch stars areevident

• Asymptotic Giant Branch starsevident as well

• Note that the stars at the Tip ofthe Red Giant Branch are brightbut not extremely bright.

• Note the accuracy of the stellarmodels and the age dating.

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Evolutionary States of Stars in H-R Diagram

• Evolution state of individual stars can also beevaluated given their location in the H-Rdiagram

– Evolutionary tracks “fit” to a star to estimate massand age.

– Observational properties of these post-main-sequence stars can then provide context to theirevolutionary state.

• Variability (pulsations)

• Rotational velocity

• Stellar winds (mass loss, dust production)

• Atmospheric compositional differences

(dredge-up of enriched material)

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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 1 day170 x 107 KSilicon

6 months150 x 107 KOxygen

1 yr120 x 107 KNeon

600 yrs60 x 107 KCarbon

5 x 105 yrs20 x 107 KHelium

7 x 106 yrs4 x 107 KHydrogn

DurationCentral

Temp.

Stage

Fusion Temperatures and Durations

for 25 Solar Mass Star

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The Curve of Binding Energy

• If you keep adding protons to a nucleus?– Coulomb repulsion continues to increase

• new proton feels repulsion from all otherprotons

– 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 whereCoulomb repulsion outweighs strongforce attraction.

• Most “stable” nucleus is 56Fe(26 protons, 30 neutrons, 56 total)

• Release energy by fusion of light nucleito make heaver ones– up to 56Fe

• Release energy by fission of heavy nucleito make lighter ones – down to 56Fe

From our text: Horizons, by Seeds

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Synthesis of Heavy Elements - II

• Nuclear synthesis creates enhancements in the CNO elements– -capture onto C12 during triple- 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 Coulombrepulsion– Elements heavier than Fe are less tightly bound

– Fusion cannot synthesize elements beyond Fe56

• Odd-even effect due to only -particles (He nuclei) being present in thesehot environments (sort of):– AGB stars and SN: -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

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Current Elemental Abundances

• Recall that the abundance of theelements can be modeled with anaccurate stellar atmosphere.

• Once the temperature anddensity profile of the atmosphereis specified the Boltzman andSaha equations can be solved

– strengths of individual spectrallines modeled to inferabundances

• Resulting abundances

– Li, Be, and Boron (lightelements) very rare

• Triple- process skips them toform Carbon

• -process creates CNO peak

• Odd-even pattern evident

• Iron peak evident as well

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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

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Proto-planetary Nebula

• Red Rectangle

– Prototype of proto-planetary nebula

– Shells evidence forpulsations expellingstellar envelope

– Thick, dusty torussurrounds post-AGB star

– Spectroscopy indicatesdust and PAH formation

– “Rays” probably resultof shadowing effects

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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

Cat’s Eye: Narrow Angle View Cat’s Eye: Wide Angle View

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Physical Properties of White Dwarfs

• Chandrasekhar Developed Models for White Dwarfs– Degenerate Equation of State:

P = k 5/3 (non-relativistic gas)

P = k 4/3 (relativistic gas)

– Combining with the definition of density ( ~ M/R3) we have:

P ~ 5/3 ~ M5/3/R5

– Hydrostatic Equilibrium Requires P ~ M2/R4

– Equating: 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

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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

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White Dwarfs in H-R Diagram

Extensive surveys of White Dwarfs in binary stars and in the nearby

volume of space have resulted in about 75 White Dwarfs with accurate

distances that can thus be placed in the H-R diagram. More than 7000

have been found in the SDSS survey.

Recall that the sequence is a cooling sequence

with the White Dwarfs distributed in the

perpendicular direction according to radius

(mass).

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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 theWhite 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)

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• 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• Core photo-dissociates

• Fe56 + 14 He4 +

– Process absorbs energy instead of producing it.

– Core produces burst of neutrinos ( )

– 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 nuclearfusion due to expanding shock wave

– Trans-Fe elements synthesized (r-process)

Evolution of Massive Stars - I

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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 recentexamples include those named for Tyco (1572) and Kepler (1604).

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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

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Possible Supernovae Precursors

• Several Galactic stars have

been suggested as possible

precursors for type-II

supernovae. These include

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.

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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 rotationalvelocities (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

• Internal Structure:

– Core: superfluid of neutrons and pions

– Mantle: superconducting fluid of neutrons and protons

– Crust: Iron crust few meters thick

Oppenheimer predicted the existence of Neutron stars if core masses were

sufficiently high. Though uncertain, the neutron star equation of state constrains

physical properties.

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Observational Evidence of Neutron Stars: Pulsars

• Pulsars: Pulsating Stars

– Rapid pulses at radiowavelengths, extremely regular

– Periods from 1 to few 1000msec

– Lighthouse beaming ofsynchrotron emission(spiraling e- in strong mag.Field)

– Field strengths of ~ 108 Teslas

– Deformation into oblatespheroid

– Steady period changes indicatespindown

– Abrupt period changes suggestcrustal shrinkage (quakes!)

Early radio telescopes (circa 1960) detected rapidly pulsating, point-like sources.

Lunar occultations and interferometry pinpointed their location.

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Crab Pulsar at X-ray Wavelengths

• Crab pulsar is thenearest, best observedpulsar– P = 0.03 sec.

• Much of what we knowabout neutron starscomes from the Crab– Optical pulses detected

by tuning photoncounting detector to theradio period.

• Pulsar powers the Crabnebula– See movie on class

website

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Observational Evidence for Neutron Stars:

Binary Systems

• Mass of neutron stars can be measured if in binarysystem.

– Detached systems:

• 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 andhence mass

– Binary pulsar provides masses for both as well as critical tests ofGeneral Relativity

– Mass Transfer Systems:

• Strong x-ray source due to hot accretion disk

• Emission lines from accretion disk (velocity and hence mass)

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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

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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

– Event Horizon

• 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)

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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

As stated, Black Holes in binary systems provide only solid evidence for

their existence. Imaging of lensing via radio interferometry may soon occur.

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Chapter 17 Homework

Chapter 17: #1, 3, 4, 13, 20

(Due Tues. April 28)