Variable Stars

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Variable Stars• Some Giants and

Hypergiants exhibit regular periodic change in luminosity

• Mira (Fabricius 1595) changes by factor of 100 with period of 332d

• LPV like Mira not well modelled

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Instability Strip• A nearly vertical region traversed

by most massive stars on HB • RR Lyrae: PII HB stars with

periods of hours. Luminosity varies little (!)

• Cepheids (PI) , W Virginis (PII) periods of days.

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Why They Pulse• Cepheids oscillate in size (radial oscillation)• Temperature and luminosity peak during rapid

expansion• Eddington: Compression increases opacity in layer

trapping energy and propelling layer up where it expands, releases energy

• Problem: compression reduces opacity due to heating

• Solution: compression ionizes Helium so less heating. Expansion reduces ionization – κ-mechanism

• Instability strip has partially ionized Helium at suitable depth

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Why We Care• Leavitt 1908: Period-Luminosity

Relation for SMC cepheids• Luminous cepheids have longer

periods• With calibration in globular clusters

cepheids become standard candles

• Later: W Virginis PLR less luminous for same period

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White Dwarfs• Bessel 1844: Sirius wobbles: a

binary• Pup hard to find. Clark 1846

• Orbits:

• Spectrum (Adams 1915):

• Surface Gravity

• Spectrum: Very broad Hydrogen absorption lines

• Estimate:

• No Hydrogen else fusion

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Degenerate Matter• White dwarves are the

degenerate cores of stars with

• Composition is Carbon Oxygen

• Masses• Significant mass loss

• Chandrasekhar:

• Relativity:

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Mass-Radius

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Roche Potential• In a binary system matter

orbits both stars• Entire system rotates. If

dropped from (rotating) rest, where will a stone fall?

• Combined gravity and rotation described by Roche potential

• Inside each star’s Roche lobe orbits stay close to that star

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Algol• Eclipsing binary Algol is

a puzzle: MS subgiant

• Massive A should have evolved earlier?

• B started out as the more massive star• In its subgiant phase, atmosphere

leaked out of its Roche lobe• Gas lost by B forms accretion disk

around A

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White Dwarf Nova• White dwarves in close binaries can

accrete Hydrogen at from partner when it

overflows its Roche lobe• Infalling gas compressed to

degeneracy and heated by immense surface gravity

• Enriched with CNO by turbulent mixing at base

• When accumulates, base temperature

• CNO fusion explosively heats gas to and luminosity

• Radiation pressure ejects accreted material

• Total energy released over months

• Can recur in• Ejected matter glows at initial

• 30/yr in M31

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Nova Remnants

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Type-Ia Supernova• Accretion adds to white dwarf mass.

What if it exceeds Chandrasekhar limit?• It doesn’t. As increased mass

compresses dwarf, pressure and temperature increase

• A turbulent convection phase leads to ignition of Carbon fusion

• In degenerate dwarf heating does not lead to expansion so violent explosive process fuses substantial fraction of star in a few seconds

• Oxygen fusion less complete

• Internal temperature exceeds• Fusion releases blowing star

apart completely releasing shock wave ejecting matter at high speeds

• Luminosity reaches and decays over months

• Spectrum has absorption lines of Si but little H He

• Decay of readioactive fusion products near iron mass in shell contributes to luminosity at late times

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What We Know• Nature of Mass donor

unclear– Single Degenerate: Donor

is MS or giant – Double Degenerate: Donor

is White dwarf ripped apart by tidal forces in merger

• Likely both occur

• Nature of explosion also debated: deflagration or detonation? Degenerate Helium flash trigger or internal CO ignition

• Fact: Luminosity (corrected by light curve) almost the same for all Ia Supernovae: Standard Candles!

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A Standard Candle

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Post-MS Massive Star• Massive stars end

Main Sequence life• When core Hydrogen fusion

ceases core contracts and envelope expands and cools

• Shell Hydrogen fusion: Red Supergiant

• Core does not become degenerate

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Massive Star HB• Helium core ignites• Hydrogen fusion in shell• Envelope contracts and

heats• Blue Supergiant• Forming CO core

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Massive Star AGB• CO core collapses until

• Carbon fusion produces Mg Ne O

• Helium and Hydrogen fusion in shells

• Many neutrinos carry energy off

• Superwind and mass loss

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More Onion Shells• At ignite Neon

fusion– Produce O Mg… – Neutrinos carry off– Last a few years

• Oxygen fusion – Produce Si S P…– Neutrinos carry off– Last about a year

• Si fusion– Produce Ni Fe– Neutrinos carry off – Last about a day

• Build up inert Fe core• Changes rapid. Envelope

never responds• s-process nucleosynthesis

produces heavier elements

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End of the (Si) Day• Inert Fe core

• High T photons cause photodisintegration destroying heavy nuclei and absorbing energy

• Fe is the end: no more nuclear energy. What next?

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The Center Cannot Hold• As gravitational crush increases,

iron core collapses from size of Earth to a few km in

• In core, emits ϒ rays leading to photodisintegration of heavy nuclei

• Outer layers fall inward at speeds up to

• As core collapses electron degeneracy overcome

• Electrons forced into

• Left with a small, incredibly dense core that is mostly neutrons

• Does collapse stop?

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Boom!• Within 0.25s core is neutrons with radius 20 km and super-nuclear

density• Very little light can escape, energy carried off by neutrinos. Power

emitted in these exceeds all known stars for 10 s• At this density core collapse stops with bounce• Colliding with infalling layers this triggers shock wave blowing outer star

into space (96% of mass for star)• In compressed heated shock wave fusion to Fe and beyond via r-process• As ejecta thin light can escape. Luminosity reaches• Energy released type-II supernova – gravitational in origin

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Seeing Them• Sung dynasty history describes a

supernova in 1054 whose remnant – Crab nebula in Taurus – is still visible (M1)

• Japanese, Arabic, Native American records concur

• Milky Way supernovae also in 1006, 1572, 1604. Estimated every 300 years but obscured by dust

• Many visible in other galaxies, currently some 20-30 bright ones

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SN 2011dh

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Classification• SN classified by spectrum:

– Ia: Strong Si no H He– Ib: Weak H Strong He– Ic: Weak Si no H He– II: Strong H

• Ia are nuclear explosion of WD• II Ib Ic are gravitational core

collapse with degrees of envelope loss

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• 168,000 years ago a B3 I supergiant collapsed in LMC

• Observed as SN 1987A• Progenitor known –

changed theory• Remnants observed in

detail

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The Nebula

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What we are Seeing

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Neutrinos• Three hours before the supernova

detected, neutrino detectors observed a burst (20) of neutrinos from the right direction.

• 20 detected implies 1058 emitted carrying 1046 J in agreement with models

• Neutrinos get out before shock wave disperses outer layers, so got here before the light

• Neutrino Astronomy launched, many new experiments planned

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What is Left of Core?• Electron degeneracy

cannot stop collapse – few electrons

• Neutron degeneracy pressure at density

• in • Surface gravity

• Physics is relativistic• Chandrasekhar Limit

depends on rotation

• Rapid Rotation expected• High magnetic field frozen

in

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Discovery• Physics Predictions:– Rapid Rotation

– Intense magnetic field

– High Temperature

• Bell 1967: Periodic 1.337s Radio pulses: LGM?

• Quickly found other sources: natural

• Soon find many pulsars

Slow down in

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LGM Data

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What are Pulsars?• Rotating star breaks up

• Only NS dense enough to survive

• Emission aligned to magnetic axis - tilted

• Crab pulsar :Neutron star SN remnant

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How They Work• General Idea: Rapidly changing intense

magnetic field creates intense electric field

• Lifts charged particles from polar regions into magnetosphere dragged around by rotation

• Accelerated to relativistic speeds – emit synchrotron radiation at all wavelengths in direction of magnetic axis

• Emitted energy slows rotation• Luminosity of Crab nebula agrees with

observed rate of slowing of pulsar

• Pulsars observed in all bands