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.

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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

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Principle of Relativity• Laws of Physics are the same measured at rest

or moving at constant velocity• determines accelerations which are

the same in both frames • At rest is meaningless. Only relative velocities

are physical

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This Week• Follow Principle of Relativity as far as it takes us• Electromagnetism will force some modifications –

Special Relativity• Find that Newtonian gravity is not invariant after all• Describe General Relativity and some Astronomically

important consequences• Black Holes

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Space and Time• Space: All possible positions• Motion described by• Plot on three axes to produce worldline• Spacetime: All possible events• Newton I: Objects upon which no forces act

have straight worldlines

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Spacetime• Velocity is

slope of worldline from axis

• Stationary objects have vertical worldlines

• Horizontal line (space) is Universe at some time

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Relativity in Spacetime• O’ moves at relative to

O• Describe same event by

different coordinates

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Velocity Addition

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Maxwell’s Problem• Maxwell’s equations predict the speed of

electromagnetic waves in terms of measured properties of electric and magnetic interactions

• Electromagnetism is not invariant under Galilean relativity

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Two Possible Solutions• Light propagates at

through aether • Maxwell’s equations

hold for observers at rest relative to aether

• Moving at measure

• Light propagates at through space

• Maxwell’s equations hold for all inertial observers

• Moving at measure

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Looking for the Aether• A light clock is two

mirrors at distance• Light bounces between

them in time• Moving light clock

relative to aether will change its rate

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Two Motions• Moving along axis • Moving transversely

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The Answer• Michelson-Morley 1887:• Viscous aether dragged by Earth?• Einstein 1905: No Aether. Maxwell’s equations

hold in any inertial frame• Galilean relativity is wrong.

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Lorentz Transformations• Send a light pulse from

• Seek

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Lorentz Transformations

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The Answer

• For and not too large,

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The Answer

• Note or else this makes no sense

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Simultaneity• Most unintuitive:

Simultaneity is Relative• Is causality lost?• Source of many

“paradoxes” Measure distance in light-seconds or time in light-meters so

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Time and Simultaneity• Since we know is

constant we can measure time of distant events

• If light from reaches 0 at time it was emitted at

• The present: Events from which light will reach us at

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Length Contraction• A ruler lies at

• This is

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Time Dilation• Clock at ticks at

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Doppler• Doppler formula modified by time dilation

– Transverse Doppler effect

– Longitudinal Doppler effect

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Is This Real?• We have lots of experimental evidence • This is real. Any ruler constructed using

Lorentz-invariant physics will contract at high speed. Any physical clock will run slow at high speed

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Velocity Addition

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The Invariant Interval• Lorentz transformations

have the property that

lightcone

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What It Means• If an

observer with gets to

• is proper time• If observer

comes from• This is future/past

past

future

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What it Means• If observer with finds is proper distance• Faster observer has order

reversed• Causal theory means no

material particle or information can propagate faster than

past

future

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Conservation Laws• Newtonian conservation laws are not Lorentz-

invariant• Find relativistic conserved quantities

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Remarks• invariant mass• transform under Lorentz like • These conservation laws hold always. Lavoisier 1777

would find that energy lost to radiation reduced mass slightly

• Decay of a particle that does not conserve mass is consistent with these – and happens

• Other conserved quantities are invariant

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Relativistic Laws• Electromagnetism (Maxwell) is Lorentz-invariant• Nuclear interactions have Lorentz-invariant form• Quantum relativistic version (Quantum Field

Theory 1940/1972.• Gravity????