radiative processes · 2011. 11. 1. · radiative processes all e.m. radiation arises from...
TRANSCRIPT
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Radiative Processes
All e.m. radiationarises from transitionbetween levels withdifference in electricor magnetic moment
Transition probability
exp(i!k.!r) = 1
∝ | 〈 f | exp(i!k.!r) !l.Σ!∇ | i 〉 |2
[ dipole approximation ]
All e.m. radiationarises from transitionbetween levels withdifference in electricor magnetic moment
- Levels could be discrete or in continuum- Between each pair of levels emisson and absorption- Transitions dipole / higher multipole
g2B21 = g1B12 A21 = 2hν3B21/c2
ν =∆Eh
;
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Continuum Radiation
P =2
3c3 (d)2 =2e2
3c3 a2 Classically any accelerated charge would radiate
Different physical situations involve different mechanisms of acceleration- Radiation mechanism classified according to source of acceleration- Radiation reaction slows the charge
Radiation
Bremsstrahlung
Radiation
Synchrotron Radiation
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Inverse Compton Scattering
high-energyphoton
Related processes: Compton ScatteringThomson Scattering
Scattering processes
Non-resonant / resonant
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log ω
log
P
ω ~ v/b
Bremsstrahlungsingle encounter
RadiationSpectrum
Electric field received by theobserver is time dependent
Fourier transform of the electric field yields thespectrum
Net observed spectrum is a sum over all emittingparticles
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Polarization
!E ∝ n × [(n − !β) × !β]
At a single particle level, over short times, radiation is always polarized.
For slowly moving particle (or nearly || to ) polarizationis || to the projected instantaneous acceleration.
Net observed polarization involves average over the particle’s trajectory, and over the distribution of emitting particles.
!β n
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Radiation Pattern
Stationarydipole
Movingdipole
Motion introduces aberration and relativistic beaming
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Cyclotron Radiation Patterncircular motion
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Synchrotron Radiation
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Synchrotron radiation patternsingle emitter
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Synchrotron spectrum from single emitter
x =ωωc
ωc = γ3ωH sinα ∝ E2
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Radio image of the active galaxy Cygnus A- Example of a powerful synchrotron source
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Curvature Radiation
Relativistic Charged Particles moving along curved field lines
- Shares most properties of Synchrotron Radiation (replace Larmor radius by the radius of curvature of field lines)
- Polarization || to the projected field lines (Synchrotron: polarization perp. to projected B)
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Inverse Compton Scattering
high-energyphoton
Related processes: Compton ScatteringThomson Scattering
Scattering processes
Non-resonant / resonant
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Thomson scattering geometry
Pol. 1 − cos2 θ1 + cos2 θ
θ
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Scattering cross section
Thomson σT =8π3
r20 =
8π3
(e2
mc2
)2
Compton σ ≈ σT
(1 − 2x +
26x2
5+ · · ·
)
σ =38σTx−1
(ln 2x +
12
)
x ≡ hνmc2 " 1,
, x! 1
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43σTcβ2γ2UB
43σTcβ2γ2Uph
Synchrotron power
Compton power
Lcomp ∝ Lsy : Compton Catastrophe : Brightness Temperature limit ~1012 K
Synchrotron Self Compton
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Bulk Comptonization / Compton Drag
Strong radiation beams collimated within can be produced by Inverse Compton Scatteringby relativistic bulk flow of charged particles
Due to aberration effects, can generate very highpolarization
1/Γbulk
Pola
riza
tion
frac
tion
θ′obs0.0
1.0
0 π/2
Lazzati et al 2004
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SpectraRadiation received from a source is the sum of emission from alarge population of particles.
Energy distribution of the particles shape the spectra
Thermal distribution Non-thermal distribution Maxwell-Boltzmann Non-Maxwellian, e.g. power-law
1e-10
1e-08
1e-06
0.0001
0.01
1
100
10000
0.1 1 10
Nu
mb
er
Energy
Maxwell-BoltzmannPower-law
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What is emitted is not what we seeRadiation is modified during propagation through matter
dIνdτν= −Iν + Sν
dIνds= −ανIν + jν
Sν for a thermal source is the Planck function Bν
Bν =2hν3
c21
exp(hν/kT) − 1
Radiative transfer
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log inte
nsity
log frequency
Blackbody function
At large optical depth a thermal source will emit blackbody intensity.Emission will be received from a photosphere
Optical depth is frequency-dependent. A source could be optically thickat some frequencies, optically thin at others.
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log inte
nsity
log frequency
ThermalBremsstrahlung
Blackbody
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X-ray emission (pink) by hot gas in Bullet Cluster- Primarily Thermal Bremsstrahlung emission
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log frequency
log
inte
nsity
Optically thinnon-thermal Synchrotronfrom power-law particledistribution
-(p-1)/2
Strong polarization in ordered field: (up to 70%) p + 1p + 7
3
N(E) ∝ E−p
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+2
+2.5Low-frequencycutoff: SynchrotronSelf Absorption
Jitter radiation can steepen the low-frequency cutoff: - Low energy particles have longer duration of E-field pulse per orbit - More affected by pitch angle scattering before pulse completion
Tired electrons
-(p-1)/2
-p/2
(Medvedev 2000)
+1/3
Emission peak of electrons at lower limit of E-distributionLow-frequency tail
of single particleemission spectrum
Spectral regimes in Synchrotron Emission
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SynchrotronFireball model
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3C 279Blazar
Synchrotron(seed)
Compton
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What is emitted is not what we seeRadiation is modified during propagation through matter
Plasma effects
Dispersion
In magnetic field,Faraday Rotation
vph
c=
1 −
ω2p
ω2
−1/2
(vph
c
)
R,L=
1 −
ω2p
ω(ω ± ωB)
−1/2
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Dust Extinction, Polarization
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Absorption by the Earth’s Atmosphere
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Nuclear / particle processes
- Radioactivity (e.g. Al26)
- Decay of heavy mesons (e.g. ) generated in nuclear scattering ( )
- Fusion
- Pair Annihilation
Change in binding energy photon emission
Π0 → 2γp + p→ Π0
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Diffuse gamma-ray emission from gal. plane
CR + gas Π0 2 γ
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Pulsars
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Pulsars
Non-accreting magnetized neutron stars - radiating via magnetospheric processes
Main presence at radio wavelengths (~2000)
A few dozen at higher energies.
Fermi single-handedly increased the number of gamma-raypulsars from half a dozen to > 50. (Abdo et al 2009)
Surface Magnetic field ~108 - 1013 G(Cyclotron fundamental ~ 1eV - 100 keV)
How do we know the field strength?- Rotation-powered pulsars : spindown torque- Accreting X-ray pulsars : cyclotron features
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Pulsar emission isa magnetosphericphenomenon
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Crab Nebula
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Spinning magnet generates magnetic dipole radiation
Vacuum Dipole Model
Yields
= −IΩΩ (Rate of loss of rotational energy)
=2
3c3 (m)2 =2
3c3 B2R6Ω4 sin2 αRadiated power
B2 ∝ PP
Measurement of spindown rate helps estimate B
B12 =
√PsP−15
Age: ~ young objects often found in SNRsP/P
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(Abdo et al 2009)
ColouredDots aregamma-raypulsars
PulsarP-Pdotdiagram
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Spin period-Magnetic field distribution of observed Pulsars
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Spin period-Magnetic field distribution of observed Pulsars
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The Pulsar MagnetosphereBasic concepts: Goldreich & Julian 1969
- A vacuum exterior would have potential drop exceeding 1015 V
- Space charge must exist, E·B=0
- Co-rotating magnetosphere can be maintained up to the light cylinder, ρ ≃ -Ω·B/2πc
- With pair production, no. density of charged particles may far exceed ρ
- ρ passes through 0 and changes sign in the magnetosphere
Plasma on open field lines cannot co-rotate. Current flows outalong these lines, creates toroidal mag. field which provides thedipole spin-down torque.
A charge-starved gap is likely onthe null ρ surface at the boundaryof the closed magnetosphere: TheOuter Gap (Cheng et al 86, Romani 94)
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Force-free magnetosphere(Spitkovsky 2006)
ρE + ( jxB ) / c = 0 everywhere
poor approximation near LC, current sheets
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Radio Pulsar emission phenomenology
- Sharp pulses, low duty cycle : strong beaming
- High Brightness Temp (~1020 K) : coherent emission [Radio only]
- Frequency-dependent pulse width : radius-to-frequency mapping
- Strong linear polarization with S-pattern position-angle sweep : curvature radiation, rotating vector model
- Strong pulse-to-pulse variation but stable average profile : stochastic phenomena within a geometric envelope
- Drifting subpulses : rotating carousel of sparks, ExB drift
Complications:Cone-core dichotomy, Orthogonal polarization modes, Multiple comp.,Mode changes, Nulling, non-RVM pol sweep, circular pol......
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Ramkumar & Deshpande 2001
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Deshpande & Rankin 99
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Deshpande & Rankin 99
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Innergap
Outergap
Slotgap
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Outer gap modelling of gamma ray pulsation: (Romani et al 1992.....)
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AG
Placing an “Annular Gap”at Current Sheets in FFmagnetosphere solution(Bai and Spitkovsky 2009)
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Pulse modelling slot-gap vs outer gap(Romani & Watters 2010)
Vela Pulsar Fermi obs (black) and model (red)
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Supernova Remnants
- Sites of supernova explosions
- Ejected material interacts with surrounding matter
- Shock heating of swept up gas and ejecta: X-ray emission
continuum and lines characteristic of ejected species
- Shock acceleration of relativistic particles (electrons and protons)
- Synchrotron emission from electrons : Radio - X-rays
- Inverse Compton and Bremsstrahlung : X - γ- γ-rays also produced by interactions of relativistic protons with local gas * secondary pairs * pion production and decay
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Thermodynamic variables across a shock
For a strong shock v2 = v1/4; ρ2 = 4ρ1 In a relativistic shock n2 = 4Γshock n1
ρ2v2 = ρ1v1
P2 + ρ2v22 = P1 + ρ1v2
1
v2(u2 + P2 + ρ2v22/2) = v1(u1 + P1 + ρ1v2
1/2)
Conservation conditions: mass
momentum
energy
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ContactDiscontinuity
CompactObject
ReverseShock
UnshockedEjecta
ShockedISM
ShockedEjecta
Forward shock
UnshockedISM
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Supernova Remnants: Dynamical Phases
Early Coasting Phase (t < a few hundred years) - small amount of mass sweep-up; constant expansion speed : R ∝ t
Adiabatic Sedov Phase (a few hundred years < t < several thousand years) - swept up mass causes deceleration; constant total energy : R ∝ t2/5
Radiative Phase (t > a few thousand years) - radiative energy loss significant; expansion slows rapidly : R ∝ t1/4
Stall (t > a few hundred thousand years) - expansion speed reaches interstellar sound speed; SNR dissipates
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Magnetic Field is amplified behind the shock
- Swept up matter ~4 times denser; frozen-in field increases by this factor
- Contact discontinuity prone to Rayleigh-Taylor instability: drives turbulence and hence turbulent dynamo (Gull 1975)
- In very high speed (relativistic) shocks two-stream Weibel instability can efficiently generate magnetic field (Medvedev & Loeb 99)
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Diffusive Shock Acceleration
Magnetic scattering of fast particles on both sides of shock - Multiple crossings; energy gain in each cycle of crossing - Finite escape probability in each crossing
En = E0(1 + η)n⟨∆EE
⟩
cyc= η Nn = N0(1 − Pesc)n
x = − ln(1 − Pesc)ln(1 + η),
p = 1 + x,
NN0
(> E) =( E
E0
)−x
N(E)dE = KE−pdE
Any acceleration process in which - Relative energy gain ∝ time [dE/E ∝ dt]
- Escape prob. per unit time ~ constant [-dN/N ∝ dt]
Will lead to a power-law energy distribution
SN shocks wouldaccelerate all speciesof charged particles=> Cosmic Rays
Max. energy decided by confinement: RL > acceleration zone escape. Radiativelosses can also limit the energy acquired.
;
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Veil Nebula, an old supernova remnant in Cygnus
Optical (Hα)
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X-ray, ROSAT
EXPLOSION IN AD 1572
Multiwavelength view of the remnant of Tycho Brahe’s supernova
Optical is faint, suffers from dustextinction
Bright radio non-thermalsynchrotronemission
X-rays primarilyfrom thermal emissionby hot shocked gas
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Cas A from CXO
Most of this is thermal emission from reverse-shocked ejecta
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Si
Ca Fe
C
Cas A heavy element map inreverse-shocked ejecta
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Fermi acceleration in shocks
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VLA Radio image of Cas A
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Cas A from CXO
Blue rim is non-thermal emission
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HESS SNR image at TeV
RX J1713.7-3946 Contours: X-ray
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W44imaged
by FermiLAT
(Abdo et al 2010)Green contours:IR image
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(Fang & Zhang 2007)
Synchrotron primary, secondary
Brems
IC
π0
Evolution of non-thermal emission in supernova remnants