Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative Processes in AstrophysicsRadiative Processes in Astrophysics
Ranjeev Misra
Inter-University Center for Astronomy and Astrophysics (IUCAA)
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Physical picture of an Accretion DiskPhysical picture of an Accretion Disk
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative ProcessesRadiative Processes
Observations
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative ProcessesRadiative Processes
Observations
Identify Radiative Process
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative ProcessesRadiative Processes
Observations
Identify Radiative Process
Estimate Parameters e.g. density, temperature
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative ProcessesRadiative Processes
Observations
Identify Radiative Process
Estimate Parameters e.g. density, temperature
Verify Dynamical Model
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative ProcessesRadiative Processes
Observations
Identify Radiative Process
Estimate Parameters e.g. density, temperature
Verify Dynamical Model
Modify or Eliminate or Construct New Model
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiative ProcessesRadiative Processes
Observations
Identify Radiative Process
Estimate Parameters e.g. density, temperature
Verify Dynamical Model
Modify or Eliminate or Construct New Model
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Some DefinitionsSome Definitions
Flux Observed at Earth:
Energy per unit area per unit timeEnergy ----> Radiation energy
Area ----> area of detector/instrument
F
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Some DefinitionsSome Definitions
Flux Observed at Earth:
Energy per unit area per unit timeEnergy ----> Radiation energy
Area ----> area of detector/instrument
Spectrum:
Energy per unit area per unit time
per unit frequencyFrequency --> frequency of photon --> wavelength of photon --> energy of photon
Fν→(F=∫ Fν d ν)
F
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
SpectrumSpectrum
Fν
ν Δ ν
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Some DefinitionsSome Definitions
Luminosity: energy/time
Energy per unit time radiated by source
If source is a sphere then:
where D is the distance to the source.
L=F 4 π D2
L
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Some DefinitionsSome Definitions
Luminosity: energy/time
Energy per unit time radiated by source
If source is a sphere then:
where D is the distance to the source.
Intrinsic Flux: energy/time/area
Energy per unit time per unit area
radiated by source
For uniform source:
L=F 4 π D2
L
F i=L /area
F i
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Some DefinitionsSome Definitions
Emissivity: energy/time/volume/solid angle/freq
Energy per unit time per unit volume per
unit solid angle per unit frequency radiated
by source
If source is a sphere then
L=∫ϵν (ν)(4 π)(43π R3
)d ν
ϵν(ν)
Fν=ϵν (ν)(4 π)(43π R3
)1
4 π D2
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
How is radiation produced?How is radiation produced?
A charged particle gives out
radiation when it is accelerated.
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
How is radiation produced?How is radiation produced?
A charged particle gives out
radiation when it is accelerated.
The power emitted is given by
Larmor's Formula
P=(2 e2/3 c3
) a2∧(F /m)
2
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
How is radiation produced?How is radiation produced?
A charged particle gives out
radiation when it is accelerated.
The power emitted is given by
Larmor's Formula
Hence electrons are efficient in
giving out radiation.
P=(2 e2/3 c3
) a2∧(F /m)
2
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Types of AccelerationTypes of Acceleration
Electro-Magnetic
Electric field of a proton:
Electron is bound --> Radiative transitions
Electron is unbound --> Bremsstrahlung
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Types of AccelerationTypes of Acceleration
Electro-Magnetic
Electric field of a proton:
Electron is bound --> Radiative transitions
Electron is unbound --> Bremsstrahlung
External Magnetic Field:
Electron is non-relativistic --> cyclotron
Electron is relativistic --> Synchrotron
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Electric Field of an ElectronElectric Field of an Electron
e_
R Es
E=E s= nRq
R2
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiation from an electronRadiation from an electron
e_
R Es
E=E s+ E r= nRq
R2+( n1 q
aRc
)sinΘ
Er
a
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiation from an electronRadiation from an electron
E r=(qaRc
)sinΘ
S=c
4 πE r
2Pyonting Flux >
Units:Energy/time/area
P=∫ S dA Power > Energy/time
P=(2 e2/3 c3
) a2Larmor's Eqn. >
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiation from an electronRadiation from an electron
E r (t)=qa( t)Rc
sinΘ
E r (ω)=1
2 π∫ E r( t)exp (iω t) dt
Fourier Transform the Electric field
S (ω)=c
4π∣E r (ω)∣2
Energy/Area/frequency
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Radiation from an electronRadiation from an electron
c4 π
R2∣E r (ω)∣2Energy/solid angle/frequency
The number of electrons per unit time per unit volume that get accelerated: n
ϵν(ν)=cn
4 πR2∣E r (ω)∣2
Energy/volume/time/solid angle/frequency
number/volume/time
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
proton
e_ (t=0) v=v0
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
proton
e_ (t=0) v=v0
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
bx
y
a x= x=(q2
me R2)(
xR
)
a y= y=(q2
m e R2)(
yR)
R2=x 2
+y2
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
1.Get a( t)
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
1.Get a( t)2. Get E (t)
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
1.Get a( t)2. Get E (t)3.Get E (ω)
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
1.Get a( t)
4.Use n=ne (vo)vo np (2 πb db)d vo
2. Get E (t)3.Get E (ω)
b
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
e_ (t = t1)
e_ (t = t2)
proton
e_ (t=0) v=v0
1.Get a( t)
4.Use n=ne (vo)vo np (2 πb db)d vo
2. Get E (t)3.Get E (ω)
b
→Get ϵν(ω , vo , b)db dvo
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
ϵν=∬ϵν(ω , vo , b )db dv o
Need to specify electron distribution. For Thermal distribution:
ne (vo)d vo∧vo2 exp(−
me vo2
2kTe
)dvo
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
ϵν=ne n p T−1 /2 exp(−h ν
kT e
)g ff (T e , ν)
ϵν
ν %h ν=kT e
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
X-ray emission from a galaxy clusterX-ray emission from a galaxy cluster
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
AbsorptionAbsorption
For every emission process :
Where X is a proton or magnetic
field, there is a corresponding
absorption process:
e+X →e+ X+ photon
e+X+ photon→e+ X
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
AbsorptionAbsorption
In Equilibrium:
The photons will have the same
temperature as the electrons and the
emergent spectrum will be a black
body i.e.
e+X ⇔e+X + photon
S ν(ν)=Bν(ν)=2 h ν
3/c2
exp(h ν/kT e)−1
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
ϵν
ν %h ν=2.73 kT e
S ν(ν)=Bν(ν)=2 h ν
3/c2
exp(h ν/kT e)−1
ν2
ν3 exp (−h ν/ kT e)
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
AbsorptionAbsorption
If the photons encounter a large
number of electrons, they will
eventually get absorbed and
equilibrium will take place
Pure Bremsstrahlung emission will
occur when density is low.
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
BremsstrahlungBremsstrahlung
ϵν=ne n p T−1 /2 exp(−h ν
kT e
)g ff (T e , ν)
ϵν
ν %h ν=kT e
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Bremsstrahlung Self absorbedBremsstrahlung Self absorbed
ϵν=ne n p T−1 /2 exp(−h ν
kT e
)g ff (T e , ν)
ϵν
ν %h ν=kT eνc
ν2
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Compton ScatteringCompton Scattering
ϵi
ϵ f
Electron at rest
Θ
ϵ f =ϵi
1+ϵi
me c2 (1−cos Θ)
ϵi
m e c2≪1
ϵ f ∼ϵi
e
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Compton ScatteringCompton Scattering
ϵiϵ f
Electron has a initial velocity
θ f
e θi
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Compton ScatteringCompton Scattering
ϵi'
ϵ f'
Transform to electron rest frame
Θ'
ϵi'= ϵi γ(1−β cosθi)
e
ϵ f'
∼ ϵi'
ϵ f = ϵ f'γ(1+β cos θ f
')
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Compton ScatteringCompton Scattering
ϵiϵ f
Electron has a initial velocity
θ f
e θi
ϵ f = ϵi γ2(1−β cosθi)(1+β cosθ f
')
ϵ f ∼ ϵi γ2
If γ≫1
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Compton ScatteringCompton Scattering
Black Body Source
Hot Cloud/Corona
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Boltzmann EquationBoltzmann Equation
n γ(ν)=c∫ d3 p∫d σ
d Ωd Ω{ne( p1) nγ(ν1)−ne( p) nγ(ν)}
p+ν⇔ p1+ν1
p Electron momentum
ν Photon frequency
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Boltzmann Eqn ---> Fokker-Planck EqnBoltzmann Eqn ---> Fokker-Planck Eqn
Assume that energy exchange is
small.
Integral equation becomes a
differential equation
This equation is a “diffusion”
equation. Diffusion of particle in
energy space instead of real space.
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Kompaneets EquationKompaneets Equation
n γ=ne σT c (k T e
m c2 )1x2
∂∂ x
{x 4(∂ nγ
∂ x+n)}+S+E
x=h ν
k T e
S
E
Source terms like bremsstrahlung or black body
Escape term depending on geometry and size
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Kompaneets EquationKompaneets Equation
y=(4 k T e
m e c2 )max (τ ,τ2)
τ=neσT L
τL
Thomson optical depth
Size of the system
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Comptonization of black body emissionComptonization of black body emission
y = 0.1
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Comptonization of black body emissionComptonization of black body emission
y = 1.0
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Comptonization of black body emissionComptonization of black body emission
y = 10.0
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
CyclotronCyclotron
If electron velocity v << c, the emission iscalled Cyclotron and is monochromatic.
h ν=1
2 π
e Bme c
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
SynchrotronSynchrotron
If electron velocity v ~ c, the emission iscalled Synchrotron and is nearly monochromatic.
h ν=γ2 12 π
e Bm e c
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Non-thermal Electron DistributionNon-thermal Electron Distribution
ne (γ)d γ = C γ−p d γ γmin < γ < γmax
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
Non-thermal Electron DistributionNon-thermal Electron Distribution
ne (γ)d γ = C γ−p d γ γmin < γ < γmax
ϵν(ν)∧ν−( p−1)/2
→
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
SummarySummary
Bremsstrahlung
Hot low density matter -- X-rays
Galaxy Cluster, Jets
Synchrotron
low density matter with non-thermal
electrons -- radio/optical/X-rays.
Radiative Processes in AstrophysicsRanjeev Misra, IUCAA, Pune, India.
Recent Trends in Astronomy and Astrophysics
Manipal Univ, Manipal, Sept 2014
SummarySummary
Black Body emission
High density matter -- optical/X-rays
Stars, accretion disk, CMBR
Comptonization
Hot low density matter – X-rays
Corona of the sun/stars and accretion
disks