Radiative Processes in Astrophysics - … · Radiative Processes in Astrophysics Ranjeev Misra, IUCAA, Pune, India. Recent Trends in Astronomy and Astrophysics Manipal Univ, Manipal,

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)




Physical picture of an Accretion DiskPhysical picture of an Accretion Disk




Radiative ProcessesRadiative Processes

Observations





Observations

Identify Radiative Process





Observations


Estimate Parameters e.g. density, temperature





Observations



Verify Dynamical Model





Observations




Modify or Eliminate or Construct New Model





Observations




Modify or Eliminate or Construct New Model




Some DefinitionsSome Definitions

Flux Observed at Earth:

Energy per unit area per unit timeEnergy ----> Radiation energy

Area ----> area of detector/instrument

F





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




SpectrumSpectrum

Fν

ν Δ ν





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





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





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




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







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




Types of AccelerationTypes of Acceleration

Electro-Magnetic

Electric field of a proton:

Electron is bound --> Radiative transitions

Electron is unbound --> Bremsstrahlung




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




Electric Field of an ElectronElectric Field of an Electron

e_

R Es

E=E s= nRq

R2




Radiation from an electronRadiation from an electron

e_

R Es

E=E s+ E r= nRq

R2+( n1 q

aRc

)sinΘ

Er

a





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. >





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





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




BremsstrahlungBremsstrahlung

proton

e_ (t=0) v=v0

b





e_ (t = t1)

proton

e_ (t=0) v=v0

b





e_ (t = t1)

e_ (t = t2)

proton

e_ (t=0) v=v0

b





e_ (t = t1)

e_ (t = t2)

proton

e_ (t=0) v=v0

b





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





e_ (t = t1)

e_ (t = t2)

proton

e_ (t=0) v=v0

1.Get a( t)

b





e_ (t = t1)

e_ (t = t2)

proton

e_ (t=0) v=v0

1.Get a( t)2. Get E (t)

b





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





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





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





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





ϵν=ne n p T−1 /2 exp(−h ν

kT e

)g ff (T e , ν)

ϵν

ν %h ν=kT e




X-ray emission from a galaxy clusterX-ray emission from a galaxy cluster




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





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





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)





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.






kT e

)g ff (T e , ν)

ϵν

ν %h ν=kT e




Bremsstrahlung Self absorbedBremsstrahlung Self absorbed


kT e

)g ff (T e , ν)

ϵν

ν %h ν=kT eνc

ν2




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





ϵiϵ f

Electron has a initial velocity

θ f

e θi





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

')





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





Black Body Source

Hot Cloud/Corona




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




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.




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




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




Comptonization of black body emissionComptonization of black body emission

y = 0.1





y = 1.0





y = 10.0




CyclotronCyclotron

If electron velocity v << c, the emission iscalled Cyclotron and is monochromatic.

h ν=1

2 π

e Bme c




SynchrotronSynchrotron

If electron velocity v ~ c, the emission iscalled Synchrotron and is nearly monochromatic.

h ν=γ2 12 π

e Bm e c




Non-thermal Electron DistributionNon-thermal Electron Distribution

ne (γ)d γ = C γ−p d γ γmin < γ < γmax




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

→




SummarySummary

Bremsstrahlung

Hot low density matter -- X-rays

Galaxy Cluster, Jets

Synchrotron

low density matter with non-thermal

electrons -- radio/optical/X-rays.




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

Documents

Radiative Processes in Astrophysics - … · Radiative Processes in Astrophysics Ranjeev Misra, IUCAA, Pune, India. Recent Trends in Astronomy and Astrophysics Manipal Univ, Manipal,