X-ray Radiation, Absorption, and Scattering

What we can learn from data depend on our understanding of various X-ray emission, scattering, and absorption processes. We will discuss some basic processes: •  Bremsstrahlung (free-free) emission •  Recombination and charge exchange •  plasma (line) emission •  Synchrotron Emission •  Photon-electron scattering

–  Thomson & Compton scattering –  Inverse Compton scattering

•  Photoelectric absorption •  Dust scattering

Physical processes •  Continuum

–  blackbody –  bremsstrahlung –  Synchrotron –  scattering –  radiative recombination

•  Lines –  thermal –  charge exchange –  fluorescence

Continuum Radiation

•  Radiation is virtually exclusively from electrons! •  Emitted when an electron is accelerated. •  In the N-R case, for example, Larmour formula

(dipole radiation): P=2e2a2/(3c3) where a is the acceleration of the electron.

•  For example, –  Bremsstrahlung – due to collision with an ion –  Compton scattering – due to collision with a photon –  Synchrotron – due to centripetal motion in a B field.

Bremsstrahlung Radiation

•  Thermal Bresstrahlung •  Assuming Maxwelliamenergy distribution •  Spectrum: I(E)=Ag(T)Z2 nine(kT)-1/2 e-E/kT

•  Emissivity: P(T) = Λ(T) ni ne

Λ(T) = 1.4x10-27 T0.5g(T) erg cm3 s-1

•  Electron life time is then ~ 3 nekT/P(T) = (1.7x104 yr) T0.5/ne

electron

ion

photon

Thermal Plasma Emission Assumptions: •  Optically thin •  Thermal equilibrium •  Maxwelliam-Boltzman energy distribution

–  Same temperature for all particles •  Spectral emissivity= Λ(E,T) neni

–  Λ(E,T) = Λline(E,T) + Λbrem(E,T) –  Λbrem(E,T)= A G(E,T) Z2 (kT)-1/2 е–E/kT

G(E,T) ---the “Gaunt factor” –  For solar abundances, the total cooling function:

Λ(T) ~ 1.0 x 10-22 T6-0.7+2.3x10-24 T6

0.5 erg cm3 s-1

McCray 1987

Plasma cooling function •  Continuum:

bremsstrahlung+ recombination

•  Strong metallicity dependent

•  For T < 107K and solar abundances, Line emission > bremsstrahlung

Gaetz & Salpeter (1983)

Thermal Plasma: Coronal Approximation

• Absence of ionizing radiation • Dominant collisional processes:

 – Electron impact excitation and ionization

– Radiative recombination, dielectronic recombination, and bremsstrahlung

• Ionization fraction is function only of  T in stationary ionization balance (CIE)

Ionic Equilibrium

Optical thin thermal plasma models • CIE (Collisional Ionization

 Equilibrium) XSPEC models: APEC

• NEI (Non-Equilibrium  Ionization)

– Ionizing plasma (Te > Tion in  term of ionization balance)    • Shock heating (e.g., SNRs)

– Recombination plasma (Te <  Tion)    • Photoionizing (e.q. plasma      near an AGN or XB)    • (e.g. adiabatically cooling      plasma, superwind, stellar      wind, etc.)

T ~ 107 K optically-thin CIE spectrum

X-ray Emission from SWCX

•  Charge exchange (CX) nature of comet X-ray emission is confirmed, spectroscopically and temporally.

•  CX has a cross-section of ~10-15 cm-2 and occurs on scales of the mean free path of hot ions at the interface.

•  PCX/Pth propto 1/ne2

Peter Beiersdorfer

SWCX is also expected at the heliosphere

X-ray spectroscopy: He-like ions •  R (or W): Resonance

line (allowed) 1s2p 1P1"1s2 1S0 electronic dipole transition

•  I (or x+y): Intercombination line

1s2p 3P1 à 1s2 1S0 (y) 1s2p 3P2 à 1s2 1S0 (x) Triple or quadruplet

•  F (or z): Forbidden line 1s2s 3S1 à 1s2 1S0

relativistic magnetic dipole transition (Aji very low)

R I

F

Simplified Grotrian diagram (Porquet & Dubau 2000) The relative intensities of the R, I, F lines are

determined by how the upper levels are populated.

Radiative Recombination

•  In many cases the RRC is weak, but it is an excellent diagnostic, if it can be measured.

Earlier Galactic center activity? Detection of recombining plasma.

S. Nakashima et al. 2013

X-ray Emission Line Spectroscopy of the Nuclear Starburst Galaxy: M82

Soft X-ray arises primarily from the interplay between a superwind and entrained cool gas clouds.

Composite of optical (HST), infrared (Spitzer), and X-ray (Chandra) images

Liu, Mao, & Wang 2011

Antennae galaxy

Optical (Yellow), X-ray (Blue), Infrared (Red)

r i f

Synchrotron radiation

e-

B

I

ν/ν c 0.3 Ginzburg, 1987

•  Characteristic emission frequency νc, although the spectrum peaks at 0.3νc.

γ ~ 2 x 104[νc(GHz)/B(µG)]1/2

~ 3 x 108[Ec(keV)/B(µG)]1/2

•  The total power radiated Ps=4/3 σT c (v/c)2UBγ2

=(9.9 x 10-16 eV/s) γ2B⊥2(µG) •  Electron lifetime

~ 1 yr [Ec(keV)B(µG)3]-1/2

Log(I)

Power-law

Individual

electron spectra

Log(ν) F.Chu ‘s book

Synchrotron spectrum (Cont.)

Assuming the power law energy distribution of electrons, dn(γ)/dγ= n0γ-m

à Iν=(1.35x10-22 erg cm-2 s-1 Hz-1) a(m)neL B(m+1)/2 (6.26 x1018/ν)(m-1)/2

Synchrotron spectrum (Cont.) But other effects may also need to be considered:

–  Opacity, including various scattering –  Self absorption and scattering –  Scattering of the ambient radiation –  Cooling due to the synchrotron radiation and the

scattering.

Thomson scattering

•  σT=6.65 x 10-25 cm2

•  dσT= re2/2 (1+cos2α)dΩ

•  Scattering is backward and forward symmetric

•  Polarized (depending on α) even if the incident radiation is not.

•  No change in photon energy E A good approximation if the electron

recoil is negligible, i.e., E << mec2 in the center of momentum frame

•  But not always, e.g., S-Z effect

α

Incident

radiation

x electron

z

y

Reading  assignment  

•  Finish  Ch  5,  if  you  have  not.  •  Wang,  Q.  D.;  Lu,  F.  J.;  Go>helf,  E.  V.2006,  MNRAS,  367,  937  

Compton Scattering •  The electron recoil is considered

and an energetic photon loses energy to a “cool” electron.

•  Frequency change: E = E’/[1+(E’/mec2)(1-cosα)]

•  Compton reflection (e.g., accretion disk)

•  In the N-R case, the cross section is the Thomson cross section

•  If either γ or E/mec2 >> 1, the quantum relativistic cross-section (Klein-Nishinaformula) should be used.

I

I

E

E

Inverse Compton scattering •  A “low energy” photon gains

energy from a hot (or relativistic) electron

ν ~ γ2 ν’ •  For relativistic electrons (e.g.,

γ~103, radio à X-ray, IR à Gamma-ray; jets, radio lobes)

•  Effect may be important even for N-R electrons (e.g., the S-Z effect)

•  Energy loss rate of the electron

•  dE/dt = 4/3σTcUrad(v/c)2γ2

I

E

I

E

Synchrotron vs. Compton scattering

For an individual electron Ps≈4/3γ2cσT UB

Pc≈4/3γ2cσT Uν à Ps/Pc= UB/Uν

They also have the same spectral dependence! The same also applies to a distribution of electrons. If both IC and synchrotron radiation are measured, all the intrinsic parameters (B and ne) can be derived.

Processes not covered

• Black Body • Optical thick cases and plasma

effects • Synchrotron-self Compton scattering • Fluorescent radiation • Resonant scattering …

Photoionization

Atom absorbs photon e-

σ

E                

 E-3

       E-I      

 Atom, ion, Molecule, or grain                

     Cross-section(s)      characterized by      ionization edges.    E

Effect of photoelectric absorption

I

interstellar cloud source observer

I

E E

X-ray Absorption in the ISM Cross-section offered at energy E is given by: σ(E) • σ= σgas + σmol + σgrains

Where σISMis normalized to NH

• Iobs(E) = exp[ - σ(E) NH ] Isource(E) • Considerable (~5%) uncertainties in existing calculations,

good enough only for CCD spectra • Suitable for E > 100 eV • ISM metal abundances may be substantially lower (~30%)

than the solar values assumed • Neglecting

– the warm and hot phases of the ISM – Thomson scattering, important at E > 4 keV – Dust scattering, important for point-like sources of moderate

high NH (~1021-23 cm-2)

J. Wilms, A. Allen, & R. McCray (2000)

X-ray Absorption in the ISM                    

 ∝E-2.6

Assuming solar abundances

Column Density Column density: NH=∫nH dl, which may be estimated: • Directly from X-ray spectral fits • From the 21cm atomic hydrogen line at high Galactic latitudes

 + partially-ionized gas (Hα-emitting). • From optical and near-IR extinction • From 100 micro emission. • At low Galactic latitudes, 100 micro emission may still be

 used, but has not been calibrated. Millimeter continuum may  be better.

dl

1 cm-3

Smooth vs. clumpy    

   observer  

 smooth

clumpy

Cold dense clouds 20 cm-3 Hot 0.1cm-3

medium

Dust scattering

E E

     grain  

• Dust grains cause X-ray scattering at small forward  angles

• X-ray photons sees the dust particles as a cloud of  free electrons

• Each electron “sees” the wave (photon) and oscillates  like a dipole (Rayleigh scattering)

• The scattered waves from individual electrons add  coherently,    – ie the flux ∝ N2; otherwise ∝ N.

Dust scattering • Scattering of X-rays passing through dust

grains in the ISM – X-ray halos – Alter the spectra of the scattered sources

• σsca = 9.03 × 10-23 (E/keV)-2

– E > 2 keV --- Rayleigh-Gans approximation – typical dust models (Mathis et al 1977)

• Total halo fraction ~ 1.5 (E/keV)-2

• For тsca = NHσsca > 1.3, multiple scatterings broaden the halo.

Smith et al. 2002

The X-ray Halo of GX 13+1

NH ~ 3 × 1022 cm-2 Smith R. 2008

Summary of radiation process •  blackbody : everything hits everything, many times •  bremsstrahlung: electrons bend in electric fields •  recombination: electrons hit atoms, get captured •  bound-bound : electrons jump down quantum levels •  charge exchange : ions hit neutrals, swap electrons •  synchrotron : electrons bend in magnetic fields •  Compton scattering : photons hit electrons •  inverse Compton : photons hit energetic electrons •  photoionization : photons hit atoms, electrons

escape •  dust scattering: photons meet dust grains