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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