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: Photon-electron scattering Thomson scattering Compton scattering Inverse Compton scattering Synchrotron Emission Bremsstrahlung (free-free) emission Recombination and plasma (line) emission Photoelectric absorption Dust scattering
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=2e 2 a 2 /(3c 3 ) 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
Thomson scattering x σ T =6.65 x 10-25 cm 2 dσ T = r e2 /2 (1+cos 2 α)dω Incident radiation electron α z Scattering is backward and forward symmetric Polarized (depending on α) even if the incident radiation is not. No change in photon energy E y A good approximation if the electron recoil is negligible, ie, E << m e c 2 in the center of momentum frame But not always, e.g., S-Z effect
Compton Scattering The electron recoil is considered and an energetic photon loses energy to a cool electron. Frequency change: E = E /[1+(E /m e c 2 )(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/m e c 2 >> 1, the quantum relativistic crosssection (Klein-Nishina formula) should be used. I I E E
Inverse Compton scattering A Low energy photon gains energy from a hot (or relativistic) electron ν ~ γ 2 ν For relativistic electrons (e.g., γ ~ 10 3, radio X-ray, IR 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 = 4/3σ T cu rad (v/c) 2 γ 2 I I E E
B Synchrotron radiation e- I Characteristic emission frequency ν c, although the spectrum peaks at 0.3ν c. γ ~ 2 x 10 4 [ν c (GHz)/B(µG)] 1/2 ~ 3 x 10 8 [E c (kev)/b(µg)] 1/2 The total power radiated P s =2e 4 γ 2 B 2 /(3m e3 c 4 ) =(9.89 x 10-16 ev/s) γ 2 B 2 (µg) Electron lifetime ~ 1 yr [E c (kev) B(µG) 3 ] -1/2 0.3 ν/ν c Ginzburg, 1987
Synchrotron spectrum (Cont.) Assuming the power law energy distribution of electrons, Log(I) dn(γ)/dγ = n 0 γ -m I ν =(1.35x10-22 erg cm -2 s -1 Hz -1 ) a(m)n 0 L B (m+1)/2 (6.26 x10 18 /ν) (m-1)/2 Power-law Individual electron spectra Log(ν) F.Chu s book
Synchrotron vs Compton scattering For an individual electron P s 4/3γ 2 cσ T U B P c 4/3γ 2 cσ T U ν P s /P c = U B /U ν 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 n e ) can be derived.
Bremsstrahlung Radiation electron photon ion Thermal Bresstrahlung Assuming Maxwelliam energy distribution Emissivity: P(T) = Λ(T) n 2 e Λ(T) = 1.4x10-27 T 0.5 g(t) erg cm 3 s -1 Electron life time is then ~ 3 n e kt/p(t) = (1.7x10 4 yr) T 0.5 /n e
Thermal Plasma Emission Assumptions: Optically thin Thermal equilibrium Maxwelliam energy distribution Same temperature for all particles Spectral emissivity = Λ(E,T) n e n i Λ(E,T) = Λ line (E,T) + Λ brem (E,T) Λ brem (E,T) = A G(E,T) Z 2 (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 T 6-0.7 +2.3x10-24 T 6 0.5 erg cm 3 s -1 McCray 1987
Plasma cooling function Continuum: bremsstrahlung + recombination Strong metallicity dependent For T < 10 7 K and solar abundances, Line emission > bremsstrahlung Continuum 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: R&S, Mekal NEI (Non-Equilibrium Ionization) Ionizing plasma (T e > T ion in term of ionization balance) Shock heating (e.g., SNRs) Recombination plasma (T e < T ion ) Photoionizing (e.q. plasma near an AGN or XB) (e.g. adiabatically cooling plasma, superwind, stellar wind, etc.) T ~ 10 7 K optically-thin CIE spectrum
Major Available Code Raymond & Smith small, fast, adequate for CCD-resolution data. SPEX available only as part of the SPEX spectral analysis package, including both CIE and NEI models Chianti used most in the solar community written in IDL Separated code and data Most UV/EUV, being extended to X-ray APEC/APED Designed for high resolution spectroscopy (using dispersed spectra) Separated code and data (FITS)
Comparison of CIE plasma codes Black body Brems APEC R&S (offset by 100) The basic error on much atomic collisional data is ~ 30% The total emissivity in APEC and R&S calculations is similar The difference are in number of lines included and their wavelengths T = 1 kev
Processes not covered Black Body Optical thick cases and plasma effects Synchrotron-self Compton scattering Relativistic beaming effects Fluorescent radiation Resonant scattering
Photoionization Atom absorbs photon E e - E-I σ E -3 Atom, ion, Molecule, or grain E Cross-section(s) characterized by ionization edges.
Effect of photoelectric absorption source interstellar cloud observer I I E E
X-ray Absorption in the ISM Cross-section offered at energy E is given by: σ(e) σ= σ gas + σ mol + σ grains Where σ ISM is normalized to N H I obs (E) = exp[ - σ(e) N H ] I source (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 N H (~10 21-23 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: N H = n H 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
Smooth vs. clumpy smooth observer 1 cm -3 clumpy Cold dense clouds Hot medium 20 cm -3 0.1 cm -3
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 N 2 ; 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 σ sca = 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(+0.5-0.1) (E/keV) -2 For т sca = N H σ sca > 1.3, multiple scatterings broaden the halo. Smith et al. 2002
Example: GX 13+1 CCD transfer streak N H ~ 3 10 22 cm -2 Significant pile-up within ~ 50 Important for sources with > 0.01 cts/s Affecting both spatial and spectral distributions CCD transfer streak Useful for estimating the source spectrum Programs available for the removal
The X-ray Halo of GX 13+1 N H ~ 3 10 22 cm -2