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=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 Thomson scattering -25 2 σT=6.65 x 10 cm x 2 2 dσT= re /2 (1+cos α)dΩ Incident • Scattering is backward and forward symmetric radiation • Polarized (depending on α) even α z if the incident radiation is not. electron • No change in photon energy E • A good approximation if the electron recoil is negligible, ie, y 2 E << mec 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 I energy to a “cool” electron. • Frequency change: E = E’/[1+(E’/m c2)(1-cosα)] e E • Compton reflection (e.g., accretion disk) • In the N-R case, the cross section is the Thomson cross section 2 I •If either γ or E/mec >> 1, the quantum relativistic cross- section (Klein-Nishina formula) should be used. E Inverse Compton scattering A “Low energy” photon gains energy from a hot (or I relativistic) electron • ν ~ γ2ν’ • For relativistic electrons E (e.g., γ ~ 103, radio Æ X-ray, IR Æ Gamma-ray; jets, radio lobes) • Effect may be important even for N-R electrons (e.g., the S-Z effect) I • Energy loss rate of the electron 2 2 E dE/dt = 4/3σTcUrad (v/c) γ Synchrotron radiation B • Characteristic emission frequency νc, although the spectrum peaks at 0.3νc. 4 1/2 • γ ~ 2 x 10 [νc(GHz)/B(µG)] e- 8 1/2 ~ 3 x 10 [Ec(keV)/B(µG)] • The total power radiated 4 2 2 3 4 Ps=2e γ B⊥ /(3me c ) -16 2 2 =(9.89 x 10 eV/s) γ B⊥ (µG) I • Electron lifetime 3 -1/2 ~ 1 yr [Ec(keV) B(µG) ] 0.3 ν/νc Ginzburg, 1987 Synchrotron spectrum (Cont.) Assuming the power law energy distribution of electrons, -m dn(γ)/dγ = n0 γ Æ -22 -2 -1 -1 Log(I) Iν=(1.35x10 erg cm s Hz ) (m+1)/2 18 (m-1)/2 a(m)n0 L B (6.26 x10 /ν) Power-law Individual electron spectra Log(ν) F.Chu ‘s book Synchrotron vs Compton scattering For an individual electron 2 Ps ≈ 4/3γ cσT UB 2 Pc ≈ 4/3γ cσT Uν Æ 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. Bremsstrahlung Radiation electron photon ion Thermal Bresstrahlung • Assuming Maxwelliam energy distribution 2 • Emissivity: P(T) = Λ(T) ne Λ(T) = 1.4x10-27 T0.5 g(T) erg cm3 s-1 •Electron life time is then 4 0.5 ~ 3 nekT/P(T) = (1.7x10 yr) T /ne Thermal Plasma Emission Assumptions: –Optically thin – Thermal equilibrium • Maxwelliam energy distribution • Same temperature for all particles Spectral emissivity = Λ(E,T) neni – Λ(E,T) = Λline(E,T) + Λbrem (E,T) 2 -1/2 –E/kT – Λbrem (E,T) = A G(E,T) Z (kT) е G(E,T) --- the “Gaunt factor” –For solar abundances, the total cooling function: -22 -0.7 -24 0.5 3 -1 Λ(T) ~ 1.0 x 10 T6 +2.3x10 T6 erg cm s McCray 1987 Plasma cooling function • Continuum: bremsstrahlung + recombination • Strong metallicity dependent •For T < 107 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 (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 T ~ 107 K optically-thin CIE spectrum plasma, superwind, stellar wind, etc.) 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 • The basic error on much atomic collisional data is ~ 30% • The total emissivity in APEC APEC and R&S Brems calculations is similar Black • The difference are in body number of lines R&S (offset by included and their 100) 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 e- Atom absorbs photon E E-I Atom, ion, σ Molecule, or grain E-3 Cross-section(s) characterized by ionization edges. E 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= σgas + σmol + σgrains Where σISM is 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 21-23 -2 high NH (~10 cm ) 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 Smooth vs. clumpy observer smooth 1 cm-3 clumpy Hot0.1 medium cm-3 Cold dense20 cmclouds-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, –iethe 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 -23 -2 • σsca = 9.03 × 10 (E/keV) – 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 тsca = NHσsca > 1.3, multiple scatterings Æ broaden the halo. Smith et al. 2002 Example: GX 13+1 CCD transfer streak 22 -2 •NH ~ 3 × 10 cm • 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 22 -2 NH ~ 3 × 10 cm.