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
Continuum Physical processes 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=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.
Bremsstrahlung Radiation electron photon ion Thermal Bresstrahlung Assuming Maxwelliamenergy distribution Spectrum: I(E)=Ag(T)Z 2 n i n e (kt) -1/2 e -E/kT Emissivity: P(T) = Λ(T) n i n 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-Boltzman 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 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 ~ 10 7 K optically-thin CIE spectrum
X-ray Emission from SWCX Peter Beiersdorfer 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. P CX /P th propto 1/n e 2 SWCX is also expected at the heliosphere
X-ray spectroscopy: He-like ions R I Simplified Grotrian diagram (Porquet & Dubau 2000) F R (or W): Resonance line (allowed) 1s2p 1 P1" 1s 2 1 S 0 electronic dipole transition I (or x+y): Intercombination line 1s2p 3 P1 à 1s 2 1 S0 (y) 1s2p 3 P2 à 1s 2 1 S0 (x) Triple or quadruplet F (or z): Forbidden line 1s2s 3 S1 à 1s 2 1 S0 relativistic magnetic dipole transition (Aji very low) 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 Liu, Mao, & Wang 2011 Composite of optical (HST), infrared (Spitzer), and X-ray (Chandra) images Soft X-ray arises primarily from the interplay between a superwind and entrained cool gas clouds.
Antennae galaxy r i f Optical (Yellow), X-ray (Blue), Infrared (Red)
B Synchrotron radiation Characteristic emission frequency ν c, although the spectrum peaks at 0.3ν c. e- 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 I P s =4/3 σ T c (v/c) 2 U B γ 2 =(9.9 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 à I ν =(1.35x10-22 erg cm -2 s -1 Hz -1 ) a(m)n e 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 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 Incident radiation y x electron α z σ T =6.65 x 10-25 cm 2 dσ T = r e2 /2 (1+cos 2 α)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 << m e c 2 in the center of momentum frame But not always, e.g., S-Z effect
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 I I E E 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 cross-section (Klein-Nishinaformula) should be used.
Inverse Compton scattering I I E E 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 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 = 4/3σ T cu rad (v/c) 2 γ 2
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 à 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.
Processes not covered Black Body Optical thick cases and plasma effects Synchrotron-self Compton scattering 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= 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 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 Hot 0.1cm -3 medium Cold dense clouds 20 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 (E/keV) -2 For т sca = N H σ sca > 1.3, multiple scatterings broaden the halo. Smith et al. 2002
The X-ray Halo of GX 13+1 N H ~ 3 10 22 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