Line Transfer and the Bowen Fluorescence
Mechanism in Highly Ionized Optically
Thick Media
Masao Sako
(Caltech)
Chandra Fellow Symposium 2002
Brief Outline
 Radiative transfer effects
 Motivation


Detailed treatment generally ignored in global modeling (e.g., in XSTAR,
Cloudy, etc.)
How do they affect the global emergent spectrum?
 Theory of resonance line scattering
 Line production/destruction mechanisms
 Line overlap and the Bowen fluorescence mechanism
 He II / O III in the UV (classical Bowen fluorescence)
 O VIII / N VII in the X-ray
 Simple spectral model
Radiative Transfer Effects
 Transfer effects are important when  > 1
 There are three important “levels” of opacity sources



Line absorption/scattering ( ~ 10-16 cm2)
Continuum absorption ( ~ 10-18 cm2)
Electron scattering ( ~ 10-24 cm2)
 Most codes assume complete redistribution / escape probability
methods for treating resonance line transfer
 Although this approximation is appropriate for isolated lines with
moderate optical depths ( ≤ 10), it does not adequately describe line
transfer when absorption and scattering in the damping wings become
non-negligible (i.e., when   100 - 1000).
 It is also difficult to apply this method when other opacity sources (e.g.
continuum absorption, line overlap) are important as well.
 In this formalism, a correct treatment of radiative transfer is nearly
hopeless when there are abundance and temperature gradients.
Theory of Line Transfer
 Has been worked out by various authors
 Unno (1952, 1955); Hummer (1962); Auer (1967); Weymann & Williams
(1969); Ivanov (1970, 1973); Hummer & Kunasz (1980)
 Problem
 Solve for the intensity given by the following transfer equation:
Continuum opacity
I
 ( , x,)  [ (x)   ]I( , x,)   (x)SL ( , x)


Line optical
depth
Line profile
Intensity
Line source
function
Theory of Line Transfer
 The source function contains intrinsic as well as scattering terms.
destruction
probability
1  
SL ( , x) 
R( x , x)J( , x )dx  G( )

 (x) 

 obtain solution
redistribution
by rewriting
function the
intrinsic source
distribution
(e.g., recombination
collisional excitation)
transfer equation as a second order
differential equation, and discretizing the spatial (optical depth),
angle, and frequency coordinates - Feautrier (1964) method
Single-Ion Line Ratios
 H-like oxygen at kT = 10 eV (weakly temperature dependent)
 When higher order Lyman lines are absorbed, there is a ~80% chance
(depending on the principal quantum number) for the line to be reemitted. The other ~20% of the time, the line is radiated in the Balmer,
Paschen, etc. lines, and eventually as either a lower-order Lyman line or
2-photon emission from the 2s level.
Bowen Fluorescence Mechanism
 Classic He II / O III Bowen fluorescence (Bowen 1934,1935;
Weymann & Williams 1969)
Bowen Lines
2p3d
2p
2p3p
2p3s
304
2p
O III
l 304
2
1s
He II
O VIII / N VII Transfer
 O VIII Ly-alpha & N VII Ly-zeta (n=7) wavelength overlap
7p
n=2~6
2p
19
1s
N VII
l 19
1s
O VIII
O VIII / N VII Transfer
 Line photons scatter around in space and frequency. Every once in a
while, an O VIII line photon scatters with N VII. When this
happens, the line is lost ~20% of the time.
 The N VII line intrinsic
source function is
negligible compared to
that of the O VIII
lines. Makes very little
difference to the final
results.
 Partial redistribution in
a Voigt profile is
assumed for all the
lines.
Conversion Efficiencies
 From the solution to the transfer equation, one can calculate the
efficiencies for the various processes. In the previous case, the
lines either:
 scatter and eventually escape the medium through the boundaries
 absorbed by the underlying continuum
 absorbed by N VII, followed by cascades to the upper levels
Emergent O VIII / N VII Spectrum
 A hypothetical medium containing
only O VIII, N VII, and some
unspecified form of background
continuum ( = 10-5). An abundance
ratio of O/N = 5 is assumed.
 At  = 100, the higher-order lines
are almost completely suppressed,
while the Ly lines are still
unaffected.
 At  = 1000, fluorescence
scattering is important, and some
of the O VIII Ly lines are
converted to the N VII Lyman,
Balmer, etc. lines. ~33% of this
radiation escape as Ly photons.
 At  = 104, most of the O VIII
Ly line is destroyed
A Few Other Important Line Overlap
 Fe XVIII - O VIII Ly
 the Fe XVIII source function
dominates over that of O VIII
 the line separation is quite large;
important for large turbulent
velocity.
3p
J=3/2
J=5/2
 Fe XVII - O VII Ly-n (n > 5)
 similar to the previous case - the
Fe XVII source function
dominates. multiple levels of O
VII contribute to the total
opacity.
2p 4 3s
7p
6p
2p 5 3s
n=2
l 16
1s
O VIII
16
n=2~5
1 7
1s
1s
Fe XVIII
O VII
l 17
1s
Fe XVII
Summary, Conclusions, Future Work
 Line transfer effects can alter not only line ratios within a given ion,
but also across different elements.
 Important for deriving CNO abundances from optically thick sources
(e.g., in accretion disks).
 Work in progress.
 Incorporate Compton scattering.

Important in very highly ionized medium where the metal abundances are
extremely low, i.e., when AZ  b-f ~ T.
 Comprehensive / global spectral modeling including all important metal
transitions.

e.g., Fe XIX - XXIV lines with O VIII continuum ( < 14.2 Å)
 relativistic effects