Multi-dimensional modelling of X-ray spectra for AGN accretion-disk outflows

Abstract

We use a multi-dimensional Monte Carlo code to compute X-ray spectra for a variety of active galactic nucleus (AGN) disk-wind outflow geometries. We focus on the formation of blue-shifted absorption features in the Fe K band and show that line features similar to those which have been reported in observations are often produced for lines-of-sight through disk-wind geometries. We also discuss the formation of other spectral features in highly ionized outflows. In particular we show that, for sufficiently high wind densities, moderately strong Fe K emission lines can form and that electron scattering in the flow may cause these lines to develop extended red wings. We illustrate the potential relevance of such models to the interpretation of real X-ray data by comparison with observations of a well-known AGN, Mrk 766. Comment: 15 pages, 13 figures, accepted for publication by MNRAS

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arXiv:0805.2251v1 [astro-ph] 15 May 2008
Mon. Not. R. Astron. Soc. 000, 1–15 ()Printed 15 May 2008 (MN LATEX style file v2.2)
Multi-dimensional modelling of X-ray spectra for AGN
accretion-disk outflows
S. A. Sim1, K. S. Long2, L. Miller3, T. J. Turner4,5
1Max-Planck-Institut f¨ ur Astrophysik, Karl-Schwarzschildstr. 1, 85748 Garching, Germany
2Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, U.S.A
3Dept. of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, U.K.
4Dept. of Physics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, U.S.A
5Astrophysics Science Division, NASA/GSFC, Greenbelt, MD 20771, U.S.A
15 May 2008
ABSTRACT
We use a multi-dimensional Monte Carlo code to compute X-ray spectra for a variety of
active galactic nucleus (AGN) disk-wind outflow geometries. We focus on the formation of
blue-shifted absorption features in the Fe K band and show that line features similar to those
which have been reported in observations are often produced for lines-of-sight through disk-
wind geometries. We also discuss the formation of other spectral features in highly ionized
outflows. In particular we show that, for sufficiently high wind densities, moderately strong
Fe K emission lines can form and that electron scattering in the flow may cause these lines
to develop extended red wings. We illustrate the potential relevance of such models to the
interpretation of real X-ray data by comparison with observations of a well-known AGN,
Mrk 766.
Key words: radiative transfer – methods: numerical – galaxies: active – X-rays: galaxies
1 INTRODUCTION
The study of active galactic nuclei (AGN) is an important topic in
contemporary astrophysics. These objects are interesting in their
own right, allowing us to study the extreme physics of accretion
in the vicinity of a supermassive black hole. Furthermore, numer-
ical simulations suggest that AGN likely have a critical role in the
formation and evolution of galaxies, highlighting theneed tounder-
stand how these objects accrete matter, grow and feedback energy
to their surroundings (e.g. Croton et al. 2006).
Since AGN are bright X-ray sources, they have been pop-
ular targets for almost all X-ray observatories. One of the most
interesting results obtained thanks to the high sensitivity of the
current generation of X-ray missions (specifically XMM-Newton
[Jansen et al. 2001], Chandra [Weisskopf et al. 2002] and, more
recently, Suzaku [Mitsuda et al. 2007]) has been the detection of
narrow absorption features in the 2 – 10 keV band of several bright
AGN (see, e.g. Pounds et al. 2003;Reeves et al.2004; Risaliti et al.
2005; Young et al. 2005; Turner et al. 2007; Braito et al. 2007).
Particularly for features in the Fe K region of the spectrum, the ob-
served energies and strengths of these lines suggest identification
with very highly ionized species (e.g. Fe XXV and XXVI) in very
fast (up to ∼ 0.1c) outflows. Blueshifted absorption lines are well-
known from observations of AGN in other wavebands and models
explaining such phenomena in terms of winds have been devel-
oped (see e.g. Murray et al. 1995, Elvis 2000, Proga & Kallman
2004). However, the new X-ray data clearly suggest a compo-
nent of very highly ionized fast outflowing plasma, the relation-
ship of which to the less ionized material observable in ultravio-
let (uv) or softer X-ray wavebands remains unclear. In particular,
moderately ionized outflows identified in soft X-ray spectra gener-
ally have somewhat lower velocity (∼
2005, McKernan et al. 2007) while uv spectra can show evidence
of either low or high velocity absorption (e.g. Elvis 2000).
<1000 km s−1; Blustin et al.
As observational evidence in support of the phenomenon has
accumulated, several theoretical studies of the physical properties
of highly ionized AGN outflows have been made. Pounds et al.
(2003) and King & Pounds (2003) discussed the blueshifted ab-
sorption features in PG1211+143 in terms of a conical outflow
subtending a large solid angle. They suggested that such a flow
might be driven by continuum radiation pressure and that emis-
sion from such a flow might be responsible for the big blue bump
which dominates the bolometric output of PG1211+143. However,
Everett & Ballantyne (2004) considered flows driven by continuum
radiation pressure in greater detail and concluded that, while this
mechanism could work in principle, the resulting outflows were
unlikely to produce spectral signatures as strong as those reported
by Pounds et al. (2003).
Sim (2005) undertook a two-dimensional (2D) Monte Carlo
(MC) radiative transfer study of parameterised conical outflow
models and concluded that, for suitable column densities, viewing
down such flows could account for the observed blueshifted, nar-
row absorption lines in PG1211+143. However, that study was lim-

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Sim et al.
ited to consideration of only the simplest conical geometry and did
not consider the effect of either rotation or off-axis lines-of-sight
on the spectrum.
Usinga chained version
(Kallman & Bautista 2001),Schurch & Done
have computed spectra for columns of outflowing gas with a
variety of density and velocity profiles. They demonstrated that
outflows can imprint a wide variety of features on X-ray spectra,
depending on the outflow conditions and that very high outflow
velocities would be required if absorption in outflows is to explain
soft excesses in AGN spectra. More recently, a similar approach
to that adopted by Schurch & Done (2007) has been used for the
calculation of transmission spectra in dynamical models of AGN
outflows by Dorodnitsyn et al. (2008).
In this paper, we extend the study of Sim (2005) to incorpo-
rate a more realistic and more versatile description of a disk wind
geometry including both rotation and off-axis lines-of-sight. We re-
tain the use of the MC method owing to its versatility for multi-
dimensional radiative transfer. Our method is complementary to
that of Schurch & Done (2007) since we account for geometric ef-
fects directly (e.g. scattering of radiation between lines-of-sight in
multi-dimensional outflow geometries) but make some simplifica-
tions in the treatment of atomic processes.
We focus on highly ionized winds and the interpretation of ob-
servable features intheFeK band. Although other spectral linesare
expected to form in outflows, Fe Kα absorption is the most relevant
for the interpretation of observed spectra since it is the clearest sig-
nature of a highly ionized flow: although more abundant, thelighter
elements are fully ionized more easily than Fe so that any spec-
tral features they imprint are weaker. Furthermore, identification of
features in the Fe K energy band is relatively secure since only K
shell transitions of heavy ions are expected at energies∼
At lower energies, where Kα transitions of light or intermediate
mass elements might arise, line identification is more ambiguous,
particularly if large velocity shifts are considered.
Although we regard Fe Kα absorption features as the best
diagnostic for a highly ionized flow, we will also investigate the
formation of emission components in the Fe K arising from line
scattering or recombination in the outflow. Such features are of
particular interest since they may explain possible P-Cygni-like
line profiles (e.g. Done et al. 2007, Turner et al. 2008) and may
affect the interpretation of Fe emission features commonly asso-
ciated with disk reflection (see e.g. Laming & Titarchuk 2004,
Laurent & Titarchuk 2007).
We begin in Section 2 by defining the class of outflow mod-
els which we will consider. In Section 3 we describe our radiative
transfer method and discuss the adopted atomic data. We present
a sample calculation for one model in Section 4 and then extend
our discussion to a a grid of outflow models in Section 5. The im-
plications of our models for observations of Fe Kα absorption are
described in Section 6 and for other spectral features in Section 7.
In Section 8 we illustrate the value of our models by comparing
them in detail with observations of a well-known AGN, Mrk 766.
We draw conclusions and discuss further work in Section 9.
ofthe1D XSTAR
(2007,
code
2008)
>5 keV.
2 MODEL
Our radiative transfer calculations were performed using a simply-
parameterised model for an outflow launched from an accretion
disk around a supermassive black hole. In this section, we describe
Figure 1. The geometrical construction used to define the wind (only the
positive xz-plane is shown – the wind is symmetric under both reflection
in the xy-plane and rotation about the z-axis). The region occupied by the
wind is shaded. The three parameters which determine the geometry (d,
rmin, rmax) are indicated. The star symbol represents the point in the wind
which is specified by the wind coordinates R and l.
the properties of the model and the parameters which must be spec-
ified to define a particular realisation of the model.
2.1Geometry
We adopt a standard disk wind geometry, namely the “displaced
dipole” model of Knigge et al. (1995). This geometry has been
adopted in radiative transfer studies of accretion disk winds for a
variety of systems including cataclysmic variables (Knigge et al.
1995; Long & Knigge 2002) and massive young stellar objects
(Sim et al. 2005). The geometry is illustrated in Fig. 1 and is de-
fined by the following three parameters (each of which is marked
in the figure):
(i) d, the distance of the focus point below the origin
(ii) rmin, the distance from the origin to the inner edge of the
wind in the xy-plane
(iii) rmax, the distance from the origin to the outer edge of the
wind in the xy-plane
The accretion disk is assumed to lie in the xy-plane. The wind
is symmetric under rotation about the z-axis and under reflection in
the xy-plane.
2.2 Velocity law in the wind
The velocity is specified at every point in the wind following the
parameterisation of Knigge et al. (1995) (see also Long & Knigge
2002). Although this velocity law is not based on self-consistent
hydrodynamical outflow models (cf. Dorodnitsyn et al. 2008), it
provides a simple and reasonably flexible description of possible
steady-state flows which we use for our exploratory radiative trans-
fer simulations.
2.2.1 Rotation
The wind rotates about the z-axis. The rotational velocity is ob-
tained by assuming that parcels of matter conserve specific angular
momentum about the z-axis as they flow outwards. The angular
momentum at the base of a streamline is set at the Keplerian value

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for the radius at which the streamline crosses the xy-plane. Thus
the rotational velocity is determined only by the choice of wind
geometry (see above) and the mass of the central object, Mbh.
2.2.2 Outflow
The outflow velocity points directly away from the focus point of
the wind. Its magnitude is given by
vl= v0+ (v∞− v0)
„
1 −
Rv
Rv+ l
«β
(1)
where l is the distance along the outflow streamline (see Fig. 1),
Rv is an acceleration length parameter and the exponent, β, sets
the rate of acceleration. The terminal velocity, v∞, is specified as a
multiple fv of the escape speed from the base of the streamline
v∞ = fv
r
2GMbh
R
(2)
where R is the radius at the base of the streamline (see Fig. 1).
2.3 Mass density
The wind is assumed to be smooth and in a steady state flow; exten-
sion of this study to clumpy flows will be the topic of a subsequent
investigation. The total mass-loss rate (˙ M) of the wind is treated
as a parameter and the mass loading of specific outflow streamlines
is determined by parameterising the mass-loss rate per unit surface
area as a function of R via
d ˙ m
dA∝ Rk
(3)
subject to the constraint that
4π
Zrmax
rmin
d ˙ m
dAR dR = ˙ M .
(4)
The mass density at a point in the wind is then obtained by com-
bining the specific mass-loss rate on local outflow streamlines with
the outflow velocity, assuming a stationary flow.
2.4 Electron temperature
The electron temperature Te of the outflowing material must be
specified since it has a role to play in determining the ioniza-
tion/excitation state of the plasma (see below). Ultimately, it should
be calculated by consideration of all relevant heating and cool-
ing processes. But the treatment of all such processes – heating
and cooling via lines, bound-free continua, free-free processes and
(inverse-)Compton scattering of photons at all energies – would re-
quire more detailed atomic physics, simulations of a much wider
range of photon energies and the self-consistent consideration of
heating by radiation from other sources (e.g. radiation emitted or
reflected by the accretion disk or surrounding structures). Such is-
sues go beyond the scope of this study and so, as in Sim (2005), Te
is assumed to be uniform and is treated as an input parameter.
2.5 Atomic level populations
In order to keep the computational requirements of our multi-
dimensional MC calculations tractable, we have not attempted a
complete non-LTE calculation, but have instead employed approx-
imate formulae for ionization and excitation. Our approach is sim-
ilar to the standard modified nebular approximation, which has
been used in a variety of other astrophysical calculations (e.g. stel-
lar winds [Abbott & Lucy 1985, Lucy & Abbott 1993, Vink et al.
1999], supernovae [Mazzali & Lucy 1993] and disk winds from
cataclysmic variables [Long & Knigge 2002]). However, as dis-
cussed inSection3.4, wehave modifiedstandard approximations to
reflect the fact that X-ray spectra of AGN are better approximated
by a power law than a blackbody.
2.5.1 Ionization
Forsimplicity, weassume ionization equilibriuminwhichthe dom-
inant ionization process for all the ions we consider is photoioniza-
tionfromtheground state.Furthermore, weneglect recombinations
fromexcitedstatessuch that thecondition of ionization equilibrium
can be expressed:
ni,0γi,0 = neni+1,0
X
l
αi+1,0→l
(5)
where ni,0is the atomic level population of an ionization state i in
its ground state (denoted 0), ne is the free electron density, γi,0 is
the photoionization rate coefficient from the ground state of ion i
and αi+1,0→lis the recombination rate coefficient from the ground
state of ionization state i + 1 to level l of ionization state i. The
summation runs over all states of the lower ion.
This can be rewritten as
ni+1,0ne
ni,0
= ζ(Te)Si(Te,Jν)Φ0,0,i(Te)
(6)
where Φ0,0,i(Te) is the population ratio ni+1,0ne/ni,0 evaluated
for LTE at the electron temperature (Te) and
ζ =
αi+1,0→0
P
lαi+1,0→l
(7)
isthe fractionof recombinations that go directlytotheground state.
Si(Te,J) =γi,0→0
γLTE
i,0→0
=
Z∞
ν0
aνJνν−1dν/
Z∞
ν0
aνBν(Te)ν−1dν
(8)
is the ratio of the true photoionization rate determined from the
mean intensity (Jν) and that which would be obtained in LTE at
Te. aν is the ground state photoionization cross-section for fre-
quency ν, Bν is the Planck function and the integrations run from
the threshold frequency, ν0, to infinity.
Equation 6 is used for all the ionization calculations in this
paper. Since Φ0,0,iand ζ depend only on the adopted electron tem-
perature these can be evaluated prior to the MC radiative transfer
simulation. Si, however, depends on the radiation field Jν and so it
is computed from the radiation field parameterisation and iterated
(see Section 3.4).

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Sim et al.
2.5.2Excitation
Since the majority of the atomic processes with which we are con-
cerned are associated with ground state absorption, the treatment
of excited level populations is relatively unimportant and there-
fore very approximate. For all excited states, we adopt a two-level
radiation-dominated Sobolev approximation
nl
n0
=gl
g0
„2hν3
¯ Jνc2
l¯β
+ 1
«−1
(9)
where hνlis the excitation energy of state l above the ground state,
glisthestatisticalweightof level l,¯β istheangle-averaged Sobolev
escape probability for the transition from level l to the ground state
and¯ Jν is the mean intensity in the transition.
3 RADIATION TRANSPORT SIMULATIONS
The propagation of radiation through the model is followed via a
MC simulation in which the quanta are indivisible packets of ra-
diative energy. The principles of the method have been developed
and described elsewhere (e.g. Abbott & Lucy1985, Lucy & Abbott
1993, Mazzali & Lucy 1993, Lucy 2002, Lucy 2003) so only those
points of specific relevance to the procedure used in this study are
given below.
3.1 Computational grid
For the radiative transfer calculations, the wind properties are first
discretised onto a grid in the natural wind parameters (R,l). Typ-
ically a 100 x 100 grid is used. For convenience when propa-
gating the packets, this grid of wind properties is then mapped
to an underlying three-dimensional (3D) Cartesian grid, typically
100x100x100. Each Cartesian cell which lies inside the wind is
assigned the density, ionization/excitation state and radiation field
properties of the closest point in the grid of wind properties while
those Cartesian grid cells which lie outside the wind are assumed
to be empty.
3.2 Initialisation of packets
Since our primary objective is to simulatespectra inthe keV energy
range, weinitiallycreatepackets between 0.1and 40 keV. A power-
law distribution of packet energies is assumed such that the input
spectrum n(E) varies with photon energy (E) according to
n(E)[photons s−1keV−1] ∝ E−Γ.
(10)
This is an adequate first-order description of the observed X-ray
spectraofAGNinthe2–10keV range withwhichweareprimarily
concerned. The power-law index (Γ) is as an input parameter for
our model.
It is assumed that the primary X-ray source is compact and
roughly appears as a point source as seen from the outflowing gas.
Thus, the packets are launched from the coordinate origin. Their
initial directions are chosen isotropically.
3.3 Propagation of packets
Once launched, the packets propagate until they reach the outer
boundary of the computational domain. As they propagate, the
packets can interact with the outflowing plasma, thereby changing
both their direction of propagation and their observer-frame fre-
quency. In all interactions, energy conservation is strictly enforced
such that, in a local co-moving frame, there is no net gain or loss of
radiative energy. The particular types of packet interaction which
may occur during the simulation are summarised below.
3.3.1 Compton scattering
By far the most common interaction is Compton scattering by free
electrons. Thisprocessistreatedusing themethodoutlined byLucy
(2005). In all our simulations, we assume the electron temperature
is small enough that inverse Compton scattering may be neglected
in the co-moving frame.
3.3.2 Photoabsorption
Bound-free continua can absorb any photons with frequency above
their edges – the cross-sections are obtained from the atomic data
sources described in Section 3.5. During the MC simulations, only
bound-free absorption by ionic ground states is included.
3.3.3 Bound-bound absorption
Atomic lines can absorb photons that come into resonance with
them. Their optical depths are computed in the Sobolev approxi-
mation using the velocity gradient and the appropriate level popu-
lations obtained from the ionization/excitation formulae.
3.3.4 Re-emission
Following photoabsorption or bound-bound absorption, the macro
atom scheme devised by Lucy (2002, 2003) is used to determine
the subsequent re-emission frequency of the packet. This approach
naturally incorporates both resonance scattering and line emission
following recombination, the two processes which are of greatest
interest for outflow features in AGN X-ray spectra. The particular
macro atom scheme adopted allows for bound-bound radiative and
electron collisional processes in both internal state changes and de-
activation. Bound-free recombination processes are also included
but, in accordance with the assumption made for Equation 6, pho-
toionization from excited states is neglected.
Packets emitted by macro atoms via bound-free continua are
radiated isotropically. For bound-bound transitions, the direction
of re-emission is determined by constructing a 2D grid of Sobolev
escape probabilities as a function of polar and azimuthal angle and
sampling this distribution to choose a new packet trajectory.
3.3.5
k-packets
When the outcome of an interaction is a conversion of a radiative
packet to a packets of thermal energy (k-packets in the nomen-
clature of Lucy 2003), we assume that the subsequent elimination
of the k-packets predominantly leads to emission at lower photon
energies such that these packets are lost to the hard X-ray energy
band.

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5
3.4 Monte Carlo estimators and the radiation field
3.4.1Parameterisation of the radiation field
The treatment of ionization requires that the radiation field be
known locally. Since the wind may be optically thick, the radia-
tion field is computed from the behaviour of the MC packets using
volume based estimators. In principle, it is possible to describe an
arbitrary radiation field using MC estimators for the mean intensity
in narrow frequency bins. However, this requires very large num-
bers of MC quanta which becomes restrictive for the exploration of
model parameter spaces. Therefore, wefollow previous MC studies
inadopting aphysically motivated parameterisation of the radiation
field.
This method has been described by Lucy (1999, 2003, 2005)
and used in various other studies (e.g. Mazzali & Lucy 1993;
Long & Knigge 2002). In these previous studies, it was assumed
that the true radiation field was black-body in character and was
thereforeusually parameterised by aradiationtemperature andadi-
lutionfactor. Here, however, weareconcerned witharadiation field
which is non-thermal in character and so parameterisation based on
a power-law is adopted:
Jν(r) = W(r)να(r)
(11)
where both the parameters W and α are functions of position.
Given our choice of input radiation field (equation 10), if the wind
is optically thin, we would expect to have α(r) = 1 − Γ at all
points. However, for optically thick winds, we expect variation in
α. Using this description, the Si-factors in the ionization equation
can be expressed as functions of only Teand the local values of W
and α
Si(Te,W,α) = W
Z∞
ν0
aννα−1dν/
Z∞
ν0
aνBν(Te)ν−1dν .
(12)
This allows the ionization state of the gas to be uniquely de-
termined from Te, the local mass-density and the radiation field
parameter pair [W, α] only.
To specify the excitation state via equation 9, we also need to
know¯ Jν for ground state transitions. Again, exact MC estimators
for¯ Jνinall transitionscan be constructed but recording and storing
them for large numbers of transitions in multi-dimensional grids
becomes expensive in terms of both processor time and memory
allocation.¯ Jν can be expressed as
¯ Jν =
1
4π
Z2π
0
Z1
−1
Iν,µ,φβµ,φdµ dφ
(13)
where cos−1µ and φ are spherical polar angles, I(ν,µ,φ) is spe-
cific intensity and β(µ,φ) is the Sobolev escape probability for the
transition. For the specific case of an homologous flow, β becomes
independent of direction but, in general, it is a function of both µ
and φ. In the interests of computational expediency, however, we
neglect this dependency and replace βµ,φ with its angle-averaged
value,¯β. This simplification allows¯ Jν to be expressed as
¯ Jν =
1
4π
¯β
Z2π
0
Z+1
−1
Iν,µ,φdµ dφ =¯βJν = Wνα¯β ,
(14)
adopting our parameterisation of the radiation field. This simplifies
equation 9 to give our final excitation formula
nl
n0
=gl
g0
„
2h
Wνα−3
l
c2+ 1
«−1
(15)
where hνlis the excitation energy of state l above the ion ground
state. This treatment of excitation avoids the need to specify any
radiation field parameters beyond those used in the ionization for-
mula and therefore places no further computational demands on the
MC simulations. It is very crude but is not of critical importance to
our study of highly ionized outflows since the excitation state is
low enough that the ground state populations of H- and He-like
species are dominant. The most important failing of this treatment
will be for the metastable triplet states of He-like ions. Thus im-
provements to the treatment of excitation will be necessary in order
to extend the code for applicability to less ionized flows and softer
wavebands.
3.4.2 Monte Carlo estimators
The values of W and α are obtained by recording two MC estima-
tors per grid cell:
E(1)
n
=
X
paths in n
ǫcmf ds
(16)
E(2)
n
=
X
paths in n
ǫcmfνcmf ds
(17)
where the summation runs over all quanta trajectories which lie in-
side the grid cell of interest (denoted by n) and in which the packet
frequency lies in the regime of interest (νmin < ν < νmax). In
these equations, ds is the length of a Monte Carlo quanta trajec-
tory length, ǫcmf is the comoving frame packet energy and νcmf is
the comoving frame packet frequency.
Values for E(1)
simulation of all the packets. At the end of the simulation, they are
used to obtain values of αnand Wnin each grid cell as follows.
TheratioE(2)
the frequency interval being simulated (νmin < ν < νmax), this ratio
is directly linked to the power-law index via:
n and E(2)
n are recorded during the Monte Carlo
n /E(1)
n givesthemeanfrequency. Sinceweknow
E(2)
n
E(1)
n
=αn+ 1
αn+ 2
ναn+2
max
ναn+1
max
− ναn+2
min
− ναn+1
min
(18)
which can be numerically solved for α.
Once αnis known, Wncan be obtained by normalizing E(1)
n :
Wn =
E(1)
n
4πVn∆t
αn+ 1
− ναn+1
ναn+1
max
min
(19)
where Vn is the volume of grid cell n and ∆t is the effective time
interval represented by the Monte Carlo simulation.
3.4.3Iteration
The formulae given above allow values of Wn and αn to be ob-
tained from the behaviour of the MC quanta. However, since the
values of these parameters also affect the MC simulation (primar-
ily owing to their importance in determining the ionization state),
these parameters must be iterated to reach a converged parameteri-
sation of the radiation field.