# A Census of X-ray gas in NGC 1068: Results from 450ks of $Chandra$ HETG
Observations

T. Kallman  NASA/GSFC  Daniel A. Evans  Harvard-Smithsonian CfA  H. Marshall,
C. Canizares, M. Nowak, N. Schulz  MIT  A. Longinotti  European Space
Astronomy Center of ESA, Madrid, Spain

###### Abstract

We present models for the X-ray spectrum of the Seyfert 2 galaxy NGC 1068.
These are fitted to data obtained using the High Energy Transmission Grating
(HETG) on the $Chandra$ X-ray observatory. The data show line and radiative
recombination continuum (RRC) emission from a broad range of ions and
elements. The models explore the importance of excitation processes for these
lines including photoionization followed by recombination, radiative
excitation by absorption of continuum radiation and inner shell fluorescence.
The models show that the relative importance of these processes depends on the
conditions in the emitting gas, and that no single emitting component can fit
the entire spectrum. In particular, the relative importance of radiative
excitation and photoionization/recombination differs according to the element
and ion stage emitting the line. This in turn implies a diversity of values
for the ionization parameter of the various components of gas responsible for
the emission, ranging from log($\xi$)=1 – 3. Using this, we obtain an estimate
for the total amount of gas responsible for the observed emission. The mass
flux through the region included in the HETG extraction region is
approximately 0.3 M⊙ yr-1 assuming ordered flow at the speed characterizing
the line widths. This can be compared with what is known about this object
from other techniques.

##  1 Introduction

X-ray spectra demonstrate that many compact sources are viewed through
partially ionized gas. This gas manifests itself as a rich array of lines and
bound-free features in the 0.1 - 10 keV energy range. The existence of this
‘warm absorber’ gas and the fact that it often shows Doppler shifts indicating
outflows, has potential implications for the mass and energy budgets of these
sources. These features have been used to infer mass outflow rates for many
accreting sources, notably those in bright, nearby active galactic nuclei
(AGN) (Turner & Miller, 2009; Crenshaw et al., 2003; Miller et al., 2009;
Krongold et al., 2003; Kaastra et al., 2011; Kaspi et al., 2002).

Intrinsic to the problem is the fact that the gas is not spherically
distributed around the compact object. If it were, resonance lines would be
absent or would have a P-Cygni character. P-Cygni profiles are observed in
X-ray resonance lines from the X-ray binary Cir X-1 (Schulz et al., 2008);
most AGN do not show this behavior clearly. Understanding the quantity of warm
absorber gas, its origin and fate, are key challenges. Interpretation of
absorption spectra is often based on the assumption that the residual flux in
the line trough is solely due to finite optical depth or spectral resolution.
That is, the effect of filling in by emission is neglected. Understanding the
possible influence of emission is desirable, both from this point of view and
since emission provides complementary information about a more extended
region. Comparison between warm absorbers and the spectra of objects in which
the gas is viewed in reflection rather than transmission provides an added
test for our understanding of the geometry of the absorbing/emitting gas.
Emission spectra also are possibly less affected by systematic errors
associated with the observation, such as internal background or calibration
errors which could affect the residual flux in the core of deep absorption
features.

Emission spectra are observed from compact objects when the direct line of
sight to the central compact object is blocked. This can occur in X-ray
binaries or in Seyfert galaxies where the obscuration comes from an opaque
torus (Antonucci & Miller, 1985). A notable example is in Seyfert 2 galaxies,
and the brightest such object is NGC 1068 (Bland-Hawthorn et al., 1997). This
object has been observed by every X-ray observatory with sufficient
sensitivity, most recently by the grating instruments on $Chandra$ and $XMM-
Newton$. These reveal a rich emission line spectrum, including lines from
highly ionized medium-Z elements, fluorescence from near neutral material, and
radiative recombination continua (Liedahl et al., 1990) (RRCs) which are
indicative of recombination following photoionization.

Apparent emission can be caused by various physical mechanisms. These include
cascades following recombination, electron impact excitation, inner shell
fluorescence, and radiative excitation by absorption of the continuum from the
central object in resonance lines. Radiative excitation produces apparent
emission as a direct complement to the line features seen in warm absorbers;
rates can exceed that due to other processes. It is also often referred to as
resonance scattering, since it is associated with scattering of continuum
photons in resonance lines. However, past treatments in the context of Seyfert
galaxy X-ray spectra have been limited to consideration of a single scattering
of an incident continuum photon by a resonance line, after which the photon is
assumed to be lost. Since there is a considerable literature on the topic of
transfer of photons in resonance lines, also sometimes referred to as
resonance scattering, here and in what follows we will not use this term.

Since radiative excitation preferentially affects lines with large oscillator
strengths arising from the ground term of the parent ion, it affects line
ratios such as the $n=$1 – 2 He-like lines, causing them to resemble the
ratios from coronal plasmas. This was pointed out by Kinkhabwala et al.
(2002), who presented high resolution spectra of NGC 1068 obtained using the
reflection grating spectrometer (RGS) on the $XMM-Newton$ satellite. The RGS
is most sensitive at wavelengths greater than approximately 10 $\AA$, and
Kinkhabwala et al. (2002) showed that the He-like lines from N and O in NGC
1068 are affected by radiative excitation. They also showed that, since
radiative excitation depends on pumping by continuum radiation from the
central compact source, this process is affected by the attenuation of the
continuum. This in turn depends on the column density of the line emitting
gas; radiative excitation is suppressed when the continuum must traverse a
high column density. Kinkhabwala et al. (2002) adopted a simple picture in
which the gas is assumed to be of uniform ionization and opacity and were able
to then constrain the column density in the NGC 1068 line emitting region from
the observed line ratios.

The High Energy Transmission Grating (HETG) on the $Chandra$ satellite is
sensitive to wavelengths between 1.6 – 30 $\AA$, allowing study of the He-like
ratios from elements Ne, Mg, Si and heavier, in addition to those from O. Ogle
et al. (2003) used an HETG observation of NGC 1068 to show that the He-like
ratios from Mg and Si show a stronger signature of radiative excitation than
do O and Ne. They interpret this as being due to the fact that all the lines
come from the same emitting region with a high column, and that attenuation of
the continuum is stronger for Mg and Si owing to ionization effects. That is,
that O and Ne are more highly ionized than the heavier elements, and point out
that this is consistent with the results of photoionization models.

The challenge of modeling X-ray emission spectra divides into parts: (i)
modeling the excitation process which leads to emission; (ii) modeling the
ionization of the gas; and (iii) summing over the spatial extent of the
emitting gas leading to the observed spectrum. Kinkhabwala et al. (2002)
include a detailed treatment of the population kinetics for emitting ions
which takes into account the effect of the continuum radiation from the
compact object on the populations, along with the attenuation of this
radiation in a spatially extended region. Ogle et al. (2003) add to this a
treatment of the ionization balance. Matt et al. (2004) have used the
intensities of lines formed by fluorescence to infer the covering faction of
low ionization, high column density gas and shown that this is consistent with
the properties of the obscuring torus.

A shortcoming of efforts so far is that none self-consistently treats the
spatial dependence of the absorption effects affecting radiative excitation
together with the corresponding effects on the ionization balance. That is,
models such as Ogle et al. (2003) adopt temperature and ionization balance
associated with optically thin photoionized gas. They then assume that this
ionization is constant throughout the cloud and use this to calculate
continuum attenuation and its effects on the population kinetics. They did not
consider the spatial dependence of the ionization of the gas associated with
attenuation of the incident continuum, along with the associated suppression
of radiative excitation.

Since the work of Kinkhabwala et al. (2002) and Ogle et al. (2003) there have
been numerous studies of absorption dominated warm absorber spectra. In
addition, a large campaign with the $Chandra$ HETG was carried out on NGC 1068
in 2008, resulting in a dataset with unprecedented statistical accuracy (Evans
et al., 2010). For these reasons, and the reasons given above, we have carried
out new modeling of the photoionized emission spectrum of NGC 1068. The
questions we consider include: To what extent can photoionized emission models
fit the observations? Which structures, known from other studies, can account
for the observed X-ray line emission? Are there patterns in the elemental
abundances in the photoionized emission spectrum which provide hints about the
origin or fate of the X-ray gas? What mass of gas is associated with the X-ray
emission, and what flow rate does this imply? In section 2 we present the
observed spectrum and in section 3 we describe model fitting. A discussion is
in section 4.

##  2 Data

The dataset that we use in this paper consists of an approximately 400 ksec
observing campaign on NGC 1068 during 2008 using the $Chandra$ HETG. A
description of these observations was reported briefly in Evans et al. (2010),
but no detailed description of the data has been published until now. In
addition, we also incorporate the earlier 46 ksec observation with the same
instrument which was carried out in 2000 and was published by Ogle et al.
(2003). A log of the observations is given in table 1.

The satellite roll angles during the observations were in the range 308 – 323
degrees. This corresponds to the dispersion direction being approximately
perpendicular to the extended emission seen in both optical and X-rays (Young
et al., 2001). The standard HEG and MEG extraction region size is 4.8 arcsec
on the sky. This is comparable to the extent of the brightest part of the
X-ray image, which is approximately 6 arcsec. It is possible to extract the
spectra from regions which are narrower or wider in the direction
perpendicular to the dispersion, and we will discuss this below.

The spectrum was extracted using the standard Ciao tools, including detection
of zero order, assigning grating orders, applying standard grade filters, gti
filters, and making response files. The dispersion axes for all the
observations were nearly perpendicular to the axis of the narrow line region
(NLR; position angle $\simeq$ 40 degrees). As pointed out by Ogle et al.
(2003) the width of the nuclear emission region in the dispersion direction
for the zeroth order image is 0.81 – 0.66 arcsec, which corresponds to a
smearing of FWHM = 0.015-0.018 Å over the 6-22 Å range in addition to the
instrumental profile ( FWHM = 0.01, 0.02 Å for HEG, MEG). Events were filtered
by grade according to standard filters, streak events were removed. First-
order HEG and MEG spectra of the entire dataset were extracted using CIAO 4.4.
Positive and negative grating orders were added.

In this paper we analyze data extracted using the standard size extraction
region from the HETG, which is 1.3 $\times 10^{-3}$ degrees or 4.8 arcsec.
Significant line emission does originate from the ‘NE cloud’, located 3.2
arcsec from the nuclear region, and was discussed by Ogle et al. (2003). This
emission is a factor 2-3 times weaker than the emission centered on the
nucleus. In section 2.2 we briefly discuss analysis of spatially resolved
data, i.e. data from smaller or larger extraction regions. A more complete
examination of the spatial dependence of the spectrum will be carried out in a
subsequent paper.

We fit the spectrum with a model consisting of an absorbed power law continuum
plus Gaussian lines. Table 2 lists 86 lines, of which 67 are distinct features
detected using the criteria described below. Gaussian line fitting was carried
out using an automated procedure which fits the spectrum in 2$\AA$ intervals.
These are chosen for convenience: narrow enough that the continuum can be
approximated by power law and containing a small number of features. Adjacent
intervals are chosen to overlap in order to avoid artifacts associated with
boundaries. Within each interval we fit a local power law continuum plus
Gaussians. The Gaussians are added to the model at wavelengths corresponding
to known lines. For each chosen centroid wavelength the width and
normalization are varied using a $\chi^{2}$ minimization procedure until a
best fit is obtained. The centroid wavelength is also allowed to vary by a
moderate amount, twice the value of a fiducial thermal Doppler width, during
this procedure. The trial line is considered to be detected if the $\chi^{2}$
improves by 10, corresponding to approximately 99$\%$ confidence for 3
interesting parameters (Avni, 1976). The fiducial thermal Doppler width is a
free parameter in this procedure (but note it does not influence the final
fitted width, only the searching procedure for the line center). For the
results shown here we adopt a value of 200 km s-1 for this parameter. Most
lines are free of blending so the results of the line search are independent
of the value of this parameter.

Also included in table 2 are tentative identifications for the lines, along
with laboratory wavelengths. These come from the xstar database (Kallman and
Bautista, 2001; Bautista & Kallman, 2001). We treat as potential
identifications the (likely) strongest feature which lies within a wavelength
range corresponding to a Doppler shift of $\leq$+5000 km s-1 from a known
resonance line or RRC. Table 2 includes the values of the implied Doppler
shift for these identifications. Note that our detection criterion does not
guarantee accurate measurement of the other line parameters, i.e. centroid
wavelength and width, so that weaker lines do not all have bounds on these
quantities. Where they are given in table 2, errors on these quantities and
the line flux represent 90$\%$ confidence ($\Delta\chi^{2}\simeq$3 for one
parameter; Avni (1976)) limits.

The NGC 1068 spectrum together with the model fits discussed in the next
section are shown in Figures 1 – 4. These are plotted in 2 $\AA$ intervals and
separated according to grating arm (HEG or MEG). We do not display wavelength
regions where the grating arm has no sensitivity, or where there are no
features. No rebinning or grouping is performed in these plots or in our
fitting procedure. We do quote values of $\chi^{2}$ in section 3, and these
were calculated using binned data. Also, when plotting the longer wavelength
regions, we bin the spectrum is binned for plotting purposes only in order to
avoid the dominance of the noisy bins with low counts at long wavelengths
(i.e. $\geq$18 $\AA$). In addition, the iron K region, 1.5 – 2.5 $\AA$ is not
plotted here, and is discussed in section 2.4.

Notable line features in the spectrum include the 1s-np lines of H- and He-
like ions of O, Ne, Mg, Si and S. Corresponding features are also present from
Ar and Ca, though not clearly detected. The 21 – 23 $\AA$ wavelength region
contains the He-like lines of oxygen. These are discussed in more detail in
section 2.3 below. The 17 – 19 $\AA$ wavelength region contains the L$\alpha$
line from H-like line of O VIII, the most prominent line in the spectrum. In
addition, lines from Fe XVII near 16.8 and 17.1 $\AA$, and n=1 – 3, 1–4 and 1
–5 lines from O VII near 17.4, 17.8 and 18.6 $\AA$, respectively. These lines
are discussed in section 2.5. The 15 – 17 $\AA$ wavelength region contains the
L$\beta$ lines from O VIII plus lines from ion stages of iron: Fe XVII – XIX.
The n=1 – 2 lines from He-like Ne are at 13.5 – 13.8 $\AA$. The 11 – 13 $\AA$
wavelength region contains the L$\alpha$ lines from Ne IX at 12.16 $\AA$, the
higher order n=1 – 3 and n=1 –4 lines from Ne IX at 11.6 and 11.0 $\AA$,
respectively, and additional lines from Fe XVII – XIX. Also apparent between
11.15 and 11.35 $\AA$ are inner shell fluorescence lines from L shell ions of
Mg: Mg V – Mg X. The 9 – 11 $\AA$ wavelength region contains the L$\beta$ line
from Ne X plus the H- and He-like lines from Mg near 8.4 and 9.15 - 9.35
$\AA$, respectively. The RRC of Ne IX is near 10.35 $\AA$. The 5 – 7 $\AA$
wavelength region contains the n=1-2 lines from both H-like and He-like Si,
near 6.2 $\AA$ and 6.7 $\AA$, respectively. The Mg XII L$\beta$ line is
apparent at 7.15 $\AA$. Inner shell fluorescence lines from L shell ions of
Si: Si VII – Si XII are between 6.85 – 7.05. Lines due to H- and He-like S are
at 4.74 and 5.05 $\AA$, respectively.

The fluxes in table 2 can be compared with those given by previous studies of
the NGC 1068 X-ray spectrum, by Kinkhabwala et al. (2002) and Ogle et al.
(2003). There is incomplete overlap between the lists of detected lines by us
and these authors. They detect 40 and 60 lines, respectively, which can be
compared with 86 in our table 2. Of these, some of the lines detected using
the $XMM-Newton$ RGS by Kinkhabwala et al. (2002) are outside of the spectral
range of the $Chandra$ HETG. There are additional discrepancies in the
significance and identification of a small number of weak lines when compared
with Ogle et al. (2003), though none of these is highly statistically
significant in either our spectra or theirs. Since the Ogle et al. (2003)
study was based on a much shorter observation than ours, it is not surprising
that we detect a larger number of lines. We find general consistency between
the fluxes in table 2 and those of Ogle et al. (2003). There are significant
discrepancies in the comparison between our line fluxes and those of
Kinkhabwala et al. (2002), generally in the sense that the Kinkhabwala et al.
(2002) are greater than ours by factors of several, possibly due to the
different characteristics of the $XMM-Newton$ telescope and the spatial extent
of the NGC 1068 X-ray emission which allows flux from a more extended region
to enter the spectrum.

###  2.1 Line wavelengths

Figure 5 and Table 2 show the Doppler shifts of the line centroids for the
strongest lines in Table 2. The shift is given in velocity units and is
measured relative to the rest frame of the AGN. Laboratory wavelengths are
taken from the xstar database (Bautista & Kallman, 2001); most are from NIST
111http://physics.nist.gov/PhysRefData/ASD/. Error bars are from the errors
provided by the automated Gaussian fitting procedure described in the previous
section. Wavelengths are only plotted if the errors on the wavelength are less
than 2000 km s-1. Most wavelengths are consistent with a Doppler shift in the
range 400 – 600 km s-1. Exceptions correspond to RRCs, eg. Ne IX 10.36 $\AA$,
for which the tabulated wavelengths are less precise, and weak lines such as O
VIII 1s – 5p which is blended with Fe XIX near 14.8 $\AA$. This figure shows
that there is evidence for wavelength shifts which are larger than the errors
on the line centroid determination. Examples of this include the O VIII
L$\alpha$ line compared with the 1s2 – 1s2s${}^{3}S$ ($f$) line of O VII.

Figure 5, lower panel, and Table 2 show the Gaussian widths of the lines for
the strongest lines. The width is given in velocity units, i.e.
$\sigma_{\varepsilon}c/\varepsilon$ where $\sigma_{\varepsilon}$ is the
Gaussian full width at half maximum in energy units and $\varepsilon$ is the
line energy. Error bars are from the confidence errors provided by our
automated fitting procedure as described above. Wavelengths are only plotted
in figure 5 if the errors on the wavelength are less than 2000 km s-1. This
shows that there is no single value for the width which is consistent with all
the lines. Examples of broader lines include the O VIII L$\alpha$ line, and
contrast with the forbidden line $f$ of O VII, for which the width is smaller.
The full width at half maximum which fits to most lines is approximately 1400
km s-1. This corresponds to a Gaussian sigma of $\simeq$ 600 km s-1 which we
adopt in our numerical models discussed below.

###  2.2 Spatial Dependence

The discussion so far has utilized data extracted using the standard size
extraction region from the HETG, which has width 1.3 $\times 10^{-3}$ degrees
or 4.8 arcsec. We have also explored possible spatial dependence of the
spectrum in the direction perpendicular to the dispersion direction by
extracting the data using regions which are half and double the angular size,
i.e. 2.4 and 9.6 arcsec wide. We then carry the fitting steps described above.
Figure 6 illustrates the positions of these regions superimposed on the zero
order image.

In this way we can study the influence of adding successive regions further
from the dispersion axis to the spectrum. Figure 7 shows the ratios of the
line fluxes in the standard extraction region (green hexagons) and the
extraction double the standard size (red diamonds) compared to the line flux
in the extraction region half the standard width. This shows that the line
emission outside half width region is significant; the values of the ratios of
essentially all the lines are greater than unity, and many are $\sim$2\. Plus,
the emission from outside the standard 4.8 arcsec extraction region is not
negligible; the values of the ratio for this region (red symbols) are on
average greater than the values of the ratio for the standard region. The
principal difference between standard region and the double size region is the
importance of the radiative excitation emission, which is larger in the
standard region. This is consistent with results from Ogle et al. (2003). For
example, for the He-like lines of Ne IX, the G ratio is larger in the standard
region spectrum than in the spectrum from the double size region. For the O
VII lines, the G ratios are similar for the two regions, but the R ratio is
lower in the standard region, implying higher density there.

These results demonstrate that most of the line emission is contained within
the standard extraction region, 4.8 arcsec wide, and most line ratios are
unaffected when emission from outside the standard extraction region is
included. It is worth noting that the physical length scale corresponding to
this angular size is approximately 1 arcsec = 72 pc (Bland-Hawthorn et al.,
1997), so the standard extraction region corresponds to a total size of 347
pc, or a maximum distance from the central source of approximately 174 pc.
This is much larger than the region where the broad line region and the
obscuring torus are likely to lie, which is $\simeq$ 2 – 3 pc (Jaffe et al.,
2004). For the remainder of this paper we will discuss primarily analysis of
data from the standard extraction region.

###  2.3 He-like lines

The He-like lines in Table 2 provide sensitive diagnostics of emission
conditions: excitation mechanism, density, and ionization balance. These
challenges of fitting these lines are apparent from the region containing the
H and He-like lines from the elements O, Ne, Mg, Si, and S. This shows the
characteristic three lines from the n=2 – n=1 decay of these ions: the
resonance ($r$), intercombination ($i$) and forbidden ($f$). These lines
provide useful diagnostics of excitation and density. These are described in
terms of the ratios $R=f/i$ and $G=(f+i)/r$ (Gabriel & Jordan, 1969a, b). $R$
is indicative of density, since the energy splitting between the upper levels
of the two lines (23S and 23P) is small compared with the typical gas
temperature and collisions can transfer ions from the 23S to the 23P when the
density is above a critical value. $R$ can also be affected by radiative
excitation from the 1s2s3S to the 1s2s3P levels, but this requires photon
field intensities which are greater than what is anticipated for NGC 1068. In
our modeling we include this process, using an extension of the global non-
thermal power law continuum, and find that it is negligible. We do not
consider the possibility of enhanced continuum at the energy of the 23S to the
23P provided by, eg., hot stars. $G$ is an indicator of temperature or other
mechanism responsible for populating the various $n=2$ levels. At high
temperature, or when the upper level of the $r$ line (21P) is excited in some
other way, then $G$ can have a value $\leq$1; in the absence of such
conditions, the 23S and 23P levels are populated preferentially by
recombination and $G$ has a characteristic large value, $G\geq 4$. Table 2
shows that the various elements have common values of $R$, in the range 1 – 3,
indicating moderate density. More interesting is the fact that there is a
diversity of values for $G$: O and Ne have values 2.5 – 3 while the other
elements all have smaller values, $G\leq$ 1.5.

The $G$ ratio is most affected by the process responsible for excitation of
the $r$ line. This can be either electron impact collisions or radiative
excitation. Collisions are less likely in the case of NGC 1068 due to the
presence of radiative recombination continua (RRCs) from H-like and He-like
species in the observed spectra (Kinkhabwala et al., 2002). This indicates the
presence of fully stripped and H-like ions, which produce the RRCs, but at a
temperature which is low enough that the RRCs appear narrow. Typical RRC
widths in NGC 1068 correspond to temperatures which are $\leq 10^{5}$K. A
coronal plasma, in which electron impact collisions are dominant, would
require a temperature $\geq 10^{6}$ K in order to produce the same ions.
Radiative excitation can produce $G$ ratios as small as 0.1. Thus, the $G$
ratios for NGC 1068 indicate the importance of radiative excitation for Mg and
Si, while O and Ne are dominated by recombination.

Radiative excitation depends on the presence of strong unattenuated continuum
from the central source in order to excite the $r$ line. A consequence of the
large cross section for radiative excitation in the line is the fact that the
line will saturate faster than continuum. At large column densities from the
source, the radiation field is depleted in photons capable of exciting the $r$
line, while still having photons capable of ionizing or exciting other, weaker
lines. Thus, the $G$ ratio is an indicator of column density. He-like lines
formed after the continuum has traversed a large column density will have
large $G$ ratios, corresponding to primarily recombination. He-like lines
formed after the continuum has traversed a small column density will have
small $G$ ratios, corresponding to radiative excitation (Kinkhabwala et al.,
2002).

Figure 8 and 9 display the G ratio for the elements O, Ne, Mg, and Si from the
NGC 1068 HETG observations. These are shown with error bars as the red crosses
in the centers of the various frames. This shows that the ratios differ
between the elements: O and Ne have G$\simeq$2 – 3, while Si and Mg have
G$\simeq$1\. This differing behavior suggests that the He-like O and Ne lines
are emitted by recombination, while the He-like lines of Mg and Si are emitted
by radiative excitation. Since radiative excitation is suppressed by large
resonance line optical depths, this suggests small optical depths in Si and Mg
and larger optical depths in the lines from other elements. The differences in
optical depths are significant; as shown by Kinkhabwala et al. (2002)
equivalent hydrogen columns of 1023 cm-2 or more are required to suppress
radiative excitation.

Also plotted in figures 8 and 9 are the values of these ratios produced by
photoionization models consisting of a single slab of gas of given ionization
parameter at the illuminated face and given column density. The solid curves
correspond to constant total slab column density, where black= 1023.5,
blue=1022.5, green=1021.5 and red=1020.5. The dashed curves correspond to
constant ionization parameter in the range 1$\leq$log($\xi$)$\leq$3\. Here the
ionization parameter is $\xi=4\pi F/n$ where $F$ is the ionizing energy flux
in the 1 – 1000 Ry range and $n$ is the gas number density. The role of
radiative excitation is apparent from the fact that the low column density
models (red curves) produce smaller $G$ values than the high column density
models (black curves).

The results in figures 8 and 9 show that no single value of the
photoionization model parameters can simultaneously account for all the
ratios. O and Ne require log($\xi$)$\simeq$1 and column$\geq 10^{23}$cm-2,
while Si requires log($\xi$)$\simeq$2 and column$\leq 10^{22}$cm-2 and Mg is
intermediate in both $\xi$ and column.

Also plotted in figures 8 and 9 are values for certain other ratios, in the
same units as for the He-like lines, and also including the model values.
These include the higher series allowed lines from some He-like ions, eg.
1-4/1-2 vs 1-3/1-2 for O VII, where 1-2 includes the $r$, $i$, and $f$ lines
while 1-4 and 1-3 include only the resonance component. These ratios depend
primarily on ionization parameter and only very weakly on column density. This
is because recombination cascades make larger values of both ratios than
radiative excitation, so recombination tends to dominate production of these
lines.

###  2.4 Iron K Line Region

The iron K lines from NGC 1068 have been the subject of previous studies by
Matt et al. (2004); Iwasawa et al. (1997), who showed that the line consists
of three components, corresponding to near neutral, and H- and He-like ion
species. The HETG provides higher spectral resolution than these previous
studies, but fewer total counts. Figure 10 shows the spectrum in the region
between 1.5 – 2.5 $\AA$ and reveals the three components of the iron K lines.
The most prominent are a feature at 6.37 keV (1.95 $\AA$), consistent with
neutral or near-neutral iron, a feature at 6.67 (1.85 $\AA$) indicative of He-
like iron, and a feature near 7 keV (1.75 $\AA$) which may be associated with
a combination of the K absorption edge from near-neutral gas and emission from
H-like iron. Matt et al. (2004) also separately identify emission from Be-like
iron; we are not able to make such an identification. We do find emission at
other nearby wavelengths, but this is suggestive of a broad component or
blended emission from various other species.

We model the Fe K line region using ‘analytic’ models which utilize the xstar
database and subroutines. These include optically thin models which include
radiative excitation (which we denote ‘scatemis’) and models which do not
include this process (‘photemis’), plus power law continuum. Both these models
are available for use as ‘analytic’ models in xspec from the xstar site
222http://heasarc.gsfc.nasa.gov/docs/software/xstar/xstar.html. Radiative
excitation cannot excite the neutral line, and we model it as emission from
gas at log($\xi$)=-3. The emission component with radiative excitation has
log($\xi$)=3, corresponding to highly ionized gas in which the H- and He-like
stages are the most abundant ionization stages of Fe. In the HETG data the He-
like triplet is not fully resolved. Nonetheless, the centroid of the He-like
component is closer to the wavelength of the Fe XXV $r$ line than it is to the
wavelength of the $f$ or $i$ lines, so we find a better fit with a resonance
excitation model. The fit is shown in figure 10. The best-fit parameters are
summarized in table 3; we find $\chi^{2}$=103 for 206 degrees of freedom for
the 1 – 2.5 $\AA$ (5 - 12.4 keV) spectral region. The flux in the neutral-like
line is 3.8 ${}^{+}_{-}0.44\times 10^{-5}$ cm-2 s-1.

We also point out what appears to be unresolved emission in the wavelength
region near $\simeq$ 1.9 $\AA$, between the He-like line and the neutral-like
line. We have not attempted to model this. It may be due to a broadened
component of the modeled lines, or an unresolved blend from other high
ionization stages of iron. These could include L shell ions between Li-like
and Ne-like. The two ionization parameters which we use to fit the iron K
lines are both higher and lower than the values used to fit the remainder of
the emission spectrum, described in the next section. The high ionization
parameter, log($\xi$)=3, may be an extension of the ionization parameter range
needed to fit the lines in the energy band below $\sim$ 5keV. The low
ionization parameter, log($\xi$)=-3, likely corresponds to the torus. Neither
of these components produces significant emission below $\sim$ 5keV, so we
will not discuss them further in the model fits described in the following
section.

The iron K line complex contains more flux than any other line in the
spectrum. This is consistent with the large normalization for the low
ionization component that is required to fit the spectrum. This was discussed
by Krolik & Kallman (1987); Nandra (2006). We have not attempted to fit for a
Compton shoulder on the on the red wing of the neutral-like iron line,
although such a component may be present in figure 10 (Matt et al., 2004). We
also test for the presence of Ni K$\alpha$ in our spectrum and find an upper
limit of 1.5 $\times 10^{-5}$ cm-2 s-1. This is less than the flux for Ni
K$\alpha$ claimed by Matt et al. (2004), which was 5.6${}^{+1.8}_{-1.0}\times
10^{-5}$ cm-2 s-1. One possible explanation could be that their data was
extracted from a much larger spatial region, $\simeq$40 arcsec, and is also
affected by a nearby point source.

###  2.5 Iron L lines

The $Chandra$ HETG observation allows study of the lines from the L shell ions
of iron, Fe XVII – XXIV, in more detail than has previously been possible.
Table 2 and figures 1 – 4 show these in the wavelength range 10 – 17 $\AA$.
Notable features include the well known ‘3C’ and ‘3D’ (Parkinson, 1973) lines
of Fe XVII at 15.01 and 15.26 $\AA$ (826 and 812 eV), respectively. The
intensity ratio of these lines is a topic of interest in the study of coronal
plasmas; we find a ratio of 2.8 ${}^{+0.8}_{-0.5}$. This is consistent with
several other lab measurements and astrophysical observations. It also
reflects the current apparent discrepancy with calculations, which generally
produce values of this ratio which are 3.5 or greater Bernitt et al. (2012).
The xstar models, described below, reflect this situation and produce a value
for this ratio which is $\simeq$3.

Other strong lines in the spectrum include the Fe XVII – XVIII complex between
11 – 11.5 $\AA$, Fe XXII 11.77 $\AA$. Fe XVII 12.12 $\AA$ is blended with Ne X
L$\alpha$. The Fe XVII 2p – 4d line at 12.26 $\AA$ is apparent, but the xstar
models with radiative excitation (described in more detail in the following
section) fail to produce as much flux as is observed. Fe XX 12.58 $\AA$ is
well fit, as is Fe XX 12.81, 12.83 $\AA$. The 13.6 $\AA$ blend contains both
Ne IX and Fe XIX 2p – 3d lines, produced primarily by radiative excitation.
Also contributing at 13.82 $\AA$ is the Fe XVII 2s – 3p line; this line can
only be produced efficiently by radiative excitation and it is clearly
apparent on the red wing of the Ne IX $f$ line. The 2p-3d lines of Fe XVIII
near 14.2 and out to 14.6 $\AA$ are fitted by the models. Longward of 15 $\AA$
the most notable feature is the Fe XVII line at 17.1 $\AA$, which is an
indicator of recombination.

Also plotted in figure 9 is the ratio 2p-4d/2p-3s vs 2p-3d/2p-3s for the Ne-
like Fe XVII. The latter ratio is sensitive to the effects of radiative
excitation since 2p-3d has a higher oscillator strength than 2p-3s, while
2p-3s is emitted efficiently via recombination cascade (Liedahl et al., 1990).
Here it is clear from figures 1 – 4 that the 2p-3d line is strong, therefore
requiring that radiative excitation be efficient and the cloud column density
must be low for the gas producing the Fe XVII lines.

###  2.6 Fluorescence Lines

Fluorescence lines are emitted during the cascade following K shell
ionization. This is a likely signature of photoionization because, for ions
with more than 3 electrons, the rate for K shell ionization by electron impact
by a Maxwellian velocity distribution never exceeds the valence shell cross
section. Fluorescence lines probe the existence of ions with valence shell
energies far below the observable X-ray range, including neutral and near-
neutral ions. In the NGC 1068 spectrum, fluorescence lines include the
K$\alpha$ line of iron shown in figure 10, plus a series of Si lines near 6.8
$\AA$. These correspond to L shell ions Si, likely Si VIII – X. The conditions
under which these ions are likely to be abundant, i.e. the ionization
parameter in a photoionization equilibrium model, are not very different from
those corresponding to N VII and O VII, the lowest ionization species in the
spectrum. Thus they do not provide additional significant insight into the
existence or quantity of material at low ionization in NGC 1068.

##  3 Model

A goal of interpreting the X-ray spectrum of NGC 1068 is to understand the
distribution of gas: its location relative to the central continuum source,
its velocity, density, element abundances, temperature, ionization state.
Fitting of models which predict these quantities to the data are the most
effective way to derive this information, although there is a range of levels
of detail and physical realism for doing this. We have examined this through
the use of photoionization table models in xspec, which are described in the
Appendix.

Based on what was presented in section 2 we can summarize some of the criteria
for a model for the NGC 1068 HETG spectrum: (i) The model must account for the
H- and He-like line strengths from abundant elements from N to Ca (we exclude
the iron region from this discussion); (ii) The model must account for the G
ratios from the elements O, Ne, Mg, Si, which have G$\simeq$3 for O and Ne but
G$\simeq$1 for Mg and Si; (iii) The model must account for 2p-3d/2p-3s ratio
in Fe XVII which is indicative of recombination rather than radiative
excitation; (iv) The model must account for the strengths of the RRCs, which
have strengths comparable to the corresponding resonance lines for O VII. From
criterion (i) it is clear that the emitting gas must have a range of
ionization parameter; no single ionization parameter can provide these ions.
From criterion (ii) it is likely that a range of gas column densities are
needed. The hypothesis that the lower ion column densities associated with
lower abundance elements (Mg and Si) can account for the diversity in $G$
ratios can be tested in this way. Criterion (iv) implies that some of the gas
must have high column in order to have a detectable contribution from
recombination.

Our fit uses three components with varying ionization parameters; these are
spread evenly between log($\xi$)=1 and log($\xi$)=2.6. The HETG spectrum is
relatively insensitive to gas outside this range of ionization parameters,
except for the iron K lines. Given the strength of both the neutral-like and
the H- and He-like iron K lines, it is plausible that there is an
approximately continuous distribution of ionization parameters which extends
beyond the range considered here. The three ionization parameter components in
our fit correspond crudely to the regions dominating the emission for the
elements of varying nuclear charge: the low ionization parameter component
dominates the emission for N and O, the intermediate component dominates the
Fe L lines and Ne and Mg, and the high ionization parameter component
dominates for Mg and Si. For each ionization parameter, we include models with
two column densities: 3 $\times 10^{22}$ cm-2 and 3 $\times 10^{23}$ cm-2. In
this way the models span the likely ionization parameter and column density
for which the strongest lines we observe are emitted. We use a constant
turbulent line width (sigma) of 600 km s-1 which adequately accounts for the
widths the majority of features. Results of our fit are summarized in table 4.

The red curves in figures 1 – 4 show that this model fits the strengths of
almost all the strong features in the spectrum. This fit adopts a net redshift
for the line emitting gas of 0.0023, corresponding to an outflow velocity of
450 km s-1. This is marginally less than typical speeds from UV and optical
lines of $\leq$600 km s-1 (both blue- and red-shifted) (Crenshaw & Kraemer,
2000), but is consistent with the velocities plotted in figure 5.

Free parameters of the fits include the elemental abundances and the
normalizations for the six model components. Experimentation shows that the
fit is not substantially improved when all the abundances are allowed to vary
independently, so we force the abundances of N, Ne, Mg, Si, S, Ar and Ca to be
the same for all the models. We allow the abundances of O and Fe to vary
independently for all the models. Our best fit is shown in figures 1 – 4 has
$\chi^{2}/\nu=2.34$ for 2561 degrees of freedom. More results are shown in
figures 11 and 12, which show the elemental abundances from the various model
components, and the masses of the various components (defined below) versus
ionization parameter.

In order to account for the diversity in the importance of radiative
excitation between various ions and elements, in the low ionization parameter
log($\xi$)=1 component, which is responsible for most of the O VII emission,
the oxygen abundance in the low column density component (component 4 in table
4) is smaller than the oxygen abundance in the high column component
(component 1 in table 4) by a factor 2.5. If not, the recombination emission
into O VII would be stronger than observed. Iron abundances are similar
between the low and high column density components, and are highest ($\sim$10)
at low ionization parameter (green in figure 12) and lowest ($\sim$1) at high
ionization parameter log($\xi$)=2.6. The normalizations and masses of the low
column density components (components 4 – 6) is generally lower than for the
high column components (components 1 – 3). The normalization for component 5
is consistent with zero, though we include it for completeness. Component 6 is
needed to provide photoexcitation-dominated lines of Fe XIX – XXI.

None of the abundances is significantly subsolar, except for O at
log($\xi$)=2.6 and column=3 $\times 10^{22}$ cm-2 (component 6). This is
necessary to avoid over-producing O VIII RRCs. It is worth noting that X-ray
observations are not generally capable of determining abundances relative to H
or He, but rather only abundances relative to other abundant metal elements
such as O or Fe. Thus, an apparent underabundance of O, for example, is
equivalent to an overabundance of other elements such as Si, S, and Fe,
relative to O.

The highest ionization parameter component is responsible for the Si and Mg
emission. Although its mass is dominated by the 3$\times 10^{23}$ cm -2
component (component 3 in table 4), the abundances of these elements are lower
than for lower Z elements, so the optical depths in the He-like resonance
lines are small enough that radiative excitation dominates the He-like lines.
It is notable that the differences in the importance of radiative excitation
between the various He-like ions, and also Fe XVII, can essentially all be
accounted for by the effects of varying amounts of resonance line optical
depth which is produced solely as a result of ionization and elemental
abundance effects. This is consistent with the hypothesis suggested by Ogle et
al. (2003). An exception is for the lines from Ne IX, for which a large ion
column density is needed in order to suppress the radiative excitation. Models
with column less than 3 $\times 10^{22}$ cm-2 produce G$\leq$1.6, while the
observations give G$\simeq$ 4${}^{+6}_{-2}$. Our model produces the Ne IX $f$
line with approximately half the the observed strength, while producing $r$
and $i$ lines which are close to the observed strengths. The Ne IX RRC is also
too weak in our models. We have found, through experimentation, that an
additional component with pure Ne and a column of 3 $\times 10^{24}$ cm-3, and
this is able to provide the observed Ne recombination features, but we have
not included this component in the fits in figures 1 – 4 or table 4.

The table models are calculated assuming that the emitting gas fills a
spherical shell defined by an inner radius
$R_{i}=\left(\frac{L}{n\xi}\right)^{1/2}$ and outer radius $R_{o}$ defined by
$\int_{R_{i}}^{R_{o}}n(R)dR=N$. Table 4 provides the normalizations
$\kappa_{i}$ of the table models as derived from the xspec fits. This
normalization can be interpreted in terms of the properties of the source as
follows: $\kappa=f\frac{L_{38}}{D_{kpc}^{2}}$ where $L_{38}$ is the source
ionizing luminosity integrated over the 1 - 1000 Ry energy range in units of
1038 erg s-1, and $D_{kpc}$ is the distance to the source in kpc. The
normalization also includes a filling factor $f$ which accounts for the
possibility that the gas does not fill the solid angle, and $f\leq 1$. We
assume the density $n$ scales as $n=n_{i}(R/R_{i})^{-2}$. With this assumption
the ionization parameter is independent of position for a given component and
the total amount of gas in each emission component $j$, is:

$M_{j}=4\pi f_{j}m_{H}n_{i}R_{i}^{2}(R_{o}-R_{i})$ (1)

Similarly, the emission measure for each component can be written:

${\rm EM}_{j}=4\pi
f_{i}n_{i}^{2}R_{i}^{4}\left(\frac{1}{R_{i}}-\frac{1}{R_{o}}\right)$ (2)

Since $n_{i}R_{i}^{2}=L/\xi$ both the mass and the emission measure depend on
the physical size of the emission region, but not directly on density. They
also depend on the ionizing luminosity. Table 4 includes values for $f_{i}$,
$M_{i}$ and EMi derived using these expressions, assuming $L=10^{44}$ erg s-1.
The $Chandra$ HETG spectrum of NGC 1068 constrains the density to be $\leq
10^{10}$ cm-3, from the strength of the O VII forbidden line. In the results
given in table 4 we have chosen the inner and outer radii of the emission
region to reflect simple conclusions from our data: the inner radius is
$R_{i}=$1 pc, based on physical arguments about the location of the obscuring
torus (Krolik & Begelman, 1988), and the outer radius is chosen to be
$R_{o}$=200 pc in order to reflect the observed extent of the X-ray emission,
and this is roughly consistent with the extraction region width. The density
is chosen such that the inner radius of the line emitting gas is at 1 pc for
all three emission components. Total masses and emission measures are also
given. The total emission measure is log(EM)=66.3 This is greater than would
be required to simply emit the observed lines if the gas had an emissivity
optimized for the maximum line emission, owing to the fact that the table
models include the gas needed to create the column density responsible for
shielding the photoionization dominated gas from the effects of
photoexcitation. Furthermore, most of the mass and emission measure comes from
hydrogen, while the $Chandra$ HETG spectrum constrains only metals. Values for
mass and emission measure are calculated using the elemental abundances given
in table 4.

It is also apparent that the assumptions described so far are not fully self-
consistent. That is, if density $\propto R^{-2}$ and if $R_{o}>>R_{i}$ then
the column density is $\simeq n_{i}R_{i}$, and an inner radius of 1pc cannot
produce an arbitrary column density and ionization parameter. A self
consistent model with density $\propto R^{-2}$ requires different inner radii
for the different ionization parameter and column density components, and
results in a total mass which is greater than that given in table 4 by
approximately a factor of 12. The emission measure is insensitive to these
assumptions. Our subsequent discussion is based on the simple scenario given
in table 4: $R_{i}$=1 pc, $R_{o}$=200 pc.

Figures 1 – 4 show general consistency between most of the lines and a single
choice for outflow velocity. This corresponds to a net redshift of
0.0023${}^{+}_{-}$0.0002, or an outflow velocity of 450${}^{+}_{-}$50 km s-1
relative to the systemic redshift of 0.00383 from Bland-Hawthorn et al.
(1997). There are apparent discrepancies between some model line centroids and
observed features when this redshift is adopted. lines which show apparent
shifts which differ significantly from this, however. An example is Mg XII
L$\beta$, which has an apparent central wavelength of 7.150 $\AA$, as shown in
table 2. The laboratory wavelength of this line is 7.110 $\AA$ Drake (1971),
which would correspond to an outflow velocity of 1688 km s-1. This is greater
than other Doppler shifts in the spectrum, and the difference cannot be easily
explained from uncertainties in the rest wavelength. Other possible line
identifications include K$\alpha$ lines from Si ions such as Si III or Si IV.
These would be associated with gas at lower ionization parameter than the
majority of the other lines in the spectrum and we have not attempted to
include them in our model.

One result of global model fits is revealing the presence of features which
are not obviously apparent from examination or Gaussian fits to the spectrum.
These are features, primarily from Fe L shell ions, which are in the model,
but which are blended or are not sufficiently statistically significant in the
spectrum to require their inclusion in Gaussian fits. Therefore, these lines
are not identified in table 2. Some are indicative of recombination vs.
radiative excitation, in a sense similar to the Fe XVII lines discussed above.
Examples can be seen from examination of figures 1 – 4: RRCs from Fe XVII and
XVIII at 9.15 and 8.55 $\AA$, respectively, and Fe Lines at 10.55 (Fe XVII
2p-5d 10.523 $\AA$ in the lab), 10.62, 10.85 (Fe XIX 2p-4d 10.6323,10.8267
$\AA$), 11.05 (Fe XVII 2s-4p 11.043 $\AA$), 11.18, 11.28 (Fe XVII 2p-5d,
11.133, 11.253 $\AA$) 11.45 (Fe XVIII 2p-5s, 11.42$\AA$) 12.15 (Fe XVII 2p-4d
12.12 $\AA$), 12.95 (Fe XIX 2s-3p, 12.92 $\AA$) 13.49, 13.53 (Fe XIX 2p-3d,
13.46,13.5249 $\AA$) 14.3 (Fe XVIII 2p-3d, 14.208 $\AA$) 15.88 (Fe XVIII
2p-3s, 15.83 $\AA$).

##  4 Discussion

It is possible to use the observed spatial extent of the X-ray emission to
make further inferences about the X-ray emitting gas. For NGC 1068, the
distance is such that 1 arcsec = 72 pc (Bland-Hawthorn et al., 1997). The
brightness profile in the zero order image is such that a significant amount
of flux is coming from outside an extraction region which is half the standard
size, i.e. 2.4 arcsec. Thus, an approximate, but convenient, size scale for
the extent of the observed X-rays is $\simeq$ 2.4 arcsec $\simeq$ 200 pc. If
so, we can compare with the sizes derived from table 4. These estimates are
based on an assumed ionizing luminosity for the nucleus of 1044 erg s-1; this
is uncertain by a factor of a few, but is bounded by $L_{bol}=4\times 10^{44}$
erg s-1 (Bland-Hawthorn et al., 1997).

The mass of material we infer based on the $Chandra$ HETG X-ray spectrum is
$\simeq 3.7\times 10^{5}M_{\odot}$, though this depends on the assumptions
about the inner and outer radii of the emission region and on the assumption
that density scales with $R^{-2}$. This can be compared with typical masses
for the entire narrow line region, which are likely to be $\sim
10^{6}M_{\odot}$, although gas with ionization parameters in the range
log($\xi$) 1 – 3 will not radiate efficiently in typical optical/UV narrow
lines. If this gas flows uniformly over a distance $\simeq$ 200 pc at the
speed we derive, then the flow timescale is 4.4 $\times 10^{5}$ yr, and the
mean mass loss rate is 0.3 $M_{\odot}$ yr-1. This is considerably greater than
the mass flux needed to power the nucleus, which is $\simeq$1.7 $\times
10^{-2}M_{\odot}$ yr-1 $(\eta/0.1)^{-1}$ L/($10^{44}$ erg s-1) where $\eta$ is
the efficiency of conversion of accreted mass into continuum luminosity.

The filling factors in table 4 can be interpreted formally as the fraction of
the total available volume in the spherical shell bounded by $R_{i}$ and
$R_{o}$ which is filled with line emitting gas. The angular distribution of
this gas is not constrained, so this can be interpreted as a conical region
with fractional solid angle given by $f$ or as a spherically symmetric
distribution in which the fractional covering of each component is given by
$f$ when averaged over solid angle. In either case it is clear that the total
covering fraction of the reprocessing gas is at most a few percent. This
suggests that, if NGC 1068 were viewed from an arbitrarily chosen angle, and
if the line of sight to the central continuum source were not blocked by the
Compton thick torus, then the probability of observing a warm absorber similar
to those seen in many Seyfert 1 galaxies would be small. If the fractional
solid angle of the obscuring torus as seen from the nucleus is $\sim$50$\%$ of
the total, then the probability of seeing a warm absorber would be
$\sim$10$\%$. This estimate is inversely proportional to the value we have
assumed for the ionizing luminosity of the nucleus in NGC 1068, which is
$10^{44}$ erg s-1. A smaller value for this quantity, which is possible
depending on the true spectral shape, would increase the inferred probability
of seeing a warm absorber toward a value $\sim$50$\%$.

Our model fits to the NGC 1068 HETG spectrum allow a simple phenomenological
test of the scenario which has been widely used to interpret the spectra of
Seyfert 1 objects. That is, Seyfert 1 X-ray spectra, which show prominent
blueshifted line absorption, have been analyzed assuming that the absorber
lies solely along the line of sight and neglecting any effect of emission
filling in the lines (McKernan et al., 2007). This can only be exactly correct
if the absorber subtends negligible solid angle as seen from the central
source. This would in turn conflict with the apparent presence of absorption
in $\sim$half of known Seyfert 1 objects (Reynolds, 1997). On the other hand,
examination of the fits shown in figures 1 – 4 and the results in table 2 show
a typical emission line flux for a strong line we measure is $\simeq$2 $\times
10^{-4}$ s-1 cm-2 for O VIII L$\alpha$. This can be compared with the amount
of energy absorbed in the same line from a Seyfert 1 galaxy; for NGC 3783 this
quantity is $\simeq$5 $\times 10^{-4}$ (Kaspi et al., 2002). Correcting for
the difference in distance, this would imply that, if the same emission line
gas seen in NGC 1068 is also present in NGC 3783, then the ratio of line flux
absorbed from the observed spectrum to emission is $\sim$8\. That is, the
apparent flux absorbed in the O VIII L$\alpha$ line, and likely other lines as
well, is actually greater than observed by $\sim$ 10 – 15 $\%$. The O VIII
L$\alpha$ line in NGC 3783 shows signs of this with an apparent weak P-Cygni
emission on the red edge of the trough, though this is not apparent in most
other lines in that spectrum. Although O VIII L$\alpha$ is one of the
strongest lines in the NGC 1068 spectrum, it is possible that other lines in
Seyfert 1 absorption spectra are more affected by filling in from emission.
Accurate fitting of these spectra, used to derive mass outflow rates and other
quantities, would need to account for this process.

It is interesting to compare our results with those from UV and optical
imaging and spectroscopy with the Faint Object Spectrograph (FOS) and the
Spave Telescope Imaging Spectrograph (STIS) on the Hubble Spate Telescope
(HST). These properties have been discussed by Kraemer et al. (1998); Crenshaw
& Kraemer (2000); Kraemer & Crenshaw (2000); Crenshaw & Kraemer (2000b);
Kraemer & Crenshaw (2000b) The strongest UV emission lines observed by the HST
instruments, eg. C IV $\lambda$1550, Si IV $\lambda$1398, and the He II and
hydrogen lines, comes from gas with a lower ionization parameter than the
inferred from X-ray emitting gas. STIS provides spatially resolved kinematic
information, which shows that the UV gas speed increases from the nucleus out
to 130 pc, then the speed decreases at larger distances. Also seen are coronal
lines from S XII, Fe XIV Ne V, Ne IV. These ions can exist at the same
ionization parameter as the lowest ionization X-ray gas. The intensity as a
function of distance from the nucleus shows apparent dilution as r${}^{-}2$,
and the emission region appears conical. The continuum spectrum most closely
resembles a nuclear power law, implying that it is scattered light from the
obscured nucleus. The contribution from stars to the continuum is smaller than
the non-thermal power law.

The gas observed by the HETG extends to $\sim$200 pc from the nucleus, while
the obscuration has a much smaller size $\sim$1 pc. The gas which extends
beyond the torus may originate near the torus, resembling a warm absorber flow
in a type 1 object, and flowing ballistically to larger distances. If so, the
outflow speed would be expected to be constant or decrease with distance owing
to gravitational forces, and the density would be subject to purely geometric
dilution. Alternatively, the X-ray and UV gas could entrain gas from narrow
line clouds, or gas evaporated from the narrow line clouds, or from some other
source. Radiation pressure could play a role in energizing the flow. The X-ray
gas could play a role in the apparent deceleration of the UV gas seen at
$\sim$100 pc. There is little strong evidence for these latter scenarios from
the HETG spectra, since we see no evidence for large changes in the ionization
balance or speed of the gas in the spectra extracted from various width
regions. Our results appear most nearly consistent with simple geometric
dilution of the outflow, leading to constant ionization parameter with
distance, and nearly constant outflow speed.

##  5 Summary

The results presented in this paper can be summarized as follows: (i) No
single ionization parameter and excitation mechanism can fit to all the lines
in the NGC 1068 X-ray spectrum obtained with the $Chandra$ HETG. The table
model fits require three components at ionization parameters ranging from
log($\xi$)=1 to log($\xi$)=3. We are able to adequately fit all the strong
identified lines in the spectrum with the exception of the lines from He-like
Ne, which show a stronger recombination component than are produced by our
models. (ii) The abundances required by all the models are approximately solar
(Grevesse et al., 1996) or slightly greater. A notable exception is a large
suppression of the abundance of oxygen at the highest ionization parameter.
Otherwise the O VIII RRCs would be stronger than observed. (iii) The masses
and emission measures of gas are greater than expected for optically thin
emission, owing primarily to the need for shielding to provide the
recombination dominated gas seen in the lines of Mg and Si. (iv) The combined
constraints on the ionization parameter and column density constrain the
location of the emitting gas relative to the continuum source, while the line
strengths constrain the amount of emitting gas. Taken together, these require
that the emitting gas have a volume filling factor less than unity; the values
differ for the various components and range up to $\sim$0.01. The mass flux
through the region included in the HETG extraction region is approximately 0.3
M⊙ yr-1 assuming ordered flow at the speed characterizing the line widths. (v)
Limited experimentation with extracting spectra from various positions on the
sky does not reveal a clear pattern which separates the various emitting
components spatially. It appears that the emitting components coexist in the
same physical region.

##  Appendix A Appendix

We make use of calculations using the xstar (Kallman and Bautista, 2001)
modeling package
333http://heasarc.gsfc.nasa.gov/docs/software/xstar/xstar.html. xstar is
freely available and distributed as part of the heasoft package. Models can be
imported into xspec and other fitting packages as tables, or via the
’analytic’ model warmabs/photemis/scatemis.

Our models are based on the assumption that the most plausible energy source
for the X-ray lines and RRCs observed from NGC 1068 is reprocessing of the
continuum from the innermost regions of the AGN. The continuum is presumably
associated with the accretion disk and related structures close to the black
hole, i.e. within a few $R_{G}\simeq 3\times 10^{11}M_{6}$ cm, where $M_{6}$
is the mass of the black hole in units of $10^{6}M_{\odot}$. The line and
recombination emission we observe is likely formed at distances
$>10^{6}R_{G}$, based on the geometry of the obscuring torus as indicated by
high spatial resolution IR imaging (Jaffe et al., 2004). If it is assumed that
the line emission is from gas where the heating, excitation and ionization are
dominated by the continuum from the black hole, and that there is a local time
steady balance between these processes and their inverses (radiative cooling,
radiative decay and recombination), then the temperature, atomic level
populations and ion fractions can be calculated. xstar carries out such a
calculation and also calculates the associated X-ray emission and absorption.
These emissivities and opacities are then applied to a simple one-dimensional
solution of the equation of radiative transfer to derive the spectrum at a
distant observer. Under the simple assumption that the gas is optically thin
the important physical quantities depend most sensitively on the ratio of the
ionizing X-ray flux to the gas density. We adopt the definition of this
ionization parameter which is $\xi=4\pi F_{X}/n$ where $F_{X}$ is the ionizing
(energy) flux between 1 and 1000Ry and $n$ is the gas number density. An
important part of our results concerns the fact that the gas is not optically
thin; this is key for explaining the varying amounts of radiative excitation
seen in the line ratios. This in turn means that the column density, or the
ion column densities, are also free parameters. We implement the models by
direct fitting, in which xstar models are used to generate synthetic spectra
which are compared to the observations within the fitting program xspec.

xstar explicitly calculates the populations of all atomic levels associated
with emission or absorption of radiation; it does not rely on the traditional
’nebular approximation’ which assumes that every excitation decays only to
ground. Therefore it is straightforward to include radiative excitation, and
this has been done. Interactive, iterative calculation of full xstar models
within xspec and simultaneous fitting to data is not practical owing to
computational limitations.

We point out, parenthetically, that the simplest way to use xstar results
within xspec is to use the associated xspec ‘analytic’ models. When called
from xspec, these read stored tables of ionic level populations as a function
of ionization parameter, and then calculate the opacity and emissivity ‘on the
fly’. The physical quantity used the xspec model fit is an emitted flux or a
transmission coefficient as a function of energy for a photoionized slab of
given column density, abundances and ionization parameter. These are
calculated from the opacity and emissivity by assuming these quantities are
uniform throughout. Advantages of this procedure compared with the use of
table models (described below) include: Ability to account for arbitrary
element abundances, arbitrary spectral resolution, and arbitrary turbulent
broadening. Limitations include the fact that it uses a saved file of level
populations calculated for a grid of optically thin models for a fixed choice
of ionizing spectrum rather than calculating the ionization balance self-
consistently. It implicitly assumes that the absorber has uniform ionization
even if the user specifies a large column, and that all emission freely
escape. In this sense it is not self-consistent. In fact, analytic models fail
when applied to the analysis of the NGC 1068 spectrum because, for column
densities large enough to suppress radiative excitation, as demanded by eg.
the Fe XVII 17$\AA$ line, the associated RRCs for Fe XVII are assumed to
escape freely and are greatly over predicted. For this reason we will not
discuss analytic models further in this paper.

In order to self-consistently include the effects of absorption of the
incident continuum in models for photoionized emission from NGC 1068 it is
necessary to use optically thick models. These are calculated using xstar, by
performing multiple model runs and using varying ionization parameter and
cloud column density. The resulting emission spectra and transmission
functions are stored as fits tables, binned in energy, using the table format
prescribed by xspec. These can be read by xspec, selected according to
parameter values, and interpolation between modeled parameter values is
performed. xspec can fit the table models to the observed spectrum and thereby
yield values for the cloud column density, ionization parameter, and the
normalization, which is described in more detail below. Owing to the fact that
the spectra are stored binned in energy the line width cannot be conveniently
treated as a free parameter, and therefore it is important that the energy
grid spacing used in constructing the table be no greater than than the
intrinsic instrumental resolution. It is also possible to treat the element
abundances as free parameters, by assuming that the escaping line and RRC
fluxes fluxes depend linearly on the abundances. This ignores the coupling of
the cloud ionization structure to abundance, via the temperature and the
opacity of the model. In our fits we use this approximation when deriving
element abundances.

Within a given optically thick model, xstar calculates the effect of
attenuation of the incident continuum using a simple single stream treatment
of the radiative transfer. This takes into account the varying ionization and
excitation through the model. The inclusion of radiative excitation
necessitates a finer spatial grid than for continuum absorption alone, since
the transfer must resolve the attenuation length of the photons in the
resonance lines. Also, line opacity varies over a large range in a very narrow
energy range and it is not feasible to accurately sample the relevant energies
for all of the many lines in a photoionized plasma. We adopt a very simple
treatment in which the line opacity is binned into continuum bins and used to
calculate the attenuated flux. This flux in continuum bins is then used in the
calculation of photoexcitation. The continuum bin size is typically
$\Delta\varepsilon/\varepsilon=1.4\times 10^{-4}$ which corresponds to $\simeq
41$km s-1 Doppler width. This is comparable to the thermal Doppler width for,
eg., oxygen at a temperature $\sim 10^{6}$K. Thus, we are not fully resolving
most lines relevant to this study. The tables used to fit to the $Chandra$
HETG spectrum of NGC 1068 include emission from both the illuminated and
unilluminated cloud faces, corresponding to the assumption that the the line
emitting material is arranged with approximate spherical symmetry around the
central continuum source. They are calculated assuming an ionizing spectrum
which is a single power law with (photon number) spectral index $\Gamma$=2 and
constant density 104 cm-3. These results are not expected to depend
sensitively on the latter two assumptions; in particular $\Gamma$ values in
the range 1.7 – 2.3 produce very similar ionization balance distributions.

xstar makes use of atomic data compiled from various sources and described by
(Bautista & Kallman, 2001). This has been extensively updated since that time,
as described by Witthoeft et al. (2007, 2009, 2011); Palmeri et al. (2002,
2003a, 2003b, 2008a, 2008b, 2011, 2012); Mendoza et al. (2004); García et al.
(2009); Bautista et al. (2003, 2004) The results presented here which flow
from the model calculations are dependent on the assumptions, computational
implementation and atomic data used by the models. The atomic data affects the
line identifications and the outflow speeds, via the line rest wavelengths. It
also affects the ionization balance, via the photoionization and recombination
rates, and the line strengths. The quantitative uncertainty associated with
the atomic data and the resulting uncertainty in the synthetic spectrum are
difficult to estimate; this is a topic of interest for many problems beyond
this one. We can point out that the emissivities of most of the lines from the
H- and He-like ions in our study depend on two processes: recombination and
photoexcitation. These depend in turn on photoionization cross sections and
line oscillator strengths, respectively. These are quantities associated with
radiative processes in relatively simple ions and therefore are generally more
reliable than collisional rate coefficients which are important for ions with
partially filled L shells in our models and in coronal plasmas. Foster et al.
(2010) have shown that uncertainties of, say, 20$\%$ on the collision
strengths for O VII can result in a range of a factor of $\simeq$3 in the
inferred temperature in a coronal plasma based on the $G$ ratio. We do not
anticipate similar sensitivity to atomic data uncertainties in the NGC 1068
models, since the rates for recombination and photoexcitation do not have the
strong non-linear dependence on temperature which is intrinsic to collisional
rates. In particular, we do not consider the rates embodied in our models to
be sufficiently uncertain to change our results qualitatively, or to allow
significantly better fits with fewer components or parameters. A more likely
shortcoming of our models is the neglect of some important physical mechanism.
Examples include: charge transfer; photo-excitation by some unseen source of
radiation; non-ionization equilibrium effects; or inhomogeneities in elemental
compositions associated with formation or destruction of dust.

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Table 1: Observation log  obsid | time | exposure
---|---|---
332 | 2000-12-04 18:11:52 | 46290
9148 | 2008-12-05 08:23:41 | 80880
9149 | 2008-11-19 04:49:51 | 90190
9150 | 2008-11-27 04:55:36 | 41760
10815 | 2008-11-20 16:23:22 | 19380
10816 | 2008-11-18 01:18:39 | 16430
10817 | 2008-11-22 17:36:37 | 33180
10823 | 2008-11-25 18:21:16 | 35110
10829 | 2008-11-30 20:16:45 | 39070
10830 | 2008-12-03 15:08:36 | 43600
Table 2: Lines Found  index | wavelength ($\AA$) | width (km/s) | flux (cm-2s-1) | lab ($\AA$) | ion | lower level | upper level | voff (km/s)
---|---|---|---|---|---|---|---|---
1 | 1.780 |  $\leq$ 2400 | 1.3${}^{+0.1}_{-0.3}\times 10^{-5}$ | 1.780 | fe xxvi | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 1100${}^{+840}_{-40}$
2 | 1.855 |  $\leq$ 2000 | 2.9${}^{+0.2}_{-0.2}\times 10^{-5}$ | 1.869 | fe xxv | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | 3400${}^{+40}_{-400}$
3 | 1.945 | 1700${}^{+17}_{-17}$ | 5.6${}^{+0.2}_{-0.3}\times 10^{-5}$ | 1.941 | fe i | K$\alpha$ |  | 500${}^{+40}_{-800}$
4 | 2.550 |  $\leq$ 2500 | 2.7${}^{+0.1}_{-1.6}\times 10^{-6}$ | 2.549 | ca xx | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | 1100${}^{+2400}_{-40}$
5 | 3.030 | 1900${}^{+550}_{-440}$ | 3.9${}^{+0.1}_{-1.6}\times 10^{-6}$ | 3.020 | ca xx | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 150${}^{+40}_{-1000}$
6 | 3.175 |  $\leq$ 3600 | 4.7${}^{+0.4}_{-0.4}\times 10^{-6}$ | 3.150 | ar xviii | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | -
7 | 3.195 |  $\leq$ 2600 | 2.3${}^{+0.4}_{-0.4}\times 10^{-6}$ | 3.180 | ca xix | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | -
8 | 3.195 |  $\leq$ 2600 | 2.3${}^{+0.4}_{-0.4}\times 10^{-6}$ | 3.190 | ca xix | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | 670${}^{+3300}_{-40}$
9 | 3.215 |  $\leq$ 2000 | 2.7${}^{+0.4}_{-0.4}\times 10^{-6}$ | 3.210 | ca xix | 1s${}^{2}(^{1}$S) | 1s12s${}^{1}(^{3}$S) | 670${}^{+5200}_{-40}$
10 | 3.380 |  $\leq$ 2200 | 5.5${}^{+0.4}_{-0.5}\times 10^{-6}$ | 3.365 | ar xvii | 1s${}^{2}(^{1}$S) | 1s13p${}^{1}(^{1}$P) | -
11 | 3.735 |  $\leq$ 2200 | 4.0${}^{+0.1}_{-1.4}\times 10^{-6}$ | 3.739 | ar xviii | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 1500${}^{+840}_{-400}$
12 | 3.945 |  $\leq$ 2000 | 5.1${}^{+0.2}_{-1.5}\times 10^{-6}$ | 3.950 | ar xvii | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | 1500${}^{+1500}_{-40}$
13 | 4.000 |  $\leq$ 2600 | 5.2${}^{+0.5}_{-0.4}\times 10^{-6}$ | 3.990 | ar xvii | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | 380${}^{+1300}_{-40}$
14 | 4.000 |  $\leq$ 2600 | 5.2${}^{+0.5}_{-0.4}\times 10^{-6}$ | 3.990 | s xvi | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | 380${}^{+1300}_{-40}$
15 | 4.000 |  $\leq$ 2600 | 5.2${}^{+0.5}_{-0.4}\times 10^{-6}$ | 4.010 | ar xvii | 1s2.1S | 1s1.2s1.3S | 1900${}^{+1300}_{-40}$
16 | 4.755 |  $\leq$ 2100 | 7.6${}^{+0.4}_{-0.9}\times 10^{-6}$ | 4.730 | s xvi | 1s1.2S | 1s0.2p1.2P | -
17 | 5.040 |  $\leq$ 2100 | 1.4${}^{+0.1}_{-0.1}\times 10^{-5}$ | 5.040 | s xv | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | 1100${}^{+1500}_{-40}$
18 | 5.100 |  $\leq$ 2000 | 8.6${}^{+0.8}_{-0.7}\times 10^{-6}$ | 5.070 | s xv | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | -
19 | 5.100 |  $\leq$ 2000 | 8.6${}^{+0.8}_{-0.7}\times 10^{-6}$ | 5.084 | si xiii | rrc |  | 180${}^{+2400}_{-160}$
20 | 5.225 |  $\leq$ 2000 | 8.6${}^{+0.7}_{-0.6}\times 10^{-6}$ | 5.212 | si xiv | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | 390${}^{+40}_{-320}$
21 | 5.690 | 1100${}^{+120}_{-130}$ | 7.0${}^{+0.3}_{-1.1}\times 10^{-6}$ | 5.680 | si xiii | 1s${}^{2}(^{1}$S) | 1s13p${}^{1}(^{1}$P) | 600${}^{+160}_{-40}$
22 | 6.195 | 1300${}^{+150}_{-27}$ | 2.2${}^{+0.0}_{-0.2}\times 10^{-5}$ | 6.180 | si xiv | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 410${}^{+280}_{-120}$
23 | 6.660 | 1500${}^{+120}_{-47}$ | 3.1${}^{+0.0}_{-0.2}\times 10^{-5}$ | 6.640 | si xiii | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | 230${}^{+480}_{-40}$
24 | 6.750 | 1700${}^{+1300}_{-2300}$ | 2.4${}^{+0.1}_{-0.1}\times 10^{-5}$ | 6.690 | si xiii | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | -
25 | 6.750 | 1700${}^{+1300}_{-2300}$ | 2.4${}^{+0.1}_{-0.1}\times 10^{-5}$ | 6.744 | si xiii | 1s${}^{2}(^{1}$S) | 1s12s${}^{1}(^{3}$S) | 870${}^{+120}_{-120}$
26 | 6.870 |  $\leq$ 2000 | 7.4${}^{+0.4}_{-0.3}\times 10^{-6}$ | 6.860 | si x | K$\alpha$ |  | 700${}^{+40}_{-120}$
27 | 6.995 |  $\leq$ 3600 | 7.3${}^{+0.1}_{-2.2}\times 10^{-6}$ | 6.930 | si ix | K$\alpha$ |  | -
28 | 7.005 | 450 | 2.9${}^{+2.5}_{-1.6}\times 10^{-7}$ | 7.001 | si viii | K$\alpha$ |  | 970${}^{+5600}_{-40}$
29 | 7.005 | 450 | 2.9${}^{+2.5}_{-1.6}\times 10^{-7}$ | 7.040 | mg xi | rrc |  | 2600${}^{+5600}_{-40}$
30 | 7.150 |  $\leq$ 2700 | 2.2${}^{+0.1}_{-0.1}\times 10^{-5}$ | 7.110 | mg xii | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | -
31 | 7.320 |  $\leq$ 2000 | 6.1${}^{+0.4}_{-0.3}\times 10^{-6}$ | 7.310 | mg xi | 1s${}^{2}(^{1}$S) | 1s15p${}^{1}(^{1}$P) | 740${}^{+640}_{-40}$
32 | 7.485 | 1400${}^{+14}_{-14}$ | 8.1${}^{+0.2}_{-1.3}\times 10^{-6}$ | 7.470 | mg xi | 1s${}^{2}(^{1}$S) | 1s14p${}^{1}(^{1}$P) | 530${}^{+40}_{-240}$
33 | 7.770 |  $\leq$ 2000 | 9.6${}^{+0.4}_{-0.5}\times 10^{-6}$ | 7.758 | al xii | 1s${}^{2}(^{1}$S) | 1s13p${}^{1}(^{1}$P) | 640${}^{+4400}_{-40}$
34 | 7.860 | 1200${}^{+200}_{-12}$ | 1.2${}^{+0.1}_{-0.0}\times 10^{-5}$ | 7.850 | mg xi | 1s${}^{2}(^{1}$S) | 1s13p${}^{1}(^{1}$P) | 750${}^{+1200}_{-40}$
35 | 8.435 | 1400${}^{+96}_{-43}$ | 3.3${}^{+0.0}_{-0.3}\times 10^{-5}$ | 8.420 | mg xii | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 600${}^{+360}_{-40}$
36 | 9.190 | 1500${}^{+230}_{-30}$ | 4.2${}^{+0.0}_{-0.4}\times 10^{-5}$ | 9.170 | mg xi | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | 480${}^{+200}_{-120}$
37 | 9.340 |  $\leq$ 2500 | 3.5${}^{+0.1}_{-0.1}\times 10^{-5}$ | 9.230 | mg xi | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | -
38 | 9.340 |  $\leq$ 2500 | 3.5${}^{+0.1}_{-0.1}\times 10^{-5}$ | 9.320 | mg xi | 1s${}^{2}(^{1}$S) | 1s12s${}^{1}(^{3}$S) | 490${}^{+40}_{-760}$
39 | 9.465 |  $\leq$ 2000 | 1.9${}^{+0.0}_{-0.3}\times 10^{-5}$ | 9.475 | fe xxi | 2p${}^{2}(^{3}$P0) | 2p14d${}^{1}(^{3}$D1) | 1500${}^{+1900}_{-80}$
40 | 9.720 |  $\leq$ 2000 | 1.9${}^{+0.1}_{-0.1}\times 10^{-5}$ | 9.679 | fe xix | 2p${}^{4}(^{1}$D2) | 2p35d${}^{1}(^{3}$D${}_{3}\\#3$) | -
41 | 9.720 |  $\leq$ 2000 | 1.9${}^{+0.1}_{-0.1}\times 10^{-5}$ | 9.800 | fe xvii | rrc |  | 3600${}^{+160}_{-79}$
42 | 10.045 |  $\leq$ 2400 | 2.5${}^{+0.0}_{-0.7}\times 10^{-5}$ | 10.014 | fe xix | 2p${}^{4}(^{1}$D2) | 2p35d${}^{1}(^{3}$D3) | 230${}^{+40}_{-400}$
43 | 10.260 |  $\leq$ 2000 | 3.9${}^{+0.1}_{-0.2}\times 10^{-5}$ | 10.240 | ne x | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | 550${}^{+1600}_{-40}$
44 | 10.365 | 1600${}^{+95}_{-120}$ | 3.4${}^{+0.0}_{-0.7}\times 10^{-5}$ | 10.388 | ne ix | rrc |  | 1800${}^{+320}_{-40}$
45 | 10.670 |  $\leq$ 2200 | 3.6${}^{+0.2}_{-0.1}\times 10^{-5}$ | 10.641 | fe xix | 2p${}^{4}(^{3}$P2) | 2p34d${}^{1}(^{3}$P2) | 320${}^{+40}_{-1300}$
46 | 10.670 |  $\leq$ 2200 | 3.6${}^{+0.2}_{-0.1}\times 10^{-5}$ | 10.660 | fe xvii |  |  | 860${}^{+40}_{-1300}$
47 | 10.830 |  $\leq$ 2000 | 2.3${}^{+0.1}_{-0.1}\times 10^{-5}$ | 10.770 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p56d${}^{1}(^{1}$P1) | -
48 | 10.830 |  $\leq$ 2000 | 2.3${}^{+0.1}_{-0.1}\times 10^{-5}$ | 10.820 | fe xix |  |  | 860${}^{+240}_{-40}$
49 | 11.025 | 1300${}^{+300}_{-13}$ | 3.5${}^{+0.1}_{-0.4}\times 10^{-5}$ | 11.000 | ne ix | 1s${}^{2}(^{1}$S) | 1s14p${}^{1}(^{1}$P) | 460${}^{+160}_{-80}$
50 | 11.555 | 1400${}^{+40}_{-70}$ | 4.0${}^{+0.0}_{-0.6}\times 10^{-5}$ | 11.500 | fe xviii |  |  | -
51 | 11.555 | 1400${}^{+40}_{-70}$ | 4.0${}^{+0.0}_{-0.6}\times 10^{-5}$ | 11.547 | ne ix | 1s${}^{2}(^{1}$S) | 1s13p${}^{1}(^{1}$P) | 930${}^{+280}_{-40}$
52 | 11.800 |  $\leq$ 2000 | 4.2${}^{+0.1}_{-0.2}\times 10^{-5}$ | 11.762 | fe xxi | 2p${}^{2}(^{3}$P1) | 2s12p23d${}^{1}(^{3}$P2) | 170${}^{+520}_{-80}$
53 | 12.165 | 1400${}^{+200}_{-14}$ | 9.5${}^{+0.1}_{-0.8}\times 10^{-5}$ | 12.100 | ne x | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | -
54 | 12.300 |  $\leq$ 2400 | 5.7${}^{+0.1}_{-1.6}\times 10^{-5}$ | 12.264 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p54d${}^{1}(^{3}$D1) | 260${}^{+40}_{-280}$
55 | 12.840 |  $\leq$ 2000 | 5.5${}^{+0.2}_{-0.3}\times 10^{-5}$ | 12.800 | fe xx |  |  | 200${}^{+1300}_{-40}$
56 | 12.840 |  $\leq$ 2000 | 5.5${}^{+0.2}_{-0.3}\times 10^{-5}$ | 12.812 | fe xviii | 2p${}^{5}(^{2}$P3/2) | 2s12p53p${}^{1}(^{2}$D5) | 480${}^{+1300}_{-40}$
57 | 13.509 |  $\leq$ 3600 | 3.2${}^{+0.3}_{-0.5}\times 10^{-5}$ | 13.447 | ne ix | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | -
58 | 13.509 |  $\leq$ 3600 | 3.2${}^{+0.3}_{-0.5}\times 10^{-5}$ | 13.500 | ne ix | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | 940${}^{+6700}_{-40}$
59 | 13.725 |  $\leq$ 3000 | 1.4${}^{+0.0}_{-0.1}\times 10^{-4}$ | 13.700 | ne ix | 1s${}^{2}(^{1}$S) | 1s12s${}^{1}(^{3}$S) | 590${}^{+360}_{-40}$
60 | 14.215 |  $\leq$ 2000 | 1.1${}^{+0.0}_{-0.2}\times 10^{-4}$ | 14.206 | fe xviii | 2p${}^{5}(^{2}$P3/2) | 2p53d${}^{1}(^{2}$D${}_{5/2}\\#$2) | 950${}^{+960}_{-40}$
61 | 14.215 |  $\leq$ 2000 | 1.1${}^{+0.0}_{-0.2}\times 10^{-4}$ | 14.250 | o viii | rrc |  | 1900${}^{+960}_{-40}$
62 | 14.415 |  $\leq$ 2100 | 7.2${}^{+0.1}_{-2.2}\times 10^{-5}$ | 14.394 | fe xviii | 2p${}^{5}(^{2}$P3/2) | 2p43d${}^{1}(^{2}$D5/2) | 710${}^{+40}_{-960}$
63 | 14.580 |  $\leq$ 2000 | 5.5${}^{+0.4}_{-0.3}\times 10^{-5}$ | 14.500 | fe xx | 2p${}^{3}(^{2}$P1/2) | 2p23s${}^{1}(^{4}$P1/2) | -
64 | 14.835 | 1600${}^{+410}_{-100}$ | 3.5${}^{+0.1}_{-0.8}\times 10^{-5}$ | 14.816 | fe xix | 2p${}^{4}(^{3}$P1) | 2p33s${}^{1}(^{1}$D2) | 740${}^{+920}_{-40}$
65 | 14.835 | 1600${}^{+410}_{-100}$ | 3.5${}^{+0.1}_{-0.8}\times 10^{-5}$ | 14.832 | o viii | 1s1.2S | 1s0.5p1.2P | 1100${}^{+920}_{-40}$
66 | 15.040 |  $\leq$ 2700 | 1.2${}^{+0.1}_{-0.0}\times 10^{-4}$ | 15.015 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p53d1 | 640${}^{+1600}_{-40}$
67 | 15.295 |  $\leq$ 3600 | 8.5${}^{+0.4}_{-0.3}\times 10^{-5}$ | 15.188 | o viii | 1s${}^{1}(^{2}$S) | 1s04p${}^{1}(^{2}$P) | -
68 | 15.295 |  $\leq$ 3600 | 8.5${}^{+0.4}_{-0.3}\times 10^{-5}$ | 15.262 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p53d${}^{1}(^{3}$P1) | 490${}^{+40}_{-990}$
69 | 15.295 |  $\leq$ 3600 | 8.5${}^{+0.4}_{-0.3}\times 10^{-5}$ | 15.418 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p53d${}^{1}(^{3}$P2) | 3500${}^{+39}_{-980}$
70 | 15.670 |  $\leq$ 2800 | 2.5${}^{+0.2}_{-0.2}\times 10^{-5}$ | 15.627 | fe xviii | 2p${}^{5}(^{2}$P3/2) | 2p43s${}^{1}(^{2}$P5/2) | 310${}^{+200}_{-200}$
71 | 16.040 | 1500${}^{+250}_{-62}$ | 8.4${}^{+0.2}_{-1.0}\times 10^{-5}$ | 16.007 | fe xviii | 2p${}^{5}(^{2}$P3/2) | 2p43s${}^{1}(^{2}$P3/2) | 520${}^{+400}_{-120}$
72 | 16.785 | 1700${}^{+500}_{-17}$ | 1.8${}^{+0.0}_{-0.3}\times 10^{-4}$ | 16.777 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p${}^{5}(^{3}$S1) | 990${}^{+40}_{-160}$
73 | 16.785 | 1700${}^{+500}_{-17}$ | 1.8${}^{+0.0}_{-0.3}\times 10^{-4}$ | 16.777 | o vii | rrc |  | 990${}^{+40}_{-160}$
74 | 17.135 |  $\leq$ 2000 | 1.6${}^{+0.1}_{-0.1}\times 10^{-4}$ | 17.050 | fe xvii | 2p${}^{6}(^{1}$S0) | 2p${}^{5}(^{3}$S1) | -
75 | 17.420 | 1100${}^{+300}_{-58}$ | 3.1${}^{+0.2}_{-0.4}\times 10^{-5}$ | 17.396 | o vii | 1s${}^{2}(^{1}$S) | 1s15p${}^{1}(^{1}$P) | 720${}^{+40}_{-200}$
76 | 17.785 | 1400${}^{+200}_{-160}$ | 5.2${}^{+0.3}_{-0.5}\times 10^{-5}$ | 17.768 | o vii | 1s${}^{2}(^{1}$S) | 1s14p${}^{1}(^{1}$P) | 850${}^{+440}_{-40}$
77 | 18.635 | 1700${}^{+470}_{-34}$ | 1.2${}^{+0.0}_{-0.2}\times 10^{-4}$ | 18.627 | o vii | 1s${}^{2}(^{1}$S) | 1s13p${}^{1}(^{1}$P) | 1000${}^{+40}_{-280}$
78 | 19.025 | 1200${}^{+56}_{-59}$ | 3.1${}^{+0.1}_{-0.2}\times 10^{-4}$ | 18.968 | o viii | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 240${}^{+80}_{-160}$
79 | 20.970 | 1500${}^{+360}_{-190}$ | 9.0${}^{+0.8}_{-1.4}\times 10^{-5}$ | 20.910 | n vii | 1s${}^{1}(^{2}$S) | 1s03p${}^{1}(^{2}$P) | 280${}^{+40}_{-600}$
80 | 21.651 | 1300${}^{+230}_{-38}$ | 2.4${}^{+0.1}_{-0.2}\times 10^{-4}$ | 21.602 | o vii | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{1}$P) | 460${}^{+440}_{-40}$
81 | 21.855 |  $\leq$ 2900 | 1.7${}^{+0.1}_{-0.6}\times 10^{-4}$ | 21.804 | o vii | 1s${}^{2}(^{1}$S) | 1s12p${}^{1}(^{3}$P) | 440${}^{+40}_{-1000}$
82 | 22.145 | 560${}^{+27}_{-11}$ | 5.8${}^{+0.5}_{-0.2}\times 10^{-4}$ | 22.110 | o vii | 1s${}^{2}(^{1}$S) | 1s12s${}^{1}(^{3}$S) | 660${}^{+80}_{-40}$
83 | 23.625 |  $\leq$ 3600 | 6.5${}^{+0.4}_{-2.1}\times 10^{-5}$ | 23.440 | o i | 2p${}^{4}(^{1}$D2) | 1s12s22p${}^{5}(^{1}$P1) | -
84 | 23.835 |  $\leq$ 2600 | 8.6${}^{+0.6}_{-2.2}\times 10^{-5}$ | 23.771 | n vi | 1s${}^{2}(^{1}$S) | 1s14p${}^{1}(^{1}$P) | 330${}^{+160}_{-720}$
85 | 24.840 | 1300${}^{+210}_{-38}$ | 3.1${}^{+0.1}_{-0.3}\times 10^{-4}$ | 24.781 | n vii | 1s${}^{1}(^{2}$S) | 1s02p${}^{1}(^{2}$P) | 420${}^{+200}_{-40}$
86 | 24.840 | 1300${}^{+210}_{-38}$ | 3.1${}^{+0.1}_{-0.3}\times 10^{-4}$ | 25.164 | ar xv | 2s${}^{2}(^{1}$S0) | 2s13p${}^{1}(^{3}$P1) | 5000${}^{+200}_{-39}$
Table 3: Model for Fe K region Parameters  component | log($\xi$) | norm | width (km/s) | velocity (km/s)
---|---|---|---|---
photemis | -3 | 2.47${}^{+0.82}_{-0.61}\times 10^{8}$ | 1.28${}^{+0.25}_{-0.23}\times 10^{3}$ | 2.41${}^{+0.51}_{-0.67}\times 10^{2}$ km s-1
scatemis | 3 | 33.1${}^{+8.7}_{-9.7}$ | 1.28${}^{+0.25}_{-0.23}\times 10^{3}$ | 2.41${}^{+0.51}_{-0.67}\times 10^{2}$ km s-1
Table 4: Fitting Results: Table Models  Component | 1 | 2 | 3 | 4 | 5 | 6 | Total
---|---|---|---|---|---|---|---
log(N) | 23.5 | 23.5 | 23.5 | 22.5 | 22.5 | 22.5 |
log($\xi$) | 1 | 1.8 | 2.6 | 1 | 1.8 | 2.6 |
N aaElemental abundances relative to solar (Grevesse et al., 1996) | 0.99 $\pm{0.19}$ | - | - | - | - | - |
O aaElemental abundances relative to solar (Grevesse et al., 1996) | 2.48 $\pm{0.3}$ | 0.86 $\pm{0.6}$ |  $\leq$0.09 | 1.1 $\pm{1.5}$ |  $\leq$10 |  $\leq$0.1 |
Ne aaElemental abundances relative to solar (Grevesse et al., 1996) | 1.91 $\pm{0.15}$ | - | - | - | - | - |
Mg aaElemental abundances relative to solar (Grevesse et al., 1996) | 1.06 $\pm{0.2}$ | - | - | - | - | - |
Si aaElemental abundances relative to solar (Grevesse et al., 1996) | 1.49 $\pm{0.1}$ | - | - | - | - | - |
S aaElemental abundances relative to solar (Grevesse et al., 1996) | 1.41 $\pm{0.3}$ | - | - | - | - | - |
Ar aaElemental abundances relative to solar (Grevesse et al., 1996) | 1.88 $\pm{0.5}$ | - | - | - | - | - |
Ca aaElemental abundances relative to solar (Grevesse et al., 1996) | 2.42 $\pm{0.9}$ | - | - | - | - | - |
Fe aaElemental abundances relative to solar (Grevesse et al., 1996) |  $\leq$100 | 2.7 $\pm{0.5}$ | 1 $\pm{0.15}$ | 8 $\pm{1}$ |  $\leq$100 | 1.88 $\pm{1.68}$ |
$\kappa$ ($\times 10^{-6}$) | 16.4 $\pm{3}$ | 22\. $\pm{3}$ | 83\. $\pm{6}$ | 6.7 $\pm{1}$ |  $\leq$0.1 | 3.9 $\pm{0.4}$ |
f ($\times 10^{-4}$) | 34.0 $\pm{6.2}$ | 45.6 $\pm{6.4}$ | 172\. $\pm{12.4}$ | 13.9 $\pm{2.1}$ |  $\leq$0.1 | 8.0 $\pm{0.8}$ |
mass($\times 10^{4}M_{\odot}$)bbNote that these quantities depend on the density according to the equations in the text. | 21.3 $\pm{3.9}$ | 4.5 $\pm{0.6}$ | 2.7 $\pm{0.2}$ | 8.7 $\pm{1.3}$ |  $\leq$0.02 | 0.13 $\pm{0.01}$ | 37.3 $\pm{6.0}$
log(EM (cm-3)) | 66.2 $\pm{0.07}$ | 64.7 $\pm{0.06}$ | 63.7 $\pm{0.03}$ | 65.8 $\pm{0.06}$ | 62.0 $\pm{0.3}$ | 62.3 $\pm{0.04}$ | 66.3 $\pm{0.88}$
Figure 1:  Spectrum showing fits to table model described in the text.
Vertical axis is counts s-1Hz-1 scaled according to the maximum flux in the
panel. Figure 2:  Spectrum showing fits to table model described in the text.
Vertical axis is counts s-1Hz-1 scaled according to the maximum flux in the
panel. Figure 3:  Spectrum showing fits to table model described in the text.
Vertical axis is counts s-1Hz-1 scaled according to the maximum flux in the
panel. Figure 4:  Spectrum showing fits to table model described in the text.
Vertical axis is counts s-1Hz-1 scaled according to the maximum flux in the
panel. Figure 5:  Plot of the widths and velocity offsets of the lines shown
in table 2 in km s-1. Only lines for which errors on the line width can be
derived are plotted. Figure 6:  Zero order image with positions of extraction
regions shown. Lines corresponds to standard extraction region (4.8 arcsec
width) plus half and double size regions as discussed in text. Only heg arm is
shown for clarity. Figure 7:  Values for the log of the ratios of line fluxes
for regions with the standard size (4.8 arcsec) (green hexagons) and double
this value (red diamonds) compared with line fluxes for a region half the
standard size. Figure 8:  Plot of the locus of points in the plane of the He/H
line ratio vs. the G-ratio. See the text for definitions. The solid curves
correspond to constant column density in where black= 1023.5, blue=1022.5,
green=1021.5 and red=1020.5. The dashed curves correspond to constant
ionization parameter in the range 1$\leq$log($\xi$)$\leq$3\. Red bars denote
the range of measured values. Figure 9:  Plot of the locus of points in the
plane of the He/H line ratio vs. the G-ratio. See the text for definitions.
The solid curves correspond to constant column density in where black= 1023.5,
blue=1022.5, green=1021.5 and red=1020.5. The dashed curves correspond to
constant ionization parameter in the range 1$\leq$log($\xi$)$\leq$3\. Red bars
denote the range of measured values. Figure 10:  Fe K line region. Lines are
apparent from near-neutral Fe near 1.95 $\AA$, He-line near 1.85 $\AA$ and
H-like near 1.75 $\AA$. The model consists of components with and without
radiative excitation from the analytic model described in section 3, plus
power law continuum.  Figure 11: Distribution of mass among the emission
components used to model the spectrum. Black points correspond to the
component with column 3 $\times 10^{23}$ cm-2 and red corresponds to the
component with column 3 $\times 10^{22}$ cm-2 Figure 12:  Element abundances
from best-fit models. Colors red, green and blue correspond to log($\xi$)=1,
1.8, 2.6, respectively; solid corresponds column 3 $\times 10^{23}$ cm-2 and
dashed corresponds column 3 $\times 10^{22}$ cm-2. Black points are average
over the best-fit model.