# The kpc Scale Fe K$\alpha$ Emission in the Compton Thin Seyfert 2 Galaxy NGC
4388 resolved by Chandra

Huili Yi  Department of Astronomy, Xiamen University, Xiamen, Fujian 361005,
China  Junfeng Wang  Department of Astronomy, Xiamen University, Xiamen,
Fujian 361005, China  Xinwen Shu  Department of Physics, Anhui Normal
University, Wuhu, Anhui, 241000, China  Giuseppina Fabbiano  Center for
Astrophysics, Harvard & Smithsonian, 60 Garden St. Cambridge, MA 02138, USA
Cirino Pappalardo  Instituto de Astrofísica e Ciências do Espaço, Universidade
de Lisboa - OAL, Tapada da Ajuda, PT1349-018 Lisboa, Portugal  Departamento de
Física, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo
Grande, PT1749-016 Lisboa, Portugal  Chen Wang  Department of Astronomy,
Xiamen University, Xiamen, Fujian 361005, China  Hanbo Yu  Department of
Astronomy, Xiamen University, Xiamen, Fujian 361005, China

###### Abstract

We present Chandra imaging and spectral observations of Seyfert 2 galaxy NGC
4388. Three extended X-ray structures around the nucleus on kpc scale are well
imaged, allowing an in-depth spatially resolved study. Both the extended hard
continuum and the Fe K$\alpha$ line show similar morphology, consistent with a
scenario where the ionizing emission from nucleus is reprocessed by
circumnuclear cold gas, resulting in a weak reflection continuum and an
associated neutral Fe K$\alpha$ line. This has been seen in other Compton
thick active galactic nuclei (AGN), but NGC 4388 is one of the rare cases with
a lower column density ($N_{\rm H}<1.25\times 10^{24}$ cm-2) along the line of
sight. Significant differences in equivalent width of the Fe K$\alpha$
emission line are found for the nuclear and extended regions, which could be
ascribed to different column densities or scattering angles with respect to
the line of sight, rather than variations in iron abundances. The north-east
and west extended structures are aligned with the galactic disk and dust lane
in the HST $V-H$ map, and located at the peak of molecular gas distribution.
The morphology implies that the kpc-scale radio outflow may have compressed
the interstellar gas and produced clumps working as the reflector to enhance
line emission. Using [OIV] emission as a proxy of the AGN intrinsic
luminosity, we find that both of the extended Fe K$\alpha$ emission and
reflection continuum are linearly correlated with the [OIV] luminosity,
indicating a connection between the AGN and the extended emission.

Galaxies: active – Galaxies: Seyfert–Individual: NGC 4388

††facilities: Chandra (ACIS), XSPEC††software: CIAO (v4.9 (Fruscione et al.,
2006)), Sherpa ((Freeman et al., 2001), (Doe et al., 2007)), XSPEC(Arnaud,
1996), DS9 ((Joye & Mandel, 2003), Smithsonian Astrophysical Observatory
2000), MARX (Davis et al., 2012) and ChaRT (Carter et al., 2003)

##  1 Introduction

The majority of nearby active galactic nuclei (AGN) are obscured by a large
amount of circumnuclear cold gas and dust (Comastri, 2004). The primary
emission from nucleus is reprocessed by these circumnuclear material, with a
resulting Compton reflection continuum and an associated fluorescent Fe
K$\alpha$ line at 6.4 keV (Shu et al., 2010; Matt et al., 1996; George &
Fabian, 1991; Winter et al., 2009; Jiang et al., 2006; Levenson et al., 2002,
2006; Yaqoob & Padmanabhan, 2004; Perola et al., 2002; Weaver et al., 2001;
Shu et al., 2011). Indeed, most of our knowledge so far about the
circumnuclear reprocessing matter, at least when their X-ray properties are
concerned, is based on the brightest Compton thick sources with absorption
column densities larger than 1.25$\times 10^{24}$ cm-2 (the inverse of the
Thomson scattering cross-section) due to their heavy obscuration. The nearby
Compton thick AGN NGC 1068 (Bauer et al., 2015), NGC 4945 (Marinucci et al.,
2017), Circinus (Marinucci et al., 2013), ESO 428-G014 (Fabbiano et al., 2017)
and NGC 5643 (Fabbiano et al., 2018b; Alonso-Herrero et al., 2018) are good
cases for which clumpy fluorescing clouds around nucleus have been spatially
resolved. Compared with the above Compton thick sources, it is more
challenging for us to resolve the circumnuclear reflector in a Compton thin
source because extended emission is usually overwhelmed by the bright nucleus.
In this work, we discover that NGC 4388 which is a Compton thin source (
$N_{\text{H}}$ $\simeq 3.6^{+0.3}_{-0.2}\times 10^{23}$ cm-2, this work)
provides us a new perspective to investigate the properties of extended
reprocessing matter.

NGC 4388 ($z=0.00842$) is one of the brightest Seyfert 2 galaxies at hard
X-ray energies (Baumgartner et al., 2013) with log L${}_{20-50}^{int}$ =43.23
$erg~{}s^{-1}$ (Ricci et al., 2017) . Several broadband observations of this
source have been performed with X-ray missions such as ASCA (Iwasawa et al.,
1997), INTEGRAL and Swift (Fedorova et al., 2011), XMM-Newton (Beckmann et
al., 2004), BeppoSAX (Elvis et al., 2004), Suzaku (Shirai et al., 2008),
NuSTAR (Kamraj et al., 2017) supporting the hypothesis of a powerful hidden
nucleus. Based on more than 30 years of X-ray observations reported in the
literature, the column density in this source shows $N_{\rm H}$ variability
spanning from 2 to 7 $\times$ $10^{23}$ cm-2 which are tabulated in Table 2.
Furthermore, a strong neutral Fe K$\alpha$ emission line is detected at 6.4
keV in above observations for the nucleus. This result has also been confirmed
by Chandra (Iwasawa et al., 2003) at an energy of $6.36^{+0.02}_{-0.02}$ keV,
with an equivalent width (EW) of $440\pm 90$ eV in agreement with ASCA
observation of EW$\sim 500$ eV (Iwasawa et al., 1997) and NuSTAR of
EW$=368^{+56}_{-53}$ eV, $394^{+131}_{-95}$ eV (Kamraj et al., 2017). However,
these broadband observations data did not allow us to spectrally and spatially
characterize the extra-nuclear extended regions with much detail.

The high angular resolution of Chandra allows such investigation with
arcsecond spatial resolution. With a 19.97 ks Chandra observation (ObsId
1619), Iwasawa et al. (2003) mainly investigated the soft extended X-ray
emission. For the extended Fe K$\alpha$ emission, only a rough morphology and
extent were reported limited by the short exposure of the observation. With
our new 28 ks observation (ObsId 12291; PI: Wang), the deeper combined Chandra
data will allow us to further map the geometrical structure of Fe K$\alpha$
emitting material and spectrally characterize these regions in detail. Also,
the fluorescent neutral Fe K$\alpha$ line is a reliable indicator of cold gas.
In this paper, we attempt to verify whether the reflecting medium such as
higher column density molecular clouds exist in the circumnuclear region of
NGC 4388 to reprocess the nuclear radiation and produce strong Fe K$\alpha$
line.

The paper is structured as follows: in Section 2, we discuss the merged
Chandra observations and data reduction. In Section 3, we present the imaging
and spectral analyses, respectively. Finally, we discuss and summarize our
results in Sections 4 and 5. The adopted distance of this galaxy is 16.7 Mpc
(Yasuda et al., 1997). The corresponding angular scale is $\sim 81$ pc
arcsec-1. We adopt the cosmological parameters $H_{0}=70$ km s-1 Mpc-1,
$\Omega_{\Lambda}=0.73$ and $\Omega_{m}=0.27$.

Figure 1: (a) Merged Chandra/ACIS-S image of the central 80$\times$80 arcsec
region of NGC 4388, in the 6.2–6.7 keV energy band. (b) Merged ACIS-S image of
the central 30$\times$30 arcsec region of NGC 4388, in the 4.0–6.0 keV energy
band. (c) ACIS-S image of the central 30$\times$30 arcsec region of NGC 4388
in the 6.2–6.7 keV energy band, shown in a binning of 0.5 native ACIS pixel
(the size of a pixel is therefore 0.246 arcsec). The image is smoothed with a
Gaussian kernel of 1.25 arcsec.

##  2 observations and data reduction

NGC 4388 has been observed with the Advanced CCD Imaging Spectrometer (ACIS;
Garmire et al., 2003) onboard Chandra in 2001 and 2011, and with the High
Energy Transmission Grating (HETG; Canizares et al., 2005) in 2008. We
summarize the four observations of interest in Table 1.

Table 1: Log of Chandra/ACIS-S Observations of NGC 4388

Obs. ID | Date | Exp. Time (ks) | Grating | Flux†
---|---|---|---|---
1619 | 2001-06-08 | 19.97 | NONE | 0.87
9276 | 2008-04-16 | 170.59 | HETG | 1.76
9277 | 2008-04-24 | 98.31 | HETG | 2.45
12291 | 2011-12-07 | 27.6 | NONE | 0.60

† The observed 2.0–10.0 keV flux in units of $10^{-11}$ erg cm-2 s-1.

As shown in Table 1, the 2–10 keV flux varied by a factor of 4.1 over the past
ten years. Flux variations is normal for NGC 4388 in light of previous
observational results (Forster et al., 1999; Beckmann et al., 2004; Fedorova
et al., 2011; Fukazawa et al., 2007). Fedorova et al. (2011) derives a maximum
variability in flux by a factor of $\approx$ 2 in the 20-60 keV band by
INTEGRAL data on time-scales of 1-2 months while Beckmann et al. (2004) shows
the flux variability by a factor of 4 over the year 1993–2002. Previous ASCA
observations in 1995 (Forster et al., 1999) gives a lower 2-10 keV flux value
0.64$\times 10^{-11}$ erg cm-2 s-1, in line with the ObsIds 1619 and 12291
results. The flux for ObsIds 9276 and 9277 in Table 1 are consistent with the
high value 2.31$\times 10^{-11}$ erg cm-2 s-1 provided by Shu et al. (2010).
We first attempted to use the zero-th order image of the deep grating
observations (ObsIds 9276 and 9277) to check the Fe K$\alpha$ extended
emission, but unfortunately their extended morphologies are dominated by the
high luminosity nuclear PSF wings. Thus, we excluded the two HETG observations
in the following analysis.

The remaining two ACIS-S observations (ObsIDs 1619 and 12291) were reduced
with the Chandra Interactive Analysis of Observations (CIAO; version 4.9) and
the Chandra Calibration Data Base (CALDB; version 4.7.8), adopting standard
procedures. We generated event files for the two observations separately with
the CIAO tool CHANDRA_REPRO and merged them into a single image using the tool
MERGE_OBS. The nucleus of this galaxy was positioned on the aimpoint of
ACIS-S3 detector. The background during observations was relatively stable.
Brief periods of high background flaring ($\geq 3\sigma$) were filtered out,
resulting in a cumulative exposure time of 47.5 ks. The data at the position
of nucleus are slightly affected by photon ”pile-up”, i.e., the phenomena of
two or more photons overlapping in a single detector frame and being read out
as a single event. The estimated pile-up fraction of NGC 4388 is about 10
percent. We correct these effects following the procedure described in Davis
(2001).

Figure 2: (a) Radial profiles of the source and ACIS-S PSF in the 4.0–6.0 keV
energy band. (b) Radial profiles of the source and ACIS-S PSF in 6.2–6.7 keV
energy band. We chose 2 pixel radius concentric annuli for the source and PSF
surface brightness, and a 30 pixel radius annulus for the background. The PSF
radial profile was normalized to the peak of the source.

Spectra from the nuclear source were extracted from a circular region with a
radius of 1.5 arcsec (Figure 4). We used a 5 arcsec radius circle for
background extraction, located in a nearby source free region, well away from
the diffuse emission. The spectra taken from extended regions between 1.5 and
10 arcsecond in radius are shown in Figure 6. Spectra were binned no less than
15 counts in each background-subtracted spectral channel. This allows the
applicability of the $\chi^{2}$ statistics. We performed the spectral modeling
using XSPEC 12.9.0 (Arnaud, 1996). Errors correspond to 90% confidence level
for parameters ($\Delta\chi^{2}=2.7$), if not stated otherwise.

Figure 3: The position angles of sectors that show counts excess in 6.2–6.7
keV and 4.0–6.0 keV (measured counter-clockwise from north), with angular bins
of $18^{\circ}$. The east (between red dashed lines) and south (between
magenta dashed lines) cones correspond to PA from $53^{\circ}$ to
$201^{\circ}$, and the west cone (between cyan dashed lines) corresponds to PA
from $225^{\circ}$ to $315^{\circ}$. Figure 4: Ratio between the Fe K$\alpha$
and continuum image, with contours extracted from the 6.2–6.7 keV image. The
Fe K$\alpha$ EW excess is consistent with the extended structure of Fe
K$\alpha$ emitting material. The cones in three different colors ranging from
1.5 arcsec to 10 arcsec in radius show position angles with counts excess. The
regions with excess of Fe K$\alpha$ EW appear clumpy and contained in the
three cones. We adopted the native ACIS instrumental pixel (0.492”) and
smoothed the image with a Gaussian kernel of 3 pixels.

##  3 Results

###  3.1 Imaging

The central 30 arcsec $\times$ 30 arcsec region of NGC 4388 is shown in Figure
1. The images were extracted from the merged event file in energy between
4.0–6.0 keV (Figure 1b) and 6.2-6.7 keV (Figure 1c). The first band was chosen
to image the circumnuclear material responsible for Compton reflection
continuum excluding any strong line contribution while the other band was
chosen to map the neutral Fe K$\alpha$ emission. To quantify the significance
of the extended components in these energy bands, we then simulated the ACIS-S
PSF contribution by using the simulation tool ChaRT
111http://cxc.harvard.edu/ciao/PSFs/chart2/ and MARX
222http://cxc.harvard.edu/ciao/threads/marx/ (Davis et al., 2012). The peak of
the PSF emission is normalized to the peak of the source radial profile.
Figure 2 shows the radial profiles of both the hard continuum band and Fe
K$\alpha$ band. The source emission is extended and well above the expected
PSF up to $10$ arcsec ($\sim 810$ pc). Furthermore, the extended Fe K$\alpha$
emission, as shown in Figure 1c, is only prominent in certain directions. In
order to better identify these extended regions, we provide the number of
counts for different azimuthal directions, with angular bins of $18^{\circ}$
(Figure 3). As can be seen from Figure 3, the position angles showing counts
excess in 6.2–6.7 keV are generally consistent with that in 4.0–6.0 keV and
can be divided into three parts (hereafter defined as the “cones”). The east
cone (red in Figure 4) is between position angles (measured counter-clockwise
from north) $53^{\circ}$ and $152^{\circ}$, the south cone (magenta in Figure
4) between $155^{\circ}$ and $201^{\circ}$, and the west cone (cyan in Figure
4) between $225^{\circ}$ and $315^{\circ}$. These angular extent should not be
treated as exact values for such diffuse features. We then divide the 6.2–6.7
keV image by the 4.0–6.0 keV one and smooth the image with a gaussian kernel
of 3 pixels (Figure 4). Adopted as a proxy for EW, this ratio map indicates
the relative strength of Fe K$\alpha$ emission line with respect to the
associated reflection continuum (Fabbiano et al., 2017; Marinucci et al.,
2017). The regions with elevated EW values are contained in the cones,
corresponding to the same sectors with counts excess shown in Figure 3.

Table 2: The column density $N_{\rm H}$ of NGC 4388 detected by X-ray
instruments for over thirty years

Instrument | $N_{\rm H}$ | Obs.date | Ref.
---|---|---|---
|  $10^{23}$ cm-2 |  |
SL2-XRT | $2.1^{+2.8}_{-1.4}$ | 1985 Jul | Hanson et al. (1990)
ASCA-SIS | $4.2^{+0.6}_{-1.0}$ | 1993 Jul | Iwasawa et al. (1997)
ASCA-GIS | $3.7^{+1.0}_{-0.5}$ | 1993 Jul | Iwasawa et al. (1997)
ASCA | $3.34^{+0.98}_{-0.84}$ | 1995 Jun | Forster et al. (1999)
BeppoSAX-1 | $3.80^{+0.2}_{-0.4}$ | 1999 Jan | Risaliti et al. (2002)
BeppoSAX-2 | $4.8^{+1.8}_{-0.8}$ | 2000 Jan | Risaliti et al. (2002)
Chandra | $3.5^{+0.4}_{-0.3}$ | 2001 Jun | Iwasawa et al. (2003)
XMM-1 | $2.45^{+0.2}_{-0.21}$ | 2002 Jul | Beckmann et al. (2004)
XMM-2 | $2.79^{+0.07}_{-0.07}$ | 2002 Dec | Beckmann et al. (2004)
Suzaku | $3.39^{+0.15}_{-0.47}$ | 2005 Dec | Shirai et al. (2008)
NuSTAR† | $6.5^{+0.8}_{-0.8}$ | 2013 Dec | Kamraj et al. (2017)
NuSTAR | $5.3^{+0.7}_{-0.7}$ | 2013 Dec | Kamraj et al. (2017)
NICER | $2.67^{+0.02}_{-0.03}$ | 2017 Dec | Miller et al. (2019)
NICER† | $2.64^{+0.03}_{-0.03}$ | 2017 Dec | Miller et al. (2019)

.

Table 3: Best-fit parameters for the spectra of nuclear and extended regions Parameter | Nucleus | Nucleus | Extended
---|---|---|---
| zTBabs$\times$(pow$+$zgauss$+$zgauss) | pcfabs$\times$(pow+zgauss+pexrav+zgauss) | pexrav+zgauss+psf-contribution
$\chi^{2}$/dof | 1.02 | 1.10 | 1.27
$N_{\text{H}}^{a}$ | 2.6${}^{+0.14}_{-0.14}$ | 3.6${}^{+0.27}_{-0.23}$ |  $\cdots$
$A_{pow}^{b}$ | 4.37${}^{+0.3}_{-0.3}$ | 2.57${}^{+0.2}_{-0.2}$ | 0.6${}^{+0.4}_{-0.4}$
$E_{\rm FeK_{\alpha}}^{c}$ | 6.35${}^{+0.02}_{-0.02}$ | 6.35${}^{+0.02}_{-0.02}$ | 6.37${}^{+0.04}_{-0.04}$
$I_{\rm FeK_{\alpha}}^{d}$ | 7.73${}^{+1.03}_{-1.03}$ | 8.31${}^{+1.15}_{-1.0}$ | 0.2${}^{+0.05}_{-0.05}$
$EW_{\rm FeK_{\alpha}}^{e}$ | 474${}^{+71}_{-70}$ | 431${}^{+77}_{-76}$ | 1415${}^{+330}_{-330}$
$E_{\rm FeK_{\beta}}^{c}$ | 7.01${}^{+0.05}_{-0.05}$ | 7.01${}^{+0.07}_{-0.07}$ |  $\cdots$
$I_{\rm FeK_{\beta}}^{d}$ | 1.91${}^{+0.76}_{-0.76}$ | 1.68${}^{+0.85}_{-0.85}$ |  $\cdots$
$EW_{\rm FeK_{\beta}}^{e}$ | 165${}^{+68}_{-66}$ | 118${}^{+176}_{-110}$ |  $\cdots$

###  3.2 Spectral fitting

As mentioned in Section 2, the bright nucleus of NGC 4388 was affected by mild
photon pile-up (estimated to be $\approx 10$%). The main consequences of the
photon pile-up are a hardening of the spectrum and a reduction in the detected
flux. We correct for these effects using the pile-up model of Davis (2001).
The spectrum of the NGC 4388 nucleus presented in Figure 5a was taken from
within 1.5 arcsec radius of the hard X-ray peak (R.A. = $12^{\rm h}25^{\rm
m}46^{\rm s}.77$, Dec. =$+12^{\circ}39^{\prime}44^{\prime\prime}.0$ J2000
(Iwasawa et al., 2003)). To eliminate contribution from the diffuse, soft
X-ray emitting gas, we focus our analysis to the energy band above 3 keV. A
simple absorbed (Tuebingen-Boulder ISM absorption model zTBabs, Wilms et al.,
2000) power law model is fitted to the 3.0–8.0 keV data (Figure 5b). The
photon index of the power-law continuum is assumed to be $\Gamma=1.6$ recently
obtained with NuSTAR data in Kamraj et al. (2017). The absorption column
density is found to be $N_{\rm H}$ $\simeq 2.6^{+0.14}_{-0.14}\times 10^{23}$
cm-2 which is consistent with previous results (Beckmann et al., 2004; Miller
et al., 2019; Iwasawa et al., 2003; Risaliti et al., 2002). We obtained a
$\chi^{2}$/dof $=$187.87/184$=$1.02, where the dof is the degrees of freedom
in fit and no strong residuals throughout the fitted energy band with
inclusion of two Gaussian emission lines.

A strong emission line consistent with iron fluorescent emission (Fe
K$\alpha$) is found at an energy of $E_{0}=6.35^{+0.02}_{-0.02}$ keV
(observer’s frame) with an EW=$474^{+71}_{-70}$ eV. The line flux is
$7.73^{+1.03}_{-1.03}\times 10^{-5}$ photons cm-2 s-1, consistent within tens
of percent, with the measurements of the last 20 years. (Shirai et al., 2008;
Beckmann et al., 2004; Shu et al., 2011). The constant Fe line emission is
probably decoupled from the direct emission of the central engine, and is
likely produced in distant obscuring torus and beyond (Beckmann et al., 2004).
The obscured nucleus has recently been further investigated by Kamraj et al.
(2017). The 2–10 keV flux observed by NuSTAR was found to be $\sim 8.0\times
10^{-12}$ erg cm-2 s-1 which is in fairly good agreement with our results
($8.21\times 10^{-12}$ erg cm-2 s-1), indicating that the source remained in a
similar relatively low flux state during NuSTAR and Chandra observations.
Thus, we fit the nuclear spectra with the same pexrav model described in
Kamraj et al. (2017). In addition to the Compton reflection component pexrav,
the model also contains an absorbed power law with two Gaussian lines. For the
absorption, we adopted a partial covering model pcfabs and found a covering
factor of 0.95 for the obscuring material. The fitting result is shown in
Figure 5c and $\chi^{2}/dof$ =200.80/182$=$1.10. The EW of Fe K$\alpha$ is
$431^{+77}_{-76}$ eV which is consistent with the recent measurement
($368^{+56}_{-53}$ eV) discussed in Kamraj et al. (2017).

There is also another weak line detected at $E_{0}=7.01^{+0.05}_{-0.05}$ keV
with a flux about 5 times lower than the neutral Fe K$\alpha$ line. The line
energy implies that it is most likely the Fe K$\beta$ line, but could be
blended with Fe XXVI K$\alpha$ at 6.97 keV from a highly ionized medium. The
spectrum shows no sign of a further line at 7.1 keV as reported from Chandra
data by Iwasawa et al. (2003), in agreement with XMM-Newton data in Beckmann
et al. (2004). To evaluate the statistical significance of the line centered
at 7.01 keV, we run Monte Carlo simulations for our data set following the
method discussed in Tombesi et al. (2010) and Walton et al. (2016). We adopted
the best fit power-law continuum model for nucleus without emission lines to
simulate a fake spectrum. Using the fakeit command in XSPEC, 10000 sets of
simulated spectra are produced with the same responses, background files,
exposure times and energy binning as the ones used for our observations. We
fit the fake spectrum using the continuum model and recorded the best fit
parameters. A new unresolved Gaussian line was added to the continuum model
and the line energy center was free and allowed to vary from 5 keV to 8 keV in
100 steps (steppar command in XSPEC). If S is the total simulated spectra and
N is the number of data sets for which the fitting results were improved, the
estimated statistical significance of this line is 1-$N/S$. For the putative
Fe K$\beta$ line at 7.01 keV, out of total 10000 simulations (S), N=207
spectra was found and the confidence level of this line is $1-207/10000=98\%$
(2.33$\sigma$).

There is no obvious excess indicating the presence of Fe XXV line in the
nuclear spectra. We also calculated the statistical significance of this line
(1-4856/10000, $<$1$\sigma$). Thus, the Fe XXV line is not further considered
in the fitting results (Table 3). We further checked the 6.7–7.1 keV image and
find that 93$\%$ counts are confined to the nucleus within two arcseconds,
hence there is no significant extended highly ionized component.

Figure 5: (a) Energy spectra with models fitting for nuclear and extended
regions. The black line refers to a simple absorbed power-law model while blue
line depicts a pexrav model for nuclear region. Green line refers to the
extended region model. (b-c) the fit residuals for the simple absorbed power-
law and pexrav model for nuclear region, respectively. (d) the fit residual
for the extended region model.

For the extended regions, in order to take into account the contamination from
the PSF wings, we extracted the spectrum from corresponding extended regions
using simulated events file of the nucleus, and fitted it with a simple model
consisting of an absorbed power-law plus Gaussian line. We create RMF and ARF
files (RMF describes the instrument response and ARF the telescope effective
area) following the procedure provided by the MARX documentation (Davis et
al., 2012). Due to the low number of counts, following Lanzuisi et al. (2013),
we binned the spectra using 10 counts per channel and used the Cstat statistic
333Extensive tests on using Cstat with binned data and comparison with
$\chi^{2}$ statistic has been carried out in the Appendix of Lanzuisi et al.
(2013) , a modified version of the Cash statistic (Cash, 1976). The photon
index of power-law is again assumed to be 1.6, as measured with the NuSTAR
data in Kamraj et al. (2017) and we obtain the $\chi^{2}$/dof $=$ 1.25. The
normalization of power-law ($5.2^{+2.0}_{-1.5}\times 10^{-5}$ photons
keV-1cm-2s-1 at 1 keV) indicates that it is about 1.2 % of the power-law
component from the nucleus.

Figure 6: 3.0–8.0 keV spectra for extended regions. Black and red line
indicate spectral model with and without contribution from nuclear psf wings,
respectively.

In the following steps, the contribution from the PSF wings was included as a
fixed model component. The final spectral model for the extended regions also
consists of a reflection continuum pexrav and a neutral Fe K$\alpha$ line at
6.4 keV. The photon index of pexrav was fixed to 1.6 and the cutoff energy
$E_{c}$ was fixed to 1000 keV (Kamraj et al., 2017). We obtained an acceptable
fit with $\chi^{2}$/dof=27.92/22=1.27. The fitting result is shown in Figure
5d. If we remove the psf-contribution from complete spectrum, the rest
spectrum with evidence of a strong Fe K$\alpha$ line is shown in Figure 6 (red
line). The equivalent width of the Fe K$\alpha$ line (without psf
contribution) for extended regions is $1.415^{+0.33}_{-0.33}$ keV. This is
different from the inferred EW=$474^{+71}_{-70}$ eV in the nuclear region by a
factor $\sim 3$, implying a different geometry or iron abundance of the
circumnuclear extended matter in comparison with the nucleus. The observed
6.2–6.7 keV flux is $2.0^{+0.5}_{-0.5}$$\times 10^{-6}$ photons cm-2 s-1and
the luminosity is $3.3^{+0.9}_{-0.9}$$\times 10^{39}$$erg/s$. The estimated
3.0–8.0 keV luminosity, excluding the iron line contribution, is 8.61 $\times
10^{39}$ erg s-1. The Fe K$\alpha$ line flux for nucleus is
7.73${}^{+1.03}_{-1.03}$$\times 10^{-5}$photons cm-2 s-1and thus the ratio of
Fe K$\alpha$ emission line intensity between the extended and nuclear region
is 2.6%. For the hard-band continuum, the flux for extended and nuclear region
is 2.36$\times 10^{-6}$ photons cm-2 s-1and 1.69$\times 10^{-4}$photons cm-2
s-1, respectively, corresponding to a ratio of 1.39%. Thus, the EW of Fe
K$\alpha$ line for extended region is about twice than that in nucleus. The
best fit parameters for the spectra of nuclear and extended regions are
summarized in Table 3.

Table 4: Properties of the Seyfert sample with Resolved Fe K$\alpha$ line emission $Sources$ | $N_{\rm H}$ | $log(L_{\rm[OIV]})$ | $log(L_{\rm[FeK\alpha]tot})$ | $log(L_{\rm[FeK\alpha]ext})$ | ratio | $EW_{[FeK\alpha]ext}$ | $log(L_{\rm[FeK\alpha]ext}/EW_{[Fe]ext})$ |
---|---|---|---|---|---|---|---|---
| $10^{23}cm^{-2}$ | $erg/s$ | $erg/s$ | $erg/s$ |  | $keV$ | $erg/s$ |
NGC 4945 | $22.0^{a}$ |  $39.37^{+0.12}_{-0.17}$f |  $39.32^{+0.04}_{-0.03}$h |  $38.18^{+0.05}_{-0.05}$j | 0.07 |  $1.10^{+0.13}_{-0.12}$j | $38.13^{+0.06}_{-0.06}$ |
Circinus | $43.0^{a}$ |  $40.50^{+0.12}_{-0.17}$f |  $40.14^{+0.01}_{-0.01}$h |  $38.82^{+0.04}_{-0.05}$k | 0.05 |  $0.9^{+0.3}_{-0.3}-2.2^{+0.5}_{-0.5}$k |  $38.65^{+0.07}_{-0.07}$${}^{k^{*}}$ |
NGC 1068 | >$100^{b}$ |  $41.78^{+0.07}_{-0.08}$f |  $40.23^{+0.03}_{-0.04}$h |  $39.62^{+0.08}_{-0.09}$l | 0.25 | $1.36^{+0.46}_{-0.34}$ | $39.51^{+0.17}_{-0.17}$ |
NGC 4388 | $2-7^{c}$ |  $41.61^{+0.01}_{-0.01}$f |  $41.00^{+0.11}_{-0.12}$h | $39.52^{+0.1}_{-0.13}$ | 0.03 | $1.415^{+0.33}_{-0.33}$ | $39.37^{+0.15}_{-0.15}$ |
NGC 5643 | >$50^{d}$ |  $40.46^{+0.03}_{-0.04}$f |  $39.70^{+0.09}_{-0.10}$h |  $39.28^{+0.07}_{-0.09}$m | 0.38 | $1.6^{+0.5}_{-0.5}$ | $39.07^{+0.16}_{-0.16}$ |
ESO-428-G014 | >$100^{e}$ |  $41.27^{+0.12}_{-0.17}$g |  $39.75^{+0.03}_{-0.05}$i |  $39.00^{+0.1}_{-0.12}$i | 0.18 | $2.1^{+0.52}_{-0.52}$ | $38.70^{+0.15}_{-0.15}$ |
Table 5: Linear regressions for [OIV] to Fe K$\alpha$ luminosity and 6.4 keV monochromatic luminosity.  Correlation | $a$ | $b$ | $a_{best}$ | $b_{best}$ | $R^{2}_{best}$ | Reference
---|---|---|---|---|---|---
log($L_{\rm OIV}$)-log$(L_{\rm[FeK\alpha]tot})$ | $0.92^{+0.08}_{-0.08}$ | $3.02^{+0.36}_{-0.36}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1
| $0.73^{+0.12}_{-0.12}$ | $10.24^{+0.45}_{-0.45}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2
| $0.48^{+0.09}_{-0.09}$ | $20.6^{+4.05}_{-4.05}$ | 0.51 | 19.34 | 0.67 | 3
log($L_{\rm OIV}$)-log$(L_{\rm[FeK\alpha]ext})$ | $0.53^{+0.09}_{-0.09}$ | $17.35^{+4.11}_{-4.11}$ | 0.59 | 14.89 | 0.93 | 3
log($L_{\rm OIV}$)-log($L_{Fe}/EW_{Fe})_{ext}$ | $0.49^{+0.12}_{-0.12}$ | $18.98^{+5.1}_{-5.1}$ | 0.54 | 16.8 | 0.92 | 3

##  4 Discussion

###  4.1 Origin of the Extended Iron K$\alpha$ Line Emission with large EW

It is not a total surprise to find extended Fe K$\alpha$ line beyond the sub-
pc scale torus region in an AGN, as bright Fe K$\alpha$ line in the molecular
clouds in our Galactic center has been discovered by Koyama et al. (1996) for
over two decades. There is strong evidence that the origin of the spatially
resolved, variable Fe K$\alpha$ emission from multiple molecular clouds is a
reflection of the primary X-ray flare from Sgr A* in the past (Nakajima et
al., 2009; Dogiel et al., 2009; Ponti et al., 2010).

In the last few years, much evidence for the presence of extended Fe K$\alpha$
emission has been found in several nearby Compton thick AGN, such as NGC
1068(Bauer et al., 2015), Circinus (Marinucci et al., 2013), NGC 4945
(Marinucci et al., 2017), ESO 428-G014 (Fabbiano et al., 2017) and NGC 5643
(Fabbiano et al., 2018b). These findings show that the reflector may extend on
scales ranging from tens to thousands of parsecs.

As shown in Figures 1 and 2, such a circumnuclear reflecting structure for NGC
4388 is spatially resolved by Chandra observation and extends to scale of
$\sim$0.8 kpc. A major difference between NGC 4388 and the former galaxies is
that the nucleus of NGC 4388 is a Compton-thin AGN. We have carefully
considered the contamination in the extended regions from the nuclear
radiation, taking into account the contribution from wings of the PSF. A
significant difference in the EWs of Fe K$\alpha$ line is found when nuclear
and extended regions are compared (a factor $\approx$ 3.0; see Table 3). Such
spatial variations in Fe K$\alpha$ EW can be ascribed to iron abundance (Matt
et al., 1997), the angle $\theta_{i}$ between polar direction and the line of
sight (Matt et al., 1991; George & Fabian, 1991), and the column density of
the illuminated material (Yaqoob, 2012), as discussed in several works using
models with a toroidal (Yaqoob et al., 2010) or a slab geometry (Matt et al.,
1997).

We first examined if the variation in Fe K$\alpha$ EW for nuclear and extended
regions is due to anomaly in iron abundance. As previously discussed in
Marinucci et al. (2013), achieving a difference of a factor 2 in EW of Fe
K$\alpha$ line requires a difference of 2-5 in iron abundance (Matt et al.,
1997). Fitting with the pexmon model in XSPEC, we inferred comparable Fe
K$\alpha$ abundances A(Fe)${}_{\rm nucleus}=0.36^{+0.08}_{-0.15}$ and
A(Fe)${}_{\rm extend}=0.45^{+0.72}_{-0.18}$ (with respect to solar value) for
the nuclear and extended regions, respectively. Typically, a Type Ia SN
produces 5-10 times more Fe than Type II SN. Thus, the enrichment due to iron
is mainly attributed to SN Ia on time-scale of 1 Gyr (late SNIa) or hundreds
of million years (early SNIa) (Loewenstein, 2006). Such an iron enrichment on
these time-scales unlikely remain confined in a region of hundreds of parsecs
but rather across the galactic disk. Thus, the difference of EW for nuclear
and extended regions due to variations of metallicity is not favored.

Figure 7: HST V-H color map (grey scale) effectively uncovering dust features
(white area) for NGC 4388. The cones in three different colors ranging from
1.5 arcsec to 10 arcsec in radius show position angles with count excess.
Dusty regions appear white in the red and cyan cones. The blue contours on
behalf of CO(1-0) morphology. The Fe K$\alpha$ extended regions (green
contours) are located at the peak CO(1-0) emission and the orientation of
north-east and west Fe K$\alpha$ regions are consistent with the galactic
disk.

Following Marinucci et al. (2013), we then tested whether the difference in EW
arise from different column densities or inclination angles with respect to
the line of sight, using MYTORUS model444http://mytorus.com/mytorus-
instructions.html (Murphy & Yaqoob, 2009; Yaqoob et al., 2010) to fit the
spectra from nuclear and extended regions. The circumnuclear obscuring matter
in this model is arranged uniformly in a toroidal geometry with a fixed half-
opening angle of 60 degree. Generally, MYTORUS model includes three
components: zeroth-orde continuum(MYTZ) with the photons neither absorbed nor
scattered, the scattered continuum (MYTS) and fluorescent emission-line
spectrum (MYTL). Furthermore, it treats both line and continuum components
self-consistently. For all three components (MYTZ, MYTS, MYTL), we link the
neutral hydrogen column density $N_{H},_{global}$, intrinsic power-law slope
$\Gamma$, inclination angle $\theta_{\rm inc}$ and normalization of the MYTZ,
MYTS, and MYTL components together. The best fit parameters are summarized as
follows: N${}_{H},_{global}=4.2^{+8.3}_{-1.5}\times 10^{23}$ cm-2,
$\theta_{i}=71.9^{+8.7}_{-10}$ degree for the nucleus ($\chi^{2}_{\nu}=0.89$)
and N${}_{H},_{global}=8.9^{+12.0}_{-5.0}\times 10^{23}$ cm-2,
$\theta_{i}<61.2$ degree for the extended regions ($\chi^{2}_{\nu}=0.98$).
N${}_{H},_{global}$ is termed as the equatorial column density angle-averaged
over all directions. Thus, it is generally assumed to be the same as the line-
of-sight column density (N${}_{H},_{Los}$). We caution that N${}_{H},_{Los}$
can be estimated using N${}_{H},_{global}$ and $\theta_{inc}$ as shown in
Murphy & Yaqoob (2009) and in this paper N${}_{H},_{Los}$ is simplified to
$N_{\text{H}}$. The NH and $\theta_{i}$ are not well constrained by the $<$10
keV Chandra data alone. Nevertheless, we show that the combination of column
density and inclination angle could account for the observed spectra as well
as the different EWs. This requires presence of some dense gas with column
N${}_{H}\sim 10^{23}-10^{24}$ cm-2 at the resolved spatial scale in the
galactic disk, which is identified next.

It is worth noting that the best fit value of hydrogen column density NH with
MYtorus model is consistent with the reported NuSTAR measurements (Kamraj et
al., 2017) within error bars. We have summarized previously published column
density measured by various X-ray missions in Table 2. It is noted that the
column density estimated by MYtorus model (Murphy & Yaqoob, 2009) is higher
than others, which could be due to the adopted more complex geometry and
physics other than a simple absorption. As the upper bound of our measured NH
reaches $10^{24}$ cm-2, it is plausible that the measured column density of
NGC 4388, generally classified as Compton thin, is statistically consistent
with being Compton thick.

Figure 8: The 6.2–6.7 keV smoothed image with VLA 3.5 cm radio contours
(Falcke et al., 1998) overlaid. The cones in three different colors ranging
from 1.5 arcsec to 10 arcsec in radius that show counts excess position
angles. The radio jet may squeeze ambient gas and produce high density clumpy
cloud to be the reflector to account for the remaining extended Fe K$\alpha$
emission (contained in the south magenta cone and part of the west cyan cone).

Figure 7 shows $V-H$ color map obtained with $HST$ images from Hubble Legacy
Archive555https://hla.stsci.edu/ which effectively uncovers dust features
(Martini, 2004). It indicates that the north-east and west extended regions
contain rich dust lanes (white area in Figure 7 with inverted color).
Furthermore, the 12 CO(1-0) map observed by IRAM-30 m telescope is also
overlaid in Figure 7 (blue contours) (Pappalardo et al., 2012). Although the
spatial resolution of CO map is much lower than Chandra, it shows that the
extended Fe K$\alpha$ emission line regions (green contours) located at the
peak of CO(1-0) molecular gas distribution, which also shows that the
orientation of extended north-east and west regions are along the disk of NGC
4388. Pappalardo et al. (2012) converted the 12 CO(1-0) integrated intensity
into molecular gas masses (M${}_{H2}=7.13^{+0.6}_{-0.6}\times 10^{8}$ M⊙)
using the standard Galactic conversion factor $X_{\rm CO}$ =
$N_{H_{2}}/I_{CO}=2\times 10^{20}cm^{-2}$ [K km s-1]-1 (Strong & Mattox, 1996;
Dame et al., 2001). We further estimated the line-of-sight H2 column density
N(H2) $\approx 1.8\times 10^{21}cm^{-2}$, orders of magnitude lower than the
neutral hydrogen column density NH towards the AGN derived from X-ray
observations ($\textgreater 10^{23}cm^{-2}$). However, this column density
estimated from CO(1-0) is averaged over a large area
($117^{\prime\prime}\times 42^{\prime\prime}$) (Pappalardo et al., 2012) and
should be taken as a lower limit of the true column density. At the peak of
the CO(1-0) emission, the value of the column density N(H2) could be much
higher. Overall it is consistent with the N (H2) found in other Seyfert
galaxies (Feruglio et al., 2020; Alonso-Herrero et al., 2018; Izumi et al.,
2018; Fabbiano et al., 2018b). In addition, N(H2) is derived for a given
conversion factor, which could be different in the nuclei of galaxies other
than our Galaxy (Wada et al., 2018).

We further note that the remaining extended regions (contained in the south
and part of the west region) could trace the edges of a known radio outflow.
Figure 8 shows the 3.5 cm radio contours (Falcke et al., 1998) superimposed on
the Fe K$\alpha$ image. The extended Fe K$\alpha$ signal suggests that the
radio outflow in kpc scale may have compressed the ambient interstellar gas in
the galaxy to dense clumps and effectively enhanced reflection and line
emission. This is similar to the case in Hydra A (Nulsen et al., 2002) for
which the expanding radio lobes compress the surrounding cooler gas.

Last but not least, in contrast to the results in Iwasawa et al. (2003), we
find a relatively smaller extent of Fe K$\alpha$ emission ($\sim$10 arcsec or
$\sim 0.8$ kpc). Due to the low signal to noise ratio of their Fe K$\alpha$
emission data, Iwasawa et al. (2003) adopted 2-arcsec binning for Fe K$\alpha$
image and the low surface brightness extended emission to a few kpc is only
0.05 percent of the nuclear brightness. Such weak signals are less significant
in our observation (ObsId 12291) and the deeper merged data, and the very
extended regions show surface brightness comparable with background. Hence, we
only focus on the most significant extended Fe K$\alpha$ emission line regions
in this work.

Figure 9: (a) The total Fe K$\alpha$ line luminosity versus log($L_{\rm
OIV}$). The blue and green lines are the best fit lines for Compton-Thin Sy2s
and Compton -Thick Sy2s in Liu & Wang (2010). Considering the overall impact
of uncertainty for each data on the fitting result, we adopt Monte Carlo
simulations. Assuming the error for each data follows Gaussian distribution,
1000 fitted lines are shown in gray with different combination of six points.
The red line represents the best fitted result. (b) the slope distribution
from our Monte Carlo analysis. We fitted it by a Gaussian model (red line) and
obtain the parameters ($\mu$ and $\sigma$) of probability density
function(PDF) (c) the intercept distribution from our Monte Carlo analysis.
(d) the linear regression coefficient distribution from our Monte Carlo
analysis.

Figure 10: (a) The extended Fe K$\alpha$ line luminosity versus log($L_{\rm
OIV}$). Similarly, we run 1000 Monte Carlo simulations. The gray region
represent the fitting results. (b) the corresponding linear slope
distribution. Red line represents the fitted Gaussian model. (c) intercept
distribution. (d) linear regression coefficient distribution.

Figure 11: (a) The extended 6.4 keV monochromatic luminosity versus
log($L_{\rm OIV}$). Similarly, we run 1000 Monte Carlo simulations. The gray
region represent the fitting results. (b) the corresponding linear slope
distribution. Red line represents the fitted Gaussian model. (c) intercept
distribution. (d) linear regression coefficient distribution.

###  4.2 Comparison with relevant Compton-Thick sources and Implications

Our results on the extended Fe K$\alpha$ emission are consistent with recent
findings in Compton thick AGNs, although the spatial extent and morphologies
are diverse in the different cases. In NGC 1068 (Bauer et al., 2015), the Fe
K$\alpha$ line has the extended components to the northeast and southwest in
the direction of the ionization cone (>140 pc). For Circinus (Marinucci et
al., 2013), the excess in EW of Fe K$\alpha$ follows an axisymmetric geometry
around the nucleus on hundred of pc scale. Moreover, part of the excess is co-
aligned with the disk of the galaxy and almost perpendicular to the [OIII]
ionization cone. In ESO 428-G014 (Fabbiano et al., 2017), the extended
component with $\textgreater$ 2 kpc diameter follows the ionization cone. In
NGC 4945 (Marinucci et al., 2017), the hard X-ray continuum and the Fe
K$\alpha$ emission are confined to a flattened ”torus” $\approx$ 200 $\times$
100 pc region along the galactic disk perpendicular to the main axis of the
ionization cone. As for NGC 5643 (Fabbiano et al., 2018b), the Fe K$\alpha$
line feature is clumpy and extend for 65 pc perpendicular to the ionization
cone. It is spatially consistent with the north-south elongation found in the
high-resolution CO (2-1) imaging with ALMA, but slightly more extended than
the rotating molecular disk of diameter $\approx$ 26 pc indicated by the
kinematics of the CO line. Compared with the above Compton thick sources, NGC
4388 is the first Compton thin source($N_{\rm H}$ $\simeq
3.6^{+0.27}_{-0.23}\times 10^{23}$ cm-2 from this work), enabling a new
perspective to investigate the properties of circumnuclear reprocessing matter
in a different environment.

These results imply that Fe K$\alpha$ lines with large EW originated from
circumnuclear reflector beyond the torus could be more common than previously
thought. To obtain better understanding of these sources, we summarize their
relevant properties in Table 4. Using the [OIV] 25.89 $\mu$m line luminosities
as a robust indicator of AGN intrinsic power (Meléndez et al., 2008) and X-ray
spectra observed by XMM-Newton/EPIC, Liu & Wang (2010) examined the
relationship between luminosity of the narrow Fe K$\alpha$ line ($L_{\rm Fe}$)
and $L_{\rm OIV}$. They compared between type I and type II AGNs of similar
luminosities and found that statistically, the Fe K$\alpha$ luminosities in
Compton-thin and Compton-thick type II AGNs are about 2.7 and 5.6 times lower
than that in type I sources, respectively.

Using six type II AGNs (Table 4), we can first verify the
$log(L_{\rm[FeK\alpha]tot})$-$logL_{\rm OIV}$ relation using linear
regression. We also explore if there exists a similar linear correlation
between extended Fe K$\alpha$ luminosity and the AGN intrinsic power
(log$L_{\rm OIV}$). For Circinus galaxy, the whole extended Fe K$\alpha$
region is divided into six smaller regions (Marinucci et al., 2013) and the
total luminosity of extended Fe K$\alpha$ is their sum. For NGC 4945,
Marinucci et al. (2017) select out four smaller circular regions only covered
part of neutral Fe K$\alpha$ extended region. Thus, we have reprocessed the
same data for NGC 4945 and obtained more precisely the luminosity of total
extended Fe K$\alpha$ emission.

In order to take into account the uncertainties of data points, we adopt Monte
Carlo simulations in the fitting process to evaluate the linear correlations.
The errors for each data are assumed to follow Gaussian distribution. For each
of the correlations ($log(L_{\rm[FeK\alpha]tot})$-log($L_{\rm OIV})$ and
$log(L_{\rm[FeK\alpha]ext})$-log($L_{\rm OIV}$) ), we run 1000 simulations and
obtain the distributions of correlation coefficients (slope and intercept) and
linear regression coefficient $R^{2}$ in Figures 9 and 10. The blue and green
lines in Figure 9a represent the correlations obtained by Liu & Wang (2010)
for Compton-thin and Compton-thick Seyferts. It is apparent that the
correlation for Compton-Thin Seyfert 2 (Liu & Wang, 2010) over-predicts
log$L_{\rm Fe}$ for these sources. The red line in Figure 9a represents the
best-fit correlation with the maximum $R^{2}$ in the simulations. We also
obtained the range (3$\sigma$) of coefficients (slopes and intercepts) in
Figures 9b and 9c, respectively. Adopting the 6.4 keV monochromatic luminosity
as a proxy for the intensity of reflection spectrum, we also plotted the 6.4
keV monochromatic luminosity log($L_{Fe}/EW_{Fe}$) of extended regions versus
log$L_{\rm OIV}$ in Figure 11 following the same method. For Circinus galaxy
(Marinucci et al., 2013), the total 6.4 keV monochromatic luminosity (total
reflective spectrum) is the sum of six smaller regions (i.e.
$L_{\rm[FeK\alpha]ext/EW_{[Fe]ext}}$$=$$\sum_{j=1}^{N}L_{\rm[FeK\alpha]ext,j/EW_{[Fe]ext,j}}$,
$N=6$). We have summarized the simulation results in Table 5. In all of the
above mentioned fittings, the error propagation caused by division, addition
and logarithm has been taken into account. The linear correlations shown in
Figures 10 and 11 indicate that the Fe K$\alpha$ extended emission is
connected with the central AGN other than alternative origin such as the
unresolved X-ray binary emission. We may speculate that the scatter may be
caused by the various covering factor, column density and clumpy distribution
of reflector material around the nucleus.

Our findings may have implications on the detectability of extended Fe
K$\alpha$ in Seyfert galaxies, no longer restricted to Compton-Thick AGNs
only. Table 4 shows that the ratio of luminosity of extended Fe K$\alpha$ to
total Fe K$\alpha$ can be up to 0.38 which indicates that the contribution
from extended emission could not be neglected. There have been extensive
studies of the molecular gas reservoir beyond the torus that can fuel the
nuclear activity from surveys of nearby galaxies (e.g., the Molecular gas in
NUclei of GAlaxies survey (García-Burillo et al., 2003, 2005). If the geometry
allows some of nuclear continuum to illuminate the dense gas available beyond
the torus scale, similar reflection continuum and fluorescent Fe K$\alpha$
line could be produced. Despite the relatively weak line luminosity compared
to the central AGN, the EW can be large as seen here and in other cases. We
speculate that if the central AGN “changes look” to a low state of inactive
accretion, one would expect to find high fraction of extended Fe K$\alpha$
among local Seyfert galaxies where kpc scale structure can be resolved, which
can be tested in future observations.

##  5 Conclusions

We presented a detailed spectral and imaging analysis of the extended X-ray
reflecting structure of Seyfert 2 galaxy NGC 4388, taking advantage of
cumulative Chandra ACIS-S observations with 47.5 ks exposure. The main results
of this paper can be summarized as follows.

  1. 1.

Compared with previous results on NGC 4388 (Iwasawa et al., 2003), we focus on
spatially resolved analysis of the kpc scale circumnuclear Fe K$\alpha$
emission with improved signal to noise ratio. The spectral analysis reveals a
spatial variation in the EW of Fe K$\alpha$ line for extended and nuclear
regions by a factor of 3. The differences are likely to be associated with
illuminated gas, in terms of angles between polar direction and the line of
sight and the column density, but not attributed to a variation in
metallicity.

  2. 2.

The HST $V-H$ color map and IRAM CO (1-0) emission indicate that the extended
Fe K$\alpha$ regions contain rich dust and gas. The orientation of fluorescent
Fe K$\alpha$ (north-east and west part) are along with the galactic disk.
Furthermore, the remaining extended regions appear to trace the edges of the
radio jet, implying that the radio outflow in kpc scale may have compressed
ambient interstellar gas, giving rise to enhanced line emission.

  3. 3.

We find that the luminosity of the extended Fe K$\alpha$ emission has a good
linear correlation with the [OIV] luminosity which indicates that this
emission is closely linked to the central AGN, instead of due to alternative
origin such as unresolved X-ray binary emission. Using the 6.4 keV
monochromatic luminosity ($L_{Fe}/EW_{Fe}$) for extended regions to represent
the intensity of reflection continuum, we also find a good linear correlation
with $L_{[OIV]}$.

We thank the anonymous referee for her/his careful reading and suggestions
that significantly improve our work. This work was supported by the National
Key R & D Program of China (2016YFA0400702) and the National Science
Foundation of China (NSFC grants U1831205, 11473021, 11522323). X.S.
acknowledges support from NSFC grant 11822301. C.P. work is supported by
Fundação para a Ciência e a Tecnologia (FCT) through the research grants
PTDC/FIS-AST/29245/2017, UID/FIS/04434/2019, UIDB/04434/2020 and
UIDP/04434/2020. H.Y. thanks Jie Zheng for assistance with data and software,
Dr. Jiangtao Li, Xiaoyu Xu and Xiaodi Yu for discussion. We retrieved data
from the NASA-IPAC Extragalactic Database (NED), the Hubble Space Telescope
Archive and the Chandra Data Archive. For the data analysis, we used the CIAO,
Sherpa and DS9, developed by the Chandra X-ray Center (CXC), and XSPEC
developed by the HEASARC at NASA-GSFC.

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