# Multiple locations of near-infrared coronal lines in NGC 5548

Daniel Kynoch,1,2 Hermine Landt,222footnotemark: 2 Maryam Dehghanian,3 Martin
J. Ward222footnotemark: 2 and Gary J. Ferland3
1Astronomical Institute, Czech Academy of Sciences, Boční II 1401, 141 00
Prague, Czech Republic
2Centre for Extragalactic Astronomy, Department of Physics, Durham University,
South Road, Durham, DH1 3LE, UK
3Department of Physics and Astronomy, University of Kentucky, Lexington, KY
40506, USA
E-mail<EMAIL_ADDRESS>Astronomer at the Infrared Telescope
Facility, which is operated by the University of Hawaii under contract
NNH14CK55B with the National Aeronautics and Space Administration
(NASA)E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the first intensive study of the variability of the near-infrared
coronal lines in an active galactic nucleus (AGN). We use data from a one-year
long spectroscopic monitoring campaign with roughly weekly cadence on NGC 5548
to study the variability in both emission line fluxes and profile shapes. We
find that in common with many AGN coronal lines, those studied here are both
broader than the low-ionisaton forbidden lines and blueshifted relative to
them, with a stratification that implies an origin in an outflow interior to
the standard narrow line region. We observe for the first time [S viii] and
[Si vi] coronal line profiles that exhibit broad wings in addition to narrow
cores, features not seen in either [S ix] or [Si x]. These wings are highly
variable, whereas the cores show negligible changes. The differences in both
the profile shapes and variability properties of the different line components
indicate that there are at least two coronal line regions in AGN. We associate
the variable, broad wings with the base of an X-ray heated wind evaporated
from the inner edge of the dusty torus. The coronal line cores may be formed
at several locations interior to the narrow line region: either along this
accelerating, clumpy wind or in the much more compact outflow identified with
the obscurer and so emerging on scales similar to the outer accretion disc and
broad line region.

###### keywords:

galaxies: Seyfert – galaxies: active – infrared: galaxies – quasars: emission
lines – quasars: individual: NGC 5548

††pubyear: 2022††pagerange: Multiple locations of near-infrared coronal lines
in NGC 5548–16

##  1 Introduction

Active galactic nuclei (AGN) display emission lines from both permitted and
forbidden transitions. The latter are usually associated with the narrow
emission line region (NLR), which is formed by gas of low densities
($\log[n_{\rm H}/\mathrm{cm}^{-3}]\sim 3$–6) located at relatively large
distances from the central ionising source (from a few pc up to several 100
pc). But some of these forbidden emission lines require energies $\gtrsim 100$
eV to form the corresponding ions, have higher critical densities for
collisional deexcitation ($\log[n_{\rm e}^{\rm crit}/\mathrm{cm}^{-3}]\sim
7$–10) and broader profiles (full widths at half maxima [FWHM] $\sim 500-1500$
km s-1) than the low-ionisation narrow emission lines (e.g., Penston et al.,
1984; Appenzeller & Oestreicher, 1988; Giannuzzo et al., 1995; Erkens et al.,
1997; Rodríguez-Ardila et al., 2002, 2011): these are the so-called ‘coronal
lines’, named after their presence in the spectrum of the solar corona (Oke &
Sargent, 1968). Coronal lines are forbidden fine-structure transitions arising
from highly-ionised states of heavy metals. Low-energy electrons or weak
interactions with high-energy electrons can efficiently excite these
transitions from the ground state, however, the formation of the ions
themselves requires relatively high energies.

Both types of AGN display coronal lines (Osterbrock, 1977; Koski, 1978), but
they are stronger in broad-line (type 1) than in narrow-line (type 2) AGN
relative to their low-ionisation narrow emission lines (Murayama & Taniguchi,
1998). Therefore, it is likely that the coronal line region has two
components, one compact and one spatially extended, with only the latter
remaining unobscured by the dusty torus in type 2 AGN. Support for this
assumption comes from the fact that the emission from this region is often
extended but much less so than that from the low-ionisation NLR (on scales of
$\sim 80-150$ pc; e.g. Prieto et al. 2005; Müller Sánchez et al. 2006; Müller-
Sánchez et al. 2011; Mazzalay et al. 2013; Riffel et al. 2021; although Negus
et al. 2021 have recently reported coronal line emission on kpc scales).
Furthermore, coronal lines are often blueshifted relative to the low-
ionisation narrow lines (e.g., Penston et al., 1984; Erkens et al., 1997;
Rodríguez-Ardila et al., 2002), which indicates an outflowing wind component.
Given their similar physical conditions, it could be that the partly ionised
gas that produces absorption lines and edges in the soft X-ray spectra of AGN,
i.e., the so-called ‘warm absorber’, produces also the coronal lines in its
(colder) outer regions (Netzer, 1993; Erkens et al., 1997; Porquet et al.,
1999). In any case, the coronal line region is most likely dust free, since
strong emission from refractory elements such as iron, silicon and calcium are
observed, which would be severely reduced in a dusty environment (Ferguson et
al., 1997).

The high ionisation potentials ($\chi$) required for the coronal lines can be
found either in a hot, collisionally ionised plasma or be produced by the hard
continuum in AGN if the gas is photoionised. In the first case, the electron
temperatures would be of the order of $\log(T_{\rm e}/\mathrm{K})\approx 6$
and in the second case much lower ($\log[T_{\rm e}/\mathrm{K}]\sim 4$–5).
Currently, photoionisation is favoured, since for most AGN the observed flux
ratios between different coronal lines can be reproduced within a factor of
$\sim 2-3$ by these models (Oliva et al., 1994; Ferguson et al., 1997; Landt
et al., 2015a, b), whereas in the case of a hot plasma either its temperature
needs to be fine-tuned within a very narrow range (Oliva et al., 1994) or no
acceptable fit can be obtained (Landt et al., 2015a, b).

More recently, growing interest in near-IR coronal lines has arisen due to
their potential for yielding estimates of the black hole mass in AGN (Cann et
al., 2018; Rodríguez-Ardila et al., 2020). Since these coronal lines can
potentially probe the accretion disc spectral energy distribution (SED) at
far-UV/soft-X-ray energies, a regime difficult to observe but most influenced
by the mass of the black hole, they could uncover the long-sought population
of intermediate black holes, which are crucial for our understanding of black
hole growth over cosmic time (Hopkins et al., 2012). Even more importantly, if
near-IR coronal lines can help identify AGN in dwarf galaxies in large numbers
(Bohn et al., 2021; Cann et al., 2021), it would open up a unique opportunity
to understand the role of AGN feedback in galaxy evolution and to test
cosmological models. Since dwarf galaxies are believed to be dark matter-
dominated, these sources serve as important probes in the low-mass halo regime
in particular for the Lambda Cold Dark Matter ($\Lambda$CDM) paradigm
(Navarro, 2019).

Variability studies can strongly constrain the properties of the coronal line
region, in particular if several lines can be studied simultaneously and
together with other AGN components such as the broad emission line region
(BLR) and the UV/X-ray continuum. However, since these emission lines are
relatively weak and so require high-quality spectroscopy, very few studies of
this kind have been attempted so far. Veilleux (1988) presented the only
systematic study of coronal line variability. In a sample of $\sim 20$ AGN, he
found firm evidence that both the [Fe vii] $\lambda 6087$ and [Fe x] $\lambda
6375$ emission lines varied (during a period of a few years) for only one
source (NGC 5548) and tentative evidence for another seven sources (including
NGC 4151). Then, within a general optical variability campaign on Mrk 110 for
about half a year, Kollatschny et al. (2001) reported strong [Fe x]
variations. Strong variability of the coronal lines manifested mainly as a
fading of the flux was first reported for IC 3599 (Grupe et al., 1995; Brandt
et al., 1995) and is now usually associated with a new class of non-active
galaxies, the so-called ‘strong coronal line emitters’ (or ‘coronal line
forest AGN’). Most of these sources have been detected in the Sloan Digital
Sky Survey (SDSS: York et al. 2000) and a stellar tidal disruption event seems
to be the most plausible explanation for the strong fading of their coronal
lines over a time period of several years (Komossa et al., 2008; Gelbord et
al., 2009; Komossa et al., 2009; Wang et al., 2011; Wang et al., 2012; Yang et
al., 2013; Rose et al., 2015; Winkler, 2016; Cerqueira-Campos et al., 2021;
van Velzen et al., 2021).

Landt et al. (2015a) and Landt et al. (2015b) presented the first extensive
studies of the coronal line variability in individual AGN. Their data sets for
the nearby, well-known sources NGC 4151 and NGC 5548 included a handful of
epochs of quasi-simultaneous optical, near-IR and X-ray spectroscopy spanning
a period of several years. They found very different variability behaviours
for the two sources, with only weak variations detected for the coronal lines
in NGC 4151, but strong flux variability (mainly a decrease) by factors of
$\sim 2-4$ observed in NGC 5548. In both sources, the coronal line gas density
was constrained to relatively low values of $\log(n_{\rm
e}/\mathrm{cm}^{-3})\sim 3$ for a relatively high ionisation parameter of
$\log U\sim 1$, which put it at a distance from the central ionising source of
a few light years and so well beyond the hot inner face of the obscuring dusty
torus. Therefore, they proposed that the coronal line region in AGN is an
independent entity rather than part of a continuous gas distribution
connecting the BLR and low-ionisation NLR, possibly an X-ray heated wind as
first suggested by Pier & Voit (1995).

Here we revisit the variability of the near-IR coronal lines in NGC 5548 with
a much improved data set that allows us to study in detail both flux and
profile shape variations. Our paper is structured as follows. In Section 2, we
briefly discuss the near-IR spectroscopy, which we analyse in detail in
Section 3. In Section 4, we present the results on the coronal line profiles
and their variability, which we compare to theoretical photoionisation
simulations in Section 5. In Section 6, we discuss the likely origin of the
near-IR coronal lines in NGC 5548. Finally, in Section 7, we present a summary
of our main results and conclusions. We quote all laboratory line wavelengths
as vacuum wavelengths and define velocities as negative if they are in the
blue-shifted (outflowing) direction.

##  2 The data

Landt et al. (2019) observed NGC 5548 between 2016 August and 2017 July with
the SpeX spectrograph (Rayner et al., 2003) at the NASA Infrared Telescope
Facility (IRTF), a 3 m telescope on Maunakea, Hawaii. The main aim of this
near-IR spectroscopic reverberation mapping campaign was to measure the time
delay of the hot dust in the obscuring torus together with estimates of the
torus radius based on thermal equilibrium arguments. Another important goal
was to study the variability of emission lines such as those from the coronal
line region.

The campaign achieved a total of 18 near-IR spectra with an average cadence of
about ten days, excluding a 3.5-month period when the source was unobservable.
They used the short cross-dispersed (SXD) mode
(0.7–$2.55\text{\,}\mathrm{\SIUnitSymbolMicro m}$) and a
$0.3^{\prime\prime}\times 15^{\prime\prime}$ slit oriented at the parallactic
angle, resulting in an average spectral resolution of $R=2000$ or full width
at half maximum (FWHM) $\sim 150$ km s-1. The spectra have in general a
relatively high signal-to-noise (S/N) ratio with an average continuum
$\mathrm{S/N}\sim 100$.

Care was taken to ensure a posteriori an accurate absolute flux calibration.
As described in detail in Landt et al. (2019) (see their section 3.3), they
used the narrow forbidden emission line [S iii] $\lambda 9531$ to align the
flux scale of the spectra and verified it with a photometric light-curve.
Furthermore, the impact of the extended low-ionisation emission line region on
the enclosed flux in the slit was assessed based on a near-IR Integral Field
Unit (IFU) observation. For our following analysis, we used the observed
spectra with their multiplicative photometric correction factors applied. We
estimated that the uncertainty on the wavelength calibrations of our spectra
is on average 0.15 Å, which corresponds to $\approx 2-5$ km s-1 at the
location of the lines studied. We report velocity shifts of the coronal lines
measured relative to the [S iii] $\lambda 9531$ narrow emission line and the
wavelength calibration uncertainty was added to the measurement uncertainties.

##  3 The spectral analysis

Table 1: Coronal emission lines and their contaminants

Coronal emission line | Contaminant emission line
---|---
Ion | $\lambda$ | $\chi$ | $\log\left(n_{\mathrm{e}}^{\mathrm{crit}}\right)$ | Ion | $\lambda$
| [$\text{\,}\mathrm{\SIUnitSymbolMicro m}$] | [eV] | [cm-3] |  | [$\text{\,}\mathrm{\SIUnitSymbolMicro m}$]
(1) | (2) | (3) | (4) | (5) | (6)
[S viii] | 0.9914 | 281.0 | 9.5 | [C i] | 0.9827
|  |  |  | [C i] | 0.9853
|  |  |  | H i (Pa $\updelta$) | 1.005
|  |  |  | He ii | 1.0126
[S ix] | 1.2523 | 328.8 | 9.4 | Unknown | 1.248
|  |  |  | [Fe ii] | 1.2570
|  |  |  | Unknown | 1.262
|  |  |  | H i (Pa $\upbeta$) | 1.282
[Si x] | 1.4305 | 351.1 | 8.1 |  |
[Si vi] | 1.9650 | 166.8 | 8.5 | H i (Pa $\upalpha$) | 1.875
|  |  |  | H i (Br $\updelta$) | 1.9440
|  |  |  | H2 | 1.957

The columns are: (1) Ion; (2) vacuum rest-frame wavelength; (3) ionisation
potential; and (4) critical density calculated with cloudy for the coronal
emission lines at temperature $\log(T_{\mathrm{e}}/\mathrm{K})=4$; (5) ion;
and (6) vacuum rest-frame wavelength for the contaminating broad and narrow
emission lines. The emission line parameters of all these lines are listed in
Table 2.

The large wavelength range our cross-dispersed near-IR spectra covers four
strong coronal lines in NGC 5548. Two of them are produced by highly-ionised
sulphur ([S viii] and [S ix]) and two by highly-ionised silicon ([Si vi] and
[Si x]). We list their basic properties in Table 1. Our main aim was to
reliably isolate the coronal lines in the individual spectra in order to
measure their fluxes, velocity shifts and profile shapes and study their
variability. However, since coronal lines are in general weak emission lines,
we analysed them first in the high-quality mean spectrum presented by Landt et
al. (2019) and then used these results as a guide for our analysis of the
individual spectra, which have a lower $S/N$ in the wavelength regions of
interest.

We performed the emission line and continuum fits using custom Python scripts
employing the package lmfit (Newville et al., 2014), which is a non-linear,
least-squares, curve-fitting routine based on the Levenberg-Marquardt
algorithm. The majority of the emission lines can be adequately modelled with
Gaussian profiles. From these fits we have calculated the emission line fluxes
and FWHMs and the associated uncertainties. All narrow emission lines were
allowed to have widths varying in the range of $\mathrm{FWHM}=100$–900 km s-1
and the widths of broad Gaussian components were allowed to vary in the range
of 1000–9999 km s-1. Values quoted for the FWHMs of the emission lines have
been corrected for instrumental broadening. The velocity shifts of the near-IR
lines are determined from the centroids of the fitted Gaussians and measured
relative to the [S iii]$\lambda 9531$ line, which is assumed to have zero
velocity shift. The uncertainties on the velocity shifts incorporate the
uncertainty on the wavelength calibration of our spectra. More details on the
fitting procedures for specific lines and blends are given in the following
subsections.

###  3.1 The mean spectrum

Figure 1: Spectral regions in the mean spectrum around the four near-IR
coronal lines studied. The coronal lines are labelled in magenta, whereas
contaminating permitted and forbidden transitions are labelled in green and
red, respectively. Forbidden transitions of iron are labelled in cyan. The
wavelengths and fluxes of all the marked emission lines are listed in Table 2.
Table 2: Emission line parameters measured in the mean spectrum

Ion | $\lambda$ | Line | Velocity | FWHM | Flux
---|---|---|---|---|---
| [$\text{\,}\mathrm{\SIUnitSymbolMicro m}$] | component | offset | [km s-1] | [$10^{-15}$ erg s-1 cm-2]
(1) | (2) | (3) | (4) | (5) | (6)
[S iii] | 0.90711 |  |  | $378\pm 11$ | $13.3\pm 0.5$
[S iii] | 0.95332 |  |  | $365\pm 7$ | $33\pm 3$
[C i] | 0.98268 |  | $+48\pm 24$ | $483\pm 27$ | $0.5\pm 0.2$
[C i] | 0.98530 |  | $+48\pm 24$ | $483\pm 27$ | $2.1\pm 0.2$
[S viii] | 0.99138 | core | $-119\pm 15^{\star}$ | $737\pm 39$ | $7.3\pm 0.4$
" |  | blue wing |  |  | $1.7\pm 0.4$
" |  | red wing |  |  | $2.8\pm 0.7$
H i (Pa $\updelta$) | 1.00521 | narrow | $-69\pm 25$ | $461\pm 26$ | $2.9\pm 0.2$
H i (Pa $\updelta$) |  | broad 1 | $-2961$ | $5091$ |
H i (Pa $\updelta$) |  | broad 2 | $+1680$ | $5149$ | $109\pm 11$
He ii | 1.01264 | narrow | $-7\pm 18$ | $461\pm 26$ | $2.9\pm 0.2$
He ii |  | broad | $+1576\pm 1025$ | $8847\pm 956$ | $49\pm 11$
Unknown | 1.2475 |  |  | $334\pm 13$ | $1.3\pm 0.2$
[S ix] | 1.2523 |  | $-120\pm 14^{\star}$ | $554\pm 24$ | $4.3\pm 0.2$
[Fe ii] | 1.25702 |  | $+25\pm 18$ | $334\pm 13$ | $2.2\pm 0.2$
Unknown | 1.2612 |  |  | $380\pm 15$ | $<0.45$
H i (Pa $\upbeta$) | 1.28216 | narrow | $-55\pm 12^{\star}$ | $334\pm 13$ | $6.4\pm 0.3$
H i (Pa $\upbeta$) |  | broad 1 | $-2961\pm 125$ | $5091\pm 197$ |
H i (Pa $\upbeta$) |  | broad 2 | $+1680\pm 112$ | $5149\pm 141$ | $215\pm 7$
[Si x] | 1.430 |  | $-138\pm 14^{\star}$ | $734\pm 43$ | $7.9\pm 0.6$
H i (Br $\updelta$) | 1.94509 | narrow | $-69\pm 41$ | $334$ | $0.9\pm 0.2$
H i (Br $\updelta$) |  | broad 1 | $-2961$ | $5091$ |
H i (Br $\updelta$) |  | broad 2 | $+1680$ | $5149$ | $39$
[Si vi] | 1.9650 | core | $-384\pm 14^{\star}$ | $607\pm 25$ | $13.0\pm 0.6$
" |  | blue wing |  |  | $3.6\pm 0.4$
" |  | red wing |  |  | $8.7\pm 0.6$
H2 | 2.0332 |  | $-66\pm 17^{\star}$ | $174\pm 25$ | $0.8\pm 0.1$
H i (Br $\upgamma$) | 2.16612 | narrow | $0\pm 22$ | $389\pm 46$ | $1.3\pm 0.2$
H i (Br $\upgamma$) |  | broad 1 | $-2961$ | $5091$ |
H i (Br $\upgamma$) |  | broad 2 | $+1680$ | $5149$ | $43.3\pm 0.3$

The columns are: (1) Ion; (2) vacuum wavelength; (3) fitted emission line
component; (4) velocity offset of the emission line peak relative to [S
iii]$\lambda 0.95332$ $\text{\,}\mathrm{\SIUnitSymbolMicro m}$: narrow line
shifts with a significance $>3\sigma$ are marked ⋆; (5) full width at half
maximum of the emission line component corrected for an instrumental
broadening of 150 km s-1; and (6) integratedline flux. We give $1\sigma$
errors. We note that all H i emission lines are assumed to have the same
double-peaked broad-line profile as Pa $\upbeta$ and that we list for them
only the total broad line flux.

Fig. 1 shows the wavelength regions around the four near-IR coronal lines in
the mean spectrum. Out of these, only [Si x] is free from contaminating,
neighboring emission lines, whereas the other coronal lines are located close
to a hydrogen Paschen broad emission line and other chemical species (Table
1). Therefore, rather than isolating the coronal lines by ‘clipping’ the
profiles to the local continuum on the red and blue sides of the line, we
carefully modelled all the line complexes around the coronal lines in order to
deblend them from neighbouring features (Fig. 2). The resultant coronal line
fluxes, their blends and other observed emission lines are listed in Table 2.
In the following we give details of the analysis.

Figure 2: The decomposition of emission line blends around the four near-IR
coronal lines using the mean spectrum. All coronal lines were masked out and
not used in the fitting process. Individual emission lines are shown as blue
dotted lines and the total models are shown as the red solid lines. The bottom
panels for each coronal line show the flux residuals across the full emission
line complex. All velocities are relative to the expected rest-frame
wavelength of the coronal line, except in the case of [S ix] where velocities
are relative to Pa $\upbeta$. See Section 3.1 in the text for more details.

####  3.1.1 The continuum

Firstly, the underlying pseudo-continuum is modelled and subtracted in four
spectral regions: 0.7–1.22, 1.12–1.33, 1.39–1.53 and 1.65–2.4
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The 1.12–1.33 and 1.39–1.53
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ regions could be satisfactorily fit
with a simple power-law, whereas the 0.7–1.22 and 1.65–2.4
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ regions required polynomial models to
reproduce the curvature of the pseudo-continuum.

There are no other emission lines in the vicinity of [Si x], therefore its
profile could be obtained by simply subtracting the local pseudo-continuum
flux. Whilst [Si x] is free from other emission lines, this spectral region is
affected by telluric absorption, particularly on the blue side of the line. We
were therefore careful to avoid the inclusion of residual telluric features
when modelling the pseudo-continuum (see Fig. 2). The coronal lines [S viii],
[S ix] and [Si vi] are all blended with other emission lines. We determined
their profiles by modelling the emission line complexes as further described
below.

Figure 3: The coronal line profiles as extracted from the mean spectrum
(black) and fit with Gaussians (red). The total profiles of the [S ix] and [Si
x] lines are fit with a single Gaussian, whereas only the central cores of the
[S viii] and [Si vi] lines are fit (solid red lines). For the latter two lines
we additionally show the best fit extrapolated across the whole line profile
(dotted red lines); blue and red excess flux is evident on these lines. For
comparison, the [S iii]$\lambda 9531$ profile (normalised in amplitude to each
coronal line profile) is plotted with a blue dashed line. The four coronal
lines are broader than [S iii] and blueshifted with respect to it.

####  3.1.2 The [S ix] line

The [S ix] coronal line is located on the blue wing of broad Pa $\upbeta$.
Schönell et al. (2017) analysed a high-spectral resolution near-IR spectrum of
NGC 5548 obtained in 2012 with the Near-Infrared Integral Field Spectrometer
(NIFS) at Gemini North. They reported that Pa $\upbeta$ has two kinematically
distinct components producing a double-peaked broad emission line. Therefore,
we decomposed the Pa $\upbeta$ emission line using two Gaussians, one red and
one blue of the line centre.

The widths of all Gaussians modelling the narrow lines were tied together. In
addition to the narrow, forbidden [Fe ii] lines at 1.2570 and 1.2791
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, we find two unidentified lines at
$\approx 1.2483$ and $\approx 1.2612$ $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$. The former unidentified line appears to be present also in the spectrum
of Schönell et al. (2017), but not mentioned by the authors, whereas the
latter unidentified line is not seen in their spectrum. No transitions near
these two wavelengths are reported in observations of classical novae (Wagner
& Depoy 1996). We fit these unknown features with narrow Gaussians, but the
$1.2612$ $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ line is very weak and we
could only obtain an upper limit on its flux. Therefore, we have not
considered this line further in the fits of the individual spectra. In order
to not make any prior assumptions about the [S ix] line profile, the narrow
window containing the [S ix] line was masked and not used in the fitting
process. Having fit for Pa $\upbeta$, [Fe ii] 1.2570
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and the unidentified line at $1.2483$
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, we take the residual flux in the
emission line complex as the [S ix] profile (Fig. 2).

####  3.1.3 The [Si vi] line

The [Si vi] coronal line is blended with both the red wing of the weak
hydrogen Br $\updelta$ broad line and the extreme red wing of the hydrogen Pa
$\upalpha$ broad line. A very weak H2 line is also expected at 1.9570
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, although we did not convincingly
detect it. A narrow window containing the [Si vi] line was masked and all
other emission lines were modelled with Gaussians.

We assumed that the broad components of the hydrogen lines Pa $\upalpha$ and
Br $\updelta$ have the same double-Gaussian profile as the Pa $\upbeta$ broad
component (see Section 3.1.2). The amplitude of the broad Br $\updelta$
profile was fixed so as not to exceed the observed flux. Since the width of
the narrow Br $\updelta$ line hit the maximum allowed value, we fixed it to
that of the narrow Pa $\upbeta$ line and fit only for the flux and velocity
offset. The resulting ratio between the Br $\updelta$ and Pa $\upbeta$ narrow
line fluxes is $0.14\pm 0.03$, which is similar to the value of 0.11 expected
for Case B and a gas temperature of 15000 K (Osterbrock & Ferland 2006). We
note that an additional, weak broad Gaussian component was required by the
fits in order to adequately model the red wing of Pa $\upalpha$, but we do not
ascribe a particular physical meaning to this component. The residuals of our
best-fit model reveal the profile of the relatively strong [Si vi] line. It
shows a prominent and extended red wing and excess blue flux in addition to a
narrow core (Figs. 2 and 3). The width, flux and velocity offset of the core
component have been determined by fitting a Gaussian to a region spanning
$\approx 800$ km s-1 across the peak of the line (the solid red line in Fig.
3); these are the values reported for the ‘core’ component in Table 2. To
determine the fluxes in the wings, we have integrated the excess flux from the
peak of the core out to $\approx-2000$ km s-1 on the blue side of the core and
$\approx+3000$ km s-1 on the red side. The integration limits for the wings
were determined by a visual inspection of the spectrum to determine the
maximum velocity extents of the excess flux. Since the red wing in particular
is shallow at its extremity, it is likely that an appreciable amount of the
integrated flux is just noise. To account for this, we estimate the noise
contribution to the integrated flux. We first calculate the noise in the
pseudo-continuum in two windows adjacent to the wings. Using this value, we
then simulate 1000 Gaussian noise ‘spectra’ on the same velocity grid over
which the wings are integrated. The positive fluxes in these mock spectra are
integrated and the mean value gives us an estimate of the amount of noise
included in the wings’ flux, which we take to be the uncertainty. These values
are reported for the ‘blue wing’ and ‘red wing’ components in in Table 2.

####  3.1.4 The [S viii] line

The [S viii] coronal line is located near the emission maximum of a blend
between the hydrogen Pa $\updelta$ and He ii broad emission lines and close to
their respective narrow components. This complex also contains the narrow,
forbidden lines [C i] 0.9827 and 0.9853 $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ and [S ii] 1.0290, 1.0323, 1.0339 and 1.0373
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$. We fit the wavelength region of
0.975–1.027 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$, which excludes the [S
ii] lines. We again used the broad Pa $\upbeta$ profile as a template for the
broad hydrogen lines (here Pa $\updelta$) and we fit for its flux only. On the
red side of the emission line blend, a single broad Gaussian was adequate to
fit the remaining flux from broad He ii. Single Gaussians were included to
model the [C i], Pa $\updelta$ and He ii narrow lines. The velocity offsets of
the two [C i] lines were tied together.

Having modelled and subtracted emission lines other than [S viii] in the
complex, we take the residual flux from our model as the [S viii] profile (see
Fig. 2). The [S viii] coronal line has a similar profile to that of [Si vi]
comprising of a red wing, excess blue flux and a narrow core (Figs. 2 and 3).
Measurements of the line core and the blue and red wings have been made in the
same manner as for [Si vi], described in Section 3.1.3; the results are
reported in Table 2.

####  3.1.5 Other emission lines

For our study, we have modelled also the hydrogen Br $\upgamma$ broad emission
line, since it is of interest for black hole mass determinations in AGN (see
Section 4.3), and the [S iii] $\lambda\lambda 9069,9531$ narrow emission line
doublet, since these lines can inform us about the intrinsic profile of
transitions from the narrow emission line region.

There are no other broad emission lines in the vicinity of Br $\upgamma$ and
we isolated the line from a linear local continuum. The broad component was
modelled with the same profile as the other hydrogen lines and we fit only for
its flux. In addition to a narrow Gaussian for Br $\upgamma$, a second narrow
Gaussian was added to model the H2 2.0332 $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ emission line, which sits on the blue wing of broad Br $\upgamma$.

The [S iii] $\lambda\lambda 9069,9531$ narrow emission line doublet is a
strong feature in our spectra. We subtracted the hydrogen Pa $\upepsilon$
broad emission line from beneath the [S iii] lines, again using broad Pa
$\upbeta$ as a template. We also subtracted a narrow Gaussian line at the
rest-frame wavelength of Pa $\upepsilon$ from the [S iii] $\lambda 9531$ line
profile. Having accounted for the Pa $\upepsilon$ emission, each [S iii] line
was adequately fit with a single Gaussian of $\mathrm{FWHM}\approx 370$ km
s-1. No significant velocity shift was measured between the two [S iii] lines.
The centroid velocity shifts of all other lines measured in the mean spectrum
were measured relative to [S iii] $\lambda 9531$. The observed flux ratio of
[S iii] $\lambda 9531$/[S iii] $\lambda 9069=2.5\pm 0.1$ is consistent with
the theoretical value of 2.58.

###  3.2 The single-epoch spectra

Because of the lower quality of the single-epoch spectra relative to the mean
spectrum, multi-Gaussian fits to the emission line complexes were not always
successful in reliably isolating the coronal lines. Therefore, we used their
emission-line profiles determined in the mean spectrum as a guide. Having
subtracted the underlying broad-band continuum following the method described
in Section 3.1.1 we then performed a fit to the emission line blend. The mean
Pa $\upbeta$ profile was again used as a template for all of the hydrogen
lines; the template was rescaled in flux to match the hydrogen lines in the
single-epoch spectra. Each narrow line profile was modelled as a single
Gaussian with its parameters taken from the fit to the same line in the mean
spectrum. If necessary, small scaling adjustments were made to the narrow
lines to improve the fit. To some spectra we added a local continuum to
correct cases in which we judged the broad-band continuum placement could be
improved. The local continuum and contaminating lines were adjusted to obtain
a good fit to the data then subtracted from the spectrum, leaving just the
coronal line profile. As can be seen in Figs. 5–10 the residuals away from the
coronal line are generally featureless (with the exception of the wings near
the [S viii] and [Si vi] profiles, and some artefacts of imperfect telluric
correction around [Si x]) indicating that this procedure generally worked
well. However, the coronal line profiles in a few epochs were of very poor
quality and we have excluded them for our further studies. As for the mean
spectrum, the fluxes, widths and velocity offsets of the narrow line cores are
determined by fitting a Gaussian to the isolated emission line profile. Again,
for [S viii] and [Si vi] we fit only the central portion of the profiles
(within a few hundred km s-1 of the peak) to avoid the wings on either side of
the line.

Because the coronal lines are low-contrast features in our spectra the FWHM
and flux measurements are very sensitive to the placement of the underlying
pseudo-continuum. If the continuum is placed too high, for example, then both
the FWHM and flux will be underestimated in the fitted profile. This is an
issue in the single-epoch spectra, in which the precise continuum placement is
less certain than in the high-S/N mean spectrum. We therefore calculate the
range in both FWHM and flux that result from moving the the local continuum to
its highest and lowest plausible levels (i.e. $\pm 1\sigma$). The value of
$\sigma$, the noise in the continuum, is calculated from the standard
deviation of flux points about the mean value in featureless windows near to
each coronal line (and typically this noise was $\sim 1$ per cent of the
continuum flux). This additional uncertainty was added in quadrature to the
Gaussian measurement uncertainties calculated by the fitting algorithm. A
similar approach was taken to estimate the uncertainties on the [S viii] and
[Si vi] wings; we calculate the error range from the maximum and minimum
excess flux integrated with the continuum is moved $\pm 1\sigma$. Because the
blue wing is weak and the red wing is very shallow at its extremity, this
results in rather large uncertainties for the wings (particularly in the noisy
part of the spectrum containing [S viii]) and there are several epochs where
no flux in excess of the Gaussian core is detected with confidence.

Our results for the four near-IR coronal lines as well as the strong [S iii]
$\lambda 9531$ line are shown in Figs. 5-10. The fluxes of the line cores and
wings over the course of the campaign are recorded in Table 3.

Table 3: Fluxes of the cores and blue and red wings in the profiles of [S
iii]$\lambda 9531$ and the near-infrared the coronal lines

| [S iii] | [S viii] | [S ix] | [Si x] | [Si vi]
---|---|---|---|---|---
|  | $\overbrace{\hskip 128.0374pt}$ |  |  | $\overbrace{\hskip 128.0374pt}$
Date | Core | Blue | Core | Red | Core | Core | Blue | Core | Red
|  | wing |  | wing |  |  | wing |  | wing
Mean spectrum | $33\pm 3$ | $1.7\pm 0.4$ | $7.3\pm 0.4$ | $2.8\pm 0.7$ | $4.3\pm 0.2$ | $7.9\pm 0.6$ | $3.6\pm 0.4$ | $13.0\pm 0.6$ | $8.7\pm 0.6$
602 16/08/02 | $34\pm 2$ | $3.5\pm{\color[rgb]{0,0,0}1.8}$ | $8.9\pm{\color[rgb]{0,0,0}3.4}$ | $4.4\pm{\color[rgb]{0,0,0}3.2}$ | $4.5\pm{\color[rgb]{0,0,0}1.3}$ | $7.7\pm{\color[rgb]{0,0,0}2.5}$ | $2.0\pm{\color[rgb]{0,0,0}1.1}$ | $13.2\pm{\color[rgb]{0,0,0}1.7}$ | $18.7\pm{\color[rgb]{0,0,0}2.4}$
611 16/08/11 | $35\pm 2$ | $1.5\pm{\color[rgb]{0,0,0}1.9}$ | $7.2\pm{\color[rgb]{0,0,0}5.0}$ | $4.7\pm{\color[rgb]{0,0,0}2.9}$ | - | $5.7\pm{\color[rgb]{0,0,0}2.6}$ | $1.7\pm{\color[rgb]{0,0,0}1.3}$ | $12.4\pm{\color[rgb]{0,0,0}1.8}$ | $16.7\pm{\color[rgb]{0,0,0}2.7}$
743 16/12/21 | - | - | - | - | $3.6\pm{\color[rgb]{0,0,0}1.3}$ | $6.0\pm{\color[rgb]{0,0,0}2.5}$ | - | - | -
759 17/01/06 | $34\pm 2$ | $<{\color[rgb]{0,0,0}4.6}$ | $8.0\pm{\color[rgb]{0,0,0}3.7}$ | $7.0\pm{\color[rgb]{0,0,0}4.1}$ | $3.6\pm{\color[rgb]{0,0,0}1.8}$ | $7.9\pm{\color[rgb]{0,0,0}2.7}$ | $2.4\pm{\color[rgb]{0,0,0}0.5}$ | $13.3\pm{\color[rgb]{0,0,0}1.7}$ | $<{\color[rgb]{0,0,0}2.1}$
773 17/01/20 | $34\pm 2$ | $4.1\pm{\color[rgb]{0,0,0}1.8}$ | $5.3\pm{\color[rgb]{0,0,0}3.4}$ | $<{\color[rgb]{0,0,0}6.2}$ | $5.2\pm{\color[rgb]{0,0,0}1.4}$ | $7.2\pm{\color[rgb]{0,0,0}2.7}$ | $3.9\pm{\color[rgb]{0,0,0}0.7}$ | $11.3\pm{\color[rgb]{0,0,0}1.7}$ | $3.4\pm{\color[rgb]{0,0,0}1.8}$
777 17/01/24 | $33\pm 2$ | - | - | - | - | $6.5\pm{\color[rgb]{0,0,0}3.6}$ | $4.7\pm{\color[rgb]{0,0,0}1.1}$ | $1{\color[rgb]{0,0,0}4.7}\pm{\color[rgb]{0,0,0}2.3}$ | $5.5\pm{\color[rgb]{0,0,0}2.4}$
789 17/02/05 | $33\pm 1$ | $3.4\pm{\color[rgb]{0,0,0}2.2}$ | $6.6\pm{\color[rgb]{0,0,0}3.3}$ | ${\color[rgb]{0,0,0}<7.2}$ | $6.1\pm{\color[rgb]{0,0,0}1.7}$ | $8.1\pm{\color[rgb]{0,0,0}2.6}$ | $4.3\pm{\color[rgb]{0,0,0}0.8}$ | $13.9\pm{\color[rgb]{0,0,0}1.7}$ | $3.4\pm{\color[rgb]{0,0,0}1.8}$
799 17/02/15 | $35\pm 2$ | $<{\color[rgb]{0,0,0}3.8}$ | $4.9\pm{\color[rgb]{0,0,0}3.3}$ | $3.6\pm{\color[rgb]{0,0,0}3.5}$ | $2.5\pm{\color[rgb]{0,0,0}1.3}$ | $6.6\pm{\color[rgb]{0,0,0}2.6}$ | $4.3\pm{\color[rgb]{0,0,0}0.9}$ | $14.7\pm{\color[rgb]{0,0,0}1.9}$ | $4.9\pm{\color[rgb]{0,0,0}2.0}$
804 17/02/24 | $34\pm 1$ | $2.4\pm{\color[rgb]{0,0,0}1.7}$ | $4.5\pm{\color[rgb]{0,0,0}3.3}$ | $3.4\pm{\color[rgb]{0,0,0}3.4}$ | $4.1\pm{\color[rgb]{0,0,0}1.5}$ | $5.5\pm{\color[rgb]{0,0,0}2.6}$ | $2.8\pm{\color[rgb]{0,0,0}1.1}$ | $11.5\pm{\color[rgb]{0,0,0}1.8}$ | $3.8\pm{\color[rgb]{0,0,0}2.4}$
829 17/03/17 | $35\pm 2$ | $2.9\pm{\color[rgb]{0,0,0}1.9}$ | $5.3\pm{\color[rgb]{0,0,0}3.2}$ | $3.7\pm{\color[rgb]{0,0,0}3.3}$ | $4.2\pm{\color[rgb]{0,0,0}1.7}$ | $5.8\pm{\color[rgb]{0,0,0}2.6}$ | $2.3\pm{\color[rgb]{0,0,0}0.7}$ | $11.3\pm{\color[rgb]{0,0,0}1.9}$ | $2.2\pm{\color[rgb]{0,0,0}1.7}$
834 17/03/22 | $35\pm 2$ | $<{\color[rgb]{0,0,0}2.7}$ | $6.3\pm{\color[rgb]{0,0,0}3.3}$ | $5.3\pm{\color[rgb]{0,0,0}2.4}$ | $5.5\pm{\color[rgb]{0,0,0}1.5}$ | $8.2\pm{\color[rgb]{0,0,0}3.0}$ | $2.3\pm{\color[rgb]{0,0,0}1.1}$ | $15.3\pm{\color[rgb]{0,0,0}2.0}$ | ${\color[rgb]{0,0,0}<5.1}$
882 17/05/09 | $33\pm 2$ | - | - | - | $3.8\pm{\color[rgb]{0,0,0}1.8}$ | $6.7\pm{\color[rgb]{0,0,0}2.6}$ | $3.1\pm{\color[rgb]{0,0,0}0.7}$ | $12.0\pm{\color[rgb]{0,0,0}1.7}$ | $4.1\pm{\color[rgb]{0,0,0}1.5}$
898 17/05/25 | $33\pm 3$ | $4.0\pm{\color[rgb]{0,0,0}2.7}$ | $8.9\pm{\color[rgb]{0,0,0}4.7}$ | $7.0\pm{\color[rgb]{0,0,0}4.5}$ | $5.2\pm{\color[rgb]{0,0,0}1.7}$ | $9.1\pm{\color[rgb]{0,0,0}3.1}$ | $4.0\pm{\color[rgb]{0,0,0}1.1}$ | $15.3\pm{\color[rgb]{0,0,0}1.7}$ | $4.9\pm{\color[rgb]{0,0,0}2.4}$
914 17/06/10 | $34\pm 2$ | - | - | - | - | - | $3.7\pm{\color[rgb]{0,0,0}0.8}$ | $13.2\pm{\color[rgb]{0,0,0}1.8}$ | $6.7\pm{\color[rgb]{0,0,0}1.7}$
924 17/06/20 | $33\pm 2$ | ${\color[rgb]{0,0,0}<6.4}$ | $12.5\pm{\color[rgb]{0,0,0}6.9}$ | $6{\color[rgb]{0,0,0}.3\pm 5.0}$ | $3.2\pm{\color[rgb]{0,0,0}1.9}$ | $7.3\pm{\color[rgb]{0,0,0}4.5}$ | $4.8\pm{\color[rgb]{0,0,0}1.3}$ | $10.5\pm{\color[rgb]{0,0,0}1.7}$ | $9.9\pm{\color[rgb]{0,0,0}2.9}$
932 17/06/28 | $33\pm 2$ | $3.0\pm{\color[rgb]{0,0,0}1.5}$ | $7.8\pm{\color[rgb]{0,0,0}3.3}$ | $7.7\pm{\color[rgb]{0,0,0}2.8}$ | $1.6\pm{\color[rgb]{0,0,0}1.2}$ | $7.0\pm{\color[rgb]{0,0,0}3.4}$ | $5.6\pm{\color[rgb]{0,0,0}1.1}$ | $9.7\pm{\color[rgb]{0,0,0}1.8}$ | $9.3\pm{\color[rgb]{0,0,0}2.5}$
937 17/07/03 | $33\pm 2$ | $2.7\pm{\color[rgb]{0,0,0}1.6}$ | $9.4\pm{\color[rgb]{0,0,0}3.4}$ | $5.3\pm{\color[rgb]{0,0,0}2.9}$ | - | - | - | - | -
RMS | 0.84 (2.5%) | 0.62 (20%) | 2.25 (32%) | 1.50 (29%) | 1.25 (31%) | 1.03 (15%) | 1.18 (35%) | 1.69 (13%) | 5.22 (79%)

The observation date is given in the formats $\mathrm{MJD}-57000$ and YY/MM/DD
and the fluxes are in units $10^{-15}$ erg s-1 cm-2.

###  3.3 Optical iron coronal lines

During one of our other observing programs, we obtained a high-resolution
optical spectrum of NGC 5548 in 2015 March at the William Herschel Telescope
(WHT), a 4 m telescope on La Palma. We dereddened this spectrum using
$E(B-V)=0.0168$ (Schlafly & Finkbeiner 2011) and the extinction curve of
Cardelli et al. (1989). The spectrum contains six high-ionisation forbidden
lines of iron: [Fe vii]$\lambda 3759,5159,5721,6087$, [Fe x]$\lambda 6374$ and
[Fe xi]$\lambda 7892$. With the exception of [Fe x] these lines are unblended
so we simply measure their profiles with a single Gaussian plus linear local
continuum. [Fe x] is blended with [O i]$\lambda 6363$ so we first determine
the profile of [O i]$\lambda 6300$ and use this as a template for [O
i]$\lambda 6363$, assuming a 1:3 flux ratio. We assume [O iii]$\lambda 5007$
to be at rest within NGC 5548 and measure all other line velocity shifts
relative to it. The FWHMs of the lines are all corrected for instrumental
broadening, assuming this is $\sim 250$ km s-1 for the ISIS instrument on the
WHT. The properties of these lines are reported in Table 4.

Table 4: Properties of optical iron coronal lines and measurements from the
2015 WHT spectrum

Ion | $\lambda$ | $\chi$ | $\log(n_{\mathrm{crit}})$ | Velocity offset | FWHM | Flux
---|---|---|---|---|---|---
| [Å] | [eV] | [cm-3] | [km s-1] | [km s-1] | [$10^{-15}$ erg s-1 cm-2]
(1) | (2) | (3) | (4) | (5) | (6) | (7)
[Fe vii] | 3759 | 99.1 | 7.60 | $-207\pm 17$ | $559\pm 38$ | $16.9\pm 1.5$
" | 5159 | 99.1 | 6.54 | $-126\pm 21$ | $<250$ | $3.01\pm 0.80$
" | 5721 | 99.1 | 7.57 | $-111\pm 11$ | $485\pm 18$ | $10.5\pm 0.5$
" | 6087 | 99.1 | 7.64 | $-201\pm 9$ | $632\pm 13$ | $20.1\pm 0.5$
[Fe x] | 6374 | 233.6 | 8.64 | $-188\pm 15$ | $605\pm 46$ | $5.24\pm 0.51$
[Fe xi] | 7892 | 262.1 | 8.81 | $-212\pm 24$ | $579\pm 57$ | $4.44\pm 0.56$

The columns are: (1) Ion; (2) vacuum wavelength; (3) ionisation potential; (4)
critical density for $\log(T_{\mathrm{e}}/\mathrm{K})=4$; (5) velocity offset
of the emission line peak relative to [O iii]$\lambda 5007$ Å; (6) full width
at half maximum of the emission line component corrected for an instrumental
broadening of 250 km s-1; and (7) line flux. We give $1\sigma$ errors.

##  4 Results

###  4.1 The mean coronal line profiles

Fig. 3 shows the profiles of the four near-IR coronal lines as observed in the
mean spectrum. In all four cases, the central (core) part can be modelled well
with a single Gaussian. It is intriguing to notice that both the [S viii] and
[Si vi] coronal lines show significant excess flux blue- and red-ward of the
core, whereas the [S ix] and [Si x] coronal lines do not.

Figure 4: FWHM (top) and centroid velocity shift (bottom) of the coronal line
and [S iii]$\lambda 9531$ cores, measured in the mean spectrum, as a function
of ionisation potential (left) and critical density (right).

In Fig. 4 we show the coronal line and [S iii] widths and velocity shifts as a
function of both their ionisation potentials and critical densities. The
coronal line (core) profiles are all broader than the [S iii] doublet lines,
with line widths of $\mathrm{FWHM}\sim 500$–$800$ km s-1, compared with
$\approx 370$ km s-1 for [S iii]. Whilst we have only five data points, Fig. 4
shows a trend of increasing FWHM with ionisation potential up to $\approx 300$
eV. It is clear in Fig. 4 that all four coronal lines have emission line peaks
blue-shifted with respect to [S iii]. The [S viii], [S ix] and [Si x] lines
have very similar average velocity offsets of $\approx-130$ km s-1; curiously,
the lowest-ionisation potential coronal line [Si vi] has a much greater
velocity offset of $\approx-380$ km s-1, so there is no simple relationship
between the velocity shift and ionisation potential. We also measured the
velocity shifts of the other forbidden, narrow emission lines in the mean
spectrum, with none of them having a significant velocity shift (see Table 2).
Although it is clear that the coronal lines have higher critical densities and
both greater line widths and velocity shifts than [S iii], no simple trend
with critical density is observed between the four coronal lines.

###  4.2 The coronal line variability

The low-ionisation narrow forbidden emission lines are assumed to be produced
in AGN at distances from the central engine large enough to not show
significant flux variability over the course of decades. But the optical
narrow-line reverberation results for NGC 5548 show that the [O iii] $\lambda
5007$ line emitting region is more nuclear than expected, with an extent of
only 1–3 pc and a density of $\sim 10^{5}$ cm-3 (Peterson et al., 2013). Since
our campaign extends over the course of roughly a year, we can still assume
that the flux of the [S iii] $\lambda 9531$ line is not variable. This
expectation is confirmed by the results in Table 3 and Fig. 5: the RMS
variability of [S iii]$\lambda 9531$ is $\approx 8.4\times 10^{-16}$ erg s-1
cm-2, only around 2.5 per cent of the mean line flux. The width of this line
is also stable during our campaign, with two-thirds of data points being
consistent with the mean value to within 1$\sigma$.

Figure 5: The [S iii] $\lambda 9531$ emission line in the mean and single-
epoch spectra. Left-hand panel: [S iii] emission line profiles isolated from
other emission lines and the underlying continuum (black). The location of the
subtracted contaminating emission lines is indicated with a grey dashed line.
The [S iii] profile extracted from the mean spectrum is shown in the
individual spectra by the thin orange line. In each spectrum the blue shaded
region was fitted with a single Gaussian (red line). Each spectrum is labelled
with the observation date in the formats $\mathrm{MJD}-57000$ and YY/MM/DD.
Right-hand panels (a) and (b) show variations of the line core flux and FWHM
obtained from the Gaussian fit. The error-weighted mean flux and FWHM are
shown by the orange dashed lines, and the orange shaded regions are the mean
$\pm\sigma$. We plot $1\sigma$ errors.

####  4.2.1 The [Si vi] and [S viii] lines

The [Si vi] line is the strongest of the four near-IR coronal lines in our
spectra; we reliably isolated its profile in 15/18 spectra (Fig. 6). We
measure a maximum flux variability of $\sim 50$ per cent for the [Si vi] line
core, with $\mathrm{RMS}\approx 13$ per cent (Table 3). In addition, we
observe variable excess emission blue- and red-ward of the line core. Both of
these flux excesses are relatively broad, with the blue- and red-shifted part
stretching over $\sim 2000$ and $\sim 3000$ km s-1, respectively (Fig. 8), and
in the mean spectrum their combined flux is similar to the flux in the core of
the line. The red flux excess variability shows a cyclical behaviour: it is
most prominent in the first spectra with a flux exceeding that in the line
core, becomes weak by the middle of the campaign and increases in flux again
at later epochs (Fig. 6 and Table 3). In the second part of the campaign
(after the seasonal gap) the blue excess varies in the same manner as the red
excess however the blue excess is weakest in the first observing epochs,
unlike the red excess, which is strongest.

The [S viii] coronal line was strong enough to be reliably isolated in 13/18
single-epoch spectra (Fig. 7). The [S viii] line core is much more variable
than that of the [Si vi] line, with maximum flux changes by a factor of
$\approx 3$ (Table 3). Like for the [Si vi] line, we observe variable and
broad excess emission blue- and red-ward of the line core (Fig. 8), but in the
mean spectrum their combined flux is only about half that of the core of the
line. Given that the [S viii] line is also on average a factor of $\sim 2$
weaker than the [Si vi] line, the isolation of the excess fluxes in the
single-epoch spectra is more problematic. However, there is a trend for this
excess emission to be strongly variable (by factors of a few) also in the [S
viii] coronal line.

Figure 6: The [Si vi] coronal line in the mean and single-epoch spectra. Left-
hand panel: [Si vi] emission line profiles isolated from other emission lines
and the underlying continuum (black). The locations of the contaminating
emission lines are indicated with grey dashed lines; the rest-frame velocity
of the coronal line is indicated by the magenta dotted line. The [Si vi]
profile extracted from the mean spectrum is shown in the individual spectra by
the thin orange line. In each spectrum the light blue shaded region was fitted
with a single Gaussian (red line). Each spectrum is labelled with the
observation date in the formats $\mathrm{MJD}-57000$ and YY/MM/DD. Right-hand
panels (a) and (b) show the flux and FWHM (in km s-1) of this Gaussian. The
error-weighted mean flux is shown by the orange dashed line, and the orange
shaded region spans the mean $\pm\sigma$. Panels (c) and (d) show the excess
flux above the fitted Gaussian on the blue and red sides of the line centre,
respectively. The excess fluxes which were integrated are shaded blue and pink
in the left-hand panel. All fluxes are in units $10^{-15}$ erg s-1 cm-2. We
plot $1\sigma$ errors. Figure 7: The [S viii] coronal line in the mean and
single-epoch spectra. Description as in Fig. 6.

In Fig. 8 we overplot all of the single-epoch line profiles of both [S viii]
and [Si vi] for easier comparison. In [Si vi] it is clear that most of the
variability in the profile is in the broad wings, with the narrow core showing
relatively little variation from the mean. This is reflected in the RMS
variability measured for the different line components (Table 3). Because of
the noisier data, it is more difficult to see the same behaviour in the [S
viii] line and the RMS variability of the core and blue and red wings are
similar ($\approx 30$ per cent). In Fig. 8 we highlight two spectra with
strong and weak wings but similar cores, so visually at least a similar trend
as observed in [Si vi] can be discerned.

|
---|---
Figure 8: The variability of the [Si vi] and [S viii] coronal line profiles.
All extracted profiles are shown in grey and the mean line profiles in orange.
An epoch with strong (weak) wings is highlighted in blue (red). The single-
epoch [S viii] profiles have been smoothed slightly for clarity.

####  4.2.2 The [Si x] and [S ix] lines

The [Si x] line is the second strongest coronal line in our spectra and is
free of blends. However, it is located in a region of telluric absorption,
which is strongest blueward of it. We extracted its profile in 15/18 single-
epoch spectra (Figure 9). Its RMS flux variability (15 per cent) is very
similar to that of the [Si vi] core.

[S ix] is the weakest near-IR coronal line in our study but was strong enough
to be reliably isolated in 13/18 single-epoch spectra. It shows a similar
variability range to the [S viii] line core, with maximum flux changes by a
factor of $\sim 3$ and RMS of 31 per cent, but without a clear trend (Fig.
10).

Figure 9: The [Si x] coronal line in the mean and single-epoch spectra.
Description as in Fig. 5. Figure 10: The [S ix] coronal line in the mean and
single-epoch spectra. Description as in Fig. 5.

####  4.2.3 Trends in coronal line variability

As can be seen from Table 3, the coronal line cores show a slightly higher
degree of variability than that of [S iii] $\lambda 9531$:
$\mathrm{RMS}\approx 10$–30 per cent for the coronal lines compared with
$\mathrm{RMS}=2.5$ per cent for [S iii]. Figs. 6, 7, 9 and 10 suggest that
there is a correspondence between the measured FWHM and flux of the coronal
line cores, in the sense that as the flux increases the line becomes broader.
However, this variability is not statistically significant and simple fits for
a constant line flux return $\chi^{2}_{\nu}=0.27$, 0.77, 0.14 and 0.85 for the
[S viii], [S ix], [Si x] and [Si vi] line cores, respectively. Given the
substantial uncertainties, we cannot make strong statements about the
variability of the narrow line cores.

It is clear from Figs. 6, 7 and 8 that most of the variability in the coronal
line profiles is in the wings of [S viii] and [Si vi]. Flux variations in the
[Si vi] red wing are statistically significant and we can reject the null
hypothesis that the variability is purely statistical with greater than 99.99
per cent confidence. A fit of constant flux to the [Si vi] blue wing
lightcurve is poor ($\chi^{2}_{\nu}=1.45$), suggesting variability of the blue
wing also, but the variability is less significant than in the red wing
($p\approx 0.12$). In Fig. 11 we show the variability of the [Si vi] and [S
viii] broad red wings and compare them to that of the hot dust. Because of the
noisier data, trends in the raw [S viii] red wing lightcurve (Fig. 7d) are
less clear. We have therefore binned the lightcurve to better show the long-
term trend and in Fig. 11 we show the error-weighted average and standard
deviations from the mean of consecutive flux points, as indicated. The dust
lightcurve is derived from spectroscopic data, with fluxes integrated over a
narrow emission line free region near the centre of the H photometric band
(1.55–1.60 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$; Landt et al. 2019). We
observe a strong similarity in the shapes of the dust and the coronal line red
wing lightcurves (particularly [Si vi]): the fluxes are initially high, but
weaken substantially during the gap in observations between MJD 57621 and
57743; the fluxes remain low in the middle of the campaign, before a
systematic rise from MJD 57882 onwards.

Figure 11:  Top: The H band (1.55–1.60 $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$) dust flux, from Landt et al. (2019). Middle and bottom: The [Si vi] and
[S viii] broad red wing fluxes, from this work. We have binned [S viii]
measurements from consecutive epochs and plot the error-weighted averages and
standard deviations. All fluxes are normalised to their mean value.

###  4.3 The black hole mass from near-IR emission line ratios

Rodríguez-Ardila et al. (2020) presented a novel method to calculate black
hole masses using the flux ratio of coronal lines to low-ionisation permitted
lines (see also Prieto et al. 2022). From flux measurements made by Riffel et
al. (2006), Rodríguez-Ardila et al. (2020) calculate the flux ratio [Si vi]/Br
$\upgamma$$=(9.97\pm 0.86)/(16.27\pm 2.0)=0.61\pm 0.09$ from which they
determined a black hole mass of $6.7\times 10^{6}$ M⊙. Considering the total
flux (core $+$ wings) in the [Si vi] line, we calculate [Si vi]/Br
$\upgamma$$=(25.3\pm 0.9)/(43.3\pm 0.3)=0.58\pm 0.02$ from our mean spectrum,
which is consistent within the uncertainties with the value determined by
Rodríguez-Ardila et al. (2020) and therefore gives the same black hole mass.
Therefore, although the absolute fluxes of the lines differ by more than a
factor two between the 2002 IRTF spectrum of Riffel et al. (2006) and our
2016–17 mean spectrum, the flux ratio has not changed, as one would expect if
the flux ratio reflects the black hole mass.

We note that using the [Si vi] core flux only results in the flux ratio
$=0.31\pm 0.01$ and so the estimated black hole mass is approximately four
times greater at $2.6\times 10^{7}$ M⊙, much closer to the $3.2\times 10^{7}$
M⊙ obtained by Pancoast et al. (2014) via reverberation mapping. The mass
obtained from the total [Si vi] line flux is 0.66 dex discrepant with the
Pancoast et al. (2014) estimate, whereas the mass from the core flux is only
0.09 dex discrepant. These compare with a 0.44 dex scatter in black hole mass
reported by Rodríguez-Ardila et al. (2020) for their scaling relation.

##  5 Photoionisation models

Figure 12: The unobscured and obscured SEDs of NGC 5548 (Mehdipour et al.
2015) are shown as solid black and red lines, respectively. Dotted green lines
indicate the ionisation potentials ($\chi$) of the low-ionisation lines (LIL)
H i, [Fe ii] and [S iii]. Dashed magenta lines show the ionisation potentials
of the coronal lines (CL), ranging from 166.8 eV for [Si vi] to 351.1 eV for
[Si x] (see Table 1).

AGN coronal lines are thought to be photoionised by the soft X-ray nuclear
continuum. Since ionic species are most effectively produced by photons with
energies just above their ionisation potentials, the flux ratios of lines with
different ionisation potentials will depend on the shape of the ionising SED.
The shape of the ionising SED depends not just on the properties of the
accretion flow (the black hole mass, accretion rate, electron temperature and
optical depths of the warm and hot coronae, etc.) but also on extrinsic
factors such as obscuration of the ionising source by gas and dust. This is of
particular relevance in studies of NGC 5548 in which a persistent obscurer,
first reported by Kaastra et al. (2014), strongly absorbs the nuclear soft
X-ray emission along certain lines of sight. Kaastra et al. (2014) described
the obscurer as a persistent, clumpy, ionised gas outflow on scales of only a
few light-days from the nucleus. Dehghanian et al. (2019) interpreted it as
the upper, line-of-sight component of an accretion disc wind; the wind
originates interior to the BLR and its dense base shields the BLR from the
nuclear continuum source. We know that this obscurer was present during the
2016–17 near-IR spectroscopic campaign because of the low-flux state NGC 5548
was observed in and the presence of persistent, broad He i $\lambda 1.08$
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$absorption associated with the
obscurer (Wildy et al. 2021).

Mehdipour et al. (2015) presented two SEDs based on 2013–14 X-ray
observations: one seen through the obscurer, and the intrinsic nuclear SED. We
show these SEDs in Fig. 12, where we mark also the ionisation potentials of
the near-IR coronal lines. Clearly the coronal line emission would be strongly
affected by the obscurer if it intervenes between the coronal line gas and the
X-ray source. We do not know a priori the location of the coronal line
emitting gas and therefore we can explore whether the line emission predicted
by the obscured or unobscured SED better match our observations. Therefore, we
used both SEDs in cloudy to make predictions about the resultant line
emission.

###  5.1 The cloudy parameter region

We used the fluxes of the coronal line cores reported in Table 2111For [S
viii] and [Si vi] these are the line core fluxes (excluding the wings)., and
calculated the equivalent widths of the lines relative to the 1215
$\mathrm{\SIUnitSymbolAngstrom}$ continuum flux of the Mehdipour et al. (2015)
SEDs. Subsequently, we searched the parameter space for regions which
reproduced the observed emission line equivalent widths within uncertainties
of $\approx 30$ per cent. Because we expect that the [S iii]-emitting gas is
not cospatial with the coronal line gas, the cloudy predictions for [S iii]
emission can be used to discriminate between models. For example, regions that
predict substantial [S iii] emission or overpredict the observed flux may be
ruled out as potential sites for the coronal line gas. On the other hand,
regions that produce little or no [S iii] are still viable, since this
emission line flux could come from elsewhere. We additionally considered the
equivalent widths of the optical Fe coronal lines (Section 3.3) to aid our
search. We note that lines were measured in a spectrum from 2015 March and are
therefore non-contemporaneous with our near-infrared data from 2016–17. Flux
variability of a factor $\sim 2$ was seen in the [Fe vii] lines over $\approx
5$ years (Landt et al. 2015b). Given this level of intrinsic variability (and
some uncertainty in the absolute flux scaling of the optical spectrum) we
reasonably expect the optical coronal lines to have fluxes within a factor
$\approx 2$–3 of those we measure in the 2015 spectrum.

Our cloudy models are “luminosity cases” similar to the studies of Ferguson et
al. (1997) and Baldwin et al. (1995). This means that we have used the
obscured and unobscured SEDs with their corresponding bolometric luminosities
estimated by Mehdipour et al. (2015). In particular, for the unobscured case,
the bolometric luminosity is
$\log(L_{\mathrm{bol}}/\mathrm{erg\,s}^{-1})=44.2$, whereas, for the obscured
case, it decreases to $\log(L_{\mathrm{bol}}/\mathrm{erg\,s}^{-1})=43.5$.
Below, we compare all results to the observed values of the coronal lines from
the 2016–17 campaign of Landt et al. (2019). While a three-year time span
between the SEDs and the coronal lines probably slightly affects the results,
it is also possible that the SEDs were quite different in 2016, which would
lead to very different predictions. For this reason, we choose not to fine-
tune the cloudy results, and we only propose them as a possible solution while
we emphasize the importance of the approach. For the future application of the
method, it would be beneficial to measure both the emission lines and ionising
continuum in the same time period.

Another source of uncertainty is the column density: the hydrogen column
density of the possible coronal line emitting cloud is unknown. The stopping
criteria for the cloudy models is set to be the column density of the cloud,
which is assumed to be $\log(N_{\mathrm{H}}/\mathrm{cm}^{-2})=23$ during most
of our calculations. This is a typical value assumed for the coronal line
emitting regions; however, it is not measured and can be a different value so
we have also created some models using
$\log(N_{\mathrm{H}}/\mathrm{cm}^{-2})=22$ and 22.5. The cloud has an
ionisation structure with the highest ionisation lines forming near its
illuminated face and the lowest ionisation lines forming near the shielded
face. Decreasing the column density of the cloud will not dramatically affect
the higher ionisation lines but will reduce the intensity of the low-
ionisation lines. To check this claim, we created two obscured models with
different column densities ($\log[N_{\mathrm{H}}/\mathrm{cm}^{-2}]=22$ and
23), and similar hydrogen density of
$\log(n_{\mathrm{H}}/\mathrm{cm}^{-3})=5$. Both clouds were located at the
same distance of $\log(R/\mathrm{cm})=18$. The cloudy calculations indeed show
that decreasing the column density by 1 dex (from
$\log[N_{\mathrm{H}}/\mathrm{cm}^{-2}]=23$ to 22) reduces the EW of high
ionization lines only by 15–30 per cent, while the low ionization lines become
at least 60 per cent weaker. Therefore, we think that the variation of the
column density does not strongly affect the high-ionisation lines, but does
impact on the low-ionisation lines. It is worth mentioning that tests have
shown that the cloud can be highly ionized in some cases. In such cases, the
temperature at the illuminated face of the cloud gets very high ($>10^{6}$ K
in some cases), resulting in almost no near-IR and UV high-ionization lines
being produced at the illuminated face. In those cases, the EWs of all coronal
lines will significantly change by varying the column density.

Fig. 13 shows the results for the models with
$\log(N_{\mathrm{H}}/\mathrm{cm}^{-2})=23$. The obscured case is shown in
plots 13(a) and (b), and the unobscured case is shown in plots (c) and (d).
Plots (a) and (c) illustrate how the equivalent width of each near-IR coronal
line (and also [S iii]) depends on the location (vertical axis) and the
hydrogen density (horizontal axis) of the cloud. The lower-right panel in
these plots show the contours for [S viii] and [Si vi] overlaid. Plots (b) and
(d) show the contours for the optical coronal lines ([Fe vii] 3759Å, [Fe x]
6374Å, and [Fe xi] 7892Å). The lower-right panels of these series of plots
have been created using the approach introduced by Dehghanian et al. (2020).
In these panels, each coloured line shows the observed value of one specific
coronal line. By tracing these lines, one might be able find the place where
they (almost) cross over each other. The crossover point would indicate the
location and the density of the cloud that produces the observed line
strengths.

|
---|---
(a) Radius $R$ versus density $n$ for the obscured SED: S and Si lines. | (b) Radius $R$ versus density $n$ for the obscured SED: Fe lines.
|
(c) Radius $R$ versus density $n$ for the unobscured SED: S and Si lines. | (d) Radius $R$ versus density $n$ for the unobscured SED: Fe lines.
Figure 13: cloudy simulations for the four near-IR coronal lines, three
optical coronal lines and [S iii] $\lambda 9530$. Plots (a) and (c) (plots [b]
and [d]) show the radius and density of the S and Si (Fe) line-emitting gas.
Contours trace the equivalent widths (EWs) of the emission lines with respect
to the continuum at 1215 Å. The blue dashed line shows the ionisation
parameter log $U=1$ in the parameter space. Plots (a) and (b) have been
calculated using the obscured SED; plots (c) and (d) using the unobscured SED.
The bottom right-hand panels in plots (a) and (c) show an overlay of the
contours for [S viii] and [Si vi] (the two coronal lines which exhibit wings)
for easier comparison. The bottom right-hand panels in plots (b) and (d) shows
the EW contours corresponding to the observed fluxes of the optical coronal
lines in a single panel.

###  5.2 Solution for the coronal line cores

Considering Fig. 13, we ran over a hundred location-density points for three
column densities of $\log(N_{\mathrm{H}}/\mathrm{cm}^{-2})=22$, $22.5$ and
$23$. Tables 5 and 6 show some of the results from the mentioned cloudy
simulations. We mainly selected those clouds that produce zero to one hundred
per cent of near-IR coronal lines within a reasonable range of uncertainty (a
tolerance of $\approx 30$ per cent). Models 3 and 5 overproduce [S viii]
beyond this uncertainty, but are still presented in the table since they
produce the right amount of [Si vi].

Regarding the optical coronal lines ([Fe ii], [Fe vii] and [Fe x]), as
explained in Section 5.1, since we lack contemporaneous measures of these
lines we search for models which agree with the observed values to within a
factor $\approx 2$–3.

As both tables indicate, there is not a single location-density solution for
which the cloud produces all of the observed coronal lines, implying that we
must be seeing emission from different regions. By comparing the models, we
note that while [S viii] and [Si vi] are produced by the same cloud, [S ix]
and [Si x] are emitted by different cloud(s). Also, since we could find more
solutions in the obscured case, it is most likely that the coronal regions saw
the photonionising source through the obscurer during this near-IR
spectroscopic campaign. However, it is also possible that the continuum source
was unobscured to some coronal line production sites (i.e. the coronal line
gas was located between the obscurer and the source), but obscured at other
locations (i.e. the gas was located between the obscurer and the observer).
The cloudy simulations indicate that models 3 (or 5) and 7 are most likely
responsible for producing the observed values of the near-IR coronal line
cores. In this scenario, cloud 7 produces almost all of the [Si x], while
cloud 3 (or 5) produces [S viii], [S ix] and [Si vi]. Model 4 is also a good
choice to produce the right amount of [S viii] and [Si vi], however this cloud
does not produce enough [S ix].

In general, it is difficult to produce sufficient [Si x] emission without
underestimating the emission from the other near-IR coronal lines.
Furthermore, the [Si x] region requires on average a gas density reduced by a
factor of $\sim 1000$ (and a somewhat larger distance from the central
continuum source).

Table 5: A comparison of cloudy coronal line flux predictions to the observed
values in the obscured case

Coronal line | model 1 | model 2 | model 3 | model 4 | model 5 | model 6 | model 7
---|---|---|---|---|---|---|---
|  | $N_{\mathrm{H}}=10^{23}$ | $N_{\mathrm{H}}=10^{22}$ | $N_{\mathrm{H}}=10^{22.5}$ | $N_{\mathrm{H}}=10^{22.5}$ | $N_{\mathrm{H}}=10^{22.5}$ | $N_{\mathrm{H}}=10^{23}$ | $N_{\mathrm{H}}=10^{22}$
|  | $R=10^{17.3}$ | $R=10^{16.3}$ | $R=10^{16.6}$ | $R=10^{16.7}$ | $R=10^{16.6}$ | $R=10^{17.6}$ | $R=10^{18}$
|  | $n_{\mathrm{H}}=10^{7.4}$ | $n_{\mathrm{H}}=10^{8}$ | $n_{\mathrm{H}}=10^{8.3}$ | $n_{\mathrm{H}}=10^{8.3}$ | $n_{\mathrm{H}}=10^{8.2}$ | $n_{\mathrm{H}}=10^{7.5}$ | $n_{\mathrm{H}}=10^{4.5}$
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
[S viii] | 0.9914 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 70% |  $<1$% | 151% | 118% | 167% | 3% |  $<1$%
[S ix] | 1.2520 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 7% | 2% | 46% | 23% | 64% |  $<1$% | 4%
[Si vi] | 1.9625 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 129% | 0% | 81% | 79% | 90% | 58% |  $<1$%
[Si x] | 1.4300 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ |  $<1$% | 39% | 5% | 2% | 12% | 0% | 81%
[Fe vii] | 3759Å | 78% |  $<1$% | 19% | 18% | 23% | 20% |  $<1$%
[Fe x] | 6374Å | 23% | 97% | 188% | 77% | 309% |  $<1$% | 212%
[Fe xi] | 7892Å |  $<1$% | 81% | 10% | 3% | 20% |  $<1$% | 167%

The columns are: (1) Ion and wavelength of the near-infrared transition;
(2)–(8) the percentage of the observed flux predicted by different cloudy
models. For [S viii] and [Si vi] the percentages are relative to the line core
fluxes (excluding the wings).

Table 6: A comparison of cloudy coronal line flux predictions to the observed
values in the unobscured case

Coronal line | model 8 | model 9 | model 10
---|---|---|---
|  | $N_{\mathrm{H}}=10^{23}$ | $N_{\mathrm{H}}=10^{23}$ | $N_{\mathrm{H}}=10^{23}$
|  | $R=10^{17.25}$ | $R=10^{16.2}$ | $R=10^{17.55}$
|  | $n_{\mathrm{H}}=10^{9.5}$ | $n_{\mathrm{H}}=10^{4.4}$ | $n_{\mathrm{H}}=10^{6.3}$
(1) | (2) | (3) | (4)
[S viii] | 0.9914 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 92% | 0% |  $<1$%
[S ix] | 1.2520 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 3% |  $<1$% |  $<1$%
[Si vi] | 1.9625 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 94% | 0% | 0%
[Si x] | 1.4300 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ | 0% | 58% | 110%
[Fe vii] | 3759Å | 8% | 0% | 0%
[Fe x] | 6374Å | 3% | 5% | 10%
[Fe xi] | 7892Å |  $<1$% | 13% | 35%

The columns are: (1) Ion and wavelength of the near-infrared transition;
(2)–(4) the percentage of the observed flux predicted by different cloudy
models. For [S viii] and [Si vi] the percentages are relative to the line core
fluxes (excluding the wings).

###  5.3 Solution for the coronal line wings

The values listed in Tables 5 and 6 are fluxes relative to the mean flux of
the narrow emission line cores. In our mean spectrum, the wings of [S viii]
and [Si vi] are $62\pm 11$ and $95\pm 7$ per cent of the core fluxes,
respectively. The ideal model to explain the coronal line wings will therefore
produce a flux in [S viii] equivalent to $\approx 62$ per cent of its core
flux, a flux in [Si vi] equivalent to $\approx 95$ per cent of its core flux,
and 0 per cent of the core flux of all of the other lines (none of which
display wings).  For the unobscured SED, we find a solution (model 8, Table 6)
at a radius $\log(R/\mathrm{cm})=17.25$ which produces fluxes in [Si vi] and
[S viii] that are very similar to the observed fluxes in the broad wings of
these lines. The model predicts a flux equivalent to 94 per cent of the narrow
core flux of [Si vi] will be produced at this location (precisely what we
measure for the flux in the wings in the mean spectrum). It also predicts an
equivalent of 92 per cent of the [S viii] flux will be produced here (an
overprediction, since we measure 62 per cent). Furthermore, no [Si x] and very
little [S ix] emission (equivalent to 3 per cent of the core flux) are
produced in this region. Model 8 is therefore a near-ideal solution for the
coronal line wings. Model 1 in the obscured case (Table 5) has some similar
properties to model 8: it is at a similar radius ($\log[R/\mathrm{cm}]=17.3$),
and produces substantial [S viii] and [Si vi] emission, with little [S ix] and
[Si x]. However, more Fe coronal line emission is produced in this model
compared with model 8: $\approx 78$ per cent of the observed [Fe vii]$\lambda
3759$ and $\approx 23$ per cent of the observed [Fe x]. Interestingly, the
radius of both of these coronal line emitting clouds
$\log(R/\mathrm{cm})\approx 17.3$ or 70 light days is exactly the radius of
the inner torus as determined from the hot dust reverberation lags by Landt et
al. (2019). However, the coronal line gas density in the unobscured case is
similar to what is expected for the dusty torus material, whereas it is a
factor of $\sim 100$ lower in the obscured case. We discuss this case further
in Section 6.2.

##  6 Discussion

We have performed an in-depth study of the near-IR coronal lines in NGC 5548,
making use of spectroscopic data recorded over a year with a roughly weekly
cadence. We were able to study not only the line profile shapes but the
changes in line shapes and fluxes. We have shown that two of the coronal lines
([S viii] and [Si vi]) have prominent broad wings as well as narrow cores
whereas only narrow cores are evident on the other two coronal lines. Whilst
the narrow line cores are persistent and clearly detected in all spectra, the
wings are highly variable; the flux in the wings is comparable to the flux in
the line cores in some epochs and in other epochs the wings are barely
visible. In the case of [Si vi] it is clear that most of the variability in
the line profile is in the wings. Broadly speaking, there must be at least two
coronal line regions in NGC 5548: one which produces the persistent, narrow
cores of all four coronal lines and another (presumably more compact) region
in which the conditions favour the production of [S viii] and [Si vi] emission
which we observe as the broad, variable wings.

The existence of multiple sites of coronal line emission in AGN has been
proposed before based on comparisons between Seyfert type 1 and type 2, but
never before shown for a single object. Murayama & Taniguchi (1998) reported
excess [Fe vii] $\lambda 6087$ emission in Seyfert 1 nuclei compared with
Seyfert 2s, implying that some coronal line emission occurs interior to the
dust torus (and so can be seen only in Seyfert 1s) and some coronal line
emission occurs beyond the torus. They proposed three main coronal line
regions: the inner face of the dust torus, highly-ionised clumps of gas in the
NLR and a further, very extended region on kpc-scales. We take up this
interpretation for the coronal line regions in NGC 5548 in more detail below
and sketch it in Fig. 14.

Figure 14: A cartoon of the possible geometry of the nucleus in NGC 5548. A
wind (Dehghanian et al., 2019) is launched from the disc: its dense base (the
‘obscurer’ in dark grey) partly shadows the BLR (light green clouds). The less
dense streamlines of the wind (light grey) extend to large distances. Gas
producing the narrow cores of the coronal lines (magenta clouds labelled ‘C’)
is located just inside of the standard NLR (light blue clouds). The outflowing
coronal line gas may be accelerating, as indicated by the magenta arrows. The
blue and red wings seen on the [S viii] and [Si vi] coronal lines (marked with
the blue and red ‘W’, respectively) may be produced on the inner face of the
torus. The torus may partially block our view of the gas producing the blue
wing.

###  6.1 The coronal line cores

In Section 3.1 we carefully analysed the emission line profiles in the high
S/N mean spectrum. In addition to the four near-infrared coronal lines we also
measured the low-ionisation forbidden line [S iii]$\lambda 9531$. In
comparison to [S iii], the cores of all four coronal lines are broader
(ranging from $\mathrm{FWHM}\approx 550$–750 km s-1) and are blueshifted with
respect to it by $\approx 120$–380 km s-1 (Fig. 3). The greater widths and
blueshifts of the coronal lines with respect to the low-ionisation forbidden
lines is commonly seen in AGN spectra and was reported in early studies (e.g.
Grandi 1978; Pelat et al. 1981). This implies that the coronal lines are
produced in different gas to the standard NLR responsible for the emission
from low-ionisation species such as [S iii] and [O iii]. This is consistent
with the idea that the coronal line emitting gas is part of an outflowing wind
on scales more compact than the standard NLR. Our measurements of the coronal
line cores over the duration of the campaign indicate that they only weakly
variable, if at all. In Section 4.2.3 we noted a positive relationship between
the FWHM and flux over time in the single-epoch measurements of the line
cores. This trend (if real) could be explained if the gas producing the
broadest part of the line profiles is more compact (and varies more rapidly)
than the gas producing the more persistent narrow cores of the lines. However,
in our data the same FWHM-flux trend can alternatively be explained by the
movement of the underlying continuum within its uncertainty range, so we
cannot draw any strong conclusion on this point. In any case, the weakness of
the variability is consistent with a geometry in which majority of the flux in
the coronal line cores is emitted at radii $\gtrsim 1$ light year and
therefore the line cores have a variability timescale longer than we can probe
with this data. Then, considering both the profile widths and variability
properties, we may deduce that the coronal line cores are produced at a
characteristic radius $18\lesssim\log(R/\mathrm{cm})\lesssim 18.5$ from the
nucleus, a scale intermediate between the BLR and NLR (Fig. 15).

Although the widths and shifts of the four coronal line cores have common
characteristics (being broader and blueshifted with respect to [S iii]), they
are not identical. It is likely that the lines are not emitted entirely
cospatially and different coronal lines originate in different parts of the
outflow. Our photoionisation simulations with cloudy (Section 5) also strongly
suggest this, since we do not find any single cloud that can account for all
of the observed lines. In the mean spectrum, [S ix] was found to be the
narrowest coronal line ($\mathrm{FWHM}=554\pm 24$ km s-1) and [S viii] the
broadest ($\mathrm{FWHM}=737\pm 39$ km s-1). Consistent with previous studies
(e.g. Rodríguez-Ardila et al. 2011; Ferguson et al. 1997; De Robertis &
Osterbrock 1986; Filippenko & Halpern 1984 Penston et al. 1984; Pelat et al.
1981), we found a trend of increasing FWHM with the ionisation potential of
forbidden emission lines (Fig. 4)222Contrary to Filippenko & Halpern (1984) we
observe a weaker relationship between emission line FWHM and critical density,
as can be seen in Fig. 4.. Rodríguez-Ardila et al. (2011) noted that this
trend extended up to $\chi\approx~{}300$ eV, above which the FWHM of lines
decreased or plateaued, which is what we observe in Fig. 4: [Si x]
($\chi=351.1$ eV) is no broader than [S viii] ($\chi=281.0$ eV) and [S ix]
($\chi=328.8$ eV) is narrower than [S viii]. Since [S viii] has the highest
critical density of the lines studied here, some of its emission may arise
from higher-density gas nearer to the nucleus where orbital motions are
greater. In this picture it is therefore expected that [S viii] will be the
broadest coronal line, as we observe. This result suggests a degree of
stratification of the coronal line emitting gas.

Pelat et al. (1981) found a relationship between line width and ionisation
potential, as well as line width and velocity shift, with the general trend
that higher-ionisation lines were broader and more strongly blueshifted. We
see such a trend to first order (the coronal lines are broader than, and
blueshifted with respect to, [S iii]); however, the reverse trend is seen
within the coronal line sequence: the lowest-ionisation coronal line [Si vi]
has the greatest blueshift (Fig. 4). The [S viii], [S ix] and [Si x] lines
have centroid shifts that are consistent within error, with a mean and
standard deviation of $-125$ and 9 km s-1, respectively; the [Si vi] line has
a significantly greater shift of $-383\pm 10$ km s-1. This difference in
blueshifts is real, and not the result of a systematic error in the wavelength
calibration at the red end of our spectra: we assessed the centroid shifts of
the low-ionisation [Fe ii]$\lambda 1.644$ $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$line near to [Si vi] and did not find any significant shift of this line.
Therefore the kinematics of the [Si vi]-emitting gas appear to be different to
that of gas emitting the other three coronal lines. Ferguson et al. (1997)
noted that their photoionisation models predicted that lower-ionisation
coronal lines ([Ne v]–[Si vii]) would form in more extended gas than the high-
ionisation lines. We see this trend in our cloudy simulations, in which the
contours of [Si vi] are displaced to larger radii compared with the other
coronal lines (see the comparison of [S viii] and [Si vi] contours in Fig.
13). We also find that the core of the [Si vi] line is narrower than that of
[S viii] and [Si x], which (if interpreting the line widths as orbital motion)
would also imply its emission occurs at typically larger radii. If the [Si
vi]-emitting gas is located at larger radii and greater velocities than the
rest of the coronal line gas, this implies that the gas is part of an
accelerating outflow. Outflows which accelerate from the nucleus to distances
of $\sim 100$ pc have been observed in several other AGN (e.g. Crenshaw &
Kraemer 2000; Crenshaw et al. 2000; Müller-Sánchez et al. 2011).

Our photoionisation simulations appear to predict a very compact origin for
the coronal line cores (Section 5.2). cloudy models 3 or 5 produce
approximately the same fluxes as we observe in the cores of the [S viii], [Si
x] and [Si vi] lines and the location of the line-emitting gas in these
solutions is $\log(R/\mathrm{cm})=16.6$, a similar scale to the BLR or outer
accretion disc (see Fig. 15). The widths of the lines do not necessarily
reflect Doppler broadening by virial motion of the emitting gas; instead the
lines may be broadened by gas turbulence as is the case in coronal line novae.
However, the blueshifts of the coronal lines strongly suggest that the
emitting gas is outflowing. It is then reasonable to assume that the outflow
is launched from the rotating accretion disc. In this case we would expect the
gas to have a large amount of rotational as well as radial motion, and for
this to be evident in the widths of the emission lines.

The cloudy simulations also suggest that the three coronal lines [S viii], [S
ix] and [Si vi] may be produced in the same cloud (either 3 or 5), and [Si x]
is produced in another cloud (7). However, the most obvious difference in the
coronal line core profiles is the much greater blueshift of [Si vi] with
respect to the other lines. This suggests that [Si vi] emitting gas is
kinematically (and spatially) distinct from the gas producing the other three
coronal lines, or alternatively has an additional component not seen in the
other lines, which would not be accounted for in our cloudy solutions.

Landt et al. (2015b) determined greater distances for the coronal line gas in
NGC 5548 than implied here. Based on measurements of the optical and X-ray
coronal lines, they calculated that the coronal lines were produced in a low-
density gas ($\log[n_{\mathrm{e}}/\mathrm{cm}^{-3}]\sim 3$) at
$\log(R/\mathrm{cm})\approx 18.9$ ($\approx 8$ light years). This distance is
approximately coincident with the [O iii] $\lambda 5007$ NLR and is just
within the black hole’s gravitational sphere of influence (see Fig. 15). In
spite of the similar size scale to the NLR, Landt et al. (2015b) proposed that
the coronal line region was likely to be an independent entity because of its
high ionisation parameter ($U\sim 1$). The modest variability of the coronal
line cores and their relatively narrow widths imply their origin in gas
interior to the standard NLR ($\log[R/\mathrm{cm}]\lesssim 18$). The
photoionisation simulations in Section 5.2 suggest an even more compact
coronal line region at $\log(R/\mathrm{cm})=16.6$. It can be seen from Tables
5 and 6 that cloudy generally predicts much higher gas densities
($\log[n_{\mathrm{H}}/\mathrm{cm}^{-3}]\sim 7$–9) than calculated by Landt et
al. (2015b). Our results are not necessarily at odds with those of Landt et
al. (2015b) since they derived physical parameters from optical and X-ray
coronal lines, whereas we do so for the near-IR coronal lines. Since emission
lines form wherever the conditions allow them to do so, it is likely that
different coronal lines trace clumps of differing density, thus mapping out
the outflowing wind that produces them.

Figure 15: Orbital velocity as a function of radius for a black hole of mass
$3.2\times 10^{7}$ M⊙. The black hole’s sphere of influence extends up to
$\log(R/\mathrm{cm})\approx 19.1$. We indicate radii of the H $\upbeta$ BLR
(green: Pei et al. 2017); hot dust (red: Landt et al. 2019) and [O iii] NLR
(cyan: Peterson et al. 2013). $H$ and $K$ band lags attributed to the outer
accretion disc (dark red: Landt et al. 2019) suggest that the disc extends
beyond its self-gravity radius (blue: Gardner & Done 2017). The X-ray obscurer
(the base of a disc wind) must be interior to the BLR (Dehghanian et al.,
2019). The stellar velocity dispersion of the bulge was measured to be
$\sigma_{\star}=183$ km s-1 (Ferrarese et al., 2001).

In summary, the kinematics inferred from the narrow line profile widths
suggest that the coronal line cores are emitted in an accelerating wind just
interior to the low-ionisation NLR. However, at odds with this interpretation,
we did not find photoionisation model solutions consistent with it, although
there are a number of limitations to this modelling, as mentioned earlier.
Therefore, it is possible that the line widths are not produced by virial
motion within the black hole’s gravitational field, but rather indicate radial
motion as in the ejecta of classical novae during their coronal line phase
(e.g. Greenhouse et al., 1990; Woodward et al., 2021).

###  6.2 The coronal line wings

Before proceeding, is worth considering whether the flux excesses seen near
[Si vi] and [S viii] (their ‘wings’), and the apparent variability of these
features, could alternatively be explained by other spectral components
unrelated to the coronal lines (i.e. the continuum or the blended broad
emission lines). We have incorporated the uncertainty on the placement of the
continuum (assumed to be locally linear) in our flux measurements and the
variability of the excess flux redward of [Si vi] is still highly significant;
therefore, we can rule out the excess flux changes being due to the imperfect
subtraction of a (smooth) continuum. Of course, the shapes of these flux
excesses do not look like parts of a smooth continuum and it does not seem
likely that the variations could be due to variations in unexplained, local
features in the continuum, either. As the spectral decomposition by Landt et
al. (2019) showed, the continuum beneath [S viii] $\lambda 0.9914$
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ is dominated by the accretion disc,
whereas the continuum beneath [Si vi] $\lambda 1.9650$
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ is dominated by emission from the hot
dust. So even if it were the case that the wings are in fact continuum
features, this interpretation requires there to be some physical link between
the disc and dust emission at the specific wavelengths $0.9914$ and $1.9650$
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, respectively, which creates the
similarly-shaped and similarly-varying flux excesses. So we do not think it
likely that the appearance and variability of these features can be attributed
to the dust or disc continua.

The other possibility is that these spectral and temporal features are caused
by the imperfect deblending of the coronal lines from the broad emission
lines. We used the mean Pa $\upbeta$ profile as a (scaled) template for all of
the broad hydrogen lines in our extraction of the coronal line profiles from
the single-epoch spectra (Section 3.2). Therefore, any deviations of the broad
lines from the average profile shape can cause features in the residuals which
we may attribute to the coronal lines. In the case of [Si vi], such an effect
is likely to be relatively minor. Our spectral decomposition of the high-S/N
mean spectrum around that line (Fig. 2) indicates that Br $\updelta$ and
particularly Pa $\upalpha$ are very weak features beneath [Si vi]. The flux in
Br $\updelta$ beneath the [Si vi] red wing is $\approx 6\times 10^{-15}$ erg
s-1 cm-2, less than the average flux in the red wing itself ($8.7\times
10^{-15}$ erg s-1 cm-2). The flux variations we attribute to the [Si vi] red
wing are of the order $10\times 10^{-15}$ erg s-1 cm-2. So, if this
variability were actually dominated by variations in Br $\updelta$ it would
require incredibly large changes in the red wing of Br $\updelta$. We would
then expect to see concomitant changes in the other broad hydrogen line
profiles, which we do not. So it appears that both Br $\updelta$ and Pa
$\upalpha$ are too weak in this part of the spectrum to satisfactorily explain
the changes we see in the flux excess. Relatively minor changes in the broad
Pa $\updelta$ profile could more plausibly induce a feature that we mistake
for [S viii] emission. But, in this interpretation it is then a coincidence
that this flux excess on the blue shoulder of Pa $\updelta$ appears at just
the right location to give the appearance of a red wing on [S viii], with a
similar shape and scale to the excess around [Si vi] (which sits on the red
wing of Br $\updelta$). Additionally, if our deblending method did not
generally work well, it is curious that we do not observe any excess flux
around [S ix] (which is blended with broad Pa $\upbeta$). This similarity in
the profile shapes and lightcurves of the [S viii] and [Si vi] wings actually
strengthens our preferred interpretation of these flux excesses as coronal
line emission, since our cloudy simulations demonstrate that emission from
both [S viii] and [Si vi] can be produced by the same gas cloud, on
$\sim$light month scales from the nucleus. We therefore conclude that the
observed excess emission around the [S viii] and [Si vi] lines (and the
variability of these features) is genuinely associated with those lines.

It is intriguing then that we see broad wings on two of the near-IR coronal
lines ([S viii] and [Si vi]) but not on the other two ([S ix] and [Si x]).
Since we observe wings on one sulphur and one silicon line, the absence of
wings on some lines cannot simply be related to the absence of that element at
that location (for example, if silicon were depleted onto dust). Our cloudy
models show that the appearance of these wings may be explained by
photoionisation: we observe wings on the two coronal lines with the lowest
ionisation potentials simply due to the combination of bolometric luminosity
of the central source and the gas density of the coronal line emitting gas.
Models 8 and 1, which we described in Section 5.3, are appealing because they
explain a number of observed properties. cloudy predicts emission from [Si vi]
and [S viii] emission at similar fluxes to those we observe in the wings
occurring at $\log(R/\mathrm{cm})\approx 17.3$. Additionally, very little [S
ix] and [Si x] emission is produced at this location, explaining the absence
of wings on these two lines. In model 8 none of the other lines we have
assessed ([S iii] or the optical Fe coronal lines) are strongly emitted,
either. Since we observe strong variability in the wings as they disappear and
reappear over the year-long campaign, we can infer that the emission must
arise on $\sim$light month scales; the radius $\log(R/\mathrm{cm})\approx
17.3$ equates to $\approx 70$ light days so the implied spatial scale is
consistent with the observed variability timescale. As can be seen in Fig. 15,
orbital motions of a few thousand km s-1 are expected at this radius which
would explain the observed extents of the wings in velocity. A value of 70
light days is also the precise radius of the inner edge of the torus
determined by Landt et al. (2019) via the reverberation of the dust in
response to the optical accretion disc emission. The strong similarity in the
shapes of the [Si vi] wing and hot dust light-curves (Fig. 11) means that the
two will have similar reverberation lags and so it is likely that the hot dust
and coronal line wings are emitted at the same radius from the nucleus.

It is clear from Figs. 3 and 8 that the broad coronal line wings are much more
prominent on the red side of the core than the blue side. If the wings are
indeed produced in a wind launched off the inner edge of the torus, then the
torus may be inclined such that our view of the approaching gas is blocked,
and we see mostly the receding gas on its far side (see Fig. 14). A similar
geometry was proposed also by Glidden et al. (2016) to explain observations of
coronal line forest AGN (see their figure 1). Pier & Voit (1995) proposed that
AGN coronal line emission would originate in an X-ray heated wind evaporated
from the inner edge of the dust torus, and this was one of the main sites of
coronal line production outlined by Murayama & Taniguchi (1998). Our findings
are consistent with these schemes. However, our chosen model is problematic in
that the torus must see the unobscured SED, yet the obscurer is located
between the torus and the X-ray source (see e.g. figure 4 of Kaastra et al.
2014). A possible solution is that, if the obscurer is an extended stream or
wind, it presents a much higher column density along our line of sight than
toward the torus. In any case, the torus emission is not sensitive to the
obscurer since it is heated mainly by the UV/optical nuclear emission and the
obscurer is transparent at these wavelengths (Dehghanian et al., 2019). But
the coronal lines can very well differentiate between the obscured and
unobscured SED through constraints on the gas density. The value of
$\log(n_{\mathrm{H}}/\mathrm{cm}^{-3})\sim 9$ in the unobscured case (model 8)
is what is expected of the material in the dusty torus.

Whilst the shapes of the [Si vi] wing and hot dust light-curves are strikingly
similar (Fig. 11), it is noteworthy that the amplitude of the [Si vi] wing
variability is substantially greater than that of the dust. The wing varies by
more than an order of magnitude whereas the dust flux variations are only at
the $\pm 25$ per cent level. Stronger variability of the coronal lines in NGC
5548 compared with the dust on timescales of several years was also reported
by Landt et al. (2015b). This behaviour is expected if the coronal line wing
emission varies mainly in dependence on the compact X-ray source which in turn
varies with a higher amplitude and on shorter timescales than the UV/optical
emission that heats the dust (Edelson et al., 2015).

Both our spectroscopic analysis and photoionisation models point to the inner
face of the torus being the origin of the coronal line wings. But we stress
that we cannot claim that our cloudy models present unique and definitive
solutions and there are several caveats to bear in mind, such as, e.g. the
assumption of particular SEDs non-contemporaneous with our emission line
observations and the inexhaustive exploration of the parameter space.
Nonetheless, these models serve to illustrate that our proposed solution for
the origin of the coronal line wings is physically plausible.

###  6.3 Links to outflowing absorption systems

We interpreted the blueshifts of the coronal line cores as evidence of
emission from outflowing gas. Outflows in NGC 5548 have been detected via
absorption lines in other wavebands including X-rays (Ebrero et al. 2016), UV
(Arav et al. 2015) and near-IR (Wildy et al. 2021). Some of the X-ray warm
absorber components in NGC 5548 are related to the UV absorbers (e.g. Ebrero
et al. 2016; Arav et al. 2015) and Wildy et al. (2021) associated several
narrow He i $\lambda 1.08$ $\text{\,}\mathrm{\SIUnitSymbolMicro m}$absorption
features with corresponding UV absorbers. Similarities between the inferred
properties of the coronal line region and warm absorber (both are thought to
originate in a highly-ionised, outflowing gas on scales intermediate between
the BLR and NLR) have prompted further investigation into the possibility that
they are in fact the same medium. Porquet et al. (1999) used photoionisation
models to demonstrate that coronal emission lines could indeed form within the
warm absorber. They found that very high gas densities
($\log[n_{\mathrm{H}}/\mathrm{cm}^{-3}]\gtrsim 10$) were required to avoid
overproduction of the coronal lines relative to observations and that the gas
was located on scales similar to the BLR. It is therefore pertinent to
investigate whether the near-IR emission features seen in the outflow of NGC
5548 (i.e. the coronal lines) can be associated with the gas responsible for
the observed absorption features.

The associations of X-ray, UV and near-IR absorption features was based on the
gaseous kinematics (i.e. similar velocity shifts), with further consideration
made of the gas properties (density, ionisation parameter). The velocity
shifts we determined for the coronal lines ($\approx-125$ km s-1 for [S viii],
[S ix] and [Si x]; $\approx-380$ km s-1 for [Si vi]) do not closely match
those reported for any of the absorption features mentioned above.
Additionally, the majority of these absorption features arise at much greater
distances from the nucleus than we infer for the coronal lines. The estimated
location of the UV absorption clouds is at the NLR radius and above ($\gtrsim
2$ pc or $\log[R/\mathrm{cm}]\gtrsim 18.8$), whereas the coronal lines are
likely to be produced interior to the NLR. The highest-ionisation components
of the X-ray warm absorber are located on smaller scales
($\log[R/\mathrm{cm}]\gtrsim 18$), similar to what we infer for the coronal
lines, although these components have much higher outflow velocities
(blueshifts of $\approx 250$–$1200$ km s-1) and much narrower widths
($\sigma_{v}\approx 20$–200 km s-1) than we observe in the coronal lines. Our
photoionisation modelling with cloudy suggests that the coronal lines observed
in NGC 5548 form in gas of densities
$\log(n_{\mathrm{H}}/\mathrm{cm}^{-3})\sim 7$–9, much lower density than the
$\log(n_{\mathrm{H}}/\mathrm{cm}^{-3})\gtrsim 10$ required by Porquet et al.
(1999) but also much higher than the range of densities calculated for the
warm absorber in NGC 5548 ($\log[n_{\mathrm{H}}/\mathrm{cm}^{-3}]\sim 3$–5:
Ebrero et al. 2016).

In summary, although the outflow velocities of the coronal line gas are of the
same order of magnitude as those of some of the observed absorbers ($\sim$few
hundred km s-1), we see little evidence of an association between the coronal
line gas and the specific X-ray/UV absorption components previously reported
in NGC 5548. Then, if the coronal line gas and the absorbers are indeed parts
of the same wind, they must arise from widely different clumps and so are
unlikely to be exactly cospatial.

##  7 Summary and conclusions

We have performed the first intensive study of the variability of the near-
infrared coronal lines in an AGN. The near-infrared spectroscopic monitoring
campaign of Landt et al. (2019) reveals a complex and multi-component coronal
line region. From measurements of the high-S/N mean spectrum of the campaign,
we observe some general trends which have been observed in previous studies of
AGN coronal lines. The narrow cores of the coronal lines are broader than, and
blueshifted with respect to, the lower-ionisation forbidden lines. The lack of
strong variability of the coronal line cores in the year-long campaign
suggests the majority of the line-emitting gas exists on scales $\gtrsim 1$
light year, whilst the line widths suggest the gas is more compact than the
standard NLR ($\lesssim 3$ light years). These findings suggest that the
narrow near-IR coronal lines in NGC 5548 form in an outflow just interior to
the inner NLR, although our photoionisation models show that coronal line
emission originating closer to the BLR is possible. An approximate correlation
between the FWHM and ionisation potential of the coronal line cores implies a
stratification of line emitting gas, with the lowest-ionisation coronal line
[Si vi] line forming at a greater distance from the nucleus than the other
lines. The greater blueshift and narrower line profile of [Si vi] with respect
to the higher-ionisation lines [S viii] and [Si x] can be understood if this
stratified wind is accelerating. We therfore propose that the narrow coronal
line cores form in a stratified, accelerating outflow from the nucleus of NGC
5548 and this emission occurs predominantly just interior to the standard NLR.

In addition to narrow cores, the two lowest-ionisation coronal lines [S viii]
and [Si vi] show extended wings, particularly on the red side of the core. The
line widths, strong flux variability on a timescale of $\sim$months and
photoionisation predictions all indicate that the wings are produced at a
radius $\log(R/\mathrm{cm})\approx 17.3$ from the nucleus. This radius is
exactly coincident with the inner dust radius determined by Landt et al.
(2019). We therefore associate these wings with an X-ray heated wind of
material evaporating from the inner face of the torus.

This study has revealed the complex and multi-faceted nature of the coronal
line region in an AGN. The recent launch of the James Webb Space Telescope
(JWST) mean it is an opportune time to investigate this complexity. The high
sensitivity and spectral resolution of JWST’s instruments will enable us to
study infrared coronal lines of AGN in much greater detail.

## Acknowledgements

DK acknowledges support from the Czech Science Foundation project No.
19-05599Y, funding from the Czech Academy of Sciences via the PPLZ program and
the receipt of a UK Science and Technology Facilities Council (STFC)
studentship (ST/N50404X/1). HL acknowledges a Daphne Jackson Fellowship
sponsored by the STFC. MJW acknowledges support from STFC grants ST/P000541/1
and ST/T000244/1. G.J.F. and M.D. acknowledge support from NSF (1816537,
1910687), NASA (ATP 17-ATP17-0141, 19-ATP19-0188), and STScI (HST-AR- 15018
and HST-GO16196.003-A).

## Data availability

The raw data underlying this work are publicly available at the NASA IRTF
Archive hosted by the NASA/IPAC Infrared Science Archive
(https://irsa.ipac.caltech.edu). The processed data are available on request
from the second author.

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##  Appendix A Taking a look into a typical coronal line emitting cloud

Fig. 16 shows the temperature inside a coronal line emitting cloud for both
unobscured (green) and obscured (red) cases. The model belongs to a cloud with
a column density of $N_{\mathrm{H}}=10^{23}$ cm-2, hydrogen density of
$n_{\mathrm{H}}=10^{7.4}$ cm-3, located at $R=10^{17.3}$ cm from the source.
Much of our previous work rejected clouds with temperatures greater than the
$\sim 10^{5}$ K peak in the cooling function since they produce negligible
optical or IR emission. However, the large column density clouds have enough
extinction to produce cooler gas near the shielded side of the cloud, so we
include these for completeness. These clouds occupy the lower left quadrant of
the density-radius plane shown in Fig. 13.

Figure 16: The variation of the temperature versus the depth into the coronal
cloud is shown.