# Optical and JWST Mid-IR Emission Line Diagnostics for Simultaneous IMBH and
Stellar Excitation in $z\sim 0$ Dwarf Galaxies

Chris T. Richardson Elon University
100 Campus Drive
Elon, NC 27278, USA  COSmS Institute
University of North Carolina
Chapel Hill, NC 27599, USA  Connor Simpson  Elon University
100 Campus Drive
Elon, NC 27278, USA  Mugdha S. Polimera University of North Carolina
141 Chapman Hall CB 3255
Chapel Hill, NC 27599, USA  Sheila J. Kannappan  University of North Carolina
141 Chapman Hall CB 3255
Chapel Hill, NC 27599, USA  Jillian M. Bellovary  Queensborough Community
College
City University of New York
222-05 56th Ave
Bayside, NY 11364, USA
American Museum of Natural History
Central Park West at 79th Street
New York, NY 10024, USA  Graduate Center
City University of New York
New York, NY 10016, USA  Christopher Greene  University of Cincinnati
290 CCM Blvd
Cincinnati, OH 45221, USA  Sam Jenkins  Elon University
100 Campus Drive
Elon, NC 27278, USA

(Received XXXX, 2020; Revised XXXX, 2020; Accepted January 31, 2022)

###### Abstract

Current observational facilities have yet to conclusively detect
$10^{3}-10^{4}M_{\odot}$ intermediate mass black holes (IMBHs) that fill in
the evolutionary gap between early universe seed black holes and $z\sim 0$
supermassive black holes. Dwarf galaxies present an opportunity to reveal
active IMBHs amidst persistent star formation. We introduce photoionization
simulations tailored to address key physical uncertainties: coincident vs.
non-coincident mixing of IMBH and starlight excitation, open vs. closed
surrounding gas cloud geometries, and different AGN SED shapes. We examine
possible AGN emission line diagnostics in the optical and mid-IR, and find
that the diagnostics are often degenerate with respect to the investigated
physical uncertainties. In spite of these setbacks, and in contrast to recent
work, we are able to show that [O III]/H$\beta$ typically remains bright for
dwarf AGN powered by IMBHs down to $10^{3}M_{\odot}$. Dwarf AGN are predicted
to have inconsistent star-forming and Seyfert/LINER classifications using the
most common optical diagnostics. In the mid-IR, [O IV] 25.9$\mu$m and [Ar II]
6.98$\mu$m are less sensitive to physical uncertainties than are optical
diagnostics. Based on these emission lines, we provide several mid-IR emission
line diagnostic diagrams with demarcations for separating starbursts and AGN
with varying levels of activity. The diagrams are valid over a wide range of
ionization parameters and metallicities out to $z\sim 0.1$, so will prove
useful for future JWST observations of local dwarf AGN in the search for
IMBHs. We make our photoionization simulation suite freely available.

galaxies – dwarf, evolution – active galactic nuclei – intermediate-mass black
holes

††journal: ApJ††software: Cloudy (Ferland et al., 2017), NebulaBayes (Thomas
et al., 2018).

##  1 Introduction

The occupation fraction of supermassive black holes (SMBHs) in massive
galaxies is near unity (Magorrian et al. 1998). While LIGO has detected
stellar mass black holes ($\leq 10^{2}M_{\odot}$) resulting from compact
object mergers, intermediate black holes (IMBHs) remain elusive in the
$10^{2}M_{\odot}$ \- $10^{5}M_{\odot}$ range (Greene et al. 2020). Detecting
black holes at the low end of this range would provide a crucial link between
early universe black hole seeds and local SMBHs.

Figure 1: Illustration depicting two different gas cloud geometries (open and
closed) and two different mixing methodologies (coincident and non-
coincident). Dwarf AGN could presumably fall into any of these four categories
and therefore photoionization models must account for this systematic
uncertainty. Note that the rays of light (arrows) only show one possible path
to the observer and do not represent all possible components of the observed
spectrum.

Dwarf galaxies show promise in the search for IMBHs based on the
$M_{*}-M_{\mathrm{BH}}$ relation (Reines & Volonteri 2015). However, the
properties of dwarf AGN hosts are different from those of massive galaxy AGN
hosts, which can complicate detecting AGN signatures. For example, most dwarfs
are gas-rich (Kannappan 2004), strongly star-forming (Geha et al. 2012), and
metal-poor (Tremonti et al. 2004). Supernova feedback preferentially expels
metal-rich gas (Mac Low & Ferrara 1999), while accretion of low metallicity,
intergalactic medium gas drives star formation (Dekel & Birnboim 2006).

Unlike in the unified AGN model, IMBHs in dwarfs often wander within 1 kpc of
the center due to the dwarfs’ weak gravitational potential (Reines et al.
2020, Bellovary et al. 2021). Therefore, it is unclear whether the AGN and
stellar radiation fields strike the same gas clouds, or spatially separated
gas clouds, as the IMBH relocates or settles down in a particular location.
This uncertainty calls into question applying the centralized geometric model
for massive AGN to dwarf AGN.

Another issue for dwarf AGN, unlike massive AGN, is that X-ray observations
that could provide valuable constraints on the AGN spectral energy
distribution (SED) remain rare for $M_{\mathrm{BH}}\approx 10^{5}M_{\odot}$,
and absent for $M_{\mathrm{BH}}\approx 10^{3}M_{\odot}$ (Desroches et al.
2009). The few sources luminous enough to observe are likely outliers having
fortuitous conditions to enable their detection (e.g. Godet et al. 2012). This
situation introduces doubts about whether physical quantities controlling the
shape of the SED scale down to the lowest black hole masses (Arcodia et al.
2020).

Photoionization models can provide the missing ingredient for IMBH detection
by systematically accounting for uncertainties pertaining to the gaseous
geometry and properties of low-mass AGN. The left panels of Figure 1
illustrate open, or plane-parallel geometries, where the covering factor is
small, as typically assumed when modeling AGN (Elvis 2000; Feltre et al. 2016)
and star-forming regions like the Orion blister (Ferland 2001). The right
panels of Figure 1 illustrate closed, or spherical geometries, where the
covering factor is close to unity, as typically assumed when modeling obscured
AGN like ULIRGs (Abel et al. 2009) and star-forming regions like 30 Doradus
(Pellegrini et al. 2011).

Similarly, photoionization models have used two methods to take into account
simultaneous AGN and stellar excitation, but rarely with justification. Figure
1, top panels, illustrates one approach where an AGN and starlight strike the
same cloud and thus the SEDs from each source are mixed a priori (e.g. Abel et
al. 2009, Satyapal et al. 2018), which we label as coincident mixing. The
bottom panels of Figure 1 show another approach where the excitation sources
illuminate spatially separated clouds and thus the models are mixed a
posteriori (e.g. Kewley et al. 2013, Meléndez et al. 2014, Richardson et al.
2014), which we label as non-coincident mixing. Since dwarfs hosting IMBHs
display a variety of morphologies (Kimbrell et al. 2021), it is unclear
whether a particular gas geometry or mixing methodology would generically
apply. Therefore, assessing all possibilities in Figure 1 is paramount.

Optical spectroscopy enables the categorization of emission line galaxies as
AGN, star-forming, or a mixture of the two using [O III]
$\lambda$5007/H$\beta$ against [N II] $\lambda$6584/H$\alpha$ (i.e., the BPT
diagram), [S II] $\lambda$6720/H$\alpha$, and [O I] $\lambda$6300/H$\alpha$ to
form diagnostic diagrams (Baldwin et al. 1981, Veilleux & Osterbrock 1987).
Previous photoionization modeling including AGN suggests that optical lines
might grow too faint for detection for black holes outside
$10^{6}-10^{9}M_{\odot}$, thus skewing $M_{\mathrm{BH}}$ distributions (Cann
et al. 2019, Bhat et al. 2020); however, none of this modeling accounts for
the multiple geometrical configurations indicated in Figure 1, for the
presence of stellar excitation, or for the uncertainty in the shape of the
IMBH SED.

Indeed, optical observations may contradict the theoretical impossibility of
detection of IMBH AGN. Broad-line selected dwarf AGN with
$M_{\mathrm{BH}}\approx 10^{5}M_{\odot}$ can be sometimes optically classified
as AGN using the BPT diagram (Barth et al. 2004), indicating high [O
III]/H$\beta$. Reines et al. (2020) used radio interferometry to identify
dwarf AGN with optical star-forming galaxies classifications, and used the
$M_{*}-M_{\mathrm{BH}}$ relation to deduce $M_{\mathrm{BH}}\sim
10^{4.1}-10^{5.8}M_{\odot}$, albeit this relation shows up to 1.0 dex scatter
for $M_{*}<10^{9}M_{\odot}$ (Greene et al. 2020). Optically classified star-
forming galaxies might contain a treasure trove of additional hidden IMBHs
that evade detection on account of the BPT diagram preferentially identifying
high metallicity AGN (Polimera et al., submitted; hereafter P21). However,
active black holes in the $10^{3}~{}M_{\odot}$ regime still remain undetected.

IR spectroscopy offers a better opportunity to reliably detect IMBHs as it
possesses a wealth of high ionization lines insensitive to gas metallicity and
dust extinction. The Spitzer era revealed the potential of the mid-IR to
separate starbursts from AGN, leading to the development of several diagnostic
diagrams involving [Ne V] and [O IV] emission lines and polycyclic aromatic
hydrocarbon (PAH) features (Dale et al. 2006). The James Webb Space Telescope
(JWST), spanning $0.6-28.3~{}\mu m$, has the potential to revolutionize the
search for black holes at the low-mass end of the IMBH distribution. Indeed,
recent work has shown the spectral range of JWST can uncover AGN eluding
detection from optical spectroscopy (Satyapal et al. 2020), although the
uncertainties stemming the from IMBH SED and the configurations presented in
Figure 1 remain unexplored.

In this paper, we fill in the gap in photoionization modeling to account for
the uncertainty in gaseous geometry, mixed excitation, and AGN SED shape. We
make emission line predictions that will be valuable for searching for
$10^{3}-10^{5}M_{\odot}$ black holes with optical spectroscopy and future JWST
observations, while freely providing our simulation suite to the
community111https://facstaff.elon.edu/crichardson17/.

##  2 Theoretical Methodology

###  2.1 Incident Radiation Field

Figure 2 displays the three different models for the AGN SED that we have
explored, assuming $M_{\mathrm{BH}}=10^{3}-10^{5}M_{\odot}$: “disk-plaw,”
“Cloudy,” and “qsosed.” The “disk-plaw” SED combines the diskbb accretion disk
model (Mitsuda et al. 1984) with a power law ($\Gamma=2.1$), normalized to
give $\alpha_{ox}=1.41$ (Grupe et al. 2010) where

$\frac{f_{\nu}(2~{}\mathrm{keV})}{f_{\nu}(2500\AA)}=\left(\frac{\nu_{2~{}\mathrm{keV}}}{\nu_{2500\AA}}\right)^{\alpha_{ox}}.$
(1)

The inner diskbb temperature is calculated using Peterson (1997),

$\small T_{\mathrm{in}}=6.3\times
10^{5}\left(\frac{\dot{m}}{\dot{m}_{\mathrm{Edd}}}\right)^{1/4}\left(\frac{M_{\mathrm{BH}}}{10^{8}~{}M_{\odot}}\right)^{-1/4}\left(\frac{R}{R_{s}}\right)^{-3/4}~{}~{}\mathrm{K}$
(2)

where we assume $\dot{m}/\dot{m}_{\mathrm{Edd}}=0.1$ and $R=3R_{S}$. The
result is a piecewise, physically motivated SED for photoionization modeling
(Cann et al. 2019, Bhat et al. 2020), but lacks physical self-consistency,
such as the accretion disk radiation generating seed photons for the hard
X-ray component.

Figure 2: AGN SEDs resulting from different models for
$M_{\mathrm{BH}}=10^{3}-10^{5}~{}M_{\odot}$. Profound differences are present
for the peak of the thermal accretion disk and the hard X-ray contribution.

The “Cloudy” SED is the Cloudy (Ferland et al. 2017) default AGN SED, which is
an empirical model that assumes the observed SED is the same as the continuum
seen by nebular clouds. The functional form of the SED is given by,

$f_{\nu}=\nu^{\alpha_{\mathrm{uv}}}e^{\frac{-h\nu}{kT_{\mathrm{peak}}}}e^{\frac{-kT_{\mathrm{IR}}}{h\nu}}+a\nu^{\alpha_{x}}$
(3)

where $T_{\mathrm{peak}}=0.77~{}T_{\mathrm{in}}$ (Mitsuda et al. 1984),
$\alpha_{\mathrm{UV}}$ is the low energy slope in the UV,
$\alpha_{\mathrm{X}}$ is X-ray slope, and $a$ is a constant adjusted to
satisfy $\alpha_{\mathrm{ox}}$. All of the spectral indices are taken from the
median of the extinction corrected BLS1s sample in Grupe et al. (2010).

The “qsosed” uses the agnsed model (Kubota & Done 2018), while fixing most
parameters to their “typical” values and assuming
$\dot{m}/\dot{m}_{\mathrm{Edd}}=0.1$, $a_{*}=0$, and $i=45^{\circ}$. This is a
physically self-consistent SED for photoionization modeling (Panda et al.
2019, Vasiliev et al. 2020, Sarkar et al. 2021) appropriate for sub-Eddington
accretion in IMBHs.

Figure 3: Stellar SEDs resulting from different SFHs. The ionization potentials for relevant species are denoted by vertical lines.  Table 1: Reference abundances and depletion factors $\delta$ used for included chemical elements $X$. We set non-refractory element He, Ne, S, and Ar to $\delta_{X}$ = 0. See Appendix A for details. X | log $X/$H | $\delta_{X}(F_{*}=0.45)$
---|---|---
He | -1.01 | 0.0
Li | -8.722 | -0.524
Be | -10.68 | -0.274
B | -9.193 | -0.546
C | -3.577 | -0.120
N | -4.21 | 0.000
O | -3.24 | -0.112
F | -7.56 | -0.147
Ne | -3.91 | 0.0
Na | -5.79 | -0.538
Mg | -4.44 | -0.659
Al | -5.57 | -1.602
Si | -4.50 | -0.625
P | -6.59 | 0.000
S | -4.88 | 0.0
Cl | -6.75 | -0.037
Ar | -5.60 | 0.0
K | -6.96 | -0.614
Ca | -5.68 | -2.356
Sc | -8.84 | -1.533
Ti | -7.07 | -1.928
V | -8.11 | -1.159
Cr | -6.38 | -1.379
Mn | -6.58 | -1.134
Fe | -4.48 | -1.510
Co | -7.07 | -1.343
Ni | -5.80 | -1.517
Cu | -7.82 | -0.757
Zn | -7.44 | -0.075

Figure 2 shows profound differences between the three SED models. In part, the
differences are due to the self-consistent physics in the qsosed that is not
featured in the other two models. The qsosed selects the inner accretion disk
radius needed to power the X-ray emission and then truncates the disk at that
point, rather than arbitrarily selecting $R_{in}=6GM/c^{2}$. This results in
the qsosed SED for $M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$ having approximately
the same peak energy as the other two SEDs for
$M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$, and also a more appreciable hard X-ray
component. Throughout the remainder of the paper, we only use the two SEDs
that represent extremes: disk-plaw and qsosed.

To model the starburst continuum, we use the binary stellar population
synthesis (SPS) code BPASS v2.0 (Stanway et al. 2016) to predict the spectrum
emitted from stars subject to binary evolution. Including binaries is
essential for a realistic treatment of the Wolf-Rayet (WR) phase, which can
result from mergers and envelope removal (D’Agostino et al. 2019). As outlined
in Richardson et al. (2019), we adopt a Kroupa IMF with exponents 1.3 and 2.35
over the mass ranges $0.1M_{\odot}<M<0.5M_{\odot}$ and
$0.5M_{\odot}<M<300M_{\odot}$ with one of three star formation histories
(SFHs): an instantaneous burst SFH at age 20 Myr, an instantaneous burst SFH
at age 250 Myr, or a continuous SFH at age 250 Myr. For a single stellar
population (SSP), 20 Myr corresponds to the age where [O III]/H$\beta$ reaches
a maximum (Xiao et al. 2018), while 250 Myr corresponds to the age where the
ionizing continuum flux for He+ and O++ ($>$54 eV) reaches a maximum. After
continuous star formation for 250 Myr, the ionizing continuum ceases to evolve
and this provides a “general” use stellar SED for photoionization modeling. We
include 11 different metallicities calibrated to Z⊙ = 0.02 spanning 0.05 Z⊙ –
2.0 Z⊙ for all SFHs. Figure 3 displays stellar SEDs for each of the three SFHs
at 0.4 Z⊙.

To mix the AGN and stellar SEDs, we use both coincident and non-coincident
mixing (Figure 1) with AGN fractions ($f_{\mathrm{AGN}}$) = 0.0, 0.04, 0.08,
0.16, 0.32, 0.5, 0.64, and 1.0, where $f_{\mathrm{AGN}}$ represents the
fraction of the total ionizing continuum attributed to the AGN SED.
Additionally, the cosmic ray background value $\xi=2.0\times
10^{-16}~{}\mathrm{s}^{-1}$ (Indriolo et al. 2007) is added to satisfy the
chemistry network.

###  2.2 Gaseous Cloud

Following Richardson et al. (2019), we select a hydrogen density of log
$n_{\mathrm{H}}$ = 2.0 [cm-3] at the illuminated face. After selecting
$n_{\mathrm{H}}$, the ionization parameter is then given by,

$U=\frac{\phi_{\mathrm{H}}}{n_{\mathrm{H}}c}$ (4)

where $\phi_{\mathrm{H}}$ is the hydrogen ionizing flux. While most emission
line galaxies indicate log $U$ = -3.5 – -2.0, an even lower limit is needed to
explain the lowest ionization dwarf galaxies and log $U$ $>$ -1.5 is needed to
explain local blue compact dwarf galaxies (Stasińska et al. 2015).
Accordingly, we run simulations with ionization parameters from log $U$ = -4.0
to log $U$ = -0.5 in increments of $\Delta$(log $U$) = 0.25. We follow Abel et
al. (2008) employing a magnetic field and constant pressure equation of state
until all simulations stop at $n_{e}/n_{\mathrm{H}}=0.01$. We include a small
amount of turbulence ($v=2$ km/s) to reduce line trapping. We consider both
open and closed geometries as given in Figure 1.

We use the methodology in Nicholls et al. (2017) for our abundances and
scaling. The solar values for Galactic Concordance abundances are largely
based off of Nieva & Przybilla (2012), Grevesse et al. (2015), and Scott et
al. (2015a, b), which we list in Table 1. The scaling of abundances with
metallicity includes a detailed prescription for accounting for specific
elemental variations due to differences in nucleosynthesis. Unfortunately, the
abundance of oxygen relative to solar has become synonymous with metallicity.
While metallicity is strictly defined as the mass fraction of metals, and
oxygen makes the greatest contribution to metallicity, the two are not
equivalent. To avoid this ambiguity, we refer to the scaling parameter
$\zeta_{\mathrm{O}}$ as the metallicity (see Nicholls et al. 2017) where the
solar metallicity is 12+log(O/H) = 8.76, corresponding to
$\zeta_{\mathrm{O}}=1$.

We assume Orion grains and PAHs throughout the cloud as implemented in Baldwin
et al. (1991) and Abel et al. (2008), respectively. The dust abundance is
typically assumed to not depend on metallicity, while the gas (hydrogen) to
dust ratio (G/D) varies as G/D $\propto Z^{-1}$ (Dwek 1998). Here, we adopt a
more sophisticated broken power law,

$\mathrm{log~{}G/D}=\left\\{\begin{array}[]{ll}2.21-\mathrm{log}\frac{Z_{\mathrm{gas}}}{Z_{\odot}}&\quad
Z_{\mathrm{gas}}\geq 0.25Z_{\odot}\\\ \\\
0.96-3.10~{}\mathrm{log}\frac{Z_{\mathrm{gas}}}{Z_{\odot}}&\quad
Z_{\mathrm{gas}}<0.25Z_{\odot}\end{array}\right.$ (5)

which shows that low metallicity dwarfs deviate from a single power law
relation (Rémy-Ruyer et al. 2014). The Orion grain abundances and PAH
abundances are scaled from their default abundances by the same factor to
satisfy this relationship at a given $Z$.

Figure 4: Common optical emission line excitation diagnostics in different
galaxy mass regimes (right label) assuming
$M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$. The width of the line represents
uncertainty due to geometry, while the colors refer to the mixing
methodologies from Figure 1 and two SEDs from Figure 2. Each line has been
thickened by 0.04 dex for clarity and the y-axis of each panel spans a 3.0 dex
range to highlight the relative sensitivity of each emission line to the
physical parameters explored.  Figure 5: Common optical emission line
excitation diagnostics in the same manner as Figure 4 except assuming
$M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$.  Figure 6: AGN diagnostics with the JWST
MIRI instrument in the same format as Fig. 4 assuming
$M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$.  Figure 7: AGN diagnostics with the JWST
MIRI instrument in the same format as Fig. 5 assuming
$M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$.

Most photoionization modeling assumes a “standard” set of gas phase depletion
factors derived from a variety of sources. In reality, however, depletion
factors $\delta_{X}$ depend on the undepleted reference abundance set being
used and the strength of the depletion $F_{*}$. We follow a self-consistent
approach where we use our unique reference abundances with the methodology
outlined in Jenkins (2009). The strength of the depletion is selected so that
the depletion factor for iron is $\delta_{Fe}=-1.5$ dex as in Thomas et al.
(2018). This results in $\delta_{O}=-0.11$ dex, which is less than the
commonly assumed Cloudy default of $\delta_{O}=-0.22$ dex, but assists in
matching optical emission line diagnostics (Gutkin et al. 2016) and matches
the depletion derived from analyzing dust grain composition (Peimbert &
Peimbert 2010), X-ray spectroscopy (Pinto et al. 2013), and $\alpha$-element
enhancement (Amayo et al. 2021). In reality, depletion factors should change
with G/D at a fixed metallicity and as a function of metallicity (Peimbert &
Peimbert 2010, De Cia et al. 2016); however, this is rarely taken into account
in photoionization modeling and beyond the scope of this work. The complete
set of adopted depletion factors are listed in Table 1 and we elaborate on our
methodology in Appendix A. Our final gas phase abundances differ from the
BPASS stellar abundances, the effects of which have been investigated in
Grasha et al. (2021), but are beyond the scope of this work. All in all, our
model suite consists of $>6.33\times 10^{4}$ simulations.

##  3 Line Ratio Sensitivity Analysis

We seek to assess the sensitivity of emission line ratios to
$f_{\mathrm{AGN}}$, AGN SED shape, mixing methodology, and geometry. In
particular, we select emission line diagnostics that are detectable in purely
star forming galaxies, enabling investigation of the connection between star
formation and AGN in dwarfs, which is not possible for all emission lines. For
example, the presence of [Ne V] 14.3$\mu$m or [Ne VI] 7.65 $\mu$m alone
signals AGN activity, but our simulations show that [Ne V] is unlikely to be
detectable in most local dwarfs where $U$ and $f_{\mathrm{AGN}}$ are small,
thus making it an unreliable tracer of AGN fraction for all galaxy masses.

Similarly, coronal lines from highly ionized states (e.g., Si VI, Fe XIII)
have been used to identify AGN (Cann et al. 2018, Bohn et al. 2021, Kimbro et
al. 2021). However, several limitations exist to this approach: (1) only about
half of AGN actually show coronal line(s), regardless of instrumental line
sensitivity (Riffel et al. 2006); (2) highly ionized states depend on physical
conditions with high $U\sim-2.0$ and high $f_{\mathrm{AGN}}>0.64$, which are
not characteristic of typical dwarfs; (3) if present, the coronal line region
lies between the BLR and NLR, which implies dust sublimation is important, a
process that presents a problem for self-consistent photoionization modeling
(Mazzalay et al. 2010, Adhikari et al. 2016); (4) coronal line emission
typically originates from metals that become heavily depleted in forming dust
grains (e.g., Si, Ca, Fe), and therefore small changes to $F_{*}$ yield large
differences in these abundances (De Cia et al. 2016). All together, these
limitations suggest that using coronal lines will be subject to strong
selection bias, and therefore alone cannot provide a complete picture of IMBH
activity in dwarf AGN.

With these caveats in mind, we have determined three different mass ranges to
evaluate the AGN emission line diagnostics within the wavelength ranges of
SDSS and JWST: lower mass dwarfs, intermediate mass dwarfs, and massive
galaxies.

  * •

For lower mass dwarfs, we use the $U-Z$ correlation presented in Kashino &
Inoue (2019), which leads to values of log $U\approx-2.0$, $Z/Z_{\odot}\approx
0.15$.

  * •

For intermediate mass dwarfs, we analyzed SDSS strong emission line
measurements (Tremonti et al. 2004) as processed by P21 for the z$\sim$0 dwarf
dominated RESOLVE Survey (Kannappan & Wei 2008) with the Bayesian analysis
code NebulaBayes (Thomas et al. 2018), but using our simulation suite. We
determine median values of log $U\approx-3.25$, $Z/Z_{\odot}\approx 0.4$ for
intermediate mass dwarfs (P21), which can be thought of as a ‘fiducial’ set of
parameters for dwarf galaxies.

  * •

For massive galaxies, we adopt log $U\approx-2.0$, $Z/Z_{\odot}\approx 1.0$
following the parameters used in (Abel et al. 2009) to model AGN in massive
galaxies such as ULIRGs.

For the rest of §3, we use the stellar SED resulting from continuous SFH at
250 Myr as it represents a “general purpose” ionizing continuum not
purposefully constructed for maximizing any particular emission line ratio.

###  3.1 Optical

Figures 4 and 5 show the emergent optical emission line predictions for
$M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$ and $M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$,
respectively. In each figure, we display [O III]/H$\beta$, [S II]/H$\alpha$,
[O I]/H$\alpha$, three common emission line ratios used in optical AGN
diagnostics (columns), as a function of AGN fraction for three galaxy mass
regimes (rows). The thickness of each line denotes the uncertainty due to
differences in assuming a spherical or plane parallel geometry, while the
color indicates the AGN SED and mixing methodology being used. Other
diagnostics are presented in Appendix B, such as the metallicity sensitive [N
II]/H$\alpha$ ratio.

A few major trends are apparent in Figures 4 and 5. First, the effect that
physical uncertainties have on emission line ratios is exacerbated for lower
$M_{\mathrm{BH}}$. Second, the greatest variation in emission line ratios due
to $f_{\mathrm{AGN}}$ occurs in the range $0.0\leq f_{\mathrm{AGN}}\leq 0.32$.
The diagnostics [O III]/H$\beta$ and [S II]/H$\alpha$ are generally poorer
tracers of $f_{\mathrm{AGN}}$. Lastly, in the dwarf galaxy mass regimes,
diagnostics show less dependence on geometry, in stark contrast to massive
galaxies where the diagnostics can show up to $\sim$1.0 dex variation for
$M_{\mathrm{BH}}=10^{3}M_{\odot}$.

The photoionization cross section of hydrogen quickly decreases as photon
energy increases (Osterbrock & Ferland 2006). As a result, X-rays due to an
AGN penetrate into neutral gas, which causes collisions that excite neutral
species. Since [O I] $\lambda$6300 partially originates from neutral gas, [O
I]/H$\alpha$ traces $f_{\mathrm{AGN}}$ rather well in dwarf galaxy mass
regimes in contrast to the other optical diagnostics. This makes it a reliable
choice for detecting AGN activity in dwarfs and constraining
$f_{\mathrm{AGN}}$. Non-ionizing photons can also pump electrons into high
energy excited states, which can cause [O I] $\lambda$6300 emission when the
electrons cascade to lower energy levels. This continuum fluorescence process
is rather inefficient for O I (Bautista 1999), leaving collision excitation as
the dominant process, and thus preserving the utility of [O I] $\lambda$6300
as an AGN diagnostic.

The AGN SED and mixing methodology can create substantial variation in all
diagnostics, although this is mitigated for emission line ratios created under
certain physical conditions. For example, the middle rows of Figures 4 and 5
show that considering $f_{\mathrm{AGN}}\geq 0.32$, the emission line ratios
converge upon [O III]/H$\beta\approx-0.3$ to $0.7$ and [O
I]/H$\alpha\approx-1.2$ to $-0.2$, generally resulting in a LINER
classification (Kewley et al. 2006). This result, combined with a star-forming
galaxy classification from the metallicity sensitive BPT diagram, corroborates
that dwarf AGN have inconsistent optical classifications (Reines et al. 2020,
P21) for black hole masses in the range $10^{3}-10^{5}~{}M_{\odot}$.

Our results also stand in contrast to other work (Cann et al. 2019),
suggesting that AGN host galaxies with $\sim 10^{3}M_{\odot}$ BHs have such
low [O III]/H$\beta\approx-1.5$ that [O III] emission might be undetectable
222Private communication with Jenna Cann, Shobita Satyapal, and Nick Abel
suggests that possible physical explanations could include differences in
assumed AGN SED shape, in choice of elemental abundances, or in geometry and
mixing, as diagrammed in Figure 1.. Figure 4 clearly shows that [O
III]/H$\beta$ is highly dependent on the physical uncertainties presented in
Figure 1 and the galaxy mass regime of interest. RESOLVE dwarf galaxies are
ubiquitously star-forming with $f_{\mathrm{AGN}}<0.6$ and are the most likely
hosts for IMBHs. For the intermediate mass dwarf galaxy regime, we see in the
majority of cases that [O III]/H$\beta\geq 0.0$, i.e. [O III] as strong as
H$\beta$.

###  3.2 Mid-IR

The most valuable AGN diagnostics for JWST come from the MIRI instrument (4.9
- 28.3 $\mu$m), as opposed to NIRspec (0.6 - 5.3 $\mu$m), based on the
availability of either emission lines originating from the same element with
different ionization potentials, or high ionization lines along with a
recombination line for comparison. Although we are focused on detecting active
IMBHs in relatively local galaxies, it is worth noting that galaxies at
$z>0.3$ will have optical diagnostics that fall within NIRspec, thereby
providing additional constraints. The following lines show diagnostic value
for AGN activity and are detectable until $z\sim 0.1$ assuming the MIRI line
sensitivity of $3.3\times 10^{-17}$ erg/s/cm-2: Pf$\alpha$, [Ne II]
12.8$\mu$m, [Ne III] 15.6$\mu$m, [Ar II] 6.98$\mu$m, [Ar III] 8.99$\mu$m, [Ar
V] 13.1$\mu$m, [S III] 18.7$\mu$m, [S IV] 10.5$\mu$m, and [O IV] 25.9$\mu$m.
This result is independent of geometry, mixing methodology, or AGN SED shape.

Figures 6 and 7 displays tracers of AGN activity observable with JWST, in the
same format as Figures 4 and 5. As in the optical, changes to the line ratios
become less pronounced as AGN fraction increases; in contrast to the optical,
IR line ratios generally show less sensitivity to geometry. Weaver et al.
(2010) suggests that [Ne III]/[Ne II] and [O IV]/[Ne III] have the ability to
effectively separate excitation mechanisms. The first column in both figures
indicates that [Ne III]/[Ne II] remains constant with AGN fraction for
intermediate mass dwarfs (second row) and massive galaxies (third row).
Therefore, [Ne III]/[Ne II] is not a robust indicator of AGN activity. It
does, however, remain an effective $f_{\mathrm{AGN}}$ diagnostic for the low-
mass dwarf galaxies, with minor sensitivity to the mixing methodology and SED
selection. The second column shows that [Ar II]/Pf$\alpha$ has strong
diagnostic potential for all galaxy masses, especially for
$M_{\mathrm{BH}}=10^{5}M_{\odot}$ (Figure 7). As $M_{\mathrm{BH}}$ decreases,
the [Ar II]/Pf$\alpha$ still effectively traces $f_{\mathrm{AGN}}$, but the
uncertainty of the AGN SED and mixing methodology introduces greater spread in
the emission line predictions.

The last column in Figures 6 and 7 shows that [O IV]/Pf$\alpha$ is also an
effective $f_{\mathrm{AGN}}$ diagnostic. At $M_{\mathrm{BH}}=10^{5}M_{\odot}$,
[O IV]/Pf$\alpha$ traces $f_{\mathrm{AGN}}$ quite well, while remaining
relatively insensitive to the shape of the AGN SED and the uncertainties given
in Figure 1. [O IV]/Pf$\alpha$ remains well-behaved for
$M_{\mathrm{BH}}=10^{3}M_{\odot}$ except for intermediate mass dwarfs where
the disk-plaw, non-coincident mixing case creates a $\sim$1.0 dex spread in
values relative to the other cases. This spread is due to the combined effect
of a low $U$ and harder accretion disk reducing the number O++ ionizing
photons.

In general, line ratios featuring [O IV] and [Ar II] show less sensitivity to
geometry than optical diagnostics, display more variation with AGN fraction
than other mid-IR line ratios, and retain their diagnostic potential over a
wider range of galaxy masses and BH masses. The mid-IR diagnostics provide
greater constraints on $f_{\mathrm{AGN}}$ for lower levels of AGN activity
expected for dwarf AGN with IMBHs, compared to optical diagnostics which are
more sensitive to higher levels of AGN activity. These results highlight the
benefit of using multiple line ratios to constrain $f_{\mathrm{AGN}}$ with
diagnostic diagrams.

Figure 8: Optical diagnostic diagrams that separate AGN activity from
starburst activity assuming $M_{\mathrm{BH}}=10^{3}M_{\odot}$ (left column)
and $M_{\mathrm{BH}}=10^{5}M_{\odot}$ (right column). The selected age of the
binary stellar population maximizes the contribution of WR stars and thereby
sets a lower limit for AGN activity. Pure starburst models (0% AGN) are
displayed as blue stars. The models for a given $f_{\mathrm{AGN}}$
approximately span the area of each hatched shape. The demarcations in each
diagram are taken from Kewley et al. (2001), Kauffmann et al. (2003), and
Kewley et al. (2006). The majority of observed dwarf AGN lie in the star
forming wing of the BPT diagram (top panels), which models with and without
AGN can reproduce.

##  4 Diagnostics Diagrams

In light of the wide range of uncertainties previously mentioned, we seek to
find diagnostic diagrams suitable for detecting AGN excitation, and ideally
measuring $f_{\mathrm{AGN}}$, for a given galaxy. To compare our models to
galaxies with spectroscopic observations, we select a subset of models
($-3.5\leq\mathrm{log}~{}U\leq-1.5$) with an instantaneous SFH, since the
harder stellar continua provide a limiting case for AGN activity.

###  4.1 Optical

We use a 20 Myr SSP for the optical diagnostics since this SFH maximizes the
[O III]/H$\beta$ line ratio used in many diagnostic diagrams that separate AGN
and star forming galaxies. For the observational sample, we choose dwarf
galaxies in the MPA-JHU sample from P21. Following P21, we classify dwarf AGN
as any dwarf galaxies not classified as definitely star forming (e.g.,
traditional AGN, LINERs, etc.) The three diagrams from Veilleux & Osterbrock
(1987) are by far the most commonly used optical diagnostics for separating
AGN and star forming galaxies, so we focus our analysis on them.

Figure 8 displays these diagrams for $M_{\mathrm{BH}}=10^{3}M_{\odot}$ (left
column) and $M_{\mathrm{BH}}=10^{5}M_{\odot}$ (right column). The models for
$f_{\mathrm{AGN}}=$ 0.04, 0.08, and $\geq$0.16 approximately span the area of
the three hatched shapes (tan, purple, and green, respectively). For models
with $f_{\mathrm{AGN}}\geq 0.16$ and a $10^{3}M_{\odot}$ black hole, there is
a wide range of possible values for [O III]/H$\beta$, highly dependent on
configurations present in Figure 1. This large spread in values relates to the
current difficulty of detecting IMBHs at this mass, but also provides promise
that optical detection is indeed possible.

Figure 8 shows that models in the range $0\leq f_{\mathrm{AGN}}\leq 0.16$
occupy similar regions of each diagram. In particular, the BPT diagram (top
row) registers observed dwarf AGN as consistent with pure star formation.
Conversely, theoretical models with pure star formation can cross over into
the AGN region of the diagram. Despite the differences in photoionization
modeling, this is also seen in Xiao et al. (2018) on account of using the
BPASS SEDs that feature substantially harder continua than many other SPS
codes.

The [S II]/H$\alpha$ diagram indicates that pure star formation can reproduce
the line ratios of all the dwarf AGN shown, but unlike for the BPT diagram,
for the [S II]/H$\alpha$ diagram this result only occurs with the particularly
hard stellar SED that we have selected. Thus, knowing the SFHs for a given
sample of dwarfs could provide justification for using [S II]/H$\alpha$ to
identify AGN. In contrast, the BPT diagram is more generally a poor diagnostic
for identifying dwarf AGN, regardless of SFH, as discussed in more detail in
P21.

The last optical diagnostic diagram shows that some dwarf AGN require models
with an AGN component to reproduce the observed [O I]/H$\alpha$, making this
diagram more reliable in separating star formation and AGN in dwarfs (Reines
et al. 2020, P21). It is worth noting that more dwarf AGN likely require an
AGN component than shown here, on account of the hard stellar SED used in this
analysis. Additionally, for [O I]/H$\alpha$ there is some modest separation
between models with different $f_{\mathrm{AGN}}$, especially with
$M_{\mathrm{BH}}=10^{3}M_{\odot}$, enabling a better assessment of AGN
activity as also shown in Figure 4.

###  4.2 Mid-IR

For our observational sample, we choose dwarf SF (Cormier et al. 2015) and
dwarf AGN (Hood et al. 2017) observations requiring that the AGN satisfy [Ne
V]/[Ne II]$>$0.1 (Inami et al. 2013). It is important to note that Pf$\alpha$,
featured in Figure 6, is not available in statistical samples due to the low
sensitivity and resolution of Spitzer and ISO. Similarly, since [Ar II]
$6.98\mu$m is unavailable for samples including dwarfs, we use massive AGN
(Sturm et al. 2002) for diagnostic diagrams with this line.

We have tested all possible emission line ratio combinations from the emission
lines listed in §3.1.2. Figure 9 shows the results of this analysis in three
diagnostic diagrams featuring emission line ratios also presented in Weaver et
al. (2010), Inami et al. (2013), and Hao et al. (2009).

Figure 9: Mid-IR diagnostic diagrams that separate AGN activity from pure
starburst activity in the same format as Figure 8. Pure starburst models (0%
AGN) are displayed as blue stars. The models for a given $f_{\mathrm{AGN}}$
approximately span the area of each hatched shape. The SF, SF and/or AGN, and
AGN regions represent pure starburst galaxies, a mix of pure starburst
galaxies and AGN, and only AGN, respectively (eqns 6, 7, 8). JWST will enable
emission lines normally missing from Spitzer spectra to serve as additional
constraints, like [Ar II] 6.99 $\mu$m (left panels).

Our new demarcations separate three distinct regions: the SF region contains
only pure starburst galaxies; the SF and/or AGN region contains a mixture of
pure starbursts and AGN; the AGN region contains only AGN. The divisions
between SF and SF and/or AGN regions are given by,

$\textrm{log [Ne III]/[Ne II]}=0.3~{}\textrm{log [O IV]/[Ne III]}-0.9$ (6)

log[O IV]/[Ne III] = 1.25 log [S IV]/[Ne II] - 0.125

(7)

log [O IV]/[S III] = 1.2 (log [S IV]/[Ar II]+1.4)${}^{\frac{1}{2}}$ \- 3.0

(8)

while the AGN region is formed by [O IV]/[Ne III]$~{}=-1$ and [O IV]/[S
III]$~{}=-0.8$.

The first diagram (top panels) has frequently been used to separate starbursts
and AGN into quadrants according to [O IV]/[Ne III] $=0$ (Weaver et al. 2010),
but this cutoff excludes dwarf AGN with [O IV]/[Ne III] $>-1$, which our new
demarcations recover. Our models indicate that the observed dwarf AGN in this
region have at least a 4-16% AGN contribution. The second diagram (center
panels) replaces the abscissa with [S IV]/[Ne II] (Inami et al. 2013),
resulting in a cleaner separation of starbursts and AGN at low ionization. The
last diagram (bottom panels) uses [O IV]/[S III] in the ordinate (Hao et al.
2009) and [S IV]/[Ar II] in the abscissa, which creates even more separation
between starbursts and AGN, and also between $f_{\mathrm{AGN}}$ values. As
mentioned above, the [Ar II] observations are poor since Spitzer was only
capable of detecting wavelengths $<$10 microns in low resolution mode ($R\sim
130$). In contrast, MIRI features the highest resolution ($R\sim 3100$) and
line sensitivity available at these wavelengths. Thus, the right panels in
Figure 9 present a promising new diagnostic for JWST observations to constrain
AGN activity.

##  5 Discussion and Conclusions

In this paper, we have explored several key uncertainties that will be
critical to assess in the upcoming era of detecting IMBHs: the shape of the
AGN SED, the surrounding gas cloud geometry, and the manner of mixing
radiation from AGN and stars. The diversity of models for the AGN SED in
Figure 2 emphasizes the importance of next generation X-ray facilities such as
Lynx and Athena that will enable proper constraints on low luminosity sources.
We show that all of the listed uncertainties have profound effects on emission
line diagnostics in the optical and mid-IR. This has implications for
statistical samples of galaxies that are analyzed with photoionization models
that implicitly assume a particular geometrical configuration or mixing
methodology in Figure 1. Such assumptions can lead to powerful selection
effects (Ferguson et al. 1997, Meskhidze & Richardson 2017). These assumptions
could limit the applicability of simple relationships that scale physical
properties (e.g., $f_{\mathrm{AGN}}$, $M_{\mathrm{BH}}$) with emission lines
ratios for large samples of galaxies.

Even though degeneracies abound in the optical, we find AGN diagnostics remain
detectable in most situations across a range of galaxy masses. This result
offers promise that surveys like SDSS have already picked up signatures of AGN
with $M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$. Unfortunately, the gold standard
for optical AGN classification, the BPT diagram, poorly traces AGN activity in
dwarf galaxies. As we argue in P21, this is due to [N II]/H$\alpha$ being
metallicity sensitive and $f_{\mathrm{AGN}}$ insensitive. It also reflects the
sensitivity of [O III]/H$\beta$ to the uncertainties explored in this paper.
Actually, as seen in Reines et al. 2020 and P21, the often forgotten [O
I]/H$\alpha$ diagnostic is a stronger metric for an active AGN in dwarfs given
its sensitivity to $f_{\mathrm{AGN}}$ and relative insensitivity to physical
uncertainties. It therefore serves as the best optical emission line ratio for
finding dwarf AGN, but the relative weakness of the [O I] line does limit the
sample that can be tested (P21).

Relatively high-mass dwarfs ($M_{*}\lesssim 10^{9.3-9.5}M_{\odot}$) classified
as LINERs present an opportunity to find the coveted $10^{3}~{}M_{\odot}$
black holes, which would fill in a major gap in IMBH empirical relationships
and help constrain the occupation fraction in dwarfs. If AGN in this BH mass
regime are confirmed by other methods (e.g., variability, line broadening,
X-rays), but still fail to show any optical signatures, this non-detection
would suggest that the column density of obscuring gas and the covering factor
around the source could be factors in the elusive nature of these AGN. The
column densities and covering factors of dwarf AGN remain relatively
unexplored. Purely star forming dwarf galaxies show a decrease in covering
factor as metallicity decreases, albeit with a large scatter in the relation
(Cormier et al. 2019). Conversely, massive galaxies show a decrease in
obscured AGN (large covering factor) with increasing luminosity (Sazonov et
al. 2015, Georgakakis et al. 2017), and therefore increasing metallicity
(Lamareille et al. 2004). It is possible that dwarf AGN could provide the
missing link between these two opposing trends if low mass IMBHs continue to
remain elusive in the optical.

In the mid-IR, we have shown that [Ar II] 6.98$\mu$m / Pf$\alpha$ and [O IV]
25.9$\mu$m/Pf$\alpha$ together have the potential to constrain AGN activity
over a range of galaxy masses while minimizing sensitivity to physical
uncertainties (Figure 6). We have revised the demarcations on the [Ne III]/[Ne
II] vs. [O IV]/[Ne III] diagnostic diagram to include dwarf AGN and presented
two new diagnostic diagrams based on the [O IV] and [Ar II] emission lines
(Figure 9). These new diagrams are capable of separating starburst activity
from AGN activity down to a 4% AGN fraction in dwarfs, which are ubiquitously
star forming. Unlike the BPT diagram, these proposed diagrams maintain their
diagnostic value over a wide range of ionization and metallicity.

We emphasize that the provided demarcations serve as theoretical boundaries
for classifying the excitation mechanism in dwarf galaxies. Observations of
optically classified starbursts can occasionally cross over into the AGN
region of these diagrams due to strong mid-IR [O IV] emission (e.g., IZw18,
Lebouteiller et al. 2017), although soft X-ray and hard X-ray emission is
typically detected in these galaxies.

Current SPS models are unable to produce enough photons $>$54 eV to account
for this crossover. High mass X-ray binaries (HMXBs) can generate the hard
photons needed to create AGN-like emission line ratios assuming a model with
high $U$, high $L_{X}/\mathrm{SFR}$, and a sufficiently hard SED (Simmonds et
al. 2021). It is unlikely that HMXBs can uniformly account for dwarfs
exhibiting emission line ratios characteristic of AGN given that the shape of
the HMXB SED remains highly uncertain and most dwarf AGN do not present these
extreme conditions (P21). Additionally, a more generic treatment of the HMXB
SED has shown that HMXBs are an inefficient means of producing photons $>$54
eV (Senchyna et al. 2020). Therefore, unless more realistic treatment of the
WR phase alters the result of our predictions in the future, our current
simulations suggest these galaxies have active AGN. The SF and/or AGN region
in each diagram can contain optically classified starbursts (see Figure 9),
and this result is reproduced by a photoionization model with multiple gas
clouds (Meléndez et al. 2014, Richardson et al. 2016). IFU observations should
help clarify whether such a model needs to be invoked.

To fully address modeling degeneracies in both the optical and mid-IR,
Bayesian analysis will be a valuable tool for extracting meaningful properties
over a range of conditions in future studies. Our simulation suite
incorporates a finer spacing of metallicities, ideal for accurate Bayesian
analysis at $<0.4~{}Z_{\odot}$ (Richardson et al. 2019), than other SPS models
(e.g., Starburst99), while robustly accounting for D/G and elemental
depletion. In addition, the mixing methodologies and geometries unique to our
models could be used in a multi-component ISM analysis, similar to work on the
multi-phase ISM in dwarfs (Cormier et al. 2019). Together with the AGN
diagnostics and excitation diagrams presented in this paper, such future
applications of our models will prove useful for addressing more complex
topologies associated with mixed AGN/SF excitation in dwarfs in the era of
JWST.

CR gratefully acknowledges the support of the Elon University FR&D committee
and the Extreme Science and Engineering Discovery Environment (XSEDE), which
is supported by National Science Foundation grant number ACI-1548562. This
work used the XSEDE resource Comet at the San Diego Supercomputing Center
through allocation TG-AST140040. MP gratefully acknowledges the support of the
2020 Hamilton Award from the UNC Department of Physics and Astronomy. SK and
MP acknowledge support from NSF AST-2007351. JB acknowledges grant support
from NSF AST-1812642 and CUNY JFRASE. We thank Nick Abel, Jenna Cann, Chris
Done, Gary Ferland, Ed Jenkins, and Shobita Satyapal for helpful discussions
that improved the quality of this paper.

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##  Appendix A Depletion Factors Due to Grains

We use the methodology presented in Jenkins (2009) (hereafter J09) to develop
a set of depletion factors that account for gas phase elements condensing to
form dust grains. This depletion depends on comparing a reference abundance
set to abundances derived from observations along a particular line of sight.
The difference provides the depletion factor, $\delta_{X}$,

$\delta_{X}=\mathrm{log}\left(\frac{X}{\mathrm{H}}\right)_{obs}-\mathrm{log}\left(\frac{X}{\mathrm{H}}\right)_{ref}$
(A1)

Despite the dependence on a reference set of abundances, most photoionization
modeling does not properly take this factor into account as shown below.
Different lines of sight yield different depletion factors for a given
element, allowing one to define a depletion strength, $F_{*}$, that accounts
for this variation. A linear fit to the logarithm of the depletion factor
gives the following form,

$\delta_{X}=B_{X}+A_{X}(F_{*}-z_{X})$ (A2)

where $A_{X}$ is the slope, $B_{X}$ is the vertical offset, and $z_{X}$
accounts for the errors in the observations. We assume that the non-refractory
elements He, Ne, S, and Ar do not become depleted in the ISM. However, sulphur
depletion remains a subject of debate (Gry & Jenkins 2017, Laas & Caselli
2019, Goicoechea & Cuadrado 2021, Hily-Blant et al. 2021).

We use the fits for the Galaxy provided in J09 for C, N, O, Mg, Si, P, Cl, Ti,
Cr, Mn, Fe, Ni, Cu, and Zn. We make this choice for two reasons. First, J09
provides the most complete sample, while extragalactic fits are mostly limited
to heavier elements that have less impact on emission line predictions.
Second, the number of observations included in the J09 analysis makes the fit
more reliable.

While we assume that depletion occurs as observed in the Milky Way, deviations
in the depletion patterns for heavy elements are known to be present for other
galaxies. For example, Mg, Ti, and Mn show noticeable deviations in the Small
Magellanic Cloud (Jenkins & Wallerstein 2017), and while the depletion pattern
is mostly Galactic in the Large Magellanic Cloud (Tchernyshyov et al. 2015),
Si does show a noticeable deviation (Roman-Duval et al. 2019).

For the rest of the elements, we have compiled a list of depletion factors
towards the highly depleted star $\zeta$ Oph to serve as the value at
$F_{*}=1.0$ in accordance with the method used by J09. Fluorine is the only
exception where we use the most depleted source in Snow et al. (2007), since
the value towards $\zeta$ Oph is unavailable. To determine the parameters
$A_{X}$ and $B_{X}$ for these elements, we rely on the general trend that
elements with larger condensation temperatures show greater depletions and
steeper slopes. The following elements have similar depletion trends to their
J09 counterparts: Li $\Leftrightarrow$ Cr; Be $\Leftrightarrow$ Mg; B
$\Leftrightarrow$ Zn, F $\Leftrightarrow$ Cl; Na, K $\Leftrightarrow$ Cu, Zn;
Al, Ca, V $\Leftrightarrow$ Ti; Sc $\Leftrightarrow$ P, Cu; Co
$\Leftrightarrow$ Ni. From these analogies, we can assume that all of the
elements in J09 have $\delta_{X}=0$ at $F_{*}\approx-0.5$ except for
$\delta_{\mathrm{Fluorine}}$, which reaches zero at $F_{*}=0.2$.

Table 2 lists the depletion factors for all elements for $F_{*}=1.0$, the
linear fit parameters need to recreate the depletion pattern, and the
reference for each depletion factor given. Note that depletion factors have
been rescaled according to our reference abundances instead of using the
abundance assumed in each cited source. Displaying the depletion factors for
$F_{*}=1.0$ makes it clear which elements are weakly depleted in the ISM as
opposed to not depleted at all. However, for our photoionization modeling, we
adjusted $F_{*}$ so that $\delta_{\mathrm{Fe}}=-1.5$ (see Table 1), which we
justified in §2.2.

The methodology we have used here is similar to what resulted in the depletion
factor sets included with the photoionization code Mappings V (Sutherland &
Dopita 2017) with two major differences. First, unlike the values included
with Mappings, our depletion factors are self-consistently scaled with our
reference abundances. Second, we do not deplete nitrogen for any value of
$F_{*}$ given the lack of evidence that nitrogen gets locked up in grains.
This is particularly important for any analysis that strongly relies upon
nitrogen emission lines for inferring metallicity values.

The depletion factors we use represent a small step toward accounting for the
different depletion patterns in gas phase abundances, much in the same way
Nicholls et al. (2017) accounts for nucleosynthesis patterns for elements as a
function of metallicity. However, obvious limitations exist since galaxies can
show more negative $F_{*}$ than we account for here (Jenkins & Wallerstein
2017).

Table 2: Depletion factors adjusted for our reference abundance set at $F_{*}=1.0$ along with the parameters necessary to scale each element with $F_{*}$. The non-refractory elements He, Ne, S, and Ar are assumed to have no depletion. X | $\delta_{X}(F_{*}=1.0)$ | $A_{X}$ | $B_{X}$ | $z_{X}$ | Ref.
---|---|---|---|---|---
He | 0.0 | - | - | - | -
Li | -0.827 | -0.552 | -0.28 | - | White 1986
Be | -0.432 | -0.288 | -0.14 | - | York et al. 1982
B | -0.862 | -0.575 | -0.29 | - | Federman et al. 1993
C | -0.176 | -0.101 | -0.16 | 0.803 | Jenkins 2009
N | 0.000 | 0.0 | 0.0 | 0.550 | Jenkins 2009
O | -0.235 | -0.225 | -0.15 | 0.598 | Jenkins 2009
F | -0.470 | -0.587 | 0.117 | - | Snow et al. 2007
Ne | 0.0 | - | - | - | -
Na | -0.850 | -0.567 | -0.283 | - | Savage & Sembach 1996
Mg | -1.208 | -0.997 | -0.74 | 0.531 | Jenkins 2009
Al | -2.530 | -1.687 | -0.843 | - | Barker et al. 1984
Si | -1.250 | -1.136 | -0.46 | 0.305 | Jenkins 2009
P | -0.520 | -0.945 | -0.04 | 0.488 | Jenkins 2009
S | 0.0 | - | - | - | -
Cl | -0.720 | -1.242 | -0.23 | 0.609 | Jenkins 2009
Ar | 0.0 | - | - | - | -
K | -0.970 | -0.647 | -0.323 | - | Chaffee & White 1982
Ca | -3.720 | -2.480 | -1.24 | - | Crinklaw et al. 1994
Sc | -2.421 | -1.614 | -0.807 | - | Snow & Dodgen 1980
Ti | -3.054 | -2.048 | -1.89 | 0.43 | Jenkins 2009
V | -1.830 | -1.220 | -0.61 | - | Savage & Sembach 1996
Cr | -2.175 | -1.447 | -1.41 | 0.47 | Jenkins 2009
Mn | -1.605 | -0.857 | -1.19 | 0.52 | Jenkins 2009
Fe | -2.216 | -1.285 | -1.49 | 0.437 | Jenkins 2009
Co | -2.120 | -1.413 | -0.707 | - | Mullman et al. 1998
Ni | -2.336 | -1.49 | -1.74 | 0.599 | Jenkins 2009
Cu | -1.147 | -0.71 | -0.94 | 0.711 | Jenkins 2009
Zn | -0.410 | -0.61 | -0.14 | 0.555 | Jenkins 2009

##  Appendix B Additional Line Ratio Sensitivity Diagrams

In this section, we present the line ratio sensitivity for additional AGN
diagnostics. Figures 10 and 11 display diagnostics in the optical for
$M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$ and $M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$,
respectively, and similarly in the mid-IR for Figures 12 and 13. The columns
of each figure represent a given galaxy mass, while the rows represent a given
line ratio. As with the diagnostics presented in the main body of the paper,
the uncertainty introduced from the AGN SED shape, cloud geometry, and mixing
methodology, decreases at higher black hole mass.

In the optical, most of the emission line ratios poorly trace
$f_{\mathrm{AGN}}$. It is noteworthy that [N II]/H$\alpha$ remains relatively
insensitive to AGN activity in most conditions, which combined with the line
ratio’s metallicity sensitivity makes it an overall poor diagnostic for dwarf
AGN. In contrast, He II/H$\beta$ and [O I]/[O III] are promising diagnostics
for dwarf AGN. However, the wind from WR stars can contaminate He II
(Brinchmann et al. 2008), therefore line ratios involving [O I] are more
reliable.

In the mid-IR, one also needs to be judicious in selecting AGN sensitive
diagnostics. For a $10^{3}~{}M_{\odot}$ black hole, [Ar V]/Pf$\alpha$, [Ar
V]/[Ar III], and [O IV]/[Ne II] suffer from large amounts of uncertainty for
most galaxy masses regimes. In contrast, [O IV]/[S III] and [Ar II]/[Ar III]
provide suitable backups for [O IV]/Pf$\alpha$ and [Ar II]/Pf$\alpha$ (Figures
6 and 7) across the black hole masses and galaxy masses we have considered.

Figure 10: Additional optical emission line excitation diagnostics in the same
format as Figure 4 with $M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$.  Figure 11:
Additional optical emission line excitation diagnostics in the same format as
Figure 5 with $M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$.  Figure 12: Additional
mid-IR emission line excitation diagnostics in the same format as Figure 6
with $M_{\mathrm{BH}}=10^{3}~{}M_{\odot}$.  Figure 13: Additional mid-IR
emission line excitation diagnostics in the same format as Figure 7 with
$M_{\mathrm{BH}}=10^{5}~{}M_{\odot}$.


# Deep COVID-19 Recognition using Chest X-ray Images: A Comparative Analysis

Selvarajah Thuseethan, Chathrie Wimalasooriya and Shanmuganathan
Vasanthapriyan  Department of Computing and Information Systems
Sabaragamuwa University of Sri Lanka
Sri Lanka
{thuseethan, wimalasooriya<EMAIL_ADDRESS>
###### Abstract

The novel coronavirus variant, which is also widely known as COVID-19, is
currently a common threat to all humans across the world. Effective
recognition of COVID-19 using advanced machine learning methods is a timely
need. Although many sophisticated approaches have been proposed in the recent
past, they still struggle to achieve expected performances in recognizing
COVID-19 using chest X-ray images. In addition, the majority of them are
involved with the complex pre-processing task, which is often challenging and
time-consuming. Meanwhile, deep networks are end-to-end and have shown
promising results in image-based recognition tasks during the last decade.
Hence, in this work, some widely used state-of-the-art deep networks are
evaluated for COVID-19 recognition with chest X-ray images. All the deep
networks are evaluated on a publicly available chest X-ray image datasets. The
evaluation results show that the deep networks can effectively recognize
COVID-19 from chest X-ray images. Further, the comparison results reveal that
the EfficientNetB7 network outperformed other existing state-of-the-art
techniques.

###### Index Terms:

COVID-19, Deep Learning, Chest X-ray, Deep Networks

##  I Introduction

Coronaviruses are a group of related viruses that can cause respiratory tract
infections, ranging from mild to lethal. In 2019, a novel coronavirus called
Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) emerged from
Wuhan, China and infected more than 229 million people with a mortality of
over 4.7 million111https://covid19.who.int/. The SARS-CoV-2 cause respiratory
disease, namely coronavirus disease 19 (COVID-19), which is the key reason for
the current COVID-19 pandemic [1]. This virus can spread from one person to
another primarily through the droplets of an infected person. Since the first
major outbreak different variants of SARS-CoV-2 have been identified, which
makes the journey towards controlling the pandemic more challenging.

Even the most developed countries like the United States of America, the
United Kingdom, Italy, Australia and Germany are heavily affected by COVID-19.
The COVID-19 pandemic has changed the world’s economy upside down, putting
most of the countries in recession [2]. In addition, COVID-19 profound various
societal challenges, causing serious psychological disorders like depression.
The consequences of COVID-19 pandemic, such as increased suicidal rates, are
expected to stay longer than the actual pandemic period [3]. Hence, in order
to save the world population from these existing and future challenges, it is
important that the COVID-19 has to be effectively handled.

Despite the efforts made towards inventing vaccines to control SARS-CoV-2,
several computed aided techniques have been proposed for modelling and
forecasting the spread pattern [4]. Further, the machine learning-based
COVID-19 recognition techniques play a vital role in the timely diagnosis of
patients. This helps to provide prompt medication and largely prevent the
virus from the spread. The majority of the existing COVID-19 recognition
algorithms used multimodal inputs [5], pre-processing [6] and complex models
[7] to obtain benchmark performances. The state-of-the-art deep networks are
however well known for image classification tasks with consistent results.
More importantly, deep networks are capable to be trained end-to-end, where
the input data can be given naturally. Hence, in this work, a set of popular
deep networks are trained to effectively detect COVID-19 from chest X-ray
images. The key contributions of this paper are as follows.

  * •

The state-of-the-art deep networks, such as VGG16, VGG19, DenseNet121,
DenseNet201, InceptionV3, ResNet101, ResNet152, Xception, EfficientNetB0,
EfficientNetB7, NASNetLarge, NASNetMobile, MobileNetV2, MobileNetV3 Small and
MobileNetV3 Large are trained on a chest X-ray dataset for effective
recognition of COVID-19 disease.

  * •

A summary of the comparative results is analysed to evaluate the feasibility
of each deep learning model.

Figure 1: The standard training and testing procedure employed.

The remaining sections of the paper are structures into three sections. The
remainder of this paper is organized into four sections. A set of literature
for COVID-19 recognition via chest X-ray images is comprehensively reviewed in
Section II. In Section III, the results obtained for all of the state-of-the-
art deep networks are compared and analysed. This conclusion of the paper is
presented in Section IV.

##  II Related Work

Deep learning-based techniques have significantly improved the performance of
various image classification tasks, ranging from emotion recognition [8] to
agriculture [9]. In the last two years, multiple approaches have been proposed
for COVID-19 recognition. Some of the closely related works are reviewed in
this section. However, authors are directed to read the surveys on the machine
and deep learning-based COVID-19 infection recognition provided in [10] and
[11].

In one of the early works, a novel deep convolutional neural network (CNN)
model called CoroNet is proposed for automatic detection of COVID-19 infection
with chest X-ray images [12]. The experimental results proved that the
proposed CoroNet model achieved promising results even in small datasets.
Authors also claim that the performance of the CoroNet can further be improved
with additional training data. In [13], a deep learning-based framework
(COVIDz) is proposed to systematically predict the existence of COVID-19. The
presented COVIDz framework yielded a classification accuracy of 99.64% and an
F-score of 99.20%. Noor and Kareem used a deep CNN to build a COVID-19
diagnosis approach that showed over 94% classification accuracies in three
different tasks [14]. Meanwhile, the attention-based deep neural networks also
attained benchmark performances in COVID-19 detection from X-ray images [15].

In another recent work, a deep CNN based architecture is proposed for
automated COVID-19 detection [16]. The abnormalities of the samples like low-
resolution images are enhanced by a well-structured data augmentation
technique. In [17], a transfer learning mechanism is adapted to implement the
proposed approach. Ahsan et. al. [18] designed a COVID-19 detection technique
utilizing a deep CNN. In their study, various deep networks are considered as
the backbone. A machine learning-based analytical framework also demonstrated
better results in COVID-19 detection [19]. A deep CNN model with chest X-ray
images taken from portable devices is used to effectively detect the COVID-19
[20]. In this work, the characteristics that are common to COVID-19 and other
diseases are differentiated using a joint response approach. An integrated
stacking InstaCovNet-19 with multiple pre-processing techniques are presented
to perform COVID-19 patient classification [21].

According to the literature, most of the existing works use multiple model
data, complex deep network architecture or heavy pre-processing. Motivated by
this, a comparative analysis of the state-of-the-art for COVID-19 recognition
is conducted and discussed in the next section.

Figure 2: The standard training and testing procedure employed.

##  III Comparative Analysis

In this section, the details about the state-of-the-art deep networks
compared, the dataset used, implementation information with standard training
and testing procedure and the results are discussed.

###  III-A State-of-the-art Deep Networks

Various state-of-the-art deep networks are evaluated in this study. The list
of state-of-the-art deep networks that are compared in this study is given
below.

  1. 1.

VGG16 and VGG19 are the earliest and simplest CNN architectures, significantly
increased the depth with very small receptive fields [22]. A set of
convolutional layers followed by three fully connected layers are stacked to
construct both of these deep architectures.

  2. 2.

DenseNet121 and DenseNet201 have introduced a dense connection mechanism,
where each layer of the network is connected to every other layer [23]. In
addition to strengthening the feature propagation, reducing the number of
training parameters and enhancing the feature reuse, both of these networks
also alleviate the gradient vanishing problem.

  3. 3.

InceptionV3 architecture is constructed based on the ideas of multiple
researchers developed over the years [24]. Factorized convolutions and
intensive use of regularization are the keys of the InceptionV3 in effectively
handling the added computational complexity.

  4. 4.

ResNet101 and ResNet152 are capable of attaining higher accuracy and easier to
optimize for image recognition tasks, in comparison to existing state-of-the-
art deep networks [25]. A residual learning process along with appropriately
placed shortcut connections are introduced in these networks.

  5. 5.

Xception was built based on depthwise separable convolution concept [26]. The
depth multiplier is set to 1 for all the depthwise separable convolution
layers. Throughout the architecture, a batch normalization layer is placed
after each traditional convolution and depthwise separable convolution layer.

  6. 6.

EfficientNetB0 and EfficientNetB7 are two prominent network variants in the
EfficientNets family of models. A scaling mechanism proposed in [27] uses a
compound coefficient to uniformly scale the dimensions, such as depth, width
and resolution with a fixed ratio.

  7. 7.

NASNetLarge and NASNetMobile are two NASNet variations that are primarily
designed for general and mobile deployment purposes, respectively [28]. To
design the NASNet models, the best convolutional layers with their parameter
settings are realized through a novel search space. In addition, a new
regularization scheme, namely ScheduledDropPath is also integrated to improve
the generalization capability.

  8. 8.

MobileNetV2, MobileNetV3 Small and MobileNetV3 Large are based on both
depthwise separable convolutions and pointwise convolutions [29]. In
MobileNets, for each input channel, single depthwise convolution filter is
applied before combining the output using pointwise convolution.

###  III-B Chest X-ray Dataset

The chest X-ray image dataset222https://github.com/drkhan107/CoroNet used in
extensive experiments contains four classes, such as COVID-19, Normal,
Pneumonia Bacteria and Pneumonia Viral. Figure 1 shows two samples for each
class available in the dataset. The publicly available version of the dataset
consists of $320$, $445$, $449$ and $424$ image samples for COVID-19, Normal,
Pneumonia Bacteria and Pneumonia Viral classes, respectively. The images
available within this dataset are in different resolutions, which are later
resized to the same dimension during the training process in supporting the
deep networks individually. For instance, images in the dataset are resized to
$224\times 224$ in order to match the input image size of the VGG16 network.

Figure 3: The visual illustration of the spatial support obtained for each
class by the EfficientNetB7 model.

###  III-C Implementation, Training and Testing

All the networks are implemented using the
Tensorflow333https://www.tensorflow.org/ platform and evaluated on Google
Colab. The deep networks are used as defined in TensorFlow Core v2.6.0. A
traditional training and testing procedure is adapted, where 80%, 10% and 10%
samples of the whole dataset are used to train, validate and test the
networks, respectively. Figure 2 shows the overall training and testing
procedure. A stochastic gradient descent (SGD) optimizer is used with a
momentum of 0.9, an initial learning rate of 0.05 and a decay of 0.0001.

TABLE I:  Comparison of state-of-the-art deep networks. Three best-performing models are highlighted.  Deep Network |  Accuracy |  Rank
---|---|---
VGG16 |  0.8040 |  11
VGG19 |  0.8162 |  9
DenseNet121 |  0.8639 |  7
DenseNet201 |  0.8792 |  5
InceptionV3 |  0.8863 |  4
ResNet101 |  0.9037 |  3
ResNet152 |  0.9138 |  2
Xception |  0.8215 |  8
EfficientNetB0 |  0.8769 |  6
EfficientNetB7 |  0.9554 |  1
NASNetLarge |  0.7608 |  14
NASNetMobile |  0.7215 |  15
MobileNetV2 |  0.8147 |  10
MobileNetV3 Small |  0.7628 |  12
MobileNetV3 Large |  0.7635 |  13

###  III-D Results and Discussion

The classification accuracy obtained for fifteen state-of-the-art deep
networks are compared in this research. Table I illustrates the comparison
results, where the deep networks that showed the best performances are
highlighted. As can be seen, the EfficientNetB7 achieved the best results with
95.54% of classification accuracy. The second and third best performances were
shown by both ResNet variants, obtaining slightly more than 90% classification
accuracies. The lightweight networks, such as NASNetMobile, MobileNetV2,
MobileNetV3 Small and MobileNetV3 Large also showed comparable performance in
recognizing COVID-19. Among them, the MobileNetV2 yielded the best accuracy
with 81.47%, followed by MobileNetV3 Large, MobileNetV3 Small and
NASNetMobile. It is interesting to note that the very deep networks like
InceptionV3 and DenseNet201 performed comparably low in COVID-19 recognition,
which could be because of the lack of training data.

Figure 3 illustrates the saliency maps acquired by the best performing
EfficientNetB7 model for one sample taken from COVID-19, normal, pneumonia
bacterial and pneumonia viral classes. Note that the selected images are
picked from the set of correctly classified samples. As can be seen, the
corresponding spatial support attained for each class are clearly
distinguishable.

The confusion matrix generated for the EfficientNetB7 deep network is
presented in Figure 4. The COVID-19 class achieved a slightly lower accuracy
of 94.06%, in comparison to other classes. The majority form the misclassified
COVID-19 samples are confused with the normal class. Amongst all other
classes, Pneumonia Viral achieved the best accuracy of 96.70%. The Normal and
Pneumonia Bacterial classes also reached more than 95% of accuracy. Overall,
the performance manifested all of the classes are at the expected level.

Figure 4: The confusion matrix obtained for the best performed EfficientNetB7
model.

##  IV Conclusion

The global outbreak of COVID-19 has impacted almost every country and its
people. Hence, it is vital to devise an effective and timely way of
recognizing COVID-19. Adapting the superiority of deep learning techniques,
many approaches have been proposed in the past. Many of them are limited due
to integrated pre-processing, complex structures and the use of multiple model
data. Knowing the fact that the existing deep networks are end-to-end
trainable and powerful in extracting visual features, in this paper, a
comprehensive comparative analysis is performed. The results obtained for
fifteen widely-used deep networks are compared and analysed. Comparison
results reveal that the EfficientNetB7 network demonstrated the best
classification accuracy in recognizing COVID-19 with chest X-ray images.
Analysing other COVID-19 datasets could be a potential future work of this
research.

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