# Accretion and Obscuration in Merger-Dominated Luminous Red Quasars

Eilat Glikman,1 Stephanie LaMassa,2 Enrico Piconcelli,3 Luca Zappacosta3 and
Mark Lacy4
1Department of Physics, Middlebury College, Middlebury, VT 05753, USA
2Space Telescope Science Institute, 3700 San Martin Drive, Baltimore MD,
21218, USA
3Osservatorio Astronomico di Roma (INAF), via Frascati 33, 00040 Monte Porzio
Catone (Roma), Italy
4National Radio Astronomy Observatory, Charlottesville, VA, USA E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present an analysis of the X-ray properties 10 luminous, dust-reddened
quasars from the FIRST-2MASS (F2M) survey based on new and archival Chandra
observations. These systems are interpreted to be young, transitional objects
predicted by merger-driven models of quasar/galaxy co-evolution. The sources
have been well-studied from the optical through mid-infrared, have Eddington
ratios above 0.1, and possess high-resolution imaging, most of which shows
disturbed morphologies indicative of a recent or ongoing merger. When combined
with previous X-ray studies of five other F2M red quasars, we find that the
sources, especially those hosted by mergers, have moderate to high column
densities ($N_{H}\simeq 10^{22.5-23.5}$ cm-2) and Eddington ratios high enough
to enable radiation pressure to blow out the obscuring material. We confirm
previous findings that red quasars have dust-to-gas ratios that are
significantly lower than the value for the Milky Way’s interstellar medium,
especially when hosted by a merger. The dust-to-gas ratio for two red quasars
that lack evidence for merging morphology is consistent with the Milky Way and
they do not meet the radiative feedback conditions for blowout. These findings
support the picture of quasar/galaxy co-evolution in which a merger results in
feeding of and feedback from an AGN. We compare the F2M red quasars to other
obscured and reddened quasar populations in the literature, finding that,
although morphological information is lacking, nearly all such samples meet
blowout conditions and exhibit outflow signatures suggestive of winds and
feedback.

###### keywords:

galaxies: active – galaxies: evolution – quasars: general – X-rays: galaxies

††pubyear: 2024††pagerange: Accretion and Obscuration in Merger-Dominated
Luminous Red Quasars–A.2

##  1 Introduction

A complete picture of galaxy evolution must include the growth of supermassive
black holes (SMBHs) at their centres, as evidence suggests a formation and
evolutionary relationship between the two. The ubiquity of SMBHs in the
centres of galaxies (Faber et al., 1997), the tight $M_{BH}-\sigma$ relation
(Gebhardt et al., 2000; Ferrarese & Merritt, 2000), and the contemporaneous
peak in star formation and black hole growth over cosmic history (Hopkins &
Beacom, 2006) all point to an energy exchange, or “feedback”, between the
black holes and their hosts. This feedback from active galactic nuclei (AGN)
is still poorly understood, and may come in the form of radiation, winds,
outflows, and/or jets (Fabian, 2012).

One way to explain these observations is through major galaxy mergers that
induce both SMBH accretion and circumnuclear star-formation, resulting in
large amounts of dust and gas that obscure much of the SMBH’s growth (Sanders
et al., 1988; Hopkins et al., 2006). According to this model, the obscuring
dust is eventually cleared by powerful quasar winds, revealing luminous,
unreddened emission from the quasar. In this scenario dust-reddened (or “red”)
quasars represent a crucial early phase in SMBH/galaxy co-evolution: the
transition from a dust-enshrouded core to a typical, unobscured quasar. In the
context of this picture, the reddened phase represents a key component of SMBH
growth with the potential to reveal the physics of feedback once the quasar
becomes luminous enough to blow away the circumnuclear material.

Recently, samples of heavily reddened quasars have been shown to fit into this
scenario as the long-sought transitioning population (e.g., Banerji et al.,
2012; Tsai et al., 2015; LaMassa et al., 2017). A red quasar sample
constructed from the cross-matching of the Faint Images of the Radio Sky at
Twenty cm (FIRST; Becker et al., 1995) survey to the Two-Micron All-Sky Survey
(2MASS; Skrutskie et al., 2006), applying red optical-to-near infrared colour
cuts, and spectroscopically confirming broad-line (Type 1) sources yielded
$\sim$130 objects that span a broad range of redshifts $(0.1<z<3)$ and
reddenings ($0.1<E(B-V)<1.5$; Glikman et al., 2004, 2007; Urrutia et al.,
2009; Glikman et al., 2012, 2013, hereafter called F2M red quasars). Extensive
observations of F2M red quasars show that they are in a transitional phase of
a merger-driven process: Hubble Space Telescope (HST) images show mergers are
very common ($>80\%$ Urrutia et al., 2008; Glikman et al., 2015); they have
high accretion rates ($L/L_{\rm Edd}\gtrsim 0.3$ Kim et al., 2015); their BH
masses are under-massive compared to their hosts, suggesting they have not
finished growing (Urrutia et al., 2012); and a high fraction of them exhibit
outflows and winds via the presence of blue-shifted broad absorption lines in
low-ionization species (i.e., LoBALS and FeLoBALs make up $>60\%$ of F2M red
quasars compared to 5% in the general quasar population; Urrutia et al., 2009)
indicative of winds and outflows. More recently, integral field spectroscopy
of three F2M red quasars show bi-conal superbubbles in [O iii] emission,
catching the short-lived “break-out” phase (Shen et al., 2023).

One way to determine whether an AGN is in the radiatively-driven “blow-out”
phase is by comparing its Eddington ratio
(${\lambda}_{\mathrm{Edd}}=L/{L}_{\mathrm{Edd}}$) to the hydrogen column
density ($N_{H}$). A study of hard X-ray-selected local ($z<0.05$) AGN showed
that they are either completely obscured, with $\mathrm{log}(\lambda_{\rm
Edd})\lesssim-1.5$ and $N_{H}>10^{22}$ cm-2, or largely unobscured, with
$\mathrm{log}(\lambda_{\rm Edd})\gtrsim-1.5$ and $N_{H}<10^{22}$ cm-2 (Ricci
et al., 2017a). There exist a unique set of conditions whereby an AGN has
sufficiently high $\lambda_{\rm Edd}$ and a not-too-high $N_{H}$ to blow out
the dust and gas (Fabian et al., 2008; Ishibashi et al., 2018). Recently,
Stacey et al. (2022) used ALMA observations to show that reddened quasars with
$E(B-V)>0.5$ reside in this “blow-out” region of $\lambda_{\rm Edd}$ vs.
$N_{H}$ space.

While we have measured black hole masses, Eddington ratios, and reddenings
($E(B-V)$) for all the F2M red quasars, our understanding of their X-ray
properties has been deficient. Twelve F2M quasars were observed with Chandra
in 2004 with $5-10$ ksec exposures (Urrutia et al., 2005). While all of the
sources show absorbed X-ray spectra, the detections were mostly too low-count
(all but one had $<100$ counts) for detailed spectral analysis and the
ancillary data for F2M red quasars had not been obtained making it difficult
to draw conclusions.

More recently, we obtained high-quality X-ray spectra of four F2M red quasars
with XMM-Newton and NuSTAR, as well as archival Chandra data (LaMassa et al.,
2016b; Glikman et al., 2017, hereafter, L16 and G17, respectively); three of
these have HST images showing merging hosts. We found that these three sources
fall squarely in the blowout region of the the $\lambda_{\rm Edd}$ vs. $N_{H}$
diagram (Glikman, 2017). The source that lies outside of the blowout region
lacks morphological information, and has a dust-to-gas ratio consistent with
the Galactic value, possibly because it is obscured by dust lanes in its host
galaxy. In addition, a fifth F2M red quasar (F2M J0915) has a 3.2 ksec Chandra
observation analyzed in Urrutia et al. (2005) as well as high-spatial-
resolution imaging revealing a merging host (Urrutia et al., 2008). We list
the properties of these F2M red quasars in Table 1 as a reference for the
remainder of the paper.

Table 1: Properties of Previously Studied F2M Red Quasars Name | R.A. | Decl. | Redshift | $E(B-V)$ | $\log L_{\rm bol}^{\dagger}$ | $L/L_{\rm Edd}^{\ddagger}$ | $\log{N_{H}}$ | Merger? | Ref
---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  | (mag) | (erg s-1) |  | (cm-2) |  |
F2M J0830 | 08:30:11.12 | +37:59:51.8 | 0.414 | $0.71\pm 0.01$ | $46.20\pm 0.01$ | $0.4\pm 0.1$ | $22.32\pm 0.04$ | Y | L16
F2M J0915 | 09:15:01.70 | +24:18:12.2 | 0.842 | $0.73\pm 0.02$ | $47.696\pm 0.006$ | $0.94\pm 0.48$ | $22.8^{+0.2}_{-0.4}$ | Y | Urrutia et al. (2005)
F2M J1113 | 11:13:54.67 | +12:44:38.9 | 0.681 | $1.26\pm 0.01$ | $47.475\pm 0.006$ | $2.29\pm 0.42$ | $23.1\pm 0.1$ | Y | G17
F2M J1227 | 12:27:49.15 | +32:14:59.0 | 0.137 | $0.828\pm 0.003$ | $45.545\pm 0.005$ | $0.8\pm 0.2$ | $21.5\pm 0.1$ | ? | L16
F2M J1656 | 16:56:47.11 | +38:21:36.7 | 0.732 | $0.519\pm 0.004$ | $46.81\pm 0.01$ | $0.76\pm 0.18$ | $23.0\pm 0.1$ | Y | G17
† Bolometric luminosities were determined by applying a bolometric correction of 7.6 (Richards et al., 2006) to the 6$\mu$m luminosity, |
which was determined by interpolating their WISE mid-infrared luminosities in the rest-frame. |
‡ As reported in Kim et al. (2015) except for F2M J0830 and F2M J1227 which were obtained from G17. |

X-rays give the best measure of an AGN’s true underlying accretion luminosity,
because they originate close to the black hole and penetrate gas and dust for
all but the most obscured AGN ($N_{H}<10^{24}$ cm-2 and $E<10$ keV). Besides
showing evidence for active radiative feedback, the studies in L16 and G17
found that the three merger-hosted sources were best fit by an absorbed power-
law model with a small fraction of the incident emission being leaked or
scattered back into the line-of-sight (we refer to this as the ‘scattering
fraction’; here, $f_{\rm scatt}=1-7\%$) and moderate line-of-sight extinction
($N_{H}=10^{22-23}$ cm-2). Intriguingly, self-consistent physically-motivated
model fitting with MYTorus (Murphy & Yaqoob, 2009) exposes the presence of
globally distributed gas suggesting a more complex environment than a simple
absorber along the line-of-sight.

In this paper we present X-ray observations for 10 additional F2M red quasars,
which doubles the initial sample to more robustly verify the previous results.
All the sources have high resolution imaging which enable us to tie host
galaxy morphology to X-ray properties, including their potential for existing
in a blowout phase. When optical magnitudes are discussed, we specify whether
they are on the AB or Vega system via a subscript. Uncertainties on X-ray
parameters are reported as 90% confidence limits. Throughout this work, we
adopt the concordance $\Lambda$CDM cosmology with $H_{0}=70$ km s-1 Mpc-1,
$\Omega_{M}=0.3$, and $\Omega_{\Lambda}=0.7$.

##  2 The Sample and Observations

###  2.1 Source Selection and Characteristics

Of the $\sim 130$ F2M red quasars, all have optical and/or near-infrared
spectroscopy, as well as photometric coverage from ultraviolet to mid-infrared
wavelengths and 27 have HST11124 red quasars have targeted HST imaging from
Urrutia et al. (2008, 13 objects) and Glikman et al. (2015, 11 objects), one
red quasar was targeted in a snapshot HST program (Marble et al., 2003), and
another was serendipitously located in the background of another HST snapshot
program (GO-11604). or other high resolution imaging (either targeted or
serendipitous). For this study, we assembled a list of F2M red quasars that
have the following observations in hand: (1) high resolution imaging from HST
or other imaging; (2) optical and/or near-infrared spectra with at least one
broad emission line enabling an estimate of a black-hole mass ($M_{BH}$). We
further required that our targets yield at least 70 counts (see §2.2) in $<20$
ksec Chandra observation and identified eight sources that obeyed these
criteria. In addition, two sources were found in the background of archival
Chandra observations, with one source appearing in two different datasets. Our
sample, therefore consists of 10 F2M red quasars with new or archival Chandra
observations.

Figure 1 shows the HST image cutouts for these sources, as well as for F2M
J0915. The images were obtained from the archives, except for F2M J1531 whose
point spread function (PSF) subtracted WFC3/IR F160W image from Glikman et al.
(2015) is reproduced here. The morphology of F2M J1106 is based on integral
field spectroscopy (IFS) with the GMOS instrument showing bi-conal bubbles in
the [O iii] (see Shen et al., 2023). Images of the remaining sources listed in
Table 1 are shown in L16 and G17.

Figure 1:  Image cutouts of 9 the 10 F2M red quasars presented in this work,
excluding F2M J1106, but including F2M J0915 which was not presented in the
analysis of L16 or G17. All data are from HST ACS camera with the F814W
filter, except for F2M J1531 which shows the PSF-subtracted image from Glikman
et al. (2015) from the WFC3/IR camera with the F160W filter. The source for
each image is listed in the final column of Table 3. All images are
$7\arcsec\times 7\arcsec$ except F2M J1324, which is $8\arcsec\times 8\arcsec$
due to it having the lowest redshift ($z=0.205$) and larger angular size, and
F2M J1531, which is $8\arcsec\times 8\arcsec$.

The fifth column of Tables 1 and 2 lists the reddening of each quasar
parametrized by the color excess, $E(B-V)$, which we determined by performing
a linear fit in log space to the ratio of each red quasar spectrum,
$f(\lambda)$, to an unreddened quasar template spectrum, i.e.

$\log{\left[\frac{f(\lambda)}{f_{0}(\lambda)}\right]}=-\frac{k(\lambda)E(B-V)}{1.086}.$
(1)

Here, $f_{0}(\lambda)$ is the optical-to-near-infrared quasar composite
template from Glikman et al. (2006) and $k(\lambda)$ is the Small Magellanic
Cloud (SMC) dust extinction law from Gordon & Clayton (1998). Although
$E(B-V)$ values were already in-hand, we recomputed them for this work as
newer spectra had been obtained for some sources which, in some cases,
broadened the wavelength coverage or, in others, improved the signal-to-noise.
The uncertainties on $E(B-V)$ were computed by heavily smoothing and
perturbing the original spectrum by its own error array and re-fitting it to
determine $E(B-V)$ 1000 times. The reported $E(B-V)$ uncertainty is then the
standard deviation of that $E(B-V)$ distribution.

We determine the black hole masses, $M_{BH}$, from a broad emission line in
the quasars’ spectra. Eight sources were analyzed using their broad emission
line widths, either from H$\beta$ or H$\alpha$, using the line with the
highest signal-to-noise ratio. We performed multi-component Gaussian fits to
the lines, including narrow emission line components combined with a broad
component. Figure 2 shows these line fits.

We use the established relations from Shen & Liu (2012),

$\log\bigg{(}\frac{M_{\rm
BH,vir}}{M_{\odot}}\bigg{)}=a+b\log\bigg{(}\frac{L_{5100}}{10^{44}\rm
erg/s}\bigg{)}+c\log\bigg{(}\frac{v_{\rm FWHM}}{\rm km/s}\bigg{)},$ (2)

to compute $M_{BH}$ for each line species, employing the full-width at half
maximum (FWHM) in km s-1 for the velocity term. When the line used was
H$\alpha$, we adopted the values $a=0.774$, $b=0.520$, $c=2.06$ for sources
with $L_{5100}<10^{45.4}$ erg s-1 and $a=1.390$, $b=0.555$, $c=1.873$ for for
sources with $L_{5100}>10^{45.4}$ erg s-1. For $M_{BH}$ estimates based on
H$\beta$, we adopted the values $a=0.895$, $b=0.520$, $c=2.00$, which apply to
sources with $L_{5100}<10^{45.4}$, erg s-1 (the $a$, $b$, $c$ coefficients are
from the calibration of Assef et al., 2011).

Two sources, F2M J0825 and F2M J1532, have only narrow H$\beta$ lines visible
in their optical spectrum, likely because the broad component has experienced
significant extinction from dust. The H$\alpha$ line is shifted into a noisy
part of the optical and near-infrared spectra precluding our ability to
perform reliable Gaussian fitting. Both sources exhibit broad Pa$\beta$
emission in their near-infrared spectrum and their $M_{BH}$ values were
computed in Kim et al. (2015) along with 14 other red quasars using a single-
epoch relation derived by Kim et al. (2010) for Paschen lines,

$\log\bigg{(}\frac{M_{\rm
BH,vir}}{M_{\odot}}\bigg{)}=a+b\log\bigg{(}\frac{L_{{\rm Pa}\beta}}{10^{42}\rm
erg/s}\bigg{)}+c\log\bigg{(}\frac{v_{\rm FWHM}}{1000\rm km/s}\bigg{)},$ (3)

where $a=7.04$, $b=0.48$, and $c=2$. Kim et al. (2010) calibrated this
relation using near-infrared spectra of unreddened quasars and found that they
agree with the Balmer-line-based relations to within 0.18-0.24 dex.

In addition to line widths, the $M_{BH}$ relations require a luminosity at a
particular wavelength to estimate the radial distance to the broad line
region. The bolometric luminosity listed in Tables 1 and 2 is determined by
applying a bolometric correction of 7.6 to the 6$\mu$m luminosity based on the
mean quasar spectral energy distribution (SED) in Richards et al. (2006).
Because the luminosities in the $M_{BH}$ relations are at optical and UV
wavelengths, which are affected by reddening in these quasars, we interpolate
their Wide-field Infrared Survey Explorer (AllWISE; Wright et al., 2010;
Mainzer et al., 2011) mid-infrared fluxes to estimate their rest-frame 6$\mu$m
luminosity, $L_{6\mu{\rm m}}$, and scale it to the optical flux using a ratio
of the bolometric corrections for 6$\mu$m (7.6) and 5100Å (10) for the
Richards et al. (2006) mean quasar spectral energy distribution (SED). To
determine the uncertainty on $L_{6\mu{\rm m}}$, each SED is perturbed by its
photometric errors, drawing from a Gaussian distribution, to generate 1000
SEDs which we interpolate to measure $L_{6\mu{\rm m}}$. The reported
uncertainty is then the standard deviation of the $L_{6\mu{\rm m}}$
distribution. $L_{6\mu{\rm m}}$ is also used to find the bolometric luminosity
($L_{\rm bol}$) of the quasars, applying a bolometric correction factor of 7.6
derived from the same SED. When combined with their bolometric luminosities,
we are able to compute an Eddington ratio ($\lambda_{\rm Edd}$) for each
source. Table 2 lists the quasars, their positions, redshifts, and $E(B-V)$.
The table also lists the source of the imaging, $M_{BH}$, $L_{\rm bol}$, and
$\lambda_{\rm Edd}$.

Table 2: Properties of Newly Added F2M Red Quasars Name | R.A. | Decl. | Redshift | $E(B-V)$ | $M_{BH}$ | Line | $L/L_{\rm Edd}$ | $\log{L_{\rm bol}}^{\sharp}$ | Merger? | Image Ref
---|---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  | (mag) | ($10^{8}M_{\odot}$) |  |  | (erg s-1) |  |
F2M J0825a | 08:25:02.00 | +47:16:52.0 | 0.804 | $0.68\pm 0.01$ | 12.25$\pm$2.98 | Pa$\beta$ | $0.67\pm 0.18$ | $47.353\pm 0.007$ | Y | U08
F2M J0834a | 08:34:07.00 | +35:06:01.8 | 0.470 | $0.91\pm 0.02$ | 31$\pm$10† | H$\alpha$ | $0.04\pm 0.01$ | $46.18\pm 0.01$ | N | U08
F2M J1106a | 11:06:48.30 | +48:07:12.3 | 0.435 | $0.443\pm 0.002$ | 8.2$\pm$2.3 | H$\alpha$ | $0.52\pm 0.15$ | $46.734\pm 0.005$ | ? | S23
F2M J1118a | 11:18:11.10 |  $-$00:33:41.9 | 0.686 | $0.61\pm 0.01$ | 6.4$\pm$1.8. | H$\alpha$ | $1.1\pm 0.3$ | $46.943\pm 0.008$ | Y | U08
F2M J1151a | 11:51:24.10 | +53:59:57.4 | 0.780 | $0.67\pm 0.01$ | 5.86$\pm$0.04 | H$\beta$ | $0.50\pm 0.02$ | $46.57\pm 0.02$ | N | U08
F2M J1324a | 13:24:19.90 | +05:37:05.0 | 0.205 | $0.326\pm 0.003$ | 5.5$\pm$1.5‡ | H$\alpha$ | $0.76\pm 0.21$ | $46.718\pm 0.005$ | Y | HST archive
F2M J1507a | 15:07:18.10 | +31:29:42.3 | 0.988 | $0.644\pm 0.003$ | 4.6$\pm$1.3⋆ | H$\alpha$ | $1.48\pm 0.42$ | $46.93\pm 0.01$ | Y | U08
F2M J1531a | 15:31:50.47 | +24:23:17.6 | 2.287 | $0.311\pm 0.004$ | 80$\pm$22. | H$\alpha$ | $1.61\pm 0.46$ | $48.21\pm 0.02$ | Y | G15
F2M J1532a | 15:32:33.19 | +24:15:26.8 | 0.564 | $0.68\pm 0.03$ | 6.12$\pm$4.87 | Pa$\beta$ | $0.29\pm 0.27$ | $46.586\pm 0.007$ | Y | U08
F2M J1715a | 17:15:59.80 | +28:07:16.8 | 0.523 | $0.786\pm 0.003$ | 8.7$\pm$2.4 | H$\alpha$ | $0.33\pm 0.09$ | $46.553\pm 0.008$ | N | M03
♯ Bolometric luminosities were determined by applying a bolometric correction
of 7.6 (Richards et al., 2006) to the 6$\mu$m luminosity which was determined
by interpolating the WISE mid-infrared luminosities in the rest-frame.
† This object has a double-peaked emission line shape, resulting in a likely
over-estimated $M_{BH}$
‡ This source was fit with multiple Gaussian components to account for the
presence of narrow lines.
⋆ This source has a blue-shifted broad line, which we do not use in our
estimate of $M_{BH}$.(see §A.1).
a $M_{BH}$ and $L/L_{\rm Edd}$ were determined in Kim et al. (2015).
Comments – M03 = Marble et al. (2003); U08 = Urrutia et al. (2008); S23 = Shen
et al. (2023); U12 = Urrutia et al. (2012);G15 = Glikman et al. (2015)

Figure 2:  Gaussian fitting to emission lines for eight quasars in our sample
that lack $M_{BH}$ from Kim et al. (2015). The black line shows the observed
flux against rest wavelength. The blue line is the best-fit model to the line
profile. The sloped dotted red line is the continuum portion of the best-fit
model. In most cases, a single Gaussian sufficiently fits the data. The three
exceptions, from left to right, are: (1) F2M J1151, whose [O iii] line doublet
is fit together with H$\beta$. (2) F2M J1324, whose H$\alpha$ line is
decomposed into a broad and narrow components and fit along with the [N ii]
nitrogen doublet. In this case the narrow line width is determined by fitting
to the [S ii] doublet shown in green. And, (3) F2M J1507, whose broad
H$\alpha$ line is double-peaked with a blue-shifted component separated by 91Å
(see Appendix A.1 for additional discussion of this source).

###  2.2 Chandra Observations

We obtained Chandra observations in Cycle 21 of eight red quasars that obeyed
our selection requirements outlined in Section 2.1 that had no archival X-ray
data (GO 21700216, PI: Glikman). We designed our observing strategy aiming for
70 counts in the Chandra energy range, which we estimated using the
interpolated 6$\mu$m luminosity and the $L_{X}-L_{IR}$ relation, modified to
reflect the trends seen for red quasars in L16 and G17 (i.e., $\sim 1$ dex
below the Chen et al. 2017 relation which accounts for any intrinsic $N_{H}$;
see §4.2), imposing a 5 ksec minimum on the brighter sources. Table 3 lists
the details of the Chandra observations for the eight sources as well as the
two sources with archival observations. Given that the scatter in the
$L_{X}-L_{IR}$ relation is on a logarithmic scale, while photon detection
rates are linear, our total counts vary significantly from the expected 70.

We processed the data with the CIAO v4.15, with CALDB v4.10.4 (Fruscione et
al., 2006), using the chandra_repro task to produce a filtered events file,
removing periods of anomalously high background. For all but one of the
observations, a spectrum was extracted using a 5″ radius aperture around the
object using the CIAO tool specextract, with the background extracted from an
annulus around the quasar with inner radius 10″ and outer radius 35″. F2M
J1532 was present in two archival observations. One of the archival
observations had F2M J1532 near the edge of the I2 chip on the ACIS-I detector
where the PSF is significantly larger; we use a 35″ radius aperture around the
source and an offset circular aperture with a 120″ radius far from any sources
for the background. The total net counts detected are listed in Table 3 as
reported by the CIAO task dmlist.

Table 3: Summary of Chandra Observations Name | ObsID | Date | $N_{\rm H,Galactic}$ | Net Exposure Time | Net Counts
---|---|---|---|---|---
|  |  | (1020 cm-2) | (ksec) | (0.5 - 7 keV cnts)
F2M J0825 | 22570 | 2019 December 20 | 4.15 | 9.94 | 218$\pm$15
F2M J0834 | 22571 | 2019 December 15 | 4.03 | 9.94 | 4$\pm$2
F2M J1106 | 22572 | 2019 October 24 | 1.38 | 5.99 | 2$\pm$2
F2M J1118 | 22573 | 2020 January 21 | 4.43 | 11.91 | 50$\pm$7
F2M J1151 | 22574 | 2020 August 7 | 1.33 | 17.83 | 22$\pm$5
F2M J1324 | 22575 | 2020 January 21 | 2.32 | 5.0 | 7$\pm$3
F2M J1507 | 22576 | 2019 November 9 | 1.66 | 19.80 | 70$\pm$9
F2M J1531 | 3336 | 2002 September 25 | 3.61 | 5.06 | 1$\pm$1
F2M J1532 |  3138† | 2001 April 30 | 4.14 | 47.13 | 441$\pm$24
… | 3338 | 2002 July 2 | … | 4.90 | 57$\pm$8
F2M J1715 | 22577 | 2019 October 5 | 3.79 | 8.95 | 255$\pm$16
† Due to being far off-axis, this source was extracted from a 35″aperture and
a nearby 120″-radius circular aperture for the background.

##  3 X-ray fitting

###  3.1 Basic fits

We perform spectral analysis only on sources with $>50$ counts. Three sources
are well detected with $>100$ counts which we grouped by a minimum of 5 counts
per bin. Another two sources have between 50 and 100 counts, which we group by
2 counts per bin. We use the X-ray fitting software XSpec v12.13.0 (Arnaud,
1996) to model these sources. We use the Cash statistics (C-stat; Cash, 1979)
with direct background subtraction (Wachter et al., 1979).

We began by fitting a simple power-law model,

${\tt phabs*zpowerlw},$ (4)

allowing only absorption from gas in the Milky Way (phabs). Table 3 lists the
Galactic hydrogen column density, determined using the colden CIAO task, which
we freeze in all our fits. Given that red quasars experience absorption at
optical wavelengths, we further fit an absorbed power-law model,

${\tt phabs*zphabs*zpowerlw},$ (5)

with absorption occurring both at the source (zphabs) and in the Milky Way to
look for potential intrinsic obscuration in the source. Finally, because the
previous analyses of the X-ray spectra of red quasars revealed an excess of
soft X-ray flux below 2 keV suggesting that there may be scattered or leaked
light at lower energies in excess of the absorbed primary continuum (; ), we
fit a double-absorbed power law with the same photon index for both
components,

${\tt phabs*(zpowerlw+zphabs*zpowerlw)}.$ (6)

We use an F-test to decide whether the additional components significantly
improves the fit with a probability of $>95\%$. We report in Table 4 the
fitted parameters for these sources, indicating in the second column the model
equation used in the best fit.

###  3.2 Complex fits

For one source, F2M 1507, there appears to be a reduction in flux around $4-5$
keV, which may be due to blue-shifted absorption from an outflow. We discuss
the unusual spectral properties and perform more detailed fitting of this
object to account for this absorption in Appendix A.1.

In another source, F2M 1532, we noted the presence of an Fe K$\alpha$ line
suggestive of reflection off a distant medium. While such emission is
typically seen in Type 2 AGN, where the reflection occurs off of the obscuring
torus, it has been seen in at least one red quasar (F2M 0830; Piconcelli et
al., 2010; LaMassa et al., 2016b), where the scattering may be due to clouds
farther out from the nucleus. To address such scenarios, we turn to the
MYTorus model of Murphy & Yaqoob (2009) which solved the radiative transfer of
X-rays from an AGN including scattering off of a torus, line-of-sight
absorption, as well as leakage or scattered light. In XSpec, the model is
defined similar to Eqn 6:

$C\times{\tt phabs}\times[{\tt zpowerlw}\times{\tt
MYTorusZ(N_{H,Z},\theta_{\rm obs},E)}\\\ +A_{S}\times{\tt
MYTorusS(}\Gamma\tt{,N_{H,S},\theta_{\rm obs},E)}\\\ +A_{L}\times{\tt
MYTorusL(}\Gamma\tt{,N_{H,S},\theta_{\rm obs},E)}\\\ +f_{\rm scatt}\times{\tt
zpowerlw}].\\\ $ (7)

where E is the observed energy and MYTorusZ, MYTorusS, and MYTorusL are tables
that contain pre-calculated parameters derived via Monte Carlo calculations
that take into account the reprocessing of the intrinsic AGN continuum in a
toroidal structure for a range of column densities. MYTorusZ is the so-called
‘zeroth-order spectrum’, and represents the intrinsic continuum that makes it
through any absorbing or scattering medium along the line-of-sight
(mytorus_Ezero_v00.fits). MYTorusS tabulates Compton-scattered emission that
is added to the zeroth-order spectrum (mytorus_scatteredH500_v00.fits).
MYTorusL provides fluorescent line emission that is also added to the zeroth-
order spectrum (mytl_V000010nEp000H500_v00.fits, where H200 refers to the
termination energy of the model of 200 keV). This model set up is the same as
previously used for the analysis of F2M red quasars (; ) as well as 3C 223,
whose complex X-ray spectrum has characteristics similar to F2M J1532 (LaMassa
et al., 2023). All three MYTorus components are needed in order to preserve
the self-consistency of the model. We discuss the detailed fitting of F2M
J1532 in Appendix A.2.

We report the results of these complex fits in A.1 and A.2. However, since the
essential parameters ($\Gamma$, $N_{H}$, $f_{\rm scatt}$) used in the
subsequent analysis are similar to the phenomenological results, we do not use
the complex fitted parameters in the subsequent analysis.

Table 4: Best fit parameters for high count sources Name | Model | $\Gamma$ | $\log{N_{H}}$ | $f_{\rm scatt}$ | C-stat | HR
---|---|---|---|---|---|---
| Eqn. |  | (cm-2) | (%) | (DOF) |
F2M J0825 | 2 | $2.38^{+0.57}_{-0.54}$ | $22.78^{+0.17}_{-0.24}$ | … | 44.49 (36) | 0.19
F2M J1118 | 2 | $2.18^{+1.18}_{-0.99}$ | $22.45^{+0.36}_{-1.85}$ | … | 10.96 (22) | $-0.06$
F2M J1507 | 3 |  $1.8$♯ | $23.5\pm 0.4$ | 16 | 28.29 (27) | 0.31
F2M J1532† | 3 | $1.3\pm 0.5$ | $22.90^{+0.19}_{-0.33}$ | 11 | 113.48 (120) | 0.44,0.38‡
F2M J1715 | 1 | $1.57\pm 0.21$ | … | … | 57.72 (42) | $-0.08$
♯ The photon index for this fit was fixed due to the small number of bins.
(See §A.1 for a more complex modeling approach).
†This source was fit jointly with both observations listed in Table 3.
‡ The HRs were computed separately for each of the observations listed in
Table 3, with the longer observation (ObsID 3138) listed first.

Figure 3: Best model fits to the X-ray spectra for counts in the energy range
0.5 – 7 keV, as described in Table 4. Data are shown as points with error
bars. The solid lines represent the best-fit model with dotted lines
representing the individual components of a partially-covered model (Eqn. 6),
when applicable. The bottom panels of each figure show the counts-to-model
ratios. For F2M J1532, the black and red points represent the two archival
data sets used for the fitting (ObsID 3138 and ObsID 3338, respectively). The
best fit models are coloured correspondingly.

###  3.3 Hardness ratios in the low count regime

For the three sources with $\gtrsim 5$ and $\lesssim 50$ counts – an
insufficient amount for spectral modeling – we instead report hardness ratios
(HRs), which are a meaningful proxy for X-ray absorption. The HR is defined by
comparing the net counts in the hard ($H$) and soft ($S$) bands, defined as
$0.5-2$ keV and $2-7$ keV in the observed frame, respectively, as appropriate
for Chandra’s energy response, by the expression $(H-S)/(H+S)$. We determine
these counts via the CIAO command dmcopy which filters the events file to
create an image with just the photons in each energy band. We then apply the
same source and background regions to measure the source counts using the CIAO
tool dmextract.

Given that we are in this low-count regime, we employ the Bayesian Estimation
of Hardness Ratios (BEHR; Park et al., 2006) code which determines HRs,
properly handling uncertainties in the Poisson limit, including non-
detections. We report in Table 5 the hard and soft counts as well as the mode
of the HR determined by BEHR. The stated uncertainties represent the lower and
upper bounds reported by BEHR.

Assuming an absorbed power-law model for these red quasars (Eqn. 5) and fixing
the power-law index to $\Gamma=1.8$, we can crudely approximate the column
density responsible for the measured HR. Following a similar approach
described in Martocchia et al. (2017), we simulate such a spectrum with the
WebPIMMS interface222https://cxc.harvard.edu/toolkit/pimms.jsp setting the
appropriate Cycle of the observations, providing the soft count rate for each
quasar, varying the intrinsic $N_{H}$, and computing the HR from the predicted
hard count rate until the lower bound reported by BEHR is reached. We then
regard the $N_{H}$ value from the simulated spectrum as representing a lower-
limit for the absorption. We report these values in Table 5 as well. We note
that the $N_{H}$ values derived from HRs are highly simplified, as they
neglect scattering or leakage of X-ray photons (e.g., Eqn. 6) and assume a
fixed power-law continuum, $\Gamma$.

Because they are computed in the observed band, HRs depend on redshift, with
the strongest dependence occurring for moderately absorbed sources
($10^{22}<N_{H}<10^{23}$ cm-2) at $z<1$ (LaMassa et al., 2016a) which is where
all the quasars with computed HRs in this paper lie. None the less, in all
cases, HRs $\gtrsim 0$ imply $N_{H}\gtrsim 10^{22}$ cm-2. Mindful of these
considerations, we compare these values to HRs measured in other red quasar
samples.

Glikman et al. (2018) surveyed the $270$ deg2 equatorial region known as SDSS
Stripe 82 (Frieman et al., 2008) which contains a wealth of multi-wavelength
ancillary data. Using near-to-mid infrared selection to a relatively shallow
flux limit of 20 mJy at 22$~{}\mu$m, they identified 21 red QSOs, most lacking
a radio detection in FIRST but with otherwise similar characteristics as the
F2M red quasars. Four red QSOs in that study had X-ray detections that allowed
for HR measurements. Their redshifts span $z=0.2$ to $z=0.83$ and HR $=-0.085$
to HR $=0.863$, with the $z=0.200$ object having HR = 0.792, thus placing them
all in the moderately absorbed ($N_{H}>10^{22}$ cm-2) regime.

In an X-ray selected red QSO sample over Stripe 82, reaching significantly
fainter sources (including SDSS drop-outs) and thus higher redshifts up to
$z=2.5$, LaMassa et al. (2017) find 12 sources displaying features consistent
with the evolutionary paradigm proposed for the F2M red quasars. LaMassa et
al. (2017) measure a range of HRs and, applying a similar translation between
HR and $N_{H}$, find that half have $N_{H}>10^{22}$ cm-2 with three sources
consistent with no absorption. The same caveats about soft excess due to
scattering and leakage apply here as well such that higher-count X-ray spectra
may reveal more complex physics than a simple absorbed power law.

Table 5: Hardness ratios and absorption in low-count sources Name | Net Soft | Net Hard | HR | $\log(N_{H})$
---|---|---|---|---
| (counts) | (counts) |  | (cm-2)
F2M J1106 | $<0.07$ | $2.33\pm 1.74$ | $0.99_{-0.39}^{+0.01}$ | $>22.9$
F2M J1151 | $5.91\pm 2.65$ | $16.31\pm 4.25$ | $0.49_{-0.21}^{+0.19}$ | $>22.8$
F2M J1324 | $2.69\pm 1.73$ | $4.44\pm 2.24$ | $0.29\pm 0.38$ | 21.7 (22.4)†
† This source’s lower and upper bound spanned a very broad range; we provide
in parentheses the $N_{H}$ corresponding to the mode value.

###  3.4 Upper limits for undetected sources

Two sources, F2M J0834 and F2M J1531, have counts consistent with non-
detections. For these sources, we follow the CIAO thread for calculating
source count rates and model-independent fluxes. We compute the flux over the
full energy range using the task srcflux modeling the flux as being absorbed
by Milky Way gas (phabs). We note that F2M J1531 is the only high redshift
source in this sample, having $z=2.287$ while the rest are all at $z<1$, and
is thus the only one with imaging from Glikman et al. (2015). Therefore,
although its morphology shows evidence of a merger, its heterogeneous imaging
aspects do not impact the results presented in Section 4.

Having extracted flux information from all ten sources, we present the soft
(0.5–2 keV), hard (2–10 keV), and full (0.5–10 keV) X-ray fluxes in Table
6333Although the hard band was defined as $2-7$ keV when computing HRs, we
define the hard band as $2-10$ keV when reporting fluxes and luminosities so
we can compare them with established X-ray relations in the literature that
use that band definition.. We also compute the X-ray luminosities in the 2-10
keV band, which are used to compare with other emission diagnostics in Section
4. For objects with sufficient counts to enable spectral fitting (i.e., those
listed in Table 4) we measure and report the observed luminosity using the
best-fit model; we omit Milky Way absorption in this calculation. We then also
report an absorption-corrected luminosity by defining a simple zpow model with
the best-fit power-law index ($\Gamma$) and its normalization. The
uncertainties on the luminosity are derived from the uncertainty on the power-
law normalization. For the low count objects (i.e., those listed in Table 5),
we determine their luminosities assuming a power-law spectrum (zpow) with an
index of $\Gamma=1.8$. We normalize this model based on a fit to the low count
data using the model in Eqn 5, and derive the uncertainties on the luminosity
from the uncertainties on the power-law normalization in this model. Given
that $N_{H}$ for these sources was estimated from the HRs, which are already
uncertain, we do not compute a luminosity from the observed data. We do not
compute a luminosity for the two sources that we deem to be undetected and for
which we report upper limits to their fluxes. Table 6 also reports the rest-
frame absorption-corrected 2-10 keV luminosities as well as their rest-frame
$6\mu$m luminosities, which are determined by interpolating between the WISE
photometric bands, as described in Section 2.1.

Table 6: Observed X-ray Fluxes Name | $F_{0.5-2~{}{\rm keV}}$ | $F_{2-10~{}{\rm keV}}$ | $F_{0.5-10~{}{\rm keV}}$ | $\log L_{2-10~{}{\rm keV,int}}$ | $\log L_{6~{}\mu{\rm m}}$
---|---|---|---|---|---
| ($10^{-14}$ erg cm-2 s-1) | ($10^{-14}$ erg cm-2 s-1) | ($10^{-14}$ erg cm-2 s-1) | (erg s-1) | (erg s-1)
F2M J0825 | $5.4_{-4.2}^{0.5}$ | $27.9_{-18.3}^{+0.7}$ | $33.3_{-32.8}^{+1.4}$ | $45.10^{+0.46}_{-0.44}$ | 46.472$\pm$0.007
F2M J0834 | … | … |  $<1.1$† | … | 45.30$\pm$0.01
F2M J1106 | $<0.0003$ | $2.4_{-1.9}^{+1.5}$ | $2.4_{-2.2}^{+1.3}$ |  $43.58^{+0.45}_{-0.80}$‡ | 45.854$\pm$0.005
F2M J1118 | $<1.4$ | $4.9_{-4.5}^{+0.1}$ | $<6.2$ | $44.08^{+0.81}$ | 46.062$\pm$0.008
F2M J1151 | $0.11_{-0.03}^{+0.02}$ | $2.8_{-0.7}^{+0.8}$ | $2.9_{-0.7}^{+0.6}$ |  $43.96^{+0.15}_{-0.18}$‡ | 45.69$\pm$0.02
F2M J1324 | $0.22_{0.09}^{+0.1}$ | $2.5_{-1.0}^{+1.3}$ | $2.7_{-1.4}^{+1.2}$ |  $42.53^{+0.27}_{-0.37}$‡ | 45.837$\pm$0.005
F2M J1507 | $1.1_{-0.6}^{+0.2}$ | $7.3_{-1.3}^{+2.6}$ | $8.4_{-2.9}^{+1.2}$ | $44.46^{+0.21}_{-0.29}$ | 46.05$\pm$0.01
F2M J1531 | … | … |  $<0.6$† | … | 47.33$\pm$0.02
F2M J1532 | $2.0_{-0.4}^{+0.2}$ | $36_{-17}^{+1}$ | $38.0_{-13}^{+1}$ | $44.56^{+0.46}_{-0.49}$ | 45.706$\pm$0.007
F2M J1715 | $13.9_{-1.5}^{+1.6}$ | $35_{-6}^{+4}$ | $48.0_{-3.7}^{+3.3}$ | $44.48\pm 0.11$ | 45.673$\pm$0.008
† These fluxes are reported over the 0.5-7 keV range as they are derived
directly from the data with the srcflux task on undetected sources.
Note – Upper limits are quoted when XSpec returns a 1-$\sigma$ lower limit of
0.
‡ These sources had too few counts for spectral modeling. Their intrinsic
luminosities are modeled from a fixed $\Gamma=1.8$

##  4 Results and Discussion

Following the definition and identification of F2M red quasars as a population
in Glikman et al. (2004), several other reddened and obscured quasar samples
have been constructed using various definitions that exhibit similar
characteristics of being in a transitional phase of quasar evolution. Many of
these samples’ selection criteria overlap the F2M selection, but extend along
other parametric axes. We summarize here the various reddened AGN populations
and compare their X-ray-derived properties to the F2M sample in this work.

F2M red quasars were selected by applying the optical to near-infrared colour
cuts of $(R-K)_{\rm Vega}>4$ mag and $(J-K)_{\rm Vega}>1.7$ mag to sources
with matches in FIRST and 2MASS. An essential selection criterion for F2M red
quasars is that they exhibit at least one broad ($v_{\rm FWHM}>1000$ km s-1)
emission line in their spectrum; therefore F2M red quasars are by definition
Type 1 sources. Although the $J-K$ colour cut avoids most low mass (M class)
stars, they remain a strong contaminant since they are abundant in the Galaxy
and have colours that resemble reddened quasars (c.f., Warren et al., 2000).
Radio selection was invoked to more thoroughly avoid them, but as a result the
F2M survey misses large numbers of radio-faint red quasars.

Banerji et al. (2012) and Temple et al. (2019) invoked a more stringent
$(J-K)_{\rm Vega}>2.5$ mag colour cut which naturally identifies more heavily
reddened systems at higher redshifts ($z\gtrsim 1.5$). The sample is
restricted to broad line (Type 1) sources and consists of $\sim 50$ objects.
These heavily reddened quasars (HRQs) are also intrinsically more luminous and
show outflows in [O iii]. Although no rest-frame high-resolution optical
imaging exists to identify whether the HRQs reside in merging hosts, an ALMA
observation of one HRQ, J2315, does show merging evidence (Banerji et al.,
2021).

Aiming to exploit the mid-infrared photometry from WISE, which is less
sensitive to dust extinction, a population of hyperluminous, hot dust obscured
galaxies (Hot DOGs; Wu et al., 2012; Tsai et al., 2015) was identified by the
“W1W2 dropout” method such that they are weak or undetected at 3.4 $\mu$m and
4.6 $\mu$m but bright at 12 $\mu$m and 22 $\mu$m. There are only $\sim 1000$
such sources across the entire extragalactic sky and their redshifts are in
the cosmic noon era ($z\simeq 2-4$). These objects likely contain buried AGN
whose presence is implied by hot dust temperatures $\sim 60-120$ K and optical
spectroscopic diagnostic features, though broad lines are often not seen. Fan
et al. (2016) investigated the morphologies of 18 Hot DOGs with HST imaging
and concluded a merger fraction of $62\pm 14$% which is lower than for the F2M
red quasars ($>80$%) but higher than unobscured AGN hosts ($\sim 30$%;
Villforth, 2023). Farrah et al. (2017) find a similar merger fraction ($\sim
75\%$) in their HST study of Hot DOGs but conclude that this high fraction is
reflective of the massive galaxy population at $z\sim 2$. Hot DOGs have been
rarely detected in X-rays, likely due to the common presence of heavy
($N_{H}>10^{24}$ cm-2) absorption (e.g., Piconcelli et al., 2015; Vito et al.,
2018). Hot DOGs are also interpreted as representing an evolutionary phase.

‘Extremely red quasars’ (ERQs) were selected by the optical-to-mid-infrared
colour $r_{\rm AB}-W4_{\rm Vega}>14$ mag in Ross et al. (2015) and $i_{\rm
AB}-W3_{\rm Vega}>9.8$ mag plus C iv line properties indicative of outflows in
Hamann et al. (2017) resulting in $\gtrsim 300$ ERQs. These criteria pick out
objects that are more heavily reddened than the F2M red quasars at redshifts
similar to the HRQs ($2<z<4$). ERQs contain Type 1 and Type 2 sources, the
latter exhibiting significant amounts of polarization (Alexandroff et al.,
2018; Zakamska & Alexandroff, 2023). Their hosts are largely not in mergers
(only 2/10 sources studied show merger activity; Zakamska et al., 2019) but
exhibit powerful winds seen in broad [O iii] emission lines in excess of 1000
km s-1 and with sufficient energy to impact their hosts (Vayner et al., 2021;
Lau et al., 2022).

Aiming to overcome the radio-selection of the F2M survey, and to exploit the
wealth of multi-wavelength data in the SDSS Stripe 82 region, LaMassa et al.
(2016a) and Glikman et al. (2018) used X-ray selection and WISE colours,
respectively, to identify additional samples of red quasars.

In addition, Jun et al. (2020) performed a meta analysis of the aforementioned
obscured AGN populations to relate their X-ray absorption and dust extinction
properties. In the following sections, we compare the F2M quasars in this work
to those compiled results and place F2M red quasars in the broader context of
luminous obscured quasars.

###  4.1 Dust-to-gas ratios

The X-ray data for the F2M red quasars presented here provide a measure of the
column density, $N_{H}$, which parametrizes the absorption due to atomic gas
along the line of sight. This value is determined via spectral fitting for the
five sources with $\gtrsim 50$ counts and is considered more reliable than the
$N_{H}$ estimated from the HR measured for sources fewer counts. The dust
extinction, parametrized by $E(B-V)$, is reported in Tables 1 and 2. Together,
$E(B-V)$ and $N_{H}$ provide constraints on the nature of the absorber, namely
its dust-to-gas ratio.

In Figure 4 we plot the dust-to-gas ratio for the F2M red quasars as a
function of their 2-10 keV X-ray luminosity with red symbols, where filled
circles are the four previously-studied quasars from L16 and G17 as well as
F2M J0915 from Urrutia et al. (2005). Filled stars represent the five quasars
that had $N_{H}$ determined via spectral fitting and open star symbols are the
three sources whose $N_{H}$ values were estimated from their HRs and are
therefore least precise.

It has already been demonstrated in Maiolino et al. (2001a) that low-
luminosity AGN (i.e., Seyfert galaxies) have dust-to-gas ratios that are
significantly lower than the interstellar medium value determined for the
Milky Way ($1.7\times 10^{-22}$ mag cm2 shown with a horizontal black dashed
line; Bohlin et al., 1978). These Seyfert AGN were selected to have simple
X-ray absorption spectra, avoiding sources with warm absorbers or cold
absorbers with partial-covering (Eqn. 6). The dust-to-gas ratios found for
these AGN, plotted with gray circles 4, is therefore descriptive of
circumnuclear material. The mean value for this sample is
$\log{E(B-V)/N_{H}}=-22.8$, shown with a horizontal dotted gray line.

Given that most of the F2M red quasars are found in mergers, are fit by a
variety of absorption models including partial covering, and are more luminous
by $\sim 1-2$ orders of magnitude, they may not have the same source of
reddening as the Seyferts in Maiolino et al. (2001a). Yet, the dust-to-gas
ratio distribution of F2M red quasars overlaps the Maiolino et al. (2001a)
sample. Since the lower dust-to-gas ratio is suggestive of larger dust grains
(Maiolino et al., 2001b), but is also consistent with dust grains being
sublimated close to the central engine, it is possible that different
mechanisms produce similar results. The two sources whose dust-to-gas ratios
are consistent with the Milky Way value are F2M J1715, which had the lowest
measured $N_{H}$ value such that its best-fit spectrum was a single power law
with no absorption (Eqn. 4)444To compute a dust-to-gas ratio, we use the
$N_{H}$ from an absorbed power-law fit (Eqn. 5; $N_{H}=6\times 10^{21}$ cm-2),
which was a poorer fit than a simple unabsorbed power law according to an
F-test, but allows for an estimate of the dust-to-gas ratio., and F2M J1227
from L16, which lacks imaging to determine whether it is hosted by a merger
and has minimal line-of-sight absorption ($N_{H}=0.34\times 10^{22}$ cm-2).
The rest of the sources have lower dust-to-gas ratios than the Milky Way value
by factors similar to the Maiolino et al. (2001a) sample. In addition, the
mean dust-to-gas ratio is $\log{E(B-V)/N_{H}}=-22.9$ (dotted red line), which
consistent with the previous studies in L16 and G17.

For comparison, we plot the average dust-to-gas ratio for six HRQs studied in
Lansbury et al. (2020) with purple triangles. Their mean value,
$\log{E(B-V)/N_{H}}=-22.3$ shown with a dotted purple line, is higher than the
F2M red quasars and the Maiolino et al. (2001a) sample. This may be explained
by the more stringent colour selection of the HRQ sample which finds
preferentially more reddened sources with higher $E(B-V)$ values. The meta
analysis of Jun et al. (2020), which includes the previously published F2M red
quasars, Type 2 AGN, ERQs, and Hot DOGs, finds a value consistent with the
Maiolino et al. (2001a) average ($\log{E(B-V)/N_{H}}=-22.77\pm 0.41$; dashed
orange line).

Figure 4: Dust-to-gas ratios versus 2-10 keV X-ray luminosity ($L_{X}$). The
Milky Way dust-to-gas value is depicted with a black dashed line. The five
previously studied quasars from L16 and G17 and F2M J0915 are shown with
filled red circles. Filled red stars are the five sources in this work that
had sufficient counts for spectral modeling. Open stars are the three low-
count sources whose absorption was estimated from HRs. The horizontal red
dotted line marks the mean value. For comparison, we plot the sample studied
by Maiolino et al. (2001a) of low-luminosity AGN with gray circles and the
mean value is depicted by a dotted gray line. We also show the HRQs from
Lansbury et al. (2020) with purple triangles and their mean value with a
dotted purple line. The orange dashed line shows the mean dust-to-gas ratio of
a compilation of red and obscured quasars in the literature (Jun et al.,
2020).

###  4.2 X-ray versus infrared luminosity

There exist various tracers of intrinsic AGN luminosity and, by extension,
SMBH accretion that must be reconciled in order to adopt a consistent physical
model for AGN. X-rays trace the innermost emission from the accretion disk,
while mid-infrared (e.g., $6~{}\mu$m) arises from reprocessed UV photons from
the accretion disk that are absorbed by nuclear dust (i.e., the ‘torus’) and
thermally re-emitted. At low luminosities, X-ray and mid-IR emission follow a
linear relation (in log-log space; Lutz et al., 2004). However, observations
of higher-luminosity quasars show a departure from this relation around
$L_{\rm bol}\sim 10^{44}$ erg s-1 (Stern, 2015; Chen et al., 2017) and are are
interpreted as being under-luminous in X-rays (Ricci et al., 2017b). The
decreasing $L_{X}/L_{\rm IR}$ ratio with increasing luminosities could also be
interpreted as due to the increasing bolometric correction in X-rays at high
$L_{\rm bol}$ (Martocchia et al., 2017).

In Figure 5 we plot the eight F2M red quasars with X-ray luminosities (Table
6) along with other samples from the literature. The black stars and green
asterisks are luminous, unobscured, Type 1 quasars from Stern (2015) and
Martocchia et al. (2017). The low luminosity relation from Lutz et al. (2004),
which is calibrated at luminosities too low to appear on this plot, is shown
by the shaded region. The relations from Stern (2015) and Chen et al. (2017),
defined based on unobscured Type 1 samples, are shown with dotted and dashed
lines, respectively, and depart from the shaded region. ERQs are shown with
orange diamonds (Goulding et al., 2018) and exist in the same part of the
$L_{X}-L_{\rm IR}$ relation as the unobscured objects. Hot DOGs, shown with
blue pentagons, fall systematically below the extended relations (Ricci et
al., 2017b).

Models of radiation-driven feedback postulate that X-rays need to be
suppressed in order to enable line-driven winds on small scales (Proga et al.,
2000). And it has been shown that quasars with strong outflows are X-ray weak
(Luo et al., 2013; Zappacosta et al., 2020).

While the F2M red quasars (red symbols, both from this and previous works) are
not as luminous in the infrared as the Hot DOGs or ERQs, they similarly lie
below the $L_{X}-L_{\rm IR}$ relation established at low luminosities, even
when corrected for absorption. F2M red quasars have an anomalously high
fraction of BAL systems indicative of line-driven outflows. In addition, F2M
J1507 shows evidence for ultra-fast out-flowing material in its X-ray spectrum
(§A.1). In this space, Hot DOGs appear to be an extension of F2M red quasars
toward more luminous IR sources whose X-rays are suppressed compared to their
IR luminosity (for a discussion on the X-raw weakness of Hot DOG, see Ricci et
al., 2017b).

We note that the open F2M symbols were in the low-count regime and had their
column density estimated from their HRs which was used to correct the X-ray
luminosity. These luminosities are therefore highly uncertain and may be
underestimated. However, given that their exposure times are similar to the
rest of the sample, while their net counts are lower by more than an order of
magnitude, they are likely intrinsically less luminous.

Figure 5: Rest frame 6 $\mu$m luminosity vs. rest-frame absorption-corrected
2-10 keV X-ray luminosity for different quasar samples. Results from this work
are shown with red circles. The six high-count sources that had successful
spectral modeling are shown with filled circles, while the open circles are
the three low-count sources that were modeled by a fixed $\Gamma=1.8$ power
law. Other red quasars from F2M (; ) are shown with red triangles. Red stars
are WISE-selected red quasars in Stripe 82 (Glikman et al., 2018), which have
not been corrected for absorption. Apart from the two lowest flux sources
whose luminosities may have been significantly underestimated due to
insufficient absorption correction, the newly added F2M red quasars populate a
similar part of this space as the previously studied red quasars. More
luminous quasar samples are shown for comparison. Black stars are unobscured,
Type 1 quasars from Stern (2015). The relation that was derived from those
data is shown with a dotted line. Hyperluminous Type 1 quasars from the WISSH
sample (Martocchia et al., 2017) are shown with green diamonds. Asterisks show
Hot DOGs (Ricci et al., 2017b), which are infrared-hyperluminous, heavily
obscured quasars. ERQs are shown with orange diamonds (Goulding et al., 2018).
The shaded region shows the Lutz et al. (2004) relation derived from local
Seyfert galaxies which breaks down at high luminosities. The dashed line
represents the relation from Chen et al. (2017) derived from luminous AGN in
deep fields.

###  4.3 Radiative feedback

The key to blowing out gas from the vicinity of an AGN – and possibly out of
the host galaxy entirely – may be radiation pressure from a high-enough
luminosity pushing against infalling material whose composition is a mixture
of partially ionized dust and gas. Such a medium has an ‘effective cross
section’, $\sigma_{i}$, that is larger than the Thomson cross section,
$\sigma_{T}$ , reducing the Eddington luminosity for the system. This
resultant ‘effective Eddington limit’ is thus lower than that for pure ionized
hydrogen, enabling AGN with a sufficiently high accretion rate, and a not-too-
high column density to blow out the dust and gas (Fabian et al., 2006, 2008;
Ishibashi et al., 2018). According to this theory, the interplay between an
AGN’s accretion, obscuration, and radiative feedback can be understood through
two parameters: $\lambda_{\rm Edd}$ and $N_{H}$, shown in Figure 6. Sources
with the right combination of $\lambda_{\rm Edd}$ and $N_{H}$ are found in the
white triangular region, referred to as the “forbidden” or “blow-out’‘ region,
where the luminosity is high enough to produce outflows and gas density is low
enough to avoid stalling them. Since the blow-out of gas as a result of
radiation pressure can involve multiple scatterings, as the opacity of the
material increases the blowout region can be expanded out to the dashed line,
which takes radiation trapping into account (Ishibashi et al., 2018).

Ricci et al. (2017a) explored the nature of obscuration for Swift/BAT AGN,
which are hard X-ray-selected AGN with $z<0.05$, in the $N_{H}$ vs.
$\lambda_{\rm Edd}$ plane and find that they lie in the region suggestive of
long-lasting obscuration whether by dust lanes in the host galaxy for sources
with $\log{N_{H}}<22$ or by a high covering fraction of nuclear obscuration
for sources with $\log{N_{H}}>22$. These sources are plotted with black
crosses in Figure 6 confirming that the vast majority of low-luminosity, local
AGN are not engaged in radiative feedback.

The F2M red quasars from L16 and G17 as well as F2M J0915 are shown with
filled red circles. The red stars are sources from this work where filled
stars are the five high-count objects whose $N_{H}$ values were determined
from spectral fitting and the open stars are the three low-count sources whose
$N_{H}$ values were estimated from HRs. The two sources with upper limits on
their X-ray counts are not shown. One of these low-count sources, F2M J1106,
is on the edge of the region modified by radiation trapping. This source shows
bi-conal outflowing superbubbles in [O iii] consistent with trapped photons
pushing against an entrained shell of gas expanding out (Shen et al., 2023).
The time-scale for these bubbles is estimated to be $\sim 10$ Myrs, which is
roughly consistent with the timeline for the most heavily absorbed simulations
in Ishibashi et al. (2018). However, it is also possible that because its
$N_{H}$ value was determined by its HR, this estimate sufficiently uncertain
that it may actually live in the unmodified blowout region. We note that F2M
J0830, whose X-ray analysis was performed in L16, also shows bi-conal
outflowing superbubbles (Shen et al., 2023).

All but one (F2M J1151) of the F2M red quasars in the blowout region show
evidence for merging morphologies in their hosts. The two source below the
$\log(N_{H})=22$ line, where the relatively low obscuration is due to dust
lanes in the host galaxy, either have undisturbed morphologies (F2M J1715) or
lack imaging (F2M J1227).

In an independent investigation of quasar outflow properties at sub-mm
wavelengths, Stacey et al. (2022) found similar differences between blue and
red quasars in archival ALMA observations of sixteen Type 1 quasars with
$J\geq 7$ CO lines. Four of these sources have $E(B-V)>0.5$ determined from
SED fitting, while the remaining sources have $E(B-V)<0.1$. We plot the red
and blue quasars from Stacey et al. (2022) in the left panel of Figure 6 with
orange and blue squares, respectively. Here, too, red quasars with molecular
outflows detected by ALMA are in the blowout region. Blue quasars without
outflows do not reside in blowout region. In addition, the analysis of the CO
lines by Stacey et al. (2022) reveals molecular outflows with velocities of
$500-1000$ km s-1 in the red quasars, while the blue quasars have weaker
velocities $\lesssim 300$ km s-1.

Figure 6: Column density, $N_{H}$, vs. Eddington ratio, $\lambda_{Edd}$ for
F2M red quasars (red points). The curved solid line (labelled $\lambda^{\rm
eff}_{\rm Edd}$) represents the region where radiation pressure is
insufficient to expel the obscuring gas, under the assumption of single
scattering, resulting in a high covering fraction (Fabian et al., 2008). In
the white triangular region, the radiation pressure is sufficiently high to
blow out the gas and produce outflows. The dashed line amends this region by
including radiation trapping (Ishibashi et al., 2018). AGNs below
$\log(N_{H})$ = 22 may be obscured by dust lanes in their hosts. Swift/BAT AGN
in the local universe are shown for comparison (black cross symbols; Ricci et
al., 2017a) demonstrating the paucity of sources in the blowout region among
normal AGNs. Left –  Filled circles are the four previously analyzed sources
from L16 and G17 and F2M J0915. Filled stars are the five sources in this work
whose $N_{H}$ was determined by spectral modeling. Open stars are the three
sources whose $N_{H}$ was estimated from their HRs. We also plot, for
comparison, a sample of 14 quasars studied in CO with ALMA (Stacey et al.,
2022) who found that only the reddened quasars ($E(B-V)>0.5$; orange squares)
and none of the unreddened quasars ($E(B-V)<0.1$; blue squares) met blowout
conditions. Right – This panel focuses on the F2M red quasars that have host
morphologies from high resolution imaging where filled sources are mergers
while open sources are undisturbed. We also plot, for comparison, three ERQs
(purple triangles) that also posses HST imaging and morphological information.
The green circle is the Hot DOG from Ricci et al. (2017b). While all the
objects with merging hosts reside in the blowout region, the region is not
exclusively populated by mergers.

Intriguingly, all of the other dust-obscured quasar samples discussed above
(HRQs, Hot DOGs, ERQs, red quasars from Stripe 82, as well as the WISSH
quasars) that have $N_{H}$ and $\lambda_{\rm Edd}$ in the literature reside in
the blowout region. Figure 7 of Lansbury et al. (2020) shows the
aforementioned sources, including the F2M red quasars from L16 and G17, on the
$N_{H}$ vs. $\lambda_{\rm Edd}$ diagram. However, high resolution imaging is
limited to only a handful of these sources. In the right hand panel of Figure
6 we plot $N_{H}$ vs. $\lambda_{\rm Edd}$ again, focusing only on sources with
known host morphologies and we distinguish between merging and undisturbed
systems with closed and open symbols, respectively. Twelve F2M red quasars are
shown with stars where the two that lack HST imaging, F2M J1227 and F2M
J1106555F2M J1106 does possess GMOS IFU imaging with
0$\aas@@fstack{\prime\prime}$4 spatial resolution, which is sufficient to
reveal galaxy-scale ($>10$ kpc) bubbles with a bi-conal morphology. However,
it is unknown whether the quasar is hosted by a merger., are omitted. While
F2M J1715, which appears to be undisturbed666We note that the among the 11 F2M
quasars with sufficient X-ray counts and imaging to be plotted in the right
panel of Figure 6, nine come from the HST observations in Urrutia et al.
(2008) that were designed to reach similar depths; the exposure times ranged
from $\sim 1600$ s to $\sim 2300$ s in the F814W filters, depending on the
redshift. However, F2M J1715 was observed in an 800 s snapshot observation,
which is $\sim 2\times$ shorter than the exposure time for, e.g., F2M J1532,
which is at a similar redshift. This means that the surface brightness limit
for the image of F2M J1715 is $\sim 0.8$ mag shallower and some merger
features might be missed., lies outside the blowout region where dust lanes
can explain its properties, F2M J1151, which is also undisturbed, lies in the
blow out region.

Three ERQs have both HR-based $N_{H}$ estimates (Goulding et al., 2018) and
$\lambda_{\rm Edd}$ (Perrotta et al., 2019) as well as HST imaging
(J0832+1615, J0834+0159, J1652+1728; Zakamska et al., 2019). All three reside
in the blowout region, shown with purple triangles (two points overlap), but
only J1652+1728 is a major merger. Though only a few Hot DOGs have X-ray data
that enable a measurement of $N_{H}$ and most are Type 2, precluding a
measurement of a black hole mass and thus $\lambda_{\rm Edd}$, we are able to
plot one source, WISE J1036+0449 from Ricci et al. (2017b), in the blowout
region with a green circle. Although this object does not have morphological
information, as noted above, the overall population of Hot DOGs has a high
merger fraction.

While all sources with merging hosts reside in the blowout region, a merging
morphology is not a necessary condition to meet the requirements needed to
blow out large amounts of dust and gas. The presence of winds and outflows may
be a more predictive indicator. The entire ERQ sample is shown to have strong
outflows in [O iii], with the highest velocities ($\sim 2000-7000$ km s-1) in
the reddest sources (Perrotta et al., 2019) and a fourth ERQ source that lacks
imaging (J0006+1215) also meets blowout conditions in $N_{H}$ vs.
$\lambda_{\rm Edd}$. Likewise, the HRQs lack host morphology information but
reside in the blowout region (see Figure 7; Lansbury et al., 2020) and exhibit
strong outflows with velocities up to 2500 km s-1 in [O iii] (Temple et al.,
2019). In a reverse approach, Kakkad et al. (2016) selected AGN in the COSMOS
survey that were located in the blowout region and conducted follow-up IFU
observations in [O iii] and find outflow velocities of $\sim 600-1900$ km s-1.
None the less, a systematic imaging campaign on the various samples of
obscured AGN in the blow out region is needed to more thoroughly investigate
any connection between mergers and outflows and better understand the
conditions under which radiative feedback dominates.

##  5 conclusions

In this paper, we investigate the accretion and obscuration properties of a
sample of merger-dominated luminous red quasars via X-ray observations. This
sample consists of 10 newly analysed X-ray observations as well as 5
previously published sources. All but two have high resolution imaging with
HST and one of those two has high resolution, high quality IFU imaging in [O
iii]. Although the sources were not chosen to reside in mergers, ten sources
have clear evidence of morphologically disturbed hosts (as previously
determined by Urrutia et al. 2008 and Glikman et al. 2015). The sample
consists of eight new observations, two sources with archival data sets, and
five previously published sources. When sufficient counts enabled it, we
performed spectral modeling to extract parameters such as $N_{H}$ that enabled
a calculation of the absorption-corrected luminosity. Lower count objects were
analyzed via their HRs to estimate $N_{H}$; in cases of non-detection, we
determine upper limits. We combine these X-ray-derived properties with host
galaxy morphological information from high resolution imaging, dust reddening,
infrared luminosity, and accretion rate ($\lambda_{\rm Edd}$). These data
allow us to investigate the connection among these properties and we find:

  1. 1.

F2M red quasars have dust-to-gas ratios that are in general lower than the
interstellar medium of the Milky Way. Their dust-to-gas ratios are consistent
with low-luminosity AGN in the local universe, though the ratio likely arises
from very different physics. The dust-to-gas ratios of F2M red quasars is
somewhat lower than, but roughly consistent with the dust-to-gas ratios of
comparison samples of luminous dusty quasars.

  2. 2.

F2M red quasars are under-luminous in X-rays at a given infrared luminosity
when compared with local, low luminosity relations as well as luminous,
unreddened sources that straddle the high luminosity relation. However, their
X-ray deficit is consistent with other, more luminous, dust-obscured quasars
such as the Hot DOGs.

  3. 3.

with the exception of two sources, F2M red quasars reside in the “forbidden”
region of $N_{H}$ vs. $\lambda_{\rm Edd}$ indicative of them being in a
blowout phase due to radiation pressure on dust. Furthermore, all F2M red
quasars with merging hosts are in the blowout region as are other luminous
dusty quasars from comparison samples. A broader investigation of the host
morphologies of blue quasars outside the blowout region is needed to better
understand any connection among reddening, feedback, and mergers.

These findings lend further support to F2M red quasars, along with other
luminous dust-reddened quasars, being in a brief transitional phase in a
merger-driven co-evolution of galaxies and their supermassive black holes.

## Acknowledgements

E.G. acknowledges the generous support of the Cottrell Scholar Award through
the Research Corporation for Science Advancement. E.G. is grateful to the
Mittelman Family Foundation for their generous support. E.P. and L.Z.
acknowledge financial support from the Bando Ricerca Fondamentale INAF 2022
Large Grant “Toward an holistic view of the Titans: multi-band observations of
z>6 QSOs powered by greedy supermassive black-holes.” We thank Laura Blecha
for useful discussions on the nature of F2M J1507. We thank Hannah Stacey for
providing the data for the ALMA-detected quasars plotted in Figure 6. We
acknowledge the efforts of Charlotte Moore in the initial phase of this
project.

Support for this work was provided by the National Aeronautics and Space
Administration through Chandra Award Number 21700216 issued by the Chandra
X-ray Center, which is operated by the Smithsonian Astrophysical Observatory
for and on behalf of the National Aeronautics Space Administration under
contract NAS8-03060. The scientific results reported in this article are based
on observations made by the Chandra X-ray Observatory, data obtained from the
Chandra Data Archive, and observations made by the Chandra X-ray Observatory
and published previously in cited articles. This research has made use of
software provided by the Chandra X-ray Center (CXC) in the application
packages CIAO. We gratefully acknowledge the National Science Foundation’s
support of the Keck Northeast Astronomy Consortium’s REU program through grant
AST-1950797.

## Data Availability

The X-ray data underlying this article are publicly available through the
Chandra archives.

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##  Appendix A Notes on the Spectral fitting for individual objects

###  A.1 F2M 1507+3129

The Balmer lines of this object have a blue-shifted broad emission component
in addition to broad lines at the systemic velocity, which is determined by
the [O iii] lines in its optical spectrum. We note that the the blue-shifted
broad emission component of H$\beta$ is similar in structure to H$\alpha$,
which is shown in Figure 2. We attribute this component to an out-flowing
wind, rather than accretion disk geometry, due to the lack of a red-shifted
component that is typically seen in double-peaked-emitting AGN. The H$\alpha$
component is blue-shifted by 91Å, corresponding to a velocity of $0.014c$,
which is slow compared with typical outflow velocities seen in BALs ($\sim
10,000-60,000$ km s-1). We use the line width from the broad component at the
systemic velocity, which we assume to represent virialized motion, to compute
the black hole mass.

As is seen in Figure 3, the X-ray spectrum exhibits some unusual features
including what appears to be a deficit of flux around $4-5$ keV. There is also
apparent soft excess at energies below 1.5 keV that required a model with a
leakage/scattering component (Eqn. 6). However, given the complexity of this
model and the small number of spectral bins, we chose to freeze the photon
index to $\Gamma=1.8$. We initially ignored the $4-5$ keV and found an
acceptable fit with $N_{H}=3\times 10^{23}$ cm-2 and a scattering fraction of
16%. We further interpret the flux deficit at $4-5$ keV as absorption of Fe
xxvi Ly$\alpha$ ($E_{\rm rest}=6.966$ keV) due to an ultra-fast outflow (UFO)
and amend the model in Eqn. 6 by adding a Gaussian absorption component.

${\tt phabs*(zpowerlw+zphabs*zpowerlw+zgauss)}.$ (8)

A fit to this model resulted in the same $N_{H}$ and scattering fraction,
while accounting for the absorption at the blue-shifted energy of 4.59 keV,
results in a UFO velocity of $0.26c$. The continuum model components are shown
as dotted lines in Figure 3. Table 7 lists the best-fit parameters for this
source.

This UFO velocity is significantly higher than that seen in the blue-shifted
Balmer emission and arises from radii closest to the central engine. While
these features are therefore not associated with the same outflowing system,
their presence may be indicative of feedback on many scales due to sustained
outflowing winds and shocks. Theoretical models predict that radiation driven
relativistic winds interact with shocks against the ISM, triggering galaxy-
wide ionized and neutral outflows (e.g., Zubovas & King, 2012). A higher count
X-ray spectrum would allow for a more thorough exploitation of the energy
resolution of e.g., XMM-Newton, to better constrain the outflow properties
closest to the SMBH. IFU spectroscopy of the Balmer lines would similarly
trace the kinematics of the large scale outflows, to fully trace the feedback
energy being injected into host galaxy by this quasar.

Table 7: UFO Model Fit Parameters Parameter | Value
---|---
$\Gamma$ | 1.8†
Power-law normalization | $1.1_{-0.2}+^{1.2}\times 10^{-4}$
$N_{H}$ (cm-2) | $3.0_{-1.7}^{+3.7}\times 10^{23}$
$E_{FeXXVI}$ Ly$\alpha$ (keV) | 6.966†
$\sigma_{E}$ (keV) |  $2.4\times 10^{-4}$‡
EW (keV) | $2.3$
$f_{\rm scatt}$ (%) | $16\pm 13$
$v_{\rm UFO}$ | $0.26c$
† This parameter was frozen.
‡ Given that this feature was fit to a region represented by only two
spectral bins, this value is highly uncertain with an unconstrained lower
bound and an upper bound of $\sigma=1.45$.
energy.

###  A.2 F2M 1532+2415

This source shows emission at 4.1 keV which is the redshifted fluorescent Iron
K$\alpha$ line ($E_{\rm rest}=6.4$ keV) suggestive of significant reflected
emission often seen atop a strongly suppressed continuum, which is typical in
Type 2 quasars. F2M J1532, however, is a Type 1 source, with broad emission
lines seen in its spectrum. We performed a self-consistent physically
motivated joint fit, with both Chandra observations, to the X-ray spectrum to
properly account for line-of-sight attenuation, scattering of photons into the
line of sight, and the fluorescent line emission responsible for the Fe
K$\alpha$ feature. We employed Equation LABEL:eqn:mytorus in XSpec in so-
called ‘coupled’ mode, where the column densities ($N_{H,Z},N_{H,S}$), torus
inclination angle ($\theta_{\rm obs}$), normalizations of the scattering and
fluorescent line coefficient components ($A_{S}$ and $A_{L}$, respectively)
are tied together to preserve the model’s self-consistency. This fit, however,
yielded poor results in a best-fit inclination angle of $60^{\circ}$, which is
the default, fixed opening angle of the torus-shaped absorber in the MYTorus
model. This suggests a grazing incidence angle which is highly unlikely.
Therefore, while this is a statistically acceptable fit, it is not a
physically meaningful result (see discussion in LaMassa et al., 2016a, 2023,
for more details on this phenomenon).

Under such circumstances, it is advisable to fit the spectrum with the same
MYTorus model (Eqn. LABEL:eqn:mytorus) but in ‘decoupled’ mode. This approach
assumes that the absorbing and X-ray reprocessing media are not necessarily
the same, nor are they smooth and homogeneous, as is assumed with a simple
torus model. In this approach the line-of-sight column density ($N_{\rm
H,los}$) is provided by the $N_{H,Z}$ parameter which is decoupled from the
global column density ($N_{\rm H,global}$) from surrounding clouds, provided
by the $N_{H,S}$ terms in Equation LABEL:eqn:mytorus, which are still tied to
each other. The inclination angles are also decoupled, such that the
transmitted component is frozen at $90^{\circ}$, while the scattered and
fluorescent line components are frozen to $0^{\circ}$. In this model, we are
not assuming a homogeneous donut-shaped absorber, but utilize the radiative
transfer determined by MYTorus to consider light passing through and
scattering off of a clumpy and patchy medium surrounding the AGN.

A fit to this model yields reassuring results. The power-law is best described
by $\Gamma=1.4$ which, while at the flat end of the range of indices for AGN,
is consistent with the value found from the phenomenological XSpec model (Eqn.
6). Additionally, the best-fit line-of-sight column density is $N_{\rm
H,Z}=7.4\times 10^{22}$ cm-2, which is also consistent with the value found
from the phenomenological XSpec model (Eqn. 6; $N_{H}=7.9\times 10^{22}$ cm-2)
which only considers line-of-sight absorption and does not account for
additional physics. The scattering fraction is also consistent, with the
MYTorus fit yielding $f_{scatt}=10\%$ compared with 11% in the
phenomenological model. Finally, the best-fit global column density is $N_{\rm
H,global}=10^{24}$ cm-2, in the Compton thick regime, which means that this
scattered component does not significantly contribute to the continuum
allowing for the strong similarity seen with the phenomenological model while
also accounting for the Fe K$\alpha$ line. This suggests that F2M J1532 is
enshrouded by a heavy amount of absorption which is non uniform and our line-
of-sight happens to coincide with an opening allowing a direct view to the
broad line emission from the quasar.

Table 8 lists the best-fit MYTorus parameters for this source. Figure 7 shows
the best fit MYTorus model plotted atop the source spectrum, with the
individual model components shown separately on the left and a contour plot of
the global ($N_{H,S}$) versus line-of-sight ($N_{H,Z}$) column densities
showing that while $N_{H,Z}$ is well constrained and consistent with the
phenomenological XSpec model, the global column density is poorly constrained
and highly uncertain.

Figure 7: Left – MYTorus plus scattered power-law (Eqn LABEL:eqn:mytorus) in a ‘decoupled’ joint fit to the observations of F2M J1532. Black points and lines represent ObsID 3138 and red points and lines represent ObsID 3338. The solid line shows the combined model, while the dotted lines are the individual model components. Right – $\chi^{2}$ contour plot of the global column density ($N_{H,S}$) vs. the line-of-sight column density ($N_{H,Z}$) from the ‘decoupled’ MYTorus fit. The cross represents the best-fit parameters at $N_{H,Z}=7.4\times 10^{22}$ cm-2 and $N_{H,S}=1.0\times 10^{24}$ cm-2. The black, red, and blue curves show the 68%, 90%, and 99% confidence levels. We see that while $N_{H,Z}$ is reasonably well-constrained and consistent with the value found for the phenomenological model (Eqn. 6) of $N_{H,Z}=7.9\times 10^{22}$ cm-2, $N_{H,S}$ is poorly constrained.  Table 8: Decoupled MYTorus Fit Parameters Parameter | Value
---|---
$\Gamma$† | $1.41_{-0.01}^{+0.28}$
Power-law normalization | $1.0_{-0.2}^{+1.3}\times 10^{-4}$
$N_{H,Z}$ (cm-2) line-of-sight | $7.4_{-2.5}^{+3.7}\times 10^{22}$
$N_{H,S}$ (cm-2) global‡ | $1.0_{-0.8}\times 10^{24}$
$f_{\rm scatt}$ (%) | $9.5_{-4.6}^{+3.4}$
C-stat (dof) | 106.99 (119)
†This parameter was constrained with a lower bound of $\Gamma\geq 1.4$.
† The error analysis of this parameter was found to have an unconstrained
upper bound, as illustrated by the contour diagram shown in Figure 7.