# Tell-Tale Spectral Signatures of MHD-driven Ultra-Fast Outflows in AGNs

Keigo Fukumura11affiliation: Department of Physics and Astronomy, James
Madison University, Harrisonburg, VA 22807<EMAIL_ADDRESS>, Mauro
Dadina22affiliation: INAF, Osservatorio di Astrofisica e Scienza dello Spazio
di Bologna, via P. Gobetti 93/3, 40129 Bologna, Italy  , Gabriele
Matzeu33affiliation: Department of Physics and Astronomy, University of
Bologna, Via Gobetti 93/2, 40129 Bologna, Italy  , Francesco
Tombesi44affiliation: Astrophysics Science Division, NASA/Goddard Space Flight
Center, Greenbelt, MD 20771 55affiliation: Department of Astronomy, University
of Maryland, College Park, MD20742 66affiliation: Department of Physics,
University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133
Rome, Italy 77affiliation: INAF Astronomical Observatory of Rome, Via Frascati
33, 00078 Monteporzio Catone (Rome), Italy , Chris Shrader44affiliation:
Astrophysics Science Division, NASA/Goddard Space Flight Center, Greenbelt, MD
20771 88affiliation: Department of Physics, Catholic University of America,
Washington, DC 20064 , and Demosthenes Kazanas44affiliation: Astrophysics
Science Division, NASA/Goddard Space Flight Center, Greenbelt, MD 20771

###### Abstract

We aim to explore spectral signatures of the predicted multi-ion UFOs in the
broadband X-ray spectra of active galactic nuclei (AGNs) by exploiting an
accretion disk wind model in the context of a simple magnetohydrodynamic (MHD)
framework. We are focused primarily on examining the spectral dependences on a
number of key properties; (1) ionizing luminosity ratio $\lambda_{\rm ion}$,
(2) line-of-sight wind density slope $p$, (3) optical/UV-to-X-ray strength
$\alpha_{\rm OX}$, (4) inclination $\theta$, (5) X-ray photon index $\Gamma$
and (6) wind density factor $f_{D}$. With an emphasis on radio-quiet Seyferts
in sub-Eddington regime, multi-ion UFO spectra are systematically calculated
as a function of these parameters to show that MHD-driven UFOs imprint a
unique asymmetric absorption line profile with a pronounced blue tail
structure on average. Such a characteristic line signature is generic to the
simplified MHD disk-wind models presented in this work due to their specific
kinematics and density structure. The properties of these absorption line
profiles could be utilized as a diagnostics to distinguish between different
wind driving mechanisms or even the specific values of a given MHD wind
parameters. We also present high fidelity microcalorimeter simulations in
anticipation of the upcoming XRISM/Resolve and Athena/X-IFU instruments to
demonstrate that such a “tell-tale” sign may be immune to a spectral
contamination by the presence of additional warm absorbers and partially
covering gas.

accretion; black hole physics; AGNs; magnetohydrodynamics; theoretical models

##  1 Introduction

AGNs in general are known to be fueled and energized by accretion process onto
their supermassive black holes. Such accretion is almost necessarily
accompanied by outflowing gas of various physical forms; i.e. molecular gas at
galactic scale (at $d\mathrel{\raise 2.15277pt\hbox{$>$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}$ kpc; e.g. Faucher-Giguère & Quataert 2012; Wagner et
al. 2013; Tombesi et al. 2015), UV outflows of weakly or moderately ionized
gas (at $d\mathrel{\raise 1.29167pt\hbox{$<$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}$ pc; e.g. Crenshaw, Kraemer & George 2003; Arav et al.
2015), and X-ray winds most likely originating from the innermost
circumnuclear region of active galactic nuclei (AGNs). Among the X-ray winds,
roughly $\sim 50\%$ of AGN populations (most notably, radio-quiet Seyfert 1s)
are historically known to exhibit a series of blueshifted absorption features
due to resonant transitions from various chemical elements at different charge
state; aka. warm absorbers (e.g. Reynolds, 1997; Crenshaw, Kraemer & George,
2003; Blustin et al., 2005; Steenbrugge et al., 2005; McKernan et al., 2007;
Holczer et al., 2007; Detmers et al., 2011; Tombesi et al., 2013; Fukumura et
al., 2018; Laha et al., 2021). While their origin and geometrical structure
are still unknown to date (e.g. their launching processes, nature of the
outflows either in a continuous or discrete patchy structure), the physical
properties of the canonical AGN warm absorbers are often characterized by i)
moderate hydrogen-equivalent column densities ($10^{20}\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}N_{H}\textmd{[cm${}^{-2}$]}\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}10^{22}$), ii) a
wide range of ionization parameter111This is defined as $\xi\equiv L_{\rm
ion}/(nr^{2})$ where $L_{\rm ion}$ is ionizing (X-ray) luminosity, $n$ is
plasma number density at distance $r$ from AGN. ($-1\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}\log(\xi\textmd{[erg~{}cm~{}s${}^{-1}$]})\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}4$) and iii)
slow to moderate line-of-sight (LoS) velocities ($v_{\rm out}/c\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}0.01$ where $c$
is the speed of light), along with turbulent velocities (e.g. $v_{\rm
turb}\mathrel{\raise 1.29167pt\hbox{$<$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}1,000$ km s-1), according to a number of exploratory
X-ray observations so far (see, e.g., Crenshaw, Kraemer & George, 2003;
Kallman & Dorodnitsyn, 2019, and reference therein). State-of-the-art
dispersive spectroscopic instruments such as Chandra/HETGS and XMM-Newton/RGS
with the unprecedented resolving power have greatly improved the quality of
X-ray spectra for warm absorber analyses.

Independently, a number of studies on X-ray warm absorbers from Seyfert 1s
have further revealed an intriguing global nature of the ionized absorbers;
i.e. a uniform column density profile as a function of ionization parameter,
observationally obtained from the absorption measure distribution (AMD; e.g.
Behar 2009; Holczer et al. 2007, 2010; Fukumura et al. 2018). Such a
characteristic distribution of X-ray absorbers along a LoS may be indicative
of a well-organized, continuous outflows rather than a patchy cloud of
discrete gas. We shall address the implication of AMD more in details in §2.2.

In parallel to grating observations with Chandra and XMM-Newton, intensive
observations primarily carried out at CCD resolution of Seyfert AGNs
(including radio-quiet, radio-loud and nearby/lensed quasars, for example)
have revealed ultra-fast outflows (UFOs) exhibiting a distinct property; i.e.
massive column ($N_{H}\mathrel{\raise 1.29167pt\hbox{$<$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}10^{24}$ cm-2) with higher ionization parameter
($\log\xi\sim 4-6$) outflowing at near-relativistic velocity ($v_{\rm
out}/c\mathrel{\raise 1.29167pt\hbox{$<$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}0.1-0.7$) in large contrast with the properties of
conventional warm absorbers as described earlier. The most prominent UFO
features detected in the X-ray spectrum is usually Fe K absorption lines
attributed to Fe xxv/Fe xxvi ions (e.g. Pounds et al., 2003; Reeves et al.,
2003, 2009, 2018a; Chartas et al., 2009; Tombesi et al., 2010a, b, 2011, 2012,
2013, 2015; Nardini et al., 2015; Parker et al., 2017). With an increasing
number of multi-epoch observations in search for Fe K UFOs across diverse AGN
populations, it is shown that UFOs can be highly variable at least on the
timescale of days (e.g. Reeves et al., 2018b), and there appears to be likely
correlations among the observed quantities (e.g. $N_{H},v_{\rm
out},\rm{equivalent~{}width~{}(EW)},\rm{spectral~{}hardness}~{}\Gamma$) (e.g.,
see, Chartas et al. 2009; Pinto et al. 2018; Parker et al. 2018; Matzeu et al.
2017, but also see, e.g., Chartas & Canas 2018; Boissay-Malaquin et al. 2019).

Some UFOs have been found in very luminous AGNs possibly accreting at a good
fraction of Eddington value (e.g. PDS 456, IRAS 13224-3809, APM 08279+5255 and
PG 1211+143)222Ultra-luminous X-ray sources (ULXs) accreting at super-
Eddington rate are also known to produce powerful X-ray UFOs, which is beyond
the scope of this paper.. However, it should be reminded that the canonical Fe
K UFOs have been ubiquitously detected also in sub-Eddington AGNs such as
radio-quiet Seyfert 1s (e.g. Tombesi et al., 2010a, 2011) and they appear to
be present even in (much) fainter sources such as Seyfert 2s when the
accretion rate is as low as $\sim 2\%$ of Eddington rate (e.g., see Marinucci
et al., 2018, for NGC 2992). This may be providing a deep insight into the
underlying UFO driving mechanism(s) as addressed below.

Independently, more thorough grating spectroscopic studies have revealed the
extstance of UV/soft X-ray UFOs (e.g. C iv, O viii, Ne ix/Ne x, Si xiv, S xvi
and Mg xii) in addition to the canonical Fe K UFOs (e.g. Gupta et al., 2013,
2015; Boissay-Malaquin et al., 2019; Hamann et al., 2018; Reeves et al., 2020;
Krongold et al., 2021; Chartas et al., 2021; Serafinelli et al., 2019). These
observations of multi-ion UFOs from a number of AGNs are thus clearly pointing
to the importance of studying their co-existing nature in the broadband
UV/X-ray spectrum perhaps within a coherent framework.

Although these near-relativistic outflows of ionized gas are most likely
launched from a nearby gas reservoir in AGNs such as an accretion disk in
their deepest part of the gravitational potential, the main driving mechanism
is yet to be well constrained observationally. Currently, the most plausible
launching processes of UFOs are the following; (i) Radiation-pressure driving
where sufficiently high UV and soft X-ray fluxes (either via line-emitting
photons or continuum radiation) are capable of accelerating weakly ionized
plasma through enhanced force-multipliers (e.g. Proga et al., 2000; Proga,
2003; Sim et al., 2008; Nomura & Ohsuga, 2017; Hagino et al., 2015; Mizumoto
et al., 2021). (ii) Magnetic driving in which the plasma is loaded onto a
global poloidal magnetic field to be accelerated by Lorentz force of
$\textbf{\em J}\times\textbf{\em B}$ (i.e. magneto-centrifugal and magnetic
pressure forces; e.g. Blandford & Payne 1982; Contopoulos & Lovelace 1994;
Köngl & Kartje 1994; Ferreira 1997; Everett 2005; Fukumura et al. 2010a, b,
2015, 2018; Chakravorty et al. 2016; Kraemer et al. 2018; Jacquemin-Ide et al.
2019, 2021).

One of the ultimate questions to be answered in UFO physics is therefore the
acceleration mechanism and morphological properties of the outflows at large
scale, which might be better understood by either detailed spectroscopic
modeling or perhaps, for example, variability study based on principal
component analysis (e.g. Parker et al., 2018). Ideally, it is conceivable that
a certain unique spectral signature of X-ray UFOs could be exploited in those
leading UFO models; i.e. the use of the shape of the UFO line profiles as a
diagnostic proxy to distinguish the underlying launching mechanisms as
described above. While this might be challenging, the difference in UFO
kinematics and stratified structure (attributed to different driving
processes) should in principle be imprinted in the resulting absorption
signatures in such a way that one could distinctively differentiate among
different scenarios (Done et al. 2021, in private communication).

To this end, in this paper we calculate broadband X-ray spectra of multi-ion
UFOs under sets of characteristic parameters for AGNs and the wind property in
trying to qualitatively extract a unique UFO spectral feature that is
primarily generic to MHD-driving. We consider, for simplicity, a pure MHD-
driving process to launch UFOs in a simplified situation where the radiation
field plays little role in their acceleration in an effort to study
characteristic effects and dependences exclusively attributed to magnetized
outflows rather than hybrid outflows (e.g. MHD + line-driving; Everett, 2005).
A detailed description of the wind model is given elsewhere (see, e.g.,
Contopoulos & Lovelace, 1994; Fukumura et al., 2010a, b, 2017; Kazanas et al.,
2012; Kazanas, 2019, and reference therein). Below, we list a number of
fundamental properties that characterize the essence of our MHD winds.

This paper is structured as follows; We briefly review in §2 the
characteristic properties of our MHD-driven disk wind model that is coupled to
radiative transfer calculations to obtain AMD and synthetic multi-ion UFO
spectra. In §3 we will discuss how changes on the model parameters could
affect the resulting spectra and show how future microcalorimeters such as
XRISM/Resolve (XRISM, 2020) and Athena/X-IFU (Barret et al., 2018) will allow
us to fully characterize them. We further consider a possible contamination
due to warm absorbers and partially covering gas in the spectrum to assess a
plausibility of realistically extracting UFO signatures that are generic to
MHD-driven fast winds. We summarize our results and discuss other implications
in §4.

##  2 Basic Models

###  2.1 Self-Similar MHD-Driven Disk Winds

The essence of the MHD wind model utilized in this work is captured by a
number of characteristic physical properties based on Contopoulos & Lovelace
(1994) under steady-state and axisymmetric assumptions. First, the outflow is
globally continuous being launched from a thin accretion disk over a large
radial extent in a stratified structure (e.g. Kazanas et al., 2012; Fukumura
et al., 2014; Kazanas, 2019). LoS wind profile is described by a self-similar
prescription such that, for example, wind density and velocity are
respectively given by

$\displaystyle n(r,\theta)\equiv n_{o}f_{D}\left(\frac{r}{R_{\rm
in}}\right)^{-p}h(\theta)~{}~{}~{}{\rm and}~{}~{}~{}v_{r}(r,\theta)\sim v_{\rm
K,in}\left(\frac{r}{R_{\rm in}}\right)^{-1/2}g_{r}(\theta),$ (1)

where the wind density drops monotonically and uniformly in a self-similar
form333Our model is reduced to BP82 MHD wind profile for $p=3/2$. of index
$p(\geq 1)$ with distance and $n_{o}=2.5\times 10^{13}$ cm-3 is its
normalization with an arbitrary factor $f_{D}$, while the wind velocity
follows the local escape velocity (i.e. Keplerian law) as a function of LoS
distance. Both quantities are normalized at the innermost launching
radius444In our calculations we set $R_{\rm in}\sim R_{\rm ISCO}=6R_{g}$, the
innermost stable circular orbit (ISCO) around a Schwarzschild BH, where
$R_{g}$ is the gravitational radius (e.g. Bardeen et al., 1972; Cunningham,
1975). $R_{\rm in}$ and the angular dependences, $h(\theta)$ and
$g_{r}(\theta)$, are calculated numerically by solving the Grad-Shafranov
equation in an ideal MHD framework (Contopoulos & Lovelace, 1994). Thus, one
of the generic features of our MHD winds is that the ionized gas is launched
faster at smaller radii (closer to AGN), and the expected amount of ionic
column density over a LoS distance depends sensitively on the density gradient
parameter $p$ such that

$\displaystyle N^{i}_{\rm ion}(w_{i},r_{i};\theta)$ $\displaystyle\equiv$
$\displaystyle\int_{r_{i}}^{w_{i}r_{i}}n(r,\theta)dr$ (4) $\displaystyle=$
$\displaystyle n_{o}f_{D}h(\theta)\
\times\left\\{\begin{array}[]{llr}\frac{1}{2(p-1)}[w_{i}^{2(p-1)}-1]r_{i}^{2(p-1)}\propto
w_{i}^{2(p-1)}&~{}~{}~{}{\rm if}~{}~{}~{}p\neq 1,\\\ \ln w_{i}&~{}~{}~{}{\rm
if}~{}~{}~{}p=1,\\\ \end{array}\right.$

where the column per ion (for a given charge state) is predominantly produced
over the LoS distance between $r=r_{i}$ and $r=w_{i}r_{i}$ ($w_{i}>1$) for
individual ions. For example, one expects an equal amount of column (i.e. a
constant $N^{i}_{\rm ion}$) for all ions per decade in distance if $p=1$ (i.e.
$N_{\rm ion}^{i}=n_{o}f_{D}h(\theta)=const$ for a given inclination $\theta$
with $w_{i}=10$). Given an ensemble of suitable objects, this can be tested
observationally.

Table 1: Primary Parameters in MHD UFO Model (mhdwind)  | Parameter |  | Range of Value
---|---|---|---
1 | Inclination [deg] | $\theta$ | $20^{\circ}-50^{\circ}$
2 | X-ray Photon Index | $\Gamma$ | $1.5-2.5$
3 | Optical/UV-to-X-ray Strength | $|\alpha_{\rm OX}|$ | $1.5-1.8$
4 | Wind Density Slope | $p$ | $1.2-1.7$
5 | Wind Density Factor | $f_{D}$ | $10^{-3}-1$
6 | Ionizing Luminosity Ratio | $\lambda_{\rm ion}$ | $0.05-0.5$

###  2.2 Radiative Transfer with Ionizing Spectra

Our wind simulations are incorporated to post-processed radiative transfer
calculations with XSTAR (e.g. Kallman & Bautista, 2001). We track the LoS
distribution of various ions of different charge state by injecting a
parameterized ionizing X-ray spectral energy distribution (SED) as is commonly
practiced in the literature (e.g. Fukumura et al., 2010a; Sim et al., 2010a,
2012; Ratheesh et al., 2021; Higginbottom et al., 2014). We consider in our
spectral simulations major ionic species over the broadband (most notably,
H/He-like ions; e.g. O viii, Ne x, Mg xii, Si xiv, S xvi, Fe xxv/Fe xxvi, Co
xxvii, Ni xxviii, among others, from atomic data in XSTAR) and their ionic
columns $N^{i}_{\rm ion}$ are thus determined by the wind density
$n(r,\theta)$. Throughout our calculations, the solar abundances are assumed
for all ions (i.e. $A_{\rm ion}=A_{\rm ion,\odot}$) to reduce extra degrees of
complications. Although the observed AGN SEDs (even within radio-quiet
Seyferts and nearby quasars) are extremely diverse often exhibiting multiple
spectral components (e.g. Fabian et al., 2000; Risaliti & Elvis, 2004), we aim
to capture the broad characteristics of AGN SED, $f_{E}$, on average. This
approach may not be sufficient to make source-specific quantitative argument,
but we feel it is justified for qualitative comparisons as a first-order
study. To this end, we employ the following parameters; (1) a power-law photon
index ($\Gamma$), (2) optical/UV-to-X-ray flux ratio555The spectral index
$\alpha_{\rm OX}\equiv 0.384\log(f_{\rm 2keV}/f_{\rm
2500\buildrel{}_{\circ}\over{\mathrm{A}}})$ measures the X-ray-to-UV relative
brightness where $f_{\rm 2keV}$ and $f_{\rm
2500\buildrel{}_{\circ}\over{\mathrm{A}}}$ are respectively 2 keV and
$2500\buildrel{}_{\circ}\over{\mathrm{A}}$ flux densities (Tananbaum et al.,
1979) (parameterized by $\alpha_{\rm OX})$, and (3) Eddington ratio
($\lambda_{\rm ion}$) determining ionizing luminosity $L_{\rm ion}$ where
$L_{\rm ion}\equiv\lambda_{\rm ion}L_{E}$ and $L_{E}$ is Eddington luminosity
assuming $M=10^{8}M_{\odot}$ such that

$\displaystyle L_{\rm
ion}\equiv\int_{13.6\rm{eV}}^{13.6\rm{keV}}f_{E}(\Gamma,\alpha_{\rm
OX},\lambda_{\rm ion})dE\ ,$ (5)

throughout this paper.

Given an input SED, $f_{E}$, parameterized by these quantities, we compute the
ionization parameter $\xi(r,\theta)$ of photoionized winds which determines
the ionic column distribution $N^{i}_{\rm ion}(w_{i})$ depending on the
ionization threshold of individual ions. In order to systematically treat
multi-ion UFOs, we consider AMD with the help from equations (1) and (2)
defined as

$\displaystyle{\rm{AMD}}(p)\equiv\frac{d\left[N^{i}_{\rm
ion}(r,\theta)\right]}{d\left[\log\xi(r,\theta)\right]}\propto
r^{1-p}\propto\xi^{\frac{p-1}{2p-1}}\ ,$ (6)

which is a useful proxy of the relative strength of multiple absorbers of
different charge states from a global perspective (e.g. Behar, 2009). For
example, one finds $\rm{AMD}=const$ with distance and ionization state if
$p=1$ as previously seen in equation (2), whereas AMD monotonically declines
with increasing distance or slowly increases with increasing ionization
parameter if $p>1$. In fact, a number of AGN warm absorber analyses of
multiple ions have indeed favored $1\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}p<1.5$ based on
AMD study666Similar AMD analyses for BH XRB disk-winds have independently
implied similar results (e.g. Trueba et al., 2019; Fukumura et al., 2021, for
4U 1630-472 and) and Fukumura et al. 2017. (e.g. Behar, 2009; Holczer et al.,
2007, 2010; Detmers et al., 2011; Fukumura et al., 2018). Since our spectral
modeling considers multi-ion UFOs of a global distribution rather than being
restricted to the most pronounced Fe K features, the $\rm{AMD}$ is extremely
important.

Figure 1: Left: An example of calculated AMD for multi-ion UFOs with MHD winds
assuming $\Gamma=2,\theta=40^{\circ},p=1.2,f_{D}=1,\alpha_{\rm OX}=1.5$ and
$\lambda_{\rm ion}=0.05$. Local hydrogen-equivalent columns (expressed on left
ordinate) are shown for major ions; Fe xxvi (green), Fe xxv (cyan), S xvi
(orange), Si xiv (yellow), Mg xii (dark blue), Ne x (red) and O viii (dark)
along with the LoS wind velocity $v_{\rm out}/c$ (purple; expressed on right
ordinate). A majority of the column is highly blueshifted ($v_{\rm out}/c>0.1$
in light yellow region) for many ions. Right: Schematics of AMD with velocity
profiles $v_{\rm out}(\xi)$ for different ionizing photons corresponding to
the ionic column (dark for less ionizing photons and red for more ionizing
photons). Filled blue circle denotes where a local column is maximally
produced. Open circle corresponds to the column produced at the innermost wind
layer where $\xi$ value is the highest in each case. Note that the wind under
higher ionization (in red) produces lower column of near-relativistic
blueshift ($v_{\rm out}/c>0.1$ in squared domain) yielding slower UFOs in
comparison with the lower ionization case (in shaded domain).

Therefore, the final UFO spectrum (mhdwind) is uniquely calculated by a set of
these model parameters ($\theta,p,f_{D},\Gamma,\alpha_{\rm OX},\lambda_{\rm
ion}$) for a given wind morphology. The range of the primary model parameters
is listed in Table 1.

##  3 Results

###  3.1 Synthetic Multi-Ion Broadband UFO Spectra

As stated above, we aim to globally model the multi-ion UFO. We thus need to
compute the ionic column densities $N^{i}_{\rm ion}$ for various chemical
elements, most notably H/He-like ions; e.g. O viii, Ne x, Mg xii, Si xiv, S
xvi, Fe xxv/Fe xxvi, Co xxvii, Ni xxviii, among others. Having this in mind,
we handle the radiative processes between the wind material and the ionizing
radiation following the prescription in our previous work (e.g. Fukumura et
al., 2010a, 2017, 2021, reference therein). The photo-absorption cross-section
$\sigma^{i}_{\rm abs}$ for a given ion is then calculated with the Voigt
profile (e.g. Mihalas, 1978; Kotani et al., 2000; Hanke et al., 2009) using
the simulated wind kinematics (e.g. Fukumura et al., 2010a).

In this framework, the line width (or shape) is naturally determined as a
result of the internal wind velocity gradient (or shear velocity) $v_{\rm sh}$
along a LoS from the MHD wind model, which is typically on the order of $\sim
10\%$ of the LoS velocity itself at a given distance. Hence, we obtain the
velocity shear directly for the Voigt function rather than employing an
arbitrary “turbulent motion” parameterization.

With these quantities being available, the synthetic multi-ion UFO spectrum
(mhdwind) is calculated by computing the line optical depth $\tau^{i}(E)$ as a
function of energy $E$ such that

$\displaystyle\tau^{i}(E)\equiv\sigma^{i}_{\rm abs}(v_{\rm sh};E)N^{i}_{\rm
ion}(E)\ .$ (7)

Therefore, the predicted broadband spectrum $f_{\rm
obs}(E)\propto\Pi_{i}e^{-\tau^{i}(E)}$ is a function of wind-related
parameters ($\theta,p,f_{D}$) coupled to the other parameters associated with
radiation field ($\Gamma,\alpha_{\rm OX},\lambda_{\rm ion}$). This is how we
simulate theoretical UFO spectra (mhdwind) as we aim to investigate spectral
signatures that could be attributed to the generic features of MHD disk-winds
perhaps in terms of the wind kinematics and/or density distribution as
described above.

To better illustrate the underlying physics responsible for characterizing
broadband absorption spectra as a consequence of radiative transfer, we show
an example of the simulated AMD in Figure 1 (left) for a series of primary
ions; local hydrogen-equivalent columns (value expressed on left ordinate) for
Fe xxvi (green), Fe xxv (cyan), S xvi (orange), Si xiv (yellow), Mg xii (dark
blue), Ne x (red) and O viii (dark) along with the LoS wind velocity $v_{\rm
out}/c$ (purple; value expressed on right ordinate) assuming a fiducial set of
parameters; i.e. $\Gamma=2,\theta=40^{\circ},p=1.2,f_{D}=1,\alpha_{\rm
OX}=1.5$ and $\lambda_{\rm ion}=0.05$. While the exact AMD profile can vary
from one case to the other depending on the input SED and wind conditions,
this is one of the typically obtained ionic distributions relevant for Seyfert
AGN UFOs in our calculations. It should be noted that the velocity profile
$v_{\rm out}(\xi)$ is always unique in the sense that the fastest part of the
wind at the innermost layer always possesses the highest ionization parameter
value. This is because acceleration mechanism in our MHD framework is not due
to radiation, but to magnetic processes (by both magnetocentrifugal and
pressure gradient forces; e.g. Blandford & Payne 1982; Contopoulos & Lovelace
1994; Fukumura et al. 2010a). It is seen that the columns $N^{i}_{\rm ion}$ of
individual ions are progressively produced over a large extent of LoS distance
(or ionization parameter) as coronal X-ray radiation traverses the wind. The
predominant fraction of the LoS-integrated column per ion is found in the
higher ionization regime (i.e. in the vicinity of the central engine where the
wind velocity is near-relativistic, $v/c\mathrel{\raise
2.15277pt\hbox{$>$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}0.1$, in the
light yellow region of the figure) responsible for the final absorption
features we observe. The shape of a typical column profile is asymmetric in a
way that the column rapidly falls off with decreasing $\xi$ (i.e. increasing
distance) past its peak point where the maximum local column is produced; i.e.
approximately at $\log\xi\sim 4.3$ for the soft X-ray absorbers while at
$\log\xi\sim 5.0-5.5$ for Fe xxv/Fe xxvi ions. This AMD hence indicates that
most of the ions (i.e. low-ionization ions such as O viii and high-ionization
ions such as Fe xxvi) are necessarily near-relativistic (i.e. highly
blueshifted) with an appreciable total column being identified as multi-ion
UFOs, especially, Fe xxv/Fe xxvi being broader and faster777In general, this
can depend on the specific ionizing SED and luminosity…etc..

Figure 1 (right) schematically depicts how the absorber’s velocity would
change for different ionizing X-ray photons with respect to AMD. The velocity
of the wind $v_{\rm out}$ at a given $\xi$ value is lower with more ionizing
photons (red) compared to that with less ionizing photons (dark) because the
velocity profile $v_{\rm out}(\xi)$ systematically shifts towards higher
ionization with increasing ionizing luminosity as the innermost wind is always
ionized the most. Given that the value of the ionic column is essentially
determined by the ionization threshold, the production of local ionic column
for a given element (e.g. Fe xxvi) occurs roughly in the same ionization range
(solid dark/red curves). Filled blue circle denotes where the local column is
maximally produced. The innermost wind irradiated by more (less) ionizing
photons are labeled by red (dark) open circle where $\xi$ is the highest, as
expected. In the presence of more ionizing photons in the illuminating SED (in
red), the ionization parameter becomes higher by definition and the wind
produces lower columns of near-relativistic blueshift (indicated by squared
domain). As a consequence, the integrated column to be observed predominantly
consists of those with lower blueshift, thus “slower” UFOs. In contrast, much
of the total column is highly blueshifted if the ionizing photons in SED are
less (in shaded domain), thus “faster” UFOs. Therefore, the differences in
blueshift and ionic column due to the amount of ionizing photons inevitably
lead to different absorption features as shall presented below in §3.1.1.

Figure 2: Theoretical multi-ion absorption spectra (ratio to the continuum)
for different photon index $\Gamma$ with
$\theta=30^{\circ},p=1.3,f_{D}=1,\alpha_{\rm OX}=1.5$ and $\lambda_{\rm
ion}=0.1$.

####  3.1.1 Model Dependencies of Multi-Ion MHD Disk-Winds

To further follow up the significance of the simulated AMD shown in Figure 1,
we calculate a number of multi-ion UFO spectra (mhdwind) by allowing for one
parameter to be varied at a time. For example, the dependence of a power-law
slope $\Gamma$ is shown in Figure 2 where we assume
$\theta=30^{\circ},p=1.3,f_{D}=1,\alpha_{\rm OX}=1.5$ and $\lambda_{\rm
ion}=0.1$. It is clear that the overall UFO signatures tend to be enhanced
with softer (steeper) power-law component in the absence of efficient ionizing
photons. Note that the trough energy in each absorption line remains almost
unchanged, while the line width is dramatically affected as a result of
ionization equilibrium because the corresponding velocity profile $v_{\rm
out}(\xi)$ with AMD is accordingly shifted when $\Gamma$ changes, as depicted
in Figure 1 (Right). When the SED is harder (i.e. smaller $\Gamma$), the inner
layer (i.e. faster moving part) of the global MHD wind can be fully ionized
producing little observable columns. Thus, the main absorption feature of the
UFOs in that case will be governed predominantly by moderate or slower layer
of the wind where the broadening is weakened but the centroid energy remains
the same. This trend is systematically found in the broadband energy ranging
from $\sim 1$ keV to Fe K complex. In particular, Fe xxv/Fe xxvi lines become
so broad that the two are blended together for softer SED (e.g. $\Gamma=2.5$)
as if it were a single edge feature.

In Figures 10-13 in Appendix A, we show more synthetic multi-ion absorption
spectra of the mhdwind model to demonstrate various dependences on the model
parameters. All in all, it is striking, and a common feature, that the most of
the absorption features from different ions in these calculations are
noticeably asymmetric such that blue tails are more extended and skewed
towards higher energy. This is a manifestation of the unique AMD coupled to
the MHD wind kinematics shown in Figure 1 as discussed in §3.1. That is, those
columns produced from the wind at near-relativistic blueshift
($v/c\mathrel{\raise 2.15277pt\hbox{$>$}\mkern-14.0mu\lower
2.58334pt\hbox{$\sim$}}0.1$) largely dictate the asymmetric character in the
spectrum as a “tell-tale” signature.

As mentioned earlier, one of the common spectral features from multi-ion UFOs
in these calculations is blueshifted tails due to the generic kinematics of
MHD-driven winds; i.e. the closer in to AGN, the faster the outflow. This
unique characteristics of the magnetized wind can imprint a distinct
absorption line profile through the shape of AMD as a consequence of
photoionization balance as illustrated in Figure 3 (Left) (see also Figure 1).
In comparison with other disk-wind models, the expected shape of the line
profile from MHD-driven winds (red) is generally unique and distinctive enough
to be separately identified. For example, line-driving (cyan) in general tends
to produce an asymmetric line shape of an extended red wing (which is reversed
to MHD-driving discussed here) due to an asymptotically increasing terminal
wind velocity, whereas thermal-driving888Due to its typically low velocity,
thermal-driving is not really relevant for UFOs. (green) allows for a
relatively narrow line shape of little asymmetry because of a generically
constant (slow) motion (C. Done and J. Reeves, in private communications). In
contrast, a phenomenological Gaussian/Voigt line profiles (dashed) are
symmetric.

Figure 3: Left: Schematic diagram showing a comparison of characteristic
absorption profiles among various wind driving mechanisms; Gaussian/Voigt
profiles (dashed), thermal-driving (green), line-driving (cyan) and MHD-
driving (red). Right: Spectral change in Fe xxv/Fe xxvi lines due to disk
truncation at the inner launching radius parameterized by $q_{T}$.

On the other hand, it should be pointed out that the exact asymmetric line
shape is very sensitive to the shape of AMD (including the velocity profile
$v(\xi)$); the asymmetry could be minimized or even reversed depending on the
underlying SED, wind property and other physical factors. Therefore, we
emphasize that the obtained asymmetric line profiles here should be regarded
as the most probable case on average.

Since we are focused on UFOs in the context of MHD driving, ionic columns are
necessarily produced at smaller distances from AGN where the velocity is near-
relativistic (see Fig. 1 (left)). Since the broadening of lines is determined
by the wind shear velocity (from the LoS velocity gradient) at a given
distance as discussed in §3.1, the line width tends to be very large
considering that $v_{\rm shear}/v_{\rm out}\sim 0.1$ along a LoS. For this
reason, the UFO spectra in our model tend to be broad such that subtle atomic
line features might be blurred. For example, despite our expectation, no
doublet structure is resolved for Fe xxvi Ly$\alpha$ lines (6.973 keV and
6.952 keV) due to blending, while it should be indeed identified in BH XRB
disk winds because of their much lower velocities (e.g. Miller et al., 2015;
Fukumura et al., 2021).

###  3.2 The Effects of the Inner Disk Truncation

Accretion disk winds in AGNs are often discussed in comparison with ionized
outflows in BH XRBs. As an ideal laboratory owing to their much shorter time
scale, sequenced X-ray observations of BH transient events can provide a
valuable insight into wind’s morphology, variable nature and likely
correlations, for example. Among those BH XRBs, a handful of systems are known
to exhibit wind signatures in X-ray spectra. While there is no clear analogy
for AGNs, pronounced disk winds are indeed present in BH XRBs during high/soft
(bright) state, while winds appear to be extremely weak (if not absent) during
low/hard (quiescent) state, as they go through a series of distinct accretion
modes in the hardness-intensity diagram (aka. q-diagram) (e.g. Fender &
Belloni, 2004; Fender et al., 2004; Remillard & McClintock, 2006; McClintock &
Remillard, 2006; Done et al., 2007; Belloni, 2010; Ponti et al., 2012). During
high/soft state, the standard thin accretion disks (Shakura & Sunyaev, 1973;
Novikov & Thorne, 1973) in the context of general relativity are thought to
extend all the way down to the ISCO based on X-ray observations of the thermal
disk continuum (e.g. McClintock et al., 2014; Li et al., 2005; Shafee et al.,
2006) and interpretations of asymmetric broad Fe line profiles (e.g. Fabian et
al., 2000). On the other hand, it has been suggested that the inner disk may
actually be truncated beyond the ISCO during low/hard state (as mass accretion
rate drops), considering that the inner part of accretion becomes optically
thin, hotter and radiatively inefficient (such as ADAF/ADIOS; e.g. Narayan &
Yi 1994; Blandford & Begelman 1999) forming a compact corona around a BH that
is surrounded by the standard thermal disk (e.g. Esin et al., 1997; Done et
al., 2007). While such a speculation has gained much attention, the disk
truncation signatures, also independently derived from reflection spectroscopy
and reverberation lags, have still remained elusive observationally (e.g.
Shidatsu et al., 2011; Petrucci et al., 2014; Plant et al., 2015; García et
al., 2015; De Marco et al., 2017).

To follow up a possibility of inner disk truncation in the context of Seyfert
UFOs, we consider here a possible consequence of such a truncation of the
inner disk. Given that the MHD-driven UFOs are primarily launched from the
innermost region of the disk (where the Keplerian motion is fast and
ionization state is high; see Figure 1), it is expected that removing the
inner part of the disk should significantly reduce the amount of near-
relativistic plasma (i.e. UFOs) to be launched. As a result, the observed UFO
line profile could be substantially less blueshifted depending on the
truncation radius $R_{T}$. To probe this effect, we take one of our template
runs (i.e. $\theta=40^{\circ},\Gamma=2,\alpha_{OX}=1.5$…) and calculate a line
spectrum by parameterizing $R_{T}$ as $R_{T}\equiv q_{T}R_{\rm in}\sim
q_{T}R_{\rm ISCO}$ where we set $q_{T}=1,10,40,80$ and $160$. That is, the
disk is not truncated for $q_{T}=1$, while extremely truncated at large
distance for $q_{T}=160$. Figure 3 (Right) demonstrates the effect of $q_{T}$
on Fe xxv/Fe xxvi lines as an example. It is seen that the most blueshifted
part of the feature is gradually disappearing with increasing $q_{T}$ as
expected, whereas the centroid absorption structure (with small blueshift)
remains almost unaffected as it is produced by the exterior wind that is
launched from the outer part of the disk. Note that the line depth is almost
independent of $q_{T}$ since it is predominantly determined by the wind
density factor $f_{D}$ which is fixed in this work.

Figure 4: Simulated 100ks XRISM/Resolve spectra for different photon index
$\Gamma$ with $\theta=30^{\circ},p=1.3,\alpha_{\rm OX}=1.5,f_{D}=1$ and
$\lambda_{\rm ion}=0.1$. Inset shows a close-up of Fe K absorbers.

###  3.3 The Effects of Soft Excess

Given that a good fraction of Seyfert 1 AGNs exhibits soft X-ray excess (SE),
another unique soft X-ray component, in their SED (i.e. more than 50% to 90%;
e.g. Turner & Pounds 1989; Crummy et al. 2006; Boissay et al. 2016), we also
consider a possible effect of SE on the UFO signatures. Although SE is present
in the energy band lower than the most of the major UFO lines (e.g. Mg xii, Si
xiv, S xvi and Fe K ions), a potential impact of radiative transfer on the
production of these UFO columns is yet to be known. For an illustration
purpose, we use a single blackbody of temperature $kT_{\rm SE}=100$ eV to
phenomenologically mimic the SE component in SED, which is usually a
reasonable representation of it. For simplicity, it is assumed here that SE
originates almost entirely from the same region producing the primary emission
or completely within the launching region of the outflows; i.e. no “diffuse”
(larger than flow cone base) component of the SE. We then make a comparison,
with and without SE in an assumed SED, by performing radiative transfer
calculations with XSTAR to see the resulting UFO spectra.

Figure 5 Left shows a representative comparison of calculated AMD for selected
ions with SE (solid; its normalization of $K_{\rm SE}=3\times 10^{-8}$) and
without SE (dashed) in the injected SED of $\Gamma=2$ and $\alpha_{\rm
OX}=1.5$ with the rest of the model parameters being the same in both cases.
It is seen that the ionization front for various transitions are almost
systematically shifted towards higher $\xi$ regime (corresponding spatially to
smaller distances to the BH) due to the extra soft photons from the SE,
allowing the produced UFOs to be more blueshifted and broader in the spectrum.
There is little change, though, in the calculated column.

To confirm this view, we further calculate a broadband UFO spectrum based on a
similar set of parameters by assuming different SE normalizations in Figure 5
Right; $K_{\rm SE}=3\times 10^{-8}$ (moderate in blue) and $6\times 10^{-7}$
(strong in red) cases. As demonstrated, the presence of SE could have a
significant impact on the broadband multi-ion UFO spectra depending on its
strength. In an extreme case of a strong SE flux, a large fraction of ionic
column per transition line can be produced in the inner faster regions of the
MHD wind in a way that the resulting absorption lines may be broad enough to
be blended together (e.g. in red) in theory purely due to radiative transfer
process (i.e. photoionization). Given that the presence of SE tends to make
ionizing spectrum softer, it is consistent that the physical role of SE in UFO
spectral features is qualitatively very similar to that by softer X-ray slope
as shown in Figure 2 in §3.1.1.

Figure 5: Left: Sample comparison of AMD, similar to Figure 1, with (solid)
and without (dashed) SE flux in the injected SED for selected ions assuming
$\theta=40^{\circ},p=1.3,\alpha_{\rm OX}=1.5,f_{D}=1$ and $\lambda_{\rm
ion}=0.05$. Right: Theoretical multi-ion absorption spectra (ratio to the
continuum) for different SE normalization of $K_{\rm SE}=6\times 10^{-7}$
(strong in red) and $3\times 10^{-8}$ (moderate in blue) in comparison with
the absence of SE (in dark) assuming $\theta=30^{\circ},p=1.3,\alpha_{\rm
OX}=1.5,f_{D}=0.1$ and $\lambda_{\rm ion}=0.05$.

###  3.4 Spectral Simulations with Microcalorimeters

By exploiting a library of theoretical spectra of multi-ion UFOs presented in
§3.1, we further investigate observational implications here in an
anticipation of upcoming microcalorimeter missions with XRISM/Resolve and
Athena/X-IFU in an effort to realistically assess a plausibility of
constraining the UFO signatures. For subsequent simulations, we use
xarm_res_h5ev_20170818.rmf for XRISM and
XIFU_CC_BASELINECONF_2018_10_10_EXTENDED_LSF.rmf for Athena through this work.

####  3.4.1 Feasibility with XRISM/Resolve Observations

Assuming a fiducial 2-10 keV X-ray flux of $\sim 2.3\times 10^{-11}$ erg cm-2
s-1 for canonical Seyfert AGNs, we perform spectral simulations of the models
considered in §3.1 with 100ks XRISM/Resolve exposure. These are idealized
simulations considering only the theoretical UFO component with no additional
spectral complexity.

Figure 4 shows the simulated spectra for different $\Gamma$ where the richness
of the UFO features seem to be well captured ranging from $\sim 0.5$ keV to
the Fe K complex band. The overall asymmetry of multi-ion absorbers are still
traceable in these simulated data to the extent that the expected “tell-tale”
MHD-driving signature can be resolved especially for softer X-ray spectrum
where the wind is less overionized when a fewer number of hard X-ray photons
can participate in ionization. The other simulated XRISM/Resolve spectra for
various dependences are also shown in Figure 14-17 in Appendix B.

####  3.4.2 Convolution of UFOs with Additional Absorbers in Simulated Data

Observed X-ray spectra of a large number of radio-quiet Seyfert AGNs are
generally well known to contain multiple absorption components including
broadband complex atomic features; e.g. warm absorbers, typically
characterized by a series of ions at different charge states (e.g. Crenshaw,
Kraemer & George, 2003; Blustin et al., 2005; Steenbrugge et al., 2005;
McKernan et al., 2007; Holczer et al., 2007; Detmers et al., 2011; Fukumura et
al., 2018; Laha et al., 2021). Due to the atomic physics, primarily dictated
by the oscillator strength and Einstein coefficient for individual resonant
transitions per ion, stronger warm absorbers on average are predominantly
given by H/He-like species appearing in the soft X-ray to UV band (also
occasionally accompanied by Fe L-shell transitions and unresolved transition
array (UTA) due to 2p-3d transitions in Fe M-shell ions as well; e.g. Behar et
al. 2001a, b; Netzer 2004). In addition, some Seyfert AGN spectra occasionally
give a hint at the presence of partially covering ionized materials (e.g.
Matzeu et al., 2016).

To make a more realistic diagnosis for a plausible detection of MHD-driven UFO
features by robustly constraining the wind parameters, we simulate another
microcalorimater spectrum based on a similar set of MHD UFO model that are now
convolved with these additional absorption components. That is, we adopt a
template spectral model, mhdwind mtable model, of $\Gamma=2,\alpha_{\rm
OX}=1.5,\theta=35^{\circ},p=1.25,f_{D}=0.1,$ and $\lambda_{\rm ion}=0.08$, as
a test case. For warm absorbers, we follow the conventional approach by
employing a three-zone warmabs model generated with xstar2xspec such that

$\displaystyle{\tt
warmabs}=\left\\{\begin{array}[]{llr}N_{H}=10^{21},\log\xi=2,v_{\rm
out}/c=0.001&~{}~{}\textmd{(cold gas)},\\\ N_{H}=10^{22},\log\xi=3,v_{\rm
out}/c=0.003&~{}~{}\textmd{(warm gas)},\\\ N_{H}=10^{23},\log\xi=4,v_{\rm
out}/c=0.01&~{}~{}\textmd{(hot gas)},\end{array}\right.$ (11)

assuming a power-law continuum of $\Gamma=2$ and a uniform turbulent
velocity999We have verified that the resulting warmabs spectrum is only weakly
sensitive to the choice of the turbulence velocity since the observed line
width (e.g. Gaussian width $\sigma$) is typically only a few hundred km s-1
(e.g. Kaspi et al., 2000; Netzer et al., 2003; Krongold et al., 2003; Blustin
et al., 2005; Gabel et al., 2005, for radio-quiet Seyfert 1s like NGC 3783),
which would be very distinct for those of UFOs (e.g. Tombesi et al., 2013;
Gofford et al., 2015; Nardini et al., 2015; Reeves et al., 2018a). of
$\sigma=500$ km s-1 (e.g. Kaspi et al., 2000; Netzer et al., 2003; Krongold et
al., 2003; Blustin et al., 2005; Gabel et al., 2005). Independently, a
partially covering ionized absorber (perhaps in a discrete patchy cloud) is
represented with zxipcf model Miller et al. (2006); Reeves et al. (2008) by

$\displaystyle{\tt zxipcf}=\left\\{\begin{array}[]{llr}N_{H}=5\times
10^{23},\log\xi=4,v_{\rm out}/c=0.01&~{}~{}\textmd{(partial absorbers)},\\\
\end{array}\right.$ (13)

with a turbulent velocity of 200 km s-1 and the covering fraction of 0.5.
Thus, the composite model is expressed symbolically as

$\displaystyle{\tt composite=tbabs\times po\times mhdwind\times warmabs_{\tt
C}\times warmabs_{\tt W}\times warmabs_{\tt H}\times zxipcf}$ (14)

where the subscript denotes each warm absorber zone in equation (11), which is
combined with the partial covering absorber (zxipcf) in equation (13) while
being multiplied by the underlying power-law spectrum (po) and the Galactic
neutral absorber (tbabs) with $N_{H}^{\rm Gal}=10^{20}$ cm-2. We then generate
a 100ks XRISM/Resolve spectrum assuming the same 2-10 keV flux of $\sim
2.3\times 10^{-11}$ erg cm-2 s-1 as is considered in §3.2.1.

Figure 6: Upper: Simulated 100ks XRISM/Resolve spectrum (in dark) for
$\theta=35^{\circ},p=1.25,\Gamma=2,\alpha_{\rm OX}=1.5,f_{D}=0.1$ and
$\lambda_{\rm ion}=0.08$ with the best-fit composite model (in red). See Table
2 for the best-fit model parameters. Middle: Unfolded best-fit model spectrum.
Lower: Residuals in the form of data/model ratio in the absence of the UFO
component (mhdwind).  Table 2: Best-Fit Composite Model for 100 ks Simulated
XRISM/Resolve Spectrum

Component | Parameter | Best-Fit Value | Model Value
---|---|---|---
tbabs |  $N_{H}^{\rm Gal}$ [cm-2] |  $10^{20}$† |  $10^{20}$†
po | $\Gamma$ | $2.00^{+0.01}_{-0.01}$ | 2
mhdwind | $\alpha_{\rm OX}$ | $1.51^{+0.02}_{\rm-1.51}$ | 1.5
| $\lambda_{\rm ion}$ | $0.081_{-0.004}^{+0.003}$ | 0.08
|  $\theta$ [deg] | $34.9_{-1.0}^{+2.1}$ | 35
| $p$ | $1.22_{-1.22}^{+0.04}$ | 1.25
| $f_{D}$ | $0.074_{-0.01}^{+0.03}$ | 0.1
warmabs | $N_{\rm H,Cold}$ | $1.01_{-1.01}^{+0.33}\times 10^{21}$ | $10^{21}$
| $\log\xi_{\rm Cold}$ | $1.95_{-0.07}^{+0.08}$ | $2$
| $v_{\rm out,Cold}/c$ | $-8.74_{-4.5}^{+3.3}\times 10^{-4}$ | $10^{-3}$
| $N_{\rm H,Warm}$ | $1.00_{-0.06}^{+0.29}\times 10^{22}$ | $10^{22}$
| $\log\xi_{\rm Warm}$ | $2.97_{-0.02}^{+0.03}$ | $3$
| $v_{\rm out,Warm}/c$ | $-2.96_{-0.14}^{+0.12}\times 10^{-3}$ | $3\times 10^{-3}$
| $N_{\rm H,Hot}$ | $1.1_{-0.16}^{+0.59}\times 10^{22}$ | $10^{22}$
| $\log\xi_{\rm Hot}$ | $4.00_{-0.04}^{+0.04}$ | $4$
| $v_{\rm out,Hot}/c$ | $-9.80_{-0.23}^{+0.24}\times 10^{-3}$ | $10^{-2}$
zxipcf | $N_{\rm H,zxipcf}$ | $4.00_{-1.09}^{+1.35}\times 10^{23}$ | $5\times 10^{23}$
| $\log\xi_{\rm zxipcf}$ | $3.98_{-0.08}^{+0.07}$ | $4$
| $v_{\rm out,zxipcf}/c$ | $-1.00_{-0.01}^{+0.01}\times 10^{-2}$ | $10^{-2}$
|  $\chi^{2}/$dof |  $15930.27/18982$ (18218.86/18987)‡ |

We assume $M=10^{8}M_{\odot}$, $f_{\rm 2-10keV}=2.3\times 10^{-11}$ erg cm-2
s-1 and $L_{\rm ion}=10^{44}$ erg s-1.
† Fixed. ‡ In the absence of the UFO component (mhdwind).

The simulated XRISM/Resolve spectrum is first generated based on the composite
wind model expressed in equation (8). We then fit the mock data with the same
model to retrieve the best-fit broadband spectrum of multi-ion UFOs by
allowing mhdwind, warmabs and zxipcf componets to be varied simultaneously
(except for the fixed turbulence velocities). The upper panel of Figure 6
shows the simulated spectrum (in dark) along with the folded best-fit model
(in red). The middle panel shows the unfolded best-fit model. A number of UFO
signatures in this simulated spectrum seems to be well accounted for by the
composite model successfully constraining the UFO parameters at a reasonable
statistical significance (yielding $\chi^{2}$/dof=15930.27/18982). The best-
fit parameters for the simulated spectrum are listed in Table 2. When fitted
with the composite wind model, the broadband UFO features are unambiguously
resolved and the correct parameter values are successfully retained within a
reasonably narrow range of uncertainties. It is seen that the predicted UFO
signatures of relatively broad line profiles of asymmetry appear to be immune
to the spectral contamination by external absorbers under this particular
parameter set. The uniquely blueshifted UFO line shape of asymmetry (discussed
in §3 and Figure 3) is still unmistakenly preserved and identified by simple
visual inspection.

To see the significance of mhdwind component in the spectrum, we subsequently
removed the UFO component (mhdwind) from the best-fit spectrum (composite).
The lower panel of Figure 6 now shows the residuals (in the form of data/model
ratio) after the subtraction of the UFO component (mhdwind) to examine whether
the “tell-tale” sign of the UFO signatures can still be observed in data. We
find that the unique spectral features of MHD-driven UFOs of multiple ions in
mhdwind are clearly seen in the residual, thus enabling mhdwind component to
be successfully disentangled. Without mhdwind component, the best-fit model
becomes significantly worse resulting in $\chi^{2}$/dof=18218.86/18987 (i.e.
$\Delta\chi^{2}=2288.59$ for $\Delta$dof = 5 by removing four mhdwind
parameters). Therefore, this simulation potentially demonstrates a realistic
viability of extracting MHD-driven UFO signatures of multiple ions in the
presence of contaminating non-UFO absorbers.

From a technical perspective, it is known that bright Seyfert AGN spectra
often exhibit reflection components resulting from photons reprocessed by
disks (e.g. Magdziarz & Zdziarski, 1995; Ross & Fabian, 2005). It is hence
conceivable that such reflection (consisting of a series of atomic features
such as emission and absorption/edges as well as Compton hump) might also
contaminate the underlying UFO signatures. We further investigate the impact
of such reflection features by implementing both xillverCp (for distant
reflection) and relxillCp (for relativistic reflection) models (García et al.,
2013) in XRISM/Resolve simulations. In Appendix C we present a 100 ks
XRISM/Resolve spectrum with a fiducial reflection component to find that even
in that case the expected MHD spectral signatures indeed remain preserved.

Figure 7: Zoom-in on simulated 100 ks XRISM/Resolve spectrum for
$\Gamma=2,\alpha_{\rm OX}=1.5,\lambda_{\rm ion}=0.08,p=1.3,f_{D}=0.1$ and
$\theta=35^{\circ}$ showing the residual (ratio) from the best-fit composite
model (composite in red) in the absence of MHD UFO component (mhdwind).

We further look into ion-by-ion UFO components in a simulated broadband
spectrum in order to support our claim that microcalorimeter data can in fact
be exploited as a powerful diagnostic tool to realistically identify MHD-
driving montages such as unique asymmetric line profiles (see Fig. 3 left). In
Figure 7 we are focused on a series of major absorption lines from a 100 ks
XRISM/Resolve simulation for $\Gamma=2,\alpha_{\rm OX}=1.5,\lambda_{\rm
ion}=0.08,p=1.3,f_{D}=0.1$ and $\theta=35^{\circ}$ showing the residual
(ratio) from the best-fit composite model (composite in red) in the absence of
MHD UFO component (mhdwind). As demonstrated earlier, a clear UFO signature of
asymmetric (broad) line is undoubtedly seen for this multi-ion MHD UFO whose
shape is not necessarily matched with the phenomenological Gaussian or Voigt
functions. While the exact shape and strength (i.e. line optical depth and
equivalent width) of each line depends sensitively on wind parameters, the
characteristic UFO features are systematically imprinted in the broadband.

In anticipating for the next generation X-ray microcalorimeter instrument
beyond XRISM mission, we also explore an observational viability of our MHD
UFO model by performing a number of simulations with Athena/X-IFU instrument.
Assuming an almost identical set of fiducial model parameters as considered
for XRISM simulations, broadband UFO spectra of multi-ion are simulated with
10 ks Athena/X-IFU exposure assuming $\Gamma=2,\alpha_{\rm
OX}=1.5,\lambda_{\rm ion}=0.1,p=1.2$ and $\theta=35^{\circ}$ in Figure 8 in
comparison with the earlier XRISM/Resolve simulations in Figure 7. It is
obvious that the same simulated UFO features are further refined at more
statistically significant level even with 10 ks exposure, owing to Athena’s
large collecting area. In this simplified comparison, it is thus implied in
principle that more than ten time-resolved observations could be made with
Athena to obtain data of the same spectroscopic quality expected from a single
100 ks XRISM observation in an attempt to ambitiously conduct an outflow
reverberation mapping for (highly) variable nature of the observed UFOs (e.g.
Matzeu et al., 2016; Parker et al., 2018).

Figure 8: Zoom-in on simulated 10 ks Athena/X-IFU spectrum for
$\Gamma=2,\alpha_{\rm OX}=1.5,\lambda_{\rm ion}=0.1,p=1.2,f_{D}=0.1$ and
$\theta=35^{\circ}$ showing the residual (ratio) from the best-fit composite
model (composite in red) in the absence of MHD UFO component (mhdwind).

Figure 9: Confidence contours of $(\theta,f_{D})$ for different values of wind
density factor $f_{D}$ derived from the best-fit models with
$\theta=35^{\circ}$ showing 68% (red), 90% (green) and 99% (blue) levels.
Left: XRISM/Resolve 100 ks exposure. Right: Athena/X-IFU 10 ks exposure.

Finally, we compare the statistical confidence in constraining, for example,
the inclination $\theta$, for different wind density factor $f_{D}$ in Figure
9 (left) where their best-fit values are shown for low ($f_{D}=0.01$),
intermediate ($f_{D}=0.1$) and high ($f_{D}=0.5$) density values assuming
$p=1.3,\theta=35^{\circ}$ and $\lambda_{\rm ion}=0.05$ for the simulated 100ks
XRISM/Resolve data. The expected uncertainties in both quantities are
relatively small enabling one to robustly retain the correct UFO parameters
with 100 ks XRISM/Resolve exposure unless the wind density (i.e. $f_{D}$) is
too low. This is because the predicted absorption lines would become very
narrow and weak due to the inner part of the wind being almost fully ionized
(where the wind is near-relativistic) if $f_{D}$ is very low. Again, a mere 10
ks exposure with Athena/X-IFU is found to drastically improve such a
limitation to constraining the UFO parameters even for very weak UFO features
(i.e. low $f_{D}$) as shown in Figure 9 (right), demonstrating a high efficacy
in accurately recovering the correct values of $f_{D}$ as well as inclination
$\theta$, as an example.

##  4 Summary & Discussion

In this work, we conduct a systematic spectral modeling of the multi-ion X-ray
UFO features (i.e. $\sim 0.5-10$ keV range) relevant for radio-quiet Seyfert
AGNs in the context of MHD-driven accretion disk winds. Considering some
generic features of MHD-driven UFOs, our primary focus is to investigate
whether or not there exist some unique spectral signatures mainly attributed
to MHD driving in predicted UFO absorption lines that can be seen in
observations. By exploiting a set of six parameters in our MHD wind model,
namely, X-ray photon index ($\Gamma$), X-ray to O/UV strength ($\alpha_{\rm
OX}$), ionizing luminosity ratio ($\lambda_{\rm ion}$), inclination angle
($\theta$), wind density factor ($f_{D}$) and wind density slope ($p$), we
have shown on average that many of the synthetic UFO spectra commonly exhibit
an asymmetric line profile of an extended blue tail toward higher energy
manifesting the underlying MHD wind kinematics through photoionization. As
demonstrated by the AMD in Figure 1, our MHD-wind model allows for
simultaneous multi-ion UFOs (i.e. ranging from low to high ionization
absorbers such as O viii and Fe xxvi) in the broadband X-ray spectrum. All the
calculations assume the solar abundances throughout this work (i.e. $A_{\rm
ion}=A_{\rm ion,\odot}$).

We further perform a series of microcalorimeter simulations based on the
synthetic UFO spectra in the broadband (mhdwind) in anticipation of the future
X-ray missions with XRISM/Resolve and Athena/X-IFU instruments to better
examine an observational viability of the model. Assuming a set of fiducial
parameters, we find that the unique asymmetric signature of blueshift in
multi-ion UFO lines can be well captured in many simulated spectra. To
realistically test its plausibility of detection, additional absorption
components are independently added to our simulations in the form of 3-zone
warm absorbers composed of cold, warm and hot plasma (warmabs) as well as a
partially covering ionized gas (zxipcf). Despite the presence of such a
spectral contamination, it is demonstrated that the predicted UFO signatures
in mhdwind are unambiguously retained in the simulated data. If indeed
imprinted in high fidelity microcalorimeter spectra, it is conceivable that
the predicted UFO lines of unique features can be potentially used as a
diagnostic proxy to differentiate different launching mechanisms proposed
today.

In the present formalism, a number of complications are not taken into account
for simplicity. First, we treat the primary parameters
($\theta,p,f_{D},\Gamma,\alpha_{\rm OX},\lambda_{\rm ion}$) being independent
of each other (see Fig. 4 and other dependences in Appendices). In reality, it
has been reported, for instance, that some observable AGN measurements appear
to be (tightly) correlated in various samples of AGN surveys; e.g. $\Gamma$,
$\alpha_{\rm OX}$, Eddington ratio and monochromatic UV luminosities (e.g.
Steffen et al., 2006; Shemmer et al., 2008; Luo et al., 2014; Laurenti et al.,
2021). Although these correlations are preferentially suggested in highly-
accreting quasars, this may well be relevant for Seyfert 1s accreting at low
Eddington rate. If this is the case, our simulation results could be less
relevant in certain parameter space that we have probed in this work; e.g.
X-ray bright AGNs at high Eddington ratio (i.e. higher $\lambda_{\rm ion}$
with smaller $|\alpha_{\rm OX}|$ and/or higher $\lambda_{\rm ion}$ with softer
$\Gamma$). This would need to be considered for quantitative simulations
specific to individual AGN/quasar UFOs.

Additional complications associated to spectral features include SE and
reflection components often seen in many Seyfert AGNs. We phenomenologically
add SE component in our fiducial AGN SED to calculate its effect and find a
significant role in changing ionization structure of the wind through
radiative transfer such that almost all major ions of various charge state
tend to be produced at smaller distances (towards the BH) in higher ionization
state where the MHD wind is faster. Stronger SE causes multi-ion UFO lines to
be more blueshifted and broader in a way similar to the role of photon index
$\Gamma$, both of which involves more soft photons being available for
photoionization. On the other hand, the presence of reflection features (i.e.
emission and absorption/edges) is also considered as another source of
spectral contamination against the expected MHD-driven UFO signatures. By
implementing xillver and relxill models, we perform a similar 100ks
microcalorimeter simulation for XRISM/Resolve. It is demonstrated that even a
relatively pronounced reflection flux (e.g. refl_frac=2 and $A_{\rm Fe}/A_{\rm
Fe,\odot}=5$) does not significantly distort the tell-tale MHD signature of
the blueshifted UFO absorbers.

We emphasize that our choice of defining the Eddington ratio, $\lambda_{\rm
ion}$, is simply a convenient way to control the X-ray luminosity $L_{\rm
ion}$ responsible for photoionization in this model (see §2.2). More subtle
factors related to $L_{\rm ion}$ (e.g. radiative efficiency in accretion
power, black hole spin, coronal geometry and disk structure) have been ignored
to avoid further complications and extra degrees of freedom in this problem.
It is also expected that X-ray luminosity should be intimately tied to wind
density (i.e. $n_{o}$ in our model) determined by the disk density that
essentially signifies accretion rate. In our calculations, a fixed value of
the wind density factor $f_{D}$ is naively decoupled from our Eddington ratio
$\lambda_{\rm ion}$. As addressed earlier, the mass accretion rate (thus the
wind density normalization parameterized by $f_{D}$) should in reality be
physically coupled to the X-ray luminosity and perhaps $\alpha_{\rm OX}$, for
example, as suggested in the past studies (e.g. Steffen et al., 2006; Shemmer
et al., 2008; Luo et al., 2014; Laurenti et al., 2021). For this reason, it is
not our primary interest to compare the absolute line properties (i.e. line
optical depth and EW), which is subject to the value of $f_{D}$. Instead, our
main focus is the relative comparison of line shape of multi-ion UFOs from one
case to the other so one can learn a systematic trend as a whole rather than a
specific quantitative change. Another prescription of X-ray luminosity such as
$L_{\rm ion}\propto f_{D}$, for example, would hence be more physically
motivated as is often employed in our past spectral analyses (e.g. Fukumura et
al., 2017, 2018, 2021), which, however, is beyond the scope of the present
work.

Our microcalorimeter simulations clearly show a high efficacy of retaining the
expected multi-ion UFO components in the composite broadband spectrum for a
given set of model parameters, indicating a persistent immunity of the UFO
features against the external contaminations due to other forms of ionized
absorbers. This immunity, however, is not always warranted depending on a
number of conditions. We simply assume a typical 2-10 keV flux of $\sim
2.3\times 10^{-11}$ erg cm-2 s-1 with certain exposures as a test case for
Seyfert 1 AGNs, but disentangling the predicted MHD-driven UFO features (i.e.
near-relativistic blueshift of asymmetry to higher energy) could obviously
become more challenging and very enigmatic in some cases (e.g. lower flux and
shorter exposure). Therefore, given the model limitation due to the fixed
value of $f_{D}$ in our simulations, the absolute values of the model
parameters that set the appearance and disappearance of multi-ion UFOs (shown
in our calculated spectra) should not be regarded as the generalized values,
although a qualitative trend can still be learned from those calculations.

With the photon statistics achievable with the current spectroscopic
instruments, it is not easy to conduct time-resolved analysis of rapid UFO
variability. As demonstrated in Figure 9 for a given UFO parameter set, only a
10 ks exposure with Athena/X-IFU appears to be sufficient to robustly resolve
these Seyfert UFOs owing to its large collecting area. This would
revolutionize the physics of UFOs since it can enable us to take a series of
snapshot spectra, each of which on a much shorter timescale that is currently
possible. By being able to study a temporal response of individual UFO
absorbers ranging from soft X-ray band to Fe K lines, spectroscopic
information can be further cast into timing property of various absorbing
ions, from which one could potentially make a geometrical (spatial) diagnosis
of multiple ions in the UFOs as the continuum varies in time. This is another
reason why multi-ion UFO modeling, and not just Fe K absorbers, is important
for understanding a global picture of the UFOs. Such a reverberation mapping
of multi-ion UFOs has been partially hinted at with the use of principal
component analysis (PCA) of XMM-Newton/EPIC data in order to study in detail
the correlations between the continuum source and the multiple ions in the
observed UFOs (e.g. Parker et al., 2018).

Concerning the expected asymmetric line profiles unique to MHD-driving
process, there have been some observational hints of the expected asymmetric
Fe K UFO features in NuSTAR and XMM-Newton data (e.g. a nearby Seyfert 2 AGN,
MCG-03-58-007 in Braito et al. 2022; a lensed broad absorption line quasar,
APM 08279+5255 in Chartas et al. 2009; a complex Fe K trough feature seen in
narrow-line Seyfert, 1H 0707-495 in Hagino et al. 2017, among others). Also,
it might be relevant for other types of disk-winds such as those of BH XRBs
occasionally detected, for example, with Chandra, in Galactic transients (e.g.
Miller et al., 2015; Chakraborty et al., 2021) as well as AGN warm absorbers
(e.g. Kaspi et al., 2000; Kallman et al., 2009; Fukumura et al., 2017). The
observed velocities of the ionized outflows in these systems are much lower
than those in UFOs; i.e. a few hundred to at most a thousand km s-1. The
expected blueshift is thus only up to $v/c\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}0.01$ meaning
that the line width is at most $\Delta E/E\mathrel{\raise
1.29167pt\hbox{$<$}\mkern-14.0mu\lower 2.58334pt\hbox{$\sim$}}0.001$. This
implies that the characteristic asymmetry would be observationally more
intangible even if indeed magnetically launched in those systems. While it
might still be plausible to differentiate between MHD-driving (with such an
asymmetry of smaller magnitude) and, for example, another promising process
such as thermal-driving (C. Done, in private communications), a robust
disentanglement could be perhaps less trivial while not impossible. Again,
analyzing multiple ions rather than a single Fe K feature would be a great
complement in order to probe a wide range of ionization structure in the wind.

In this work, we do not incorporate emission lines also expected to originate
from the same outflowing gas or separate regions. For example, Monte Carlo
approach has been often employed to calculate self-consistent emission and
scattering components (e.g. Hagino et al. 2015, 2016, 2017 with MONACO and Sim
et al. 2008, 2010a, 2010b also including special relativistic effects), while
XCORT has utilized XSTAR runs (Schurch & Done, 2007). More recently, Luminari
et al. (2018) has proposed WINE model with a special focus on detailed special
relativistic dimming for UFOs (see also Luminari et al., 2020, 2021). Such
emission process might be important to accurately assess the physical
properties of ionized absorbers because they can “fill in” the intrinsic
absorption features. For example, some very luminous quasars accreting at
near-Eddington rate such as PDS 456 is found to show a broad P-Cygni profile
in Fe K band associated with its prototype UFO where the wind may well be
Compton-thick (Nardini et al., 2015). On the other hand, one of the well-
studied Seyfert 1 AGN showing canonical X-ray warm absorbers, NGC 3783, is
also known to exhibit a handful emission lines in UV/soft X-ray band mostly
from the He-like triplets (resonance, intercombination, and forbidden lines)
of O vii, Ne ix, and Mg xi as well as Ly$\alpha$ lines from the H-like species
of these elements with a very small systematic velocity shift ($130\pm 290$ km
s-1; Kaspi et al. 2000, e.g.; Gabel et al. 2005, e.g.; Kallman et al. 2009,
e.g.). However, given a moderate accretion rate in Seyfert 1 population with
typically very weak (if not none) P-Cygni profiles in X-ray spectra, it is
reasonable to speculate that X-ray absorbing gas is most likely optically
thin. Scattering within the absorbers might then be less efficient.

While we further investigate in this paper a possible effect of inner disk
truncation on UFO spectra (see §3.2), a slight change in UFO kinematics and/or
wind density could also naturally change UFO line profiles without invoking a
geometric change in disk configuration (i.e. truncation). Hence, such a
degeneracy may make it physically challenging to uniquely attribute variable
nature of UFOs to only disk truncation in observations especially in AGNs
where phenomenology of accretion flows still remains very enigmatic (e.g.
Antonucci, 2013). It is also hard to identify “state transition” of accretion
mode due to their much longer time scales. On the other hand, we have
similarly considered a potential impact of disk truncation in the context of
AGN warm absorbers and BH XRB disk-winds in the past (Fukumura et al., 2021),
and we would like to note, in the context of MHD scenario, that the inner disk
truncation in those slow/moderate disk winds would not significantly change
the absorption features in contrast with UFOs. This is because the ionized
ions responsible for non-UFOs are produced in a part of the wind that is
predominantly launched from much larger disk radii from the BH, thus the inner
truncation would play little role in reshaping the absorption lines. The inner
disk truncation therefore results in a distinct consequence in absorption
spectra between UFOs and non-UFOs.

Considering the elusive origin of the UFO and its launching mechanism, this
work is originally motivated by the notion that a detailed UFO spectral
feature may potentially shed light on the underlying physics of UFOs. As one
of the promising scenarios, we exploit the MHD-driving process by calculating
synthetic UFO spectra of multiple ions in the broadband X-ray. As illustrated
in Figure 3 (left), the predicted UFO line shape is generally found to be
uniquely asymmetric with an extended blue tail attributed to the generic
kinematics of MHD disk-winds; i.e. the closer in to the BH, the faster the
wind. While this is indeed a generic spectral signature in most of the
calculations made so far, such a claim should be understood with care. That
is, it is conceivable that the degree of such characteristic asymmetric
signature may be made very small to the extent that the expected asymmetry
could become virtually unnoticeable in observations depending on the wind
condition and or AGN properties. This point is intimately related to AMD and
velocity distribution addressed in §3.1 (see Figure 1). On the other hand,
another leading scenario, line-driving process tends to imprint a different
tell-tale sign in the UFO line shape that is generally reversed101010Note,
however, that even some line-driven absorption spectra may look similar to
those from MHD-driven outflows under certain wind kinematics (e.g. Giustini &
Proga, 2012). to MHD-driven UFO spectra because of its different underlying
wind kinematics; i.e. the gas accelerates along a LoS by radiation pressure
until it asymptotically reaches a finite terminal velocity (thus coasting) at
large distance (e.g. Shlosman & Vitello, 1993; Kniggle et al., 1995; Long &
Kniggle, 2002; Sim et al., 2008; Hagino et al., 2015). Such a distinct
velocity field of line-driven UFOs is generally expected to produce a broad
asymmetric UFO line spectrum with an extended red tail being fundamentally
distinct from that by MHD-winds (e.g. Long & Kniggle, 2002; Sim, 2005; Sim et
al., 2010a, b; Hagino et al., 2015; Mizumoto et al., 2021, also Reeves J. N.
in private communication). Nonetheless, it is possible again that the apparent
difference between two models could be made either too small or too subtle in
some specific cases to observationally enable us to robustly differentiate.
Hence, we emphasize that our claim for obtaining the unique spectral features
due to MHD-driving should be viewed as an average feature. With this caution
in mind, we believe that our modeling and simulations in this work can help
improve our fundamental understanding of the physics of X-ray UFOs that could
otherwise be observationally inaccessible.

K.F. is grateful to James Reeves, Daniel Proga, Maria Diaz Trigo and Chris
Done, for a number of inspiring comments and questions that have partly
motivated this project. We appreciate a number of constructive comments and
questions by an anonymous referee to improve the manuscript. This work is
supported in part by NASA grants, NNH18ZDA001N-ADAP and NNH20ZDA001N-ADAP,
through Astrophysics Data Analysis Program. M.D. and G.A.M. acknowledges the
financial support from Attività di Studio per la comunità scientifica di
Astrofisica delle Alte Energie e Fisica Astroparticellare: Accordo Attuativo
ASI-INAF n. 2017-14-H.0.

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## Appendix A: Model Dependences of Synthetic Multi-Ion Broadband UFO Spectra

As part of investigating the model parameter dependences, we explore the
effect of X-ray hardness via $\Gamma$ on the UFO line profiles in §3.1. In the
Appendix A, the effects of the other model parameters (see Table 1) are
considered and demonstrated. We examine the dependence of X-ray strength
relative to optical/UV flux parameterized by $\alpha_{\rm OX}$ in Figure 10
with $\theta=30^{\circ},\Gamma=2,p=1.3,f_{D}=1$ and $\lambda_{\rm ion}=0.1$.
Although the selected range of $\alpha_{\rm OX}$ in this work is limited, we
clearly see its strong effect on the UFO spectra. By suppressing more X-ray
photons relative to UV photons (i.e. larger $|\alpha_{\rm OX}|$ value), for
example, the resulting velocity curve $v(\xi)$ tends to shift towards lower
$\xi$ domain with AMD (see Figure 1b) producing more blueshifted UFO lines
with larger width. As similarly seen in Figure 2, soft X-ray UFO features are
more sensitive to the change in X-ray strength compared to Fe K UFOs. Trough
energies in individual lines are more noticeably blueshifted with increasing
$|\alpha_{\rm OX}|$, while there is little change due to $\Gamma$ in Figure 2.

The effect of ionizing luminosity in units of Eddington luminosity
$\lambda_{\rm ion}$ is explored in Figure 11 with
$\theta=30^{\circ},\Gamma=2,p=1.3,f_{D}=1$ and $\alpha_{\rm OX}=1.5$. In a
simplified situation where only ionizing luminosity is varied while being
decoupled from spectral shape (i.e. $\Gamma$ and $\alpha_{\rm OX}$), we find
that the UFO signatures are weakened in general with increasing $\lambda_{\rm
ion}$ as naturally expected. In comparison, the spectral dependence is less
sensitive to $\lambda_{\rm ion}$ than it is to spectral indices, especially
for soft X-ray UFOs. Understanding of this trend, however, needs some caution
because the variation of X-ray luminosity in AGNs is often accompanied by the
change in spectral shape as well, which is not currently taken into account in
these calculations for simplicity. We shall discuss more on this point later
in §4.

Figure 10: Theoretical multi-ion absorption spectra (ratio to the continuum)
for different X-ray strength $\alpha_{\rm OX}$ with
$\theta=30^{\circ},\Gamma=2,p=1.3,f_{D}=1$ and $\lambda_{\rm ion}=0.1$.

Figure 11: Theoretical multi-ion absorption spectra (ratio to the continuum)
for different ionizing luminosity ratio $\lambda_{\rm ion}$ with
$\theta=30^{\circ},\Gamma=2,p=1.3,f_{D}=1$ and $\alpha_{\rm OX}=1.5$.

Figure 12: Theoretical multi-ion absorption spectra (ratio to the continuum)
for different density slope $p$ with $\theta=30^{\circ},\Gamma=2,\alpha_{\rm
OX}=1.5,f_{D}=1$ and $\lambda_{\rm ion}=0.1$.

Figure 13: Theoretical multi-ion absorption spectra (ratio to the continuum)
for different inclination $\theta$ with $\Gamma=2,\alpha_{\rm
OX}=1.5,p=1.3,f_{D}=1$ and $\lambda_{\rm ion}=0.1$.

In addition to the effect of photoionization due to differences in the
radiation field, we further study the dependence on the wind conditions. In
Figure 12 we show the UFO spectra for various wind density gradients with $p$
assuming $\theta=30^{\circ},\Gamma=2,\alpha_{\rm OX}=1.5,f_{D}=1$ and
$\lambda_{\rm ion}=0.1$. In this exercise, soft X-ray UFOs (located at larger
distances from AGN) have lower density with increasing $p$, whereas Fe K UFOs
are impacted the least, as the innermost wind at the launching radius remains
fixed (at $r\sim R_{\rm in}=6R_{g}$). As a result, soft X-ray UFO signatures
in the spectrum are significantly weakened, for example, for $p=1.4$, as
expected. With $p=1.2$ wind density structure, on the other hand, the
broadband UFO features are clearly present being attributed to an almost equal
column $N^{i}_{\rm ion}$ for all ions as expected from AMD (see §2.2).

Finally, we consider spectral dependence on inclination $\theta$ in Figure 13
assuming $\Gamma=2,\alpha_{\rm OX}=1.5,p=1.3,f_{D}=1$ and $\lambda_{\rm
ion}=0.1$. The obtained dependence is two-fold; i.e. a combination of velocity
change and wind density variation with $\theta$. This is because the LoS wind
velocity (i.e. velocity component projected onto LoS direction) is dependent
on the relative angle between the LoS orientation and a tangential direction
of magnetic field lines. At the same time, the wind density is lower by many
orders of magnitude near the funnel region close to the symmetry axis (e.g.
Blandford & Payne, 1982; Contopoulos & Lovelace, 1994; Fukumura et al., 2014;
Chakravorty et al., 2016). These factors combined together generally cause the
absorption lines to be dramatically weaker and less blueshifted with
decreasing $\theta$.

## Appendix B: Model Dependences of Simulated Multi-Ion Broadband UFO Spectra

To further follow up the XRISM/Resolve simulations of our MHD UFO models
discussed in §3.3.1, we present here in Figures 14-17 the other simulated
spectra for various model parameters listed in Table 1.

In Figure 14, the well-defined blueshifted UFO features of asymmetry is
similarly seen in which X-ray-weak AGNs (e.g. $\alpha_{\rm OX}=1.8$) can
clearly imprint such an asymmetric blueshift structure in the spectrum, most
notably seen in Fe K lines. Note that Fe xxv and Fe xxvi lines are made so
broad that they are blended together to form a single feature, for example,
for $\Gamma=2.5$ and $\alpha_{\rm OX}=1.8$. As expected from the synthetic
spectra in Figure 11, simulated data for different ionizing luminosity
$\lambda_{\rm ion}$ in Figure 15 do not seem to change much with $\lambda_{\rm
ion}$, while the suppression of atomic lines, especially in the soft X-ray
band, are found. Since the wind density slope and inclination can probably
provide the most direct effect on the absorption spectra, dramatic changes in
UFO signatures are indeed coded in XRISM/Resolve data as demonstrated in
Figures 16 and 17. For example, it is found that microcalorimeters are capable
of detecting a series of blueshifted lines of unique asymmetry in the soft
X-ray UFOs as well as a pronounced Fe K UFOs for $p=1.2$ winds. For a fixed
wind density factor $f_{D}=1$, the simulated spectrum would exhibit little
wind features for $p=1.5-1.7$, as is previously shown from the model with
$p=1.4$ in Figure 12. Similarly, very weak line features expected from a polar
wind with $\theta=20^{\circ}$ would not be visible even with 80ks
microcalorimeter observation under this parameter set, as indicated earlier in
Figure 13. On the other hand, low inclination winds of
$\theta=30^{\circ}-40^{\circ}$, being relevant for canonical Seyfert 1 AGNs,
would be securely resolved. Moderate inclination winds of $\theta=50^{\circ}$
would prominently exhibit stronger UFO features.

Figure 14: Simulated 100ks XRISM/Resolve spectra for different X-ray strength
$\alpha_{\rm OX}$ with $\theta=30^{\circ},p=1.3,f_{D}=1,\Gamma=2$ and
$\lambda_{\rm ion}=0.1$.

Figure 15: Simulated 100ks XRISM/Resolve spectra for different ionizing
luminosity ratio $\lambda_{\rm ion}$ with
$\theta=30^{\circ},p=1.3,f_{D}=1,\Gamma=2$ and $\alpha_{\rm OX}=1.5$.

Figure 16: Simulated 100ks XRISM/Resolve spectra for different density slope
$p$ with $\theta=30^{\circ},\Gamma=2,\alpha_{\rm OX}=1.5,f_{D}=1$ and
$\lambda_{\rm ion}=0.1$.

Figure 17: Simulated 100ks XRISM/Resolve spectra for different inclination
$\theta$ with $\Gamma=2,p=1.4,\alpha_{\rm OX}=1.5,f_{D}=1$ and $\lambda_{\rm
ion}=0.1$.

## Appendix C: Impact of Reflection Component on Simulated Multi-Ion Broadband
UFO Spectra

One of the characteristic spectral features often identified in bright Seyfert
AGNs is reflection features from disks; i.e. Compton hump and various atomic
lines including emission and absorption/edges due to reprocessed photons (e.g.
Magdziarz & Zdziarski, 1995; Ross & Fabian, 2005). To follow up our
investigations on a persistent presence of MHD signatures in UFO spectra, we
further examine the effects of such reflection component and see if the
expected characteristics of asymmetric line profiles might be contaminated or
distorted to the extent that identification of the MHD-driven UFO features may
be difficult as a consequence.

To this end, we replace a single power-law (po) by adding both xillverCp (for
distant reflection) and relxillCp (for relativistic reflection) models in the
original composite model (as shown in Table 2 and Fig. 6) for XRISM/Resolve
simulations; i.e. a new composite model is expressed symbolically as

$\displaystyle{\tt tbabs\times(relxillCp+xillverCp)\times mhdwind\times
warmabs_{\tt C}\times warmabs_{\tt W}\times warmabs_{\tt H}\times zxipcf}$
(15)

where we have fixed a number of baseline parameter values in the reflection
components to minimize the extra degrees of freedom, while others are to be
varied to find the bestfit solution. Figure 18 demonstrates a feasibility of
extracting the MHD signatures of the expected UFO spectrum lines in such a
case. We set the normalizations of the reflection components such that the
2-10 keV flux remains of the order of $10^{-11}$ erg cm-2 s-1 as considered
earlier in §3.3.2 where reflection feature is absent. In this simulation, we
assume a relatively strong reflection contribution to the underlying
continuum; e.g. refl_frac = 2 and $A_{\rm Fe}/A_{\rm Fe,\odot}=5$. In order to
reduce the extra degrees of freedom in the model, we fix the emissivity
profile of the disk emission in such a way that $\epsilon(r)\propto r^{-6}$
for $r/R_{g}\leq 10$ (the innermost) and $\propto r^{-3}$ for $r/R_{g}>10$
(the outer part) to take into account relativistic effects under strong
gravity (these parameters are thus frozen throughout fitting) for the
dimensionless BH spin of $a=0.98$. The assumed parameter values and the
bestfit model parameters are listed in Table 3.

It is clearly demonstrated that the spectral signatures of UFOs due to the MHD
wind component are still unambiguously imprinted in the broadband spectrum
(i.e. extended asymmetric blue tails) despite the complex spectral curvature
of relatively strong reflection flux including the extra absorption lines.
Identification of the individual MHD-driven UFO lines in the bestfit model is
equally robust as that in the power-law continuum simulation (in the absence
of reflection; see Fig. 6) indicating that the reflection features interfere
very little with the UFO lines to the extent that the predicted tell-tale MHD
signatures are less likely to be washed out. The adopted parameter values of
MHD wind component (mhdwind) are almost all well retained by fitting the
simulated spectra in both cases (see Tables 2 and 3). Note that even strong Fe
K emission lines (both narrow and broad) in this simulation does not
significantly distort the original Fe K UFO absorption feature.

Figure 18: Similar to Figure 6 but in the presence of reflection component.

Table 3: Best-Fit Composite Model for 100 ks Simulated XRISM/Resolve Spectrum
with Reflection

Component | Parameter | Best-Fit Value | Model Value
---|---|---|---
tbabs |  $N_{H}^{\rm Gal}$ [cm-2] |  $10^{20}$† |  $10^{20}$†
xillverCp | $\Gamma$ | $2.01^{+0.01}_{-0.01}$ | 2 ♭
|  $\theta$ [deg] | $36.8_{-1.9}^{+2.5}$ |  $35$ ♭
| AFe [AFe,⊙] | $5.04_{-0.61}^{+0.98}$ | 5 ♭
|  $kT_{e}$ [keV] |  $163$ △ | 150 ♭
| refl_frac | $1.82_{-0.37}^{+0.44}$ | 2 ♭
| $\log n_{D}\rm{[cm^{-3}]}$ | $18.9_{-0.11}^{+0.08}$ | 19 ♭
| $\log\xi$ | $0.96_{-0.09}^{+0.09}$ | 1
| Kref [$10^{-4}$] | $0.73_{-0.11}^{+0.17}$ | 1 ♭
relxillCp♯ | $a/M$ | $0.979_{-0.013}^{+0.010}$ | 0.98
| $\log\xi$ | $2.96_{-0.10}^{+0.09}$ | 3
mhdwind | $\alpha_{\rm OX}$ | $1.50^{+0.01}_{p}$ | 1.5
| $\Gamma$ | $2.01^{+0.01}_{-0.01}$ | 2 ♭
| $\lambda_{\rm ion}$ | $0.084_{-0.003}^{+0.003}$ | 0.08
|  $\theta$ [deg] | $36.8_{-1.9}^{+2.5}$ |  $35$ ♭
| $p$ | $1.26_{-0.03}^{+0.03}$ | 1.25
| $f_{D}$ | $0.093_{-0.01}^{+0.02}$ | 0.1
warmabs | $N_{\rm H,Cold}$ | $1.01_{-1.01}^{+0.33}\times 10^{21}$ | $10^{21}$
| $\log\xi_{\rm Cold}$ | $2.05_{-0.05}^{+0.05}$ | $2$
| $v_{\rm out,Cold}/c$ | $-8.74_{-4.5}^{+3.3}\times 10^{-4}$ | $10^{-3}$
| $N_{\rm H,Warm}$ | $1.00_{-0.06}^{+0.29}\times 10^{22}$ | $10^{22}$
| $\log\xi_{\rm Warm}$ | $2.97_{-0.02}^{+0.03}$ | $3$
| $v_{\rm out,Warm}/c$ | $-2.96_{-0.14}^{+0.12}\times 10^{-3}$ | $3\times 10^{-3}$
| $N_{\rm H,Hot}$ | $1.0_{-0.02}^{p}\times 10^{23}$ | $10^{23}$
| $\log\xi_{\rm Hot}$ | $4.00_{-0.01}^{+0.01}$ | $4$
| $v_{\rm out,Hot}/c$ | $-1.0_{-0.07}^{+0.08}\times 10^{-2}$ | $10^{-2}$
zxipcf | $N_{\rm H,zxipcf}$ | $4.05_{-0.9}^{+1.0}\times 10^{23}$ | $5\times 10^{23}$
| $\log\xi_{\rm zxipcf}$ | $3.95_{-0.07}^{+0.06}$ | $4$
| $v_{\rm out,zxipcf}/c$ | $-1.00_{-0.09}^{+0.01}\times 10^{-2}$ | $10^{-2}$
|  $\chi^{2}/$dof |  $19681.51/18975$ (20972.51/18979)‡ |

♯ Disk emissivity law is fixed as $\epsilon\propto r^{-6}$ and $r^{-3}$ across
$R_{\rm break}/R_{g}=10$ in relxill.
△ Unconstrained. ♭ Tied among models. ‡ In the absence of the UFO component
(mhdwind).
p Pegged values.