###### Abstract

X-ray polarimetry has been suggested as a prominent tool for investigating the
geometrical and physical properties of the emissions from active galactic
nuclei (AGN). The successful launch of the Imaging X-ray Polarimetry Explorer
(IXPE) on 9 December 2021 has expanded the previously restricted scope of
polarimetry into the X-ray domain, enabling X-ray polarimetric studies of AGN.
Over a span of two years, IXPE has observed various AGN populations, including
blazars and radio-quiet AGN. In this paper, we summarize the remarkable
discoveries achieved thanks to the opening of the new window of X-ray
polarimetry of AGN through IXPE observations. We will delve into two primary
areas of interest: first, the magnetic field geometry and particle
acceleration mechanisms in the jets of radio-loud AGN, such as blazars, where
the relativistic acceleration process dominates the spectral energy
distribution; and second, the geometry of the hot corona in radio-quiet AGN.
Thus far, the IXPE results from blazars favor the energy-stratified shock
acceleration model, and they provide evidence of helical magnetic fields
inside the jet. Concerning the corona geometry, the IXPE results are
consistent with a disk-originated slab-like or wedge-like shape, as could
result from Comptonization around the accretion disk.

###### keywords:

X-ray polarimetry; active galactic nuclei; relativistic jets

1 1 0 Academic Editor: Ilaria Ruffa 29 February 2024 5 April 2024 12 April
2024 https://doi.org/ Investigating the Properties of the Relativistic Jet and
Hot Corona in AGN with X-ray Polarimetry Investigating the Properties of the
Relativistic Jet and Hot Corona in Agn with X-ray Polarimetry Dawoon E.
Kim1,2,3,*, Laura Di Gesu 4, Frédéric Marin 5, Alan P. Marscher 6, Giorgio
Matt 7, Paolo Soffitta 1, Francesco Tombesi 3,8,9, Enrico Costa 1 and
Immacolata Donnarumma 4 Dawoon E. Kim, Laura Di Gesu, Frédéric Marin, Alan P.
Marscher, Giorgio Matt, Paolo Soffitta, Francesco Tombesi, Enrico Costa and
Immacolata Donnarumma Kim, D.E.; Di Gesu, L.; Marin, F.; Marscher, A.P.; Matt,
G.; Soffitta, P.; Tombesi, F.; Costa, E.; Donnarumma, I. Correspondence:
<EMAIL_ADDRESS>
##  1 Introduction

Active galactic nuclei (AGN) stand out as fascinating and powerful sources
(with bolometric luminosities $\sim$$10^{42}$–$10^{46}$ erg s-1; e.g., Woo and
Urry (2002); Perna et al. (2017)) that emit electromagnetic radiation across
the entire spectrum, ranging from radio wavelengths to gamma rays.
Specifically, in the X-ray regime, emissions originate from the vicinity of
the central engine, in either the inner part of the jet or in an X-ray corona.
The high penetration power of X-ray radiation facilitates the unobstructed
study of processes near black holes. So far, X-ray probes have been limited to
spectral and timing techniques Bambi and Sangangelo (2022). Although these
methods provide clues about the radiative processes producing X-rays in the
inner AGN region, they are insensitive to some key characteristics, such as
the geometry of the emitting region or the magnetic field, which so far have
remained largely unconstrained.

In this context, polarimetric studies have been suggested as a prominent tool
for investigating the geometrical and physical properties of AGN emissions
Rybicki and Lightman (1979). The successful launch of the Imaging X-ray
Polarimetry Explorer (IXPE) on 9 December 2021 marked a significant
advancement in polarimetry by extending it into the X-ray range Weisskopf et
al. (2022). IXPE is a collaborative mission between NASA and the Italian Space
Agency (Agenzia Spaziale Italiana, ASI). It comprises three identical X-ray
telescope systems, each one composed of one mirror module assembly and one
detector unit hosting a gas pixel detector Costa et al. (2001) with a full
calibration and filtering system. IXPE is designed to measure the linear
polarization in the 2–8 keV band using polarization mapping techniques. It
offers a field of view greater than $11^{\prime}$ and an angular resolution of
less than or equal to $30^{\prime\prime}$. Over the first two years of
operation, IXPE has detected X-ray polarization from several AGN, helping to
address the long-standing uncertainty about the jet magnetic field structure
and acceleration process and the geometry of the X-ray corona.

Traditionally, AGN are divided into two main classes: radio-loud (RLAGN) and
radio-quiet (RQAGN), based on their radio to optical flux ratio Urry and
Padovani (1995); Padovani et al. (2017). In some cases, they are classified as
jetted or non-jetted based on the presence or absence of strong relativistic
jets Padovani (2017). Among the population of RLAGN, blazars are ideal targets
for studying relativistic jets because, in these sources, the jet flow is
relatively closely aligned to the observer’s line of sight, and their emission
is dominated by jet emission across the entire spectral energy distribution
(SED) due to relativistic Doppler boosting, e.g., Hovatta et al. (2016). The
SED of blazars exhibits two broad non-thermal radiation components as shown in
Figure 1. One component, located in the lower-frequency range, covers
emissions from radio to optical/UV (and, in some cases, to X-ray) and is
generally ascribed to synchrotron emission from relativistic electrons. The
other component may be explained in two different scenarios: leptonic or
hadronic models. In the leptonic process, the high-energy emission is
attributed to Compton scattering of synchrotron photons (synchrotron self-
Compton or SSC; e.g., (Jones et al., 1974; Maraschi et al., 1992)) or photons
originating outside the jet (external Compton or EC; e.g., (Dermer and
Schlickeiser, 1993; Sikora et al., 1994; Begelman and Sikora, 1987)). In the
hadronic scenario, proton synchrotron emission, $\pi_{0}$ decay photons,
synchrotron, and Compton emission from secondary decay products of charged
pions have been suggested, e.g., (Mannheim, 1993; Aharonian, 2000; Böttcher et
al., 2013). These emission processes are predicted to produce different X-ray
polarization properties depending on the acceleration mechanism in both
leptonic and hadronic scenarios Blandford et al. (2019). Furthermore,
depending on the position of the peak frequency of the electron synchrotron
emission hump ($\nu_{peak}$), blazars are separated into low-
($\nu_{peak}<10^{14}~{}$Hz or 3 $\upmu$m; LSP), intermediate- ($\nu_{peak}$
$\sim 10^{14}~{}$Hz–$10^{15}~{}$Hz; ISP), and high-synchrotron-peak
($\nu_{peak}>10^{15}~{}$Hz or 0.3 $\upmu$m; HSP) subclasses (Abdo et al.,
2010). Therefore, studying various subclasses of blazars with X-ray
polarimetry allows us to explore different physical processes. First, with HSP
targets, the particle acceleration process and geometrical features of the
magnetic field inside the jets can be studied. Second, with ISP and LSP
blazars, the superposition of synchrotron emission and leptonic or hadronic
emission in spectra enables tests of the acceleration mechanisms behind the
high-energy emission hump.

In the case of RQAGN, given that they are not typically dominated by jet
emissions, we can observe other emission components surrounding the central
engine (see Figure 1). The primary X-ray emission of AGN is believed to
originate from a corona of hot (with a temperature of 10–100 keV) and
optically thin (or mildly thick) plasma that Compton scatters the optical/UV
photons from the accretion disk, e.g., Haardt and Maraschi (1991).
Additionally, these X-ray photons are reflected (backscattered) either by the
accretion disk or by the more distant torus, which results in additional X-ray
spectral components as secondary emissions Marin et al. (2018). RQAGN are
divided into Seyfert 1 and 2 galaxies based on whether or not both broad and
narrow emission lines are observed in the optical band, which partially
depends on the differences in the line of sight direction Antonucci (1993). In
the X-ray regime, Seyfert 1 galaxies, which have a relatively small
inclination angle between our line of sight and the axis of the system,
averaging $39^{\circ}$ Wu and Han (2001); Singha et al. (2022), show
unobscured X-ray coronae and disk reflection, while the emission from Seyfert
2s is dominated by photons reprocessed through reflection from the strongly
absorbing dusty torus and from the polar winds due to the larger inclination
angle.

The spectrum of the corona typically follows a power law with a high-energy
cutoff, e.g., (Sunyaev and Titarchuk, 1980). The slope of the power law is
determined by the electron temperature and the optical depth, while the cutoff
energy depends mostly on the electron temperature. The size and geometry of
the corona remain elusive, although these characteristics are crucial for
differentiating between models for the formation of AGN coronae, e.g., (Di
Matteo, 1998). Regarding the geometric characteristics of the hot corona,
several possibilities have been suggested, including lamppost, spherical,
conical, slab, and wedge. In particular, spherical or conical structures
located on the rotation axis above and below the black hole would suggest a
potential connection between the corona and the jet, e.g., (Ghisellini et al.,
2004; Markoff et al., 2005). In this context, it is predicted that the X-ray
polarization of the corona emission depends on the geometry, e.g., (Haardt and
Matt, 1993), and demonstrates that X-ray polarization measurements can serve
as a powerful tool for probing the disk/corona geometry, e.g., (Matt et al.,
1989, 1993). Hence, the polarization observations of unobscured RQAGN can
provide valuable insights into the geometric features of the corona.

In this short review, we will briefly summarize the theoretical expectations
and remarkable discoveries obtained from the first two years of IXPE
observations of RLAGN and RQAGN. These concern the magnetic field geometry and
particle acceleration mechanisms in the jets, as well as the geometry of the
hot corona. We will then discuss future prospects.

Figure 1: A schematic representation of SED for RLAGN (HSP: red solid line,
and LSP: gray dotted line) and RQAGN (black solid line with labeled colored
lines for different emission components). The yellow shaded area indicates the
X-ray regime. The figure is reproduced from Figure 1 in Padovani et al.
(2017).

##  2 X-ray Polarization from Relativistic Jets

###  2.1 Theoretical Expectations

The observed emission coming from relativistic jets is often well-described by
a power law spectrum within a given frequency band. Theoretically, this can be
explained as synchrotron radiation produced by a power law energy spectrum of
electrons with Lorentz factor $\gamma$, $N_{e}(\gamma)\propto\gamma^{-p}$,
which produces a power law synchrotron radiation spectrum
$F_{\nu}\propto\nu^{-\alpha}$, with $\alpha=(p-1)/2$. This results in a
polarization degree ($\Pi$) of Rybicki and Lightman (1979)

$\Pi_{Sync}=\frac{p+1}{p+7/3}=\frac{\alpha+1}{\alpha+5/3}.$ (1)

Considering the typical power law index obtained from blazars $\sim$$p$ = 2–3,
a polarization degree of the electron synchrotron emission in a homogeneous
magnetic field is expected to be $\Pi$$\sim$$70\%$. The polarization angle
($\psi$) is perpendicular to the averaged magnetic field direction projected
onto the sky plane. However, in reality, polarization can be reduced by the
geometrical and physical properties within the jet, such as temporal variation
effects occurring over timescales shorter than the integration time of the
polarization measurement Jorstad et al. (2005); Kiehlmann et al. (2017);
Blinov et al. (2018). Thereby, in order to explain the polarization
measurements and variability, various geometrical and physical models have
been suggested. For instance, for the geometrical model, there have been
several suggestions: a bending jet Larionov et al. (2013), a spiral motion
model in which a blob propagates in a spiral trajectory within a helical
magnetic field Marscher et al. (2008), and the ballistic motion of an emission
blob in a jet with a helical magnetic field Lyutikov and Kravchenko (2017). In
the case of the physical conditions, there have been several suggestions as
well: many turbulent cells, the TEMZ model, (Marscher, 2014; Marscher et al.,
2017; Marscher and Jorstad, 2021), shock and kink instabilities that can
efficiently dissipate jet bulk energy to accelerate particles Achterberg et
al. (2001); Spitkovsky (2008); Mizuno et al. (2009); Alves et al. (2018), and
magnetic reconnection Sironi and Spitkovsky (2014); Guo et al. (2014); Zhang
et al. (2018, 2022). Refs. Tavecchio (2021); Di Gesu et al. (2022) have
presented the predicted X-ray and simultaneous multiwavelength polarization
characteristics among various theoretical models as follows: (1) in the shock
acceleration model, particle acceleration is characterized by a strong self-
generated magnetic field. Hence, a large degree of polarization, $\Pi_{\rm
X}$$\sim$40$\%$, and relatively stable $\Pi_{\rm X}$ and $\psi_{\rm X}$ over
time (variability in a few days to a week) are predicted Tavecchio et al.
(2020, 2018). Moreover, a chromatic feature in X-ray and optical polarization,
where $\Pi_{\rm X}$/$\Pi_{\rm O}$ $\gtrsim$ 2, is anticipated because
particles emitting at longer wavelengths, due to their longer synchrotron
cooling time, travel away from the shock front to regions with a more
disordered magnetic field; (2) in the magnetic reconnection model, the
reconnection episodes are triggered by instability induced, for example, by
current sheets Guo et al. (2015); Sironi and Spitkovsky (2014). $\Pi_{\rm X}$
$\lesssim$ $20-30\%$ and similar characteristics for $\Pi_{\rm O}$ are
predicted as a result of the simultaneous contribution of several active
current sheets with different orientations. Additionally, the evolution of the
instability results in significant variations, and $\psi_{\rm X}$ can show
variability on a daily timescale; (3) in the TEMZ model, $\Pi_{\rm X}$
$\lesssim$ $30\%$ and rapid changes in $\Pi_{\rm X}$ and $\psi_{\rm X}$ less
than a day timescale are predicted because of the superposition of the
emission of several cells, in which the magnetic field is uniform but randomly
oriented Marscher (2014). In addition, mild chromatic behavior, $\Pi_{\rm
X}$/$\Pi_{\rm O}$ $\lesssim$ 2, is expected as a large number of cells can
radiate at lower frequencies. Thus, the variability is erratic and somewhat
driven by the dimension and number of cells. Consequently, expanding
multiwavelength polarimetric measurements on synchrotron emission to the X-ray
band provides clues about the layout of the magnetic field as particles
emitting at different energies can assist in identifying the predominant
acceleration process.

Compton scattering of unpolarized seed photons by highly relativistic
electrons produces zero polarization in the scattered radiation Zhang and
Böttcher (2013). Therefore, detecting X-ray polarization from LSP blazars,
whose emission component is primarily dominated by Compton scattering in
X-rays, would effectively rule out the possibility of EC processes. In
contrast, under the conditions of proton synchrotron radiation, the
polarization levels could potentially reach around $70\%$, consistent with the
proton spectral indices in Equation (1), where $p$ is approximately 2–3 Zhang
and Böttcher (2013). A polarization degree significantly higher than that at
mm-waves and similar to or greater than that at optical wavelengths, and a
slope of the X-ray emission that is sufficiently flat, could be interpreted as
an indication of proton synchrotron emission. Furthermore, for cases involving
a combination of synchrotron emission at soft X-ray energies and SSC/EC at
harder X-rays, detailed SED modeling and decomposition of the polarization
properties of each component are required. The model considering multiple
emission zones with turbulent magnetic fields predicts
$\Pi_{SSC}/\Pi_{Sync}\approx 0.3$ Peirson and Romani (2019).

###  2.2 IXPE Observations of High Synchrotron Peak Blazars

IXPE observations of HSP blazars have been conducted for Mrk 501 Liodakis et
al. (2022),Mrk 421 Di Gesu et al. (2022, 2023); Kim et al. (2024), 1ES1959+650
Errando et al. (2024), PG1553+113 Middei et al. (2023), and 1ES0229+200 Ehlert
et al. (2023). The X-ray polarization of each target was estimated through
time-averaged analysis by considering the entire observation period and time-
and energy-resolved analyses by dividing the observations into sub-segments
using model independent event Stokes parameter analysis Kislat et al. (2015)
and spectropolarimetric analysis Strohmayer (2017). In addition, during all
the IXPE blazar observations, a simultaneous multiwavelength polarimetry
campaign was conducted, including radio, infrared (IR), and optical
wavelengths, to examine the synchrotron emission properties across different
wavelengths. In this section, we summarize the reported X-ray and
multiwavelength polarimetry features of each observation, as well as the X-ray
spectral properties. Table 1 presents a summary of the time-averaged
multiwavelength polarization information for all the HSP observations, and
Table 2 provides a summary of the X-ray spectral characteristics, including
the photon index and flux derived based on the log parabolic model Massaro et
al. (2004). The log parabolic model represents power laws with a photon index
that varies according to a log parabola in energy:

$\begin{split}N(E)=K(E/E_{pivot})^{(\alpha-\beta\log(E/E_{pivot}))},\end{split}$
(2)

where the pivot energy $E_{pivot}$ is a scaling factor, $\alpha$ describes the
slope of the photon spectrum at $E_{pivot}$, $\beta$ expresses the spectral
curvature, and $K$ denotes a normalization constant.

Table 1: Contemporaneous multiwavelength polarization properties of HSPs.

Source |  X-ray |  Optical & IR a |  Radio a
---|---|---|---
|  $\Pi(\%)$ $\psi(^{\circ})$ |  $\Pi(\%)$ $\psi(^{\circ})$ |  $\Pi(\%)$ $\psi(^{\circ})$
Mrk 501 I 1 |  10 $\pm$ 2 134 $\pm$ 5 |  4 $\pm$ 1 119 $\pm$ 9 |  1.5 $\pm$ 0.5 152 $\pm$ 10
Mrk 501 II 1 |  11 $\pm$ 2 115 $\pm$ 4 |  5 $\pm$ 1 117 $\pm$ 3 |  – –
Mrk 421 I 2 |  15 $\pm$ 2 35 $\pm$ 4 |  2.9 $\pm$ 0.5 32 $\pm$ 5 |  3.4 $\pm$ 0.4 55 $\pm$ 2
Mrk 421 II 3 |  10 $\pm$ 1 Rotation |  4.4 $\pm$ 0.4 140 $\pm$ 6 |  2.4 $\pm$ 0.1 139 $\pm$ 8
Mrk 421 III 3 |  10 $\pm$ 1 Rotation |  5.4 $\pm$ 0.4 145 $\pm$ 1 |  – –
Mrk 421 IV 4 |  14 $\pm$ 1 107 $\pm$ 3 |  4.6 $\pm$ 1.3 206 $\pm$ 9 |  1.8 $\pm$ 0.1 167 $\pm$ 4
1ES1959+650 I 5 |  8 $\pm$ 2 123 $\pm$ 8 |  4.5 $\pm$ 0.2 159 $\pm$ 1 |  – –
1ES1959+650 II 5 |  $<$5 – |  4.7 $\pm$ 0.6 151 $\pm$ 19 |  $<$1.6 –
PG1553+113 6 |  10 $\pm$ 2 86 $\pm$ 8 |  4.2 $\pm$ 0.5 Rotation |  2.6 $\pm$ 0.7 133 $\pm$ 7
1ES0229+200 7 |  18 $\pm$ 3 25 $\pm$ 5 |  3.2 $\pm$ 0.7 $-$5 $\pm$ 9 |  $<$7 –

1–7 Results compiled from the following references: Liodakis et al. (2022); Di
Gesu et al. (2022, 2023); Kim et al. (2024); Errando et al. (2024); Middei et
al. (2023); Ehlert et al. (2023); a median polarization properties during the
IXPE observation. Especially for optical and IR polarization, only corrected
polarization values, accounting for the dilution of polarization by
unpolarized starlight from the host galaxy, were considered for calculation; b
at the lowest radio frequency (4.85 GHz).

Table 2: X-ray spectral properties of HSPs during IXPE observation.

Source | Photon Index | Flux${}_{2-8\;{\rm keV}}$ | Telescopes
---|---|---|---
|  | ($\times 10^{-11}$ erg s-1 cm-2) |
Mrk 501 I 1 | 2.27 $\pm$ 0.01 | 10.0 $\pm$ 0.5 | IXPE + Swift-XRT+NuSTAR
Mrk 501 II 1 | 2.05 $\pm$ 0.02 | 21.0 $\pm$ 0.6 | IXPE + Swift-XRT
Mrk 421 I 2 | 2.97 $\pm$ 0.01 | 8.67 $\pm$ 0.03 | IXPE + XMM-Newton+NuSTAR
Mrk 421 II 3 | 2.32 $\pm$ 0.01 a | 15.7 $\pm$ 0.1 | Swift-XRT
Mrk 421 III 3 | 2.13 $\pm$ 0.01 a | 30.2 $\pm$ 0.2 | Swift-XRT
Mrk 421 IV 4 | 2.82 $\pm$ 0.01 | 22.5 $\pm$ 0.4 | IXPE + XMM-Newton
1ES1959+650 I 5 | 2.50 $\pm$ 0.02 | 12.4 $\pm$ 0.2 | IXPE + XMM-Newton
1ES1959+650 II 5 | 2.29 $\pm$ 0.01 | 14.7 $\pm$ 0.1 | IXPE + XMM-Newton
PG1553+113 6 | 2.49 $\pm$ 0.01 | 2.55 $\pm$ 0.03 | IXPE + XMM-Newton
1ES0229+200 7 | 1.82 $\pm$ 0.01 | 0.84 $\pm$ – | IXPE + XMM-Newton

1–7 Results compiled from the following references: Liodakis et al. (2022); Di
Gesu et al. (2022, 2023); Kim et al. (2024); Errando et al. (2024); Middei et
al. (2023); Ehlert et al. (2023); a average value between variation over time.

Mrk 501 was the first observed HSP blazar. This target was observed at two
different epochs (Mrk 501 I: 8–10 March 2022 and Mrk 501 II: 26–28 March
2022). The time-averaged X-ray polarization in the 2–8 keV range of these
observations was consistent within a 3$\sigma$ error range, as shown in Table
1. There was no significant variability within the duration of the individual
IXPE observations over time and energy, and the X-ray activity was in an
average state. The polarization in the optical, IR, and radio bands was
significantly lower than in the X-rays by a factor of $\sim$2, indicating
strong chromatic behavior (Figure 2). Additionally, $\psi$ is aligned with the
jet direction, $\psi_{43{\rm GHz}}=119.7\pm 11.8$, obtained from the 43 GHz
Very Long Baseline Array (VLBA) observation Liodakis et al. (2022). These
multiwavelength polarimetric results suggest, among the various proposed
models, the “energy-stratified shock acceleration model” in which particles
accelerated by shocks experience increasing turbulence as they move away from
the accelerating site, resulting in a decrease in the polarization degree.
Moreover, shocks can push the particles far away, causing a decrease in
$\Pi_{\rm X}$. In addition, the energy-stratified shock acceleration model
predicts $\psi_{\rm X}$ along the jet axis. Thereby, the different
polarization angles at different wavelengths suggest a scenario where
particles emitting at different energies experience different magnetic field
conditions.

Mrk 421 has been observed four times (Mrk 421 I: 4–6 May 2022; Mrk 421 II: 4–6
June 2022; Mrk 421 III: 7–9 June 2022; and Mrk 421 IV: 6–8 December 2022). Mrk
421 I exhibited a slightly higher $\Pi_{\rm X}$ of $15\%$ compared to Mrk 501
within a statistical difference of less than $2\sigma$ and a $\Pi_{\rm
X}$/$\Pi_{\rm O}$ ratio of $\sim$5, indicating a stronger chromatic behavior
relative to Mrk 501. These results are consistent with the energy-stratified
shock acceleration model based on the $\Pi_{\rm X}$/$\Pi_{\rm O}$ , where a
smaller value was predicted in magnetic reconnection, and the TEMZ models.
Subsequent observations of Mrk 421 II and III did not reveal significant
polarization information in the time-averaged polarization during the
observation periods. However, the time-resolved results, as shown in Figure 2,
revealed a smooth rotation of $\psi_{\rm X}$ by more than 360∘ between two
consecutive observations (Mrk 421 II: from $9\pm 1^{\circ}$ to $130\pm
11^{\circ}$ and Mrk 421 III: from $222\pm 7^{\circ}$ to $360\pm 20^{\circ}$).
The rotation rates of $\psi_{\rm X}$ were measured as 80 $\pm$ 9∘ per day and
91 $\pm$ 8∘ per day for the two observations, respectively, while the
polarization degrees remained consistent within uncertainty as $\Pi_{\rm
X}$$=10\pm 1\%$. During the observed period, the X-ray flux increased by
approximately a factor of two between the two observations and then decreased
to a level similar to that at the beginning of the observation, and the
spectrum properties showed a decrease in the photon index and an increase in
the hardness ratio (i.e., the spectrum became harder and flatter), although we
cannot be sure whether this is directly related to the rotation in the
polarization angle. The multiwavelength polarimetry results showed chromatic
trends conistent with previous findings. Therefore, the results of Mrk 421 II
and III suggest a geometric structure where the energy-stratified shock
propagates linearly or radially along the helical magnetic field within the
jet Di Gesu et al. (2023). Additionally, the Mrk 421 IV showed similar
characteristics to those of Mrk 421 I in terms of $\Pi_{\rm X}$, but
$\psi_{\rm X}$ exhibited a different value compared to previous observations
(Mrk 421 I, II, and III) and varied across all the observations.. In
particular, Mrk 421 IV confirmed temporal episodic variability in polarization
during this observation period. In particular, Ref. Kim et al. (2024) showed a
possible correlation between the rotation of $\psi_{\rm X}$ and the
observation of a highly polarized knot emerging from the jet core and moving
away from the “core” based on the 43 GHz VLBA observations performed during
the observation periods of Mrk 421 II, III, and IV. In addition,
multiwavelength polarization monitoring of Mrk 421 I, II, III, and IV showed a
rotation of $\psi$ in the optical and radio bands over a longer period
compared to the X-ray band, with a direction opposite to the rotation of
$\psi_{\rm X}$. This result suggests the possibility that emission regions at
longer wavelengths (millimeter, infrared, and optical) were separate from, or
only partially coincident with, those of the X-ray emission but also contain a
helical magnetic field that is presumably a continuation of the helical field
manifested in the X-ray polarization observations.

Figure 2: IXPE observation results of Mrk 501 and Mrk 421. (Left)
Multiwavelength polarization degree of Mrk 501 from radio rays to X-rays. The
black symbols represent observations conducted between March 8th and 10th,
while the red symbols represent observations from March 26th to 28th. The open
symbols indicate the intrinsic optical polarization degree corrected for the
host galaxy. The figure was reproduced from Figure 3 in Liodakis et al.
(2022). (Right) X-ray polarization angle rotation in Mrk 421. The symbols
identify multiwavelength polarimetry measurements obtained from telescopes as
labeled. The figure was reproduced from Figure 2 in Di Gesu et al. (2023).

In addition, the observations of 1ES1959+650 Errando et al. (2024), PG1553+113
Middei et al. (2023), and 1ES0229+200 Ehlert et al. (2023) exhibited
significant chromatic behavior on $\Pi$ across multiwavelengths, consistent
with the energy-stratified shock acceleration model. Furthermore, concerning
energy stratification and cooling inside the shock, the $\Pi_{\rm
X}$/$\Pi_{\rm O}$ratio from all the IXPE HSP observations has typically been
found to be around $\sim$2–6, with a trend between the $\Pi_{\rm X}$/$\Pi_{\rm
O}$ ratio and $\Pi_{\rm X}$ , as shown in the left panel of Figure 3.
Consequently, as $\Pi_{\rm X}$/$\Pi_{\rm O}$ increases, X-ray emission occurs
in smaller volumes due to a relatively shorter cooling timescale, indicating
well-ordered magnetic fields closer to the shock front and increased
turbulence in the downstream direction Peirson et al. (2023). Moreover, the
comparison between the $\Pi_{\rm X}$/$\Pi_{\rm O}$ ratio and the time-averaged
photon index in the right panel of Figure 3 suggests a possibility of
relatively higher $\Pi_{\rm X}$/$\Pi_{\rm O}$ ratios when the spectrum is
softer and steeper, but excluding the observations of 1ES0229+200. Especially
in the case of 1ES0229+200, an $E_{pivot}$ scale factor of 1 was used in the
log parabolic model instead of the common 5 used in other observations Kim et
al. (2024); Di Gesu et al. (2023); Liodakis et al. (2022). Therefore, it is
possible that this factor may have influenced the observed results compared to
other observations, and this could be improved through analysis under similar
conditions in the future. Additionally, this characteristic can be interpreted
based on the same physical interpretation as when the X-ray emission
originates further away from the peak frequency on the spectrum, indicating
that the emission is from well-ordered magnetic fields in a smaller volume
with a shorter cooling timescale closer to the shock front.

Regarding the variability in polarization properties, smooth rotation on
$\psi_{\rm X}$ and transient $\psi_{\rm X}$ variation have been observed only
in Mrk 421. Hence, it is speculated that the polarization variability observed
exclusively in specific targets may be linked to the inherent physical
properties of jets. However, it is imperative to scrutinize statistically
significant results through concurrent observations based on a larger sample
of targets in future studies. Finally, concerning the variability identified
through the multiwavelength polarimetry observations of Mrk 421 and an orphan
polarization rotation exhibited by PG1553+113 supports the scenario that the
X-ray emission region is separate from that at longer wavelengths.

Figure 3: Physical properties of energy-stratified shock emissions from HSP
blazars. (Left) X-ray polarization vs. the $\Pi_{\rm X}$/$\Pi_{\rm O}$ratio;
(Right) X-ray power law photon index vs. the $\Pi_{\rm X}$/$\Pi_{\rm O}$ ratio
of HSP blazars observed by IXPE . Each colored point indicates different IXPE
observations labeled in the legend.

###  2.3 IXPE Observations of Intermediate and Low Synchrotron Peak Blazars

In the case of ISP and LSP blazars, IXPE observations have been carried out
for BL Lac Middei et al. (2023); Peirson et al. (2023), 3C 273, 3C 279, 3C
454.3, and S5 0716+714 Marshall et al. (2023). BL Lac is typically classified
as an LSP or ISP, where the Compton hump dominates the soft X-ray band. The
X-ray flux and photon index of this target are typically $<2\times
10^{-11}$erg s-1and $<2$, respectively. BL Lac has been observed by the IXPE
three times: during an average flux state (BL Lac I and II; (Middei et al.,
2023)) and during an outburst (BL Lac III; (Peirson et al., 2023)). From BL
Lac I and II, the upper limits of $\Pi_{\rm X}$ $\leq~{}14.2\%$ and $\Pi_{\rm
X}$ $\leq~{}12.6\%$ were estimated, respectively, and the median optical
polarization values corresponding to $\Pi_{\rm O}$ = 6.8$\%$, $\psi_{\rm O}$ =
107∘ (during BL Lac I), and $\Pi_{\rm O}$ = 14.2$\%$ and $\psi_{\rm O}$ = 42∘
(during BL Lac II) were measured from contemporaneous multiwavelength
polarimetry observations. These results were interpreted as follows: (1) In
the leptonic scenario, considering that emission originating from SSC
dominates over EC emission in the IXPE energy band according to SED modeling,
approximately$\sim$3$\%$ of $\Pi_{\rm X}$ is predicted from given polarization
in radio band, $\Pi_{\rm R}$(BL Lac I$\sim$4$\%$ and BL Lac II$\sim$$6\%$)
Peirson and Romani (2019). Therefore, the measured X-ray upper limit is
consistent with the leptonic scenario. (2) In the hadronic scenario, $\Pi_{\rm
X}$ similar to or higher than $\Pi_{\rm O}$ is predicted, but $\Pi_{\rm O}$
was observed to be high. Therefore, the hadronic scenario is disfavored. In
conclusion, this disfavors a significant contribution of proton synchrotron
radiation to the X-ray emission at these epochs. Instead, it supports a
leptonic origin for the X-ray emission in BL Lac.

Furthermore, in the case of BL Lac III, a distinct synchrotron contribution
was observed alongside the outburst, with $F_{2-8{\rm keV}}~{}=~{}2.77\pm
0.21\times 10^{-11}$erg s-1 and a photon index of 2.10 $\pm$ 0.09.
Subsequently, Ref. Peirson et al. (2023) investigated the flux and
polarization contributions of the synchrotron emissions across both the soft-
energy range (2–4 keV) and the entire IXPE band (2–8 keV) using two power law
components. Through time-resolved polarization analysis, dividing the total
observation period into three equal sub-periods, a significant X-ray
polarization, exceeding $99\%$ significance, with $\Pi_{\rm X}$ =
21.7${}^{+5.6}_{-7.9}$ and $\psi_{\rm X}$ = $-$28.7 $\pm$ 8.7, was detected
only in the first sub-period (upper limits were observed for the remaining
sub-periods). This was accompanied by a decrease in the flux contribution of
the synchrotron emission component. Moreover, the $\Pi_{\rm X}$ value was
higher than the concurrently measured $\Pi_{\rm O}$ = 13.1 $\pm$ 2.4$\%$.
These results were explained by the influence of turbulence in the magnetic
field, closer to the particle acceleration site in a smaller volume with well-
ordered magnetic fields, akin to the characteristics of synchrotron emission
observed in HSPs, leading to the higher $\Pi_{\rm X}$ observed in the high-
energy regime. Consequently, BL Lac III was concluded to probe the high-
frequency end of the synchrotron component, which diminished during the
observation.

For the remaining LSP and ISP sources (3C 273, 3C 279, 3C 454.3, and S5
0716+714), only upper limits could be estimated from IXPE observations in the
2–8 keV band (3C 273: $\Pi_{\rm X}$ < $9.0\%$, 3C 279: $\Pi_{\rm X}$ <
$12.7\%$, 3C 454.3: $\Pi_{\rm X}$ < $28.0\%$, and S5 0716+714: $\Pi_{\rm X}$ <
$26.0\%$). These observational results, when compared with polarization in the
optical and radio domains, suggest that $\Pi_{\rm X}$ < $\sim 10\%$ and is
likely to be less than or comparable to contemporaneous $\Pi_{\rm O}$.
Therefore, although hadronic models are not completely eliminated, these X-ray
polarization measurements seem to favor the leptonic process, wherein photons
are upscattered by relativistic electrons in the jets of blazars. Lastly, Ref.
Marshall et al. (2023) emphasizes that further IXPE observations can provide
additional insights into the X-ray emission mechanism in LSP and ISP blazars.

##  3 X-ray Polarization from Hot Coronae

###  3.1 Theoretical Expectations

The geometry and size of the X-ray corona serve as indicators for exploring
its physical origin. The corona could manifest as a slab-like or wedge-like
structure originating from the accretion disk, e.g., (Haardt and Matt, 1993;
Poutanen et al., 2023), and it could assume a conical shape if it forms the
base of a jet, e.g., (Henri and Pelletier, 1991; Henri and Petrucci, 1997;
Markoff et al., 2005), or a failed jet, e.g., (Ghisellini et al., 2004).
Often, it has been assumed for simplicity as a point- or sphere-like
configuration located above and below the black hole rotation axis, called
lamppost geometry, e.g., (Martocchia and Matt, 1996; Miniutti and Fabian,
2004; Wilkins and Fabian, 2012).

The X-ray polarization from the corona is expected to depend on its size,
geometry, and position in the system. Recent simulation results using the
Monte Carlo Comptonization code (MONK) Zhang et al. (2019); Ursini et al.
(2022) yield the following polarizations for different corona geometries: (1)
the slab geometry is predicted to exhibit a maximum polarization, $\Pi_{\rm
X}$ up to $12\%$, with $\psi_{\rm X}$ oriented parallel to the disk axis,
i.e., parallel to the direction of the jet; (2) conical geometry is expected
to result in $\psi_{\rm X}$ parallel to the major axis of the projection of
the disk on the sky with $\Pi_{\rm X}$ up to $7\%$; (3) in the case of
spherical lamppost geometry, $\Pi_{\rm X}$ of $1-3\%$ and the same $\psi_{\rm
X}$ as conical geometry are predicted (see Figure 4).

Figure 4: Schematic view of different X-ray corona geometries: slab, conical,
and lamppost. The bluish and reddish areas represent the corona and disk
emission regions, respectively. Blue and orange arrows indicate upscattered
X-ray and UV/optical disk photons, respectively. The black arrow represents
the predicted polarization properties (degree in number and angle in direction
of the arrow), estimated from Ursini et al. (2022).

###  3.2 IXPE Observations of Unobscured Radio-Quiet AGN

Since the beginning of IXPE operation, three unobscured radio-quiet Seyfert 1
galaxies have been observed (NGC 4151: Gianolli et al. (2023), IC 4329A:
Ingram et al. (2023), and MCG-05-23-16: Tagliacozzo et al. (2023); Marinucci
et al. (2022)). The X-ray polarization analysis for RQAGN was conducted using
both model-independent and spectropolarimetric analysis methods. These methods
were employed to examine the time-averaged polarization and the variability in
polarization over time and energy. In particular, the relatively more complex
spectral features of RQAGN were examined based on simultaneous observations
from XMM-Newton and NuSTAR, which cover a wider energy range with higher
spectral resolutions. This allows for a more detailed spectropolarimetric
analysis, resulting in the measurement of X-ray polarization characteristics
for each emission component. Finally, the polarization properties measured by
the IXPE were used to constrain the geometric characteristics of the corona by
comparing the expected X-ray polarization results predicted under the
different geometrical conditions of the corona with the MONK simulation
results.

First, NGC 4151 exhibited X-ray polarization in the 2–8 keV energy range, with
$\Pi_{\rm X}$ = 4.9 $\pm$ 1.1$\%$ and $\psi_{\rm X}$ = 86 $\pm$ 7∘ (as shown
in the left panel of Figure 5), corresponding to $\sim$4.4$\sigma$
significance, as determined by a model-independent polarization analysis.
Moreover, NGC 4151 revealed statistically significant variations in the
energy-resolved polarization analysis; i.e., we found $\Pi_{\rm X}$ = 4.3
$\pm$ 1.6$\%$ and $\psi_{\rm X}$ = 42 $\pm$ 11∘ in the soft-energy range of
2–3.5 keV, deviating from the measurements in other energy ranges.
Additionally, spectropolarimetric analysis (middle panel in Figure 5) takes
into account the polarization dilution effect due to the soft-energy regime
and sets the polarization angles of the primary emission and reflection
emission components perpendicular to each other. As a result, for the primary
emission component, $\Pi_{\rm X}$ = 7.7 $\pm$ 1.5$\%$ and $\psi_{\rm X}$ = 87
$\pm$ 6∘ were derived, while, for the reflection component, an upper limit of
$\Pi_{\rm X}$$<27\%$ was obtained. Additionally, NGC 4151 exhibits a radio jet
feature in VLBI observations Williams et al. (2017), and the measured
$\psi_{\rm X}$ shows that it aligns with the direction of the radio jet
emission, $\sim$83∘ Harrison et al. (1986); Ulvestad et al. (1998). This
indicates that the corona emission originates from the equatorial plane. These
polarization results ruled out lamppost and conical geometry scenarios among
the proposed coronal geometries. Furthermore, a comparison with the MONK
simulations (right panel in Figure 5) confirmed that the IXPE observational
results agree well with the predicted polarization results from the slab or
wedge geometry. Moreover, the observed $\psi_{\rm X}$ in the soft-energy band
is similar to that of the extended narrow-line region (NLR), with a confirmed
orientation by HST Evans et al. (1993); Das and Crenshaw (2003), supported by
a Chandra observation Wang et al. (2011) value of $45\pm 5^{\circ}$,
suggesting that a new emission component may influence the X-ray polarization,
which is to be confirmed through additional observations.

Figure 5: IXPE observation result of NGC 4151. (Left) Polarization contours
($68\%$, $90\%$, and $99\%$ detection significance levels); (middle) X-ray
spectrum analysis result; (right) comparison of IXPE measurements and expected
X-ray polarization in slab and wedge geometry coronae calculated from MONK
simulations. The figure was reproduced with kind permission from Oxford
University Press and the Royal Astronomical Society from Gianolli et al.
(2023).

Next, MCG-05-23-16 underwent two observations (MCG-05-23-16 I: May 2022 and
MCG-05-23-16 II: November 2022), yielding upper limits of $\Pi_{\rm X}$ $\leq
4.7\%$ and $\Pi_{\rm X}$ $\leq 3.3\%$, respectively. The integrated analysis
of MCG-05-23-16 I and II resulted in an upper limit of $\Pi_{\rm X}$ $\leq
3.2\%$, and Figure 6 illustrates the comparison of the X-ray polarization
contour plot with the predicted polarization characteristics from the MONK
simulations of the proposed corona geometries. Thus, despite $\psi$ being
estimated at a $\sim$$1\sigma$ confidence level, considering the direction of
the NLR estimated by the HST [O III] emission observations to be
$\sim$$40^{\circ}$ Ferruit et al. (2000), and taking into account the
perpendicular orientation of the NLR and the accretion disk, the results hint
at a coronal geometry in the form of a slab or wedge rather than a lamppost or
conical shape. Additionally, the disk inclination estimated in Serafinelli et
al. (2023) of $\sim$30–50∘ supports the results of a coronal structure like a
slab or wedge.

Figure 6: X-ray polarization contours of the integrated analysis of
MCG-05-23-16 I and II (red; $68\%$, $90\%$, and $99\%$ detection significance
levels). The black dashed line indicates the direction of the NLR, while the
dotted line denotes the perpendicular direction, implying an angle parallel to
the disk. Each colored area represents the expected polarization properties
calculated by MONK, with relatively saturated regions indicating the expected
degree of polarizaton for inclinations in the range of approximately 30–50∘.
The figure was reproduced with kind permission from Oxford University Press
and the Royal Astronomical Society from Figure 8 in Tagliacozzo et al. (2023).

Finally, IC 4329A has a detected X-ray polarization of the hot corona of
$3.3\pm 1.1\%$ for $\Pi_{\rm X}$ and $78\pm 10^{\circ}$ for $\psi_{\rm X}$ in
the 2–8 keV band, utilizing simultaneous observational data from IXPE , XMM-
Newton, and NuSTAR for the spectropolarimetric analysis. For the spectral
model, a Comptonization and a reflection component have been applied. The
$\psi_{\rm X}$ was roughly aligned with the position angle of the extended
radio emission at $\sim$90∘, e.g., (Unger et al., 1987). This result,
consistent with NGC 4151 and MCG-05-23-16, supports the geometric properties
of a radially extended corona within the plane of the disk. Additionally, in
Ingram et al. (2023), through a more detailed examination using MONK
simulations, a test of the slab and wedge geometry corona system has been
conducted. This tentatively suggests, at a 90% confidence level, a lower limit
for $\Pi_{\rm X}$, favoring asymmetric configurations possibly characterized
by outflowing coronal geometries extended within the disk plane, which would
generate highly polarized emissions aligned with the jet.

##  4 Summary

The IXPE mission has pioneered X-ray polarimetry, achieving the first-ever
detections of X-ray polarization from AGN. The diverse physical
characteristics of AGN observed in the X-ray range, particularly in the RLAGN
population represented by blazars and the RQAGN population represented by
unobscured RQAGN, have provided crucial insights into estimating the particle
acceleration processes within relativistic jets, the physical and geometrical
properties of magnetic fields, and the intrinsic geometry of hot coronae. The
IXPE observations of blazars, notably the HSP subclass starting with the first
observation of Mrk 501, are consistent with the possibility that the
synchrotron emission within the jet originates from energy-stratified shocks.
Subsequent observations of Mrk 421 have further supported this scenario and
indicated the presence of helical magnetic fields by discovering the smooth
rotation of the polarization angle for the first time in the X-ray range.
Additionally, other HSP observations, including 1ES1959+650, PG1553+113, and
1ES0229+200, showed values of the $\Pi_{\rm X}$/$\Pi_{\rm O}$ ratio around
$\sim$2–6, supporting the conclusions drawn from Mrk501 and Mrk421.
Furthermore, extensive comparisons of all the HSP observations have led to a
physical interpretation suggesting that synchrotron jet emission at high
frequencies takes place in environments with smaller volumes of well-ordered
magnetic fields close to shock fronts. The polarization information at longer
wavelengths is diluted by magnetic field turbulence. This interpretation could
gain further solidity through additional IXPE observations focusing on
spectral properties and polarization angles. Furthermore, temporal variations
in polarization properties have been solidly observed only in Mrk 421 to date.
Hence, the characteristic of significant polarization variability observed
only in specific targets should be meticulously investigated in future
studies, considering additional parameters such as the physical
characteristics of the jet and utilizing more extensive observational data.
Lastly, the individual variations in polarization observed across multiple
wavelengths imply spatial segregation between X-ray emissions and emissions at
other wavelengths.

IXPE observations of other subclasses of blazars, including LSPs and ISPs,
were carried out to explore the particle acceleration mechanisms of the
Inverse Compton emission component situated in the jet’s higher-energy band.
The observations of BL Lac objects confirmed that the polarization
characteristics predicted by the leptonic-based SSC acceleration mechanisms
better explain the IXPE observations than hadronic scenarios. However, the
relatively low X-ray flux compared to HSPs poses challenges in achieving
statistically significant observational results for many targets. Thus,
further exploration through observations during higher-source activity states
such as future outbursts or longer exposure times should be considered.

The IXPE observations of RQAGN explore the geometry of the X-ray corona
centered around the unobscured central engine. Observations of NGC4151,
MCG-05-23-16, and IC4329A with IXPE detected polarization within 3–5$\%$ from
the coronal emission, aligned with the inferred jet direction. These results
suggest that the corona, instead of being located on the black hole axis as
expected if it is the base or possibly failed jet, is better explained by a
slab-like or wedge-like shape, believed to originate from Comptonization
around the accretion disk, such as a disk outflow. The IXPE findings were
further validated through a comparison with the predicted X-ray polarization
characteristics calculated via MONK simulations based on various geometrical
structures. Furthermore, observations of NGC 4151 suggested the possibility of
other emission components in the soft-energy band influencing the X-ray
polarization, a characteristic that will be further explored in depth through
future additional IXPE observations. Finally, future IXPE observations aimed
at probing the different states of the corona emission process and reflection
emission in the accretion disk will provide additional evidence to expand our
understanding of the physical emission processes occurring inside AGN.

Conceptualization, formal analysis, visualization, and writing—original draft
preparation, D.E.K.; writing—review and editing, L.D.G., F.M., A.P.M., G.M.,
P.S., F.T., E.C. and I.D. All authors have read and agreed to the published
version of the manuscript.

The Imaging X-ray Polarimetry Explorer (IXPE) is a joint US and Italian
mission. The US contribution is supported by the National Aeronautics and
Space Administration (NASA) and led and managed by its Marshall Space Flight
Center (MSFC), with industry partner Ball Aerospace (contract NNM15AA18C). The
Italian contribution is supported by the Italian Space Agency (Agenzia
Spaziale Italiana, ASI) through contract ASI-OHBI-2017-12-I.0, agreements ASI-
INAF-2017-12-H0 and ASI-INFN-2017.13-H0, and its Space Science Data Center
(SSDC), and by the Istituto Nazionale di Astrofisica (INAF) and the Istituto
Nazionale di Fisica Nucleare (INFN) in Italy. This research used data products
provided by the IXPE Team (MSFC, SSDC, INAF, and INFN) and distributed with
additional software tools by the High-Energy Astrophysics Science Archive
Research Center (HEASARC) at NASA Goddard Space Flight Center (GSFC). The
research of APM was partially supported by National Science Foundation grant
AST-2108622, NASA Swift grant 80NSSC23K1145, and NASA NuSTAR grant
80NSSC22K0537.

IXPE data are publicly available at
https://heasarc.gsfc.nasa.gov/docs/heasarc/missions/ixpe.html (accessed on 17
March 2024). The authors declare no conflict of interest.

References

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