.gifpng.pngconvert gif:#1 png: .gif

11institutetext: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,
D-53121 Bonn, Germany 22institutetext: Institut für Theoretische Physik und
Astrophysik, Universität Würzburg, Emil-Fischer-Str. 31, D-97074 Würzburg,
Germany 33institutetext: Department of Astronomy, Institute of Physics and
Astronomy, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117
Budapest, Hungary 44institutetext: ELKH-ELTE Extragalactic Astrophysics
Research Group, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117
Budapest, Hungary 55institutetext: Konkoly Observatory, ELKH Research Centre
for Astronomy and Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121
Budapest, Hungary 66institutetext: CSFK, MTA Centre of Excellence, Konkoly
Thege Miklós út 15-17, H-1121 Budapest, Hungary 77institutetext: Institute of
Physics and Astronomy, ELTE Eötvös Loránd University, Pázmány Péter sétány
1/A, H-1117 Budapest, Hungary 88institutetext: Shanghai Astronomical
Observatory, Chinese Academy of Sciences, Shanghai, 200030, People’s Republic
of China 99institutetext: Joint Institute for VLBI ERIC, Oude Hoogeveensedijk
4, 7991 PD Dwingeloo, The Netherlands 1010institutetext: Faculty of Aerospace
Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The
Netherlands 1111institutetext: Theoretical Physics IV, Faculty for Physics and
Astronomy, Ruhr University Bochum, D-44780 Bochum, Germany 1212institutetext:
Astronomical Institute, Faculty for Physics and Astronomy, Ruhr University
Bochum, D-44780 Bochum, Germany 1313institutetext: Ruhr Astroparticle and
Plasma Physics Center, Ruhr-Universität Bochum, D-44780 Bochum, Germany
1414institutetext: Key Laboratory of Radio Astronomy and Technology, Chinese
Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing, 100101, P. R.
China

# From binary to singular: the AGN PSO J334.2028+1.4075 under the high-
resolution scope

P. Benke 1122 K. É. Gabányi 33445566 S. Frey 556677 T. An 881414 L. I. Gurvits
991010 E. Kun 1111121213135566 P. Mohan 88 Z. Paragi 99 E. Ros 11

(Received ; accepted )

###### Abstract

Context. PSO J334.2028+1.4075 (PSO J334) is a luminous quasar located at
redshift $z=2.06$. The source gained attention when periodic flux density
variations were discovered in its optical light curve. These variations were
initially interpreted as the variability due to the orbital motion of a
supermassive black hole binary (SMBHB) residing in a single circumbinary
accretion disk. The orbital separation was determined to be $0.006$ pc with an
in-spiral time of $7$ yr in the rest frame of PSO J334. These findings
suggested the quasar could be in the gravitational wave emitting phase of its
merger and so extended multi-wavelength observations were commenced. However,
subsequent observations provided evidence against the binary hypothesis as no
optical periodicity was found on extended time baselines. On the other hand,
detailed radio analysis with the Karl G. Jansky Very Large Array (VLA) and the
Very Long Baseline Array (VLBA) revealed a lobe-dominated quasar at kpc
scales, and possibly a precessing jet, which could retain PSO J334 as a binary
SMBH candidate.

Aims. We aim to study both the large- and small-scale radio structures in PSO
J334 to provide additional evidence for or against the binary scenario.

Methods. We observed the source at $1.7$ GHz with the European Very Long
Baseline Interferometry Network (EVN), and at $1.5$ and $6.2$ GHz with the
VLA, at frequencies that complement the previous radio interferometric study.

Results. Our images reveal a single component at parsec scales slightly
resolved in the southeast–northwest direction and a lobe-dominated quasar at
kiloparsec scales with a complex structure. The source morphology and
polarization in our VLA maps suggest that the jet is interacting with dense
clumps of the ambient medium. While we also observe a misalignment between the
inner jet and the outer lobes, we suggest that this is due to the restarted
nature of the radio jet activity and the possible presence of a warped
accretion disk rather than due to the perturbing effects of a companion SMBH.

Conclusions. Our analysis suggests that PSO J334 is most likely a jetted AGN
with a single SMBH, and there is no clear evidence of a binary SMBH system in
its central engine.

###### Key Words.:

Galaxies: jets – Galaxies: active – Techniques: interferometric – Techniques:
high angular resolution – Polarization

Figure 1: VLA images of PSO J334 at $1.5$ and $6.2$ GHz. Each color bar
represents total intensity in mJy beam-1. Restoring beam sizes (FWHM) are
$1218\,\mathrm{mas}\times 1665\,\mathrm{mas}$ at the major axis position angle
$\mathrm{PA}=-30.5\degr$ at $1.5$ GHz, and $340.6\,\mathrm{mas}\times
422.4\,\mathrm{mas}$ at $\mathrm{PA}=-25.4\degree$ at $6.2$ GHz, respectively.
The lowest contours are at $0.12$ and $0.03$ mJy beam-1, respectively, and
further contour levels increase by a factor of two. The eastern and western
lobes are marked as EL and WL, and the core is denoted as C. The red cross
marks the position of the VLBI core at $1.7$ GHz. Table 1: Map properties of
the clean images shown in Figs. 1 and 3, as well as the re-analyzed VLBA
images from Mooley et al. (2018).

$\nu$ [GHz]aa$a$Observing frequency. | Arraybb$b$Interferometer array performing the observation. |  $S_{\mathrm{tot}}$ [mJy]cc$c$Total flux density. |  $S_{\mathrm{peak}}$ [mJy beam-1]dd$d$Peak brightness. |  $\sigma$ [mJy beam-1]ee$e$Rms noise. |  $b_{\mathrm{maj}}$ [mas]ff$f$Beam major axis. |  $b_{\mathrm{min}}$ [mas]gg$g$Beam minor axis. | PA [°]hh$h$Beam position angle.
---|---|---|---|---|---|---|---
1.5 | VLA | 35.41 | 14.7 | 0.04 | 1665 | 1218 | $-30.5$
6.2 | VLA | 11.48 | 4.52 | 0.01 | 422.4 | 340.6 | $-35.4$
1.7 | EVN | 6.8 | 2.1 | 0.035 | 3.4 | 3.4 | $0$
4.38 | VLBA | 4.83 | 2.54 | 0.049 | 5.86 | 2.46 | $11.2$
7.40 | VLBA | 3.24 | 1.41 | 0.036 | 3.48 | 1.46 | $12.1$
8.67 | VLBA | 3.45 | 1.56 | 0.06 | 2.13 | 0.86 | $-0.27$
15.37 | VLBA | 1.19 | 0.85 | 0.036 | 1.29 | 0.48 | $-3.99$

111

##  1 Introduction

The discovery of PSO J334.2028+1.4075 (FBQS J2216+0124; hereafter denoted as
PSO J334) (Liu et al. 2015) as a supermassive black hole binary (SMBHB)
candidate attracted significant interest due to the rarity of confirmed
SMBHBs. Supermassive black holes are expected to be at the center of most
galaxies. Since galaxies evolve hierarchically, SMBHBs are believed to be
abundant, especially at small separations (An et al. 2018). However,
confirming the existence of such objects has so far been mostly unsuccessful,
with a few exceptions. The most notable examples are the dual AGN system in
NGC 6240 (Komossa et al. 2003), which resides in an ultraluminous infrared
galaxy, and 0402+379, which was detected with the Very Long Baseline Array
(VLBA) and has two radio cores separated by a projected distance of $7.3$ pc
(Rodriguez et al. 2006).

The SMBHB candidate quasar PSO J334 was discovered through a systematic search
in the Pan-STARSS1 Medium Deep Survey (Liu et al. 2015). Based on an observed
$542\pm 15$ day period in the variation of the optical flux density and an
estimated total black hole mass of $10^{9.97\pm 0.5}M_{\odot}$ (with a mass
ratio between $0.05$ and $0.25$), an orbital separation of $0.006$ pc was
inferred. According to this, the coalescence of the SMBHB would occur in
approximately $7$ yr in the rest frame of the quasar. Unfortunately, current
astronomical instruments are not capable of resolving the two components at
such a small separation, so evidence for the existence of a second component
could only be indirect, such as the detected periodic variability in the
optical flux density. This variability could be caused by a secondary black
hole passing through the primary black hole’s accretion disk, as proposed for
OJ 287 (Lehto & Valtonen 1996). A similar explanation has been suggested in
the case of the recently discovered SMBHB candidate SDSS J143016.05+230344.4
as well, which shows a periodic optical variability with a decay in both
period and amplitude (Jiang et al. 2022; An et al. 2022). However, the
detected $2.6$ cycles of the putative periodicity are likely insufficient to
claim sinusoidal variations (Vaughan et al. 2016), and other processes, such
as quasi-periodic eruptions (Miniutti et al. 2019) and quasi-periodic
oscillations (Gierliński et al. 2008) may also explain the periodic flux
density variability observed in PSO J334. Indeed, subsequent observations with
extended time baselines of the optical monitoring failed to find any evidence
of periodic variability in PSO J334 (Liu et al. 2016).

The radio structure of PSO J334 has been investigated in a multi-frequency
study with the Karl G. Jansky Very Large Array (VLA) and the VLBA by Mooley et
al. (2018). In the VLBA images obtained at four frequencies from $4.4$ to
$15.4$ GHz, the quasar is resolved into two components, a compact core and a
jet. Their separation is $3.6$ milliarcsec (mas), corresponding to a projected
linear separation of $30$ pc. The VLA images at $2.8$ and $4.38$ GHz reveal a
lobe-dominated structure extending $66$ kpc from opposite sides of the core.
In addition, the $39\degr$ difference between the position angles of the outer
lobes and the inner jet is significant enough to suggest a perturbation of the
jet by the second SMBH (Begelman et al. 1980), or alternatively a restarted
double-double source. Thus, despite the results from the recent optical light
curve, PSO J334 can still be considered as a SMBHB candidate (Mooley et al.
2018). Multi-wavelength observations aimed at determining the accretion mode
of the quasar by Foord et al. (2017) have not found any feature that would
convincingly distinguish PSO J334 from a single active galactic nucleus (AGN).
However, there are still untested scenarios that would allow the object to
retain its SMBHB status.

Figure 2: VLA $1.5$ GHz (left panel) and $6.2$ GHz (right panel) polarimetric
images of PSO J334. The colors represent the polarized intensity in $\mu$Jy
beam-1, while the contours are the same as in the total intensity map in Fig.
1. EVPAs are represented by the black ticks in the image.

We study the radio structure of PSO J334 using the technique of very long
baseline interferometry (VLBI) with the European VLBI Network (EVN) at $1.7$
GHz and with the VLA at $1.5$ and $6.2$ GHz. Here we present our results and
compare them with those obtained with the VLBA at higher frequencies by Mooley
et al. (2018). In Sect. 2, we describe the observations and the data reduction
process. We then discuss our results in Sect. 3. Finally, a summary is given
in Sect. 4. In this paper we assume a $\Lambda$CDM cosmological model with
$H_{0}=70$ km s-1 Mpc-1, $\Omega_{\Lambda}$=0.73, and
$\Omega_{\mathrm{M}}$=0.27. At the redshift of the object, $z=2.06$ (Becker et
al. 2001), $1\arcsec$ of angular distance in the sky corresponds to $8.569$
kpc of projected linear distance (Wright 2006).

##  2 Observations and data reduction

###  2.1 VLA data

Observations with the VLA (project code AG980, PI: K.É. Gabányi) were carried
out at $1.5$ and $6.2$ GHz (L and S/C bands) on 2016 October 28 and 2016
October 26, respectively. The VLA was observing in its most extended A
configuration with $27$ antennas. The on-source time was $0.5$ h in both
bands. The primary flux density calibrator in both experiments was 3C 48, and
the polarization D-term calibrator was J2355+4950. The secondary calibrators
were J2212+0152 ($1.5$ GHz) and J2218$-$0335 ($6.2$ GHz). The $1.5$ GHz data
were recorded in $16$ spectral windows between $1.008$ and $1.968$ GHz with
$64$ channels, each with a bandwidth of $64$ MHz. The $6.2$ GHz data contained
$48$ spectral windows, but the first $16$ were only used to set up the
observations, so the target and calibrators were observed between $4.226$ and
$8.096$ GHz frequencies in $32$ spectral windows, each with $64$ channels and
a bandwidth of $128$ MHz.

Data reduction was performed in the Common Astronomy Software Applications
(CASA, McMullin et al. 2007; The CASA Team 2022) package version $7.15.0$.
First, phase, delay, bandpass, and gain calibrations were derived for the
primary calibrator. Then, to calibrate polarization, we determined cross-hand
delays, solved antenna-based D-terms for the unpolarized calibrator, and
finally calibrated the polarization angle for the primary calibrator. We then
used the calibration tables generated in the previous steps to transfer the
solutions to the secondary calibrator and then to our target source222For the
calibration, we followed this VLA tutorial:
https://casaguides.nrao.edu/index.php/VLA_Continuum_Tutorial_3C391-CASA5.5.0.
As 3C 48 was undergoing an active phase during
2016333https://science.nrao.edu/facilities/vla/docs/manuals/obsguide/modes/pol,
we inspected the polarimetric calibration carefully, imaged all calibrators to
determine the polarization angle and fractional polarization values, and
compared them to those available in the literature. In the case of the D-term
calibrators, we found no significant polarization signatures and fractional
polarization values were close to $0$. In the case of 3C $48$, polarization
angles and fractional polarization values in the two bands differ by less than
$15$% compared to the values in the literature3.

Hybrid imaging was performed by iterating tclean and self-calibration, while
imaging all four Stokes parameters together, and then deriving polarized
intensity and polarization fraction images from the Stokes IQU images. The
$1.5$ and $6.2$ GHz VLA images are shown in Fig. 1, and the polarized
intensity and electric vector position angle (EVPA) images are shown in Fig.
2.

###  2.2 EVN data

Our EVN observation (project code RSG08, PI: S. Frey) at $1.7$ GHz was
performed on 2015 October 18, with the participation of eleven radio
telescopes: Jodrell Bank Lovell Telescope (United Kingdom), Westerbork (single
dish; the Netherlands), Effelsberg (Germany), Medicina (Italy), Onsala
(Sweden), Sheshan (China), Toruń (Poland), Hartebeesthoek (South Africa),
Svetloe, Zelenchukskaya, and Badary (Russia). The data were recorded at a $1$
Gbit s-1 rate in left and right circular polarizations, with 8 basebands (IFs)
per polarization, each divided into thirty-two $500$-kHz wide spectral
channels. The total bandwidth was $128$ MHz per polarization. The correlation
was performed at the Joint Institute for VLBI ERIC (Dwingeloo, the
Netherlands) with $4$ s integration time. The observation lasted for a total
of $2$ h. We used phase-referencing to a nearby (separated by
$0\aas@@fstack{\circ}96$) compact calibrator source, J2217+0220, with duty
cycles of $6.5$ min, including $3$ min $20$ s scans spent on the target. The
total accumulated observing time on PSO J334 was $1$ h.

Figure 3: $1.7$-GHz EVN image of PSO J334. The image is restored with a
$3.4$-mas circular Gaussian beam. The lowest contours are at $0.09$ mJy beam-1
and increase by a factor of two. The source shows an elongated shape in the
southeast–northwest direction, which is consistent with the structure reported
in Mooley et al. (2018).

The data were calibrated with the U.S. National Radio Astronomy Observatory
(NRAO) Astronomical Image Processing System (AIPS, Greisen 2003), following
the usual procedures. The amplitudes of the raw correlated visibility data
were calibrated using the antenna gain curves and measured system temperatures
(where available), as provided by the participating stations. Nominal system
temperature values were used for Jodrell Bank, Sheshan, Svetloe,
Zelenchukskaya, and Badary. The data were then corrected for the dispersive
ionospheric delay by invoking the task TECOR that uses total electron content
maps derived from global navigation satellite systems data. Phase changes due
to the time variation of the source parallactic angle were also corrected for
azimuth–elevation mounted radio telescopes in the network. Global fringe-
fitting was performed using the task FRING on the phase-reference calibrator
J2217+0220 and the bright fringe-finder source J2148+0657 also observed for a
$12$-min scan at the beginning of the experiment. These calibrated visibility
data were exported to Difmap (Shepherd 1997) for imaging. Conventional hybrid
mapping with several iterations of the clean algorithm (Högbom 1974) and
phase-only self-calibration was performed. Then antenna-based gain correction
factors were determined. These values were within $\pm 5\%$ for the compact
bright fringe-finder source, suggesting a reliable initial amplitude
calibration. The clean component model obtained for the phase-reference source
J2217+0220 in Difmap was fed back to AIPS, before repeating fringe-fitting,
now taking the calibrator source structure into account for determining
visibility phases. The fringe-fit solutions obtained for J2217+0220 were
interpolated to the target source, PSO J334, within the atmospheric coherence
time using the task CLCAL. The final calibrated visibility data file for PSO
J334 was then transferred to Difmap for imaging and brightness distribution
modeling.

The peak of the dirty image was offset by about $1\aas@@fstack{\prime\prime}1$
from the center because of an inaccurate a-priori position used for radio
telescope pointing. Therefore we started the imaging by shifting the phase
center to the actual brightness peak. Because PSO J334 is relatively weak with
$\sim 7$ mJy total flux density, and it appeared slightly resolved at $1.7$
GHz with the EVN, self-calibration in general was not attempted during hybrid
imaging in Difmap, except for phase self-calibration for the European stations
(Effelsberg, Jodrell Bank, Onsala, Westerbork, Medicina, and Toruń). We used
gradually decreasing solution intervals from $60$ to $1$ min. Amplitude self-
calibration was not made at all. The naturally weighted clean image of PSO
J334 is shown in Fig. 3. A circular two-dimensional Gaussian brightness
distribution model component fitted directly to the self-calibrated visibility
data in Difmap can adequately describe the source, allowing us to
quantitatively characterize its size and flux density (Table 2). Neither an
elliptical Gaussian, nor a two-component circular Gaussian model could
significantly improve the goodness of fit.

###  2.3 Archival VLBA data

To be able to perform brightness distribution model fitting in the visibility
domain, we downloaded from the NRAO data archive444https://data.nrao.edu/, re-
calibrated, and imaged the VLBA data of Mooley et al. (2018) measured at
$4.38$, $7.40$, $8.67$, and $15.37$ GHz (project code BM438, PI: K.P. Mooley).
For details on the observations, we refer to the original paper (Mooley et al.
2018). Calibration was carried out in AIPS. After loading the data with FITLD,
we performed parallactic angle and digital sampling corrections, corrected for
the Earth orientation parameters, and applied ionospheric corrections that are
especially important for phase-referenced observations performed at low
frequencies and low source declination. At first, fringe-fitting was performed
on the phase-reference calibrator, J2217+0220, using the task FRING. After
applying the calibration tables and writing the data out of AIPS, we performed
hybrid imaging in Difmap, in a similar way as described in Sect. 2.2 for the
EVN data. Since the gain corrections for all the VLBA antennas were within
$\pm$5%, we did not perform any additional antenna-based amplitude correction
in AIPS. The clean image of J2217+0220 was then loaded into AIPS and used
during the second round of fringe-fitting. Delay and rate solutions were
applied to both the calibrator and the target, PSO J334. The calibrated
visibility data of the target source were written out. Imaging again was
carried out in Difmap by only using clean iterations without self-calibration.
The total flux densities, i.e. the sum of the individual clean components, and
peak brightnesses agree with the values published in Mooley et al. (2018)
within 10% (see image properties in Tab. 1). Gaussian brightness distribution
model components (Table 2) were fitted to the visibility data using the
modelfit command in Difmap.

Figure 4: Two-point spectral index distribution maps of PSO J334 based on: (a)
quasi-simultaneous VLA images at $1.5$ and $6.2$ GHz, and (b) $1.7$-GHz EVN
and $4.38$-GHz VLBA images. Lowest contours are at $0.12$ and $0.14$ mJy/beam,
respectively, and contour levels increase by a factor of two. Colors represent
spectral index values. We note that the VLBI images were taken half a year
apart, so flux density variability cannot be excluded and therefore the
spectral index map in panel (b) should be treated with caution.

##  3 Results and discussion

###  3.1 Source structure and polarization

The $1.7$-GHz EVN image of PSO J334 (Fig. 3) restored with a $3.4$-mas
circular Gaussian beam (full width at half maximum, FWHM) shows a single
component that is slightly resolved in roughly the southeast–northwest
direction. The structure is consistent with the higher-frequency VLBA images
(Mooley et al. 2018), where two components – a southeastern synchrotron self-
absorbed core and a northwestern jet – were identified with $3.6$ mas
separation along the position angle of $139\degr$. (Position angles are
conventionally measured from north through east.) The $39\degr$ misalignment
in position angles between the VLA and VLBA jets led Mooley et al. (2018) to
restore the SMBHB status of PSO J334, however, alternative interpretations are
still viable to explain the observations. Double-double radio sources, such as
B0925+420 and B1450+333 (Schoenmakers et al. 2000), that retain signs of
several active phases show similar morphology to PSO J334. In this case, the
lobes seen on kpc scales with the VLA would be relics of past activity, and
the compact, mas-scale core–jet morphology was formed more recently. The
change in jet position angle can be interpreted as precession either due to
interaction with a companion SMBH (Begelman et al. 1980) or caused by a warped
accretion disk changing the orientation of the jet (Pringle 1997).

Our VLA observations at $1.5$ and $6.2$ GHz show details of the complex
structure of PSO J334 (Fig. 1). The source, as shown in the $2.8$-GHz VLA
B-configuration Caltech–NRAO Stripe $82$ Survey (CNSS) image of Mooley et al.
(2018), is a lobe-dominated quasar oriented at a large angle with respect to
our line of sight. The projected linear size of the object is approximately
$79$ kpc, which is typical of $z=2$ AGN (Blundell et al. 1999). The lengths of
the arms are unequal, with the eastern arm being longer at both frequencies.
However, contrary to expectations that the longer arm is pointing towards the
observer and is brighter due to Doppler boosting (Longair & Riley 1979), here
the western, shorter arm appears brighter in both images. In addition, the
eastern arm shows a sharp turn before ending in a hotspot, which suggests an
interaction with the surrounding interstellar medium (ISM), similarly as,
e.g., in the high-redshift radio galaxy 4C $41.17$ (Gurvits et al. 1997).
However, we do not detect polarized emission at the turning point as, e.g., in
PKS 0637$-$752 (Lovell et al. 2000), where the highly polarized bent jet
region also gives rise to bright X-ray emission (Schwartz et al. 2000). By
inspecting the polarimetric images, we also see that the polarized intensity
is higher in the western lobe and that EVPAs are close to perpendicular to the
jet propagation on both sides, indicating the presence of a termination shock
where the lobe material interacts with the ambient medium. The asymmetric
structure together with the polarimetric results suggest that PSO J334 is
embedded in a large-scale environment that is not intrinsically symmetric, and
the jet interacts with clumps of the ISM that are disrupted upon contact with
the jet material.

Inspecting the inner $2\arcsec-3\arcsec$ in our $6.2$-GHz VLA image (Fig. 1),
we see a remarkably straight jet that cannot be described with any precession
model. Jet precession itself would be revealed by a helical jet shape that is
physically external or intrinsic to the jet. In the first case, the main
driver might be e.g. binary motion (e.g. Kun et al. 2014), Lense–Thirring
precession (e.g. Lense & Thirring 1918; Liska et al. 2018), or disk precession
induced by a secondary black hole (e.g. Caproni & Abraham 2004). In this case,
the jet components move more or less on straight or ballistic paths, and the
pitch of the jet is constant. The helical pattern simply reflects the periodic
ejection direction of the newborn jet components. The second case appears,
e.g., due to instabilities in the jet (e.g. Perucho et al. 2006) and
components actually move along helical path. In this case, the spatial
wavelength of the jet along its symmetry axis is increasing with increasing
core separation. The jet appearing in the $6.2$-GHz VLA image (Fig. 1) has no
resemblance to any of these scenarios. However, we cannot rule out the
possibility that more sensitive images with higher angular resolution could
recover jet structures indicative of precession or the presence of
instabilities (see, e.g., the case of 3C $279$, Fuentes et al. 2023). This
structure seems hard to reconcile with the jet precession suggested by Mooley
et al. (2018) based on lower-resolution VLA data, and rules out the last
argument supporting the binary nature of the source.

###  3.2 Spectral analysis

Spectral index maps ($S_{\nu}\propto\nu^{\alpha}$) were created between our
two VLA images at $1.5$ and $6.2$ GHz, as well as between our $1.7$-GHz EVN
image and the $4.38$-GHz VLBA image of Mooley et al. (2018), plotted with
black contours in Fig. 6. To align the images on the optically thin jet
components, we used 2D cross-correlation.

Figure 5: Spectra of the core (SE) and jet (NW) components of the VLBA images.

The image pairs had the same restoring beam, map and pixel size, as well as
the same minimum and maximum $(u,v)$ distance. The resulting spectral index
maps are shown in Fig. 4. Due to the low signal-to-noise ratio outside of the
peaks of the core and lobe regions, we do not recover spectral index solutions
there.

Spectra are flat in the VLA core, i.e. the central component, and the eastern
lobe, however, $\alpha$ values indicating a steeper spectrum are measured in
the western lobe (Fig. 4). The flat spectrum of the eastern lobe might
indicate a shock region, which is supported by the bending seen in the
$6.2$-GHz VLA image (Fig. 1), possibly happening due to the interaction with
the ISM. The steeper spectrum of the western lobe, however, can be explained
by an older population of electrons present in this region. The VLBI spectral
index map created between $1.7$ and $4.38$ GHz shows a flat spectrum both for
the core and the northwestern jet component. Since we assume that the
amplitude calibration is accurate within $10\%$, spectral index errors are
estimated to be $\pm 0.15$. See also figure $3$ of Mooley et al. (2018) for
the spectral index map between $8.67$ and $15.37$ GHz that show steep spectra
in both VLBI components. We also plot the spectra of the core and jet
components of the VLBI images in Fig. 5, where both the core and the jet
components show a steep spectrum between $1.7$ and $4.38$ GHz. In addition,
the steepening towards the jet edge might be an artifact due to the low
brightness of the component. While our results confirm the southeastern
component as the core (Mooley et al. 2018), here we must note that the
observations used to create the spectral index map were made half a year
apart, so these results must be interpreted cautiously because of possible
flux density variability.

The radio spectrum compiled in Benke et al. (2018), as well as the broadband
spectral energy distribution (SED) in Foord et al. (2017) show no deviation
from single AGN spectra. The two models investigated by Foord et al. (2017)
are the mini-disk and cavity models that represent different stages of the
binary evolution and manifest in the SED as missing emission at different
frequencies. However, they found that the optical to X-ray bands are well
modeled with a composite non-blazar SED (Shang et al. 2011) and the radio
emission falls between what is expected from radio-loud and radio-quiet
sources.

Table 2: Characteristics of modelfit components.

$\nu$ [GHz]aa$a$Frequency of the observation | Array | Component |  $S_{\mathrm{comp}}$ [mJy]bb$b$Flux density of the component |  $b_{\mathrm{comp}}$ [mas]cc$c$Size of the component (FWHM) |  $T_{\mathrm{b}}$ [$10^{8}$ K]dd$d$Brightness temperature
---|---|---|---|---|---
1.7 | EVN |  | $7.15\pm 0.72$ | $6.58\pm 0.68$ | $2.2\pm 0.5$
4.38 | VLBA | SE | $2.43\pm 0.24$ | $1.53\pm 0.49$ | $2.0\pm 1.3$
|  | NW | $2.64\pm 0.26$ | $1.23\pm 0.49$ | $3.4\pm 2.7$
7.40 | VLBA | SE | $1.71\pm 0.17$ | $0.8\pm 0.29$ | $1.8\pm 1.4$
|  | NW | $1.75\pm 0.18$ | $0.9\pm 0.29$ | $1.5\pm 1.0$
8.67 | VLBA | SE | $1.97\pm 0.2$ | $0.59\pm 0.17$ | $2.8\pm 1.6$
|  | NW | $2.03\pm 0.2$ | $0.83\pm 0.17$ | $1.5\pm 0.6$
15.37 | VLBA | SE | $0.95\pm 0.1$ |  $0.16$**$*$Component is unresolved based on eq. $2$ from Kovalev et al. (2005) |  $>6.0$**$*$Component is unresolved based on eq. $2$ from Kovalev et al. (2005)
|  | NW | $0.8\pm 0.08$ | $0.38\pm 0.1$ | $0.9\pm 0.4$
555

Figure 6: $15.37$-GHz VLBA image overplotted with the Gaia position and its
uncertainty (red cross). White contours are at $0.83$ mJy beam-1 $\times$
($-15$, $15$, $30$, $60$)%, and the restoring beam size is
$1.29\,\mathrm{mas}\times 0.48\,\mathrm{mas}$ at $\mathrm{PA}=-3.96\degree$.
Black contours representing the $8.67$ GHz source structure are at $1.56$ mJy
beam-1 $\times$ ($-7.5$, $7.5$, $15$, $30$, $60$)%, and the FWHM of the
restoring beam is $2.13\,\mathrm{mas}\times 0.86\,\mathrm{mas}$ at
$\mathrm{PA}=-3.99\degree$.

###  3.3 Brightness temperatures

To study the brightness temperature of the compact radio emitting features in
the VLBI images (Figs. 3 and 6, also Mooley et al. 2018), we fitted circular
Gaussian components in the visibility domain with modelfit in Difmap.
Characteristics of the modelfit components are summarized in Table 2. We
assume flux density errors to be 10% and the error in component size to be 20%
(Lister et al. 2009). We calculate the observed brightness temperature as

$T_{\mathrm{b,obs}}[\mathrm{K}]=1.22\times
10^{12}\Bigg{(}\frac{S_{\nu}}{\mathrm{Jy}}\Bigg{)}\Bigg{(}\frac{\nu}{\mathrm{GHz}}\Bigg{)}^{-2}\Bigg{(}\frac{b_{\mathrm{min}}\times
b_{\mathrm{maj}}}{\mathrm{mas}^{2}}\Bigg{)}^{-1}(1+z),$ (1)

where $b_{\mathrm{min}}$ and $b_{\mathrm{maj}}$ are the minor and major axis
(FWHM) of the component. The resolution limit was computed based on eq. $2$ in
Kovalev et al. (2005). For the one component for which the size fell below
this limit, we can only calculate a lower limit of its brightness temperature.
$T_{\mathrm{b,obs}}$ values fall between $10^{7}-10^{9}$ K. This confirms that
the emission originates from AGN activity and not from spatially extended star
formation in the host galaxy (Condon et al. 1991). The measured brightness
temperatures are lower than the average core brightness temperatures of
blazars in the MOJAVE sample666https://www.cv.nrao.edu/MOJAVE/ of $1.39\times
10^{11}$ K (Homan et al. 2021). This indicates that the emission of PSO J334
is likely not beamed and the jets are probably inclined at a large angle to
our line of sight.

###  3.4 VLBI and Gaia astrometry

Both the EVN and VLBA observations were carried out in phase-referencing mode,
enabling precise relative astrometric measurements. We determined the position
of the brightness peak in the VLBI images using MAXFIT in AIPS. Since we
expect that the optical emission originates from the vicinity of the central
engine, i.e., the accretion disk and the inner jet (Kovalev et al. 2017), we
can use Gaia data (Gaia Collaboration et al. 2016) from the third data release
(DR3, Gaia Collaboration et al. 2023) to identify the nucleus position. The
standard error of the optical position is $0.27$ mas in right ascension and
$0.32$ mas in declination based on Gaia DR3. VLBI astrometric errors are
comparable and estimated to be $0.3$ mas for low declinations with the VLBA
based on the analysis of Pradel et al. (2006). We also take into account the
uncertainty of the position of the calibrator, J2217+0220. The source is in
the 3rd realization of the International Celestial Reference Frame (ICRF3,
Charlot et al. 2020), and the formal position errors are $0.0765$ mas and
$0.1137$ mas in right ascension and declination, respectively. We add these
error estimates in quadrature, and estimate errors to be $0.31$ mas in right
ascension and $0.32$ mas in declination. We find that the southeastern
component at $8.67$ GHz is closer to the optical position of the source (see
black contours in Fig. 6). We also see that the differences in right ascension
are within the expected uncertainties, except at $4.38$ GHz where $\sim 2$ mas
offset was found between the Gaia and the VLBI core positions. However, the
optical–radio differences in declination reach up to $\sim 4$ mas, but show no
frequency dependence.

We suspect that these differences in declination arise from uncorrected
tropospheric and ionospheric effects. The contribution of the ionosphere to
phase errors is significant at low frequencies, and since its rapid changes
are difficult to model, we expect that this affects the measurement of the
source position considerably. Based on $22$ GHz VLBA observations, Petrov
(2023) determined that the ionospheric effects contribute around $0.1$ mas to
the error budget both in right ascension and declination for northern
hemisphere sources. However, for southern hemisphere targets, the accuracy of
ionospheric corrections in declination is only $0.3$ mas. In addition, at low
elevations, errors from the wet tropospheric component were shown to dominate
over other systematic errors, and affect the precise measurement of source
declination far more seriously than of the right ascension (Pradel et al.
2006). In order to be able to account for the ionospheric and tropospheric
effects on VLBI astrometry more accurately, we need more extended studies such
as in Brisken et al. (2002), Pradel et al. (2006), and Petrov (2023), to
explore how these effects influence the error budget of our measurements for
various VLBI arrays (see e.g. the Long Basline Array and the VLBI Exploration
of Radio Astrometry, Petrov et al. 2019; Honma et al. 2008) and to develop
methods to correct for them in the most effective way.

##  4 Summary

Liu et al. (2015) originally proposed that PSO J334 might be a SMBHB based on
the periodic variability observed in the optical light curves. The scenario
was later disfavored as extended time baselines revealed no sinusoidal
periodicity in the optical flux (Liu et al. 2016), and SED reconstruction did
not show any signatures expected from a binary AGN system (Foord et al. 2017).
The only remaining indication of a companion SMBH was the possible precession
inferred from multi-frequency radio observations of Mooley et al. (2018),
where the large misalignment of $39\degr$ between the pc- and kpc-scale
structures led the authors to reinstate PSO J334 as a SMBHB candidate.

Our high-resolution radio observations carried out with the VLA at $1.5$ and
$6.2$ GHz reveal a lobe-dominated quasar (in agreement with the findings of
Mooley et al. 2018), likely oriented at a large angle to our line of sight.
Based on polarimetric imaging and the analysis of the arm length and
brightness ratios, we suggest that the source is embedded in an asymmetric
environment and similarly to the high-redshift radio galaxy 4C 41.17 (Gurvits
et al. 1997), its morphology is affected by the surrounding ISM, creating a
bending in the eastern jet. PSO J334 also shows remarkably straight jets at
6.2 GHz, that disfavor jet precession, the only argument left to support the
SMBHB status of the object. In addition, our $1.7$ GHz EVN observations
confirm the significant misalignment between the outer lobes and the inner jet
observed by Mooley et al. (2018). We suggest that this misalignment can be
explained by a newer phase of AGN activity where the orientation of the
component ejection has changed. In conclusion, we find no evidence to support
the binary nature of PSO J334, and it should be considered an ordinary quasar.

###### Acknowledgements.

The authors would like to thank the anonymous referee for their useful
suggestions. We thank J. Livingston for his valuable comments to the
manuscript. The EVN is a joint facility of independent European, African,
Asian, and North American radio astronomy institutes. Scientific results from
data presented in this publication are derived from the following EVN project
code: RSF08. The National Radio Astronomy Observatory is a facility of the
National Science Foundation operated under cooperative agreement by Associated
Universities, Inc. This research was supported through a PhD grant from the
International Max Planck Research School (IMPRS) for Astronomy and
Astrophysics at the Universities of Bonn and Cologne. This work was supported
by the Hungarian National Research, Development and Innovation Office (NKFIH,
grant number OTKA K134213).

## References

  * An et al. (2018) An, T., Mohan, P., & Frey, S. 2018, Radio Science, 53, 1211
  * An et al. (2022) An, T., Zhang, Y., Wang, A., et al. 2022, A&A, 663, A139
  * Arshakian et al. (2006) Arshakian, T. G., Ros, E., & Zensus, J. A. 2006, A&A, 458, 397
  * Becker et al. (2001) Becker, R. H., White, R. L., Gregg, M. D., et al. 2001, ApJS, 135, 227
  * Begelman et al. (1980) Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287, 307
  * Benke et al. (2018) Benke, P., Frey, S., Gabányi, K., et al. 2018, 14th European VLBI Network Symposium & Users Meeting (EVN 2018), 98
  * Blundell et al. (1999) Blundell, K. M., Rawlings, S., & Willott, C. J. 1999, AJ, 117, 677
  * Brisken et al. (2002) Brisken, W. F., Benson, J. M., Goss, W. M., et al. 2002, ApJ, 571, 906
  * Caproni & Abraham (2004) Caproni A. & Abraham Z., 2004, MNRAS, 349, 1218
  * Charlot et al. (2020) Charlot, P., Jacobs, C. S., Gordon, D., et al. 2020, A&A, 644, A159
  * Condon et al. (1991) Condon, J. J., Huang, Z.-P., Yin, Q. F., et al. 1991, ApJ, 378, 65
  * Foord et al. (2017) Foord, A., Gültekin, K., Reynolds, M., et al. 2017, ApJ, 851, 106
  * Fuentes et al. (2023) Fuentes, A., Gómez, J., Martí, J., et al. 2023, in prep.
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, in press
  * Gierliński et al. (2008) Gierliński, M., Middleton, M., Ward, M., et al. 2008, Nature, 455, 369
  * Giovannini et al. (2001) Giovannini, G., Cotton, W. D., Feretti, L., et al. 2001, ApJ, 552, 508
  * Greisen (2003) Greisen, E. W. 2003, Information Handling in Astronomy - Historical Vistas, 285, 109
  * Gurvits et al. (1997) Gurvits, L. I., Schilizzi, R. T., Miley, G. K., et al. 1997, A&A, 318, 11
  * Homan et al. (2021) Homan, D. C., Cohen, M. H., Hovatta, T., et al. 2021, ApJ, 923, 67
  * Honma et al. (2008) Honma, M., Tamura, Y., & Reid, M. J. 2008, PASJ, 60, 951
  * Högbom (1974) Högbom, J. A. 1974, A&AS, 15, 417
  * Jiang et al. (2022) Jiang, N., Yang, H., Wang, T., et al. 2022, arXiv:2201.11633
  * Komossa et al. (2003) Komossa, S., Burwitz, V., Hasinger, G., et al. 2003, ApJ, 582, L15
  * Kovalev et al. (2005) Kovalev, Y. Y., Kellermann, K. I., Lister, M. L., et al. 2005, AJ, 130, 2473
  * Kovalev et al. (2017) Kovalev, Y. Y., Petrov, L., & Plavin, A. V. 2017, A&A, 598, L1
  * Kun et al. (2014) Kun E., Gabányi, K. É ., Karouzos, M. et al. 2014, MNRAS, 445, 1370
  * Lense & Thirring (1918) Lense, J. & Thirring, H., 1918, Phys. Z., 19, 156
  * Liska et al. (2018) Liska, M., Hesp, C., Tchekhovskoy, A. et al. 2018, MNRAS, 474, 81
  * Lehto & Valtonen (1996) Lehto, H. J. & Valtonen, M. J. 1996, ApJ, 460, 207
  * Liu et al. (2015) Liu, T., Gezari, S., Heinis, S., et al. 2015, ApJ, 803, L16
  * Liu et al. (2016) Liu, T., Gezari, S., Burgett, W., et al. 2016, ApJ, 833, 6
  * Lister et al. (2009) Lister, M. L., Cohen, M. H., Homan, D. C., et al. 2009, AJ, 138, 1874
  * Longair & Riley (1979) Longair, M. S. & Riley, J. M. 1979, MNRAS, 188, 625
  * Lovell et al. (2000) Lovell, J. E. J., Tingay, S. J., Piner, B. G., et al. 2000, Astrophysical Phenomena Revealed by Space VLBI, 215
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., et al. 2007, Astronomical Data Analysis Software and Systems XVI, 376, 127
  * Miniutti et al. (2019) Miniutti, G., Saxton, R. D., Giustini, M., et al. 2019, Nature, 573, 381
  * Mooley et al. (2018) Mooley, K. P., Wrobel, J. M., Anderson, M. M., et al. 2018, MNRAS, 473, 1388
  * Perucho et al. (2006) Perucho, M., Lobanov, A. P., Martí, J. M., et al. 2006, A&A, 456, 493
  * Petrov et al. (2019) Petrov, L., de Witt, A., Sadler, E. M., et al. 2019, MNRAS, 485, 88
  * Petrov (2023) Petrov, L. 2023, AJ, 165, 183
  * Pradel et al. (2006) Pradel, N., Charlot, P., & Lestrade, J.-F. 2006, A&A, 452, 1099
  * Pringle (1997) Pringle, J. E. 1997, MNRAS, 292, 136.
  * Rodriguez et al. (2006) Rodriguez, C., Taylor, G. B., Zavala, R. T., et al. 2006, ApJ, 646, 49
  * Schoenmakers et al. (2000) Schoenmakers, A. P., de Bruyn, A. G., Röttgering, H. J. A., et al. 2000, MNRAS, 315, 371
  * Schwartz et al. (2000) Schwartz, D. A., Marshall, H. L., Lovell, J. E. J., et al. 2000, ApJ, 540, 69
  * Shang et al. (2011) Shang, Z., Brotherton, M. S., Wills, B. J., et al. 2011, ApJS, 196, 2
  * Shepherd (1997) Shepherd, M. C. 1997, Astronomical Data Analysis Software and Systems VI, 125, 77
  * The CASA Team (2022) The CASA Team, Bean, B., Bhatnagar, S., et al. 2022, PASP, 134, 114501
  * Vaughan et al. (2016) Vaughan, S., Uttley, P., Markowitz, A. G., et al. 2016, MNRAS, 461, 3145
  * Walker et al. (1994) Walker, R. C., Romney, J. D., & Benson, J. M. 1994, ApJ, 430, L45
  * Wright (2006) Wright, E. L. 2006, PASP, 118, 1711