# Detection of a Parsec-Scale Jet in a Radio-Quiet Narrow-Line Seyfert 1
Galaxy with Highly Accreting Supermassive Black Hole

Su Yao,1 Xiaolong Yang,2,3 Minfeng Gu,4 Tao An,2 Jun Yang,5 Luis C. Ho,3,6
Xiang Liu,7 Ran Wang,3 Xue-Bing Wu,3,6 Weimin Yuan8
1Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn,
Germany
2Key Laboratory of Radio Astronomy, Shanghai Astronomical Observatory, Chinese
Academy of Sciences, Shanghai 200030, China
3Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing
100871, China
4Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, Shanghai 200030, China
5Department of Space, Earth and Environment, Chalmers University of
Technology, Onsala Space Observatory, SE-439 92 Onsala, Sweden
6Department of Astronomy, School of Physics, Peking University, Beijing
100871, China
7Key Laboratory of Radio Astronomy, Xinjiang Astronomical Observatory, Chinese
Academy of Sciences, 150 Science 1-Street, Urumqi 830011, China
8Key Laboratory of Space Astronomy and Technology, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received 2021; in original form)

###### Abstract

The jet in active galactic nuclei (AGN) is a key ingredient in understanding
the co-evolution of galaxies and their central supermassive black holes
(SMBHs). Unfortunately, the mechanism of jet launching and collimation is
still elusive. The observational evidence of decreasing radio loudness with
increasing Eddington ratio implies that the jet should be coupled with the
accretion process. To further explore the relationship between the jet and
accretion, it is necessary to extend our knowledge of the jet to an extreme
end of the Eddington ratio distribution of AGN. Using Very Long Baseline Array
(VLBA), we report the detection of the parsec-scale radio structure in Mrk
335, a radio-quiet narrow-line Seyfert 1 galaxy with an Eddington ratio close
to/above unity. The VLBA image at 1.5 GHz reveals an elongated structure
extending $\sim 20$ parsec in north-south direction with a peak flux density
of $1.98\pm 0.05$ mJy/beam and radio brightness temperatures as high as
$6\times 10^{7}$ K. This feature provides a strong evidence of a parsec-scale
(bipolar) jet launched from a highly accreting SMBH. We discuss the result by
comparing Mrk 335 with other highly accreting systems, e.g. Galactic black
holes and tidal disruption events, and recall the discovery of collimated
corona in the vicinity of SMBH in Mrk 335 by previous X-ray observations,
whose relation to the parsec-scale radio jet should be explored by future
simultaneous X-ray spectroscopy and high resolution radio observations.

###### keywords:

galaxies: active – galaxies: nuclei – galaxies: jets – galaxies: Seyfert –
galaxies: individual: Mrk 335

††pubyear: 2021††pagerange: Detection of a Parsec-Scale Jet in a Radio-Quiet
Narrow-Line Seyfert 1 Galaxy with Highly Accreting Supermassive Black
Hole–Detection of a Parsec-Scale Jet in a Radio-Quiet Narrow-Line Seyfert 1
Galaxy with Highly Accreting Supermassive Black Hole

##  1 Introduction

The collimated outflowing plasma, also termed as ‘jet’, launched from active
galactic nuclei (AGN) is suggested to be one of the important forms of AGN
feedback which regulates the coevolution of supermassive black hole (SMBH) and
their host galaxy (Fabian, 2012; Kormendy & Ho, 2013). The AGN jets typically
peak their radiation in the radio band by synchrotron processes and could be
luminous radio sources. However, only 15–20 per cent of the AGN are radio-loud
(Urry & Padovani, 1995; Ivezić et al., 2002), indicating that not all of the
AGN launch jets. This raises the questions of why we only observe jets in a
small fraction of AGN and how the jets are formed.

The observational evidence of a strong anti-correlation between the radio
loudness parameter $\mathcal{R}$111The radio loudness parameter $\mathcal{R}$
is defined as the ratio of radio-to-optical flux density, conventionally at 5
GHz and $B$-band (4400Å), respectively, with $\mathcal{R}\approx 10$ as the
dividing of radio-quiet and radio-loud AGN (e.g. Kellermann et al., 1989).
and the bolometric luminosity expressed in Eddington units, i.e. Eddington
ratios $\lambda_{\rm Edd}$, implies coupling of the jet and accretion process
(Ho, 2002, 2008; Greene et al., 2006; Sikora et al., 2007; Yang et al., 2020);
the launch of jet may be dependent on the Eddington ratio and underlying
physics such as the mass accretion rate, the state of accretion disk and the
growth of SMBH. But the detailed mechanism remains elusive. Given the anti-
correlation of the radio loudness and the Eddington ratio, questions arise as
to whether the collimation of outflows is suppressed as the Eddington ratio
increases, and whether there is a limiting Eddington ratio above which the
collimation is quenched. On the other hand, while the origin of radio core
emission is clear in the radio-loud AGN as dominated by the non-thermal
radiation from jets, the case of the radio-quiet AGN is more complex. With
milli-arcsecond (mas) resolution radio images achieved by very-long-baseline
interferometry (VLBI), it was found that some of the radio-quiet AGN reveal
compact parsec-scale nuclear radio emission with brightness temperatures of
$T_{\rm B}\gtrsim 10^{7}\rm\,K$ and occasionally accompanied by collimated
features which provide the evidence of small, weak jets (e.g. Mundell et al.,
2003; Middelberg et al., 2004; Giroletti & Panessa, 2009; Panessa & Giroletti,
2013; Doi et al., 2013; Wang et al., 2021), while others only show radio
emission from the presumably star forming region, disk wind or hot corona
(e.g. Gallimore et al., 2004; Bontempi et al., 2012, see also Panessa et al.
2019 for a review). Questions arise as to why the collimated outflows do form
in some radio-quiet AGN but not in others, and whether they are intrinsically
different from their powerful analogs in blazars and radio galaxies.

Keeping in mind the above questions, we have proposed imaging observations on
the central parsec-scale nuclear region of a sample of nearby radio-quiet
narrow-line Seyfert 1 (NLS1) galaxies with accretion rates approaching to or
exceeding the Eddington limit (Yang et al., 2020) using the Very Long Baseline
Array (VLBA) of the National Radio Astronomy Observatory (NRAO). The NLS1
galaxies are believed to rapidly growing their central SMBHs that are in a
relatively low mass range of $\sim 10^{6}-10^{8}\rm\,M_{\odot}$ (Zhou et al.,
2006). They are often being radio-quiet and have a lower radio-loud fraction
compared to the normal Seyfert galaxies and quasars (Yuan et al., 2008). While
the parsec-scale jets have been detected in the radio-loud NLS1 galaxies (e.g.
Doi et al., 2011; Gu et al., 2015), the case is still elusive for the radio-
quiet ones, especially when it approaches the highest Eddington ratio regime.
In recent years, the work dedicated to study parsec-scale region of the radio-
quiet NLS1 galaxies has found jet features in several of them (Doi et al.,
2013), but only Mrk 1239 has a reliably measured Eddington ratio close
to/higher than one222Another one is Ark 564, the VLBI image of which shows an
elongated structure as reported by Lal et al. (2004). However, it is noted in
their paper that the ($u$, $v$) coverage obtained was relatively poor, and
they do not feel confident that the elongated feature is an accurate
representation of the VLBI-scale structure of the source. (Doi et al., 2015;
Pan et al., 2021). So further studies on the parsec-scale nuclear region in
radio-quiet NLS1 galaxies with highest Eddington ratios should provide general
clues of the interplay between the jet and accretion disk. Our observations
will not only search the signature of jet in these radio-quiet highly
accreting systems, but also extend our knowledge of the parsec-scale radio
properties of AGN to a rarely explored parameter space.

In this paper, we present the result of our VLBA observation on Mrk 335
($z=0.025785$; Huchra et al., 1999) as one of the outcomes in the course of
our ongoing project (Yang et al. in preparation). Mrk 335 is a well-known NLS1
galaxy with a SMBH weighing $\sim 10^{7}\rm\,M_{\odot}$ (Peterson et al.,
2004; Grier et al., 2012; Du et al., 2014) hosted in a disk galaxy (Kim et
al., 2017). It has been extensively observed in optical (e.g. Peterson et al.,
2004; Grier et al., 2012; Du et al., 2014) and X-rays (e.g. Grupe et al.,
2008; Gallo et al., 2018; Gallo et al., 2019; Tripathi et al., 2020; Komossa
et al., 2020). Based on its optical luminosity and hard X-ray spectrum, Mrk
335 was suggested to host a candidate of super-Eddington accreting massive
black hole (Wang et al., 2013; Wang et al., 2014). But the knowledge of its
radio emission is rather limited. Mrk 335 has been observed by the VLA with
various angular resolution (see Table 1 and the literatures therein). All
these observations reveal a compact unresolved weak source. Based on the
nuclear optical flux derived from the decomposition of HST $V$-band (F550M)
image (Du et al., 2014) and an assumed optical spectral index of $\alpha=-0.5$
($S_{\nu}\propto\nu^{\alpha}$), the radio loudness of Mrk 335 is estimated to
be $\mathcal{R}\approx 0.8$, falling into the radio-quiet category.
Interestingly, a collimated outflow near the accretion disk has been
discovered in Mrk 335 from the X-ray spectral analysis by Gallo et al. (2019).
Here we report the detection of a parsec-scale jet feature in Mrk 335 using
VLBA. Throughout this work a cosmology is assumed with $H_{0}=70$ km s-1
Mpc-1, $\Omega_{\Lambda}=0.73$ and $\Omega_{\rm M}=0.27$; 1 mas corresponds to
a scale of 0.512 parsec at the distance of Mrk 335.

Table 1: Previous VLA observations on Mrk 335.

Frequency | Flux density | Date | Resolution | Reference
---|---|---|---|---
[GHz] | [mJy] |  |  |
(1) | (2) | (3) | (4) | (5)
1.4 |  4.1$\pm$0.9 | 1983.07 |  1$\aas@@fstack{\prime}$5 | E87
|  6.19$\pm$0.29 | 1992.12 |  2$\arcsec$ | N99,Y20
|  7.3$\pm$0.4 | 1993.11 |  45$\arcsec$ | C98
5 | 3.9 | 1982.11-1983.05 |  18$\arcsec$ | K89,M93
|  3.3$\pm$0.2 | 1983.07 |  15$\arcsec$ | E87
|  3.58$\pm$0.05 |  2003.06∗ |  0$\aas@@fstack{\prime\prime}$3 | L06
|  3.21$\pm$0.02 | 2015.07 |  0$\aas@@fstack{\prime\prime}$4 | B18,Y20
8.4 | 2.05 | 1991.06 |  0$\aas@@fstack{\prime\prime}$3 | K95
| 2.23 | 1992.04 |  2$\aas@@fstack{\prime\prime}$5 | K95
|  2.14$\pm$0.06 | 1992.12 |  0$\aas@@fstack{\prime\prime}$3 | N99,Y20
|  2.3‡ | 1997.01-1999.04 |  1$\arcsec$–3$\arcsec$ | B05

Note. E87: Edelson (1987); N99: Nagar et al. (1999); C98: Condon et al.
(1998); K89: Kellermann et al. (1989); M93: Miller et al. (1993); L06: Leipski
et al. (2006); B18: Berton et al. (2018); Y20: Yang et al. (2020); K95: Kukula
et al. (1995); B05: Barvainis et al. (2005).

∗ This observation date is obtained from the VLA data archive.

‡ This measurement is the mean flux density obtained from a number of
observations (see B05).

##  2 Observations and Data Reduction

###  2.1 VLBA Observation and Data Reduction

We observed Mrk 335 on September 15, 2018 using 10 antennas of the VLBA
(project code: BY145, P.I. Yao). The observation was made in the L-band with a
central frequency of 1.548 GHz ($\lambda\sim 19.4\rm\,cm$), and a total
bandwidth of 256 MHz. The observation was performed in the phase-referencing
mode: the target field was observed for 1.53 hours in 4-minute scans,
interleaved with 1-minute scans of the phase referencing calibrator
J0004$+$2019 (RA: 00h04m35${}^{\mathrm{s}}.758287$, Dec:
$+$20∘19′42$\aas@@fstack{\prime\prime}$31786, J2000), with the phase
calibrator located at 0.42 deg away from the target. We also inserted a scan
of the bright radio source 3C 454.3 for fringe and bandpass calibration. The
data were recorded at 2 Gbps in dual circular polarization. The raw data was
correlated with the software correlator DiFX (Deller et al., 2007; Deller et
al., 2011).

The visibility data was calibrated using the NRAO Astronomical Image
Processing System (aips, Greisen, 2003) following the standard procedure. A
prior amplitude calibration was performed with the system temperatures and the
antenna gain curves. The earth orientation parameters were obtained and
corrected by using the measurement from the U.S. Naval Observatory data base
and the ionospheric dispersive delays were corrected according to a map of
total electron content provided by the GPS satellite observations. The opacity
and parallactic angle corrections were also applied according to the attached
information in data. Phase delay from the instrument was removed by fringe-
fitting over the scan of 3C 454.3. The bandpass solutions were also determined
from the fringe finder calibrator 3C 454.3. Finally, we performed a global
fringe-fitting on the phase-referencing calibrator J0004$+$2019\. The
calibrated data of the phase-referencing source J0004$+$2019 was averaged in
aips and then exported into difmap software package (Shepherd, 1997) for
imaging and self-calibration. J0004$+$2019 shows a bright and compact
structure in our observation, consistent with the model assumed in fringe-
fitting in aips.

The deconvolution of the visibility data was performed in difmap. The source
is relatively weak, with a peak flux density of only $1.98\pm
0.05\,\mathrm{mJy/peak}$ and a signal-to-noise ratio of $\sim 47$. Therefore,
we did not perform the self-calibration procedure.

We also check the historical VLBA observations of Mrk 335 in projects BB0056
and BG0093 from the NRAO archive. The observation in project BB0056 is
performed in the X-band on June 9, 1996 with a total bandwidth of 32 MHz and a
total on-source time of 48 minutes, while the observation in project BG0093 is
performed in the S/X-band333We note that the observing band of BG0093 in the
NRAO archive is wrongly marked as L-band. on July 9, 1999 with a total
bandwidth of 192 MHz and also a total on-source time of 48 minutes. We have
processed all these data following similar procedures as described above.
Unfortunately, Mrk 335 is not detected in the X-band observation during BB0056
and BG0093. This is consistent with the result reported by Blundell & Beasley
(1998), which also analyzed BB0056 data and gave an upper limit of the flux
density $<0.8$ mJy at 8.4 GHz. In the S-band (2.3 GHz), Mrk 335 is only
marginally detected with a very low signal-to-noise ratio of 6.17 and a peak
flux density of $0.82\pm 0.24$ mJy/beam.

###  2.2 Archival VLA Data

To compare the radio morphology of Mrk 335 on different scales, we also
retrieve two sets of archival data observed on 1992 December 31 using the VLA
A-array configuration in the L-band and X-band (AM0384). The L-band data were
taken at a central frequency of 1.4 GHz and the X-band data were taken at a
central frequency of 8.4 GHz. Both observations have a total bandwidth of 100
MHz. The data are manually calibrated using the Common Astronomy Software
Application (casa v5.1.1; McMullin et al., 2007) following the standard
procedures described in casa Cookbook. The final images are made using the
difmap software package. The detailed description of the data reduction and
analysis can be found in Yang et al. (2020).

##  3 Results

Figure 1:  (a) The VLA 1.4 GHz image of Mrk 335. (b) The VLA 8.4 GHz image of
Mrk 335. (c) The VLBA 1.5 GHz image of Mrk 335. The green contours in the VLBA
image are plotted as 3$\sigma\times(-1,1,2,4,8,16)$, where $\sigma=0.03$
mJy/beam is the rms noise. The peak flux density is $1.98\pm 0.05$ mJy/beam.
The elongated jet structure is fitted using the two-dimensional Gaussian
models. The red circles mark the locations and sizes of the best-fit Gaussian
components. The optical position of Mrk 335 obtained by Gaia is represented by
the black cross. The synthesized beam size is illustrated as an ellipse at the
lower left corner of each image.

###  3.1 Source Structures

The naturally weighted images of Mrk 335 observed by the VLA A-array
configurature at 1.4 GHz and 8.4 GHz, and by the VLBA at 1.5 GHz are shown in
Figure 1a, 1b and 1c, respectively. As can be seen, while Mrk 335 is compact,
unresolved in the VLA images, it reveals an elongated structure extending
along the south-north direction in the VLBA image. The structure is resolved
at $\sim 40$ mas, corresponding to a projected physical scale of $\sim 20$
parsec at the redshift of Mrk 335. We also show the naturally weighted image
of the archival S-band (2.3 GHz) data in Figure 2. Due to the short exposure
time and narrow bandwidth, the 2.3 GHz image has a low signal-to-noise ratio
and only recovers the brightest component (southern structure) as seen in the
1.5 GHz image. Thus, we only consider the structure revealed by the new VLBA
data at 1.5 GHz in the following analysis.

Figure 2:  The archival VLBA S-band (2.3 GHz) image of Mrk 335 (project ID:
BG0093). The image was produced by using a natural weight. The contours are
plotted as $3\sigma\times(-1,~{}1,~{}1.41,~{}2,~{}2.82)$, where $\sigma=0.13$
mJy/beam is the rms noise. The blue cross marks the location of the Gaia
detection of Mrk 335. The beam is centred on Gaia position to show a VLBI
positional uncertainty, with its size of $8.31\times 3.47$ mas and a position
angle of $-2.81^{\circ}$.

In order to further explore the structure seen in 1.5 GHz VLBA image, we
perform a two dimensional Gaussian model fitting to the visibility data using
the modelfit procedure in the difmap package. The best-fit five components are
listed in Table 2. The uncertainty of the flux density of each component is
estimated by combining the fitting error with the initial calibrating error
(Hovatta et al., 2012). The entire structure of Mrk 335 has a total flux
density of $6.46\pm 0.06$ mJy. The positions and sizes of the best-fit five
components are displayed in Figure 1 as red circles, which likely reveals an
S-shaped distribution.

Table 2: Model-fitting results of 1.5 GHz image obtained by our VLBA
observation on Mrk 335.

Comp. | Flux Density | Size | $\Delta\alpha$ | $\Delta\delta$ | $\sigma_{\Delta}$ | $T_{\mathrm{B}}$ |
---|---|---|---|---|---|---|---
| [mJy] | [mas] | [mas] | [mas] | [mas] | [K] |
(1) | (2) | (3) | (4) | (5) | (6) | (7) |
N2 | $0.97\pm 0.01$ | $24.18$ | $0.14$ | $31.55$ | $0.38$ | $1.3\times 10^{6}$ |
N1 | $1.06\pm 0.01$ | $11.10$ | $5.51$ | $12.31$ | $0.16$ | $6.6\times 10^{6}$ |
S1 | $1.77\pm 0.02$ | $6.35$ | $-2.93$ | $-3.40$ | $0.05$ | $3.3\times 10^{7}$ |
S2 | $1.64\pm 0.02$ | $4.50$ | $-9.04$ | $-11.29$ | $0.04$ | $6.2\times 10^{7}$ |
S3 | $1.03\pm 0.01$ | $16.59$ | $-8.32$ | $-22.64$ | $0.25$ | $2.8\times 10^{6}$ |

Note. Column 1: labels of the components from north to south in Figure 1c;
Column 2: 1.5 GHz flux density and its uncertainty of the component; Column 3:
full-width-half-maximum of the 2 dimensional Gaussian model fitted to the
component; Column 4 and 5: the offset between the position of the radio
component and the Gaia optical position in right ascension and declination,
respectively; Column 6: uncertainty of the offset; Column 5: the radio
brightness temperature calculated using Eq. 1.

The Gaia mission (Gaia Collaboration et al., 2016) has reported an optical
position of Mrk 335 as RA=00h06m19s.537304$\pm$0s.00001,
Dec=$+$20∘12′10$\aas@@fstack{\prime\prime}$61670$\pm$0$\aas@@fstack{\prime\prime}$0002
(black cross in Figure 1c). As can be seen in the figure, even considering the
positional uncertainties of Gaia and the radio components, there is still a
significant offset between the optical position and the centre of nearest
radio component. With Gaia position as reference, the north and south radio
components are respectively labelled as N2, N1 and S1, S2, S3. The symmetric
distribution indicates a bipolar structure, with ‘S’ (bright) components being
the approaching jet boosting radio emission and ‘N’ (faint) components being
the receding jet fading away.

###  3.2 Radio Brightness Temperature

We calculate the radio brightness temperature for each model component from

$T_{\rm B}=1.8\times 10^{9}(1+z)\frac{S_{\nu}}{\nu^{2}\phi^{2}}$ (1)

in Kelvin (K, Ulvestad et al., 2005) in the rest frame of Mrk 335, where $z$
is the redshift, $S_{\nu}$ is the integrated flux density in mJy at the
observing frequency $\nu$ in GHz, and $\phi$ is the fitted FWHM of the
Gaussian components in units of mas. All the Gaussian components have the
radio brightness temperature $T_{\rm B}>10^{6}$ K and the component “S2” has
the highest brightness temperature of $T_{\rm B}\approx 6.2\times 10^{7}$ K
(Table 2).

##  4 Discussion

At parsec scales, we have resolved Mrk 335 at 1.5 GHz into an elongated
structure. The two dimensional Gaussian model fitting to the visibility data
has revealed five components distributed along the elongated structure, among
which “S1” and “S2” components have $T_{\rm B}>10^{7}$ K, indicating the non-
thermal emission from jet. This provides a strong evidence for a parsec-scale
jet launched by the SMBH in Mrk 335. As mentioned in Section 1, although the
detailed physical mechanism for launching a jet is still elusive, it is
generally suggested that the jet is coupled with the accretion process. Any
detection of jet features in an object with accretion rate close to or above
the Eddington limit would be of high value for the investigation of jet-
accretion disk coupling. In the following we discuss the Eddington ratio of
Mrk 335, the origin of its radio emission, and the implication for its jet
formation based on our detection.

###  4.1 Eddington ratio of Mrk 335

Based on the reverberation mapping technique, the estimations of the black
hole mass of Mrk 335 ranges from $8.3\times 10^{6}\rm\,M_{\odot}$ to
$2.6\times 10^{7}\rm\,M_{\odot}$ (Peterson et al., 2004; Grier et al., 2012;
Du et al., 2014), much lower than those in the classical blazars and radio
galaxies (e.g. Falomo et al., 2002; Barth et al., 2003). Besides the black
hole mass, the determination of Eddington ratio requires an estimate of the
bolometric luminosity $L_{\rm bol}$ which is the integration of thermal
emission released by the accretion process. A direct way to estimate $L_{\rm
bol}$ is to integrate the luminosity over a set of broad bands dominated by
the emission from accretion disk. Elvis et al. (1994) have constructed a
spectral energy distribution (SED) from radio to X-rays of Mrk 335 and
calculated the integral luminosity as $\sim 3\times 10^{45}$ $\rm erg\,s^{-1}$
by simply interpolating through the observed data, which would yield an
Eddington ratio of $\lambda_{\rm Edd}\approx 0.9$–$3$ considering the black
hole mass range from the reverberation mapping. Vasudevan & Fabian (2009) have
built two sets of simultaneous SEDs from optical to X-rays of Mrk 335, one of
which was in its historical low X-ray flux state (Grupe et al., 2008). They
calculated the integral bolometric luminosities based on the accretion disk
(optical/UV) and the power-law (X-ray) model fitted to the data. The
bolometric luminosities are $2\times 10^{45}$ $\rm erg\,s^{-1}$ and $1\times
10^{45}$ $\rm erg\,s^{-1}$, respectively, at those two epochs, which would
yield an Eddington ratio of $\lambda_{\rm Edd}\approx 0.3$–$1.9$.

There are several main factors contributing to the uncertainty of $L_{\rm
bol}$. One is the lack of extreme ultraviolet (EUV) data, where the emission
from Mrk 335’s accretion disk is supposed to peak. While the simple
interpolation of the EUV gap between optical and X-rays may lead to an
underestimation of $L_{\rm bol}$, the physically reasonable estimate of EUV
peak is model-dependent. Another one which could lead to the underestimation
of $L_{\rm bol}$ is the internal extinction of the optical/ultraviolet
emission. On the other hand, the contamination from the host galaxy can lead
to an overestimation, mainly at longer wavelength, of $L_{\rm bol}$. In
optical, the host galaxy contribution to the emission at 5100 Å was estimated
as $\lesssim 20\%$ from a decomposition of Mrk 335 HST image (Bentz et al.,
2009; Du et al., 2014). Finally, the variability can also lead to the
uncertainties in $L_{\rm bol}$. The flux of Mrk 335 varied by only a few per
cent in the optical and by $\sim 20\%$ in the UV (Du et al., 2014; Gallo et
al., 2018). Meanwhile it has exhibited much higher variability in X-rays by a
factor of $\sim 50$ (e.g. Gallo et al., 2018; Tripathi et al., 2020). However,
since the coronal optical emission lines, which are supposed to be driven by
EUV and soft X-rays, do not vary much in Mrk 335 (Grupe et al., 2008), it was
suggested that such huge X-ray variability is due to the variable column
density and covering factor of the X-ray absorbers near the SMBH (Komossa et
al., 2020). Therefore, even considering the above uncertainties of $L_{\rm
bol}$, the Eddington ratio of Mrk 335 is still high.

At last, we should note that, according to the current understanding of the
accretion physics, the ‘slim disk’ is used to describe the accretion process
around SMBH when Eddington ratio approaches unity (Abramowicz et al., 1988;
Mineshige et al., 2000). The optical depth of such slim disk is so large that
the majority of photons will be trapped in the disk until advected into the
black hole rather than being radiated out, significantly reducing the
radiation efficiency. It means that the actual mass accretion rate will be
even higher than predicted from the luminosity assuming typical radiation
efficiencies in a standard optically thick, geometrically thin disk (Wang et
al., 2014). Thus, the SMBH in Mrk 335 should reliably be a highly accreting
black hole.

###  4.2 Origin of Radio Emission

Mrk 335’s radio emission is relatively weak. At 1.4 GHz, de Bruyn & Wilson
(1976) have observed Mrk 335 with the Westerbork telescope but were only able
to set a 3$\sigma$ upper limit of $f_{1.4}<8$ mJy. Bicay et al. (1995) have
observed Mrk 335 with the Arecibo telescope and reported an upper limit of
$f_{1.4}<5$ mJy. The observation at 2.3 GHz performed by the Parkes-
Tidbinbilla Interferometer with a sub-arcsec resolution gives a flux density
of $f_{2.3}=5$ mJy (Roy et al., 1994). The observation at 20 GHz with the
Owens Valley Radio Observatory reveals an upper limit of $f_{20}<1.7$ mJy
(Edelson, 1987).

During the past decades, Mrk 335 has also been observed by the VLA with
various angular resolutions (Table 1). The angular resolution of these
observations vary from 0$\aas@@fstack{\prime\prime}$3 to
1$\aas@@fstack{\prime}$5, corresponding to a linear size from 150 parsec to 46
kpc. Only a compact unresolved source was found in Mrk 335 in all of these
observations, and no extended emission has been detected. At 1.4 GHz and 5
GHz, Mrk 335 shows slight variability. At 8.4 GHz, Barvainis et al. (2005)
have carried out several epochs of the VLA observations between 1997 January
and 1999 April, but didn’t find significant variability. Thus, the radio
emission of Mrk 335 is compact and rather stable, with slight variability at
lower frequencies. We estimate the radio spectral index between 1.4 GHz and
8.4 GHz using the simultaneous flux measurements on February 1992 (Table 1)
and obtain $\alpha_{\rm r}\approx-0.6$. The spectral index between 5 GHz and
8.4 GHz is estimate as $\alpha_{\rm r}\approx-0.8$ to $-1.0$ using the flux
measured at the angular size of $0\aas@@fstack{\prime\prime}3$ (Table 1). If
we consider the peak flux densities measured by the VLBA observations in the
L-band (1.5 GHz) and S-band (2.3 GHz) (Section 2.1), an even steeper spectral
index of $\alpha_{\rm r}\sim-2$ is obtained, although the uncertainty of this
index would be large due to the possible flux variability at different epochs
and the low signal-to-noise ratio of the S-band image. While the GHz emission
from the star-forming regions is usually characterized by steep spectra Condon
(1992), the steep spectral radio emission was also observed from nuclear
outflows and jets (e.g. Gallimore et al., 2004; Bontempi et al., 2012). We
address the contributions to the observed radio emission in Mrk 335 from star-
forming activity, outflows and jets as follows.

####  4.2.1 Star-forming activity

It was suggested that the NLS1 galaxies typically have stronger star-forming
activities compared to the normal Seyfert galaxies (e.g. Deo et al., 2006;
Sani et al., 2010). In this case, the star formation process in their dusty
spirals or circumnuclear regions can have significant contributions to the
radio emission. By analysing the mid-infrared (mid-IR) colors and the ratio of
the radio to mid-IR flux for a sample of radio-loud NLS1 galaxies, Caccianiga
et al. (2015) found that the star-forming activities can contribute a
significant fraction of radio emission even in some radio-loud NLS1 galaxies.
But this is not likely the case in Mrk 335. The overall radio morphology of
the star-forming regions are typically extended, diffuse and clumpy (e.g.
Hummel et al., 1987; Olsson et al., 2010), while the radio images of Mrk 335
only reveal a compact source at various resolutions (e.g. Figure 1a and 1b).
The flux densities measured at scales from tens of kpc to a few tens of parsec
are quite consistent, indicating that the star-forming activity makes very
little contribution to the total radio emission. This is supported by the fact
that Mrk 335 has a very low star formation rate (SFR) among NLS1 galaxies. Xie
et al. (2021) have estimated a SFR of $\sim 1\,M_{\odot}\rm\,yr^{-1}$ based on
the infrared SED and spectroscopy, which would yield a radio flux density $<1$
mJy at 1.5 GHz following the empirical relation derived by Condon (1992).

####  4.2.2 Wind-driven outflows

The accretion disk winds can drive wide-angle outflows, which are suggested to
be prevalent in luminous AGN and are likely stronger in objects with higher
Eddington ratios (e.g. Laor & Brandt, 2002; Ganguly et al., 2007; Zhang et
al., 2014). In the nuclear region, these outflows have been typically observed
as the blueshifted absorption lines in the UV/X-ray spectroscopy (e.g.
Longinotti et al., 2019). On the galactic scales, they have been detected as
the blue-wing components in the narrow emission line profiles (e.g. Komossa et
al., 2008) or the molecular line profiles (e.g. Feruglio et al., 2015). The
wind-driven outflows may also produce radio emission via bremsstrahlung free-
free process from ionized plasma (Blundell & Kuncic, 2007) or synchrotron
process of the relativistic electrons accelerated by the wind shocks (Zakamska
& Greene, 2014), with the later being used to explain the correlation between
radio emission and the [O iii] line velocity width in the radio quiet AGN
(e.g. Zakamska & Greene, 2014; Hwang et al., 2018). In the case of Mrk 335,
evidence for outflows with velocity of a few thousand $\rm km\,s^{-1}$ is
observed as blueshifted absorption lines in its X-ray and UV spectra (e.g.
Longinotti et al., 2013, 2019). But, again, we note that the radio images of
Mrk 335 do not reveal any extended diffused radio emission on scales from kpc
all the way down to a few tens of parsec. Thus, if the wind-driven
uncollimated outflows have made any detectable contribution to the radio
emission, it would likely originate from the central parsec-scale region.

####  4.2.3 Parsec-scale bipolar jet structure

On parsec scales, the VLBA image at 1.5 GHz shows a linear elongation in the
north-south direction. The two dimensional model fitting to the visibility
data has revealed components in the elongated structure with the brightness
temperature of $T_{\rm B}>10^{7}$ K (Table 2), indicating a non-thermal,
synchrotron origin. It strongly suggests that the radio emission detected on
parsec scale is from the jet (Panessa et al., 2019). The offset between Gaia
optical position and the nearest radio peak position is $\Delta\approx 5$ mas,
corresponding to a projected linear offset of 2.5 parsec. Taking the
uncertainties in both R.A. and Dec. from the Gaia measurement ($<0.1$ mas) and
the VLBA measurement (Table 2) into account, this offset is still significant.
The nuclear optical emission is usually from the accretion disk of the central
engine. If the position of the central engine is really offset from either of
the radio peaks, and is located between ‘N’ and ‘S’ components, considering
the symmetric jet distribution with regards to the central engine represented
by Gaia (Figure 1), the radio structure is likely to indicate the bipolar
ejection with a moderate angle between its axis and the line of sight. The
larger flux density of the south branch than the north one could be due to the
beaming effect as the south jet is approaching the observers. And if the ‘S’
components and ‘N’ components represent where the jet and counterjet is
located, respectively, we would derive a low jet-to-counterjet ratio of $\sim
2.2$. A low jet-to-counterjet ratio usually results from either that the jet
has a large viewing angle between its axis and the line of sight, e.g. close
to the sky plane, or that the jet has a low velocity. Given that Mrk 335 is a
type 1 AGN, the viewing angle is unlikely to be very large. So the low jet-to-
counterjet ratio may imply a low jet speed in Mrk 335. For instance, assuming
a viewing angle of $45^{\circ}$ and a spectral index of $-0.5$, we obtain a
jet speed of $\beta_{\rm j}=(v_{\rm j}/c)\approx 0.2$ by using the equation in
Bempong-Manful et al. (2020).

The total flux density of the detected components in the VLBA image is
$6.46\pm 0.06$ mJy, which is similar to the measurements on larger scales
taken by the VLA with poorer resolution (Table 1). Especially, the total radio
flux density detected in the VLBA L-band is consistent with the $1.4$ GHz VLA
flux density of $6.19\pm 0.29$ mJy measured with a resolution of $\sim$2
arcsec (Yang et al., 2020) within uncertainty, indicating that the radio
emission within 2 arcsec (corresponding to $\sim 1$ kpc) is dominated by the
central parsec-scale bipolar jet structure and that the contribution from the
star-forming activity and wind-driven outflows is very small even if it can
not be totally ruled out.

We notice that the two dimensional Gaussian models fitted to the VLBA
visibility data at $1.5$ GHz reveal an S-shaped distribution, likely implying
a helical jet or slowly drifting of the position angle of the jet axis. One of
the scenarios adopted to explain the change of the jet axis is the binary
black hole system, in which the secondary black hole causes the precession of
the black hole orbit or the primary accretion disc, resulting in an S-shaped
jet (e.g. Roos et al., 1993; Rubinur et al., 2017). But there is not yet
evidence, e.g. double-peaked emission lines, systematic line shifts, periodic
behaviour or dual bright compact radio cores, for the existence of binary
black hole system in Mrk 335. Another possible mechanism causing the S-shaped
jet would be the warped disk near the jet launching site, arising from non-
axisymmetric radiation (Pringle, 1996) or accretion events, the latter of
which would be interesting given that Mrk 335 is accreting at such high
Eddington ratio and has been detected for several flares in optical and X-rays
during the past decades (Komossa et al., 2020). However, the current data set
is not adequate to confirm the validity of they S-shaped jet structure in Mrk
335. Further observations are required to investigate the outer structures at
both jet sides with medium-resolution and the inner jet structures with high-
resolution, which are crucial to confirm the S-shaped jet structure and its
origin.

###  4.3 Implications on Jet Formation

The jets have been widely observed in different types of accreting sources.
During the past decades, great efforts have been made on theoretical work to
explain the jet formation. So far, several popular models have been proposed
such as the Blandford–Znajek (BZ) process, in which the jet is driven by
extracting the rotational energy of the black hole via a large-scale magnetic
field (Blandford & Znajek, 1977), and Blandford–Payne (BP) process, in which
the jet is driven by extracting the rotational energy of the accretion disk
via the magnetic fields threading the disk (Blandford & Payne, 1982).
Recently, some numerical simulations have been done for the jet formation in
super-Eddington accreting supermassive black holes, in which the jet is driven
by radiation pressure (e.g. Ohsuga & Mineshige, 2011; Tchekhovskoy et al.,
2014; Sądowski & Narayan, 2015). However, although a lot of important progress
has been made, we still do not fully understand the physical mechanism for
launching the jet.

####  4.3.1 Analog to Galactic black holes?

The radio structure observed in Mrk 335 by VLBA provides a good evidence of
jet launched by a highly accreting SMBH in the radio-quiet Seyfert galaxy.
Although the detailed mechanism of jet formation is still unknown, a possible
way to explore the jet formation in Mrk 335, in the framework of current
knowledge, is through the comparison with other highly accreting sources. As
the down-scaled analogues to the accreting SMBHs in AGN, the Galactic black
holes (GBH) of stellar mass in the X-ray binaries also display the phenomenon
of accretion (in X-rays) and jet (in radio). In the GBH, the steady jet is
always associated with low-luminosity hard X-ray spectral state (low/hard
state), while the radio emission is suppressed in the high-luminosity soft
X-ray spectral state (high/soft state). In addition, an intermediate state
(i.e. very high state) is also observed when GBH’s soft X-ray luminosity rises
to a peak and the jet becomes choked and episodic, associated with the radio
outburst (Fender et al., 2004).

Considering the high Eddington ratio, Mrk 335 may be the scaled-up version of
GBHs at the end of their very high state. If this is the case, the radio
observations may capture the evidence of its past ejecting activities during
the state transition. Previous observations have found several NLS1 galaxies
showing kiloparsec-scale radio structures, implying the past ejecting
activities (e.g. Gliozzi et al., 2010; Doi et al., 2012; Richards & Lister,
2015; Yang et al., 2020). However, such evidence has not yet been detected in
Mrk 335 by observations spanning the past decades. Alternatively, Mrk 335 may
have already transitioned to the high/soft state so long ago that the energy
of the ejecta, if it had existed, has already dissipated, therefore
kiloparsec-scale radio emission tracing the past ejecting activities is not
detected. If this is the case, the elongated structure detected by our VLBA
image should be newly ejected after the steady/episodic jet being switched
off, which implies that the collimation of the outflows in Mrk 335 could be
maintained/established on small scales even after the accreting source has
transitioned to the high/soft state.

####  4.3.2 Comparison to tidal disruption event

Another kind of highly accreting source is the tidal disruption event (TDE;
Komossa, 2015), in which a star passing by a SMBH is tidally disrupted and
accreted by the SMBH, leading to a bright flare with an accretion rate near or
exceeding the Eddington limit. Several dozens of TDEs have been discovered
based on their large-amplitude brightening in X-rays, UV and/or optical. But
so far only three TDEs have been reported to launch jets (Bloom et al., 2011;
Burrows et al., 2011; Levan et al., 2011; Zauderer et al., 2011; Cenko et al.,
2012; Alexander et al., 2016; van Velzen et al., 2016). For instance, as the
most representative jetted–TDE, Swift J1644+57, which hosts an inactive
galactic nuclei, has revealed an apparent luminosity $\sim 10^{3}$ times of
the Eddington limit for its black hole mass, and a spectral energy
distribution characterized by synchrotron and inverse Compton processes (Bloom
et al., 2011; Burrows et al., 2011; Levan et al., 2011; Zauderer et al.,
2011), leading inevitably to a scenario of a jet pointing to the observer. A
variable radio synchrotron emission was detected a few days after the rapid
rise in its X-rays (Zauderer et al., 2011), providing evidence for jet
launched by the highly accreting SMBH. Recent numerical simulations of the
super-Eddington compact disk used to explain the TDEs have shown that,
together with a geometrically thick disk and a fast outflow, a relativistic
jet can also be produced under optimal conditions given a spinning black hole
and a large-scale ordered magnetic field (Dai et al., 2018). If the accretion
process in the highly accreting AGN is the same as that in the TDE, this gives
hints to the jet feature in Mrk 335: the jet may be driven by the magnetic
field threading the spinning SMBH and the disk, and is powered by the black
hole spin energy. This is consistent with a high spin parameter measured for
Mrk 335 based on the blurred reflection model fitted to the X-ray spectrum
(Gallo et al., 2015, 2019). The size of the jet in Mrk 335 is very small and
only resolved at parsec scales (Figure 1). Coincidently, the radio structure
in jetted-TDE was also found to be very compact (Yang et al., 2016; Romero-
Cañizales et al., 2016). Considering the low jet speed and the high Eddington
ratio in Mrk 335, the small size of the jet may be due to the jet deceleration
by interaction with surrounding dense medium in the nuclear region.

####  4.3.3 Missing radio core?

In a jet structure, a parsec-scale compact radio core with flat or inverted
spectrum is usually present at the position of jet base in the vicinity of
accreting SMBH. As shown in Figure 1, even taking into account the
uncertainties, the optical position of Mrk 335 measured by Gaia does not
coincide with the position of any radio components. If the optical position
represents the position of the central SMBH and its accretion disk, our
results imply an offset between the radio components and the central engine in
Mrk 335, and we do not explicitly find the radio core near the position of the
central engine.

The symmetric jet structure lacking a detectable core was also reported in
other kind of radio sources such as some compact symmetric objects, in which
the core is so weak due to the jet axis very close to the sky plane (e.g.
Taylor et al., 2000). But this is unlikely the case in Mrk 335 as it is a type
1 AGN. We note that the emission centre in optical and radio may not always
coincide due to that the centroid of the radio component may be shifted with
observing frequency Kovalev et al. (2008); Petrov & Kovalev (2017). So a
possible reason for the ‘missing core’ in our observation may be that the core
is too weak to be detected at 1.5 GHz due to the synchrotron-self-absorption
at lower frequencies (Kovalev et al., 2017), and it is buried in other radio
components and not resolved by our observation. If this is the case, the core
may reveal itself at higher frequencies. Unfortunately, the archival VLBA
observation of Mrk 335 at 8.4 GHz (project ID: BB0056 and BG0093) does not
reveal any detection, and only gives an upper limit of $<0.8\rm\,mJy$
(Blundell & Beasley, 1998). Deeper VLBI observations at higher frequencies,
e.g. 8.4 GHz and 15 GHz, are needed to test if there exists a compact core.

####  4.3.4 Jet-corona connection

A collimated corona has been suggested to launch from the accretion disk based
on the past X-ray spectroscopic observations on Mrk 335 during its X-ray
flares (e.g. Wilkins & Gallo, 2015; Gallo et al., 2019). Generally, the X-ray
emission is produced by the hot electrons in corona above the accretion disk
via inverse Compton scattering of the soft photons from disk. Then a fraction
of X-ray emission illuminates the disk and is reflected, contributing to the
reflection component in the observed X-ray spectrum. During the X-ray flares
of Mrk 335, it was found that the reflection fraction dropped significantly
and the emissivity profile of the outer disk steepened, indicating that the
corona is illuminating less to the disk, which is expected if the corona is
moving away from the disk at high speed and beaming its radiation (Gallo et
al., 2019). In addition, it was suggested that the AGN corona might be
magnetically heated, and the radio and X-ray emission originating from the
coronal activities would reveal a ratio of $\sim 10^{-5}$, similar to those in
the coronally active stars (Laor & Behar, 2008). Using the X-ray fluxes
provided in Grupe et al. (2008) and the radio measurements in Table 1 as well
as by our VLBA measurement, the flux ratio of radio-to-X-ray is in the range
$\sim 10^{-6}$ to $\sim 10^{-5}$ which is similar to the suggested relation in
Laor & Behar (2008). It implies the possibility that the corona is the jet
base, which was also suggested by previous works, e.g., in Wilkins & Gallo
(2015) and Gallo et al. (2019).

However, the ejecta in the collimated corona detected by the X-ray can only
reach a height of no more than ten gravitational radius $R_{\rm g}$ as
estimated in Gallo et al. (2019) (see their Figure 10), while the projected
scale of the jet structure detected in our VLBA image is $\sim 20$ parsec,
corresponding to $\sim 10^{7}\,R_{\rm g}$. It is not clear whether the parsec-
scale radio jet in Mrk 335 has any relation to the collimated X-ray corona,
and, if they are related, how the particles can be accelerated to such large
distance from within a few $R_{\rm g}$ above the accretion disk. This may be
tested by the future higher-resolution radio observations and by the
correlation of simultaneous X-ray and radio monitoring observations.

##  5 Summary

We report the VLBA observation at 1.5 GHz on a nearby radio-quiet NLS1 galaxy
Mrk 335 in which its central SMBH accretes near/above Eddington limit. The
image reveals an elongated jet structure extending $\sim 20\rm\,parsec$, with
the brightness temperature as high as $\sim 6\times 10^{7}\rm\,K$. This work
increases the number of known parsec-scale jet in the highly accreting radio-
quiet NLS1 galaxies, which is rare so far. The consistence of the flux
measured by VLBA with the historical measurements at larger scales by VLA
shows that the radio emission of Mrk 335 is dominated by the central parsec-
scale jet. We discuss the comparison with other highly accreting jetted black
holes, and the possible connection between the X-ray corona and the jet. The
discovery of jet features in the highly accreting AGN will provide us with
further constraints on the physics of the accretion-jet coupling in high
Eddington ratio regime. In our future work, we will report results of the
observations on the parse-scale nuclear region in other highly accreting
radio-quiet NLS1 galaxies (Yang et al. in preparation).

## Acknowledgements

SY acknowledges the support by an Alexander von Humboldt Foundation
Fellowship. XLY thanks the support by Shanghai Sailing Program (21YF1455300)
and China Postdoctoral Science Foundation (2021M693267). XLY and TA thank the
financial support by the National Key R&D Programme of China (2018YFA0404603)
and the Chinese Academy of Sciences (114231KYSB20170003). MFG is supported by
the National Science Foundation of China (11873073). LCH, RW and XW was
supported by the National Science Foundation of China (11721303, 11991052) and
the National Key R&D Program of China (2016YFA0400702 and 2016YFA0400703). The
National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. This work made use of the Swinburne University of Technology software
correlator, developed as part of the Australian Major National Research
Facilities Programme and operated under licence. This work has also made use
of the NASA Astrophysics Data System Abstract Service (ADS), and the NASA/IPAC
Extragalactic Database (NED) which is operated by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the
National Aeronautics and Space Administration.

## Data Availability

The VLBA data of BY0145 will be shared on reasonable request to the
corresponding author. The archival VLBA data (BB0056, BG0093) and the VLA data
(AM0384) underlying this article are available in the NRAO data archive
(https://science.nrao.edu/facilities/vla/archive/index).

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