# Revisiting the Dragonfly Galaxy I. High-resolution ALMA and VLA Observations
of the Radio Hotspots in a Hyper-luminous Infrared Galaxy at $z=1.92$

Yuxing Zhong1 (仲宇星), Akio K. Inoue1,2, Yuma Sugahara2,3, Kana Morokuma-
Matsui4, Shinya Komugi5, Hiroyuki Kaneko6,7,3, and Yoshinobu Fudamoto2,3
1Department of Pure and Applied Physics, Waseda University, 3-4-1 Okubo,
Shinjuku, Tokyo 169-8555, Japan
2Waseda Research Institute of Science and Engineering, Waseda University,
3-4-1, Okubo, Shinjuku, Tokyo 169-8555, Japan
3National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181–8588, Japan
4Center for Computational Sciences, University of Tsukuba, Ten-nodai, 1-1-1
Tsukuba, Ibaraki 305-8577, Japan
5Department of Liberal Arts, Kogakuin University, 2665-1 Nakano-cho, Hachioji,
Tokyo 192-0015, Japan
6Joetsu University of Education, 1, Yamayashiki-machi, Joetsu, Niigata
943–8512, Japan
7Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Radio-loud active galactic nuclei (RLAGNs) are rare among AGN populations.
Lacking high-resolution and high-frequency observations, their structure and
evolution stages are not well understood at high redshifts. In this work, we
report ALMA 237 GHz continuum observation at $0\aas@@fstack{\prime\prime}023$
resolution and VLA 44 GHz continuum observation at
$0\aas@@fstack{\prime\prime}08$ resolution of the radio continuum emission
from a high-redshift radio and hyper-luminous infrared galaxy at $z=1.92$. The
new observations confirm the South-East (SE) and North-West (NW) hotspots
identified by previous low-resolution VLA observations at 4.7 and 8.2 GHz and
identify a radio core undetected in all previous observations. The SE hotspot
has a higher flux density than the NW one does by a factor of 6, suggesting
that there can be a Doppler boosting effect in the SE one. In this scenario,
we estimate the advance speed of the jet head, ranging from $\sim$0.1c – 0.3c,
which yields a mildly relativistic case. The projected linear distance between
the two hotspots is $\sim 13$ kpc, yielding a linear size ($\leq 20$ kpc) of a
Compact-Steep-Spectrum (CSS) source. Combined with new high-frequency
(${\nu}_{\mathrm{obs}}\geq 44$ GHz) and archived low-frequency observations
(${\nu}_{\mathrm{obs}}\leq 8.2$ GHz), we find that injection spectra of both
NW and SE hotspots can be fitted with a continuous injection (CI) model. Based
on the CI model, the synchrotron ages of NW and SE hotspots have an order of
$10^{5}$ yr, consistent with the order of magnitude $10^{3}-10^{5}$ yr
observed in CSS sources associated with radio AGNs at an early evolution
stage. The CI model also favors the scenario in which the double hotspots have
experienced a quiescent phase, suggesting that this RLAGN may have transient
or intermittent activities.

###### keywords:

galaxies: active – galaxies: jets – radio continuum: galaxies

††pubyear: 2023††pagerange: Revisiting the Dragonfly Galaxy I. High-resolution
ALMA and VLA Observations of the Radio Hotspots in a Hyper-luminous Infrared
Galaxy at $z=1.92$–7

##  1 Introduction

Radio galaxies hosting radio-loud active galactic nuclei (RLAGNs,
$L\mathrm{{}_{6GHz}\gtrsim 10^{23.2}\ erg\ s^{-1}}$; Kellermann et al. 2016)
have their radio emissions dominated by magnetobremsstrahlung, i.e.,
synchrotron radiation attributed to the central AGN. RLAGNs are rare amongst
all AGN populations ($15-20\%$; Kellermann et al. 1989; Williams et al. 2018).
In the local Universe, RLAGNs are found to preferentially reside in early-type
galaxies with high stellar masses, low star formation rates, and radiatively
inefficient AGNs (Best et al., 2005; Heckman & Best, 2014; Gürkan et al.,
2015). At higher redshifts, there is an increasing number of RLAGNs related to
active supermassive black holes (SMBHs) showing high accretion rates, and
these AGNs are intrinsically radiatively efficient (Williams et al., 2018;
Hardcastle & Croston, 2020). This different feature provides a good channel to
access a more complete picture of the AGN evolution itself, as well as the co-
evolution with its host galaxy.

To select radio AGNs hosted by high redshift radio galaxies (HzRGs), a feature
called Ultra-Steep-Spectrum (USS), with a spectral index $\alpha\leq-1.3$
($S_{\nu}\propto\nu^{\alpha}$) in the low-frequency radio spectral energy
distribution (SED) has been proven an effective technique (De Breuck et al.,
2000). Such a steeper slope at high redshifts is considered a result of two
possible causes. The first one is the Malmquist effect, due to which the cut-
off frequency may migrate towards lower frequencies since it is anti-
correlated with the radio luminosity. The second possibility is that HzRGs may
reside in denser environments because of the evolution of cosmic neutral
hydrogen density, leading to a steeper initial power-law of the energy
distribution (Miley & De Breuck, 2008). Recent studies have emphasized the
importance of cosmic microwave background (CMB) radiation (e.g., Saxena et
al., 2017). The inverse Compton scattering that involves CMB photons and
synchrotron-radiating electrons could be the dominant energy loss and result
in a rapid decrease in the energy of synchrotron-emitting relativistic
electrons.

Other than USS, many HzRGs show Peaked-Spectrum (PS) or Compact-Steep-Spectrum
(CSS) (O’Dea & Baum, 1997). PS sources always have a frequency at which the
flux density peaks. This frequency is known as peaked or turnover frequency,
below which the medium is optically-thick for the synchrotron-emitting source
due to the synchrotron self-absorption (SSA) and/or free-free absorption
(FFA), showing an inverse spectral index (Condon & Ransom, 2016; Snell et al.,
2019). These sources are considered the youngest populations of radio AGNs.
The PS sources may evolve into CSS sources with evolving jets, characterized
by a typical projected linear size $\leq 20$ kpc and $\alpha\leq-0.5$ at low
frequencies (O’Dea & Saikia, 2021).

Many high redshift CSS sources have been observed at low frequencies over the
decades, while the high-frequency observations are still lacking (Pentericci
et al., 2000; Patil et al., 2020; Sotnikova et al., 2019). The high-frequency
behavior of the synchrotron radiation is crucial to investigate the evolution
of the radio AGN, especially when the radio jets launched by the AGN have
interacted with their ambient medium. Radio hotspots that are working surfaces
where the radio jet has interacted with the medium are essential to answer
this question. The synchrotron age of the radio hotspot is determined by the
break frequency above which the spectrum steepens, together with the magnetic
field in equipartition. This break frequency can be estimated by fitting the
observed radio spectrum covering a range of frequencies from low to high to an
injection spectrum of the accelerated synchrotron-emitting electrons.

In this work, we have studied a HzRG – MRC 0152-209, named Dragonfly galaxy,
which has a star formation rate (SFR) of $\mathrm{\sim 3000\ M_{\odot}\
yr^{-1}}$ and $M_{\star}\sim\mathrm{5\times 10^{11}\ M_{\odot}}$ (Emonts et
al., 2015b, a). This galaxy constitutes of three components: the North-West
(NW) galaxy, the South-East (SE) galaxy, and a Companion (C) with massive
molecular gas (see panels (a), (NW), and (SE) in Fig. 1). The low-frequency
observations at 4.7 and 8.2 GHz using the Very Large Array (VLA) were studied
by Pentericci et al. (2000), and they identified two radio hotspots, the NW
and SE ones, while the radio core remained non-detection (see green contours
in panel (a) in Fig. 1). New VLA Band Q observations (Project ID: VLA/15A-316
and VLA/17B-444, PI: Bjorn Emonts), combined with high-angular resolution
Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 4 (Project ID:
2016.1.01417.S, PI: Bjorn Emonts) and 6 (Project ID: 2018.1.00293.S, PI: Bjorn
Emonts) observations in Band 6, allow us to have a deeper investigation into
the radio properties including the lifetime of hotspots and the geometry of
radio jets.

Throughout this paper, we assume a $\mathrm{\Lambda CDM}$ cosmology with
$\Omega_{m}=0.309$, $\Omega_{\Lambda}=0.691$, and $H_{0}=\mathrm{67.7\ km\
s^{-1}\ Mpc^{-1}}$ (Planck Collaboration et al., 2016). Based on these
assumptions, the luminosity distance of the Dragonfly galaxy is $\sim$15200
Mpc, and $1\arcsec$ corresponds to a projected physical scale of 8.62
kpc.111The calculation has made use of Wright (2006).

Table 1: Summary of the Observations Observation | Date | Frequency | Band | beam size | $\sigma\ (\mathrm{mJy\ beam^{-1}})$
---|---|---|---|---|---
VLA A-configuration | 5th and 13th August, 2015 | 44 GHz | Band Q | $0\aas@@fstack{\prime\prime}07\times 0\aas@@fstack{\prime\prime}04$ | 0.01
VLA BnA-configuration | 29th May, 2015 | 44 GHz | Band Q | $0\aas@@fstack{\prime\prime}14\times 0\aas@@fstack{\prime\prime}08$ | 0.018
VLA B-configuration | 30th December, 2017 | 44 GHz | Band Q | $0\aas@@fstack{\prime\prime}26\times 0\aas@@fstack{\prime\prime}13$ | 0.024
ALMA Cycle 4 | 9 and 17th August, 2017 | 237 GHz | Band 6 | $0\aas@@fstack{\prime\prime}11\times 0\aas@@fstack{\prime\prime}08$ | 0.011
ALMA Cycle 6 | 23th June, 2019 | 237 GHz | Band 6 | $0\aas@@fstack{\prime\prime}026\times 0\aas@@fstack{\prime\prime}023$ | 0.0065

##  2 Observations

In this section, we briefly describe the observational data used in this work,
including observation setups, calibration procedures, and imaging strategies.
The observation dates, frequencies, bands, restored beam sizes, and root-mean-
squares (RMS, $\sigma$) are summarized in Table. 1.

###  2.1 VLA Band Q

The VLA observations were conducted in B-, BnA-, and A-configurations. All the
observations were centred at 44 GHz with an effective bandwidth of 7.5 GHz.
The total on-source time is 42 min for B- and BnA-configuration observations,
and 178 min for A-configuration. For all the observations, calibrator
J2253+1608 was chosen to calibrate the bandpass response, calibrator
J0204-1701, which is separated from the Dragonfly galaxy by $4.4^{\circ}$, was
chosen to calibrate complex gain, including amplitude and phase, between the
scans of the science target, and 3C147 was chosen to calibrate the flux
density scale.

The B-configuration observation was calibrated by means of running the VLA
calibration script that is provided by the National Radio Astronomy
Observatory (NRAO) on the Common Astronomy Software Applications (CASA)
package version 6.2.1 embedding the VLA calibration pipeline (McMullin et al.,
2007; THE CASA TEAM et al., 2022). The BnA- and A-configuration observations
were calibrated by requesting pipeline calibrations through the NRAO Science
Helpdesk. All the imaging procedures were performed on CASA version 6.4.0. For
all the observations, using the ’hogbom’ deconvolution algorithm, we imaged
the data choosing the ’briggs’ weighting with a robustness parameter +0.5, and
put a mask on the strongest signal to avoid artefacts. Due to the low signal-
to-noise ratio of each spectral window, no self-calibration in any dataset can
be applied, leaving low-level sidelobe contamination on the clean images.

###  2.2 ALMA Band 6

The ALMA Cycle 4 observations were performed on 9 and 17 August 2017 for 1.2
hours of on-source time with 45 antennas and baselines up to $\sim 3.6$ km.
The ALMA Cycle 6 observations were conducted on 23 June 2019 for 2.2 hours of
on-source time with 48 antennas and the longest baseline is up to 11.5 km. For
both observations, there are four spectral windows configured to cover two 4
GHz bands, one of which includes $235.83-239.58$ GHz to observe the redshifted
CO(6-5) line emission $(\nu\mathrm{{}_{rest}\approx 691.47\ GHz})$ and another
includes $251.20-255.95$ GHz such that only continuum is observed. The data
calibrations were performed via the ALMA pipeline that is included in CASA
version 4.7.2 for Cycle 4 and 5.4.0 for Cycle 6, respectively, by running the
calibration script supplied with the data by the North American ALMA Science
Center (NAASC).

The main objective of these observations is to image the CO(6-5) line
emission, which is beyond the scope of this paper. An analysis of CO(6-5) line
emission based on Cycle 4 data is discussed in Lebowitz et al. (2023) and
another analysis of CO(6-5) using combined data from Cycles 4 and 6 will be
presented in a forthcoming paper (Paper II; Zhong et al. in prep.) The
detailed analysis of CO(6-5) line emission will be presented in a forthcoming
paper (Paper II; Zhong et al. in prep.). We adopt a uniform method for Cycle 4
and 6 observations to image the continuum in this work. Prior to imaging the
continuum, we flagged the channels with CO(6-5) line emission, as well as
pseudo-lines due to the severe atmospheric absorption. Next, we created a
dirty image without any clean to calculate the root-mean-square noise
$(\sigma)$ under the ’briggs’ weighting with a robustness parameter +0.5.
Then, we cleaned the image non-interactively by setting $3\sigma$ as the stop
threshold of the cleaning.

###  2.3 Alignment

The imaging of ALMA Cycle 4 and 6 and VLA 44 GHz observation in three
configurations is the direct ’tclean’ product of the measurement sets that are
calibrated from raw files using the calibration pipeline provided by NRAO or
under the assistance of the NRAO and EA ALMA staff. No postprocessing,
including self-calibration and manipulations on the WCS of the imaging
results, was performed. Then the contours from different observations are
overlaid on false-color images based on their WCS using Cube Analysis and
Rendering Tool for Astronomy (CARTA, Comrie et al., 2021). VLA 8.2 GHz
observation is a reproduction of Pentericci et al. (2000). It was self-
calibrated, and thus its WCS cannot be trusted222See Post-processing Section
at
https://science.nrao.edu/facilities/vla/docs/manuals/oss2015B/performance/positional-
accuracy. We, therefore, take the peak pixel of the SE hot spot observed in
VLA A-configuration at 44 GHz as the reference to shift the WCS of VLA 8.2 GHz
such that they match.

Taking the SE peak pixel as the reference, the ALMA Cycle 6 has an offset of
$0\aas@@fstack{\prime\prime}025$ between VLA 44 GHz in BnA-configuration along
RA, and an offset of $0\aas@@fstack{\prime\prime}011$ between VLA 44 GHz in
A-configuration along RA. Offsets along the DEC are completely negligible.
Although these offsets can be larger than the typical position uncertainty of
one-tenth of beam size since there can be low-level systematic uncertainties,
the current alignments are sufficient to suggest that the features originate
from the same radio source.

Figure 1: (a) ALMA Cycle 6 Band 6 continuum image $\mathrm{(\sigma=6.5\ \mu
Jy\ beam^{-1})}$ with contour levels [3, 5, 10, …, 30, 35]$\times\sigma$. The
yellow contours indicate the ALMA Cycle 4 Band 6 continuum of the Companion
component with $[3,5]\times\sigma$ levels, where $\sigma=10.7\mathrm{\ \mu Jy\
beam^{-1}}$. The white contours indicate the VLA BnA-configuration
observation, as explained in panel (b). The green contours indicate the VLA
8.2 GHz observation (Pentericci et al., 2000). (b) VLA BnA-configuration image
$\mathrm{(\sigma=0.018\ mJy\ beam^{-1})}$. The white contours start at
4$\sigma$ and increase by a factor of 1.5 with a step of $3\sigma$. The
contour levels are given by
$\mathrm{[start,start+step,start+(1+factor)*step,start+(1+factor+factor^{2})*step,...]}$.
(c) VLA B-configuration image $\mathrm{(\sigma=0.024\ mJy\ beam^{-1})}$. The
white contours start at 5$\sigma$ and increase by a factor of 1.5. (d) VLA
A-configuration image $\mathrm{(\sigma=0.01\ mJy\ beam^{-1})}$. The white
contours start at 5$\sigma$ and increase by a factor of 1.5 with a step of
$10\sigma$. (NW) Zoom in on the NW galaxy. The white contours indicate the VLA
BnA-configuration. (SE) Zoom in on the SE galaxy. The white and green contours
indicate the VLA BnA- and A-configuration, respectively. In all images, the
black contours indicate the ALMA Cycle 6 Band 6 continuum, the yellow contours
indicate the ALMA Cycle 4 Band 6 continuum imaging of the Companion component,
and the yellow dashed line indicates the direction of the propagation of the
radio jet. The beam size of each false-color image is shown at the lower left
by the white ellipse. The new observations have identified a radio core that
in general overlaps with the NW galaxy. The Companion component lies 10 kpc
southeast of the SE galaxy in projection. The Companion and SE and NW galaxies
are nearly in alignment with the propagation direction of the collimated radio
jets. The ALMA Cycle 6 observation reveals a sub-component, adjacent to the SE
galaxy, that perfectly coincides with the SE hotspot identified by VLA 4.7 and
8.2 GHz observations. Table 2: Flux Measurements of the Dragonfly galaxy

Frequency | Component | $S_{\nu}$ | Spectral Index | $L_{\mathrm{radio}}$ | $P_{\nu_{0}}$ | Aperture | Ref. |
---|---|---|---|---|---|---|---|---
(MHz) |  | (mJy) |  | (W Hz-1) | $\mathrm{(erg\ s^{-1})}$ |  |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) |
74 | Total | $3100\pm 620$ | - | $(2.9\pm 0.6)\times 10^{28}{}^{a}$ | $(2.2\pm 0.4)\times 10^{43}$ | $80\arcsec$ | 1 |
147 | Total | $2620\pm 10$ | $-0.25\pm 0.29$ | $(3.2\pm 1.0)\times 10^{28}$ | $(4.7\pm 1.5)\times 10^{43}$ | $25\arcsec$ | 2 |
365 | Total | $1580\pm 30$ | $-0.56\pm 0.02$ | $(2.7\pm 0.1)\times 10^{28}$ | $(9.9\pm 0.3)\times 10^{43}$ | $6\arcsec$ | 1 |
$1.4\times 10^{3}$ | Total | $453\pm 91$ | $-0.93\pm 0.15$ | $(1.2\pm 0.3)\times 10^{28}$ | $(1.6\pm 0.4)\times 10^{44}$ | $45\arcsec$ | 1 |
$4.7\times 10^{3}$ | Total | $115\pm 12$ | $-1.13\pm 0.19$ | $(3.6\pm 0.8)\times 10^{27}$ | $(1.7\pm 0.4)\times 10^{44}$ | - | 3 |
$8.2\times 10^{3}$ | Total | $47\pm 4.7$ | $-1.61\pm 0.25$ | $(2.5\pm 0.6)\times 10^{27}$ | $(2.0\pm 0.4)\times 10^{44}$ | - | 3 |
$44\times 10^{3}$ | Total | $2.42\pm 0.32$ | $-1.77\pm 0.08$ | $(1.5\pm 0.2)\times 10^{26}$ | $(6.7\pm 1.1)\times 10^{43}$ | - | 4 |
$4.7\times 10^{3}$ | NW | $7.2\pm 0.72$ | - | - | - | $1\aas@@fstack{\prime\prime}16\times 0\aas@@fstack{\prime\prime}44$ | 3 |
$8.2\times 10^{3}$ | NW | $2.8\pm 0.28$ | $-1.7\pm 0.25$ | $1.6\times 10^{26}$ | $1.3\times 10^{43}$ | $0\aas@@fstack{\prime\prime}72\times 0\aas@@fstack{\prime\prime}24$ | 3 |
$44\times 10^{3}$ | NW | $0.29\pm 0.07$ | $-1.35\pm 0.16$ | $(1.2\pm 0.3)\times 10^{25}$ | $(5.1\pm 1.5)\times 10^{42}$ | $0\aas@@fstack{\prime\prime}4\times 0\aas@@fstack{\prime\prime}2$ | 4 |
$4.7\times 10^{3}$ | SE | $95.9\pm 9.6$ | - | - | - | $1\aas@@fstack{\prime\prime}16\times 0\aas@@fstack{\prime\prime}44$ | 3 |
$8.2\times 10^{3}$ | SE | $44\pm 4.4$ | $-1.4\pm 0.25$ | $1.9\times 10^{27}$ | $1.5\times 10^{44}$ | $0\aas@@fstack{\prime\prime}72\times 0\aas@@fstack{\prime\prime}24$ | 3 |
$44\times 10^{3}$ | SE | $1.88\pm 0.09$ | $-1.87\pm 0.07$ | $(1.3\pm 0.1)\times 10^{26}$ | $(5.9\pm 0.3)\times 10^{43}$ | $0\aas@@fstack{\prime\prime}5\times 0\aas@@fstack{\prime\prime}4$ | 4 |
$237\times 10^{3}$ | SE | $0.12\pm 0.01$ | $-1.64\pm 0.06$ | $(6.6\pm 0.7)\times 10^{24}$ | $(1.6\pm 0.2)\times 10^{43}$ | $0\aas@@fstack{\prime\prime}07\times 0\aas@@fstack{\prime\prime}12$ | 4 |
$44\times 10^{3}$ | Core | $0.23\pm 0.06$ | - | - | - | $0\aas@@fstack{\prime\prime}4\times 0\aas@@fstack{\prime\prime}3$ | 4 |

  * •

Column (1): frequency. Column (2): the measurement of the individual
component. Total$=$NW+SE+core. See texts for details. Column (3): Integrated
flux densities over a certain region. For flux measurements from references 1,
2, and 3 in Column (8), the radio emissions are unresolved such that the
integration region can be considered as the beam size. Column (4): the
spectral index (positive convention, $S_{\nu}\propto\nu^{\alpha}$) between two
observed frequencies, one in this line and the other in the line just above.
Column (5): the spectral luminosity $L_{\nu}=S_{\mathrm{obs}}4\pi
D^{2}_{L}/(1+z)^{1+\alpha}$, where $S_{\mathrm{obs}}$ is the observed
integrated flux densities and $D_{L}$ is the luminosity distance. Column (6):
the radio power $P_{\nu_{0}}=4\pi
D^{2}_{L}(1+z)^{-\alpha-1}S_{\nu_{0}}\nu_{0}$ (Cavagnolo et al., 2010). Column
(7): the aperture size used to integrate the flux density. Column (8):
references to flux measurements. 1: Vollmer et al. (2010); 2: de Gasperin et
al. (2018); 3: Pentericci et al. (2000); 4: this work.
a The radio luminosity is calculated assuming the spectral index $\alpha=0$

##  3 Results

###  3.1 Spatial Distribution

In Fig. 1 we show the imaging results of VLA 44 GHz and ALMA Band 6
observations, supplemented with previous VLA observation centred at 8.2 GHz
(Pentericci et al., 2000). Observed by VLA at 8.2 GHz (green contours in Fig.
1), the radio emission shows clear double components that potentially
correspond to the hotspots where the radio jet launched from the AGN interacts
with the ambient medium. The double hotspots are also visible in the VLA
observation at 4.7 GHz (Pentericci et al., 2000). Thanks to the high flux
density, the SE hotspot is clearly detected in all VLA 44 GHz observations,
while the NW hotspot falls below a $5\sigma$ detection threshold in the
B-configuration. South of the SE hotspot, there is a diffuse emission region
that may be corresponding to the expanding radio lobe, which is clearly shown
in the B-configuration imaging. We draw a yellow dashed line in Fig. 1 to
indicate the direction of the propagation of the radio jets under the
assumption that the radio hotspots originate from the well-collimated jets.

In addition to the double hotspots, another radio emission is detected at a
position very close to the NW galaxy in BnA-configuration (see panel (NW) in
Fig. 1), while it remains non-detection in VLA B- and A-configurations.
Although slightly spatially offset by $\sim 0\aas@@fstack{\prime\prime}06$,
which is insignificant compared with the beam size
$0\aas@@fstack{\prime\prime}14\times 0\aas@@fstack{\prime\prime}08$, this
radio source coincides well with the location of the NW galaxy in which the
AGN resides. This source also lies on the dashed line that links the double
hotspots, suggesting that it can be the radio core – the launch point of the
bipolar radio jets – of the RLAGN.

One serendipitous and interesting finding is a sub-component adjacent to the
SE galaxy through the ALMA Band 6 observation (see panel (SE) in Fig. 1). This
sub-component has its location perfectly coincided with the SE hotspot, which
is identified in VLA observations, that is supposed to be dominated by
synchrotron radiation arising from the in situ acceleration due to a jet-ISM
interaction. However, the rest-frame frequency of the ALMA observation is
$\sim 700$ GHz which corresponds to $\sim 400\ \micron$, entering the far-
infrared (FIR) regime. A mixture of different emission mechanisms, including
dust thermal emission, synchrotron radiation, and free-free emission, can
contribute to the observed flux density of this sub-component.  The
$\mathrm{SFR}$ of the entire system is $\sim 3000\ M_{\odot}\ yr^{-1}$,
adopting a power-law black body radiation (Drouart et al., 2014). The
integrated flux density of this sub-component is about 10 per cent of the dust
thermal emission from SE and NW galaxies at 237 GHz. Then, if this sub-
component is dominated by jet-induced star formation, it may have an
$\mathrm{\sim 300\ M_{\odot}\ yr^{-1}}$, which corresponds to a synchrotron
flux density of $3\ \mu$Jy and free-free flux density of $10\ \mu$Jy.
Therefore, synchrotron and free-free radiations attributed to the SFR
contribute negligible contaminations to the sub-component at 237 GHz. However,
since a jet-induced star formation cannot be confirmed and its associated dust
thermal emission cannot be evaluated in the current phase, we treat this sub-
component as dominated by synchrotron radiation related to AGN activities
throughout this work.

###  3.2 Spectral Energy Distribution (SED)

Although the Dragonfly galaxy has been observed at low frequencies over
decades, the low angular resolutions leave the radio emissions unresolved.
Hence, there is no available structural information on radio emissions in
observations at ${\nu}_{\mathrm{obs}}\leq 1.4$ GHz. We listed the available
archived data at different frequencies in Table 2 and plot the integrated flux
density against frequency in Fig. 2. The specific luminosity has exceeded
$\mathrm{10^{28}\ W\ Hz^{-1}}$ at ${\nu}_{\mathrm{obs}}\leq 1.4$ GHz, making
this object an unambiguous radio-bright AGN (Yuan & Wang, 2012; Kellermann et
al., 2016; Hardcastle & Croston, 2020), though this radio luminosity can be
smaller than that of the extreme populations found at $z>5$ by two orders of
magnitude (van Breugel et al., 1999; Saxena et al., 2018).

Based on the imaging results, we divide the radio emissions into three
components: radio core, SE, and NW hotspots, and the total is the sum of these
components. All observations at $\leq 1.4$ GHz have no resolved components,
thus the integrated flux densities of these observations are simply treated as
the sum of all three components.

As shown in Fig. 2, the radio spectrum of the sum of different components
shows no apparent turnover point, below which the spectral index becomes
positive due to SSA and/or FFA and the medium is optically-thick to the radio
emission (Condon & Ransom, 2016). The globally negative spectral index
suggests that the medium is likely to remain optically thin to the radio
emission. However, we do observe a gradual flattening of the slope towards
lower frequencies, by which we cannot exclude the possibility that there can
be a broad peak around 74 MHz at the observed frequency because of SSA/FFA.

At 4.7 and 8.2 GHz, we treated the peak flux densities of NW and SE hotspots
as the integrated flux densities, i.e.,
$S_{\mathrm{peak}}=S_{\mathrm{total}}$, since both NW and SE hotspots are
marginally resolved (Prandoni et al., 2001; Bondi et al., 2008). At $\geq 4.7$
GHz, the SE hotspot dominates over the observed flux densities, indicating
that the SE hotspot may be Doppler boosted (see §5.1). The slope of the SE
hotspot becomes slightly shallower at 237 GHz than that at 44 GHz
$(\mathrm{\alpha=-1.87^{+0.07}_{-0.07}\to-1.64^{+0.06}_{-0.06}})$ because of a
possible mixture of various emission mechanisms other than pure synchrotron
radiation at 237 GHz. Otherwise, since contaminations from the radio lobes at
8.2 GHz may result in an overestimation of the spectral index at 44 GHz (see
§5.2 and §5.4), this slight flattening is not robust. The NW hotspot falls
below the $3\sigma$ detection limit in ALMA Cycle 6 observation and has its
slope steepened at 4.7 and 8.2 GHz, but becoming shallower at 44 GHz (see
column (4) in Table. 2).

Since the radio core is only observed at 44 GHz, we here estimate its
contribution to flux densities at other frequencies and investigate its impact
on the global shape of the total radio SED. At 44 GHz, the radio core
contributes to less than 10% of the sum of different components, thus the
absence of a core has negligible influence on the total radio SED. As we will
see in §5.2, the radio core contributes to less than 1 per cent of the
observed flux densities at 4.7 and 8.2 GHz. Therefore, the contamination from
the radio core cannot alter the shape of the observed spectral slope.

Figure 2: Integrated flux density against frequency of the Dragonfly galaxy
based on the measurements given in Table. 2. The horizontal axis shows the
rest-frame frequency and the observed frequency is shown by the data points.
The green dashed line indicates the best-fitting of the observed
$S_{\mathrm{Total}}$ by adopting a curved power-law model. The NW hotspot is
not detected at $3\sigma$-level in ALMA Cycle 6 and we set $3\sigma$ as an
upper limit for its flux density to proceed with the discussion in §5.1. The
blue solid line indicates a spectral index $\alpha=-1.3$ and a spectrum
steeper than this is classified as a USS source (De Breuck et al., 2000).
Because of the smallness of uncertainties, some error bars are not clearly
visible in the figure but can be found in Table 2.

##  4 The Curved SED

###  4.1 Compact-Steep-Source

To better investigate the spectrum as a curve, we fit the observed flux
densities at frequencies $\leq 8.2$ GHz by a curved power-law model given by
(Callingham et al., 2017)

$S_{\nu}=a\nu^{\alpha}e^{q(\ln\nu)^{2}},$ (1)

where $S_{\nu}$ is the flux density at the observed frequency $\nu$ in GHz,
$\alpha$ is the spectral index, $a$ is a factor that determines the amplitude
of the non-thermal spectrum, and $q$ is the curvature parameter that optimizes
the spectral curvature, by which the peaked frequency (or turnover frequency)
is defined as $\nu_{\mathrm{peak}}=e^{-\alpha/2q}$. The best-fitting result of
the sum of integrated flux densities is shown in Fig. 2 by the green dashed
line with $q=-0.175\pm 0.01$ and $\alpha=-1.05\pm 0.03$, showing no evidence
of a significant curvature ($|q|\geq 0.2$, Duffy & Blundell 2012). The
corresponding peaked frequency is $\nu_{\mathrm{peak}}=e^{-\alpha/2q}\sim
50-60$ MHz. The curved power-law colossally deviates from the observational
data higher than 44 GHz due to the energy loss, which will be studied in §4.2.

Since the projected linear separation of the two hotspots is only $\sim
1\aas@@fstack{\prime\prime}5$ ($\sim 13$ kpc at $z=1.92$), the Dragonfly
galaxy can be classified as a CSS source (O’Dea & Saikia, 2021). By fitting a
single Gaussian component to the image plane, the size of the SE hotspot
deconvolved from the beam is $(0\aas@@fstack{\prime\prime}054\pm
0\aas@@fstack{\prime\prime}015)\times(0\aas@@fstack{\prime\prime}033\pm
0\aas@@fstack{\prime\prime}01)$, corresponding to a radius of $r\sim~{}0.47$
kpc at $z=1.92$, which yields a typical hotspot size of CSS sources (Jeyakumar
& Saikia, 2000), providing additional support for a CSS classification. Using
an empirical relation that correlates the projected angular size ($l$ in kpc)
and $\nu_{\mathrm{peak}}$ (in GHz) for CSS sources (O’Dea & Baum, 1997),

$\log\nu_{\mathrm{peak}}=-0.21(\pm 0.05)-0.65(\pm 0.05)\times\log l,$ (2)

the estimated turnover frequency is $116\pm 20$ MHz for $l\sim 13$ kpc. This
estimation is close to the value given by the curved power-law but can be
underestimated since the observation may not detect the full extent of the
synchrotron radiation due to the diffuse emission attributed to radio lobes
(see panel (c) in Fig. 1 and the discussion in §5.2).

CSS sources can be young AGNs with evolving radio jets or can be old
populations that have their radio jets confined by the dense ISM of their host
galaxies (O’Dea & Saikia, 2021). A young CSS source may merely have
intermittent or transient activities as well, incapable of forming large
structures (O’Dea & Saikia, 2021). However, confined by the dense ISM of the
AGN host galaxy, the radio jet can strongly couple with the surrounding
material, leading the jet to slow down and lose kinetic energy. When the jet
is not sufficiently powerful to overcome the confining pressure of the ISM,
such strong couplings may result in the disruption of the jet and the
formation of radio lobes (Mukherjee et al., 2016; Bambic et al., 2023). In the
Dragonfly, since the jet has obviously left its host galaxy, i.e., the NW
galaxy, and interacted with the ambient medium to create the hotspots,
confinement by the host galaxy is not favored. Therefore, the RLAGN residing
in the Dragonfly galaxy is likely to be a CSS source that is associated with
an AGN at an early evolution stage (Dicken et al., 2012). A CSS source that
launches powerful radio jets can escape more quickly from the confining medium
than their low-power counterparts and may evolve into a Fanaroff-Riley II
(FRII) radio galaxy (O’Dea, 1998; Mukherjee et al., 2016; Callingham et al.,
2017). Nonetheless, we have to consider the possibilities of transient or
intermittent radio AGN activities and this requires a further investigation
into the synchrotron age.

###  4.2 Synchrotron Ageing

At higher frequencies, there is no cut-off but a steepening of the slope at
$\nu_{\mathrm{obs}}\geq 4.7$ GHz with $\alpha<-1.3$. Such a steep slope in
HzRGs is often found at $\sim 1.4$ GHz in the radio SED of USS sources (De
Breuck et al., 2000). One possible interpretation for this feature is that the
increasing cosmic microwave background (CMB) radiation at higher redshifts
causes stronger inverse-Compton (IC) losses, and the strength of the magnetic
field equivalent to the CMB $(B_{\mathrm{CMB}})$ dominates over the magnetic
field (Saxena et al., 2017; van Weeren et al., 2019). However, in the SE
hotspot, adopting a lower limit of the magnetic field in energy equipartition
$B\mathrm{{}_{eq}}$, Pentericci et al. (2000) gives $B\mathrm{{}_{eq}}=160\
\mu$G, which is much higher than the expected $B_{\mathrm{CMB}}$ (see §4.2.1).
Therefore, for the Dragonfly galaxy, the dominated energy loss at high
frequency should be explained by synchrotron ageing, that is, since the
electron energy loss rate $-dE/dt$ is proportional to $E^{2}$, higher-energy
electrons deplete their energy faster.

Figure 3: Fitting results of the SE hotspot using synchrofit. The vertical
axis is in an arbitrary unit and all data points are the same but shifted
along the vertical axis for display purposes. The shaded regions embed
2$\sigma$ of the modeled spectrum and $\chi_{\mathrm{red}}^{2}$ indicates the
reduced-$\chi^{2}$ statistics. Top: The black and blue lines indicate the
fittings without and with ALMA data, respectively. Middle: Fittings with the
remnant fraction $T$ fixed to 0. The dashed and solid lines indicate the
fittings without and with ALMA data, respectively. Without a remnant fraction
$T$, the fitting is almost a straight line and cannot reproduce the curvature
of the observed SED. Bottom: Fittings with ALMA data and fixed injection
spectral index $\alpha_{\mathrm{inj}}$. The $\alpha_{\mathrm{inj}}$ is chosen
to lie within the range of a DSA scenario.

####  4.2.1 Synchrotron Fitting

The injection of new synchrotron-emitting electrons can be described by a
power-law spectrum that is referred to as the injection spectrum – a well-
established method to investigate high-frequency energy losses. The injection
spectrum is the ensemble of all relativistic electron populations with an
injection spectral index $\alpha_{\mathrm{inj}}$ that describes the slope of a
synchrotron radiation spectrum. The CI (continuous injection) model describes
a source with continuous replenishment of new relativistic particles over its
lifetime (Pacholczyk, 1970). The JP (Jaffe-Perola) and KP (Kardashev-
Pacholczyk) models describe a source that undergoes a single burst of particle
acceleration and then ages rapidly, with and without a continuous
isotropization of the electron pitch angle, respectively (van Weeren et al.,
2019; Jaffe & Perola, 1973; Pacholczyk, 1970; Kardashev, 1962).

We fit the radio SED of NW and SE hotspots using synchrofit to estimate the
break frequency $\nu_{\mathrm{br}}$, above which the synchrotron radiation
ages, and injection index $s$ that reflects the initial power-law of the
electron energy distribution (Turner et al., 2018; Turner, 2018). The
injection spectral index can be calculated from
$\alpha_{\mathrm{inj}}=(1-s)/2$. The fitting also returns an estimate of the
remnant fraction $T$, which is defined as $T=t_{\mathrm{off}}/\tau$, where
$t_{\mathrm{off}}$ is the time the source spent in an inactive phase and
$\tau=t_{\mathrm{off}}+t_{\mathrm{s}}$ is the total source age, where
$t_{\mathrm{s}}$, synchrotron age, is the duration of the continuous
injection. The synchrotron age is determined by $\nu_{\mathrm{br}}$ together
with the magnetic field strength $B$. The uncertainties are estimated using
1000 Monte Carlo iterations. The number of increments used to sample the
allowing ranges for free parameters $\nu_{\mathrm{br}}$, $s$, and $T$, is set
by default. Three iterations have been performed such that the free parameters
fitted by the former one of two consecutive iterations will be fed to the
latter one as initial guesses.

Prior to performing the fitting, we assume that the integrated flux densities
in unresolved observations (${\nu}_{\mathrm{obs}}\leq$1.4 GHz) only emanate
from the NW and SE hotspots, with negligible contamination from NW and SE
galaxies and the radio core for the reasons stated in §5.2. To divide the flux
densities of unresolved components into those of SE and NW hotspots, we adopt
a flux ratio that follows the values found in 4.7 and 8.2 GHz observations,
that is $S_{\mathrm{SE}}:S_{\mathrm{NW}}=15:1$. Further fittings considering
different flux ratios and contaminations from the radio lobes are presented in
Appendix A. We only present the fitting results using observational data at
$\geq 147$ MHz here since a shallower slope towards 74 MHz due to ionization
losses may aggravate the fitting results, though an inclusion or omission of
74 MHz data does not affect our conclusion (see Appendix A).

Previous studies have shown that the injection spectrum of a radio hotspot is
better described by the CI model, which is natural considering the radio jet
continuously accelerates the electrons in situ (Carilli et al., 1991; Murgia
et al., 2011; Maccagni et al., 2020). Additionally, the reduced-$\chi^{2}$ of
the JP and KP models is larger than that of the CI model by at least a factor
of three. Furthermore, we have performed fitting by fixing $T=0$, assuming
that there is no quiescent phase during the jet-medium interaction. However,
as clearly shown in Fig. 3, with or without ALMA 237 GHz data, the observed
curvature of the SED of the SE hotspot cannot be reproduced by the algorithm
in $T=0$ cases, and this scenario can be rejected. Hence, we only discuss the
fitting results of the CI model with non-zero $T$ here.

####  4.2.2 Fitting Results

The synchrotron age, i.e., the time-scale during which the continuous
acceleration lasts, is calculated by (Turner et al., 2018; Maccagni et al.,
2020):

${t}_{\mathrm{s}}=1610\frac{B_{\mathrm{eq}}^{1/2}}{B_{\mathrm{eq}}^{2}+B_{\mathrm{CMB}}^{2}}\frac{1}{\nu_{\mathrm{br}}(1+z)^{1/2}},$
(3)

where $B_{\mathrm{CMB}}=3.25(1+z)^{2}\ \mu$G is the magnitude of the magnetic
field equivalent to the CMB. The estimation of $B_{\text{eq}}$ in an energy
equipartition condition can be calculated using (Miley, 1980; Maccagni et al.,
2020):

$B_{\mathrm{eq}}=9.6\times
10^{-12}\left(\frac{P_{\text{1.4GHz}}(1+k)}{V^{3}}\right)^{2/7},$ (4)

where $P_{\text{1.4GHz}}$ is the radio power at 1.4 GHz in a unit of W Hz-1, k
is the protons to electrons energy ratio in the hotspot and set as 1, and V is
the hotspot volume in kpc3. We corrected the observed flux density to its
rest-frame considering the Doppler boosting effect (see §5.1 and §5.3) to
calculate $P_{\text{1.4GHz}}$. The hotspot is assumed to occupy an elliptical
cylinder volume, in which the cross-section corresponds to the beam size and
the height is the transverse size of the hotspot. The estimated
$B_{\text{eq}}$, taking a Doppler boosting factor $\delta=2-4$ (see the
discussion in §5.3), is $175-213\ \mu$G for the SE and $214-261\ \mu$G for the
NW hotspot, respectively. These estimates lie within
$B\mathrm{{}_{eq}=160-700\ \mu G}$ given by Pentericci et al. (2000) for a
sample of HzRGs including the Dragonfly galaxy.

The NW hotspot is fitted without 237 GHz data, and the fitting result is
$\nu_{\mathrm{br}}=980\pm 180$ MHz, $\alpha_{\mathrm{inj}}=-0.59\pm 0.01$, and
$T=0.08\pm 0.02$. Considering a quiescent phase during the continuous
acceleration, the above fitting gives $t_{\mathrm{s}}\sim 2-3\times 10^{5}$
yr.

Without ALMA 237 GHz data, the SE hotspot has $\nu_{\mathrm{br}}=760\pm 140$
MHz, $\alpha_{\mathrm{inj}}=-0.51\pm 0.01$, $T=0.13\pm 0.03$, and
$t_{\mathrm{s}}\sim 3-4\times 10^{5}$ yr. With ALMA 237 GHz data, i.e., under
the assumption that the sub-component observed at 237 GHz has synchrotron-
dominance, the SE hotspot then has $\nu_{\mathrm{br}}=2.95\pm 0.5$ GHz,
$\alpha_{\mathrm{inj}}=-0.82\pm 0.02$, $T=0.08\pm 0.02$, and
$t_{\mathrm{s}}\sim 2\times 10^{5}$ yr. Although the model flux density well
reproduces the observed value at 237 GHz in this case, it slightly exceeds the
observation at 44 GHz (blue curve in the top panel of Fig. 3). Naturally, one
will expect a further steepening of the spectrum slope due to both synchrotron
ageing and IC loss, and thus, at 237 GHz, the synchrotron radiation is
supposed to have a much lower flux density than the currently observed value.
Considering that the 237 GHz data lies within the FIR regime at the rest-
frame, a reasonable explanation is that the sub-component perfectly coincided
with the SE hotspot and observed in ALMA Cycle 6 may be contaminated from
thermal bremsstrahlung and/or the Rayleigh-Jeans tail of the thermal dust
emission. Another explanation is that, as we will see in §5.2 and §5.4, this
may be a result that the undetected diffuse radio lobes have contaminated low-
resolution observations such that the observed flux densities of the SE
hotspot at $\leq 8.2$ GHz used for the fitting are over-assumed. Accordingly,
at 44 GHz, the true spectral slope should be shallower than the current one
and steepens towards 237 GHz.

The First-order Fermi Acceleration, or diffusive shock acceleration (DSA), is
one important mechanism for particle acceleration due to jet-medium
interaction (Carilli et al., 1991; van Weeren et al., 2019). In a non-
relativistic shock acceleration case, the injection index can be expressed by
the compression ratio $\chi$ of downstream to upstream proper particle
densities (Dermer & Menon, 2009). For a strong shock with velocity $u\gg
c_{s}$, where $c_{s}$ is the sound speed, in a uniform ISM, $\chi=4$,
corresponding to $\alpha_{\mathrm{inj}}=-0.5$. For the SE hotspot, without 237
GHz data, the calculated $\alpha_{\mathrm{inj}}=-0.51$ agrees well with this
scenario. While for $\alpha_{\mathrm{inj}}=-0.59$ found in the NW hotspot, the
shock dynamics may be altered by the relativistic particles slightly (Carilli
et al., 1991). When the ALMA 237 GHz data is considered, the SE hotspot has
$\alpha_{\mathrm{inj}}=-0.82$, which is significantly different from the
values expected for the case above. Based on current observations, we cannot
decompose the 237 GHz data into different emission mechanisms which may
contaminate the observed flux density of pure synchrotron radiation. As a
result, the modeled flux density at 237 GHz and its corresponding
$\alpha_{\mathrm{inj}}=-0.82$ can be an overestimation. We further fitted the
spectrum with fixed $\alpha_{\mathrm{inj}}$ and found that as
$\alpha_{\mathrm{inj}}$ increases, $T$ and $\nu_{\mathrm{br}}$ decrease (see
Fig. 3). Therefore, albeit there can be a mixture of different emission
mechanisms, in this case, we treat the current fitting up to 237 GHz data with
$\alpha_{\mathrm{inj}}=-0.82$ as a lower limit for the synchrotron age.
Moreover, if $\alpha_{\mathrm{inj}}=-0.82$ is robust, it may reflect
significant environmental differences between SE and NW hotspots. The SE
hotspot might reside in a denser environment such that the fluid velocity of
upstream relativistic particles ${v}_{\mathrm{up}}$ becomes smaller, resulting
in a decrease in $s$ which is given by
$s=\frac{2+\chi}{\chi-1}=\frac{v_{\mathrm{up}}+2v_{\mathrm{down}}}{v_{\mathrm{up}}-v_{\mathrm{down}}}$,
where ${v}_{\mathrm{down}}$ is the downstream fluid velocity (Dermer & Menon,
2009). Accordingly, the injection spectral index steepens.

The synchrotron ages of both NW and SE hotspots have an order of $10^{5}$ yr,
lying within the order of magnitude $10^{3}-10^{5}$ yr observed in typical CSS
sources that are argued to be related to AGNs at an early evolution stage
(O’Dea, 1998; Murgia, 2003). Since a remnant fraction is essential to fit the
observed curved SED by a CI model, the RLAGN hosted by the Dragonfly galaxy is
not only young but may also have intermittent or transient activities. This
may indicate that the central SMBH is in a transition phase towards an active
one because the gas inflow arising from the merging events fuels the SMBH
growth.

##  5 Discussions

In this section, we first discuss the Doppler boosting effect because of the
highly imbalanced flux densities between the SE and NW hotspots. However, the
flux ratio of SE to NW changes from $S_{\text{SE}}/S_{\text{NW}}\approx 15:1$
at 4.7 and 8.2 GHz to $S_{\text{SE}}/S_{\text{NW}}\approx 6:1$ at 44 GHz,
suggesting that there is contamination in low-resolution observations and/or
the intrinsic flux densities of the SE and NW hotspots may differ. We then
discuss the possible scenarios. Next, considering the proximity of the sub-
component to the SE galaxy, we discuss the energetic input of the radio jet
into the ISM. Finally, we discuss the caveats to the results and conclusions
we make in this work.

###  5.1 Doppler Boosting?

The radio core and the SE and NW hotspots are well aligned in a straight line.
However, the flux densities between SE and NW hotspots are highly imbalanced.
This feature may be a result of the significantly different environments
between SE and NW hot spots, which is an implication of the fitting results of
the SE hot spot including ALMA 237 GHz data. If this is the case, adopting
equation (9) in Araudo et al. (2019), the upstream energy density of
relativistic electrons of the SE hotspot can be larger than that of the NW one
by an order of magnitude. However, an investigation into the detailed
environments is impossible with the current data set.

Here we consider the Doppler boosting effect as another scenario to explain
the flux density imbalance. In this case, the SE hotspot is associated with
the approaching jet while the NW one, as the counterpart, is associated with
the receding jet. Therefore, the SE hotspot has its observed flux density
Doppler boosted arising from relativistic beaming, and the NW hotspot is
dimmed accordingly (Condon & Ransom, 2016). On the other hand, the global
structure is not perfectly symmetric since the projected distance between the
hotspot and radio core is $l\mathrm{{}_{SE}=0\aas@@fstack{\prime\prime}472\sim
4\ kpc}$ for SE and $l\mathrm{{}_{NW}=0\aas@@fstack{\prime\prime}678\sim 5.8\
kpc}$ for NW hotspot. This can be explained by a misalignment angle between
the two jets because the initially inclined jet may interact with the gas in
the circumnuclear disk, resulting in a further bending of the jet (Mukherjee
et al., 2018; García-Burillo et al., 2019; Talbot et al., 2022). This can also
be explained by that the SE jet has encountered the ISM of the SE galaxy,
resulting in a shorter jet-traveled distance compared with the NW jet that may
interact with the intergalactic medium.

The enhancement or dimming of the intrinsic flux density is dependent on the
spectral index and Doppler factor $\delta$ (see discussion in §5.3) which is
determined by the inclination angle and advance speed of the jet head. With
observations of NW and SE hotspots at multiple frequencies, the flux density
ratios of the approaching and receding one provide constraints on the
parameter space of jet geometry. Denote the flux density ratio by $R$, one can
expect (Kappes et al., 2019; An et al., 2012)

$R=\frac{S_{\mathrm{adv}}}{S_{\mathrm{rec}}}=\frac{S_{\mathrm{SE}}}{S_{\mathrm{NW}}}=\left(\frac{1+\beta\cos{\theta}}{1-\beta\cos{\theta}}\right)^{3-\alpha},$
(5)

where $\theta$ is the inclination angle of the approaching jet relative to
LOS, $\beta=v/c$ is the advance speed of jet head in the unit of light speed,
and $\alpha$ is the spectral index, defined as $S_{\nu}\propto\nu^{\alpha}$.

Since there are two values of ratios dependent on the frequency, that is,
$R\sim 15$ at $\nu_{\mathrm{obs}}=4.7$ and 8.2 GHz and $R\sim 6$ at
$\nu_{\mathrm{obs}}=44$ and 237 GHz 333The values of $\alpha$ for each hotspot
at 8.2, 44, and 237 GHz follow those listed in Table. 2, and $\alpha=-1.13$ is
assumed for both hotspots observed at 4.7 GHz. The NW hotspot is not detected
in ALMA Band 6. We assumed an upper limit of the NW component based on
$3\sigma$ level to estimate the flux ratio at 237 GHz, which gives
$S\mathrm{{}_{NW,237GHz}=0.0194\ mJy}$., we find two ranges for $\beta$: $\sim
0.2$c$-0.3$c for $R\sim 15$ and $\sim 0.1$c$-0.2$c for $R\sim 6$. Both ranges
are in agreement with powerful FRII radio galaxies that have $\beta$ varying
within 0.1c – 0.5c with mildly relativistic jets and giant radio lobes (Bondi
et al., 2008; O’Dea et al., 2009). Therefore, a mildly relativistic scenario
is valid regardless of the exact value of the flux density ratio.

###  5.2 Bi-modal Flux Ratios

Since the low-resolution VLA 4.7 and 8.2 GHz observations have much larger
flux ratios $(S_{\mathrm{SE}}/S_{\mathrm{NW}}\sim 15:1)$ compared with high-
resolution and high-frequency VLA 44 GHz observations
$(S_{\mathrm{SE}}/S_{\mathrm{NW}}\sim 6:1)$, we consider several possibilities
to explain this difference.

First, the low-frequency radio emission of the SE hotspot is contaminated by
the synchrotron radiation, which is attributed to the cosmic-rays accelerated
in the supernova remnants, and free-free emission, which originates from H ii
regions, from the SE galaxy located at $\sim 1$ kpc away. Although the
Dragonfly galaxy is a starburst galaxy, its observed radio luminosities at 4.7
and 8.2 GHz are well beyond the star formation-powered synchrotron regime
(Kellermann et al., 2016). Following Condon (1992), we estimated the thermal
and non-thermal flux densities associated with star formation at 8.2 GHz, with
a spectral index ${\alpha}_{\mathrm{non-thermal}}=-0.75$,
${\alpha}_{\mathrm{thermal}}=-0.1$, and $\mathrm{SFR\sim 3000\
M_{\odot}yr^{-1}}$ (Paper II; Zhong et al. in prep.). The resulting
$S_{\nu,\text{non-thermal}}\sim 0.07$ and $S_{\nu,\text{thermal}}\sim 0.11$
mJy are smaller than the observed flux density by more than two orders of
magnitude. Hence this scenario can be undoubtedly rejected.

Radio core is the second possibility, but can be immediately rejected because
the core component in general shows flatter spectral indices relative to radio
hotspots and lobes (Kellermann et al., 1994; Zajaček et al., 2019). Assuming
$\alpha_{\mathrm{core}}=-0.5$, the observed flux density $0.23$ mJy at 44 GHz
corresponds to $\sim 0.5$ mJy at 8.2 GHz and $\sim 0.7$ mJy at 4.7 GHz. This
explains why the core is only identified in high-sensitivity VLA 44 GHz
observation but remains non-detection in VLA 4.7 GHz and 8.2 GHz observations.

The third possibility is reflected in the spectral index between 8.2 and 44
GHz. By adopting $\alpha_{\mathrm{NW}}=-1.35$ instead of
$\alpha_{\mathrm{SE}}=-1.87$, the expected flux density of the SE hotspot at
44 GHz is $\sim 4.5$ mJy, and the corresponding flux ratio becomes
$S_{\mathrm{SE}}/S_{\mathrm{NW}}\approx 15$. Hence, it is clear that the
steeper slope of the SE hotspot results in a change in flux ratios. A
plausible explanation for this steepening is that, in VLA 4.7 and 8.2 GHz
observations, the unresolved SE component contains flux densities not only
from the SE hotspot but also the expanding radio lobes associated with it. At
44 GHz, the diffuse radio lobes are not fully imaged, leading to a significant
decrease in the observed flux densities linked to the SE hotspot. This is
supported by the low-resolution Australia Telescope Compact Array continuum
observation at 40 GHz that has a total flux density $S_{\nu}=5.1\pm 1.5$ mJy
(Lebowitz et al. 2023; Emonts et al., 2011), which is about twice the sum of
flux densities of the radio core and SE and NW hotspots observed at VLA 44
GHz.

Last but not least, the possibility that the intrinsic flux densities of SE
and NW hotspots may differ exists. In this scenario, this more rapid
steepening can be explained by that the SE hotspot has lost more energy at
higher frequencies compared with the NW one. As discussed in §4.2.2, this
might be a consequence that the SE jet has interacted with a medium with
higher density than the NW one, resulting in a steeper initial power-law
energy distribution of the injected electrons. An additional explanation is
that, due to the 3D geometry of the bipolar jets, the jet-traveled distance
has a projection onto the LOS. Then, the total projection will be
$l_{\text{LOS,total}}=l_{\text{LOS,NW}}+l_{\text{LOS,SE}}$. This is an
additional light-traveled distance for the synchrotron radiation from the NW
hotspot. Accordingly, the NW hotspot is intrinsically younger than the SE one
by $l_{\text{LOS,total}}/$c yr at the time of observation, and thus has a
higher magnetic field strength than the SE hotspot does.

###  5.3 The Possible Jet-ISM Interaction

A serendipitous discovery of ALMA Band 6 continuum imaging is the sub-
component adjacent to the SE galaxy and coincides with the location of the SE
hotspot. The radio continuum to the east of the SE galaxy is consistent with
the distribution of CO(6-5) line emission regions. However, west to the SE
galaxy, no line emission has been detected around the SE hotspot and only the
continuum is detected as the sub-component in high-resolution observations,
while extended CO(6-5) line emission is found at this location in the low-
resolution observation (Lebowitz et al. 2023; Paper II; Zhong et al. in
prep.). Additionally, there is only a faint rest-frame UV continuum at this
location. Furthermore, Emonts et al. (2015b) has found a giant molecular cloud
lying close to the propagation direction of the SE jet, offset from the jet
propagation axis by $\sim 0\aas@@fstack{\prime\prime}3$ and indicated by the
Companion in panel (a) in Fig. 1. Considering also the small offset ($\sim 1$
kpc) of the sub-component to the centroid of SE galaxy, this sub-component may
indicate an interaction between jet and ISM, through which the radio jet has
driven a massive molecular outflow.

To examine this scenario, we estimate the spatial separation of SE and NW
galaxies, which is $\sim 7$ kpc in the projected plane. Assuming this
Companion in the form of molecular gas that may reach an outflow velocity of
$\sim 1000$ km s-1 (Wagner et al., 2012), the Companion takes $\sim 7$ Myr to
travel such a distance. However, the upper limit of the lifetime of the SE
hotspot has an order of $10^{5}$ yr, suggesting that the bulk of the massive
molecular gas cannot be the outflow driven by the jet-ISM interaction.

Nonetheless, we can still estimate the intrinsic flux density of the SE
hotspot through $\delta^{2+\alpha}<S/S_{0}<\delta^{3+\alpha}$ (Condon &
Ransom, 2016), where $S$ is the observed flux density, $S_{0}$ is the
intrinsic flux density, $\delta\equiv[\gamma(1-\beta\cos\theta)]^{-1}$ is the
Doppler factor and $\gamma\equiv(1-\beta^{2})^{-1/2}$ is the Lorentz factor.
Using equation (4), we find the observed flux amplified by $\delta\sim 2$ and
$\delta\sim 3-4$ for $S_{\mathrm{SE}}/S_{\mathrm{NW}}\sim 6$ and
$S_{\mathrm{SE}}/S_{\mathrm{NW}}\sim 15$, respectively. Conservatively, at
$\mathrm{\nu_{obs}}\sim 1.4$ GHz, we assume that SE hotspot contributes to
$\sim 90\%$ of the total observed flux densities and Doppler boosted by a
factor of 2 as an upper limit, the corresponding intrinsic radio power is
$P_{\text{1.4GHz}}=(7.3\pm 1.9)\times 10^{43}\ \mathrm{erg\ s^{-1}}$.

Adopting an empirical correlation between the radio power at 1.4 GHz and the
kinetic power of the jet $P_{\mathrm{jet}}$ (Cavagnolo et al., 2010), the
approaching jet associated with the SE hotspot has a total jet kinetic power
$P\mathrm{{}_{jet}=(7\pm 9)\times 10^{46}\ erg\ s^{-1}}$. The total energy
injection for the ambient gas to be accelerated by the radio jet can be
estimated via an energy conservation argument (Nesvadba et al., 2006):

$M_{\mathrm{out}}=2\times 10^{11}E_{\mathrm{out,60}}v^{-2}_{\mathrm{esc,500}}\
\mathrm{M_{\odot}},$ (6)

where $E_{\mathrm{out,60}}$ is the energy of the outflow in units of $10^{60}$
ergs and $v^{-2}_{\mathrm{esc,500}}$ is the outflow velocity in units of 500
$\mathrm{km\ s^{-1}}$. Even taking a lower limit on the SE jet lifetime, the
total energy injection is $E\sim 1\times 10^{59}$ erg, suggesting that the jet
kinetic energy can result in a significant molecular gas outflow of
$M_{\mathrm{out}}\sim 7\times 10^{9}\ \mathrm{M_{\odot}}$ even reaching an
outflow velocity $\mathrm{\sim 1000\ km\ s^{-1}}$ for the most powerful jets
(Wagner et al., 2012). This may explain why there is merely diffuse CO(6-5)
line emission in the west of the SE galaxy, that is, the molecular gas has
been blown away by the jet-ISM interaction through the jet kinetic power, and
the gas has been excited to higher excitation levels through the jet thermal
power.

The jet-driven large-scale molecular outflows (${M}_{\mathrm{H_{2}}}\sim
10^{9-10}\ \mathrm{M_{\odot}}$), which indicates a removal of a significant
fraction of the ISM from the AGN host galaxy, have been observed in some
massive galaxies ($M_{\star}\sim 10^{11}\ \mathrm{M_{\odot}}$) at high
redshifts (e.g., Nesvadba et al., 2006; Nesvadba et al., 2007, 2017; Emonts et
al., 2023). However, a jet-ISM interaction in the Dragonfly galaxy discussed
here happens between the jet and the merging pair (SE galaxy) of its host
galaxy (NW galaxy), making it a unique sample at high redshifts without
parallels. A detailed investigation into the AGN feedback and its associated
outflow traced by CO(6-5) line emission through an interaction of the jet and
the ISM of the NW galaxy will be presented in Paper II.

###  5.4 Caveats

The interpretation of the remnant fraction should be careful. It may simply
indicate that the jet has been switched off and the jet-medium interaction has
ceased at the observation timing, which is a general understanding of non-zero
remnant fraction in the CI model (Murgia et al., 2011; Turner, 2018; Maccagni
et al., 2020). We further speculate on the interpretation of the remnant
fraction in our work considering the complexity of the particle acceleration
in realistic models. The radio source may have experienced a quiescent time-
scale after the first phase of continuous acceleration, following a second
phase in which the restarted radio jets interact with the medium again and
replenish a new population of relativistic electrons. In this restarting
scenario, if the restarted jet reaccelerates the particles universally, then
the entire radio spectrum will be altered and the break frequency no longer
traces the time-scale since the initial acceleration begins (Carilli et al.,
1991). In this case, a flattening in radio SED at high frequencies will be
observed because of the accelerated electrons. However, this feature is not
found in our target. Then, the restarted jet could happen shortly before the
observation timing or it is not sufficiently powerful to alter the ensemble of
synchrotron-emitting electrons. Therefore, compared with those dying radio
sources, which have been inactive for a long period with ${t}_{\mathrm{s}}\sim
10^{6}-10^{7}$ yr, ${B}_{\mathrm{eq}}\sim\text{tens}\ \mu$G, and remnant
fraction of $T\geq 0.2$, the small remnant fraction found in the Dragonfly
galaxy indicates that this CSS source may have experienced a past radio
activity, and our conclusion that the RLAGN may have transient or intermittent
activities remains unchanged.

We note that the age estimations of the radio hotspots can be uncertain
because of the magnetic field strengths, ambient medium densities, and volumes
of hotspots. Additionally, the contribution of the diffuse radio lobes to the
low-resolution flux densities cannot be measured with the current
observations. Furthermore, the exact flux ratio between the two hotspots
cannot be determined unambiguously because of the limited resolution and
sensitivity throughout all observations. As a consequence, the true spectral
shapes of NW and SE hotspots will change together with the flux densities of
the lobes and flux densities ratios at $\nu\leq 8.2$ GHz. Hence, the obtained
synchrotron age is just an order of magnitude estimation.

We show the distributions of the best-fit parameters under the assumptions
that, at low frequencies, the fractional contamination of diffuse emissions to
the observed flux densities ranges from 1 to 55 per cent by a step of 1, and
flux ratios vary from 4 to 15 by a step of 1, in Fig. 7. Based on the current
estimate of ${B}_{\mathrm{eq}}$, unless $\log{\nu}_{\mathrm{br}}$ is smaller
than 8.1 (corresponding to $\sim 150$ MHz), the age cannot exceed $10^{5}$ yr.
A very low break frequency smaller than 150 MHz is not expected for all the
fittings, suggesting that the conclusion of a young radio source is not
sensitive to the limited number of data points and uncertain contaminations
and flux ratios. Although a non-zero remnant fraction is favored in most
fittings, when the SE hotspot is fitted only up to 44 GHz, a zero remnant
fraction does happen in some cases. These are unavoidable uncertainties in
this work due to the limited resolved low-frequency observations and possibly
contaminated 237 GHz data, by which we cannot constrain the real spectral
shapes. Future observations are essentially required to decompose the ALMA 237
GHz data and fill the gap between 44 and 237 GHz to confirm whether the
curvature is robust and in need of a non-zero remnant fraction to interpret.
We, therefore, emphasize the importance of high-frequency observations which
can help us investigate the aging problem of radio sources. We also note the
importance of multi-frequency data since the limited number of data points can
dilute the curvature of the radio SED, leading to further uncertainties in the
estimation of the remnant fraction.

##  6 Conclusion

In this work, we have studied the synchrotron radiation from the radio
hotspots in the Dragonfly galaxy, a hyper-luminous infrared galaxy at $z=1.92$
using joint VLA and ALMA observations. Our major findings are as follows:

  1. 1.

The NW hotspot, SE hotspot, and radio core constitute the synchrotron
radiation from the Dragonfly galaxy and the SE hotspot dominates the observed
flux density. The synchrotron source has a projected linear size of $\sim 13$
kpc and $\alpha<-0.5$ at $\nu_{\mathrm{obs}}\geq 365$ MHz, being classified as
a CSS source.

  2. 2.

ALMA Band 6 observation catches a sub-component offset from the SE galaxy by
$\sim 1$ kpc and coincided perfectly with the location of the SE hotspot. This
sub-component may be a mixture of different emission mechanisms, including
synchrotron radiation, thermal bremsstrahlung, and Rayleigh-Jeans tail.

  3. 3.

The NW hotspot has a synchrotron age $t_{\mathrm{s}}\sim 2-3\times 10^{5}$ yr,
while the SE one can vary amongst $t_{\mathrm{s}}\sim 2-4\times 10^{5}$ yr.
These age estimates agree with typical orders of magnitude observed in CSS
sources related to radio AGNs that are robustly young. Furthermore, the
fittings of both hotspots may indicate that the radio jets have been switched
off at the observation timing, or that the RLAGN has past radio activities and
re-launched radio jets that are not powerful enough to alter the energy
density of high-frequency synchrotron-emitting electrons. This suggests that
this RLAGN may have transient or intermittent activities because the central
SMBH of the AGN residing in the NW galaxy is possibly in a fast transition
phase.

  4. 4.

The NW hotspot has an $\alpha_{\mathrm{inj}}=-0.59$ and the SE one has
$\alpha_{\mathrm{inj}}=-0.51$ in fittings without ALMA 237 GHz data, both
consistent with the values expected for the first-order Fermi acceleration.
When the 237 GHz data is considered, the SE hotspot has
$\alpha_{\mathrm{inj}}=-0.82$. If this value is correct, it may indicate that
the particle acceleration in the SE hotspot may not simply be explained by the
first-order Fermi acceleration for a non-relativistic strong shock in a
uniform-density ISM, reflecting an environmental difference between the NW and
SE hotspots. However, because of the limited resolution, the possibility that
this difference is a result of the contaminated 237 GHz and low-frequency data
exists.

  5. 5.

The observed flux ratios between the SE and NW spots indicate that the
intrinsic flux density of the SE hotspot has been Doppler boosted as a result
of the smaller inclination angle of the radio jet relative to the LOS, while
the NW one dimmed. The SE (NW) hotspot then corresponds to the approaching
(receding) jet. The advance speed of the jet head ranges from $\sim$0.1c –
0.3c, in agreement with the mildly relativistic jet case observed in typical
FRII galaxies.

  6. 6.

If the sub-component identified in ALMA Cycle 6 observation indicates an in
situ jet-ISM interaction, the jet can drive a massive molecular gas outflow
within its lifetime and excite the CO gas to higher rotational transition
levels, providing an explanation for the extended and diffuse CO(6-5) line
emission on the west side of the SE galaxy, as well as the steep
$\alpha_{\mathrm{inj}}$ found in the SE hotspot fitted by the CI model.

The remnant fraction is robust for a reproduction of the curvature of the
observed radio SED, suggesting that this RLAGN may have transient or
intermittent activities. Considering also its young age, this suggests that
high-redshift RLAGNs may have short duty cycles because of the stochastic
accretion flows onto SMBHs. Still, this requires a larger sample to confirm.
We note the importance of high-frequency observations to investigate the
behavior of radio-loud AGNs at high redshifts to understand when they interact
with their ambient medium, such that we can gain a more complete view of AGN-
host galaxy co-evolution.

The sub-component adjacent to the SE galaxy may be a chance alignment.
Otherwise, this HzRG is a merging galaxy in which the radio jet launched from
the AGN interacts with the merging pair of the AGN host galaxy. There are only
a few cases of such kind of a system observed at lower redshifts (e.g., Hota
et al., 2022) and this galaxy may be the first one identified at high
redshifts. Therefore, subsequent observations, including both radio and
optical observations, are required to confirm this scenario, as well as to
decompose the different emission mechanisms at 237 GHz.

## Acknowledgements

We thank the staff in ALMA and NRAO helpdesk for their kind help in data
calibration and reduction. We thank Bjorn Emonts and Sophie Lebowitz for
sharing their paper before it becomes public. We also thank Niinuma Kotaro for
his comments. This paper makes use of the following VLA data: VLA/15A-316 and
VLA/17B-444. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2016.1.01417.S and ADS/JAO.ALMA#2018.1.00293.S. Data analysis was
carried out on the Multi-wavelength Data Analysis System operated by the
Astronomy Data Center (ADC), National Astronomical Observatory of Japan. AKI,
YS, and YF are supported by NAOJ ALMA Scientific Research Grant Numbers
2020-16B. ALMA is a partnership of ESO (representing its member states), NSF
(USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan),
and KASI (Republic of Korea), in cooperation with the Republic of Chile. The
Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National
Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.

Software: python (Van Rossum & Drake, 2009), matplotlib (Hunter, 2007),
astropy (Astropy Collaboration et al., 2013, 2018, 2022), synchrofit (Turner,
2018; Turner et al., 2018), carta (Cube Analysis and Rendering Tool for
Astronomy, Comrie et al., 2021), numpy (Harris et al., 2020), and scipy
(Virtanen et al., 2020).

## Data Availability

The ALMA data used in this work are publicly available at
https://almascience.nao.ac.jp/aq/. The VLA data used in this work are publicly
available at https://data.nrao.edu.

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##  Appendix A Fitted Parameters of Synchrofit

We show the corner plots of the break frequency $\nu_{\mathrm{br}}$, injection
index $s$ (the injection spectral index is calculated by
$\alpha_{\text{inj}}=(1-s)/2$), and remnant fraction $T$ fitted by synchrofit
in Fig. 4. For comparison, we show the fittings with and without 74 MHz data
in the left and right columns, respectively. A shallower slope from 147 MHz
towards 74 MHz has no significant impact on the fitted free parameters.

To investigate the impact of diffuse radio emissions on the fitting results
and their implications for the young AGN and transient or intermittent radio
activities, we performed more fittings assuming a flux ratio of
${S}_{\mathrm{SE}}:{S}_{\mathrm{NW}}=6:1$. We further assume that the diffuse
radio emission accounts for $\sim$50 per cent of the total observed flux
densities at GHz. And at 4.7 and 8.2 GHz, the flux density of the SE hot spot
is then six times the NW one. The corresponding fitting results are shown in
Fig. 5 and Fig. 6. We have also performed a fitting using only 4 data points
following the same flux ratio as above to test whether the algorithm can still
constrain the physical parameters. The corresponding fitting result in shown
in the right panel of Fig. 5. We further perform fittings assuming that the
fraction of lobe contamination ranges from 1 to 55 per cent by a step of 1,
and the flux density ratio varies from 4 to 15 by a step of 1 at low
frequencies. The statistics of the fitted parameters are shown in Fig. 7.

(a) NW hotspot, starts from 74 MHz.

(b) NW hotspot, starts from 147 MHz.

(c) SE hotspot without ALMA data, starts from 74 MHz.

(d) SE hotspot without ALMA data, starts from 147 MHz.

(e) SE hotspot with ALMA data, starts from 74 MHz.

(f) SE hotspot with ALMA data, starts from 147 MHz.

Figure 4:  Corner plots of the fitted parameters for comparisons between
fittings with and without 74 MHz data.

(a) Fitting of the NW hotspot assuming a flux ratio of 6:1

(b) Fitting of the NW hotspot assuming a flux ratio of 6:1. Only flux
densities at 1.4, 4.7, 8.2, and 44 GHz are used.

Figure 5:  Corner plots of the fitted parameters of the NW hot spot for
comparisons between fittings using 6 and 4 data points, respectively. Although
there is a relatively large difference between the injection indices, the
break frequency and remnant fraction do not significantly differ. These
fitting results, compared with those presented in the main text, do not
contradict the conclusions that the AGN is young and may have transient or
intermittent activities. We do note that because the limited number of data
points used in the right one dilutes the curvature of the observed SED, a
smaller remnant fraction is returned.

(a) SE hotspot without ALMA data, assuming a flux ratio of 6:1.

(b) SE hotspot with ALMA data, assuming a flux ratio of 6:1.

Figure 6:  Corner plots of the fitted parameters of the SE hot spot for
comparisons between fittings with and without ALMA 237 GHz data, assuming a
flux ratio of 6:1 and subtracting possible contaminations from the low-
resolution observations. The injection index fitted without ALMA data, similar
to the case of a flux ratio of 15:1 without considering contamination, is
larger than that of the fitting with ALMA data. Compared with the fittings
presented in the main text, the break frequency can slightly migrate towards
lower frequencies and there is a shorter time-scale of the quiescent phase.
However, these differences do not alter the conclusions we make in the main
texts, that is, the AGN is young and may have transient or intermittent
activities. Figure 7: Fitting results of NW and SE hotspot assuming the
fractional contamination of diffuse radio emission ranging from 1 to 55 per
cent by a step of 1 per cent and flux ratios ranging from 4 to 15 by a step of
1 to estimate the low-frequency flux densities.