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

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.

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.

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.

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.

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.

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)

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),

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.

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.

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)

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.

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.

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):

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.

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.