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ABSTRACT Low-frequency radio observations show an increasing number of radio galaxies located in galaxy clusters that display pe- culiar morphologies and spectral profiles. This is the result of the dynamical interaction of the galaxy with the surrounding medium. Studying this phenomenon is key to understanding the evolution of low-energy relativistic particles in the intracluster medium. We present a multi-frequency study of the three head-tail (HT) radio galaxies and the radio halo in the galaxy cluster ZwCl0634.1+4747. We make use of observations at four frequencies performed with LOFAR LBA (53 MHz), HBA (144 MHz), GMRT (323 MHz) and VLA (1518 MHz) data. The use of extremely low radio frequency observations, such as LOFAR at 53 and 144 MHz, allowed us to detect the extension of the tails up to a distance of ∼ 1 Mpc. We extracted spectral profiles along the tails in order to identify possible departures from a pure ageing model, such as the Jaffe-Perola (JP) model, which only involves synchrotron and inverse-Compton losses. We found clear evidence of departures from this simple ageing model, such as surface brightness enhancement and spectral flattening along all of the tails. This can be interpreted as the consequence of particle re-acceleration along the tails. Possible explanations for this behaviour include the interaction between a shock and the radio tails or a turbulence-driven re-acceleration mechanism. We show that the latter scenario is able to reproduce the characteristic features that we observed in our profiles.
Key words: galaxies: clusters: general – radio continuum: galaxies – radio continuum: ISM
Galaxy clusters host a large variety of radio emission, generally divided between diffuse radio sources (van Weeren et al. 2019) and radio galaxies (Hardcastle & Croston 2020). These non-thermal emissions are the results of relativistic cosmic-ray electrons (CRe) interacting with the cluster or galactic magnetic field.
Radio galaxies in clusters of galaxies usually show distorted mor- phologies (O’Dea & Owen 1985; Feretti & Giovannini 2008; Garon et al. 2019), because of the dynamical interaction between the ra- dio jets and the surrounding dense (𝑛e ∼ 10−2 − 10−4 cm−3), hot (107 − 109 K) intra-cluster medium (ICM). The first morphological classification by Owen & Rudnick (1976) is based on the angle be- tween the radio tails and the core of the galaxy (see also Miley 1980, for a review). Narrow-angle tails (NATs; Venkatesan et al. 1994; Fer- etti et al. 1998) have angles between the two jets smaller than 90◦, because of the high ram pressure they experience that leads to the narrow V- or L-shape they assume. Wide-angle tails (WATs; Klamer
et al. 2004; Mao et al. 2010) show C-type morphologies with angles between the two tails greater than 90◦ but smaller than 180◦. They are usually thought to experience weaker ram pressure, caused by low velocities relative to the cluster centre and/or lower density of the surrounding ICM. Among these types, we focus on the head-tail (HT) radio galaxies (Ryle & Windram 1968; Hill & Longair 1971; Miley 1973; Sebastian et al. 2017; Cuciti et al. 2018; Srivastava & Singal 2020; Lal 2020; Müller et al. 2021; Botteon et al. 2021), NATs whose distinctive feature is a very elongated structure formed by the radio jets. In HT radio galaxies, both jets are bent in the same direc- tion and thus it is not always possible to resolve them. Their radio surface brightness usually peaks close to the host (optical) galaxy and gradually decreases along the tail that can reach up to hundreds of kiloparsecs (e.g., Srivastava & Singal 2020; Botteon et al. 2021). Their spectral index becomes steeper, moving from the core towards the tail (e.g., Cuciti et al. 2018; Wilber et al. 2018), while the frac- tional polarisation increases along the jets (Feretti et al. 1998; Müller et al. 2021), reflecting an increase of the degree of ordering of the magnetic field. However, after the jets are launched into the ICM, relativistic electrons are visible only for tens of Myrs at GHz fre-
quencies because of their energy losses, owing to synchrotron and Inverse-Compton (IC) emission. Thus, these tails left behind by the galaxy moving within the cluster are expected to fade quickly, be- coming invisible at high frequencies. Because of the longer cooling times of low-energy CRe, low-frequency observations are crucial for identifying and tracing CRe for much longer.
In fact, with the advent of low-frequency (< 1 GHz) radio astron- omy, tails extending to very long distances have become more com- mon and can be studied in detail (Sebastian et al. 2017; Wilber et al. 2018; Botteon et al. 2021; de Gasperin 2017; Edler et al. 2022). In this context, the LOw-Frequency Array (LOFAR; van Haarlem et al. 2013a), being the largest and most sensitive radio-interferometer in the 10-240 MHz regime, has made many recent contributions to the field (e.g. Mandal et al. 2020; Pal & Kumari 2023).
Moreover, in some cases the tails show peculiar properties, such as an increase in surface brightness and flattening of the spectral index along the tail (e.g., Sĳbring & de Bruyn 1998; Parma et al. 1999; Giacintucci et al. 2007; de Gasperin 2017). To explain such behaviours far from the host galaxy, the presence of re-energetization processes has been proposed. In fact, re-acceleration of CRe would be able to power the population of aged electrons initially injected by the AGN, making them visible at larger distances, where they would be expected to disappear owing to radiative losses. For ex- ample, de Gasperin (2017) proposed a re-acceleration mechanism invoking turbulence driven into the tail by interactions with the ICM. This would create the so-called gently re-energized tail (GReET; de Gasperin 2017; Edler et al. 2022) sources. Müller et al. (2021) sug- gest the transition from laminar to turbulent flow as the cause of gentle re-acceleration of the electrons along the tail. They also point out that for complex morphologies, more than one AGN cycle, i.e. a change in the injection rate, must be taken into account to explain the entire appearance of the jets. In other cases, adiabatic compression (Enßlin & Gopal-Krishna 2001; Enßlin & Brüggen 2002) would be able to form radio phoenices, revived fossil plasma from old radio lobes. Radio phoenices usually show an irregular morphology, steep spectral index (𝛼 ∼ < −1.5 with the 𝑆𝜈 ∝ 𝜈 𝛼 for the synchrotron emission) and curved integrated spectra (Kempner et al. 2004; van Weeren et al. 2009, 2011; de Gasperin et al. 2015; Mandal et al. 2019; Duchesne et al. 2021; Pasini et al. 2022). A first attempt to systematically study radio phoenices was performed by Mandal et al. (2020). They found a non-uniform spectral index across the sources, suggesting a possible mix of cosmic-ray populations with different ages, losses, and re-acceleration efficiencies. Regardless of the type of mechanism that generates them, sources that trace re-energised AGN radio plasma are characterized by very steep spectra. Thus, low-frequency facilities, such as LOFAR, are ideal to study these phenomena.
An increasing number of galaxy clusters is also observed to host diffuse Mpc-scale sources, called radio halos (see van Weeren et al. 2019, for a review). Radio halos are steep spectrum (𝛼 < −1.1), centrally located sources, whose morphology roughly follows the distribution of the thermal ICM. Turbulent re-acceleration is thought to be the main mechanism responsible for generating radio halos (see e.g., Brunetti & Jones 2014). In this scenario, a population of seed particles are re-accelerated by turbulence generated in the ICM dur- ing cluster mergers. Thus, the presence of radio halos is connected to the merging history of the systems and the cluster mass, which sets the available energy budget during mergers. Observational ev- idences for this scenario are the connection between the dynamical status of the cluster and the presence of radio halos (Buote 2001; Cassano et al. 2010; Cuciti et al. 2015, 2021) and the correlation between radio halos power and the mass of the host cluster (Cassano
et al. 2013; Cuciti et al. 2021; van Weeren et al. 2021; Duchesne et al. 2021; Cuciti et al. 2023). A key prediction of the turbulent re-acceleration model is that the cutoff in the synchrotron spectrum scales with the energetics of the merger (e.g., Cassano & Brunetti 2005; Cassano et al. 2006). This means that more massive systems suffering major mergers, host radio halos visible up to ∼GHz fre- quencies, while less massive systems and/or minor mergers produce radio halos with steeper spectra (𝛼 < −1.5), preferentially detectable at lower frequencies. These are generally referred to as Ultra-Steep Spectrum radio halos (USSRH; Brunetti et al. 2008).
ZwCl 0634.1+4747 is a massive (𝑀500 = (6.65 ± 0.33) × 1014 M⊙, Planck Collaboration et al. (2016)) nearby (𝑧 = (2017)) galaxy cluster located at et 0.174, Rossetti ′ R.A.(J2000) 06h38m02s.5 , DEC.(J2000) + 47◦ 47 , also known as PSZ1 G167.64+17.63/ PSZ2 G167.67+17.63, CIZA J0638.1+4747, MCXC J0638.1+4747 or RXC J0638.1+4747. Chan- dra X-ray observations show evidence of a non-relaxed dynamical state, such as the presence of substructures in the X-ray surface brightness distribution (Cuciti et al. 2015). The morphology of the cluster is elongated in the east-west direction (see Fig. 1).
ZwCl 0634.1+4747 hosts a variety of peculiar radio sources. A radio halo was already detected at 323 and 1518 MHz by Cuciti et al. (2018). It extends over ∼600 kpc in the E-W direction following the morphology of the X-ray emission of the cluster. More recently, a radio megahalo has been discovered in this system using LOFAR 144 MHz observations (Cuciti et al. 2022). The megahalo covers the whole cluster volume, with a linear size of 2.8 Mpc and an integrated spectral index between 53 and 144 MHz of 𝛼 = −1.62 ± 0.25. In addition, LOFAR observations clearly revealed the presence of three head-tail (HT) radio galaxies in the cluster field, with ∼ 0.6 − 1 Mpc linear size, labelled HT-A HT-B and HT-C in Fig. 2, which are the focus of this paper. The HT-B has been studied at high frequency (323 and 1518 MHz) by Cuciti et al. (2018). Possible signs of re-energetisation have been found through the analysis of the spectral index and surface brightness along the tail. In that case, the interaction between the tail and a shock has been proposed to explain the emission.
In this paper we present a multi-wavelength radio study of the galaxy cluster ZwCl 0634.1+4747, combining data from 53 MHz to 1.5 GHz. First, we focus our analysis on the three extended HT radio galaxies residing in ZwCl 0634.1+4747 (Section 3.1). We produce flux density and spectral index profiles along the tails of the HT radio galaxies (Section 3.1), comparing them with a standard ageing model (Section 3.2). In Section 3.3 we complement the analysis of the cluster with X-ray information using XMM-Newton data. Additionally, we present a new study of the radio halo down to the very-low frequencies in Section 3.4. In Section 4, we discuss possible scenarios that involve the interaction of HT radio galaxies with the external ICM. We summarize our results in Section 5.
the paper we adopt a ΛCDM cosmology with H0 = 70 km s−1Mpc−1, ΩΛ = 0.7 and Ω𝑚 = 0.3. Thus, 1′′ cor- responds to a physical scale of 2.95 kpc at the redshift of ZwCl 0634.1+4747. We use the convention 𝑆𝜈 ∝ 𝜈 𝛼 for the radio syn- chrotron emission, with 𝛼 < 0.
Figure 1. Background-subtracted exposure-corrected XMM image of ZwCl 0634.1+4747, in [0.5-2] keV band. The contour levels start at 3 · rms where rms = 5 · 10−6 cts s−1. As a size reference, green circle indicates 𝑅500 = 1299 kpc (Lovisari et al. 2017), namely the radius within which the mean mass over-density of the cluster is 500 times the cosmic critical density at the cluster redshift.
Figure 2. Composite radio-optical image of ZwCl 0634.1+4747. LOFAR HBA at 144 MHz superimposed on the DSS image (Pâris et al. 2014).
The data used in this work cover a broad range of frequencies, includ- ing The LOFAR Low Band Antennas (LBA) at 53 MHz, High Band Antennas (HBA) at 144 MHz, Giant Meterwave Radio Telescope (GMRT) at 323 MHz and Karl G. Jansky Very Large Array (VLA) at 1.5 GHz data. A summary of the observations used is listed in Table 1. GMRT and VLA data of this cluster were already analysed by Cuciti et al. (2018), while LOFAR LBA and HBA data are exten-
sively described is Cuciti et al. (2022). Thus, we briefly summarize the data reduction procedure in next sections.
This cluster was observed at ultra-low frequencies using LOFAR LBA for a total of 8 hours integration time in the frequency range 30 - 77 MHz, using the LBA_OUTER antenna configuration. Obser- vations were conducted using the multi-beam mode, with one beam continuously pointed at the calibrator and one beam at the target. First, following de Gasperin et al. (2019), the calibrator solutions are derived and applied to the target field together with the primary beam correction. The data of the target field were self-calibrated first for direction-independent, and then for direction-dependent effects (de Gasperin et al. 2020). Finally, the image quality was improved via extraction and self-calibration of a small region around the tar- get, adapting the procedure used for HBA analysis of van Weeren et al. (2021) for LBA data. The final model and solutions from the direction-dependent calibration are used to subtract sources outside a circular region of 23′ centered on the target. Then, the dataset is phase-shifted to the centre of this region, corrected for the primary beam in this direction and additional rounds of self-calibration on the target are performed to further improve the image quality. For more details on the data used, we refer the reader to Cuciti et al. (2022), where the observations used in this work were first presented.
The LOFAR HBA data used in this work are part of the LOFAR Two- metre Sky Survey (LoTSS; Shimwell et al. 2017, 2019, 2022), a low- frequency (120-168 MHz) radio survey of the northern sky. Data were processed through the Survey Key Science Project reduction pipeline v2.2 presented in Tasse et al. (2021); Shimwell et al. (2022), which includes direction-independent and direction-dependent calibration (prefactor (de Gasperin et al. 2019); killMS (Smirnov & Tasse 2015); DDFacet (Tasse et al. 2018)). Finally, the data sets have undergone the extraction procedure generally used for HBA observations to enhance the quality of the image (van Weeren et al. 2021; Botteon et al. 2022). For more details, we refer again to Cuciti et al. (2022), where the observations used in this work were firstly used.
A flux-scale correction factor 𝑓 = 0.992 has been applied to the nominal LOFAR HBA map values to align the images with the flux density scale of the LOFAR Two-Metre Sky Survey (Hardcastle et al. 2021; Shimwell et al. 2022).
ZwCl 0634.1+4747 has been observed with the GMRT at 320 MHz for a total time on source of ∼5 h (Cuciti et al. 2018). First, amplitude and gain corrections were calculated for the calibrator sources and then transferred to the target. Radio frequency interference (RFI) has been removed automatically using Common Astronomy Software Applications package (CASA McMullin et al. 2007) and the central 220 channels were averaged to 22 to reduce the size of the data-set. Finally, a few steps of phase-only self-calibration were performed to reduce phase variations. Moreover, similarly to the extraction pro- cedure, bright sources in the field of view were subtracted from the 𝑢v-data using the peeling method (see Cuciti et al. 2018, for more details on the data reduction of this dataset).
Table 1. Observational overview: LOFAR LBA, HBA, GMRT and VLA observation. References: (1) Cuciti et al. (2022), (2) Cuciti et al. (2018)
VLA L-band observations of ZwCl 0634.1+4747 include D and B array configuration with a total time on source of ∼45 and 40 mins respectively (Cuciti et al. 2018). First, the complex gain solutions for the calibrator sources (and the phase calibrator when present) on the full bandwidth were obtained, applying the bandpass and delay solution beforehand. Then, the calibration tables were applied to the target and an automatic radio frequency interference (RFI) removal was made using CASA. The 48 central channels of each spectral window were averaged to 6 to reduce the size of the data-set. All images were corrected for the primary beam attenuation.
After cycles of calibration and self-calibration on each array con- figuration, the B and D array observations were combined. Since the two pointings did not coincide perfectly, bright sources far from the phase center are subtracted separately for each spectral window from the 𝑢v-data before combining the data-set. The combined B+D array image is used for the HT analysis (Section 3.1), while the D array only is used for imaging the extended radio halo (Section 3.4).
Discrete sources embedded in the extended radio halo, contaminate the diffuse emission and thus, we proceeded to remove them. This allows to properly study the low surface brightness emission from the radio halo. Previous work (Cuciti et al. 2018, 2022) presented the source subtraction for the low frequency (53 and 144 MHz) and high frequency (323 and 1518 MHz) data set separately. To be consistent through our analysis, we apply the same source subtraction procedure for all four data sets. We describe here briefly the general process. First, we produced high (4′′ × 5′′) resolution images, to identify the compact sources. Then, we selected the corresponding components in the model image and we proceeded to remove them, subtracting these clean components directly from the 𝑢v−data. Finally, we im- aged the source-subtracted data sets at low angular resolution (see Fig. 3), maintaining a negative Briggs weighting with robust param- eter −0.25, using a common inner 𝑢v-cut of 135λ (equivalent to an angular scale of ∼ 25′), which corresponds to the shortest baseline of the VLA data set. Moreover, we taper down the long baselines (i.e., using Gaussian taper with a FWHM of 30′′) to gain sensitivity towards the diffuse emission. Throughout the paper, the images were created with WSClean soft- ware (Offringa et al. 2014). The uncertainty Δ𝑆 associated with a flux density measurement 𝑆 is estimated as
X-ray data for ZwCl 0634.1+4747 are available in the XMM-Newton Science Archive (XSA), OBSID 0692932601. The data reduction of the XMM-Newton data is performed using HEASoft version 6.29 (Nasa High Energy Astrophysics Science Archive Research Center (Heasarc) 2014) and the Science Analysis Software (SAS1) version 20.0.0. Hereafter, we provide a summary of the procedure. For a more extended description of the steps, the reader can refer to Veronica et al. (2022).
The first step consists of identifying Good Time Intervals (GTI), filtering out those that are affected by the presence of soft proton flares (SPF) (De Luca & Molendi 2004; Kuntz & Snowden 2008). This is achieved by creating a light curve for each of the three instru- ments of EPIC on board of XMM-Newton, namely MOS1, MOS2 and pn. For all instruments, we also generate count histograms. In the absence of SPF contamination the histogram is well fitted by a Poisson distribution. This allows us to estimate a mean value for the counts and apply a ±3𝜎 cut to discard the time intervals affected by flares and, for this reason, falling outside this range. Additionally, the IN/OUT ratio test (De Luca & Molendi 2004; Leccardi & Molendi 2008) allows us to further check the quality of our flare filtering pro- cedure by comparing the count rates within the FoV (IN) to those of the unexposed region of the detectors (OUT). An IN/OUT ratio close to 1 for each detector indicates that the contamination by SPF was successfully removed. After the SPF filtering procedure the exposure time is reduced from ∼ 21 ks to ∼ 13 ks for the MOS cameras and from ∼ 18 ks to ∼ 10 ks for pn. Note that MOS1-3 and MOS1-6 were not in use at the time of this observation. Moreover we model and rescale the instrumental background, eventually we subtract it to the observation of ZwCl 0634.1+4747 and obtain background subtracted and exposure corrected images (Fig. 1). The procedure for this step is extensively described in Ramos-Ceja et al. (2019) and Migkas et al. (2020).
Since we are interested in the diffuse X-ray emission associated with the ICM in ZwCl 0634.1+4747, we mask the point sources that contaminate the field of view. First, we apply an automated procedure described in Pacaud et al. (2006) which detects point sources and stores them in a catalog. Afterwards, we manually remove any further sources by looking at images in the soft (0.5-2 keV) and hard (2- 10 keV) X-ray bands. The surface brightness analysis, described in Sec. 3.3, is performed on the masked images.
where 𝑁beam = 𝑁pixel/𝐴beam is the number of independent beams in the source area, and 𝜎c indicates the systematic calibration error on the flux density. Typical values of 𝜎c are within 10% for LOFAR LBA (de Gasperin et al. 2021), HBA (Shimwell et al. 2022) and GMRT (e.g. Chandra et al. 2004), while 2.5% is used for VLA (Perley & Butler 2013).
The three HT galaxies in ZwCl 0634.1+4747 are all very extended and bright at lower frequencies (reaching up to ∼ 1 Mpc projected size at 144 MHz). They are spread over the cluster volume and show peculiar spectral properties. We named them HT-A, HT-B and HT-C
Figure 3. Low-resolution source-subtracted images of the radio halo hosted by ZwCl 0634.1+4747. The beam is shown in the bottom left corner of each image. The contour levels start at 2𝜎rms (where 𝜎rms is shown in the top right area of the images) and are spaced with a factor of 2. The 2𝜎rms contours are dotted in white. The −3𝜎rms contours are dashed in red colour. The green circle indicates the region with 𝑅 = 300 kpc used to extract the flux densities (Table 4).
(see Fig. 2). Their properties, including the position and redshift of the optical counterpart, the projected distance from the cluster centre and their maximum extension measured from the 3𝜎rms contours of the LOFAR HBA image, are listed in Table 3. The cluster-centric dis- tances are projected, and are thus lower limits. Wide-field, medium- resolution images are shown in Fig. 4 while zoomed-in images in
Fig. 5. The locations of the optical counterparts are shown in Fig. 4. Photometric redshift are taken from the DESI DR9 photometric red- shift catalogue (Zhou et al. 2021).
Every tail shows a bright head, followed by a lower surface bright- ness tail, which shows ripples in the radio brightness. The presence of multiple radio bumps could be interpreted as other radio-galaxies
Table 2. Images used in this work
within the cluster volume rather than a continuation of the tails. In order to exclude the possibility of a sequence of multiple radio galax- ies, we produced spectral index map between 53 MHz and 144 MHz (Fig. 6, left) and 144-320 MHz (Fig. 6, right). To this end, we re- imaged LBA and HBA data, using Briggs weighting with Robust parameter 𝑅 = −0.25, common 𝑢v-range and convolved to the same beam size. In each map, we measured spectral index values for pixels with flux density ≥ 2𝜎rms in both frequencies. We find that 𝛼144 MHz 53 MHz has flatter values where the heads of the AGN are located (consistent with values Fig. 7) and steepens along the tails. Hence, the bright bumps are unlike other AGN which are expected to have 𝛼 ∼ −0.5. Moreover, no other optical counterparts at the cluster redshift are present in the DESI DR9 photometric redshift catalogue (Zhou et al. 2021).
In order to identify possible departures from a pure-ageing model (see Section 3.2 for details), we extracted flux densities and spectral index profiles (Fig. 8). The flux densities are extracted using beam- size sliding regions from the nucleus until the end of the tail, based on their largest linear extent at 144 MHz (Fig. 8, first row). The sliding regions are separated by a few kpc from each other. In this way, we relaxed the requirement of independent measurements, which is not relevant in this case, as we do not use those values for fitting purposes. We then calculated the spectral index profiles between 54-144, 144- 323 and 54-1518 MHz, considering only the regions with fluxes ≥ 3𝜎rms for each pair of frequencies (Fig. 8, second and third row). Another common method to analyse synchrotron spectra is through colour-colour plots (e.g. Katz-Stone et al. 1993; Stroe et al. 2013; Edler et al. 2022; Rudnick et al. 2022). This method employs two, two-point power laws to characterize the curved shape of a source spectrum. For these plots, we use measurements made over beam- size separated regions of the source. The results are then compared to the expected trajectories in the color-color space, predicted by the standard model of spectral ageing (Fig. 8, fourth row). This method is useful to identify points that still follow the same spectral curvature even though they are spatially distant from each other. In the next section, we describe our model and we study their behaviour separately.
3.2 Spectral ageing
Once injected in the ICM from the AGN, the relativistic plasma starts loosing energy due to synchrotron and inverse Compton losses. At the point of the initial acceleration, the energy distribution of the electron population is assumed to be a power law in the form 𝑁 (𝐸) = 𝑁0𝐸 − 𝛿, where 𝛿 is the power-law index. At later times 𝑡 > 0, we expect the energy distribution of the electron population to have a characteristic form depending on 𝑡. Since the characteristic time-scale for synchrotron losses is ∝ 1/𝐸, the electron energy distribution at 𝑡 > 0 will be characterized by a depletion of the highest-energy electrons. The same reasoning applies to the synchrotron spectrum, which steepens with time away from the initial power law shape 𝑆 ∝ 𝜈− 𝛼 with 𝛼 = (𝛿 − 1)/2. In the case of HT radio galaxies, this results in a spatial evolution of the spectrum from the head down to the tail. Specifically, the further from the nucleus, the older the electrons, i.e. they were accelerated at earlier times, and the more curved the spectrum is expected to be. In the absence of re-acceleration mechanisms, we expect to see the aged synchrotron spectrum assuming a characteristic curved shape.
Here we first consider a pure-ageing scenario to describe the flux and spectral index evolution. One of the most commonly used models to describe ageing of radio galaxies is the Jaffe-Perola (JP; Jaffe & Perola 1973) model. It accounts for ageing of plasma assuming: (i) negligible adiabatic losses, in line with models where the tail flow is contained and channeled along magnetic field lines; (ii) a single initial injection event with given injection index 𝛼inj, that represent the plasma spectral index when it is first injected in the ICM by the AGN, i.e. before any ageing; (iii) a given uniform magnetic field that we decide to keep fixed at the minimum aging value 𝐵 = 𝐵min. This choice means maximizing the lifetime of the emitting electrons by minimizing their losses due to synchrotron and IC: higher or lower values of the magnetic field would cause the radio source to fade faster. This equals to 𝐵min = 𝐵CMB/ 3, where 𝐵CMB = 3.2 × (1 + 𝑧)2 𝜇G is the equivalent magnetic field of the Cosmic Microwave Background at the source redshift, which for ZwCl 0634.1+4747 corresponds to 𝐵min = 2.55 𝜇G. We calculated the spectra of each head in a region 1.5 times bigger than the beam, centered on the head (Fig. 7). We fix the injection index using the lowest frequencies available in this work 𝛼inj = 𝛼144 MHz , since they 53 MHz are the less affected by ageing (Table 3).
In order to obtain the JP profiles we used the pysinch2 libraries (presented in Hardcastle et al. 1998, and subsequent work). Through these libraries, we built an initial electron spectrum (with the injec- tion energy index 𝛿inj derived from the observed 𝛼144 MHz ) and let 53 MHz
Table 3. Col. 1: Tail name; Col. 2: Coordinate of the optical counterpart; Col. 3: Photometric redshift from (Zhou et al. 2021); Col. 4: Projected distance from the cluster centre; Col. 5: Largest linear extension above 3𝜎rms at 144 MHz; Col. 6: injection index 𝛼inj =𝛼144 MHz , shown in Fig. 7; Col. 7: tails’ projected 53 MHz velocity;
it age in the minimum magnetic field condition, following the JP model. We then evolved the JP spectrum at 53, 144, 323, 1518 MHz and obtained the flux density (together with the spectral-index). We normalized the initial JP flux density to the first data point, which corresponds to the head of the tail. The time-ageing of the JP model spectra can be converted to space-ageing along the tail, considering a given constant velocity. We thus obtain a rough estimation of the projected velocity on the plane of the sky v⊥ which is of the order of 200 − 300 km s−1 (Table 3). We point out that this is a lower limit for multiple reasons. First, magnetic field and velocity are strongly correlated, which means that it is not possible to discern between the minimum ageing scenario and any other value of the magnetic field 𝐵, far from 𝐵min, combined with higher velocities of the tail. Secondly, this velocity is projected, meaning that there could be a non-negligible component along the line of sight.
HT A The radio galaxy HT A shows unusual properties: after the bright nucleus (the head), we note another bright peak in the surface brightness at ∼ 380 kpc (Fig. 8, second rows). Correspondingly, the spectral index profile shows a flattening, jumping from ∼ −0.5 of the head to ∼ −1.5 and then stabilizing at ∼ −1.3 in both 𝛼144 and 53 𝛼320 . The flattening extends to ∼ 550 kpc (Fig. 8, third rows). We 144 overplot the JP model (solid lines) for all frequencies. Up to 200 kpc, the spectral index profile decline as expected due to radiative losses of the electron population accelerated by the radio galaxy. In this first part, the JP model is able to reproduce the profiles. At larger distances, it is not trivial to account for the bump in the flux density profile and the flattening of the spectral index, using this pure-ageing scenario. Moreover, the color-color plot shows that points corresponding to 380-550 kpc are progressively moving from the expected curved JP towards the power-law line. That means the shape of the spectrum is getting flatter instead of continuing the steepening due to ageing. Thus, we conclude a mechanism able to re-energise the relativistic population of CRe, initially injected by the AGN, must have occurred. We also note that there are few points in the range 740 - 800 kpc from the head that surprisingly cross the power-law line, lying in the area where 𝛼323 . We argue this is an effect due to mixing 144 of the electrons along the line of sight. Such an effect is common at very large distances from the AGN.
HT B Using GMRT and VLA observations, Cuciti et al. (2018) found a surface brightness jump at ∼ 150 kpc from the head of the tail, in correspondence with a flattening (150−300 kpc) of the spectral index. This was interpreted as evidence for electron re-energisation and they suggested that an interaction with a shock can explain the brightness and spectral index properties. The proposed scenario in- cluded the presence of a weak shock (Mach number M ≲ 2), moving
from the back end of the tail until the point of the brightness bump ∼ 200 kpc. The geometry of this scenario includes the tail travelling outward from the cluster centre with an angle 𝜃0 = 60◦ to the line of sight. This model was able to explain the high-frequency radio observations for reasonable choices of the model parameters, as for example the velocity of the tail of the order of 𝜎v ∼ 1400 km s−1. Nonetheless, they did not detect any shock at the jump position in the X-ray image. Thus they concluded that, if the shock is present, it should be moving with a significant inclination with respect to the plane of the sky (see Fig. 13 in Cuciti et al. 2018).
Our results at high frequencies are consistent with the brightening starting at ∼ 150 kpc, and the subsequent spectral flattening. As a reference with the analysis of Cuciti et al. (2018), in Fig. 9 we show 𝛼144 . The spectral profile shows a peculiar 53 feature: the flattening starts at different distances depending of the frequencies used. To better appreciate this feature, we zoom in the first 400 kpc of HT-B and performed spectral index profiles comparing 𝛼53 and 𝛼323 . In Fig. 9, the flattening point appears to be 144 1518 spatially shifted from 150 kpc (𝛼323 ) and 80 1518 kpc (𝛼53 ). This frequency-dependent feature would discourage the 144 shock scenario, since the latter would create re-energisation feature happening simultaneously at the same point of the tail. We discuss and test possible scenarios in Section 4. Interestingly, we also find a residual emission with 𝛼53 < −2.5 at the very end of the HT B 144 (Fig. 4). This is clearly visible only in the LOFAR low-frequencies images and after a region where there is no emission. If this steep spot is part of the tail, the total extent of the HT galaxy would be of 1.2 Mpc. However, we cannot rule out that it may be a residual emission, also present in other parts of the image. In addition, given the large distance and the significant spectral index uncertainty associated with it, we exclude the radio spot from further analysis.
compared to 𝛼1518 323
HT-B is the tail with the most extended frequency coverage. This means we can follow the flux density and spectral index evolution up to ∼ 400 kpc at all the available frequencies in this work. Therefore, in addition to the profiles shown in Section 3.2, we performed local spectral fitting along HT-B. This allows us to study possible variations of the synchrotron spectrum along the tail. To do that, we extracted the spectra in eight circular beam-size independent regions along the source and fitted each local spectrum with a JP model using synchrofit3 package. The result of the local JP fitting is shown in Fig. 10. The model has three free parameters: the energy injection index 𝛿inj, the break frequency 𝜈break and the normalisation factor 𝑁 for correct scaling. From the syncrhotron theory (see e.g., Longair
Figure 4. Images of the head-tail galaxies hosted in ZwCl 0634.1+4747 at different frequencies. In each image, the contour levels start at 2𝜎rms, where 𝜎rms √ shown in the top right area of the images, and are spaced with a factor of 2. The 2𝜎rms are dotted white coloured and −3𝜎rms contours are dashed red coloured. The beam is shown in the bottom left corner of each image and has a FWHM of 20′′. Black crosses indicate the optical counterparts of the HT radio galaxies (Table 3). The blue diamond is the location of the Brightest Cluster Galaxy (BCG) (Cutri et al. 2003).
2011), the break frequency is related to the spectral age 𝑡𝑠 as
CMB)(𝜈break (1 + 𝑧))0.5 where the magnetic field 𝐵 and the equivalent magnetic field of the CMB 𝐵CMB are in 𝜇𝐺, while 𝜈break in GHz. The initial energy spectrum spectrum undergoes a gradual transformation, with an ex- ponential decline emerging beyond the point 𝜈break. If no source of
re-acceleration is present, the measured break frequency decreases systematically along the tail as 𝜈break ∝ 𝑡 −2 𝑠 . In the approximation of constant velocity that leads to 𝜈break ∝ 𝑑 −2, in agreement with the scenario in which the oldest particles are those at a larger distance from the AGN. We first fitted the spectra with the injection index free to vary in the range [1.5, 3.5] (purple, Fig. 11). We noticed that the injection index does not show a clear trend but fluctuates around 2.2 ± 0.2. Thus we fitted again the same regions fixing the energy
Figure 5. Zoom-in on the source HT-A (first column), HT-B (second column) and HT-C (third column) at all frequencies, from 53 MHz (top) to 1518 MHz (bottom). For each cut-out, the resolution and 𝜎rms are the same as Fig. 4, listed in Table 2.
Figure 6. Left panel: Spectral index map between 53 MHz and 144 MHz at a spatial resolution of 36′′ × 36′′ (top) and relative spectral index error Δ𝛼53 MHz 144 MHz (bottom). Pixels with surface brightness values below 2𝜎rms in the two images were blanked. Black contours start at 3𝜎145 MHz and are spaced by a factor of 2. Right panel: Spectral index map between 144 MHz and 320 MHz at a spatial resolution of 20′′ × 20′′ (top) and relative spectral index error Δ𝛼144 MHz 320 MHz (bottom). Pixels with surface brightness values below 2𝜎rms in the two images were blanked. Black contours start at 3𝜎320 MHz and are spaced by a factor of 2.
injection index to 2.2 (i.e. 𝛼inj = 0.6), which is also in agreement with the low-frequency power-law index of synchrotron emission, 𝛼144 MHz , observed of HT-B (Fig. 7). Thus we can limit the number 53 MHz of free parameters and we show the trend of the best-fit parameters 𝜈break and 𝛿inj in Fig. 11 (teal). Keeping 𝛿inj fixed or free to vary, does not influence the overall trend of the frequency break along the tail. Interestingly, we notice that after an initial decrease (up to re- gion 3), the break frequency remains fairly constant. The distance at which this happens coincides with the distance of the spectral index flattening at ∼ 150 kpc. This confirms that at some point along the tail, there must be a mechanism that stops the natural ageing (spectral index flattens and the break frequency stops decreasing). To quanti-
tatively assess the slowdown of the break frequency steepening, we employed a general power-law model of the form 𝑓 (𝑑) ∝ 𝑑 −𝑎 to fit the data points spanning from Region 2 to 8 (Fig. 11, left), where 𝑑 is the distance from the core and 𝑎 the power-law index. We excluded the break frequency value in Region 1, as is strongly vary among the two JP fitting models, and it can be considered as a lower limit since it is much higher than the highest spectral point in the case 𝛿inj = 2.2. The best fit (blue solid) shows a power-law index 𝑎 = 1.06 ± 0.09. Notably, this value indicates a slower rate of change compared to expected law based on the relationship between spectral age and break frequency (see Eq. (2)) and assuming a constant tail speed, 𝜈break ∝ 𝑑 −2 (dashed blue line for comparison). Similar evidence
Figure 7. Integrated flux densities of the HTs nuclei, extracted from Fig. 4 in regions with ∼ 1.5 beam area size.
has been found in (Parma et al. 1999), who claimed re-acceleration processes for four of the radio galaxies in their sample.
HT C Analysing HT C is difficult because of its morphology and extension. In fact, the radio galaxy is more compact at ∼ GHz frequency (see also Fig. 5), while revealing a longer structure only in LOFAR images. Nevertheless, also in this case a pure-ageing JP model cannot account for the emission observed at distances larger than 200 kpc. Again, we see evidence for re-energised CRe left behind the AGN. These CRe do not age as expected by the considered model: the flattening of the spectral index implies that the energy distribution of the CRe is boosted toward higher energies.
3.2.1 Other ageing models
Another widely used model for spectral ageing is the Kardashev (1962) and Pacholczyk (1970) model (KP). The JP and KP models differ in the treatment of the emitting electrons’ pitch angles, i.e. the angle between the magnetic field B and velocity v of the charged par- ticle. In the KP model, the pitch angles of the electrons are fixed over their radiative lifetime, while in the JP model, pitch angle scattering takes place. This difference influences the way CRe lose energy, and thus, affects the resulting synchrotron spectra (Harwood et al. 2013). The pitch angle scattering of the JP model is a more likely scenario than that of the fixed pitch angles of the KP model (Tribble 1993). The reason for this is that for a turbulent magnetic field configura- tion, the expected resonant scattering of the particles is effective on scales comparable to the Larmor radius of CRe, and thus smaller than the resolution of observations (Carilli et al. 1991; Hardcastle 2013). Finding the best model for radiative ageing is beyond the scope of this work (see Section 4). We note that the differences between JP and KP model spectra would not change our conclusion, i.e. stan- dard ageing cannot account for the observed profile and thus other re-acceleration mechanisms need to operate in this system.
We use XMM-Newton observations to study the environment of the HT galaxies, i.e. the ICM that deflects their jets. From previous
studies, it is known that this cluster appears to be in a non-relaxed state (Cuciti et al. 2015).
We first studied the X-ray surface brightness to check for jumps in the azimuthal profile. We used pyproffit4 (Eckert et al. 2020) to compute and model the surface brightness with a single, spherically symmetric 𝛽-model (Cavaliere & Fusco-Femiano 1976) of the form:
(cid:16) 𝑟 𝑟c
where 𝐼0 is the central surface brightness, 𝑟c the core radius, 𝛽 describes the ratio between thermal and gravitational energy of the plasma and one additional parameter 𝑏 to describe the background (Eckert et al. 2020). We extracted a profile in circular annuli centered on the X-ray peak, with a bin size of 15′′ until 𝑅500. The azimuthal fit shows that a smooth 𝛽-model accounts for the emission, which does not show bumps or discontinuities (Fig. 12).
In order to look for features in the ICM that can be connected to the HT galaxies, we used standard X-ray image processing tech- niques. When studying galaxy clusters, particularly relaxed objects, the bright core of ICM emission gives rise to steeply peaked surface brightness profiles, where it can be difficult to detect variations such as edges, filaments, cavities or ripples. Thus, filtering techniques are frequently used to see and enhance variations in the surface bright- ness distribution. Among the different techniques, we used the adap- tive version of the Gaussian Gradient Magnitude5 (GGM; Sanders et al. 2016a,b) filter. In standard GGM filter, the image is convolved with a function that is the gradient of a Gaussian with a particular scale, measuring the gradients on this scale. This is a useful method to detect edge-like structures, such as shocks and cold fronts, which lead to strong gradients (Sanders et al. 2018). Since the accuracy of the gradient depends on the number of counts within the scale probed, this standard GGM filtering becomes noisier in regions where the count rate is lower, i.e. the outskirts of galaxy clusters. Therefore, we used the adaptively smoothed GGM described in Sanders et al. (2022) that dynamically choses the appropriate scale that reduces this effect. The main input parameter of this software is the signal- to-noise ratio, which is used to calculate the smoothing scale from the input counts. Following Sanders et al. (2022) we set it to 32, and we used the image counts in the energy band from 0.5 to 2 keV. We note the presence of bright regions, i.e., high gradient values, in the central left part of the GGM-filtered image (Fig. 13) but this region does not intersect any of the tails. Hence, we conclude that the ICM does not show features that appear to interact with the radio tails.
Based on the 3𝜎rms-contours, the radio halo in ZwCl 0634.1+4747 has a diameter of ∼ 400-800 kpc in the E-W direction, depending on the frequency (see Table 4).
Following the procedure of Cuciti et al. (2018), we measure the flux density within a circular area of ∼ 600 kpc diameter, which
Figure 8. First row: HT extension at 144 MHz, where the tails are more visible. Reference points are shown to help the reader in matching the profiles with images; Second row: flux profile; Third row: spectral index profile considering regions with flux above 3𝜎rms; Fourth row: three frequency (53, 144, 323 MHz) color-color plot with the bisector indicating the set of point where 𝛼53 323 , which means that the spectrum resembles a power-law (PL). The dashed red line represents the curved spectrum (𝛼53 323 ) of the JP model. The colorbar reflects the distance from the head of each point. The profiles are shown for HT-A (first column), HT-B (second column) and HT-C (third column).
, 𝛼144 323 . Vertical lines trace the shift of the flattening point from ∼ 150 to
roughly follows the 3𝜎rms-contours of the images (see Fig. 3), using the source-subtracted tapered images described in Section 2.5. This region avoids the two HT-A and HT-B radio galaxies, which are ex- tended sources, and thus cannot be subtracted from the uv-data with the same procedure used for the compact sources in Section 2.5. The results are listed in Table 4. We point out that we find high-frequency flux densities that are slightly different from Cuciti et al. (2018). Our values of 𝑆1.5GHz = 2.5 ± 0.2 mJy and 𝑆320 MHz = 14 ± 2 mJy are nevertheless still consistent with measurements reported in Cuciti et al. (2018). The difference could be due to different sources sub- traction methods. Cuciti et al. (2018) measured the compact-sources flux density from the high-resolution images and subtracted that from the measurement on the radio halo region of the low resolution im- ages, while here we subtracted the compact sources directly from the 𝑢v-data.
In order to obtain a size and flux estimate that is independent of the signal-to-noise ratio of the radio images (i.e., that does not rely on the 3𝜎rms−contours), we fit the the same low-resolution source- subtracted images of Fig. 3 with Flux Density CAlculator software6 (FDCA-Halo; Boxelaar et al. 2021). This method fits the surface brightness profile of halos to a 2D-model using Bayesian inference. The general exponential model used is 𝐼 (r) = 𝐼0𝑒−𝐺 (r) , where 𝐼 (r) is the surface brightness and 𝐺 (r) the function that takes different forms depending on the complexity of the model (see Boxe- laar et al. 2021, for details). In the circular model case, 𝐺 (r) = |r|/𝑟e, where the e-folding radius 𝑟e is the length-scale at which the surface brightness drops to 𝐼0/𝑒. To avoid contaminating sources, we first masked the regions corresponding to extended radio sources other than the radio halo. Masked regions, model and residuals can be found in Appendix A, while the fitting results in Table 4.
The fitted 𝑟e values are more uniform across the frequency range
(120 − 145 kpc) compared to the size based on the 3𝜎rms-contours (𝐷 ∼ 480 − 850 kpc) and consistent with each other because they are less affected by the noise. Flux densities with FDCA-Halo are integrated up to a radius 𝑅 = 3𝑟e that contains 80% of the total flux 𝑆𝜈 (< 3𝑟e) = 0.8𝑆∞
To date, this is one of the few radio halos where we can study the radio spectrum from 1.5 GHz down to 50 MHz. In the near future, observations by the LOFAR LBA Sky Survey (LoLSS; de Gasperin et al. 2021, 2023), combined with archival data from other telescopes (such as uGMRT and VLA), will increase the number of systems with such a large frequency coverage (Pasini et al., in prep.).
The spectrum of the radio halo in ZwCl 0634.1+4747 is shown in Fig. 14: green points represent flux densities extracted within a radius of 300 kpc 𝑆𝜈 (< 300 kpc), while purple points are values obtained via FDCA-Halo procedure 𝑆FDCA (< 3𝑟e). We note that the fitted size of the halo, i.e. 3𝑟e, is wider than the circular extraction region with 𝑅 = 300 kpc (based on the 3𝜎rms−contours), and thus the FDCA-Halo flux is higher. Despite of this, the spectral shape remains unchanged (Fig. 14). We fit the spectrum using a power law, finding a best-fit spectral index between 53 Hz and 1518 Hz of 𝛼 = −1.18 ± 0.04 and 𝛼FDCA = −1.24 ± 0.03, respectively. These values are consistent with previous high-frequency (Cuciti et al. 2018) and low-frequency (Cuciti et al. 2022) studies. Spectral indices 𝛼 < −1.1 are expected for the radio halos and are in agreement with other radio halos studied over the whole radio spectrum (e.g., A1758 Botteon et al. (2018, 2020), Coma Bonafede et al. (2022)). Moreover, this halo is under- luminous in the power-mass correlation in both 𝑃1.5GHz − 𝑀500 (Cuciti et al. 2021) and 𝑃150MHz − 𝑀500 (Cuciti et al., submitted); and has an emissivity 𝐽1.4GHz = (3.2 ± 0.2) × 10−43 erg/(s cm3Hz) slightly lower compared to the emissivity of classical radio halos at 1.4 GHz in the range of [5×10−43; 4×10−42] erg/(s cm3Hz) (Cuciti et al. 2022). Statistical studies showed that halos not lying on the 𝑃1.5GHz − 𝑀500 correlation are usually associated with non-merging clusters or with USSRHs. In the framework of the turbulent re- acceleration scenario, this means that either the radio halo is not present at all, or the system is less massive and has experienced minor mergers, thus producing radio halos with steeper spectra.
In this work, we studied HT radio galaxies that show ripples in the surface brightness profiles and spectral index flattening along the tail. In order to assess whether this is in line with pure radiative ageing due to IC and syncrothron losses, we compared the data to the JP model. This is a standard and widely used spectral ageing model, that assumes electrons are injected with a constant power- law energy spectrum. Moreover, in this analysis, we work under the assumptions of uniform minimum magnetic field, constant velocity and fixed inclination of the radio galaxy (see Section 3.2). Though simple, these are reasonable hypotheses given, for example, that the tails do not show sudden changes in direction. More complex models that include variations of the magnetic field etc. would require more data. Our results show that the jet emission deviates from the pure radiative ageing due to IC and syncrothron losses. We conclude that this is evidence for re-acceleration. In this section we discuss possible scenarios that can affect the tail’s spectral behaviour and morphology. Particular focus is on the long flattening of the spectral index and a frequency-dependent feature, only clearly visible in HT B (Fig. 9). This is due to the lack of high frequency information to use for measuring the spectral index 𝛼1518 at distances > 150 − 200 323 kpc from the head for HT A and HT C.
Figure 10. Spectra extracted in 8 circular beam-sized independent regions along the HT-B. The light blue line represent the best fit of the JP model and the model parameters ( 𝛿inj, 𝜈break) are listed in the legend of each plot. The image of HT-B at 144 MHz is shown in the bottom right panel with the 8 regions overlapped. We plot the 3-, 6- and 12𝜎rms contours at 144 (cyan) and 1518 (white) MHz, as a reference of the tail extension at different frequencies.
A first simple explanation for ripples in the brightness profile can be a varying output of the AGN. The standard JP model (Section 3.2) uses a single injection event. Thus, we are assuming that the AGN injection rate remains constant with time. A varying AGN would reproduce the ripples in the surface brightness profiles but not the flattening in the spectral index that we see in Fig. 8. Thus, although a varying AGN is still a plausible mechanism that contributes to the observed profiles, we exclude it as the main mechanism creating the observed features. We point out that possible changes of inclination during the motion through the cluster can also alter the observed
surface brightness and spectral index profiles, causing deviations from the expected JP profile. However, we argue that this scenario is very unlikely for two main reasons. First, the morphology of the tails does not show sharp bends that could suggest such a scenario of varying direction of motion. Secondly, even if projection effects happened along the tail, in those regions we would be summing younger “foreground” electrons with older “background” ones. The result would be a spectral index decreasing faster with respect to the standard ageing, not slower, as we observe.
Figure 11. Best-fit break frequency and energy spectral index trend along HT-B. In purple the result with energy injection index free to vary, 𝛿inj ∈ [1.5, 3.5]; in teal it is kept fixed 𝛿inj = 2.2 (i.e. 𝛼inj = 0.6, in agreement with the HT-B head spectrum of Fig. 7). Left panel: A power-law function was fitted to 𝜈fit break corresponding to regions number 2 to 8. The best fit power-law index results to be 𝑎 = −1.06 ± 0.09 (blue solid line). The break frequency trend expectation from a pure ageing scenario 𝜈break ∝ 𝑑−2 is plotted as a reference (blue dashed line).
Col. 1: Frequency; Col. 2: Linear extension corresponding to the 3𝜎rms contour in the E-W direction as a size reference; Col. 3: Flux density measured within a circular region with 𝑅 = 300 kpc (see Fig. 3); Col. 4: Radio power calculated from 𝑆𝜈 (< 300 kpc) with the K-correction applied, assuming 𝛼 = −1.2; Col. 5: Central surface brightness from FDCA-Halo fitting, using a circular halo model; Col. 6: e-folding radius from FDCA-Halo fitting, using a circular halo model; Col. 7: Flux density measured within the 3𝑟𝑒 calculated by FDCA-Halo; Col. 8: Radio power calculated by FDCA-Halo corresponding to 𝑃FDCA (< 3re ),
The interaction between shocks and tails is a possible scenario that can alter the tail morphology and physical properties. It is well known that when a shock encounters a population of aged electrons, it can re- energize particles, leading to observable synchrotron emission. How- ever, the expected very high sound speed of the relativistic plasma does not allow the shock to penetrate into the radio tail (Enßlin & Gopal-Krishna 2001).
However, a shock can adiabatically compress the fossil plasma and increase the magnetic field (Enßlin & Gopal-Krishna 2001; Enßlin & Brüggen 2002). In fact, adiabatic compression is able to re-energize an electron population, inducing brightening and spectral flattening. This kind of interaction was already investigated in the past, either in combination with the presence of a shock (van Weeren et al. 2017; Botteon et al. 2019; Wilber et al. 2019), or a cold front (Botteon et al.
2021; Giacintucci et al. 2022). The shock scenario was also proposed by Cuciti et al. (2018) as a possible explanation to the HT-B observed radio properties. There are very few examples of HT-radio galaxies formation (O’Neill et al. 2019a) or shock-radio galaxy interaction (Nolting et al. 2019a,b; O’Neill et al. 2019b) simulations in the literature that can shed light on this complicated scenario. Although none of these simulations are tuned to reproduce the geometrical configuration proposed by Cuciti et al. (2018), we can use them for a general comparison. In particular, Nolting et al. (2019a) studied the interaction between a shock and an active radio galaxy, in the case where jets are aligned with the shock normal. They show that, as the shock travels along the jets, vortices are generated behind it (see Fig. 5 of Nolting et al. (2019a)). This toroidal vortex was found also in other simulations of a shock wave interacting and adiabatically compressing a radio plasma cocoon (Enßlin & Brüggen 2002; Pfrommer & Jones 2011). The fact that we do not observe
Figure 12. Surface brightness profile with the fitted single 𝛽-model. The best fit parameters are 𝛽 = 0.59 ± 0.05, 𝑟𝑐 = 1.24 ± 0.02 arcmin, I0 = 0.079 ± 0.006 cts/s/arcmin2, with a reduced 𝜒2 = 1.2.
Figure 13. X-ray 0.5 - 2 keV image filtered with an adaptive GGM filter, using a signal-to-noise ratio of 32. Radio contours from Fig. 4b are overplotted.
this morphological feature suggests that there is no shock travelling through the tail. However, we cannot completely rule out this option since signs of jets disruption might be present on scales smaller than our resolution. Moreover, we point out the need of tailored simulations, where a shock crosses a head-tail radio galaxy whose morphology has been already modified by the interaction with the ICM. As mentioned in Section 3.2, a shock interacting with the tail in the same configuration proposed by Cuciti et al. (2018) would create re-acceleration features at the same point of the tail (i.e., simultaneous
Figure 14. Integrated spectrum of the radio halo from 1.5 GHz down to 53 MHz. Green points indicate the integrated flux values measured in a circular region with 𝑅 = 300 kpc. Purple points represent 𝑆FDCA (< 3re ), the flux calculated via FDCA-Halo fitting procedure within three 𝑒-folding radii. Values at 320 MHz and 1.5 GHz from Cuciti et al. (2018) are displayed in blue.
brightness jumps and flattening of the spectra in correspondence of the shock location), while in HT-B we observe a shift of the point where the spectrum flattens (Fig. 9). This will be discussed in detail in Section 4.2. Finally, we point out that the XMM-Newton observation does not show any shocks at or near the radio tails, (see Section 3.3). For all the arguments mentioned above, we consider the presence of a shock as an unlikely scenario to explain the data.
Turbulence within the tail can arise from hydrodynamic instabilities that result from the interaction between the relativistic plasma and the surrounding medium. (Mignone et al. 2004; Jones et al. 2017; Mukherjee et al. 2021; Kundu et al. 2021; Ohmura et al. 2023). This turbulence can trigger several mechanisms of stochastic acceleration of particles, such as gentle acceleration, which has been suggested as a possible explanation for the GReET in Abell 1033 (de Gasperin 2017; Edler et al. 2022).
As mentioned in Section 3.2, data for HT-B suggest that the spec- tral index flattens at different distances, depending on the frequency. In particular, the spectrum measured at higher frequencies flattens at greater distances from the head. Considering the kinematics of the tails, this corresponds to a situation in which the spectrum at higher frequencies flattens over longer times. This scenario agrees with the fact that spectral flattening is more evident at higher fre- quencies: 𝛼144 remains almost constant in the first 400 kpc around 53 a value of −0.6, −0.8, while 𝛼1518 shows a well-defined decrease 323 up to ∼ −1.4 before flattening (see Fig. 9). This evidence allows us to understand something more about the mechanisms of particle re-acceleration. In practical terms, the flattening of the spectrum at higher frequencies over longer times indicates a gradual shift of the particles towards high energies. This, in turn, places constraints on the re-acceleration times. Fig. 9 suggests that the energy of the emit- ting electrons essentially doubles in about 80 kpc, corresponding to about 260 Myr (considering a speed of the tail ∼ 300 km/s). We can conceive of two scenarios. In the first scenario, the electrons cool due to losses for a time 𝑡start without being re-accelerated. After a
time 𝑡start, necessary for the development of the instabilities in the head tail and possibly also necessary for the turbulence to cascade to resonant scales, the same particles are re-accelerated on a time scale, 𝜏acc. This causes the spectrum to increase again at higher energies if 𝜏acc < 𝑡start (𝜏acc ≥ 𝑡start would otherwise simply balance cooling on time scales 𝜏acc). In this case, 𝜏acc ∼ 260 Myr and 𝑡start ∼ 500 Myr (from kinematics ∼ distance spectral flattening/velocity). A second option could be that a second component of (relativistic) particles is re-accelerated starting at 𝑡start with 𝜏acc ∼ 200 − 300 Myr. These particles might be present in the tail at lower energies and poten- tially filling a different volume with respect to the other component. This second scenario could explain the strong brightness increase observed in the re-acceleration phase and might also suggest that volume is not uniformly filled with CR particles. Discriminating be- tween the two possibilities and constraining model parameters by fitting the data is beyond the scope of the current work and will de- serve a future study. Finally, we point out that galaxies in clusters are expected to move with a velocity of the order of the velocity dispersion (∼ 103 km/s), which is not compatible with the value of a few hundreds km/s, derived from our modelling in Section 3.2. This suggests deficits in the JP model, even in the first kpc from the AGN. This means that no part of the tail is ageing subject to pure radiative synchrotron and IC losses, and we are facing a mechanism that acts broadly along the tail and starts as soon as the jets interact with the external medium. Recent simulations by Ohmura et al. (2023) show the effect of turbulent reacceleration on HT galaxies. They simulated AGN jets in an ICM wind and computed the evolution of CRe, con- sidering both energy losses and stochastic acceleration. Their work clearly shows that in the presence of re-acceleration, the spectral in- dex does not decrease substantially along the tail but remains fairly flat (𝛼150 600 ∼ −0.8, −1) for about 150 Myrs. This is in agreement with our observations at low frequencies. At higher frequencies, we find a decrease of the spectral index in the first kpc from the head, which we attribute to the factors described above.
In this work, we have studied the radio halo and three HT radio galaxies of the same cluster ZwCl 0634.1+4747 (z=0.174). We make use of LOFAR LBA 53 MHz, LOFAR HBA 144 MHz, GMRT 323 MHz, VLA 1.5 GHz and X-ray XMM-Newton data. The cluster has already been studied at higher frequencies (Cuciti et al. 2018). However, the addition of low-frequency LOFAR observations has enabled us to study low brightness emission on large scales, both, in terms of diffuse halo emission and radio galaxies. Our main results can be summarized as follows:
MB acknowledges support from the Deutsche Forschungsgemein- schaft under Germany’s Excellence Strategy - EXC 2121 "Quantum Universe" - 390833306. CS acknowledge support from the German Federal Ministry of Economics and Technology (BMWi) provided through the German Space Agency (DLR) under project 50 OR 2112. RJvW acknowledges support from the ERC Starting Grant ClusterWeb 804208. GDG acknowledges support from the Alexan- der von Humboldt Foundation. AB acknowledges financial support from the European Union - Next Generation EU. LOFAR (van Haar- lem et al. 2013b) is the Low Frequency Array designed and con- structed by ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and that are collec- tively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefited from the following recent major funding sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and In- novation (DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities Council, UK; Ministry of Science and Higher Education, Poland; The Istituto Nazionale di Astrofisica (INAF), Italy. This research made use of the Dutch national e-infrastructure with support of the SURF Cooperative (e-infra 180169) and the LO- FAR e-infra group. The Jülich LOFAR Long Term Archive and the German LOFAR network are both coordinated and operated by the Jülich Supercomputing Centre (JSC), and computing resources on the supercomputer JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John
von Neumann Institute for Computing (NIC). This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computing facility located at the Univer- sity of Hertfordshire and supported by STFC [ST/P000096/1], and of the Italian LOFAR IT computing infrastructure supported and op- erated by INAF, and by the Physics Department of Turin university (under an agreement with Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing Centre, Italy.
Raw data are publicly available in the archives. FITS files of LOFAR HBA can be found at https://lofar-surveys.org/. Processed data used in this work will be made available upon reasonable request.
Cuciti V., et al., 2021, A&A, 647, A51 Cuciti V., et al., 2022, Nature, 609, 911 Cuciti V., et al., 2023, A&A, 680, A30 Cutri R. M., et al., 2003, 2MASS All Sky Catalog of point sources. De Luca Molendi 2004, A&A, 419, 837 Duchesne S. W., Johnston-Hollitt M., Bartalucci I., 2021, Publ. Astron. Soc.
Edler H. W., et al., 2022, A&A, 666, A3 Enßlin T. A., Brüggen M., 2002, MNRAS, 331, 1011 Enßlin T. A., Gopal-Krishna 2001, A&A, 366, 26 Feretti L., Giovannini G., 2008, in Plionis M., López-Cruz O., Hughes D., eds, , Vol. 740, A Pan-Chromatic View of Clusters of Galaxies and the Large-Scale Structure. p. 24, doi:10.1007/978-1-4020-6941-3_5
Giacintucci S., et al., 2022, ApJ, 934, 49 Hardcastle M. J., 2013, MNRAS, 433, 3364 Hardcastle M. J., Croston J. H., 2020, New Astron. Rev., 88, 101539 Hardcastle M. J., Birkinshaw M., Worrall D. M., 1998, MNRAS, 294, 615
Kardashev N. S., 1962, Soviet Ast., 6, 317 Katz-Stone D. M., Rudnick L., Anderson M. C., 1993, ApJ, 407, 549 Kempner J. C., Blanton E. L., Clarke T. E., Enßlin T. A., Johnston-Hollitt M., Rudnick L., 2004, in Reiprich T., Kempner J., Soker N., eds, The Riddle of Cooling Flows in Galaxies and Clusters of galaxies. p. 335 (arXiv:astro-ph/0310263), doi:10.48550/arXiv.astro-ph/0310263
McMullin J. P., Waters B., Schiebel D., Young W., Golap K., 2007, in Shaw R. A., Hill F., Bell D. J., eds, Astronomical Society of the Pacific Confer- ence Series Vol. 376, Astronomical Data Analysis Software and Systems XVI. p. 127
Pacholczyk A. G., 1970, Radio astrophysics. Nonthermal processes in galactic
Sanders J., Walker S., ZuHone J., Bellomi E., 2018, Chandra News, 25, 1 Sanders J. S., et al., 2022, A&A, 661, A36 Sebastian B., Lal D. V., Pramesh Rao A., 2017, AJ, 154, 169 Shimwell T. W., et al., 2017, A&A, 598, A104 Shimwell T. W., et al., 2019, A&A, 622, A1 Shimwell T. W., et al., 2022, A&A, 659, A1 Sĳbring D., de Bruyn A. G., 1998, A&A, 331, 901 Smirnov O. M., Tasse C., 2015, MNRAS, 449, 2668 Srivastava S., Singal A. K., 2020, MNRAS, 493, 3811 Stroe A., van Weeren R. J., Intema H. T., Röttgering H. J. A., Brüggen M.,
de Gasperin F., et al., 2019, A&A, 622, A5 de Gasperin F., et al., 2020, A&A, 642, A85 de Gasperin F., et al., 2021, A&A, 648, A104 de Gasperin F., et al., 2023, A&A, 673, A165 van Haarlem M. P., et al., 2013a, A&A, 556, A2 van Haarlem M. P., et al., 2013b, A&A, 556, A2 van Weeren R. J., Röttgering H. J. A., Brüggen M., Cohen A., 2009, A&A,
van Weeren R. J., Röttgering H. J. A., Brüggen M., 2011, A&A, 527, A114 van Weeren R. J., et al., 2017, Nature Astronomy, 1, 0005 van Weeren R. J., de Gasperin F., Akamatsu H., Brüggen M., Feretti L., Kang
H., Stroe A., Zandanel F., 2019, Space Sci. Rev., 215, 16
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Flux Density CAlculator (FDCA) results for the 2D surface brightness fitting to study the central radio halo (see Section 3.4). The first column refers to the original source-subtracted images shown in Fig. 3.
Figure A1. FDCA-Halo results for the radio halo in ZwCl 0634.1+4747 at LBA (first row), HBA (second row), GMRT (third row), VLA (fourth row) frequency. Left panel: Original image with the contaminating regions masked out. Middle panel: Circular model map. Right panel: Residual image. The contour shows the 2𝜎rms level of the model. The red contours show the masked regions, the contamination sources are visible.
