Abstract We present the detection of a giant radio halo (GRH) in the Sunyaev-Zel'dovich (SZ)-selected merging galaxy cluster ACT-CL J0256.5+0006 (z = 0.363), observed with the Giant Metrewave Radio Telescope at 325 MHz and 610 MHz. We find this cluster to host a faint (S 610 = 5.6 ± 1.4 mJy) radio halo with an angular extent of 2.6 arcmin, corresponding to 0.8 Mpc at the cluster redshift, qualifying it as a GRH. J0256 is one of the lowest-mass systems, M 500,SZ = (5.0 ± 1.2) × 10 14 M , found to host a GRH. We measure the GRH at lower significance at 325 MHz (S 325 = 10.3 ± 5.3 mJy), obtaining a spectral index measurement of α 610 325 = 1.0 +0.7 −0.9 . This result is consistent with the mean spectral index of the population of typical radio halos, α = 1.2 ± 0.2. Adopting the latter value, we determine a 1.4 GHz radio power of P 1.4GHz = (1.0 ± 0.3) × 10 24 W Hz −1 , placing this cluster within the scatter of known scaling relations. Various lines of evidence, including the ICM morphology, suggest that ACT-CL J0256.5+0006 is composed of two subclusters. We determine a merger mass ratio of 7:4, and a lineof-sight velocity difference of v ⊥ = 1880 ± 210 km s −1 . We construct a simple merger model to infer relevant time-scales in the merger. From its location on the P 1.4GHz -L X scaling relation, we infer that we observe ACT-CL J0256.5+0006 just before first core crossing. INTRODUCTION Multiwavelength observations of galaxy clusters provide a wealth of information about the physics of the intracluster medium (ICM) and its relationship with cluster galaxies. The optical and X-ray bands have historically been used to identify merger activity via optical substructure (Carter & Metcalfe 1980; Geller & Beers 1982; Rhee & Katgert 1987; Dressler & Shectman 1988; Rhee, van Haarlem & Katgert 1991; Wen & Han 2013) and morphological parameters determined from X-ray images (Mohr, Fabricant & Geller 1993; Jeltema et al. 2005; O'Hara et al. 2006; Santos et al. 2008 ). In the last decade, a link has been found between a cluster's merger status and the presence of large-scale diffuse synchrotron emission (see Brunetti & Jones 2014 , and references therein). This cluster-scale radio emission, dubbed a giant radio halo (GRH) if ∼Mpc in size, exhibits a steep spectrum and has no obvious link to the individual cluster galaxies citepBuote.2001. GRH, FerettiGiovannini.2008 .GRH, Ferrari.2008 .GRHReview, Feretti.2012 .Review. Radio halos (RHs) appear to trace the non-thermal ICM and typically have spectral indices of α ∼ 1.1-1.5. However, ultra-steep spectrum radio halos (USSRHs, α ∼ 1.6-1.9), presumably associated with more pronounced synchrotron ageing, have also been detected within the population Dallacasa et al. 2009; Venturi et al. 2013) . INTRODUCTION The existence of USSRHs is predicted by one of the current leading theories for the origin of RHs , namely the turbulent re-acceleration model in which the synchrotron emission is powered by turbulence generated during cluster mergers (Brunetti et al. 2001; Petrosian 2001; Brunetti & Lazarian 2011; Beresnyak et al. 2013 ). In this model one expects an USSRH to be seen when the turbulent energy in the cluster has decreased sufficiently for it to be less efficient in accelerating high energy electrons in the cluster. This scenario can also explain the observed bimodality in scaling relations between the 1.4 GHz RH power and thermal cluster properties, in which clusters are observed to be either radio loud or radio quiet. This dichotomy has been observed in cluster samples selected via X-ray luminosity Cassano et al. 2008 ) and the Sunyaev-Zel'dovich (SZ) effect (Sunyaev & Zel'dovich 1972) , although it is less pronounced in the latter case (Sommer & Basu 2014) . In practice, one anticipates a population of clusters in transition between these two states that will have intermediate radio power. INTRODUCTION The observed bimodality was initially thought to be due in part to selection effects in the cluster sample (Basu 2012) , but this has since been ruled out (Sommer & Basu 2014; Cuciti et al. 2015) . A more likely reason is a physical effect related to the cluster evolutionary state. Magnetohydrodynamic (MHD) simulations by Donnert et al. (2013) show that a RH is a transient phenomenon that exhibits a rise and fall in radio halo emission over the course of a merger. This evolutionary model suggests that for a merging cluster, the observable diffuse radio emission depends strongly on the phase of the merger in which the cluster is being observed, which likely contributes to the scatter in the observed P1.4GHz scaling relations with thermal cluster properties. INTRODUCTION Moreover, one would expect to find two separate types of systems that populate the intermediate region of radio power: late-stage mergers with old RHs that are in the process of switching off, and early-stage mergers in which the radio halo emission has recently switched on but not yet reached its maximum radio power. The former scenario is a possible explanation for some of the observed USSRHs, which are starting to fill in the region between the correlation and upper limits. Clusters that are in the early stages of merging would also be interesting systems to identify and study as they would complete the evolutionary picture; however due to their expected low radio power, they are potentially more difficult to detect. INTRODUCTION In line with the above, Cassano et al. (2010) find that the observed dichotomy is strongly related to cluster dynamical state, with morphologically disturbed systems hosting RHs. However, several RH non-detections in merging clusters are seemingly incongruent with this trend (A141, A2631, MACSJ2228: Cassano et al. 2010 ; A119: Giovannini & Feretti 2000; and A2146: Russell et al. 2011 ). In the case of A2146, Russell et al. (2011) postulate that the lack of a RH in this strongly-merging system is due to the relatively low mass of the cluster. They estimate a radio power upper limit more than an order of magnitude below the correlation. Low-mass systems are expected to generate less turbulent energy during their mergers, yielding weaker synchrotron emission, and hence RHs that are too faint to observe with current telescopes. The era of LOFAR (Vermeulen 2012) , SKA precursors such as MeerKAT (Booth & Jonas 2012) and ASKAP (DeBoer et al. 2009) , and the SKA itself (Taylor 2013) will bring with it highly sensitive observations of these systems, and should reveal the underlying RH emission. INTRODUCTION In this paper we present the detection of a GRH in a low-mass system that we argue is in the early stages of merging. As discussed, such early-stage merging systems are interesting because they allow us to probe the full evolutionary cycle of GRHs and are expected to fill in the intermediate region in radio halo power. INTRODUCTION The paper is organised as follows: we present existing multiwavelength data on ACT-CL J0256.5+0006 in Section 2, and we describe the radio observations and data reduction process in Section 3, with the radio results presented in Section 4. X-ray and optical morphological analyses are discussed in Sections 5.1 and 5.2, respectively. We construct a model for the merger geometry in Section 6 and infer merger time-scales from this model in Section 7. We conclude with a discussion in Section 8. In this paper we adopt a ΛCDM flat cosmology with H0 = 70 km s −1 Mpc −1 , Ωm = 0.27 and ΩΛ = 0.73. In this cosmology, at the redshift of our cluster (z=0.363), one arcminute corresponds to 305.8 kpc. We assume Sν ∝ ν −α throughout the paper, where Sν is the flux density at frequency ν and α is the spectral index. Colour versions of all figures are available in the online journal. ACT-CL J0256.5+0006 ACT-CL J0256.5+0006 (hereafter J0256) lies at z=0.363 and was detected by the Atacama Cosmology Telescope Menanteau et al. (2013) c Integrated 0.1-2.4 keV X-ray luminosity using the spectrum of Majerowicz et al. (2004) , corrected for the cosmology adopted in this paper. ACT-CL J0256.5+0006 d Integrated Compton y-parameter and B12 SZ mass from Hasselfield et al. (2013) . e Total mass for the main cluster component using β-model fit "a" for the NE region (Majerowicz et al. 2004 ). ACT-CL J0256.5+0006 (ACT; Kosowsky 2006) equatorial SZ cluster survey with a 148 GHz decrement signal-to-noise ratio of 5.4 (Hasselfield et al. 2013) . It was first identified in ROSAT PSPC data and is included in the Bright sharc catalog (RX J0256.5+0006; Burke et al. 1997) . Majerowicz et al. (2004) identify J0256 as undergoing a major merger based on observations carried out with XMM-Newton. ACT-CL J0256.5+0006 In the following sub-sections we describe the existing multiwavelength data for J0256 in the X-ray (XMMNewton), optical (Gemini), millimetre (ACT), and radio (VLA) bands. The relevant cluster properties are given in Table 1 . Majerowicz et al. (2004) , hereafter M04, carry out a comprehensive X-ray study of J0256 based on their 25.3 ks XMMNewton observations (obs ID: 005602301) X-ray 1 . The X-ray image shows two components in the direction of the cluster: a bright main component and a less luminous structure to the west. To investigate whether these are physically connected or serendipitously aligned, M04 fit an elliptical β-model to the hot gas distribution of the main component, excluding point sources and the western component. After subtraction of the best-fit model from the data, the residuals reveal that the western component is a small galaxy cluster exhibiting a comet-like morphology, with the tail to the west (see Figure 2 in M04). This orientation indicates that gas in the subcluster is undergoing ram pressure stripping as it interacts with the main cluster component. Based on the orientation of the subcluster isophots away from the main component and numerical simulations by Ricker & Sarazin (2001) , M04 conclude that the subcluster has not yet passed through the main cluster centre and thus that J0256 is in the pre-core crossing stage of its merger. X-ray For the full cluster, M04 determine a temperature of T = 4.9 +0.5 −0.4 keV within ∼ 0.8R500 and a bolometric X-ray luminosity 2 of LX = (7.88 ± 0.53) × 10 44 erg s −1 , which is over-luminous compared to the LX-T relation measured by Arnaud & Evrard (1999) . M04 conclude that this discrepancy between observed and predicted luminosity, coupled with their evidence for ram pressure stripping of the subcluster, suggests J0256 is not in dynamical equilibrium. Using xspec 3 to model the M04 spectrum using the cosmology in this paper, we determined a 0.1-2.4 keV band-limited luminosity of L500,X = (3.01 ± 0.36) × 10 44 erg s −1 , incorporating a conservative 10% uncertainty due to the spectrum being extracted within ∼0.8R500. X-ray From β-model fitting, M04 calculate an X-ray mass for the main cluster component of M500,X = 3.7 +0.8 −0.6 × 10 14 M , which is equivalent to M500,X = 5.2 X-ray 14 M using the cosmology in this paper. The M04 M200 mass for the main cluster component is M200 ∼ 5.9 × 10 14 M . Using count rates in the residual map in the region of the subcluster and translating this into a luminosity, they estimate the M200 mass of the subcluster to be between 1-2 ×10 X-ray 14 M and determine a merger mass ratio of ∼ 3:1. However, this calculation requires several broad assumptions due to a lack of ancillary data, making the result somewhat uncertain. Millimetre Wide area, untargeted SZ surveys detect large numbers of galaxy clusters via inverse Compton scattering of cosmic microwave background (CMB) photons by electrons within the hot ICM, which causes a distortion of the CMB spectrum in the direction of clusters. ACT is a 6 m telescope that observes the millimetre sky with arcminute resolution (Swetz et al. 2011) . Between 2008 and 2011, ACT surveyed a 455 deg 2 strip centred at δ = -55 • , as well as a 504 deg 2 strip centred at δ = 0 Millimetre • overlapping the Sloan Digital Sky Survey (SDSS) Stripe 82 (Marriage et al. 2011; Hasselfield et al. 2013) , at 148, 218, and 277 GHz. ACT has detected over ninety clusters via the SZ effect. Millimetre J0256 was identified in the ACT equatorial 148 GHz map, with a decrement signal-to-noise ratio of 5.4 for a filter scale of θ500 = 7.06 (see Hasselfield et al. 2013 , hereafter H13, for details). H13 investigated prescriptions for the pressure profile used to obtain a Y500-M500 scaling relation, where Y500 is the integrated Compton parameter. H13 investigated several profiles computed from simulations (e.g., Battaglia et al. 2012) or empirical models (e.g., Arnaud et al. 2010 ), leading to a SZ mass range of 2.9 ×10 14 M < M500 < 7.5×10 14 M for J0256, taking into account the range of uncertainties on all mass estimates. The pressure profile from Battaglia et al. (2012) is currently preferred, and in this paper we use the corresponding SZ mass estimate of M500,SZ = (5.0 ± 1.2) × 10 14 M . Optical The ACT collaboration has completed spectroscopic observations of J0256 using Gemini and identified 78 cluster members (Sifón et al. 2015) . This distribution of spectroscopi- cally confirmed cluster members is ∼85% complete within R200, up to an r-band magnitude limit of 22. Using this redshift information, we can estimate an independent dynamical mass and re-examine the merger geometry proposed by M04 (see Section 5.2 below). The cluster members are shown in Figure 1 where red circles (blue boxes) denote members that are at lower (higher) redshifts than the cluster redshift of z = 0.363. We identify these two sets of galaxies as separate kinematic components (see Section 5.2 below), each of which has a brightest cluster galaxy (BCG) that is indicated by a large, bold symbol. If the cluster is not in the core passage phase of its merger, the superposition of the two populations in the plane of the sky indicates that the merger is occurring at least partially along the line-of-sight. Radio J0256 has been leonardsteven@example.com GHz in the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) mJy and 3.66 ± 0.27 mJy, respectively. This source is not detected in the VLSS data; however, there is a source 1.16 away, closer to the SZ peak of the cluster, detected 3σ above the map noise. The rms and resolution of each image is given in the caption for Figure 2 . NEW RADIO OBSERVATIONS We observed J0256 with the Giant Metrewave Radio Telescope (GMRT) as part of an ongoing project involving the radio follow-up of ACT equatorial clusters. Initial observations were carried out for 10 hours at 610 MHz in August 2012 (PI: Knowles), using a 33 MHz bandwidth split into 256 channels and a 16s integration time. The data were acquired in the polarization channels RR and LL, and the total on-source time was 7.5 hrs. Flux and bandpass calibrator 3C48 was observed at the beginning, middle, and end of the observing block. This source was also used to estimate the instrument's antenna gains and ionospheric phase calibration which in turn were used to correct observations of the target field. of 8s. The total on-source time was 6.5 hrs. As with the 610 MHz observations, 3C48 was used as the sole calibrator. Observational details are given in Table 2 . The pointing centre for both sets of observations was the same and was defined to be that of the SZ peak, given in Table 1 . NEW RADIO OBSERVATIONS The 610 MHz and 325 MHz data were subjected to the same calibration procedure, which is based on AIPS (NRAO Astronomical Image Processing System), SPAM (Intema et al. 2009 ), and Obit (Cotton 2008) tools. The main calibration steps are outlined here. First, strong radio frequency interference (RFI) is removed by statistical outlier flagging tools. As a compromise between imaging speed and spectral resolution losses due to bandwidth smearing, the datasets are then averaged down to 24 channels. Phase calibration starts from a model derived from the VLSS (Cohen et al. 2007 ) and the NVSS (Condon et al. 1998) , followed by a succession of self-calibration loops. To compensate for the non-coplanarity of the array, we use the polyhedron (facetbased) wide-field imaging technique available in AIPS. We perform several rounds of imaging and self-calibration, inspecting the residual visibilities for more accurate removal of low-level RFI using Obit. To correct for ionospheric effects, we then apply SPAM calibration and imaging. The presence of strong sources in the field of view enables one to derive direction-dependent (DD) gains for each source and to use these gains to fit a time variable phase screen over the entire array. The phase screen was used during imaging to correct the full field of view for ionospheric phase effects. NEW RADIO OBSERVATIONS As J0256 lies at close to zero declination, bright sources in the field are subject to strong north-south sidelobes that interfere with emission in the cluster region. To reduce the impact of these bright sources during further imaging, we modeled and subtracted all sources in the field outside of a 13 arcminute radius centred on the cluster, leaving a dataset with only the inner portion of the field. This edited uv-dataset was then imported into the Common Astronomy Software Applications package (CASA; McMullin et al. 2007 ) for imaging. NEW RADIO OBSERVATIONS For each dataset we created several target field images, all with Briggs robust R = 0 weighting (Briggs 1995) . We first made full resolution (FR) images, shown in Figures A1 (610 MHz) and A3 (325 MHz) in the Appendix, using all of the uv-data, cleaning until the residuals were noise-like. We then created high-resolution (HR) images in the following way. As the 610 MHz data have more long baselines than the 325 MHz data, we matched the uv-coverage of the two datasets by selecting a uv-range from 4 kλ (∼52 ) to 30 kλ (∼6 ), and imaging using a 25 kλ outer taper. The HR images were cleaned until their residuals showed no indication of emission in the cluster region. The clean components from the HR images were used as compact source models and were subtracted from the uv-data to create a point source-subtracted datasets. Using these datasets, we imaged The highest resolution available, defined by the synthesised beam. NEW RADIO OBSERVATIONS † The largest scale to which the image is sensitive, defined by the shortest baseline/uv-wavelength. ‡ PSSUB-LR convolved with a 1 Gaussian. 1 corresponds to ∼3.5 kλ. NEW RADIO OBSERVATIONS at full resolution (PSSUB-FR) to visually check that the point source subtraction was successful. 610 MHz HR and PSSUB-FR images of the cluster region are compared in the left and right panels of Figure 3 respectively. The PSSUB-FR image shows no visual indication of residual emission from the compact sources; however, we nevertheless investigate contamination from the source removal process in Section 4.2. Once satisfied, we re-imaged with a uv-cut of < 4 kλ and an outer taper of 3 kλ to gain sensitivity to diffuse emission on scales of 1 Mpc, creating point source subtracted, low-resolution (PSSUB-LR) images. We convolved each PSSUB-LR image with a 1 Gaussian, providing better sensitivity to extended features while retaining useful data, to create our final smoothed, point source subtracted, lowresolution (LR) maps shown in Figures A2 (610 MHz) and A4 (325 MHz) in the Appendix. The final LR 610 MHz (325 MHz) map has a maximum angular resolution of 17 (32 ) . A summary of the different images created is given in Table 3 . RADIO RESULTS With the angular resolution and short baselines of the GMRT, we are able to investigate emission from both compact sources and extended diffuse structures. In the following, we discuss our results from both the 610 MHz and the 325 MHz datasets. Compact radio sources There are seven bright radio sources in the cluster region identified in both 325 MHz and 610 MHz full-resolution maps, five of which are associated with spectroscopically confirmed cluster members. The 610 MHz HR contours can be seen in the left panel of Figure 4 , along with source labels. The only source detected in NVSS and FIRST, as discussed in Section 2.4, is detected in our maps as S7. The flux densities and spectral index we measure for this source, provided in Table 4 , imply a consistent 1.4 GHz flux density of 4.61 ± 0.64 mJy. Several of these sources exhibit resolved tail emission, possibly due to merging activity in the cluster. The BCG of the subcluster is associated with the radio source S5. This source has a wide extension to the west of the galaxy, and although our highest resolution image cannot resolve finer structure within the extended tail, it may be a bent narrow angle tail radio galaxy contorted by ram pressure stripping due to the merger (Bliton et al. 1998 ). The multi-frequency radio properties of all seven sources are given in Table 4 . Here and in Section 4.3.2, the spectral indices are determined using a Monte-Carlo simulation, in which we draw from Gaussian flux density distributions with means and widths represented by the flux densities and their uncertainties, respectively. The spectral index and uncertainties are then determined from the median and 68th percentiles of the resulting spectral index distribution. Point source contamination To unveil any low surface brightness extended cluster emission, the HR radio sources, particularly in the cluster region, have to be removed from the uv-data as described in Section 3. Although the point source removal is reasonably successful, as is clear from the right panel of Figure 3 , it is not exact. In order to quantify the residual (low) level of contamination, we perform a statistical analysis of the LR image using both radio source and random off-source positions in the following way: Point source contamination (i) In the HR image, we select a large number (>100) of random off-source positions. Point source contamination (ii) For each position, we calculate the LR map flux density in a LR beam-sized area centred on that position. Point source contamination (iii) From this set of flux densities we calculate the mean, µ rand , and standard deviation, σ rand , of the distribution. We expect µ rand to be close to zero for Gaussian noise. Point source contamination (iv) We then select all sources outside of the cluster region that are detected above 5σ in the HR map; we find 28 resolved and 53 unresolved sources. Point source contamination (v) We repeat steps (ii)-(iii), now using the point source positions. µptsrcs quantifies the bias in subtraction of point source emission. σptsrcs contains both the map uncertainty and a measure of the noise added by the subtraction process, σsyst, i.e. σ [3, 10, 20, 40, 80] ×1σ. The HR beam is shown as the yellow ellipse in the lower left corner. Individual radio galaxies are labelled from S1 to S7. Flux densities for these sources can be found in Table 4 . The red X marks the position of the SZ peak. Right: Smoothed XMM-Newton MOS X-ray contours (arbitrary levels from the reprocessed image starting at 12 counts per second per square degree -see The results of this analysis are given in Table 5 . We find that we are systematically over-subtracting a low level of point source emission, more so when the sources are resolved. Moreover, the subtraction process does add a small but non-negligible amount of noise into the LR image, as expected. Using the relation in step (v) above, this systematic noise is σsyst,610 = 0.3 mJy beam A graphical representation of this process is shown in Figure 5 . In the HR and LR maps, we stack on the source and random off-source positions separately. The left panels of Figure 5 show the stacked results from the HR map. As expected, the random positions produce a noise-like result and the stacked source positions produce a clear compact source at the centre. Point source contamination Repeating this process in the LR image, we find a negative stacked signal slightly off-centre from the source position, in agreement with the over-subtraction implied by in Table 5 . The shifted peak is due to the varying noise in the map, shown by the random stacked result (middle panels of Figure 5 ). We note that the rms of the LR source and off-source stacked maps are comparable. Point source contamination As a final check, we stack on the radio source positions in the PSSUB-FR map and smooth this result to the same resolution as the LR map. These results are shown in the right panels of Figure 5 . There is a net residual after source subtraction mostly caused by imperfect subtraction of resolved sources, the peak of which is ∼10% of the peak brightness of the average source in the stacked HR map. When we smooth to the same beam as the LR map (lower, right panel), we largely recover the structure of the LR stacked source result (upper, middle panel). Diffuse emission After removal of the radio sources in the field, the LR 610 MHz map, shown in Figure A2 , reveals distinct extended emission in the cluster region with a 6σ peak above the map noise. The 3σ angular extent of the emission is 2.6 , corresponding to a physical scale and largest linear size (LLS) of 0.8 Mpc at the cluster redshift. Due to the centralised position and size of this emission, we classify it as a giant radio halo, making J0256 one of the lowest-mass clusters to host one known to date. The right panel of Figure 4 shows the 610 MHz GRH overlaid with smoothed X-ray contours. The GRH roughly follows the X-ray emission and is centred on the cluster SZ peak. The GRH radio properties are listed in Table 6 . Our LR 325 MHz map is shown in Figure A4 . The radio peak of the GRH lies to the west of the cluster SZ peak and is only marginally detected at a significance of 3σ in the 325 MHz map. Flux measurements The flux density is measured within an aperture of radius 90 , centred on the 610 MHz emission such that all 610 MHz halo flux is captured. From the results of the point source contamination analysis in Section 4.2, the bias at 610 MHz is only at the 1σ level, i.e., µ610,ptsrcs = , which is a bias measured at a significance of 3σ that leads to a fractional flux density increase of over 50%. We thus correct the measured flux densities and incorporate the systematic uncertainties introduced by the point source removal into the flux density uncertainties. We also include ∼10% absolute flux calibration and residual amplitude errors (Chandra, Ray & Bhatnagar 2004) . The final flux density, Sν , and corresponding uncertainty, ∆Sν , are calculated as follows: Flux measurements where σrms is the central map noise, σsyst is the systematic error due to point source removal, and NS is the number of independent beams within the flux aperture. We measure integrated halo flux densities of S610 = 5.6 ± 1.4 mJy and S325 = 10.3 ± 5.3 mJy. The additional contributions to the flux density uncertainty lower the significance of the 610 MHz detection to 4σ which is low, but still reliable. The 325 MHz flux, however, now has a signal-to-noise of less than 2. Higher sensitivity observations at 325 MHz are required to reliably confirm our detection at this frequency. Spectral index We can estimate a theoretical spectral index for the GRH in J0256 from the distribution of measured radio halo spectral indices from the literature, shown in Figure 6 . Assuming this cluster is in the early stages of merging, based on the X-ray morphology determined by M04 (see Section 2.1 above), we expect J0256 to host a young, and therefore flatter spectrum, radio halo. We therefore exclude the USSRHs (α 1.6) from the literature and use the mean and rms of the remaining 17 radio halo spectral indices to determine our theoretical value and error respectively. We determine a spectral index for the typical radio halo population of α = 1.2 ± 0.2. Our measured spectral index, α 610 325 = 1.0 Spectral index −0.9 , obtained using S610 and the noisy S325 measurement, is consistent with the above value. However, given the large uncertainties on α 610 325 , driven by the large error on S325, we choose to adopt the spectral index of the regular radio halo population, α = 1.2 ± 0.2, to extrapolate our measured GRH flux density to other frequencies. Radio power The 1.4 GHz GRH radio power, P1.4GHz is correlated with thermal cluster properties and cluster mass . To constrain P1.4GHz, we use our 610 MHz flux density measurement and the assumed spectral index from the previous section to extrapolate a flux leonardsteven@example.com GHz. We account for the effect of redshift on the flux density and apply a k-correction to calculate a halo radio power of P1.4GHz = (1.0 ± 0.3) ×10 24 W Hz −1 in the cluster rest frame. The error on P1.4GHz is propagated from the spectral index uncertainties. We note that the radio power is consistent with the non-detections in NVSS, FIRST, and VLSS, as it corresponds to a GRH surface brightness far below the noise levels of these surveys. J0256 is shown as the red star on the radio power correlations in Figure 7 . The cluster lies within the scatter, and on the same side, of all three correlations from the literature. J0256 appears to lie slightly further away from the P1.4GHz-Y500 relation, compared to its relative position in the other planes. However, the position of the cluster, relative to the distance away from each correlation, is consistent within the error bars for the cluster mass and thermal parameters. CLUSTER MORPHOLOGY As current observations favour a theory of merger-driven radio halo formation, it is important to understand the dynamical state of J0256. With the X-ray and optical redshift information available to us, we can perform a morphological analysis of J0256. X-ray morphology Visual inspection of the reprocessed J0256 X-ray image in Figure 8 shows the cluster to be disturbed. This image is produced by following the ESAS reduction thread for extended X-ray sources 4 , in which the Al and Si lines are modelled in xspec. The image has been both exposure-corrected and background-subtracted. We exclude the pn camera data as the pn CCD is marginally flared and has a chip gap near the cluster core. Point sources were removed during the reprocessing using the cheese task in the standard XMM SAS tools 5 . The masked regions are shown in Figure 8 by yellow, dashed, excluded circles. In order to quantify the level of substructure in the reprocessed XMM-Newton combined MOS1 + MOS2 image, we follow the work of Cassano et al. (2010) three morphological parameters. To determine the measurement uncertainty on each of our parameters, we adopt the simulation method of Böhringer et al. (2010) whereby a Poisson resampled X-ray image is used to compute the standard deviation of a parameter measurement, which is then used to estimate the measurement uncertainty. Concentration parameter, cSB The concentration parameter, proposed by Santos et al. (2008) as a probe of cluster substructure, is the ratio of the cluster core and the larger-scale X-ray surface brightnesses. We calculate the concentration parameter as cSB = S(< 100 kpc) S(< 500 kpc) , Concentration parameter, cSB where S is the X-ray surface brightness within a particular radius, centred on the X-ray peak. We determine a value of cSB = 0.151 ± 0.007 for J0256. Centroid shift, w Poole et al. (2006) show that, compared to other X-ray morphological estimators, the centroid shift is the most sensitive to cluster dynamical state and least sensitive to cluster image noise. It is defined as the rms deviation of the projected separation between the X-ray peak and the centre of mass in units of the aperture radius, Rap, computed in a series of concentric circular apertures centred on the cluster X-ray peak ( (2010), the aperture radius is decreased in steps of 5% from a maximum aperture of radius Rap = 500 kpc to 0.05 Rap. We compute the centroid shift as Centroid shift, w where ∆i is the distance between the X-ray peak and the centroid of the ith aperture. We measure a value of w = 0.045 ± 0.006 for J0256. Power ratio, P3/P0 The power ratio of a cluster is calculated using a multipole decomposition of the potential of the two-dimensional projected mass distribution. The idea of using the power ratio of the X-ray surface brightness to probe the underlying mass distribution was first introduced by Buote & Tsai (1995) and has since been widely used as an indication of substructure within a cluster (Jeltema et al. 2005; Ventimiglia et al. 2008; Böhringer et al. 2010; Cassano et al. 2010) . We use the normalised hexapole moment, P3/P0, which is the lowest power ratio moment providing a clear measure of substructure , calculated in an aperture of radius Rap = 500 kpc centred on the X-ray cluster centroid. For J0256, we calculate a value of P3/P0 = (3.76 ± 0.30) × 10 −6 . Comparison with the literature Using the methods described in Sections 5.1.1-5.1.3, Cassano et al. (2010) study the morphological parameters for all clusters in the GMRT Radio Halo Survey and find a link between cluster dynamical state and the presence of a radio halo. They define a cluster to be dynamically disturbed if its morphological parameters satisfy the following conditions: cSB < 0.2, w > 0.012 and P3/P0 > 1.2 × 10 −7 . The majority of dynamically disturbed clusters are found to show radio halo emission. All of the parameter values we determine in our analysis of J0256 (cSB = 0.151 ± 0.007, w = 0.045 ± 0.006 and P3/P0 = (3.76 ± 0.30) × 10 −6 ) satisfy the above conditions for a merging cluster, as expected. Comparison with the literature We note that the Cassano et al. (2010) results were obtained using Chandra data whereas our results are obtained with XMM-Newton data, which has a larger PSF. To investigate the effect of the different instruments on the various morphological parameters, we use archival Chandra and XMM-Newton data on a known merging cluster, A2631, and compare the derived morphological parameters from each image. The exposure times for the Chandra and XMM observations, after flare rejections, are 16.8 ks and 13.4 ks, respectively. We find that the resolution difference between the two instruments has a negligible effect on the concentration or centroid shift parameters. However, the power ratio is higher in the XMM image by a factor of between 2 and 5, depending on the level of smoothing applied. Even with a reduction by a factor of five, the P3/P0 value for J0256 (7.5 ×10 −6 ) is still well above the threshold of 1.2 × 10 −7 Comparison with the literature for dynamically disturbed clusters. Optical redshift distribution X-ray morphological parameters are largely insensitive to substructure along the line of sight. To gauge any disturbed morphology in this direction, we use the redshift distribution of 78 spectroscopically confirmed cluster member galaxies (see Section 2.3 above). This distribution is shown in Figure 9 ; there is an indication of bimodal structure in the histogram. Statistical analysis using GMM To gauge its significance, we perform a Gaussian mixture model (GMM) analysis of the member galaxy redshifts. We use the GMM code developed by Muratov & Gnedin (2010) to fit a 2-mode Gaussian mixture to our data and compare it to a unimodal fit. The code calculates the kurtosis of the distribution, K, and the maximum log likelihood, log L, to which each model converges. For a bimodal fit, the peak separation of the modes relative to their widths, D, is also calculated. A statistically significant bimodality would have K < 0, D > 2, and a log-likelihood value greater than that for a unimodal fit. Parametric bootstrapping of the unimodal distribution is performed to determine the probabilities of the observed K, D, and log L difference values being sampled from a unimodal distribution. The latter probability defines the confidence interval at which a unimodal fit can be rejected. Statistical analysis using GMM The results of our analysis are given in Table 7 . The multi-variance bimodal mixture model and unimodal Gaussian fits are superimposed on the distribution in Figure 9 , Table 7 . GMM statistics from the redshift distribution of 78 cluster members. All errors are at the 1σ level. Statistical analysis using GMM Unimodal 78 0.363 ± 0.001 0.005 ± 0.000 299.6 ---Bimodal, multi-variance 53.9 ± 15.9 0.360 ± 0.002 0.004 ± 0.001 300.7 49.0 46.6 69.4 24.1 ± 15.9 0.369 ± 0.003 0.003 ± 0.001 † The maximum log likelihood to which the fit converges. The difference in log L values defines a χ 2 proxy. ‡ Measure of how likely it is that the same statistic can be drawn from a unimodal model. Statistical analysis using GMM shown by the dashed and dot-dashed curves respectively. The data satisfy the K < 0 and D > 2 criteria for bimodality, with the largest log L value coming from the multivariance bimodal fit. The improvement in the log L value for the multi-variance bimodal model relative to the unimodal model is not significant due to the difference in degrees of freedom; a likelihood-ratio test indicates that the bimodal fit is rejected in favour of the unimodal fit at 53%. According to the parametric bootstrapping, the unimodal distribution is consistent with the data at the 69% level when only the log(L) probability is considered, with bootstrapped probabilities of K = 49% for the kurtosis, and D = 47% for the peak separation. A unimodal fit thus cannot be ruled out. Statistical analysis using GMM However, statistical tests run on mock bimodal datasets, with the same population ratio and number of members as our real data, show that the GMM test results in a log(L) probability of 70% or higher about 10% of the time. An unambiguous bimodal preference is only consistently achieved once the total population size is greater than 200. This implies that, when the distribution size is small, the GMM test could show a slight preference for a unimodal fit even when the input redshift distribution is bimodal, given the population ratio of our true sample. Therefore, with the available number of redshifts for J0256, the GMM log(L) test is not a strong discriminator between the two models. However, based on the following additional evidence, we adopt the bimodal model in further analysis of this cluster. Statistical analysis using GMM Firstly, there are two BCGs (cluster members with the lowest SDSS magnitudes) that are spatially separated, as seen from the SDSS image in Figure 1 , which are also separated in velocity space as shown in Figure 9 . This provides support for the existence of two distinct galaxy populations. These galaxies coincide with the peaks in the XMM-Newton X-ray emission (see Figure 4) . Secondly, the DS test, which measures the deviation of the velocity distribution in spatially localised regions of a cluster with respect to the cluster as a whole, indicates the presence of substructure in J0256, with S∆ < 0.01 at the 68% confidence level (Sifón et al. 2015) . Statistical analysis using GMM We use the GMM code to provide, for each member galaxy, the probability that the galaxy belongs to each of the kinematic components in the multi-variance bimodal case. In the following section we use these probabilities to calculate physical properties for the cluster and its components. Velocity dispersions and dynamical masses By fitting a 2-mode GMM to our data, each cluster member is assigned a probability of belonging to each of the modes. These probabilities can be used to determine the mean and variance for each mode by integrating over all members and weighting by the probabilities. Since we have a discrete number of member galaxies, the mean and variance for component n are given bȳ Velocity dispersions and dynamical masses where n ∈ {1, 2}, zi is the redshift of the i-th member galaxy, and pn(zi) is the probability that this member belongs to the n-th component. The mean and variance of each mode in the redshift distribution correspond to the peak redshift and velocity dispersion for each kinematic component, respectively. We use the velocity dispersion and the galaxies-based scaling relation from Munari et al. (2013) to determine M200 and R200 for each component 6 , using a value of h = 0.7 in the Munari et al. (2013) equation. Using the concentration parameter from Duffy et al. (2008) , we integrate a NFW profile (Navarro, Frenk & White 1997 ) and interpolate to determine M500 and R500. The results are given in Table 8 , with all uncertainties determined via bootstrapping. We follow the same process using the unimodal fit, the difference being that the probability for every member is 1. Velocity dispersions and dynamical masses From the mean redshifts of the components, we find a line-of-sight velocity difference of v ⊥ = 1880 ± 210 km s −1 . We also calculate individual component masses of M500,main = (3.23 ± 0.66) × 10 14 M and M 500,subcl. = (1.83 ± 0.74) × 10 14 M , leading to a merger mass ratio of 7:4, smaller than but within the errors of the ∼ 3:1 ratio determined by M04. Combining the component masses, we calculate a cluster dynamical mass of M500,opt = (5.06 ± 0.99)×10 Velocity dispersions and dynamical masses 14 M , which agrees with the SZ cluster mass given in Table 1 to better than 0.5σ. The combined M200,opt mass, M200,opt = (7.66 ± 1.54) × 10 14 M , agrees within 1σ with the estimated M200,X total cluster mass range from M04 of M200,X ≈ 9.7 − 11.1 × 10 14 M , assuming a 15% uncertainty on their M200,NE value 7 . Velocity dispersions and dynamical masses 6 M 200 = (4π/3)ρ 200 R 3 200 7 Corrected for the cosmology in this paper. If we model the cluster as a single component, we estimate a total mass M500,tot = (7.74 ± 0.02) × 10 14 M , which is 2.3σ away from the SZ mass. This reinforces our argument in favour of the bimodal model. The corresponding M200 measurement, M200,tot ∼ 11.7 × 10 14 M , still agrees with the total X-ray mass estimate from M04, although this comparison is not particularly meaningful given the large uncertainties on their estimate. MERGER GEOMETRY M04 construct a simple merger model for J0256 using projected distances and the line-of-sight velocity difference between the main and subcluster components. We adopt a similar approach but update two aspects: we use a more current cosmology and the increased number of galaxy spectroscopic redshifts (78 vs. 4) discussed in Section 2.3. The optical galaxy redshift distribution also allows us to determine dynamical masses for the main and subcluster components. MERGER GEOMETRY For simplicity, we assume the same merger geometry as in M04, schematically outlined in Figure 10 . Working in the rest frame of the main component, we assume the same simplification of a point mass subcluster and ignore dynamical friction. However, rather than using a β-model, we assume the mass distribution of the main component is defined by a NFW profile (Navarro, Frenk & White 1997) : MERGER GEOMETRY where Rs = R/c is a characteristic scale radius, c is the concentration parameter for radius R, and ρ0 is the typical NFW dark matter density for the cluster. Using the c(M, z) relation from Duffy et al. (2008) to determine c for our cluster, we have c = 3.018 and ρ0 = 5.497 × 10 14 M Mpc −3 . MERGER GEOMETRY Using the above mass profile and modelling the gravitational infall of the subcluster, we obtain the following relation between subcluster infall velocity, v, and physical separation, d, between the centres of the subcluster and the main component: MERGER GEOMETRY where M0 = 4πρ0R 3 s . The subcluster redshift z sub is greater than that of the main cluster component, zmain. As we argued in Section 2.1, the X-ray emission pattern indicates that the subcluster is moving towards the main component. This implies that the impact angle must be less than 90 MERGER GEOMETRY • . Using simple trigonometry, it follows from the merger geometry in Figure 10 that MERGER GEOMETRY where dmin is the projected separation between the main component and the subcluster, and v ⊥ is the velocity difference along the line-of-sight. Using the X-ray peaks of each component, the projected separation between cluster components is ∼0.78 , which corresponds to a physical projected distance of dmin = 237.6 kpc (as compared to 350 kpc in M04). In Section 5.2.1 we found v ⊥ = 1880 ± 210 km s −1 which is consistent with the value estimated by M04. Based on the X-ray arguments in Section 2.1, the two cluster components have begun interacting and we can place the following limits on the physical separation and the infall velocity: dmin < d < R200 and v > v ⊥ , where R200 is the cluster radius for the main component. MERGER GEOMETRY Simultaneously solving equations 8 and 9 with these constraints provides two sets of solutions for the merger model. These are listed in Table 9 , with the graphical solutions given in Figures 11 and 12 . The uncertainties on v, d, and θ are shown in Figures 11 (v and d) and 12 (d and θ), and are propagated from the uncertainties on the R200 mass and radius of the main cluster component, the R200 radius of the subcluster, and measured line-of-sight velocity difference. We consider these solutions in the next section to estimate relevant time-scales in the merger. MERGER AND RADIO HALO TIME-SCALES To better understand the formation history and mechanism(s) of GRHs, we would like to relate the GRH formation time-scale to the merger time-scale. It is possible to model the physics of turbulent re-acceleration using simulations. Donnert et al. (2013) (hereafter D13) used MHD simulations of a 10 15 M and 8:1 merger to study the strength and pattern of diffuse radio emission at various merger stages. They found that the cluster needs to have been actively merging for a minimum amount of time, approximately 15% into the merger, such that there is sufficient turbulence generated, before the radio emission switches on. Estimates for merger time-scales To estimate the merger time-scales for J0256 we assume a simple merger taking place in a linear fashion along the merger axis determined by the impact angle, θ, schematically outlined in Figure 13 . In Section 2.1, we ruled out a scenario in which the subcluster has already passed through the core. In Figure 13 , we isolate three distinct times during the merger: (A) first virial crossing; (B) core passage; and (C) second virial crossing. Even though we refer to virial crossing, we use R200 as a proxy for the virial radius. Estimates for merger time-scales From the optical analysis in Section 5.2, R Table 9 . Estimates for merger time-scales For each merger model solution found in the previous section, we compute the merger times Estimates for merger time-scales where n ∈ {A, B, C}, R0 is the observed position of the subcluster, and v NFW is the velocity function given in equation 8. The total time of the merger, at least for the first passage, is given by ttot = tC − tA. We define the relative time phase of the merger as the ratio Γ = |tA/ttot|. The results for each model solution are given in Table 9 . For case 2, we find that J0256 would have completed first virial crossing 1.41 Gyr ago with ∼120 Myr until first core passage occurs. This puts the cluster Γ2 = 46 +1 −2 % of the way into its merger. In case 1, J0256 is closer to the beginning of its merger with ∼460 Myr until first core passage. The time-scales for case 1 result in J0256 having a relative time phase of Γ1 = 35 +7 −18 %. According to D13, these conclusions lead to very different theoretical predictions for the observed strength and morphology of the radio emission. In the following section we compare our time-scale results with the D13 simulations. Comparison with MHD simulations The simulated radio powers and morphologies in D13 are for leonardsteven@example.com GHz of a massive 10 15 M cluster undergoing a 8:1 mass ratio, plane-of-the-sky merger. J0256 is about 50% of the total simulated mass but has a much smaller mass ratio of 7:4. As the strength, and hence observability, of the radio emission is related to cluster mass and the amount of turbulent energy created during a merger, we caution that, for
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