Are Radio Minihalos Confined by Cold Fronts in Galaxy Clusters? Minihalos and Large-scale Sloshing in A3444 and MS 1455.0+2232

We present radio and X-ray studies of A3444 and MS1455.0+2232, two galaxy clusters with radio minihalos in their cool cores. A3444 is imaged using the Giant Metrewave Radio Telescope (GMRT) at 333, 607, and 1300 MHz and the Very Large Array at 1435 MHz. Most of the minihalo is contained within r < 120 kpc, but a fainter extension, stretching out to 380 kpc southwest of the center, is detected at 607 MHz. Using Chandra, we detect four X-ray sloshing cold fronts: three in the cool core at r = 60, 120, and 230 kpc, and a fourth one at r = 400 kpc—in the region of the southwestern radio extension—suggesting that the intracluster medium (ICM) is sloshing on a cluster-wide scale. The radio emission is contained within the envelope defined by these fronts. We also analyzed archival 383 MHz GMRT and Chandra observations of MS 1455.0+2232, which exhibits a known minihalo with its bright part delineated by cold fronts inside the cool core, but with a faint extension beyond the core. Similarly to A3444, we find a cold front at r ∼ 425 kpc, containing the radio emission. Thus the entire diffuse radio emission seen in these clusters appears to be related to large-scale sloshing of the ICM. The radio spectrum of the A3444 minihalo is a power law with a steep index α = 1.0 ± 0.1. The spectrum steepens with increasing distance from the center, as expected if the minihalo originates from reacceleration of relativistic particles by the sloshing-induced turbulence in the ICM.

Minihalos are often contained within the cluster central cooling region (r < 0.2R 5003 ; Giacintucci et al. ( 2017)), suggesting a close relation between the radio emission and the properties of the thermal plasma in the cool cores.The existence of positive relations between radio luminosity and cluster global and cool-core X-ray luminosity supports a connection between the thermal and non-thermal cluster components (e.g., Kale et al. 2015;Bravi et al. 2016;Gitti et al. 2018;Richard-Laferrière et al. 2020;Giacintucci et al. 2019).
Most of the minihalo emission is often confined by X-ray cold fronts (e.g., Mazzotta & Giacintucci 2008;Hlavacek-Larrondo et al. 2013;Giacintucci et al. 2014a,b;Gendron-Marsolais et al. 2017;Savini et al. 2018;Timmerman et al. 2021;Riseley et al. 2022), hinting at a link between the origin of the diffuse emission and sloshing motions of the central cool gas (for reviews of cold fronts see, e.g., Markevitch & Vikhlinin 2007;ZuHone & Su 2022).Sloshing can strengthen the magnetic field and inject turbulence in the cool core (e.g., Fujita et al. 2004;Keshet 2010;Vazza et al. 2012;ZuHone et al. 2013), which in turn can confine and reaccelerate seed electrons, generating diffuse radio emission in the region enveloped by the cold fronts (ZuHone et al. 2013), as observed in actual minihalos.
Recent radio observations have further complicated our understanding of minihalos, and of their relation to giant halos in merging clusters (e.g., van Weeren et al. 2019), by unveiling diffuse emission outside the sloshing cool core in a few minihalo clusters (Gendron-Marsolais et al. 2017;Savini et al. 2018Savini et al. , 2019;;Biava et al. 2021;Perrott et al. 2021;Riseley et al. 2022).Diffuse emission extending far beyond the inner sloshing region has also been found in a few non-cool core clusters (e.g., Storm et al. 2015;Venturi et al. 2017;Giacintucci et al. 2022;Bruno et al. 2023;Lusetti et al. 2023;Riseley et al. 2023).These findings may indicate a co-existence of multiple components of diffuse emission in the same cluster, which may be powered by different processes or mechanisms acting on different spatial and time scales (e.g., Bruno et al. 2023).
Past powerful outbursts of the central AGN may also be responsible for very extended, steep-spectrum radio emission located outside of the cluster core, as in Ophiuchus (Giacintucci et al. 2020) where a 500 kpc-wide fossil radio lobe was found well beyond the central sloshing region occupied by the minihalo (see also discussion on A 2319 in Ichinohe et al. (2021)).
In this paper, we study the minihalos at the center of A 3444 and MS 1455.0+2232,two coolcore clusters at z = 0.254 and z = 0.258, respectively.The minihalo in A 3444 was first reported by Venturi et al. (2007) using a Giant Metrewave Radio Telescope (GMRT) observation at 610 MHz and by Giovannini et al. (2009) with the Very Large Array (VLA).It was later confirmed by VLA images 1435 MHz presented in Giacintucci et al. (2019), where it was detected on a scale of r ∼ 120 kpc.Recently, Trehaeven et al. (2023) presented new, deeper MeerKAT images at 1283 MHz, in which the diffuse radio emission was found to further stretch toward South/South-West into a ∼ 100 kpc-long, faint extension.
MS 1455.0+2232(also known as Z1760) hosts a known minihalo at 607 MHz and 1435 MHz (Venturi et al. 2008;Giacintucci et al. 2019), with its bright part delineated by sloshing cold fronts inside the cool core (Mazzotta et al. 2001;Mazzotta & Giacintucci 2008).It was recently imaged at higher sensitivity by Riseley et al. (2022) with MeerKAT at 1283 MHz and the LOw-Frequency ARray (LOFAR) at 145 MHz.Similarly to A 3444, a faint radio extension was found toward the South and South-West, extending beyond the sloshing cool core.
Here, we present new GMRT observations of A 3444 at 607 MHz and 1300 MHz.We complement these observations with archival GMRT data at 333 MHz and VLA 1435 MHz data from Giacintucci et al. (2019) to study the spectral properties of the diffuse emission, which can provide information on the origin of the radioemitting electrons.We also present the analysis of an archival upgraded GMRT (uGMRT) observation in Band 3 (250-500 MHz) containing MS 1455.0+2232 in its field of view, at ∼ 12 ′ from the phase center.For both clusters, we use archival Chandra X-ray observations to search for cold fronts at large radii and investigate the connection of the minihalos (including their extensions past the cool core) with sloshing of the intracluster medium (ICM) on large scale.

RADIO OBSERVATIONS OF A 3444
We present new GMRT images at 607 MHz, which allow us to image the minihalo with a higher sensitivity than previously achieved in Venturi et al. (2007).We also present new, high resolution GMRT data at 1300 MHz, and analyze archival GMRT data at 333 MHz.We summarize these observations in Table 1 along with details on the archival VLA datasets reanalyzed in Giacintucci et al. (2019).For each dataset, we report the largest detectable angular scale (θ LAS ) set by the minimum uv spacing.
All datasets are nominally able to detect extended emission on a maximum angular scale of at least 7 ′ which corresponds to a physical scale of ∼ 1.6 Mpc at the redshift of A 3444 (note that the VLA BnC and DnC datasets were combined together in the uv plane to produce the final images).This scale is much larger than the extent of the minihalo inferred from previouslypublished images, i.e., ∼ 1 ′ = 240 kpc in diameter (Venturi et al. 2007;Giacintucci et al. 2019).

GMRT 607 and 1300 MHz observations
We observed A 3444 on July 24 and August 20 2016 using the GMRT at the frequencies of 607 MHz and 1300 MHz (project 30 − 065) for a total of 8.5 hours and 5.6 hours, respectively (including time overheads for calibration).The visibilities were acquired in spectral-line observing mode using the GMRT software backend with a total observing bandwidth of 33 MHz, subdivided in 512 channels, and both RR and LL polarizations.
The data were reduced using the Astronomical Image Processing System (AIPS4 , Greisen 2003).We used the task RFLAG to excise visibilities affected by radio frequency interference (RFI), followed by manual flagging to remove residual bad data.Gain and bandpass calibrations were applied using the primary calibrators 3C147 and 3C286 at 607 MHz and 3C286 at 1300 MHz.The sources 1018-333 and 1526-138, observed several times during the observations, were used to calibrate the data in phase.A number of phase self-calibration cycles were applied to the target visibilities.Non-coplanar effects were taken into account using wide-field imaging by decomposing the primary beam area into ∼80 smaller facets at 607 MHz and ∼ 50 facets at 1300 MHz.
The final images at 607 MHz were obtained in AIPS using multi-scale imaging.The final self-calibrated data set at 1300 MHz was first converted into a measurement set using the Common Astronomy Software Applications (CASA5 , version 5.1 CASA Team et al. 2022) and then imaged using the multi-scale deconvolution option in WSClean (Offringa et al. 2014;Offringa & Smirnov 2017).The root mean square (rms) sensitivity level (1σ) achieved in the images at full resolution, obtained setting the Briggs robustness weighting to 0 (Briggs 1995), is 35 µJy beam −1 both at 607 MHz and 1300 MHz (Tab.1).
We also produced images with lower angular resolution increasing the robustness parameter and/or applying tapers to the uv data during the imaging process.The noise in these images is 50 µJy beam −1 at 607 MHz (20 ′′ resolution) and 43 µJy beam −1 at 1300 MHz (15 ′′ resolution).
Finally, for flux density measurements, we corrected the final images for the GMRT primary beam response6 using PBCOR in AIPS.All flux densities are given on the Perley & Butler (2017) wide-band scale.Residual amplitude errors are estimated to be within 5% at both frequencies (e.g., Chandra et al. 2004).

Archival GMRT data at 333 MHz
We analyzed archival GMRT observations of A 3444 at 333 MHz.The cluster was observed in April 2004 as part of the GMRT Cluster Key Project (05VKK01) for a total of ∼ 1 hour on source.The data were recorded using the old hardware correlator and both the upper and lower side bands (USB and LSB), providing a total observing bandwidth of 32 MHz.The default spectral-line mode was used with 128 frequency channels per band, each of width 125 kHz.3C286 was observed as flux density and bandpass calibrator.We calibrated the USB and LSB data sets individually in AIPS.
A combination of RFLAG and manual flagging was used to remove RFI and bad data.After bandpass calibration and a priori amplitude calibration using the Perley & Butler (2017) flux density scale, a number of phase-only selfcalibration cycles and imaging were carried out for each data set.Wide-field imaging was im-plemented in each step of the data reduction, with 25 facets covering the primary beam area.The final self-calibrated USB and LSB data sets was then converted into measurement sets using CASA 5.1 and imaged together using joint deconvolution in WSClean.The rms noise in the final image at full resolution (14 ′′ × 12 ′′ for a robust of 0) is 550 µJy beam −1 .Residual amplitude errors are estimated to be < 10% (e.g., Chandra et al. 2004).

UGMRT RADIO OBSERVATIONS OF MS 1455.0+2232
We reduced and imaged an archival uGMRT observation in Band 3 (250-500 MHz; project 38 − 010) containing MS 1455.0+2232 at 12 ′ .3from the phase center (the FWHM of the GMRT primary beam in Band 3 is 75 ′ ).The observation was made on 2020 Jul 29, for a total of ∼ 260 minutes on target (excluding calibration overheads; Tab. 2).
We used the Source Peeling and Atmospheric Modeling (SPAM; Intema et al. 2009) pipeline7 to process the uGMRT data, adopting a standard calibration scheme that consists of bandpass and complex gain calibration and direction-independent self-calibration, followed by direction-dependent self-calibration.The flux density scale was set using 3C 286 and Scaife & Heald (2012).The wide-band dataset was first divided into six narrower subbands, each 33.3 MHz wide.Each sub-band was then individually processed by the pipeline.The SPAM self-calibrated visibilities were converted into measurement sets using CASA and finally imaged together using joint-channel and multi-scale deconvolution in WSClean.For the imaging, we applied different weighting schemes (from uniform weights to a robust of +0.2) and uv tapers.
Correction for the GMRT primary-beam response was applied using the task PBCOR in AIPS and the primary-beam shape parameters given in a December 2018 GMRT memo8 .The systematic amplitude uncertainty was assumed to be 15%.

RADIO IMAGES OF A 3444
We present our new GMRT image (contours and colors) at 1300 MHz in Figure 1(a) The image has been obtained using a robust of 0.5 and restored with a 3 ′′ circular beam.In Figure 1(b), we overlay the same radio contours (black) on the optical Pan-STARRS-19 z-band image.In red, we overlay contours from a 1300 MHz image made using pure uniform weighting and with a higher angular resolution of 2 ′′ .A compact source, labelled S1, is associated with the brightest cluster galaxy (BCG).At this sensitivity level and resolution, no clear jets/lobes are detected from S1.Its < 2 ′′ angular size implies a physical extent of less than 8 kpc.
The compact source is enshrouded by diffuse emission from the larger-scale minihalo.In Figures 1(c) and 1(d), we show two lower-resolution images at 1300 MHz obtained with a robustness parameter of 2 and a beam of 5 ′′ and 15 ′′ , respectively.The green box marks the region covered by panel (a).For a visual comparison, in (d) we also overlay in cyan the +3σ = 0.1 mJy beam −1 isocontour of our new image at 607 MHz, which is presented in Figure 2(a), along with a VLA image at 1435 MHz (b).At 607 MHz, the minihalo reaches a radial distance of r ∼ 120 kpc from the cluster center.The minihalo is also detected on a similar scale in the GMRT images at 333 MHz.We show one of these images, at 20 ′′ resolution, in Fig. 3.
We made images with a coarser angular resolution to highlight the diffuse emission and show a pair of them in Figures 2(c) and 2(d) with a beam of 20 ′′ .These images were obtained using a common minimum uv baseline (0.4 kλ) and by tapering down baselines longer than 20 kλ.The minihalo does not appear to grow significantly in size in any direction but toward South West.Along this direction, the 607 MHz image reveals a "tail" of fainter emission (labelled SW extension) that extends well beyond the average minihalo radius of 120 kpc, reaching a distance   of ∼ 380 kpc from the center.This tail of emission is not detected in the images at 333 MHz and 1435 MHz because of their lower sensitivity, but it is well detected in the new MeerKAT images at 1.28 GHz (Trehaeven et al. 2023).Due to the higher sensitivity (1σ ∼ 9 µJy beam −1 for a beam of 7 ′′ ), the MeerKAT images trace the emission from this tail out to r ∼ 400 kpc.

RADIO FLUX DENSITY OF A 3444
We summarize the radio properties of S1 (BCG) and of the surrounding minihalo in Table 3.The flux density of S1 at 1300 MHz and 1435 MHz was measured on our highestresolution images by fitting the source with a Gaussian model (task JMFIT in AIPS).At 607 MHz, we report the JMFIT peak flux density measured within a r = 4 ′′ =16 kpc central re-gion on images obtained after cutting the innermost 10 kλ region of the uv plane to suppress the surrounding larger-scale emission from the minihalo.The flux density of S1 at 333 MHz, where it is not possible to separate well the point source from the minihalo due to the lower angular resolution, is instead extrapolated using the 607-1435 MHz best-fit spectral index (α fit, S1 = 0.6 ± 0.2, as calculated in Section 8.1).
To measure the flux density of the minihalo, we first made images at all frequencies using a common minimum projected baseline in the uv plane of 0.4 kλ.This spacing corresponds to a nominal largest detectable scale of ∼ 10 ′ , which is significantly larger than the average area covered by the minihalo emission (∼ 1 ′ in diameter).We then measured the total flux density on these images using a circular region centered on the cluster center and with a radius r = 40 ′′ (160 kpc) that encompasses the +3σ iso-contour at 607 MHz.Finally, we subtracted the flux density of S1 from the total emission and obtained a measurement of the minihalo total flux density, reported in Table 3 as MH, total.
Even though the BCG emission is unresolved in our highest-resolution images (Fig. 1(b)), we also provide measurements of the minihalo emission after excision of a larger region around S1 (i.e., in the interval 12 ′′ < r < 40 ′′ ) that avoids any possible contamination of the BCG into the immediately surrounding structure of the minihalo.These measurements are reported in Table 3 as MH, outer.We also provide flux density values for the inner 4 ′′ < r < 12 ′′ region of the minihalo (16 kpc < r < 50 kpc), referred to as MH, inner.In the VLASS Epoch 2.2 quick-look image, we found a faint, compact source at the position of the BCG.A Gaussian fit to the source gives a peak flux density of 1.05 ± 0.21 mJy beam −1 (this value was corrected for a low-flux density bias of 10% that affects faint sources in quick-look images from VLASS 1.2 onward, as reported in the NRAO Quick-Look Image web page 10 ; a total uncertainty of 20% was assumed).The extended emission from the minihalo is not detected in the VLASS image due to the high angular resolution (∼ 2 ′′ ), noise level (1σ = 130 µJy beam −1 ) and sparse uv coverage at short baselines of the VLA in its B configuration.

Low-frequency radio surveys
A radio source is detected at the cluster center in the 74 MHz VLSSr image at 3σ level (1σ = 80 mJy beam −1 ) and in the GLEAM image at 200 MHz at 16σ (1σ = 6.3 mJy beam −1 ).In both images (not shown here), the radio structure is unresolved at a resolution of 75 ′′ and 136 ′′ × 128 ′′ , respectively.A 16σ, marginally extended source is visible in the TGSS-ADR image at 150 MHz (not shown here), that has a smaller beam of 36 ′′ × 25 ′′ and a local noise of 1σ = 3.5 mJy beam −1 .
We also obtained an image from the first RACS data release (DR1) in the lowest band (888 MHz; RACS-low), convolved to a reso-   In Table 4, we summarize the total flux density measured on the survey images within the same r = 40 ′′ kpc central region used for the minihalo total emission in Table 3 these frequencies is expected to be only a few %.At 888 MHz, the total (MH+S1) flux density is 18.9 ± 1.9 mJy, of which 1.9 ± 0.2 mJy are expected to be from S1, leaving 17 ± 2 mJy in minihalo emission.

MS 1455.0+2232: RADIO IMAGES AND FLUX DENSITY AT 383 MHZ
We present uGMRT images of MS 1455.0+2232 at the central frequency of 383 MHz in Fig. 5.In (a) we show a high-resolution image, made with uniform weights, and mark the position of the compact source at the BCG (black cross) and other discrete radio sources in the region identified above 3σ = 0.075 mJy beam −1 (cyan crosses).In (b) we show a lower-resolution im-age of the diffuse emission after subtraction of the clean components associated with discrete sources from the uv data.The image was obtained adopting a robust of +0.2, a 10 ′′ Gaussian uv taper, and restored with a beam of 15 ′′ .The diffuse emission spans a total area of ∼ 145 ′′ × 110 ′′ (∼ 580 kpc × 400 kpc), which is significantly larger than measured in previous GMRT and VLA images (Venturi et al. 2008;Giacintucci et al. 2019), and in good agreement with the new MeerKAT and LOFAR images of Riseley et al. (2022).
Using Fig. 5(a), we measure a 383 MHz flux density of 9.7 ± 1.5 mJy for the BCG, which agrees well with the integrated radio spectrum of the source presented by Riseley et al. (2022).
From Fig. 5(b), we measure a total flux density in diffuse emission of 60 ± 9 mJy within the 3σ = 0.2 mJy beam −1 contour.On a similar scale, Riseley et al. (2022) measured a total of 18.7 ± 0.9 at 1283 MHz and 154.5 ± 15.6 mJy at 145 MHz, and computed a spectral index of α = 0.97 ± 0.05.Our measurement at 383 MHz is consistent with this spectral index: we find 0.97 ± 0.19 in the 145-383 MHz interval, and 0.96 ± 0.13 between 383 MHz and 1283 MHz.  3 and 4 and the regions in Fig. 6(a).
The spectrum of S1 has a power-law best-fit spectral index of α fit, S1 = 0.6 ± 0.2.The empty red circle is the VLASS 2.2 data point at 3 GHz.Due to the preliminary nature of the VLASS 2.2 quick-look images, we did not include this point in the spectral fitting.It is, however, in agreement with the best fit within the errors.
The total spectrum of the minihalo (black filled triangles) is described by a power law in the 333-1435 MHz range, with a steep slope of α fit, total = 1.0 ± 0.1.Its outer region (> 50 kpc; magenta squares) has a steeper spectrum with α fit, outer = 1.3 ± 0.1, whereas its inner region in blue (i.e., between the red and blue circles in Fig. 6(a)) has α fit, inner = 0.8 ± 0.1.
The best fits in Figure 6(b) were computed using only the pointed observations presented in this paper (filled points).Empty triangles are the data points from the radio surveys (Table 4).Despite the different angular resolution, sensitivity and uncertainties on the BCG contribution, the survey points show marginal scatter and appear in general agreement with the overall spectrum of the minihalo.
We note that Trehaeven et al. ( 2023) measured a MeerKAT in-band spectral index of α = 1.5 ± 0.4 for the minihalo, which is steeper than the spectral index we measure here (α fit, total = 1.0 ± 0.1), even though it is still consistent within the 1σ errors.For the spectral analysis, Trehaeven et al. (2023) used a region enclosed by the 5σ contour of each MeerKAT sub-image.This region is larger (by ∼ 10 ′′ ) than our extraction region (black circle in Fig. 6) and includes the brightest part of the SW extension, which may contain emission with a steeper spectrum (Trehaeven et al. 2023, see also Sect.8.3.).Therefore, it is unclear whether the steeper spectral index measured by MeerKAT reflects an actual steepening of the integrated radio spectrum of the minihalo at higher frequencies (the highest-frequency end of the MeerKAT band is 1.7 GHz) and/or whether the steeper measurement is affected by the contribution of the SW extension.

Radio spectral index distribution
In Figure 7, we show a color image of the spectral index distribution between 607 MHz and 1435 MHz (a) and associated error map (b), obtained by comparing a pair of primary-beam corrected images made with the same interval of projected baselines in the uv plane (0.4 − 50 kλ) and a circular restoring beam of 8 ′′ .The two images have a similar noise of ∼ 40 µJy beam −1 .Contours at 607 MHz are overlaid on both panels to provide a reference for the source morphology.The white cross marks the cluster center and the red and blue circles are the same as in Fig. 6(a).
The flattest spot in the center (α ∼ 0.6) coincides with the region occupied by S1, associated with the BCG, and is consistent with the slope of its integrated spectrum in Fig. 6(b).The surrounding diffuse emission has a spectral index that ranges from α ∼ 0.8 − 1.2 within the central 50 kpc (blue circle) to ∼ 1.2 − 1.5 at larger radii, and becomes even steeper in some of the outermost regions, though with large uncertainties (> 0.4).This behavior suggests a ); all, but RACS, include S1 (its contribution is estimated to be a few %).The solid lines are power-law fits (with slopes) to the data using only the filled data points.
steepening of the minihalo spectral index with increasing distance from the center.
To investigate this possible steepening, we obtained a spectral index radial profile (Fig. 8(a)), by extracting the 607 MHz and 1435 MHz flux density in annuli centered on the cluster center (Fig. 8(b)) and then computing the corresponding spectral indices.We used the same 8 ′′ -resolution images used to derive the spectral index map and a radial step of 4 ′′ for the annuli.The red and blue vertical dashed lines mark r = 4 ′′ (S1) and r = 12 ′′ (inner region).The profile confirms the trend hinted at by the spectral index map, showing a gradual radial increase in spectral index within the diffuse emission, with α = 0.8 ± 0.1 to α = 1.3 ± 0.3 going from r ∼ 20 kpc to ∼ 80 kpc.

Spectral index of the SW extension
For the SW extension detected in the lowresolution image at 607 MHz (Fig. 2(c)), we were not able to derive a spectral index image or a radial profile of the spectral index because the signal is mostly below the 3σ level at all other frequencies.For this reason, we only obtained an estimate of its overall spectral index by measuring the total flux density at 607 MHz and 1435 MHz within a sector containing the SW extension and ranging from ∼ 100 kpc to ∼ 380 kpc from the cluster center.We found a spectral index of α ∼ 1.4.This value is very uncertain, but it indicates that the SW tail may be slightly steeper than the minihalo emission in the outer r ∼ 50 − 100 kpc range (α ∼ 1.3; Fig. 8a).A steeper spectral index in the SW tail is also suggested by the MeeKAT in-band  spectral index image presented by Trehaeven et al. (2023).

X-RAY ANALYSIS: COLD FRONTS IN THE CORE OF A 3444
MS 1455.0+2232exhibits a pair of prominent sloshing cold fronts in its cool core in the Chandra image (Mazzotta et al. 2001;Mazzotta & Giacintucci 2008).Here we search for sloshing signatures in A3444 using the archival Chandra ACIS-S data (OBSID 9400, 36 ks).We refer to Giacintucci et al. (2017) for details on the data reduction and image preparation.All radial distances r are from the peak of the X-ray extended emission in the Chandra 0.5-2.5 keV image (10h23m50.0s,−27 • 15 ′ 24.1 ′′ ).
In Figure 9, we show a Chandra image of the central r ∼ 50 kpc region of the cluster with GMRT 1300 MHz contours overlaid from Fig. 1(b).No obvious X-ray cavities, associated with the extended radio emission, are visible in this inner region.The red cross marks the position of a weak X-ray point source that is coincident with the BCG, suggesting the presence of an AGN (Hamer et al. 2012).The peak of the extended X-ray emission is marked by a black cross.This peak is offset by ∼ 2 ′′ .5 (∼ 10 kpc) from the BCG (Hamer et al. 2012).A 3444 is one of the few clusters in which such a significant offset of the gas peak from the optical galaxy has been observed (e.g., Johnson et al. 2010;Hamer et al. 2012Hamer et al. , 2016;;Werner et al. 2016;Pasini et al. 2019Pasini et al. , 2021;;Giacintucci et al. 2022).These offsets may be a transient phenomenon caused by sloshing motions of the ICM in the cluster core, which can temporarily displace the densest and coolest gas from the optical nucleus.
In Figures 10 and 11, we present Chandra images showing the ICM emission on a larger scale.We see three surface brightness edges in these images.One (CF1) is located ∼ 60 kpc southwest of the X-ray peak, CF2 is located at r ∼ 120 kpc, and CF3 is at r ∼ 230 kpc.These edges appear to define a spiral-shaped pattern, similar to the structure seen in numerical simulations of gas sloshing in cluster cores (e.g., Ascasibar & Markevitch 2006) and often observed in the X-ray images of cool cores with cold fronts (e.g., Markevitch & Vikhlinin 2007;ZuHone & Su 2022, for reviews).An additional edge (CF4) is located well outside of the core, at r ∼ 400 kpc, suggesting that the ICM is sloshing on a cluster-wide scale.
We used pyproffit (Eckert et al. 2020) to extract and model the surface brightness profiles across these edges using a source-subtracted Xray image in the 0.5-2.5 keV band and corresponding exposure map.To account for the detector and sky background, we also included a re-projected, normalized blank-sky background image and the ACIS readout artifact (Markevitch et al. 2000).To compute the X-ray surface brightness profiles, we used the sectors indicated in Figs.10(a, c) and 11(a, c).Each profile is centered on the center of curvature of the front (note that these centers are not coincident with the cluster X-ray peak).The profiles are shown in Figs.10(b, d) and 11(b, d).We modeled these profiles assuming spherical symmetry and a broken power-law density profile in 3D (e.g., Markevitch & Vikhlinin 2007), with the powerlaw slopes and the position and amplitude of the density jump as free parameters.We found that the surface brightness discontinuities at the fronts are well described by density jumps with factors C CF1 = 1.6 ± 0.1, C CF2 = 1.4 ± 0.1, C CF3 = 1.4 ± 0.1, and C CF4 = 1.8 ± 0.1, as given by the best-fit broken power-law models shown in Figs.10(b, d) and 11(b, d).
We measured gas temperature profiles across these edges (Fig. 12) by fitting spectra as described in Giacintucci et al. (2017).Even though statistical errors are large, panels (a) and (b) show that the temperature increases moving outward across the surface brightness edge, indicating that both CF1 and CF2 are  cold fronts.For CF3 and CF4, the statistics is too low to constrain the temperature variation across this front; however, their temperature profiles (not shown) are consistent with cold fronts, as is the large-scale spiral pattern formed by CF1, CF2, CF3 and CF4.

DISCUSSION
In a number of clusters, radio minihalos have been found to be confined within the X-ray cold fronts.The likely origin of those X-ray fronts is gas sloshing, which would drive turbulence inside the cores and orient the ICM magnetic fields along the fronts.This would naturally explain the confinement of the radio emission within those fronts, if the synchrotronemitting electrons are reaccelerated by turbulence (ZuHone et al. 2013).MS 1455.0+2232 was one of the first examples of the confinement of the radio emission by cold fronts (Mazzotta & Giacintucci 2008).However, deeper radio images of a few minihalos, including MS 1455.0+2232, have revealed diffuse emission that "leaks out" beyond the cold fronts (e.g., Gendron-Marsolais et al. 2017;Savini et al. 2018Savini et al. , 2019;;Biava et al. 2021;Riseley et al. 2022), in apparent tension with the above picture.Below we see if there is indeed a tension.

Large-scale sloshing in A 3444
In Section 9, we have identified three sloshing cold fronts in the Chandra images of A 3444, at r = 60, 120, and 230 kpc.In addition, we have found an outer, prominent X-ray surface brightness edge at r ∼ 400 kpc.This edge is likely an old, large-scale sloshing cold front that has risen outwards.Numerical simulations of gas sloshing show that, as they age, cold fronts should propagate radially from the center into the outer regions of the cluster and should be long-lived (e.g., Ascasibar & Markevitch 2006;ZuHone et al. 2010;Bellomi et al. 2023).Largescale sloshing cold fronts have been in fact found in several clusters, including extreme cases, such as the Perseus cluster, A 2142, and RXJ 2014.8-2430, in which they have been detected out to ∼ 1 Mpc from the center (Simionescu et al. 2012;Rossetti et al. 2013;Walker et al. 2014Walker et al. , 2018)).
In Figures 13 and 14, we compare the radio emission to the position of the X-ray cold fronts in A 3444, marked by cyan arcs.In Fig. 13(a), we overlay contours at 1435 MHz of the innermost region of the minihalo, and in (b) we compare the X-ray and radio brightness profiles extracted in the sector containing CF1.The radio profile shows a clear edge at the position of CF1, suggesting a connection to the cold front.Beyond this edge, however, fainter radio emission is detected toward the region occupied by the SW radio extension.In Fig. 13(c), we overlay the 607 MHz contours on the X-ray image.In the northern region of the core, the minihalo is edged by CF2 at r ∼ 120 kpc.Panel (d) shows the X-ray/radio profiles across this front.The radio emission drops abruptly at the cold front location.Beyond the front, we do not detect any significant radio emission, at least at the sensitivity level of our 607 MHz image (1σ = 37 µJy beam −1 ) that allows us to detect emission at least 2 orders of magnitude below the radio peak.We note that the largest detectable scale of our 607 MHz dataset is ∼ 10 ′ , i.e., 10 times larger than the minihalo extent, thus the drop in radio brightness at the front is not caused by a limit in the scale that can be reconstructed by the interferometric data.This indicates that the minihalo is confined here by the cold front.
In Fig. 14(a), we show a Chandra image with the low-resolution contours at 607 MHz, showing the SW radio extension beyond CF1.In (b) we compare the X-ray and radio profiles extracted within the sector containing the radio extension and CF4.The radio profile traces remarkably well the X-ray profile inside the cold front.The radio signal falls below the 1σ level before CF4, however the radio emission appears to reach the cold front radius in the deeper MeerKAT images of Trehaeven et al. (2023).This suggests that the origin of the entire diffuse radio emission seen in A 3444 is related to large-scale sloshing motions of the ICM.10.2.Large-scale sloshing in MS 1455.0+2232 Our findings for A 3444 raise the question whether there are outer cold fronts also in MS 1455.0+2232 that may contain the radio emission seen outside of the sloshing cool core.To check whether there are indeed signatures of large-scale sloshing, we used an archival Chandra X-ray observation (OBS ID 4192) and produced images of MS 1455.0+2232following the procedure described in Giacintucci et al. (2017).In the following, all radial distances r are computed from the position of the X-ray peak (14h57m15.1s,+22• 20 ′ 33.9 ′′ ).
In Fig. 15(a), we show a Chandra image in the 0.5-2.5 keV band with the well-known sloshing cold fronts marked as CF1 and CF2 (Mazzotta et al. 2001;Mazzotta & Giacintucci 2008).We extracted an X-ray surface brightness profile in a sector that contains both CF1 and the radio extension seen at larger radii.The sector is marked by white lines in Fig. 15(a) and is centered on the center of curvature of CF1.The resulting profile is shown in (b), where the CF1 radius is indicated by the vertical, black-dotted line at d ∼ 0.3 ′ from the center of the sector (r ∼ 36 kpc from the X-ray peak).The profile reveals an additional prominent edge (CF3) at d ∼ 1.9 ′ (r ∼ 425 kpc), probably a larger and older cold front.To quantify this surface brightness edge, we fit the brightness profile in the immediate vicinity of the edge using a broken power-law model, with power-law slopes and the position and amplitude of the jump being free parameters.The best-fit model (blue line in Fig. 15(d)) gives a jump factor of C CF3 = 1.4 ± 0.2.
To highlight the position of this newlydetected front, we applied a Gaussian Gradient Magnitude (GGM; Sanders et al. 2016) filter to a point-source subtracted Chandra image assuming Gaussian derivatives with a width σ = 2.5 pixel (5 ′′ ).In black, we overlay the uGMRT radio contours at 338 MHz, showing that the diffuse radio emission is well contained within CF3.
As in A 3444, the detection of an outer X-ray front points to gas sloshing motions on cluster scale and suggests that the whole diffuse radio emission seen in MS 1455.0+2232 is sustained, through turbulent particle reacceleration, by large-scale sloshing motions of the hot ICM.

Origin of minihalos
Key information that can discriminate between the possible physical mechanisms for the origin of the relativistic electrons in minihalos is the slope and shape of the integrated radio spectrum and spectral index distribution across the region occupied by the diffuse emission (e.g., Brunetti & Jones 2014).If minihalos are sustained by turbulent re-acceleration of relativistic electrons (primaries or secondaries), depending on the spatial distribution of turbulent dissipation processes and magnetic field in the emitting region, the radio spectral index can range within a large interval of values, including very steep values (α ≳ 1.5; e.g., ZuHone et al. 2013;Brunetti & Jones 2014).Significant spatial variations of the spectral index are also expected across the emitting region.Furthermore, in the case of homogeneous magnetic field distribution and turbulence in the emitting region, the emitted synchrotron spectrum may show a break resulting from a cutoff in the electron energy distribution, at a frequency that depends on the acceleration efficiency (e.g., ZuHone et al. 2013).
The minihalo in A 3444 has a total spectral index of α fit, total = 1.0 ± 0.1 in the 333-1435 MHz range.Its innermost region (12 ≤ r ≤ 50 kpc) has a slighly flatter slope (α fit, inner = 0.8 ± 0.1), whereas the spectrum of its outer region (50 kpc < r < 160 kpc) steepens to α fit, outer = 1.3 ± 0.1.All of these spectra are consistent with an unbroken power law in the interval of frequency covered by our data, which is insufficient to discriminate between a re-acceleration or pure hadronic origin for the minihalo based on its integrated spectrum.A spectral break may still be present above 1435 MHz, as possibly indicated by a steeper spectral index measured for the minihalo emission by MeerKAT in the 0.8-1.7 GHz band, even though with large uncertainties (Trehaeven et al. 2023).
Similar to A 3444, the integrated spectrum of the minihalo in MS 1455.0+2232 is a single power-law with α = 0.97±0.05 in 145-1283 MHz range (Riseley et al. 2022).
For both minihalos, sensitive observations above 2 GHz would be therefore needed to search for a possible spectral break at high frequency.We note that power-law spectra extending to frequencies as high as 10-20 GHz have been reported for a couple of minihalos (Timmerman et al. 2021;Perrott et al. 2021), indicating the absence of a high-frequency break.The lack of a spectral break in the integrated spectrum does not necessary rule out re-acceleration.The radio spectrum may be, in fact, stretched into a power-law shape if it results from the combination of different spectral components tracing local fluctuations in the physical properties (magnetic field intensity, electron energy distribution, turbulence strength) within the emitting region (e.g., Donnert et al. 2013).
In Sec.8.2, we studied the spatial distribution of the radio spectral index over the minihalo in A 3444, which can provide important constraints on the origin of the diffuse emission.Our 8 ′′ -resolution spectral index image shows that the spectrum is relatively uniform at α ∼ 0.8 − 1.2 (with < 0.1 uncertainty) within the central 50 kpc.Spatial fluctuations from 1.2 to 1.5 (with uncertainties of ∼ 0.1−0.2) are seen outside of this region, with a hint of a steepening toward the outskirts.A radial profile confirms this trend, showing a gradual steepening from α = 0.8 ± 0.1 to α = 1.3 ± 0.3 from r ∼ 20 kpc to r ∼ 80 kpc.This behavior is expected if the minihalo originates from turbulence reacceleration of relativistic particles, in particular if the magnetic field (or re-acceleration rate) is declining radially, as discussed for giant radio halos (e.g., Brunetti et al. 2001;Bonafede et al. 2022).As a note of caution, it is possible that the innermost and flatter (α ∼ 0.8) region of the minihalo in A 3444 is contaminated by the activity of the BCG.No large-scale jets and lobes are seen in our high-resolution images, where the BCG is detected as a compact source (< 8 kpc).Furthermore, no hints of AGNdriven X-ray cavities are seen in the Chandra image, further suggesting the absence of AGN extended emission on large scale.However, we cannot completely rule out the possibility that the AGN has faint extended structure projected over the innermost region of the minihalo, thus affecting our spectral index measurement within this region.
Spectral index images of the minihalo in MS 1455.0+2232 were presented by Riseley et al. (2022) at 15 ′′ and 8 ′′ resolution.A relatively uniform spectral index was found over the minihalo extent, with possible fluctuations seen at large radii at the highest resolution.However, no clear radial spectral steepening was observed, with the exception of a possible steeper spectral index in the region of the SW radio tail.The lack of large variations in spectral index may result from the integration of different turbulent substructures along the line of sight, and therefore it may still be consistent with a turbulent reacceleration origin for the minihalo (Riseley et al. 2022).

SUMMARY AND CONCLUSIONS
We presented radio and X-ray studies of A 3444 and MS 1455.0+2232,two cool-core galaxy clusters that host diffuse radio minihalos in their centers.
In our GMRT (333, 607 and 1300 MHz) and VLA (1435 MHz) images of A 3444, the minihalo fills the inner r ∼ 120 kpc region of the cluster and encloses the central radio galaxy, that remains unresolved in our highestresolution image (2 ′′ ).South-West of the cluster center, a much fainter radio extension is detected at 607 MHz, out to a distance of ∼ 380 kpc.This structure is also seen in MeerKAT images at 1283 MHz (Trehaeven et al. 2023).We derived the integrated radio spectrum of the A 3444 minihalo, which is consistent with a power law with α = 1.0 ± 0.1, and studied the distribution of the spectral index between 607 MHz and 1435 MHz.We found a systematic steepening of the spectrum with increasing distance from the center.This behavior is expected if the minihalo originates from turbulence reacceleration of relativistic particles.
We analyzed an archival uGMRT observation at 383 MHz of MS 1455.0+2232.Similarly to A 3444, a large-scale faint radio extension beyond the previously-known minihalo is detected in the 383 MHz images.This radio extension was previously reported by Riseley et al. (2022) using LOFAR and MeerKAT observations.We found three sloshing cold fronts in the Chandra X-ray images of the cool core of A 3444, at r = 60, 120 and 230 kpc.A fourth, larger and older cold front is located well outside the core at r = 400 kpc -in the region of the SW radio extension -suggesting that the ICM is sloshing on a cluster-wide scale.We also found a prominent cold front at r = 425 kpc in MS 1455.0+2232,well beyond its cool core.In both clusters, the diffuse radio emission is contained within these outer fronts.This strongly suggests that the whole radio emission detected in these clusters arises from electrons confined and re-accelerated in turbulent fields in largescale sloshing motions of the hot ICM.
funding.We thank the staff of the GMRT that made the observations possible.GMRT is run by the National Centre for Astrophysics of the Tata Institute of Fundamental Research.RK acknowledges the support of the Department of Atomic Energy, Government of India, under project no.12-R&D-TFR-5.02-0700.The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.This scientific work makes use of the data from the Murchison Radioastronomy Observatory and Australian SKA Pathfinder, managed by CSIRO.Support for the operation of the MWA and ASKAP is provided by the Australian Government (NCRIS).ASKAP and MWA use the resources of the Pawsey Supercomputing Centre.Establishment of ASKAP, MWA and the Pawsey Supercomputing Centre are initiatives of the Australian Government, with support from the Govern-ment of Western Australia and the Science and Industry Endowment Fund.We acknowledge the Wajarri Yamatji people as the traditional owners of the observatory sites.This paper employs a list of Chandra datasets, obtained by the Chandra X-ray Observatory, contained in [Chandra Data Collection (CDC)

Figure 1 .
Figure 1.A 3444.(a) GMRT 1300 MHz image with robust 0.5 and 3 ′′ beam.The noise is 1σ = 35 µJy beam −1 .Contours are spaced by a factor of √ 2 from 0.1 mJy beam −1 .No levels at −0.1 mJy beam −1 are present.(b) GMRT 1300 MHz contours (black) from (a), overlaid on the optical z-band Pan-STARRS-1 image.Red contours are from a 2 ′′ -resolution image at 1300 MHz made with pure uniform weighting, and are spaced by a factor of 2 from 0.1 mJy beam −1 .The compact source S1 is associated with the BCG.(c, d) GMRT 1300 MHz images (colors and white contours) with robust 2 and 5 ′′ and 15 ′′ circular beams, respectively.The noise levels are 1σ = 43 µJy beam −1 and 70 µJy beam −1 .Contours are spaced by a factor of √ 2 from +3σ.No levels at −3σ mJy beam −1 are present.The green box marks the region covered by panels (a) and (b).The lowest contour of the minihalo at 607 MHz (from Fig. 2(a)) is reported in cyan for a visual comparison.

Figure 3 .
Figure 3.A 3444.GMRT image at 333 MHz (colors and white contours) with a 20 ′′ beam (white circle).The noise is 1σ = 800 µJy beam −1 and contours are spaced by a factor of 2 from 2.5 mJy beam −1 .No levels at −3σ mJy beam −1 are present.The lowest contour at 607 MHz (from Fig. 2(a)) is reported in cyan.The cyan circle shows the 8 ′′ beam at 607 MHz.
10 https://science.nrao.edu/vlass/data-access/vlassepoch-1-quick-look-users-guide lution of 25 ′′ , and a higher-resolution image (13 ′′ ) of the A 3444 field(McConnell et al. 2020) from the CSIRO ASKAP Science Data Archive (CASDA).Both are shown in colors in Fig.4.The morphology of the minihalo agrees well with the structure detected at 607 MHz (contours).The brightest part of the SW extension is marginally detected in the RACS-low image (at ∼ 2σ).

Figure 5 .
Figure 5. MS 1455.0+2232.(a) uGMRT 338 MHz high-resolution image with uniform weights.The beam is 4.5 ′′ × 5.5 ′′ (ellipse in the corner) and 1σ = 25 µJy beam −1 .Contours are spaced by a factor of 2 from 0.07 mJy beam −1 .Negative levels at −0.07 mJy beam −1 are shown as dashed contours.The black cross marks the compact source at the BCG.Cyan cross show the location of other discrete radio sources.(b) uGMRT 338 MHz low-resolution MHz image of the diffuse emission, after subtraction of discrete sources.The image was made using robust +0.2, a Gaussian taper of 10 ′′ , and restored with a beam of 15 ′′ (also shown in the corner).Contours are spaced by a factor of 2 from +3σ = 0.2 mJy beam −1 .No negative contours at −0.2 mJy beam −1 are present.For reference, the position of the BCG (which was subtracted out) is shown by the black cross.
Integrated radio spectraIn Figure6(b), we show the radio spectra of the BCG (S1, red) and diffuse emission (black, magenta and blue) based on the flux densities in Tables

Figure 6 .
Figure 6.A 3444.(a) Regions used to measure the flux densities in Tab. 3 of S1 (red circle), MH, total (between the black and red circles), MH, inner (between the red and blue circles) and MH, outer (between the blue and black circles).The red circle has r = 4 ′′ = 16 kpc, the blue circle has r = 12 ′′ = 50 kpc, and the black circle has r = 40 ′′ =160 kpc.The image is from Fig. 2(a).(b) Radio spectra of S1 (red), MH, total (black filled triangles), MH, outer (magenta) and MH, inner (blue), computed using the regions in (a) and the flux densities in Tab. 3. The empty red circle is the VLASS 2.2 flux density of S1. White empty triangles are from the radio surveys (Tab.4); all, but RACS, include S1 (its contribution is estimated to be a few %).The solid lines are power-law fits (with slopes) to the data using only the filled data points.

Figure 7 .
Figure 7.A 3444.Color-scale image of the spectral index distribution between 607 MHz and 1435 MHz (a) and associated error map (b), computed from primary beam corrected images with noise of 1σ = 40 µJy beam −1 , same uv range, pixel size and circular beam of 8 ′′ (black circle).The spectral index was calculated in each pixel where the surface brightness is above the 3σ level in both images.Overlaid are the 607 MHz contours, spaced by a factor of 2 from 3σ = 0.12 mJy beam −1 .The white cross marks the cluster center.The red and blue circles have r = 4 ′′ (S1) and r = 12 ′′ (MH, inner; see also Fig. 6(a)).

Figure 8 .
Figure 8.A 3444.(a) Spectral index between 607 MHz and 1435 MHz as a function of the distance from the cluster center, derived using the regions shown (b), centered on the cluster center (white cross) and with a radial step of 4 ′′ .The red and blue dashed lines mark r = 4 ′′ (S1) and r = 12 ′′ (MH, inner; see also Fig. 6).The radio image is at 1435 MHz (Fig. 2(b)) and the black contour is at +3σ = 40 µJy beam −1 .

Figure 9 .Figure 10 .
Figure 9.A 3444.(a) Chandra X-ray image in the 0.5-2.5 keV energy band, smoothed with a Gaussian with σ = 1 ′′ .The background is subtracted and the image divided by the exposure map.The red cross marks the position of an X-ray point source coincident with the BCG.The black cross is the peak of the extended X-ray emission, which is offset from the BCG (see also Hamer et al. 2012).(b) The same Chandra image with GMRT 1300 MHz contours from Fig. 1(b), with 3 ′′ (cyan) and 2 ′′ (blue) resolution.

Figure 12 .
Figure 12.A 3444.Radial projcted temperature profiles across CF1 (a) and CF2 (b) measured within the sectors shown in Fig. 10.The zero of the x-axis is at the front radius (dotted lines).Error bars are 1σ.

Figure 13 .Figure 14 .
Figure 13.A 3444. (a, c) Radio contours overlaid on the Chandra X-ray images (from Fig. 10).VLA contours at 1435 MHz are spaced by a factor √ 2 starting from 3σ = 0.12 mJy beam −1 (6 ′′ beam).Contours at 607 MHz are from Fig. 11(a).The cross marks the X-ray peak.Cyan arcs mark the cold fronts CF1, CF2 at the best-fit radii from Figs. 10 and 11.The radio (blue, red) and X-ray (black) brightness profiles, extracted in sectors marked by white lines, are shown in (b) and (d).The x-axis zero is at the cold front radius.The blue profiles use radial bins of 1 ′′ .The red points are radial bins as wide as the FWHM (6 ′′ and 8 ′′ ).Blue horizontal dotted lines indicate the noise level of the radio images.

Figure 15 .
Figure 15.MS 1455.0+2232.(a) Chandra X-ray image in the 0.5-2.5 keV band, background subtracted, divided by the exposure map and binned by a factor of 4 (1 pixel is 2 ′′ ).The red cross is the X-ray peak.The known cold fronts are marked as CF1 and CF2.(b) X-ray surface brightness profile extracted using the sector marked by white lines in (a).Vertical, black-dotted lines mark the position of CF1 and of an additional edge CF3.(c) GGM-filtered Chandra image with σ = 2.5 pixel (5 ′′ ).The red cross is the X-ray peak.Arcs show CF1 and CF2.The outermost cold front is indicated as CF3.uGMRT 383 MHz contours at 7 ′′ resolution are overlaid in black, spaced by a factor of 2 from 0.05 mJy beam −1 .(d) X-ray surface brightness profiles across CF3 extracted using the sector in (a).The blue lines are the best-fit broken power-law model with residuals (χ 2 /d.o.f.=8/12).

Table 1 .
Radio observations of A 3444

Table 4 .
Flux density of A 3444 from surveys Notes.Flux density of the A 3444 minihalo from low-frequency radio surveys measured within r = 40 ′′ kpc.The 200 MHz value is from the GLEAM catalog.All values have been re-scaled to the Perley & Butler (2017) flux density scale adopted in this paper.
a Includes S1.
184].This research has made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO.This research has made use of the CIRADA cutout service at URL cutouts.cirada.ca,operated by the Canadian Initiative for Radio Astronomy Data Analysis (CIRADA).CIRADA is funded by a grant from the Canada Foundation for Innovation 2017 Innovation Fund (Project 35999), as well as by the Provinces of Ontario, British Columbia, Alberta, Manitoba and Quebec, in collaboration with the National Research Council of Canada, the US National Radio Astronomy Observatory and Australia's Commonwealth Scientific and Industrial Research Organisation.