The velocity structure of the Intracluster Medium of the Centaurus cluster

There are few direct measurements of ICM velocity structure, despite its importance for understanding clusters. We present a detailed analysis of the velocity structure of the Centaurus cluster using XMM-Newton observations. Using a new EPIC-pn energy scale calibration, which uses the Cu Ka instrumental line as reference, we are able to obtain velocity measurements with uncertainties down to $\Delta v \sim 79$ km/s. We create 2D spectral maps for the velocity, metallicity, temperature, density, entropy and pressure with an spatial resolution of 0.25'. We have found that the velocity structure of the ICM is similar to the velocity structure of the main galaxies while the cold fronts are likely moving in a plane perpendicular to our line of sight with low velocity. Finally, we have found a contribution from the kinetic component of<25\% to the total energetic budget for radius $>30$ kpc.


INTRODUCTION
Theoretical simulations predict that the intracluster medium (ICM) should contain turbulent, or random motions, and bulk flows caused by the merger of other clusters and subcomponents (Lau et al. 2009;Vazza et al. 2011;Schmidt et al. 2017;Ha et al. 2018;Li et al. 2018;Vazza et al. 2021). In addition there can be relative bulk motions of ∼ 500 km/s due to sloshing of the ICM in the potential well, generated by merging substructures (Ascasibar & Markevitch 2006;Ichinohe et al. 2019;Vazza et al. 2018;ZuHone et al. 2018). The action of the relativistic jets and inflation of bubbles by the central AGN also likely generates motions of a few hundred km/s (Brüggen et al. 2005;Heinz et al. 2010;Randall et al. 2015;Yang & Reynolds 2016;Bambic & Reynolds 2019). This is also important for several other reasons. Turbulent motions affects calculations of hydrostatic equilibrium and cluster mass estimates given that they provide additional by measuring the Fe-K line. Tamura et al. (2011Tamura et al. ( , 2014 placed upper limits on relative velocities of 300 km/s over scales of 400 kpc in Perseus. (Ota & Yoshida 2016) examined several clusters with Suzaku, although systematic errors from the Suzaku calibration were likely around 300 km/s and its PSF was large. Other direct methods of measuring velocities include using XMM-Newton RGS spectra to measure line broadening and resonant scattering, showing low turbulence motion with velocities between 100 − 300 km/s Pinto et al. 2015;Ogorzalek et al. 2017), but limited to the cluster core. Finally, indirect measurements of velocity structure in clusters include looking at the power spectrum of density fluctuations and linking this via simulations to the velocity spectrum (e.g. Zhuravleva et al. 2014) or examining the magnitude of thermodynamic perturbations (Hofmann et al. 2016). However, these methods are model-dependent.
Random and bulk motions in the ICM were directly measured by the microcalorimeter Soft X-ray Spectrometer (SXS) X-ray detector on board of the Hitomi observatory using the Fe-K emission lines. In the core of the Perseus cluster it measured a gradient of 150 km/s bulk flow across 60 kpc of the cluster core and a line-of-sight velocity dispersion of 164 ± 10 km/s between radii of 30 − 60 kpc (Hitomi Collaboration et al. 2016). They indicate that the measured level of turbulence may be sufficient to offset radiative cooling if driven on scales comparable with the size of the largest bubbles in the field (about 20-30 kpc). On the other hand, the low level of turbulence in the system indicates that it might not be fast enough to replenish heating in the short time necessary to balance cooling, although shocks or sound waves could plausibly do this . Gravity waves, which could replenish turbulence, do not propagate efficiently radially . Simulations analyzed by Bambic et al. (2018) indicated that in the presence of large-scale magnetic fields the resulting production of turbulence is inefficient, even when able to preserve AGN-drive bubbles. In their analysis of XMM-Newton observations of the cool core clusters RXCJ1504.1-0248 and Abell 1664 done by Liu et al. (2021), they found that the turbulent energy density is less than 9% and 27%, respectively, thus insufficient for AGN heating to propagate the cool core via turbulence. Unfortunately, due to the loss of Hitomi we will not be able to make further measurements in other clusters or in different regions of Perseus. The next planned observatories with instruments capable of measuring velocities are likely XRISM (XRISM Science Team 2020), to be launched in 2023 and Athena (Barret et al. 2018) in 2030. Sanders et al. (2020) present a novel technique to improve velocity measurements calibrating the absolute energy scale of the detector to better than 150 km/s at Fe-K by using background X-ray lines seen in the spectra of the XMM-Newton EPIC-pn detector. Using this technique, (Sanders et al. 2020) mapped the bulk velocity distribution of the ICM over a large fraction of the central region of two nearby clusters of galaxies, Coma and Perseus. For the Coma cluster, they found that the velocity of the gas is close to the optical velocities of the two central galaxies, NGC 4874 and NGC 4889, respectively. In the case of the Perseus cluster, they detect evidence for sloshing associated with a cold front. Following the same methodology, Gatuzz et al. (2021) analyzed the velocity structure of the Virgo cluster. They identified a complex high velocity structure, most likely indicating the presence of an outflow near the AGN. Moreover, they found that the hot gas located within the radio flows move in opposite directions (i.e. blueshifted, redshifted) possibly driven by the radio jets or bubbles and with velocities of ∼ 331 km/s ∼ −258 km/s, with respect to M87.
The Centaurus cluster is an excellent target to apply such technique due to it being one of the X-ray brightest in the sky, its proximity allowing measurements on small scales (z = 0.0104, Lucey et al. 1986), high metallicity giving a strong Fe line and being a system with a merger and AGN feedback. Using optical observations Lucey et al. (1986) identified two subgroups in the Centaurus cluster, the main one centered on the galaxy NGC 4696 (refereed as Cen 30) and a second one centered on the galaxy NGC 4709 (refereed as Cen 45) 5 arcmin to the east with a line-of-sight (see Figure 1). The heliocentric velocities of the main galaxies are NGC 4696: 2958 ± 15 km/s (de Vaucouleurs et al. 1991), NGC 4709: 4678 ± 4 (Smith et al. 2000 and NGC 4696B: 3111 ± 7 (Smith et al. 2000). Walker et al. (2013) found evidence for a shock-heated region between the two systems, which could be explained by a simple shock-heating model. Despite this, Ota & Yoshida (2016) found that the velocity of Cen 45 was consistent with the main cluster velocity, with a velocity difference of < 750 km/s (90% limit). However, Suzaku had a large PSF and the spatial regions examined were large. The cluster contains three or more cold fronts, likely caused by the ICM sloshing in the potential well. These are seen as discontinuities in surface brightness, temperature and metallicity . Centaurus has probably the clearest cold front morphology seen in any nearby galaxy cluster. There is a possible large-scale Kelvin-Helmholtz instability in the core . Moreover, by analyzing Chandra observations, Sanders et al. (2016) have shown that the central AGN appears to have been repeatedly active over long timescales with periods of 10s of Myr. This is seen in edge-filtered Chandra X-ray images which show multiple cavity-like structures and possible sound waves. There is also extended low frequency ra-  192.20 -41.31 2006-07-24 124.3 0823580101 192.51 -41.38 2007-07-27 43.1 0823580301 191.75 -41.34 2007-12-27 34.9 0823580501 192.44 -41.29 2018-07-03 11.4 0823580701 192.26 -41.23 2018-07-13 113.9 0406200101 192.08 -41.16 2018-07-20 117.0 0504360201 192.13 -41.42 2018-07-26 116.9 0823580201 191.96 -41.34 2018-07-30 116.9 0823580401 192.31 -41.48 2018-08-09 114.9 0823580601 192.47 -41.27 2019-01-22 140.8 0823580801 192.26 -41.45 2019-06-30 137.9 dio emission associated with some of these cavities. Finally, in the core of the cluster there are also two weak shocks, surrounding the nucleus and inner cavities. Given all these highly energetic processes, we expect to find high velocities and, perhaps, velocity structure.
We present an analysis of the ICM velocity structure in the Centaurus galaxy cluster using XMM-Newton observations. The outline of this paper is as follows. We describe the data reduction process in Section 2. The fitting procedure is shown in Section 3 while a discussion of the results is included in Section 4. Finally, Section 5 presents the conclusions and summary. Throughout this paper we assume assumed a distance of Centaurus of (z = 0.0104, Lucey et al. 1986) and a concordance ΛCDM cosmology with Ωm = 0.3, ΩΛ = 0.7, and H0 = 70 km s −1 Mpc −1 .

DATA REDUCTION
Information on the Centaurus cluster observations analyzed in this paper is provided in Table 1, including IDs, coordinates, dates and clean exposure times. We reduced the XMM-Newton European Photon Imaging Camera (EPIC, Strüder et al. 2001) spectra with the Science Analysis System (SAS 1 , version 18.0.0). Each observation was processed with the epchain SAS tool, including only single-pixel events (PATTERN==0) and filtering the data with FLAG==0 to avoid regions close to CCD edges or bad pixels. Bad time intervals were filtered from flares applying a 1.0 cts/s rate threshold.
In order to obtain velocity measurements down to 150 km/s at Fe-K, we have applied the technique described in Sanders et al. (2020) to calibrate the absolute energy scale of the EPIC-pn detector using the background X-ray lines identified in the spectra of the detector. This calibration method include corrections (1) to the average gain of the detector during the observation, (2) to the spatial gain variation across the detector with time and (3) to the energy scale as function of detector position and time. In particular, we used the calibration files computed by Gatuzz et al. 1 https://www.cosmos.esa.int/web/xmm-newton/sas (2021). However, we do not expect changes with new caldb as observations are older than 2020. Figure 2 shows the X-ray image obtained in the 0.5 to 9.25 keV energy band (left panel). We have identified point sources using the SAS task edetect_chain, with a likelihood parameter det_ml > 10. In the following analysis we have excluded the point sources. Figure 2 top right panel shows the number of counts in each 1.59 arcsec pixel in the Fe-K complex (6.50 to 6.90 keV, in restframe), after subtracting neighbouring scaled continuum images (6.06 to 6.43 and 6.94 to 7.16 keV, in restframe). A gaussian smoothing of σ = 4 pixels was applied for illustrative purposes. The image shows that a large number of counts in the multiple directions around the cluster center, due to the spatial offset in the observations. Figure 2 bottom right panel shows the total exposure time in the 4.0-9.25 keV energy range. Figure 3 shows the fractional difference in 0.5 to 9.25 keV surface brightness from the average at each radius. The central region of the cluster exhibits a complex structure, no clear center and a very faint point source at the location of the AGN , thus preventing us from perform a velocity analysis using RGS spectra.

DATA ANALYSIS
In order to account for the possible presence of a multitemperature plasma, we constructed a model to describe a log-normal temperature distribution (namely lognorm). Such a log-normal temperature distribution associated with galaxy clusters was identified by Frank et al. (2013) in their analysis of 62 galaxy clusters using XMM-Newton spectra. The model takes as input a central temperature (T ), width of the temperature distribution in log space (σ), metallicities, redshift and a normalization. The output spectrum is constructed by summing a number of apec components with log-normal relative normalisations assuming they have the same redshift and metallicities. The relative normalisation of each component is given by where log Ti varies between log T − N σ to log T + N σ in n steps (where N = 3 and n = 21 by default). The relative normalizations are scaled so that the total is the overall normalization. Figure 4 shows a comparison between the apec and lognorm models for different σ parameter values.
We included a tbabs component (Wilms et al. 2000) to account for the Galactic X-ray absorption. For each spatial region analyzed, we combine the spectra from different observations together and rebinned the spectra to have at least 1 count per channel. Then, we load the data twice in order to fit separately, but simultaneously, the 1.5-4.0 keV and hard 4.0-10 keV energy bands. The free parameters in the model are the metallicity, log(σ) of the temperature distribution, temperature and normalization. The redshift is a free parameter only for the 4.0-10 keV energy band given that for lower energies the new EPIC-pn energy calibration scale cannot be applied. We note that the inclusion of the lower energy band data, for which the redshift parameter is fixed to the cluster value, leads to a better constrain for the temperatures and metallicites. We fixed the column density  to 8.10 × 10 20 cm −2 , although it is important to note that in the energy range analyzed the absorbing component has a weak effect in the modeling. For the data analysis we used the xspec spectral fitting package (version 12.10.1 2 ). We assumed cash statistics (Cash 1979  are given relative to Lodders & Palme (2009). As background components we have included Cu-Kα, Cu-Kβ, Ni-Kα and Zn-Kα instrumental emission lines, and a powerlaw component with its photon index fixed at 0.136 (the average value obtained from the archival observations analyzed in Sanders et al. 2020).

Spectral maps
We created a velocity map of the cluster following the method shown in Sanders et al. (2020) and Gatuzz et al. (2021). We created elliptical regions with a 2:1 axis ratio, rotating them such that the longest axis lay tangentially to a vector pointing to the central core. In order to reduce un- certainties on the velocities, the radii of the ellipses changed adaptively to have ∼ 500 counts in the Fe-K complex after continuum substraction. We moved in grid with a spacing of 0.25 arcmin. For each region we extracted the spectra for all observations and performed a combined fit. Then, we created weighted-average ancillary responses files (arf) for each ellipse from the individual ones for each observation but used the same response matrix for all the pixels. Figure 5 shows the velocity maps obtained. In order to improve the clarity we use a red-blue color scale to indicate whether the gas is moving away from the observer (red) or towards (blue). The map shows the complexity of the velocity structure in the system. Interestingly, there is no clear spiral pattern associated with gas sloshing (see for example Figure 18 in Sanders et al. 2020) nor an opposite blueshifted-redshifted structure around the cluster center (see for example Figure 11 in Gatuzz et al. 2021). Such features could point out that our line-of-sight is perpendicular to the sloshing plane of the system (see for example ZuHone et al. 2016). There is a clear blueshifted structure along the south-west direction from the cluster center with velocities larger than 1000 km/s, which could be due to the impact of AGN outflows from the NGC 4696 system. This could be a hint of azimuthal structure in the velocity. However, such structure corresponds to a region with large velocity uncertainties, which could also be a feature of gas sloshing (see for example Figure 19 in Gatuzz et al. 2021). The velocity spectral map shows a large blueshifted region southward from the Galactic cluster core. Such velocity increasing could be associated to gas sloshing signatures (see Figures 2 and 3 in ZuHone et al. 2018). The blueshifted gas displays an X-shape, which we have not identified in magnetohydrodynamic simulations. It is important to note that the resolution obtained in these spectral maps (∼10 kpc for the smallest ellipse) is larger than the radio observations (see for example Taylor et al. 2006), therefore preventing us from performing a direct analysis of the velocity structure within the extended component of the central radio source. Moreover, Taylor et al. (2006) shown that the radio emission seems initially directed north-south whit hints of interaction with the thermal gas which leads to a eastwest collimation. However, the main velocity field along the structure of the radio source is fairly close to the plane of the sky. Figure 6 shows the temperature, log(σ) and metallicity spectral maps. Near the Centaurus cluster core there is a high-metallicity region with low-temperature. A similar structure was identified, with higher resolution due to the Chandra instruments, by Sanders et al. (2016, see Figure 3). Outside the central region the temperature and metallicities changes smoothly, with the temperature increasing and the metallicity decreasing as we move to the outskirts of the cluster. We note that the two opposite regions with large velocity uncertainties located NE and SW from the cluster core, correspond to regions with large log(σ) and large temperature uncertainties where the Fe-K line is weak and broad.
Using these spectral maps we calculated projected pseudo-density, pressure and entropy in each spatial bin and assuming a constant line-of-sight depth for all spectral regions. We calculate the pseudo-density as n ≡ √ η, where η is the normalization of the lognorm model. Then, we estimated pseudo-entropy as S ≡ n −2/3 × kT and pseudo-pressure as P ≡ n × kT (see Hofmann et al. 2016). Figure 7 shows the density, pressure and entropy maps created from the bestfit results. We noted that the cluster center displays a high density gas and low entropy, similar to the maps obtained by Sanders et al. (2016). However the region with larger density seems to be displaced in the west direction with respect to the cluster center.

Fitting spectra concentric rings
We studied the velocity structure by analyzing manually extracted regions for two cases: • Case 1: complete concentric rings, square root spaced and with the center located in the cluster center.
• Case 2: concentric regions divided in E-W zones (i.e. following the cold fronts location), square root spaced and with the center located in the cluster center.    The top panel in Figure 8 shows the exact regions analyzed for Case 1. Table 2 shows the best-fit results obtained per region. Figures 9 and 10 show the velocities, temperatures, log(σ) and metallicities obtained from the best-fit per region. We have obtained velocities measurements with uncertainties down to ∆v ∼ 89 km/s (for ring 5). The largest blueshift/redshift, with respect to the main cluster redshift, correspond to −254 ± 114 km/s and 295 ± 197 km/s for rings 2 and 14, respectively. Both, the metallicity and temperature profiles, display a discontinuity at ∼ 50 kpc and at ∼ 100 kpc. We noted a complex structure in the temperature profile below such discontinuity (similar to results from Walker et al. 2013). Previous analyses of the Centaurus cluster have shown a drop in metallicity near the cluster center within < 10 kpc (e.g. Panagoulia Figure 8 shows the exact regions analyzed for Case 2. Figures 11 and 12 show the velocities, temperatures, log(σ) and metallicities obtained from the best-fit per region. In the plot green points correspond to results obtained with the E direction while blue points correspond to W direction. We have obtained velocities measurements with uncertainties down to ∆v ∼ 123 km/s (for ring 7, east direction). The largest blueshift/redshift, with respect to the main cluster redshift, correspond to −434 ± 265 km/s for ring 1 (east direction) and 457 ± 232 km/s for ring 15 (west direction). Both, the metallicity and temperature profiles, display a discontinuity at ∼ 30 kpc. We noted a difference in the metallicity profiles when comparing the outer region (i.e > 50 kpc), with larger values in the E direction compared to those rings in the W direction.

Cluster velocity substructures
We extracted spectra for spatial regions following the Xray surface brightness and having roughly equal number of counts in the Fe-K complex (∼2000). Figure 13 top panel shows the specific regions analyzed. The best-fit results are listed in Table 3. Figure 13 bottom panel shows the complex distribution of velocities obtained. We have obtained velocities measurements with uncertainties down to ∆v ∼ 120 km/s (for region 12). The largest blueshift/redshift, with respect to the Centaurus cluster, correspond to −223 ± 250 km/s and 1760 +514 −564 km/s for regions 3 and 17, respectively. In the following, we compare the ICM X-ray velocities obtained with the optical spectroscopic redshifts measured for the individual galaxies NGC 4696, NGC 4709 and NGC 4696B.
We have found that, for the regions 1,2 and 3, close to the main system NGC 4696, there is an excellent agreement between the obtained redshift and the Centaurus clus- ter redshift. For these points we obtain an average redshift of 0.0102 ± 0.0007. That is ∼ −61 km/s with respect to the Centaurus cluster. Other regions surrounding the Cen 30 system display similar velocities to that of the system (indicated in blue color in Figure 13 top panel), except for region 7 (261±200 km/s). Figure 14 shows the temperatures, log(σ) and metallicites profile obtained. The overall metallicity and temperature distribution is in good agreement with the spectral map shown in Figure 6. Regarding the metallicity and temperature, we have found that region 4 and 5, located south-west from the cluster core, has lower metallicities and larger temperatures than those located north-east from the cluster core (e.g. regions 6 and 7). The largest metallicity  and lowest temperature correspond to the cluster core (i.e. region 1 and 2). We note that region 22, containing NGC 4709 (i.e. the main galaxy of Cen 45), displays a velocity of 216 ± 258 km/s (with respect to the Centaurus cluster), within the velocity of the Cen 30 system, but significatively smaller than the Cen 45 system velocity (∼ 1500 km/s above Cen 30). Ota & Yoshida (2016) found an upper limit for the velocity around NGC 4709 < 750 km/s. They suggested that such results indicate that the Centaurus cluster has experienced a subcluster merger along the line of sight and gas near NGC 4969. The temperature obtained for that region is in good agreement with the temperature obtained by Walker et al. (2013) which could large be due to heating of gas near NGC 4696 by the strong shock along the merger process. On the other hand, for the region beyond NGC 4709 the velocity is 696 ± 310 km/s (region 23). For region 17 we have found a velocity of 1759 +565 −515 km/s, in good agreement with the NGC 4709 system velocity. As suggested by Ota & Yoshida (2016), such offset between the galaxy distribution and the mass centroids of the ICM along the sightline could be a fingerprint of a previous subcluster merger. For region 15, which contains the NGC 4696B, we have found a velocity of 642 +267 −249 km/s, much larger than the system velocity which is close to the Centaurus cluster velocity. We found that the most external region beyond NGC 4709 (region 23) displays the largest temperature (4.48 +0.11 −0.17 K) and lowest metallicity (0.47 ± 0.03). However, for regions with high kT and low Z the Fe K lines become fainter leading to larger uncertainties.

The cold fronts
We have created regions to measure the velocity structure in the cold fronts identified in the Chandra observations by Sanders et al. (2016). Figure 15 shows the exact regions analyzed (top panel) while the best-fit results are listed in Ta- ble 4. Figure 15 shows the velocity obtained for each region (bottom panel). For two cold fronts, there is a hint of larger velocities in the hottest region (i.e. region 2 compared to regions 1), however the uncertainties are too large to provide a good constrain on the velocities. These results suggest that the cold front motion is difficult to observe because the gas is moving in a plane perpendicular to our line of sight. Figure 16 shows the temperatures, the log(σ) and the metallicities obtained. As expected, there are clear differences in metallicity and temperatures in the interface between the cold fronts. The lack of significant metal mixing in cold fronts is likely due to its properties as a transient wave phenomena (Roediger et al. 2011). Following the fractional difference in 0.5 to 9.25 keV surface brightness, we have manually selected multiple regions in the innermost part of the cluster to study the velocity structure. Top panel in Figure 17 shows the extraction regions analyzed. Figures 17 and 18 shows the best-fit results while Table 5 list the best-fit parameters. We have obtained velocities measurements with uncertainties down to ∆v ∼ 79 km/s (for region 5). The average velocity for all regions is 52 ± 171. We note that regions in the east direction (i.e. 1 and 2) display lower velocity, larger temperature and larger metallicity than regions located in the west direction (i.e. regions 5 and 6).

Energy budget
We estimated the ratio of turbulent to thermal energy by measuring velocities for non-overlapping elliptical regions obtained in the spectral maps for different radius. Figure 19 shows the ellipse extraction regions analyzed, where different radius are indicated by different colors. For each radius we measured the velocity mean and σ-width, assuming a gaussian distribution, as function of the distance to the cluster center. Figure 20 top panel shows that the σ-width decreases Figure 19. Non-overlapping regions selected to analyze the energy profile for the spectral map obtained in Section 3.1. Different colors indicate the different radius assigned.
as we move away from the inner radius. As a comparison, we included the values obtained for the Virgo cluster by Gatuzz et al. (2021). The σ-width decreases faster for the former, due to the strong influence of the AGN outflows near the cluster center. However, uncertainties are large in both cases. We compute the sound speed for each region as cs = γkT /µmp, where kT is the best-fit temperature, γ is the adiabatic index, µ is the mean particle mass and mp is the proton mass. Then, we computed the Mach number as a function of the radius, by dividing the bulk velocity by the sound speed and assuming that velocities are isotropic. We have found that for the innermost radius the Mach number is ∼ 1.12, a value expected for AGN-driven outflow, while for radius > 30 kpc the Mach number is M ∼ 0.17 − 0.33, a range of values expected for gas sloshing (see middle panel in Figure 20). Bottom panel in Figure 20 shows upper limits for the ratio of turbulent ( turb ) to thermal ( ther ) energy computed as turb / ther = γ 2 M 2 . For radius > 30 kpc we found a contribution from the turbulent component < 25%.
It is important to note that we are assuming that motions are isotropic. Simulations computed by ZuHone et al. (2018) have shown that the kinetic energy may be underestimated near the cluster core by ∼ 10 − 60% depending on the line of sight, due to the conservative assumption of isotropy. Sanders et al. (2016) identified multiple substructures in the Centaurus cluster by analyzing Chandra observations, including a 1.9 kpc radius shell around the core which could be a shock generated by an AGN outburst, small cavities, filaments and a plume-like structure. Walker et al. (2015), in their analysis of Chandra observations, found onecomponent velocities in the range 100-150 km/s on spatial scales of 4-10 kpc. Due to the lower spatial resolution in the XMM-Newton observations we are not able to study the velocity distribution in such structures. We have found for most of regions velocities similar to the Centaurus cluster velocity, including for regions near the NGC 4709 subsystem, in good agreement with the upper limits obtained in the Suzaku data analysis done by Ota & Yoshida (2016). The velocities measured near the cluster center are much lower than those found by Dupke & Bregman (2006) in their analysis of Chandra observations. Finally, the temperature and metallicity profiles obtained in our analysis in the > 20 kpc scale (see Figures 10 and 12) are in good agreement with previous Chandra and XMM-Newton results (Takahashi et al. 2009;Panagoulia et al. 2013;Walker et al. 2013;Lakhchaura et al. 2019).

DISCUSSION
Idealized merger simulations indicate that sloshing motions can produce line shifts in the order of 100 − 200 km/s near the cluster core (ZuHone et al. 2016. Idealized AGN simulations are also capable of produce low line-ofsight velocity dispersions 150 km/s consistent with those observed by Hitomi in the Perseus cluster (Bourne & Sijacki 2017;Ehlert et al. 2021). Velocities obtained from cosmological simulations, on the other hand, vary between 100 − 400 km/s (Lau et al. 2017;Roncarelli et al. 2018). In this sense, the theoretical predictions are in good agreement with the velocity measurements.

CONCLUSIONS AND SUMMARY
We have analyzed the velocity structure in the Centaurus cluster using the technique developed by Sanders et al. (2020) to calibrate the absolute energy scale of the XMM-Newton EPIC-pn detector. Our results indicates that the ICM is dominated by the low velocity motions and, possibly, by the impact of the AGN in the NGC 4696 system. In this Section we briefly summarize our findings.
(i) We have obtained accurate velocity measurements with uncertainties down to ∆v ∼ 79 km/s.
(ii) We have created 2D projected maps for velocity, temperature, log(σ), metallicity, density, entropy and pressure distribution for the Centaurus cluster. There is no clear indication of the spiral pattern in the velocity map associated to gas sloshing. While there is a hint for blueshifted motion near the cluster center, most likely due to the influence of AGN ouflows, the velocity uncertainties are large.
(iii) We have studied the velocity distribution by creating non-overlapping circular regions. We found that the gas located at < 20 kpc from the cluster core displays low blueshifted velocities (with respect to the Centaurus cluster velocity) while gas located at 20 − 150 kpc displays a velocity close to the velocity of the cluster. Finally, gas located at large distance (i.e. > 150 kpc) displays a redshift behavior with low velocities (< 500 km/s).
(iv) We have analyzed the velocity distribution along E and W directions, by creating non-overlapping circular regions. We have found that, while the metallicity distribution shows larger values along the E direction for large distances, together with the lower temperatures in the same direction, the velocity distribution is similar along both directions (including the uncertainties). The velocities are < 600 km/s.
(v) We have analyzed spectra for spatial regions with similar number of counts to study the substructures within the cluster. We have found that the gas located near the cluster center display velocities similar to the velocity from the main system NGC 4696. We have found a region that displays a large redshift similar to the velocity of the system NGC 4709, suggesting an offset between the galaxy and the ICM velocity distribution.
(vi) We have analyzed the velocity structure following the surface brightness near the cluster core. We have found that the velocities are similar to the velocity of the Centaurus cluster.
(vii) We have analyzed the velocity structure following the 3 cold fronts located towards the E and W direction from the cluster core. Our measurements indicate that despite lack of significant metal mixing, the velocities are close to the velocity from the NGC 4696 system. In that sense, the cold front are likely moving tangentially (i.e. in a plane perpendicular to our line of sight with low velocity).
(viii) By fitting multiple non-overlapping regions, we have found the the width of the velocity distribution decreases as we move away from the cluster center. We have found a Mach number of M ∼ 0.17 − 0.33 for radius > 30 kpc from the cluster core, a range of values expected for gas sloshing. We also have found a contribution from the turbulent component of < 25% to the total energetic budget for radius > 30 kpc.
Future work will include the analysis of the soft band (< 1.5 keV).

ACKNOWLEDGEMENTS
This work was supported by the Deutsche Zentrum für Luftund Raumfahrt (DLR) under the Verbundforschung programme (Kartierung der Baryongeschwindigkeit in Galaxienhaufen). This work is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

Data availability
The observations analyzed in this article are available in XMM-Newton Science Archive (XSA 3 ). Ratio Energy (keV) Figure A1. Best-fit spectra obtained for the innermost region in the Case 1 analysis. The spectra have been rebinned for illustrative purposes. The background lines as well as the astrophysical Fe K line are indicated.
APPENDIX A: XMM-NEWTON SPECTRA AND FITTING PROCEDURE Figure A1 shows best-fits spectra obtained for the inner region analyzed in Case 1 in Section 3.2, as an example of the EPIC-pn spectra analyzed in this work. As described in Section 3, we load the data twice in order to fit separately, but simultaneously, the 1.5-4.0 keV and hard 4.0-10 keV energy bands. The instrumental emission lines used as part of the background emission for the energy scale calibration are Ni Kα (7.47 keV), Cu Kα (8.04 keV), Zn Kα (8.63 keV) and Cu Kβ (8.90 keV). Figure A2 shows the instrumental Cu-Kα redshift variation for each region in the Case 1 analysis, after applying the energy calibration scale correction. This plot shows a systematic uncertainty ∼ 75 km/s coming from the calibration uncertainty. This could be compared with the residual calibration uncertainties at ∼ 150 km/s level found by Sanders et al. (2020), which depends on the CCD spatial location. We also note that the Cu Kα redshift is obtained from the background fit which also includes the Ni Kα, Zn Kα and Cu Kβ lines, thus increasing the uncertainty.
Previous analysis of the Centaurus cluster have shown the presence of a multi-temperature component near the Centaurus cluster center Sanders & Fabian (2008); Panagoulia et al. (2013); Lakhchaura et al. (2019). In that sense, we have tested a two-temperature model (tbabs*(apec+apec)) in our fitting procedure, however we note that for multiple extraction regions the second temperature component was not well constrained. In order to avoid switching between 1T and 2T models in some arbitrary way, we decided to use the lognorm model. Figure A3 shows a comparison of the best fit statistic obtained for all regions in Case 1 analysis when fitting the spectra with the lognorm model and with 1-apec mode. In all cases the lognorm leads to a better fit, from the statistical point of view.  Figure A3. Statistical comparison between the lognorm (red) and the apec (blue) models for each region in the Case 1 analysis.