SUBSTRUCTURE IN THE COLD FRONT CLUSTER ABELL 3667

The parent photometric catalog was obtained from the Supercosmos Sky Survey (SSS) server⁴ using the object catalog extraction function. Objects classified as galaxies (SSS class  = 1) within a radius R = 53' (3.4 Mpc) of the central dominant cluster galaxy at R.A. = 20^h12^m2738, decl. = −56° 49' 387 were included. We further filtered the catalog such that for R ⩽ 2 Mpc, only objects with magnitudes r_F ⩽ 19.0 were included, whereas for 2 < R ⩽ 3.4 Mpc a brighter magnitude limit of r_F ⩽ 18.0 was adopted. These selection criteria limited the catalog to a manageable size, given the available telescope time, while retaining the objects most likely to be cluster members. This resulted in a total of 2163 galaxies being included in our parent catalog.

To maximize the efficiency of our spectroscopic observations in terms of targeting cluster members, we ranked each galaxy in the parent catalog on the basis of its position in the color–magnitude (CM) plane (see Figure 1), as well as its projected distance from the cluster center. The position of galaxies relative to Abell 3667's red CM sequence was used as a means to weight our target selection, with the red sequence being identified using 160 spectroscopically confirmed members obtained from the NED catalog. These, and further spectroscopically confirmed members as determined in Section 3, are represented by the green points in Figure 1, and at magnitudes fainter than r_F ∼ 16.5 are seen to delineate a red sequence which exhibits the usual negative slope in the CM diagram. At r_F < 16.5, this red sequence persists, but exhibits a positive slope, which we can only assume is due to some systematic problem in the photometry at these brighter magnitudes. This behavior, however, is not problematic for preselecting targets, since all we want to do is use the red sequence to define a likely upper red envelope, below which most cluster members reside (galaxies above are almost certainly more distant nonmembers). The solid straight line shown in Figure 1 (for which b_J − r_F = 0.168 × r_F − 1.771) represents the red envelope that was adopted. Its position and slope were set to best include all galaxies on and bluewards of the red sequence, allowing for the systematic change in its slope and the increasing photometric scatter at fainter magnitudes. Galaxies meeting these criteria at R⩽ 500 kpc from the cluster center were given the highest rank. For more remote galaxies, the rank was decreased for each additional 500 kpc step in distance from the cluster center. Galaxies lying above the red envelope were all given lower rank than those below, as well as being ranked in a similar manner by their cluster-centric distances.

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For completeness, we also plot in Figure 1 objects which have been shown in Section 3 to be foreground stars (shown as the dark blue stars), foreground galaxies (light blue stars), and background galaxies (red squares). The small black points indicate objects in the field without spectra.

Substantial new spectroscopy of Abell 3667 was obtained with the two degree field (2dF)/AAOmega multiobject spectrograph facility on the 3.9 m Anglo-Australian Telescope (AAT) during the nights of 2007 July 14–18. AAOmega is a bench-mounted dual-beam spectrograph which is fed by 400 fibers which are robotically placed within the AAT's two degree field of view at prime focus (Saunders et al. 2004; Smith et al. 2004; Sharp et al. 2006). All observations were taken using the medium resolution (R ≃ 1300) 580 V (blue arm) and 385 R (red arm) gratings. In combination with the 2 arcsec diameter fibers, they deliver a spectral resolution at the detector (a 2 k × 4 k 15 μm pixel E2V CCD in each arm) of 3.6 Å in the blue and 5.5 Å in the red. The wavelength range covered by the two arms is 3700–8800 Å.

The large number of galaxy targets and their highly clustered distribution on the sky, together with 30 arcsec restriction on the minimum separation between fibers, meant that six different plate configurations were required to obtain a high level of spectroscopic completeness and adequate coverage in the central regions of Abell 3667 where the cold fronts are located. The fiber allocations for each of these configurations were done automatically using the AAOmega specific CONFIGURE program.⁵ This program uses a "simulated annealing" algorithm (Miszalski et al. 2006) to ensure the optimal allocation of fibers in terms of maximizing the number of objects observed. In doing so, it uses the rankings/weights assigned to targets (Section 2.1) to determine what priority they have in being allocated a fiber.

The use of the simulated annealing algorithm required the input catalog be reduced to no more than ∼800 objects for fiber allocation. To achieve this, the catalog was first split into the 1452 higher priority objects, on or blueward of the of the red sequence, and the 711 lower priority ones, redward of the red sequence (Section 2.1). The higher priority group were further subdivided into 830 objects with r_F ⩽ 18 and the 622 with 18 < r_F ⩽ 19. Two fiber configurations were required to observe the high priority r_F ⩽ 18 catalog. The small number of objects in the r_F ⩽ 18 catalog that were not observed in these two configurations were added to the 18 < r_F ⩽ 19 high priority catalog. Finally we constructed a catalog made up of those objects not already allocated, plus previously allocated objects with unreliable redshifts (see below) and a small number of low-priority objects. Hence in total, six configurations were observed, the majority of which targeted objects lying on or blueward of the Abell 3667's red sequence. Observing conditions were generally cloud free, but the seeing was rather poor, being in the range 2.4–4.0 arsec (FWHM). However, given the extended nature of our galaxy targets due to their relatively low redshifts, mediocre seeing did not have any serious impact on our program. The dates, exposure times, magnitudes, and conditions for the observations are summarized in Table 1.

Table 1. Summary of the AAT/AAOmega Observations for Abell 3667

Date	Object Priority	Magnitude	Frames	Seeing
2007 Jul 14	High	rF <18.0	4 × 1800 s	2.8–29
2007 Jul 16	High	rF <18.0	3 × 1800 s	2.8–35
2007 Jul 16	High	rF <19.0	4 × 1800 s	2.4–30
2007 Jul 16,18	High	rF <19.0	2 × 1800 + 3 × 1200 s	35
2007 Jul 17,18	High + Low	rF <19.0	3 × 900 + 3 × 1800 s	2.8–4''
2007 Jul 18	High + Low	rF <19.0	3 × 1200 s	35

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For sky subtraction, >40 fibers per configuration were allocated to blank sky regions, selected using the "Generate sky grid" command in the CONFIGURE software and visually inspected to ensure they were free of objects. Approximately 35 known "fringing" fibers were excluded from the configuration process. Prior to each fiber configuration being observed, tungsten and arc lamp exposures were taken for flat-field and wavelength calibration, respectively. The data were fully reduced at the telescope using the AAO 2dfdr⁶ pipeline reduction system. This system extracts and produces fully flat-fielded, wavelength-calibrated, and sky-subtracted (but not flux-calibrated) spectra for each exposure frame, coadds the spectra in each exposure set, and then splices together the blue and red-arm spectra.

Redshifts were identified and measured from the reduced spectra using the runz code written by Will Sutherland for the Two Degree Field Galaxy Redshift Survey (2dFGRS; Colless et  al. 2001). This program utilizes the cross-correlation method of Tonry & Davis (1979). Each spectrum was visually inspected and given a redshift quality classification, Q, ranging from 1 to 6, as described in Paper I. A Q value of 3, 4, or 5 indicates a reliable redshift was obtained (with a larger value indicating a higher quality spectrum), whereas Q values less than 3 indicate either an unreliable redshift or no redshift was obtained. A value of Q = 6 was used in cases where the redshift indicated the object to be a star. We obtained 1714 spectra during the run, of which 1570 yielded reliable (Q > 2) redshift measurements containing 910 extragalactic objects and 660 stellar objects (Q = 6), indicating the unreliability of the SSS star/galaxy classifications.

Of the objects observed twice, 50 had two reliable (Q > 2) redshift measurements and so in these cases we were able to compare redshifts to assess the robustness of our measurements and determine their uncertainty. After excluding one obvious outlier where the redshift difference was Δcz = 12732 km s⁻¹, we found $\overline{\Delta cz}= 50\pm 20$ km s⁻¹ for the difference between the first and second groups of measurements. We also have 117 high-quality measurements in common with the redshift catalog of Johnston-Hollitt et al. (2008) and we found $\overline{\Delta cz}= -18\pm 9$ km s⁻¹, again after excluding one outlier with Δcz = 16134 km s⁻¹. These redshift comparisons are encapsulated in Figure 2, noting that we only consider objects in the redshift range 0.045–0.065 (i.e., that appropriate to Abell 3667). The upper panel of Figure 2 shows that the redshift comparisons scatter about a one-to-one relationship (solid line with slope unity), indicating there are no redshift-dependent systematic effects. The redshift differences are shown in the lower panel. We derive an RMS redshift difference of 151 km s⁻¹ for the AAOmega double observations, which implies a redshift uncertainty of 107 km s⁻¹ for the sample, comparable to the RMS of the individual redshift uncertainties which is 112 km s⁻¹. An external check is given by the RMS of the differences between our AAOmega and Johnston-Hollitt et al. (2008)'s redshifts, which gives an uncertainty of 64 km s⁻¹, much lower than the quadrature sum of 148 km s⁻¹ for the uncertainty above and the uncertainty of the (Johnston-Hollitt et al. 2008) sample (∼100 km s⁻¹). We take the precision of our redshift measurements to be the more conservative value of 107 km s⁻¹.

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In cases where a galaxy had multiple redshift measurements, the following policy was adopted in determining which value would be used for our analysis. If both the measurements were made with AAOmega, we adopted the redshift with the higher Q value. If the Q values were equal, then we took the redshift with the smallest measurement uncertainty (as provided by the runz program). If the second redshift measurement came from Johnston-Hollitt et al. (2008)'s catalog, we used our AAOmega redshift (for consistency). Only 25 extra redshifts were added to our catalog from the Johnston-Hollitt et al. (2008) catalog, taking our total number of redshifts to 1595.

The completeness of our redshift measurements was determined by calculating the fraction of galaxies in the parent photometric catalog for which reliable redshifts were obtained. In the left panel of Figure 3 we plot the completeness as a function of cluster-centric radius for the magnitude ranges r_F < 16, 16 ⩽ r_F < 17, 17 ⩽ r_F < 18, and 18 ⩽ r_F < 19. It shows that we have achieved excellent completeness within a cluster-centric radius of 2.5 Mpc. We also plot the completeness as a function of r_F magnitude in right-hand panel of Figure 3 which demonstrates a high level of completeness across all magnitude bins. The cluster is very well sampled at magnitudes brighter than r_F = 19 for all radii less than 2.5 Mpc. If we assume the cluster $M^*_{r_F}=-20.84$ (Eke et al. 2004) and neglect K-correction and galactic extinction terms, we probe ∼3 mags down the luminosity function.

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Dynamically relaxed clusters are expected to have line-of-sight velocity distributions which are very close to Gaussian. Departures from Gaussianity in cluster velocity distributions can signify a number of different physical phenomena, e.g., highly radial orbits, interloper contamination, circular orbits and, most commonly, substructure within the cluster. It must be noted, however, that nondetection of departures from Gaussianity is not necessarily evidence of a relaxed system (Pinkney et al. 1996; see also Paper I).

Our initial test for departures from Gaussianity involves the use of the Kolmogorov–Smirnov (K-S) statistic (Press et al. 1992) which measures the largest absolute departure between the cumulative probability distribution of a data sample and a theoretical distribution describing the data (here, a Gaussian) and determines the significance of the difference by calculating the likelihood that the data are drawn from a parent distribution which is Gaussian, taking into account the sample size. The K-S test reveals no evidence for non-Gaussianity at the 50% level.

The disadvantages of the K-S test are its lack of sensitivity in the tails of a distribution (it is most sensitive in the vicinity of the median), its spurious results in the presence of interlopers and also its failure to quantify the way in which a distribution may differ from Gaussianity, which is clearly important in determining the physical driver of the departure from Gaussianity. Thus, we used the method first applied to galaxy cluster velocity distributions by Zabludoff et al. (1993) where the distribution is approximated by a series of three Gauss–Hermite functions: the coefficient of the zeroth-order term, h₀, multiplies a best-fitting Gaussian, the third-order term, coefficient h₃, describes asymmetric deviations from Gaussianity (similar to skewness), and the fourth-order term, coefficient h₄, describes symmetric deviations (similar to kurtosis). It has the advantage of being insensitive to outliers in the tails of the distribution (compared to the Gaussian skewness and kurtosis measurements). For Abell 3667, the third- and fourth-order terms had values of h₃ = 0.009 and h₄ = 0.047.

To determine the significance of the results, we generated 10,000 Monte Carlo realizations of Gaussians with N = 550 and mean and dispersion equal to the best-fitting value derived for our data, and determined the number of times our observed values occurred in the simulations. Values of |h₃| ⩾ 0.009 occur in 77% of the realizations, so we conclude the observed h₃ term is not significantly different from zero. Values of |h₄| ⩾ 0.047 occur only 10% of the time, thus we conclude the observed h₄ term is mildly significant. The positive value of the h₄ term means that the velocity distribution has slightly longer tails and is more peaked than the best-fitting Gaussian, suggestive of either radial orbits or substructure. In Figure 7 we plot the binned velocity distribution, with both a Gaussian (with a mean of zero and a standard deviation of 1056 km s⁻¹) and the Gauss–Hermite reconstruction curves overlaid.

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We searched for possible segregation in the velocity distribution using weighted gaps (Beers et al. 1990), where the velocities are sorted in increasing order and the ith velocity gap is given by g_i = v_{i + 1} − v_i. The weight for the ith gap is w_i = i(N − i) and the weighted gap is defined as $\sqrt{w_i g_i}$. The weighted gaps are normalized through dividing by the mid-mean (MM) of the ordered weighted gap distribution given by

$$\begin{equation} MM = 2/N \sum ^{3N/4}_{i=N/4}\sqrt{w_ig_i}, \end{equation} \tag{ 1 }$$

where N = 550. Normalized weighted gaps which have values larger than 2.5 occur 1.4% of the time when selecting gaps at random from a Gaussian distribution (Wainer & Schacht 1978), thus eight such gaps are expected for Abell 3667. In fact we find four such gaps, shown as arrows in Figure 7 where the positions of each peculiar velocity in the sample is plotted in a strip density plot. We conclude that the weighted gap analysis does not provide significant evidence for segregations in the velocity distribution of Abell 3667.

While the tests for Gaussianity are useful for detecting mergers occurring along our line of sight, where the velocity distribution is significantly perturbed, they can be ineffective in the case of a merger occurring near the plane of the sky (Pinkney et al. 1996, and Paper I). In these cases, projected galaxy density maps are useful tools for searching for evidence of substructure, but are contaminated by background or foreground interlopers projected along the line of sight when redshift information is not available.

Given the presence of significant substructure apparent in the projected galaxy density maps of Proust et al. (1988) and Sodre et al. (1992), and the nondetection in of significant substructure in the maps of spectroscopically confirmed cluster members in Johnston-Hollitt et al. (2008), we use our much larger sample to produce a galaxy density map to search for signs of substructure. We plot the distribution of all galaxies in the sample, along with the associated surface density contours in the left-hand panel in Figure 8. The contours were generated by smoothing the distribution with a variable-width Gaussian, where σ varies from 140 kpc in the center to 500 kpc in the outskirts. We find similar results to Proust et al. (1988) and Sodre et al. (1992), finding Abell 3667's galaxy surface density distribution is clearly bimodal, with a high surface density core at the center and also a high-density region offset by ∼1 Mpc to the northwest which is coincident with the second dominant cluster galaxy. There are two other clear peaks in the surface density, one ∼1.2 Mpc to the southeast and one ∼1.1 Mpc just west of due north.

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As a first-order test for correlation between multipeaked surface density distribution and the velocity distribution, we split the catalog into positive and negative peculiar velocities and plot the spatial distributions. The two segregations are shown in the middle and right-hand panels of Figure 8, along with the associated galaxy surface density contours, generated using the same Gaussian smoothing described above. The most notable features upon comparing the positive and negative maps are; the southeast and northeast peaks, which are clearly more significant in the negative peculiar velocity map and the northwest peak appears in both the positive and negative maps, although it is more significant in the positive velocity map and slightly offset in the negative velocity map.

In the previous section, we searched for spatial/velocity correlations by crudely splitting the catalog into positive and negative velocity samples. In this section, we combine both velocity and spatial information to test for substructure in a more refined manner. In general it has been found that tests simultaneously employing both spatial and velocity information are most successful at detecting substructures (Pinkney et al. 1996). Here, we incorporate the k-statistic, hereafter κ_s, which was first used in the analysis of substructure within Coma by Colless & Dunn (1996). The κ_s tests for departures between local and global kinematics by determining the probability that the local velocity distribution differs from the global one. In brief, the evaluation of κ_s is performed as follows: the nearest $n=\sqrt{N}$ neighbors in projected radius from each galaxy in the sample are selected, where N is the number of cluster members. The velocity distribution of the n neighbors is compared to the velocity distribution of the remaining N − n galaxies using the K-S D-statistic and the likelihood of finding a D-statistic larger than the observed D-statistic is determined. Hence, low likelihoods give an indication that the local and global velocity distributions are significantly different. The negative log of the likelihoods are summed to give an overall measure of the substructure present within the cluster. The significance of the substructure is determined by repeating the above analysis for 10,000 Monte Carlo realizations, where any correlation between the spatial and velocity distributions due to substructure within the cluster is erased by randomly shuffling the peculiar velocities in the sample, whilst maintaining spatial information. For Abell 3667, we measured an overall κ_s of 422. In contrast, the κ_s distribution produced in our Monte Carlo realizations is well modeled by a log–normal distribution with a mean of μ(ln κ_s) = 5.44 and standard deviation σ(ln κ_s) = 0.15, indicating our result is significant at the 3.96σ level, and a value as large as 422 was not obtained in any realization.

Pinkney et al. (1996) showed that strong radial gradients in the cluster velocity dispersion profiles can produce high false positive detection rates for 3D substructure tests. With this in mind, and given that Figure 6 shows a significant gradient in the σ(R) profiles for Abell 3667, we remeasured κ_s within the 2 Mpc region shown in Figure 9. The observed κ_s in the smaller region is 312, and a value of this order is obtained in only 12 of our 10,000 Monte Carlo realizations which produce a mean of μ(ln κ_s) = 5.27 and standard deviation σ(ln κ_s) = 0.17, indicating the observed κ_s is significant at the 3.13σ level, again indicating the existence of substructure within Abell 3667 at high significance.

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The most effective way to illustrate the substructure within the cluster is to present ``bubble'' plots, where circles with radii proportional to the negative log of the measured K-S likelihood are plotted at each cluster member position. This is shown in Figure 9, where regions of clustered large circles indicate the existence of substructure. Circles in this plot are color-coded, red for galaxies with positive v_pec, and blue for galaxies with negative v_pec. Also, galaxies having K-S likelihoods which occur in only 5% of the simulated cases are emboldened. The circles are plotted on top of the galaxy surface density contours, generated as described in Section 4.2.

There are a number of regions where the presence of groupings of significantly large ``bubbles'' indicate localized velocity structure, confirming our measure of significant substructure being present within Abell 3667. These localized regions of velocity structure are generally coincident with surface density enhancements, and, most significantly in terms of the cold front, we observe a galaxy density enhancement 700 kpc to the southeast of the front which is coincident with a clustering of large bubbles, indicating the presence of a subgroup. Interestingly, the significant enhancement in galaxy density to the northwest, coincident with the second-ranked cluster galaxy, shows little to no deviation in its local velocity distribution, despite being coincident with a peak in the projected mass maps of Joffre et al. (2000). There is, however, localized velocity structure surrounding the substructure which may be associated.

It is possible that the nondetection of localized velocity structure around the region of enhanced galaxy density to the northwest is due to the difference in the scale probed by the test compared to the physical scale of the substructure. Since the local velocity distribution is defined using a fixed number of near neighbors, rather than the near neighbors within some fixed projected radius, it is difficult to determine exactly which scales are being probed at each galaxy position in Figure 9. All that is known is that where the galaxy density is high, smaller scales are probed and, conversely, where the galaxy density is low, larger scales are probed. To remedy this, and also to address the fact that substructures can have a range of different physical scales, we use a multiscale analysis. This involves remeasuring κ_s in a similar fashion to that described above, but rather than using a fixed number of n nearest neighbors to define the local velocity distributions, we use the near neighbors within a fixed projected radius, R_NN, of the galaxy of interest. The analysis is repeated for near neighbors within R_NN = 200, 400, 800, and 1600 kpc and the resulting bubble plots are shown in Figure 10. For these radii, we measure κ_s values of 342 (4.15σ), 405 (3.71σ), 762 (4.62σ), and 1114 (4.04σ), respectively, where the bracketed values are the significances, measured as above from 10,000 Monte Carlo realizations. Across the four scales presented in Figure  10, all of the substructures seen in Figure  9 are reproduced and, most significantly, on scales 800 and 1600  kpc the northwest substructure appears as a region containing significant local velocity substructure.

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Our concern regarding the σ(R) gradient affecting the κ_s measurement seems warranted, given the detection of significant velocity structure >2 Mpc to the southeast in Figure 9 and the lower panels of Figure 10. This structure is not offset significantly in peculiar velocity; however its dispersion is much lower than the total cluster value and therefore it is unlikely to be a bound infalling substructure. Rather it is likely to be an artifact of the declining σ(R) profile.

Having identified significant substructure within Abell 3667, we now use the KMM algorithm (Ashman et al. 1994) to partition the different substructures. The algorithm fits a user-specified number of Gaussians to a data set and determines the improvement of the fit over that of a single Gaussian. Here, we utilize the combination of spatial and velocity information and fit 3D Gaussians. Inspection of Figure 9 reveals four regions of interest (outlined by green circles) where there is localized velocity structure and/or there is structure in the galaxy surface density. These regions serve as an initial estimate of the number of partitions into which the KMM algorithm should divide the cluster, and we restrict our analysis to the region containing these structures defined by the black dot-dash region in Figure 9. Within the regions of interest, obvious velocity outliers are rejected, and the mean and standard deviation are measured for the spatial distributions, while the median and median absolute deviation (Beers et al. 1990) are measured for the velocity distribution. The measurements serve as initial inputs to the algorithm and, along with the outputs from the KMM algorithm, are shown in Table 2, where the final $\overline{v}$ and σ_v values are determined using the median and gapper estimators in cases where N_G < 15, and the biweight location and scale estimators in cases where N_G ⩾ 15 members, respectively.

Table 2. Input and Output Parameters for the KMM Algorithm. The Final Column Gives the Estimates for the Correct Allocation Rate for Each KMM Partition.

	Initial Inputs			KMM Outputs
Group	($\overline{x},\overline{y}, \overline{v}$)	(σx, σy, σv)	Ngal	$(\overline{x},\overline{y}, \overline{v})$	(σx, σy, σv)	Ngal	Rate (%)
KMM1	(130, 1145, −1388)	(112, 66, 353)	10	(153, 1169, −1483)	(83, 58, 395)	9	100
KMM2	(905, 747, 408)	(368, 370, 829)	110	(879, 824, 422)	(530, 560, 1039)	164	89
KMM3	(528, −373, 1375)	(91, 89, 704)	9	(563, −415, 1457)	(64, 44, 426)	7	100
KMM4	(-542, −798, −523)	(292, 238, 489)	36	(-761, −659, −638)	(412, 326, 209)	27	73
KMM5	(0, 0, 55)	(827, 853, 1020)	284	(-144, −173, −103)	(676, 739, 1073)	242	87

Notes. The units of $\overline{x},\overline{y},\sigma _x$, and σ_y are kpc, and the units of $\overline{v}$ and σ_v are km s⁻¹. For $\overline{v}$ and σ_v, the median and gapper estimators are used when N_G < 15 and where N_G ⩾ 15, the biweight location and scale estimators are used.

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In Figure 11, we show the spatial distribution of the partitions, along with the associated velocity histograms for each partition. The cluster is essentially divided into northwest and southeast partitions, with the southeast one associated with the dominant cluster galaxy, and the northwest one associated with the second-ranked galaxy coincident with the second major overdensity in the galaxy surface brightness maps. The velocity dispersions of these components are very similar (1039 ± 66  km s⁻¹ for KMM2 and 1073 ± 64 km s⁻¹ for KMM5), but their velocities are slightly offset, with KMM2 having $\overline{v} = 422\pm 82$ km s⁻¹, similar to the peculiar velocity of the of the second-ranked galaxy which is at 432 km s⁻¹, and KMM5 has $\overline{v} = -103\pm 71$ km s⁻¹. There are two other minor structures (KMM1 and KMM3) which appear to be small bound groups, and a low-velocity dispersion structure to the southeast (KMM4), which is associated with an overdensity in the galaxy surface density maps.

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The multiwavelength data at hand may be reconciled with a simple two-cluster merger. The structure to the northwest is clearly significant in the 2D galaxy density maps and is coincident with the second dominant cluster galaxy. The structure is also coincident with a significant mass concentration in the weak-lensing maps of Joffre et  al. (2000). There is only a small offset in peculiar velocity of ∼422 km s⁻¹, and very little difference in the velocity dispersion between the northwest substructure and the main cluster. This suggests a merger between subclusters of similar masses taking place roughly in the plane of the sky.

The direction of motion of the northwest substructure cannot be determined from the optical data alone, however it can be constrained by considering the radio and X-ray data in the literature. Regarding the radio data, the pertinent observation is the northwest radio relic described in Rottgering et al. (1997) where inference can be made regarding the direction of motion by consideration of the spectral index and brightness distribution of the relic. Rottgering et al. (1997) find that the relic brightness steepens at the northwest edge and is more diffuse to the southeast, while the spectral index is flat at the northwest edge and steepens towards the southeast. The model of Roettiger et al. (1999) explains these features as due to a shock front moving from the southeast to northwest, where the steepening of the brightness and the flatness of the spectral index at the northwest edge occur because this is where the shock acceleration of electrons is currently occurring. Since the shock moves from southeast to northwest, the electrons to the southeast no longer have a source of energy for acceleration, and the spectral index steepening is caused by the aging of the particles as the shock moves off to the northwest. It should be noted, however, that recent observations (Johnston-Hollitt 2003) have cast doubt on the existence of a flat spectral index at the northwest edge of the relic and show only a moderate spectral gradient across the source. Even without these arguments, the curvature of the radio relic is consistent with a shock propagating to the northwest. The ROSAT X-ray observations of Knopp et al. (1996) find significant evidence for extended X-ray emission associated with the northwest subcluster. In Figure 12, we present the Digital Sky Survey r-band image of Abell 3667 with X-ray contours from Chandra and ROSAT overlaid. The contours clearly extend to encompass the northwest substructure. The fact that the subcluster hosts an X-ray halo, together with the arguments based on the radio data, suggest that the northwest subcluster has significant mass and is moving from southeast to northwest with the majority of its motion in the plane of the sky.

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In Figure 12, the cold front is seen as a compression of the X-ray contours to the southeast of the cluster center. Vikhlinin et al. (2001a) argued that the cold front is moving in a southeasterly direction at approximately the sound speed of the ICM. Based on arguments about the constant shape and the stability of the front, Vikhlinin & Markevitch (2002) predict the existence of a dark halo associated with the front, with its centroid ∼ 90 kpc from the leading edge of the front. We find no evidence for any structure in the galaxy distribution in this region, and note that the weak lensing maps of Joffre et al. (2000) do not show any significant mass concentrations here either. In the two-body merger scenario, the cold front is produced when core gas is "sloshed" out of the central potential well after the core passage of KMM2, and an excellent example of this is seen in Poole et al. (2006)'s Figure 18 which shows entropy maps from the 3:1 mass ratio, offset impact parameter simulations. Interestingly, the structure that Mazzotta et al. (2002) interpret as a hydrodynamic instability is seen in these simulations and interpreted as a ``plume'' of cool gas ejected from the main cluster's cool core due to the subcluster's pericentric passage. These simulations also produce two shock fronts on opposite sides of the main cluster moving in opposite directions, which would account for the observed radio relics in Abell 3667. This scenario is essentially the same as that proposed in Roettiger et al. (1999), although the simulations of Poole et al. (2006) are at higher resolution and thus provide a better view of the cold front. In this scenario, KMM4 can be interpreted in two ways; in the first, KMM4 is a group either infalling from the foreground, or is a background structure that is not physically associated with the cluster, nor with any of the X-ray and radio features or the merger. The second interpretation is that KMM4 was once associated with KMM2, and was tidally stripped from the main KMM2 structure during its approach to the main cluster core and survives as a dynamically distinct substructure within the cluster.

An alternative scenario for the features seen in Abell 3667 involves a three-body merger, between KMM2, KMM4 and KMM5 where the arguments regarding KMM4 and its association with the X-ray and radio structures observed in the northwest presented above are essentially unchanged, however the cold front is the remnant core of KMM4, the centroid of which lies ∼550 kpc to the southeast of the front. A shock front driven by KMM4 is responsible for the radio relic in the southeast. In this scenario, KMM4 has traveled from the northwest and passed through the cluster core where its ICM was significantly slowed by ram pressure, while the collisionless galaxies and dark matter continued their passage towards the southeast, similar to that seen in the Bullet cluster (Markevitch et al. 2002). The mass maps of Joffre et al. (2000) indicate a significant mass concentration not quite coincident with KMM4, but offset by ∼300 kpc to the southwest. This lies well within the 2σ boundary seen in Figure 11, and the mass is highly likely to be associated with KMM4. The velocity dispersion of KMM4 is low and is unlikely to reflect the initial mass of the system, since the group must have been strongly affected by tidal forces and dynamical friction during its passage through the cluster core. The mass of the group was probably not comparable to the Abell 3667 system, since its gravitational potential well was unable to stop the gas from being completely stripped from the group (see Ascasibar & Markevitch 2006, for a comparison of the effects of different mass ratios on ram pressure stripping of core gas).

We have presented an optical analysis of the cold front cluster Abell 3667 based on a large sample of (550) spectroscopically confirmed cluster members using data obtained on the AAT AAOmega facility. We find the cluster has a velocity dispersion of σ = 1056 km s⁻¹ and redshift z = 0.0553. Although the velocity distribution does not differ significantly from a Gaussian, the cluster shows clear evidence of subclustering in the galaxy density plots, and also contains significant local velocity substructure according to the k-statistic. Using the KMM algorithm, the cluster can be partitioned into three main components—the main cluster (KMM5) with 242 members, σ = 1073  km s⁻¹, $\overline{v}_{\rm pec} = -103$ km s⁻¹, a northwest subcluster (KMM2) with 164 members, σ = 1039 km s⁻¹, $\overline{v}_{\rm pec} = 422$ km s⁻¹, and a southeast subgroup (KMM4) with 27 members, σ = 209  km s⁻¹, and $\overline{v}_{\rm pec} = -638$ km s⁻¹.

We confirm that Abell 3667 is a merging cluster, and the physical phenomena associated with observations at X-ray and radio wavelengths can be associated with substructure observed in the galaxy distribution, although it is apparent that detailed, combined N-body/hydrodynamical simulations are required to determine the plausibility of the two scenarios presented. This study highlights the need for large, deep spectroscopic samples to be used in conjunction with the full multiwavelength observations when determining the dynamical state of a cluster of galaxies. Future work will involve using the spectroscopic sample to study the galaxy properties within Abell 3667, and to correlate them with substructures within the cluster.

We have now studied in detail two clusters from our sample of "cold front" clusters selected from the Chandra archive, finding here, as for Abell 1201 in Paper I, that despite difficulties in determining precise merger histories, cold fronts can be directly related to cluster merger activity and thus are reliable signposts of ongoing mergers. However, it must be noted that both Abell 1201 and Abell 3667 harbor signs of merger activity (other than cold fronts) in their Chandra images, thus were expected to show evidences of merger activity at other wavelengths. The acid test for this claim will come from detailed observations of cold front clusters with relaxed X-ray morphologies.