CLASH: COMPLETE LENSING ANALYSIS OF THE LARGEST COSMIC LENS MACS J0717.5+3745 AND SURROUNDING STRUCTURES^*

We analyze deep BVR_ci'z' images of MACSJ0717 observed with the wide-field camera Suprime-Cam (34' × 27'; Miyazaki et al. 2002) at the prime focus of the 8.3 m Subaru Telescope. We observed the cluster on the night of 2010 March 17, in $B,{R_{\rm C}},z^{\prime }$, to augment shallower observations that existed in the Subaru archive, SMOKA.²⁶ Some of the archival data for this cluster were taken as part of the "Weighing the Giants" program (von der Linden et al. 2012). The seeing full-widths at half-maximum (FWHMs) in the co-added mosaic images are 095 in B (3.84 ks), 069 in V (2.16 ks), 079 in ${R_{\rm C}}$ (2.22 ks), 096 in i' (0.45 ks), and 085 in z' (5.87 ks) with 020 pixel⁻¹, covering a field of approximately 36' × 34'. The limiting magnitudes are obtained as B = 26.6, V = 26.4, ${R_{\rm C}}=26.1$, i' = 25.4, and z' = 25.6 mag for a 3σ limiting detection within a 2'' diameter aperture.

To improve the accuracy of our photometric redshifts, we also include UV observations from the Megaprime/MegaCam in the u*-band and near-IR observations from the WIRCAM in the J, K_s-bands on the Canada–France–Hawaii Telescope (CFHT), available from the CFHT archive.²⁷ Although shallower, and in the case of near-IR data the coverage is only of the inner 15' × 15', these extra bands add important information to help better constrain the spectral energy distribution (SED) of galaxies with degenerate fits.

The observation details of MACSJ0717 are listed in Table 2. Figure 1 shows a u*BVR_ci'z' composite color image of the cluster central 28 ' × 28 ', produced automatically using the publicly available Trilogy software (Coe et al. 2012).²⁸ We overlay it with the DM map determined from WL (white contours, see Section 8) and the smoothed X-ray luminosity map (red contours, see Section 9.2).

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Our reduction pipeline derives from Nonino et al. (2009) and SDFRED (Ouchi et al. 2004; Yagi et al. 2002) and has been optimized for accurate photometry and WL shape measurements. Standard reduction steps include bias subtraction, flat-field correction (super-flat averaged from all exposures of the same night where objects have been masked), and point-spread function (PSF) matching between exposures in the same band (if PSF variation is evident) as we normally use multi-epoch images taken under different conditions. Masking of saturated star trails and other artifacts is then applied.

To obtain an accurate astrometric solution for Subaru observations, we retrieved processed MegaCam r-band (Filter Number: 9601) images from the CFHT archive and used it as a wide-field reference image. A source catalog was created from the co-added MegaCam r image, using the Two Micron All Sky Survey catalog²⁹ as an external reference catalog. The extracted r catalog has been used as a reference for the SCAMP software (Bertin 2006) to derive an astrometric solution for the Suprime-Cam and other CFHT images. We do not use the CFHT r-band image in our photometry as the band is overlapping the Subaru ${R_{\rm C}}$ band, but with much lower resolution and depth, and therefore, does not carry added information.

For an accurate measure of photometry, we first smear the single exposures of the same band to the worst seeing. This step is done by using SDFRED/psfmatch procedure, after suitable point-like sources have been previously selected. The WL band is chosen to be the band with a combination of best seeing and deepest observation, ${R_{\rm C}}$ in this case (see Table 2).

Finally, the Swarp software (Bertin et al. 2002) is utilized to stack the single exposures on a common world coordinate system grid with pixel-scale of 02 using the accurate registration that was achieved in the previous step. This assures minimal distortion of the final image. Note that for the WL band, we separately stack data collected at different epochs and different camera rotation angles.

The photometric zero-points for the co-added Suprime-Cam images were derived from a suitable set of reference stars identified in common with the calibrated MegaCam data. These zero-points were refined in two independent ways: first, by comparing with the HST/ACS magnitudes of cluster elliptical-type galaxies, translated to Subaru magnitudes using an elliptical SED template with the BPZ code; subsequently, by fitting SED templates with the BPZ code (Bayesian photometric redshift estimation; Benítez 2000; Benítez et al. 2004) to Subaru photometry of 12 galaxies having measured spectroscopic redshifts from the literature³⁰ (Limousin et al. 2012) and calculating model magnitudes. This leads to a final photometric accuracy of ∼0.01 mag in all passbands (see also Section 3.3).

The eight-band u*BVR_ci'z'JK_S photometry catalog was then measured using SExtractor (Bertin & Arnouts 1996) in dual-image mode on PSF-matched images created by ColorPro (Coe et al. 2006), where a combination of B + V + R + z' bands were used as a deep detection image (we exclude the i' band which is of lesser quality). The stellar PSFs were measured from a combination of 100 stars per band and modeled using IRAF routines.

For shape measurements, we use our well-tested WL analysis pipeline based on the IMCAT package (Kaiser et al. 1995, KSB hereafter), incorporating modifications and improvements developed and outlined in Umetsu et al. (2010). Our KSB+ implementation has been applied extensively to Subaru cluster observations (e.g., Broadhurst et al. 2005b, 2008; Umetsu et al. 2007, 2009, 2010, 2011a, 2011b; Umetsu & Broadhurst 2008; Okabe & Umetsu 2008; Medezinski et al. 2010, 2011; Zitrin et al. 2011, 2013; Coe et al. 2012; Umetsu et al. 2012). Full details of our CLASH WL analysis pipeline are presented in Umetsu et al. (2012).

Based on simulated Subaru Suprime-Cam images (see Section 3.2 of Oguri et al. 2012; Massey et al. 2007a), we found in our earlier work (Umetsu et al. 2010, 2012) that the WL signal can be recovered with |m| ≃ 5% of the multiplicative shear calibration bias (as defined by the STEP project: see Heymans et al. 2006; Massey et al. 2007a), and c ∼ 10⁻³ of the residual shear offset, which is about one order of magnitude smaller than the typical distortion signal in cluster outskirts (|g| ∼ 10⁻²). Accordingly, we include in our analysis a calibration factor of 1/0.95 as g_i → g_i/0.95 to account for residual calibration.³¹

In this analysis, we use the ${R_{\rm C}}$-band data taken in 2005 and 2010, which have the best image quality in our datasets, taken in fairly good seeing conditions. Two separate co-added ${R_{\rm C}}$-band images are created, one from 2005 (with a total of 450 s, observer Yasuda) and one from 2010 (with a total of 2160 s, observed by us on 2010 March). We do not smear the single exposures before stacking (as done for photometric measurements), so as not to degrade and destroy the WL information derived from the shapes of galaxies. A shape catalog is created for each epoch separately, and the catalogs themselves are then combined by properly weighting and stacking the calibrated distortion measurements for galaxies in the overlapping region. The combination of both epochs increases the number of measured galaxy shapes and improves the statistical measurement, while not degrading the quality of the shape measurement due to different seeing and anisotropy at different observing epochs.

In Figure 2, we show the $B-{R_{\rm C}}$ versus ${R_{\rm C}}-z^{\prime }$ distribution of all galaxies to our limiting magnitude (cyan). To identify our cluster-dominated area in this CC space, we also plot up B − R_c versus ${R_{\rm C}}-z^{\prime }$ only of galaxies with small projected distance R < 3' (≲ 1 Mpc at z_l = 0.546) from the cluster center. A region is then defined according to a characteristic overdensity in this space (shown as a solid green curve in Figure 2). Then, all galaxies within this distinctive region from the full CC diagram define the "green" sample (green points in Figure 2), comprising mostly the red-sequence of the cluster and a blue trail of later-type cluster members. We note that the small overdensity seen bluer (lower-left, $B-{R_{\rm C}}, {R_{\rm C}}-z^{\prime }\sim 0.7$) than our green sample does not lie at the same redshift of the cluster and is not a bluer population that is part of the cluster, but is in fact comprised of early-type galaxies lying in the foreground of the cluster, at about z ∼ 0.33, which we will discuss further as part of our multi-halo mass modeling (Section 8.2).

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The number density profile of the green sample is steeply rising toward the center (Figure 6, green crosses). The low number density at large clustercentric radius is indicative of negligible contamination of background galaxies of this sample. The WL signal for this population is found to be consistent with zero at all radii (Figure 5, green crosses), also indicating the reliability of our procedure. For this population of galaxies, we find a mean photometric redshift of 〈z_phot〉 ≈ 0.56 (see Section 3.3), consistent with the cluster redshift. Importantly, the green sample marks the region that contains a majority of unlensed galaxies, relative to which we select our background samples, as summarized below.

A careful background selection is critical for a WL analysis so that unlensed cluster members and foreground galaxies do not dilute the true lensing signal of the background (Broadhurst et al. 2005b; Medezinski et al. 2007, 2010; Umetsu & Broadhurst 2008). This dilution effect is simply to reduce the strength of the lensing signal when averaged over a local ensemble of galaxies (by a factor of 2–5 at R ≲ 400 kpc h⁻¹; see Figure 1 of Broadhurst et al. 2005b), particularly at small radii where the cluster is relatively dense, in proportion to the fraction of unlensed galaxies whose orientations are randomly distributed.

We use the background selection method of Medezinski et al. (2010) to define undiluted samples of background galaxies, which relies on empirical correlations for galaxies in color–color–magnitude space derived from the deep Subaru photometry, by reference to evolutionary tracks of galaxies (for details, see Medezinski et al. 2010; Umetsu et al. 2010) as well as to the deep photometric-redshift survey in the COSMOS field (Ilbert et al. 2009).

For MACSJ0717, we have a wide wavelength coverage (BVR_ci'z') of Subaru/Suprime-Cam. We therefore make use of the (B − R_c) versus (R_c − z') CC diagram to carefully select two distinct background populations which encompass the red and blue branches of galaxies. We limit the red sample to z' < 25 mag in the reddest band, corresponding approximately to a 5σ limiting magnitude within 2'' diameter aperture. We extend the magnitude limit of the blue samples further to z' < 26 mag, where the number density of galaxies grows significantly higher, especially for bluer galaxies whose faint-end slope of the luminosity function is rising, giving a much improved WL statistical measurement.

For the background samples, we define conservative color limits, where no evidence of dilution of the WL signal is visible, to safely avoid contamination by unlensed cluster members and foreground galaxies. The color boundaries of our "blue" and "red" background samples are shown in Figure 2. For both the blue and red samples, we find a consistent, rising WL signal (see Section 4.1) all the way to the center of the cluster, as shown in Figure 5.

As a further consistency check, we also plot in Figure 6 the galaxy surface number density as a function of clustercentric radius, n(θ), for the blue and red samples. As can be seen, no clustering is observed toward the center for the background samples, which demonstrates that there is no significant contamination by cluster members in these samples. The red sample systematically decreases in projected number density toward the cluster center, caused by the lensing magnification effect. A more quantitative magnification analysis is given in Section 4.2.

To summarize, our CC selection criteria yielded a total of N = 10,490, 1252, and 11,998 galaxies, for the red, green, and blue photometry samples, respectively (see Table 3). For our WL distortion analysis, we have a subset of 4856 and 4738 galaxies in the red and blue samples (with usable ${R_{\rm C}}$ shape measurements), respectively (see Table 4).

The lensing signal depends on the source redshift z_s through the distance ratio $\beta (z_s)={D_{\rm ls}/D_{\rm s}}$, where D_ls, and D_s are the angular diameter distances between the lens and the source, and the observer and the source, respectively. We thus need to estimate and correct for the respective depths 〈β〉 of the different galaxy samples when converting the observed lensing signal into physical mass units.

For this, we utilize BPZ to measure photometric redshifts (photo-zs) z_phot using our deep Subaru+CFHT u*BVR_ci'z'JK_s photometry (Section 2.1). BPZ employs a Bayesian inference where the redshift likelihood is weighted by a prior probability, which yields the probability density P(z, T|m) of a galaxy with apparent magnitude m of having certain redshift z and spectral type T. In this work, we used a new library (N. Benitez 2012, in preparation) composed of 10 SED templates originally from PEGASE (Fioc & Rocca-Volmerange 1997) but recalibrated using the FIREWORKS photometry and spectroscopic redshifts from Wuyts et al. (2008) to optimize its performance. This library includes five templates for elliptical galaxies, two for spiral galaxies, and three for starburst galaxies. In our depth estimation, we utilize BPZ's ODDS parameter, which measures the amount of probability enclosed within a certain interval Δz centered on the primary peak of the redshift probability density function, serving as a useful measure to quantify the reliability of photo-z estimates.

We only consider galaxies from the WL-matched catalogs, as those are the galaxies from which we estimate the lensing signal and finally, the mass profile. To make this estimate more robust, we use galaxies for which the photo-z was determined using all available eight bands. We show the normalized redshift distribution of these galaxies in each of the green, red, and blue samples in Figure 3. Still, since only 12 spectroscopic redshifts are publicly available in this field, it is difficult to estimate the reliability of our photo-z's. Therefore, we further compare our results with the more reliably estimated depths we derive from the COSMOS catalog (Ilbert et al. 2009), which has robust photometry and photo-z measurements for the majority of galaxies with i' < 25 mag. For each sample, we apply the same CC selection to the COSMOS photometry and obtain the redshift distribution N(z) of field galaxies. Since COSMOS is only complete to i' < 25 mag, we derive the mean depth as a function of magnitude (Figure 4) up to that limit, and extrapolate to our sample limiting magnitude, z' = 25 in the case of the red sample and z' = 26 in the case of the blue sample.

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For each background population, we calculate a weighted mean of the distance ratio β (mean lensing depth) as

$$\begin{equation} \langle \beta \rangle = \frac{\int \!dz\,w(z) N(z)\beta (z)}{\int \!dz\,w(z)N(z)}, \end{equation} \tag{ 1 }$$

where w(z) is a weight factor; w is taken to be the Bayesian ODDS parameter for the BPZ method, and w = 1 otherwise. The sample mean redshift 〈z_s〉 is defined similarly to Equation (1).

In Table 4, we summarize the mean depths 〈β〉 and the effective source redshifts z_{s, eff} for our background samples. For each background sample, we obtained consistent mean-depth estimates 〈β〉 (within 2%) using the BPZ- and COSMOS-based methods. In the present work, we adopt a conservative uncertainty of 5% in the mean depth for the combined blue and red sample of background galaxies, 〈β(back)〉 = 0.48 ± 0.03, which corresponds to z_{s, eff} = 1.26 ± 0.1. We marginalize over this uncertainty when fitting parameterized mass models to our WL data.

The shape distortion of an object is described by the complex reduced-shear, g = g₁ + ig₂, where the reduced-shear is defined as (in the subcritical regime; see, e.g., Bartelmann & Schneider 2001)

$$\begin{equation} g_{\alpha }\equiv \gamma _{\alpha }/(1-\kappa), \end{equation} \tag{ 2 }$$

where γ is the complex gravitational shear field and is non-locally related to the convergence, κ = Σ/Σ_crit, which is the surface mass density in units of the critical surface-mass density for lensing, Σ_crit = (c²/4πGD_l)β⁻¹. The tangential component of the reduced-shear, g₊, is used to obtain the azimuthally averaged distortion due to lensing, and computed from the distortion coefficients (g₁, g₂):

$$\begin{equation} g_{+}=-(g_{1}\cos 2\theta + g_{2}\sin 2\theta), \end{equation} \tag{ 3 }$$

where θ is the position angle of an object with respect to the cluster center. The uncertainty in the object g₊ measurement is $\sigma _{+} = \sigma _{g}/\sqrt{2}\equiv \sigma$ in terms of the rms error σ_g for the complex reduced-shear measurement. For each galaxy, σ_g is the variance for the reduced shear estimate computed from 50 neighbors identified in the r_g–${R_{\rm C}}$ plane. To improve the statistical significance of the distortion measurement, we calculate the weighted average of g₊

$$\begin{equation} g_{+,i} \equiv g_+(\theta _i)= \left[ \displaystyle \sum _{k\in i} w_{(k)}\, g_{+(k)} \right] \left[ \displaystyle \sum _{k\in i} w_{(k)}\right]^{-1}, \end{equation} \tag{ 4 }$$

where the index k runs over all objects located within the ith radial bin with a weighted center of θ_i, and w_(k) is the weight for the kth object,

$$\begin{equation} w_{(k)}=1/\left(\sigma _{g(k)}^2+\alpha ^2\right), \end{equation} \tag{ 5 }$$

where α² is the softening constant variance. We choose α = 0.4, which is a typical value of the mean rms $\bar{\sigma }_g$ over the background sample. The uncertainty in g_{+, i} is calculated from a bootstrap error analysis (for details, see Umetsu et al. 2012). Since WL only induces curl-free tangential distortions, the 45° rotated component, g_× = −(g₂cos 2ϕ − g₁sin 2ϕ), is expected to vanish. It is therefore useful as a check for systematic errors.

In Figure 5, we plot the radial profile of g₊ of the green, red, and blue samples defined above. The black points represent the red+blue combined sample (also shown in Figure 8, upper panel), showing the best estimate of the lensing signal, which is detected at 11.6σ significance over the full radial range. The red and blue sample profiles rise continuously toward the center of the cluster, and agree with each other within the errors, except at the very central bin, θ ≲ 2', where measurements are approaching the nonlinear regime, given the extremely elliptical shape of the tangential critical curve (see Figure 1 of Zitrin et al. 2009a). The overall rising trend and agreement demonstrate that both the red and blue samples are dominated by background galaxies and are not contaminated by the cluster at all radii. The g₊ profile of the green sample agrees with zero at all radii. The measured zero level of tangential distortion reinforces our CC selection of the green sample to consist mostly of cluster members.

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We follow the prescription of Umetsu et al. (2011a) to measure the magnification bias signal as a function of distance from the cluster center, which depends on the intrinsic slope of the luminosity function of background sources s, as

$$\begin{equation} n_\mu ({\boldsymbol {\theta }})=n_0\mu ({\boldsymbol {\theta }})^{2.5s-1}, \end{equation} \tag{ 6 }$$

where n₀ = dN₀(< m_cut)/dΩ is the unlensed mean number density of background sources for a given magnitude cutoff m_cut, approximated locally as a power-law cut with slope, s = dlog₁₀N₀(< m)/dm > 0. We use the red sample of background galaxies (Section 3.2), for which the intrinsic count slope s at faint magnitudes is relatively flat, s ∼ 0.1, so that a net count depletion results (Broadhurst et al. 2005b; Umetsu & Broadhurst 2008; Umetsu et al. 2010, 2011a). In contrast, the blue background population has a steeper intrinsic count slope close to the lensing invariant slope (s = 0.4).

Here we use the approach developed in Umetsu et al. (2011a) to measure the azimuthally averaged surface number density profile of the red galaxy counts, n_{μ, i} ≡ n_μ(θ_i) (red triangles in Figure 6), taking into account and correcting for masking of background galaxies due to bright cluster galaxies (BCGs), foreground objects, and saturated objects. The errors σ_{μ, i} for n_{μ, i} include both contributions from Poisson errors in the counts and contamination by intrinsic clustering of red background galaxies. The normalization and slope parameters for the red sample are reliably estimated outside the lensed region, by virtue of the wide-field imaging with Subaru/Suprime-Cam. We find n₀ = 13.3 ± 0.3 galaxies acrmin⁻² and s = 0.123 ± 0.048.

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In the bottom panel of Figure 8, we show the measured magnification profile from our flux-limited sample of red background galaxies (z' < 25 mag; see Table 3) with and without the masking correction applied (red circles and green crosses, respectively). A clear depletion of the red counts is seen in the central, high-density region of the cluster and detected out to ≲ 4' from the cluster center. The radially integrated significance of the detection of the depletion signal is 5.3σ.

The high-level WL shear and magnification profile we derived here can be combined together to reconstruct the underlying mass profile. However, to better resolve the core of the profile, we require further constraints which are enabled by SL. Therefore, we derive the SL mass profile in the next section.

We derive the cluster mass profile as a function of clustercentric radius from a joint likelihood analysis of independent WL distortion (g₊), magnification-bias (n_μ), and SL projected mass (m) constraints, $\lbrace g_{+,i}\rbrace _{i=1}^{N_{\rm wl}}$ (Section 4.1), $\lbrace n_{\mu, i}\rbrace _{i=1}^{N_{\rm wl}}$ (Section 4.2), and $\lbrace m_i\rbrace _{i=1}^{N_{\rm sl}}$ (Section 5), respectively, following the Bayesian approach of Umetsu (2013), who extended the shear-and-magnification analysis method of Umetsu et al. (2011a) to include the inner SL information. Such a multi-probe approach is critical for improving the accuracy and precision of the cluster lens reconstruction, effectively breaking the mass-sheet degeneracy (see Bartelmann & Schneider 2001; Umetsu et al. 2012). Adding SL information to WL is needed to provide tighter constraints on the inner density profile (e.g., Umetsu & Broadhurst 2008; Umetsu et al. 2011a, 2012). The shear+magnification method of Umetsu et al. (2011a) has been extensively used to reconstruct the projected mass profile in a dozen clusters (Umetsu et al. 2011a, 2012; Zitrin et al. 2011, 2013; Coe et al. 2012). In all cases, we find a good agreement between independent WL and SL mass profiles in the region of overlap.

Briefly summarizing, the model is described by a vector ${\boldsymbol {s}}$ of parameters containing the discrete convergence profile $\lbrace \kappa _{\infty, i}\rbrace _{i=1}^N$, given by N = N_wl + N_sl binned κ values, and the average convergence enclosed by the innermost aperture radius θ_min for SL mass estimates, $\overline{\kappa }_{\infty, {\rm min}}\equiv \overline{\kappa }_\infty ({<}\theta _{\rm min})$, where we have introduced the convergence for a fiducial source in the far background of the cluster, κ_{∞, i} ≡ κ(θ_i; z_s → ∞). The model ${\boldsymbol {s}}=\lbrace \overline{\kappa }_{\infty, {\rm min}},\kappa _{\infty, i}\rbrace _{i=1}^{N}$ is then specified by a total of (N + 1) parameters. Additionally, we account for the uncertainty in the calibration parameters, ${\boldsymbol {c}}=(w_g,w_\mu, n_0,s)$, namely, the population-averaged lensing strengths for the distortion and magnification measurements (see Table 4), w_g ≡ 〈β(back)〉/β(z_s → ∞) and w_μ ≡ 〈β(red)〉/β(z_s → ∞), the normalization and slope parameters (n₀, s) of the red-background counts (see Section 4.2). The covariance matrix C_ij for the profile reconstruction is also constructed and used for calculating the likelihood function of the combined WL+SL observations.

In the present analysis, we calculate the g₊ and n_μ profiles in N_wl = 10 clustercentric radial bins, spanning the range θ = [15, 16'], with a constant logarithmic radial spacing Δln θ ≃ 0.237. Additionally, we use our projected mass measurement within a radius of 60'', m = M_2D(< 60'') = (4.87 ± 0.35) × 10¹⁴ M_☉ h⁻¹ (N_sl = 1), tightly constrained by our detailed strong-lens modeling (Section 5). Note that enclosed masses at the location around the Einstein radius (θ_Ein ≈ 60'' at z_s = 2.963 here) are less sensitive to modeling assumptions and approaches (see Umetsu et al. 2012), serving as a fundamental observable quantity in the SL regime (Coe et al. 2010). Hence, we have a total of N_tot = 2N_wl + N_sl = 21 constraints. The mass profile model is described by N + 1 = 12 profile parameters and additional four calibration parameters (${\boldsymbol {c}}$) to marginalize over.

The resulting mass profile ${\boldsymbol {s}}$ from a joint SL+WL likelihood analysis of our HST+Subaru observations is shown in the top panel of Figure 9 (red squares; see also Figure 13, red squares). We find a consistent mass profile solution ${\boldsymbol {s}}$ as displayed in Figure 8 (solid areas). The projected cumulative mass profile M_2D(< θ) is shown in the lower panel (red curve). It is given by integrating the density profile ${\boldsymbol {s}}=\lbrace \overline{\kappa }_{\infty, {\rm min}},\kappa _{\infty, i}\rbrace _{i=1}^{N}$ (see Appendices A and B of Umetsu et al. 2011a) as

$$\begin{eqnarray} M_{\rm 2D}({<}\theta _i)&=& \pi (D_l\theta _{\rm min})^2 \Sigma _{\rm crit}\overline{\kappa }_{\rm min} +2\pi D_l^2 \Sigma _{\rm crit} \nonumber\\ && \times \int _{\theta _{\rm min}}^{\theta _i}\! d\ln \theta \,\theta ^2\kappa (\theta). \end{eqnarray} \tag{ 7 }$$

The total projected mass enclosed within a radius of $\theta \approx 7{^\prime }\approx 1.88\,{{\rm Mpc}\,h^{-1}}$ is found to be M_2D = (3.1 ± 0.5) × 10¹⁵ M_☉ h⁻¹.

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As is evident from the cored density profile in the central region derived by SL, as well as from the flattened outer profile at large radii seen by WL (Figure 13), MACSJ0717 is a complex, non-relaxed cluster whose matter distribution is not well described by a single Navarro–Frenk–White (NFW, Navarro et al. 1996) profile. However, in order to derive a total (spherical) mass estimate of the main cluster component in a complementary (yet model-dependent) approach, we choose here to fit our full-lensing mass profile with a spherical NFW model.

To that end, the projected radial mass profile ${\boldsymbol {s}}$ is fitted with a model consisting of a halo component described by the two-parameter universal NFW profile, κ_NFW(θ), and a constant mass-sheet component, κ_c:

$$\begin{equation} \hat{\kappa }(\theta) = \kappa _{\rm NFW}(\theta) + \kappa _c, \end{equation} \tag{ 8 }$$

where the constant κ_c approximates the inherent "two-halo" term contribution due to the clustering of halos (see Oguri & Hamana 2011). The NFW mass density profile is given by the form

$$\begin{equation} \rho _{\rm NFW}(r)=\frac{\rho _{s}}{(r/r_s)(1+r/r_s)^{2}}, \end{equation} \tag{ 9 }$$

where ρ_s is the characteristic density, and r_s is the characteristic scale radius at which the logarithmic density slope is isothermal. The halo virial mass is then given by integrating the NFW profile (Equation (9)) out to the virial radius r_vir, ${M_{\rm vir}}\equiv M({<}r_{\rm vir})$. We specify the projected NFW model with the halo virial mass, M_vir, and the degree of concentration, ${c_{\rm vir}}\equiv r_{\rm vir}/r_s$. We refer all of our virial quantities to an overdensity of Δ_c ≡ Δ_vir ≈ 138 based on the spherical collapse model using the fitting formula by Kitayama & Suto (1996, their Appendix A).³²

We constrain the model parameters ${\boldsymbol {p}}=(M_{\rm vir}, c_{\rm vir}, \kappa _c)$ with our full-lensing mass profile ${\boldsymbol {s}}$. The χ² function for our SL+WL observations is³³

$$\begin{equation} \chi ^2({\boldsymbol {p}}) = \sum _{i,j} [{\boldsymbol {s}}_i-\hat{\boldsymbol {s}}_i({\boldsymbol {p}})]{\cal C}^{-1}_{ij} [{\boldsymbol {s}}_j-\hat{\boldsymbol {s}}_j({\boldsymbol {p}})], \end{equation} \tag{ 10 }$$

where $\hat{\boldsymbol {s}}_i$ is the model prediction for the convergence profile ${\boldsymbol {s}}_i$ at θ_i and ${\cal C}$ is the full covariance matrix of ${\boldsymbol {s}}$ defined as ${\cal C}=C + C_{\rm lss}$, with C_lss being the cosmic covariance matrix responsible for the uncorrelated LSS projected along the line of sight. For details, see Umetsu et al. (2011b).

Our best-fit NFW model to the combined lensing constraints (Equation (10)) is shown in Figure 9 as the gray shaded area. To summarize our results from this analysis, we obtain a total virial mass estimate of ${M_{\rm vir}}=(2.13^{+0.49}_{-0.44})\times {10^{15}\,M_\odot \, h^{-1}}\sim (3\pm 0.6)\times 10^{15}\,M_\odot$ with the minimized χ² of 10 for 9 dof (see a summary in Table 5). We will compare and discuss all of the mass estimates yielded by the different modeling and reconstruction methods explored in the paper in Section 9.1.

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Table 5. Best-fit NFW Parameters to Non-parametric Mass Reconstruction and Comparison with X-Ray and SZE Masses

Method	Rvir	Mvir	$M({<}500\,{{\rm kpc}\, h^{-1}})$	κca	$M_{\rm vir}/L_{{R_{\rm C}}}$	χ2/dofb
	(Mpc h−1)	(1015 M☉ h−1)	(1015 M☉ h−1)		(h M☉/L☉)
1D WL+SLc	1.94 ± 0.14	$2.13^{+0.49}_{-0.44}$	0.63 ± 0.17	<0.01	301 ± 66	10/9
2D WLd	1.97 ± 0.15	$2.23^{+0.44}_{-0.38}$	0.54 ± 0.12	0.03 ± 0.01	310 ± 57	25/7
X-ray			$0.54 ^{+0.04} _{-0.08}$
SZE			0.50 ± 0.04

Notes. ^aThe constant dimensionless mass-sheet component. ^bThe goodness-of-fit, minimized χ² over number of dof. ^cThe NFW model was fitted to the mass profile fully reconstructed from WL+SL (see Section 7.1), constrained by 1D WL (shear+magnification)+SL Einstein-radius. ^dThe NFW model was fitted to the mass profile reconstructed from WL alone (see Section 7.2), using WL (2D shear+1D magnification), without SL constraints.

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At larger radii, a flattening of the mass profile is observed, possibly indicative of the surrounding LSS. The deviation of the profile from a single spherical NFW halo at large radius is indicative of substructure associated with this cluster region, and therefore merits a more careful 2D analysis, which we present in the next sections.

We follow Umetsu et al. (2012) to extend the one-dimensional (1D) Bayesian method above (Section 7.1) into a 2D mass distribution by combining the spatial shear pattern $(g_1({\boldsymbol {\theta }}),g_2({\boldsymbol {\theta }}))$ with the azimuthally averaged magnification measurements n_μ(θ) (Section 4.2), imposing a set of azimuthally integrated constraints on the underlying $\kappa ({\boldsymbol {\theta }})$ field.³⁴ For details of the method, we refer the reader to Umetsu et al. (2012, their Appendix A.2).

By combining complementary WL distortion and magnification data in a non-parametric manner, we construct a 2D mass map over a 48 × 48 grid with 05 spacing covering the central 24' × 24' field.³⁵ We show in Figure 13 (black circles) the azimuthally averaged radial mass profile Σ(R) produced from the resulting mass map, given in 10 linearly spaced radial bins spanning from θ = 15 to 16'. The innermost bin with the horizontal bar represents the mean interior mass density $\overline{\Sigma }({<}1\buildrel{\prime}\over{.} 5)$ as marked at the area-weighted center $\overline{\theta }=1{^\prime }$. We find a model-independent constraint on the total enclosed mass within θ ≈ 7' to be M_2D = (3.4 ± 0.6) × 10¹⁵ M_☉ h⁻¹.

We fit an NFW + mass-sheet model (Equation (8)) to the WL radial mass profile derived here by minimizing the total χ² function defined as in Equation (10), marginalizing over the mean background depth uncertainty in z_{s, eff}. We find the total virial mass to be ${M_{\rm vir}}=(2.23^{+0.44}_{-0.38})\times {10^{15}\,M_\odot \, h^{-1}}$. We summarize all of the results from our analyses in Table 5 and discuss the differences in Section 9.1.

WL distortion measurements (g) can be used to recover the underlying projected mass density field $\Sigma ({\boldsymbol {\theta }})$. Here we use the linear map-making method outlined in Section 4.4 of Umetsu et al. (2009) to derive the projected mass distribution from the HST+Subaru distortion data presented in the previous sections.

In Figure 10 (top left panel), we show the surface-density field $\kappa ({\boldsymbol {\theta }})$ in the central 28' × 28' region, reconstructed from the background (blue+red) sample (Section 3.2), where, for visualization purposes, the mass map is smoothed with a Gaussian of θ_FWHM = 15. We overlay the mass map with contours starting at 2.5σ_κ above the background, which is equivalent to a detection threshold of $\Sigma _{2.5\sigma _\kappa }=3.66\times 10^{14}\,h\,M_\odot \,{\rm Mpc}^{-2}$, and separated by 2σ_κ intervals.

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A very elongated structure is evident, and several mass clumps seem to comprise the cluster. Some clumps lie outside of the estimated virial radius which is at ∼2 Mpc h⁻¹. Some of these mass structures may in fact lie in the foreground of the cluster and not be physically associated with it, yet contribute to the overall lensing of the background galaxies. Therefore, we need to estimate the mean redshift of each of these significant structures.

In order to estimate the distances to the detected structures, and to correlate the galaxy distribution in this cluster and its surrounding structure with the DM distribution, we utilize the green sample defined in Section 3.1, which comprises mostly cluster galaxies and some lower-level contamination of foreground galaxies. We construct both a 2D galaxy number-density map (Figure 10, top right panel) and a K-corrected ${R_{\rm C}}$-band luminosity density map (Figure 10, bottom right panel). Both maps are smoothed with a Gaussian of the same scale as the mass map above, θ_FWHM = 15. The white contours are overlaid with 5σ increments starting at 2.5σ above the background level of the equivalent map. We also overlay the surface mass density map (red contours) as determined above to illustrate the correlation.

Overall, the DM distribution is well traced by the galaxy distribution, as evident by the overlapping contours and the proximity of the mass peaks to the light peaks. The good agreement seen is consistent with the smaller mass halos being in the process of accreting onto the main halo. A further detailed analysis of individual structures is presented below (Section 8.2).

To estimate individual masses of the structures comprising the cluster and its surroundings as seen within the scope of the Subaru, ∼0.25 deg², we now present a multi-halo fitting approach. We first identify the most dominant peaks from the convergence map presented above (Section 8.1, Figure 10). These are defined as all peaks lying 2.5σ_κ above the background level, estimated from a bi-weighted scale and mean (Beers et al. 1990), respectively, outside the region of 8' from the cluster center, so as not to be biased by the cluster potential. The 2.5σ_κ detection level is indicated as the first red contour in Figure 10, corresponding to Σ_2.5σ = 3.66 × 10¹⁴ h M_☉ Mpc⁻².

We have detected nine distinct mass peaks, numbered z₁–z₉ in Figure 10 (top left, the peak locations are marked with red points) and in Table 5. To help identify whether these peaks are part of the same structure as the cluster or unassociated systems projected along the line of sight, we estimate the photometric redshift of each component. For this we take the mean photometric redshift of matching member galaxies in the green sample (Section 3.1) lying within 1' from the respective mass halo peak. As evident, only five of the nine structures lie at approximately the same redshift (z₂, z₃, z₅, z₆, z₉) as that of the cluster, whereas the other mass clumps lie at z₁ = 0.29, z₄ = 0.42, z₇ = 0.43, and z₈ = 0.34 in the foreground of the cluster.

We then perform a 2D shear analysis to constrain the mass properties of the cluster and its surrounding structure, modeled as the sum of nine mass halos in projection space. The multi-halo shear modeling procedure described here is similar to those of Watanabe et al. (2011), Okabe et al. (2011), and Zitrin et al. (2012a), but including an elliptical halo model as described below. More details will be presented in our forthcoming paper (K. Umetsu et al. 2013, in preparation).

First, we construct a reduced-shear map $(g_1({\boldsymbol {\theta }}),g_2({\boldsymbol {\theta }}))$ on a regular grid of N_cell = 42 × 42 independent cells, covering a 28' × 28' region centered on the cluster. We exclude from our analysis those cells lying within 15 from the cluster center and those lying within 05 from the other less-massive halo peaks, to avoid potential systematic errors due to contamination by unlensed cluster member galaxies (Section 3). This leaves us with a total of 1813 usable measurement cells, corresponding to 3626 constraints.

We describe the primary mass peak, responsible for the main cluster, as an elliptical NFW (eNFW, hereafter) model specified with six parameters, namely, the halo virial mass (M_vir), concentration (c_vir), ellipticity (e = 1 − b/a), position angle of the major axis (θ_e), and centroid position (X_c, Y_c). We introduce the mass ellipticity e in the isodensity contours of the projected NFW profile Σ(X, Y) as R² = (X − X_c)² + (Y − Y_c)² → (X − X_c)²(1 − e) + (Y − Y_c)²/(1 − e) (see Oguri et al. 2010; Umetsu et al. 2012). For each of the other eight less massive halos, we assign a spherical NFW profile parameterized with the virial mass (M_vir), where the centroid position is fixed at the respective mass peak location. Since these less massive halos are less resolved by our WL observations, their concentration parameters are set according to the mass–concentration relation c_vir(M_vir, z) given by Duffy et al. (2008).

We use the MCMC technique with Metropolis–Hastings sampling to constrain the multi-halo lens model from a simultaneous nine-component fitting to the reduced-shear map. The best-fit parameters are reported in Table 5. We find virial masses of ${M_{\rm vir}}= (1.71\pm 0.26)\times 10^{15}\,M_\odot \, h^{-1}$ for the main cluster halo, z₆, and masses of ${M_{\rm vir}}=(0.15\pm 0.09),(0.27\pm 0.11),(0.25\pm 0.11),\,{\rm and}\,(0.19\pm 0.10)\times 10^{15}\,M_\odot \, h^{-1}$ for the other smaller halos, z₂, z₃, z₅, z₉, respectively, that lie at the same redshift. The high value of the ellipticity, e = 0.59 ± 0.08, inferred from our elliptical lens modeling (similar to the cases of, e.g., MACS J0416 by Zitrin et al. 2013; RX J0152.7-1357 by Jee et al. 2005 and Umetsu et al. 2005) supports that the central component of MACS0717 represents a merging, interacting system of multiple clumps in the process of formation (as shown in Ma et al. 2009; Mroczkowski et al. 2012).

Comparing the cluster luminosity and galaxy maps, most of the significant mass structures detected in the mass map are also probed by the galaxies, with the exception of two lower-significance structures, marked as z₈ and z₉. The mass structure z₈ is not evident in the galaxy density map, but can be explained by the existence of lower-redshift galaxies seen therein, z₈ = 0.34, which is close to the limit probed by our color-selection method (see Figure 3, green). The other mass structure, z₉, is not detected in the galaxy density map, however, a low-significance peak is seen (more evident in the luminosity map) offset by ∼15 to the north-east, where visual inspection reveals a BCG, albeit also at z ≈ 0.34, therefore not part of the cluster structure. A ∼15 offset is comparable to our smoothing scale, therefore within errors.

To further determine if the detected and modeled halos are real, and if their content represents the typical stellar content of cluster-sized halos, we calculate the mass-to-light (M/L) ratio of the individual halos modeled. We divide the fitted virial mass of each halo, ${M_{\rm vir}}_{,i}$, by the total luminosity of "green" galaxies within the equivalent virial radius of the halo (virial ellipse in the case of the main halo modeled with eNFW, z₆), $L_{i}=\sum _{k\in r<{r_{\rm vir}}_{,i}}{L_{{R_{\rm C}},k}}$. We list the M/L ratios in Table 6, and we plot the resulting ${M_{\rm vir}}/L$ versus ${M_{\rm vir}}$ in Figure 11. All of the halos, apart from halos z₈ and z₉ discussed above, show values that are expected for group- to cluster-sized halos, ranging from ≈200–300 (Rines et al. 2000, 2004; Katgert et al. 2004). However, the large uncertainties in the M/L ratios measured, especially for the low-mass halos, limit us from determining if there is any trend in this relation.

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Table 6. Best-fit NFW Multi-halo Parameters of the 2D Shear Analysis

Halo	ΔXa	ΔYa	zlb	zsc	Rvir	Mvird	ee	θef	$M_{\rm vir}/L_{{R_{\rm C}}}$
	(arcmin)	(arcmin)			(Mpc h−1)	(1015 M☉ h−1)		(deg)	(h M☉/L☉)
z1	−12.11	6.23	0.29	1.21	1.45	0.58 ± 0.16	⋅⋅⋅	⋅⋅⋅	230 ± 63
z2	−9.73	−3.57	0.56	1.27	0.79	0.15 ± 0.09	⋅⋅⋅	⋅⋅⋅	243 ± 142
z3	−6.37	−9.17	0.54	1.26	0.97	0.27 ± 0.11	⋅⋅⋅	⋅⋅⋅	176 ± 74
z4	−5.81	6.79	0.42	1.24	1.09	0.30 ± 0.11	⋅⋅⋅	⋅⋅⋅	322 ± 119
z5	−4.55	−3.01	0.55	1.26	0.95	0.25 ± 0.11	⋅⋅⋅	⋅⋅⋅	158 ± 70
z6	−0.21 ± 0.06	−0.09 ± 0.07	0.54	1.26	1.81	1.71 ± 0.26	0.59 ± 0.08	50 ± 5	245 ± 37
z7	2.73	−7.77	0.43	1.24	1.04	0.27 ± 0.11	⋅⋅⋅	⋅⋅⋅	256 ± 103
z8	5.39	10.85	0.34	1.22	0.82	0.12 ± 0.07	⋅⋅⋅	⋅⋅⋅	422 ± 237
z9	7.91	3.15	0.56	1.27	0.86	0.19 ± 0.10	⋅⋅⋅	⋅⋅⋅	539 ± 273

Notes. For the main cluster component (z₆), the halo centroid was allowed to vary, and an eNFW model was fitted. The concentration parameter was also fitted here, whereas for all other less massive halos the concentration was set by the mass–concentration relation given by Duffy et al. (2008). ^aThe centroid position of each halo is given relative to the cluster center (see Table 1) in units of arcminutes. ^bThe median photometric redshift for each halo estimated from the green sample. ^cThe photometric source redshift for each halo. In the multi-halo shear fitting process, we assumed a flat prior over the range z_s ± 0.1. ^dMarginalized bi-weight center and scale locations are reported. ^eThe projected mass ellipticity of our eNFW model is defined as e = 1 − b/a < 1 with a and b the major and minor axes of the isodensity contours. ^fThe position angle of the eNFW halo major axis is given in units of degrees, measured north of west.

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For a consistency check, we also calculate the M/L ratios for the single-halo NFW models we fit to our reconstructed mass profiles in Sections 7.1 and 7.2 (listed in Table 5), and compare with the M/L ratio we get for the main halo from our multi-halo modeling, M/L₆ ∼ 245. Within the errors, we get comparable M/L values for the 1D NFW fit (Sections 7.1), M/L ∼ 300, which are reasonable for a cluster as massive as MACSJ0717, whereas the values for the NFW fit to the 2D mass reconstruction method given in Section 7.2, M/L ∼ 310, are only slightly higher, reflecting the higher total mass found, due to the inclusion of the second massive halo at larger radii in the virial mass fitted.

We perform a complementary joint SL+WL reconstruction using the method of Merten et al. (2009, 2011, hereafter SaWLens). The SaWLens method combines central SL constraints from multiple-image systems with WL distortion constraints in a non-parametric manner to reconstruct the underlying lensing potential on a multi-scale grid. Here, the density of constraints sets our resolution scale. Inside the HST region, we combine constraints from HST WL shape distortions with those of SL multiple-image sets. This yields a very high-resolution scale of 9'' box size. Beyond this, we rely on Subaru WL shape distortion constraints, yielding a resolution scale of 25''. There is good consistency between the mass structures probed by the mass map derived here and in Section 8.1. We further derive an azimuthally averaged mass profile in order to compare with our other mass profiles derived with the methods presented in the previous sections (see Figure 13, blue triangles). SaWLens error bars were derived from 1000 bootstrap realizations of the WL input catalog and from 2000 resamplings of the SL input data. Since many of the multiple image systems have only (less certain) photometric redshifts as derived from HST imaging, SL realizations were obtained by randomly assigning redshifts within the equivalent uncertainties of each system. We further present the inner substructure seen by this method in the next subsection.

In this subsection, we present the 2D analysis of the WL shear map as measured from background galaxies in the HST field, defined in Section 6. We also present the inner region of the SaWLens reconstruction as an independent analysis of the cluster core.

To avoid systematic effects due to the finite-field of the HST FOV, we combine our HST background sample with the Subaru background sample (Section 6), where we remove Subaru objects that match with HST objects to avoid duplication. We also correct for the different depths of the HST relative to the Subaru background samples, as explained in Section 6. In order to avoid infinite noise issues, we first smooth the 2D shear field with a Gaussian of 025 FWHM. This essentially limits our sensitivity to mass structure at small angular scales, depending on the local source number density (${\rm S/N}\propto n_g^{1/2}$).

We reconstruct the high-resolution mass map in the central 5' × 5' region from the 2D shear map, using an entropy-regularized maximum-likelihood reconstruction method (hereafter, maximum entropy method, or MEM) of Umetsu & Broadhurst (2008). We present the resulting mass distribution in Figure 12 (upper left) in terms of the reconstruction S/N map, with 3, 5, 7σ_κ mass contours overlaid. The errors for the mass map are based on the theoretical covariance matrix (Umetsu & Broadhurst 2008). As an independent comparison, we also present the inner region of the mass map derived from the SaWLens method, described in the previous section. This is shown in Figure 12 (right panel). A grid-size of ∼9'' is possible in this region due to several SL multiple-image systems, augmented by the HST measured WL galaxy shapes. We overlay the light distribution in both maps (white contours) as determined from the cluster members selected in Section 6.

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Broadly, both maps show a mass distribution that follows the light as determined by the member galaxies. Substantial substructure is probed by both methods, and several distinct mass peaks are evident throughout. The complexity of the mass distribution demonstrates that a clear center is not well-defined in this cluster, which instead of a dominant BCG has several bright galaxies associated with the different mass clumps. This level of substructure was previously reported by Ma et al. (2009) from Chandra X-ray data, showing several brightness peaks (see their Figure 1) and an extended shock feature. We overlay the X-ray map (also rederived here in Section 9.2 below) on the HST color image (Figure 12, bottom right). Combining with dynamical measurements, Ma et al. (2009) concluded the existence of four main mass halos (denoted A, B, C, and D in their figure) suggesting a triple-merger. One of those clumps (B) was shown to still be in its infancy at a very high collision velocity of s ∼ 3000 km s⁻¹, infalling through the cluster. Using their SL model, L12 also find a similar substructure in the DM distribution, and attempt to model the mass map with 1–5 mass halos, finding a best solution given by 4 mass halos. We note L12's peaks on both maps (blue crosses, denoted as A–D following Ma et al.'s designation).

We also overlay the MEM mass contours on the SL model derived in Section 5, shown along with L12 mass peak locations in the bottom-right panel of Figure 12. We note that the WL–MEM results agree very well with our parametric SL results (Section 5), both demonstrating an overall agreement between the distributions of the galaxies and DM, although our parametric SL method does use the light distribution as an initial approximation of the mass. For the WL–MEM results, this is not trivial at all, because the WL–MEM method is entirely non-parametric and is not aware of the distribution of cluster members, hence providing a model-independent reconstruction of the underlying total mass distribution.

Although we find an overall agreement with previous and current SL analyses where the DM follows the location of the galaxies, some differences are noticeable. From the MEM-derived mass map, the peak location of the main clump "C" is somewhat offset from those of cluster galaxies and X-ray emission (that rather agree with each other) by about ∼033 ≈ 90 kpc h⁻¹, although their extended features overlap well with each other.

The SaWLens derived map, on the other hand, shows much larger differences between the mass and light distributions. The mass peaks in the SaWLens reconstruction are mostly offset from those of cluster galaxies. Most notably, the location of the SaWLens mass peak nearest to clump "A" is further displaced to the center than the light or the location found by L12, and clump "B" is much less pronounced in this mass map.

The current analysis is limited by the spatial resolution set by the number density of background galaxies, and may be prone to potential systematics, especially in the critical lensing regime. Therefore, in this work, we cannot draw any significant conclusion about the level of offsets between the DM, galaxies, and hot gas.

The mass profiles we constructed in the previous sections using various methods are summarized in Figure 13: a parametric light-traces-mass SL mass profile (green; Section 5), a non-parametric Bayesian mass profile incorporating WL 1D shear+magnification constraints and the SL mass constraint (red squares; Section 7.1), a non-parametric approach combining WL 2D shear+ 1D magnification constraints (black circles; Section 7.2), and finally, a mass profile obtained with SaWLens (blue triangles; Section 8.3), an independent non-parametric reconstruction combining SL+WL shear constraints on a joint multi-scale grid. Here we summarize and compare the different results.

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As can be seen, overall good agreement is found in the regions of overlap between the different reconstruction methods, within the errorbars. The relatively good agreement we find on large scales is reassuring, given that it is all based on the same Subaru imaging data. At $r>1\,{{\rm Mpc}\,h^{-1}}$, there is general change in the sign of the gradient of the mass profile, where a clear flattening tendency is seen. A similar behavior was also found in our recent CLASH lensing analysis of the high-mass relaxed cluster MACSJ 1206-08 at z = 0.44 (M_vir ≃ 1.1 × 10¹⁵ M_☉ h⁻¹; Umetsu et al. 2012), albeit to a lower extent, and may in both cases reflect the relative prominence of the surrounding filamentary pattern of structures extending beyond the virial radius, and hence the relatively less evolved stage of these very massive clusters at z ∼ 0.5 compared to their lower redshift counterparts, such as A1689 and A1703, where the outer mass profile continues to steepen (Broadhurst et al. 2005b; Umetsu et al. 2011a) and for which no prominent filamentary network is visible.

MACSJ0717 has recently been analyzed by Jauzac et al. (2012) using multiple HST/ACS pointings aimed at covering the filamentary structure around the cluster. Their mass reconstruction shows slightly higher densities at all radii and most notably at the outer radii, albeit still in agreement with our 2D shear+magnification density profile (black circles), within the errors. This small systematic difference may arise due to Jauzac et al.'s strategy of surveying only the area where the filamentary structure is dominant, so that the mean lensing signal that we obtain with our larger FOV is on average expected to be lower, as observed.

The total masses of the cluster are presented in Section 9.4 where we compare with prediction for the highest mass halos expected in the context of the ΛCDM model.

Here we compare complementary X-ray derived total masses to our 1D lensing-derived total masses. One mass estimator uses the assumption that the gas fraction at r₂₅₀₀ is constant (for this work we assume f_gas ≡ M_gas/M_total = 0.11). The other common mass estimator uses the assumption that the primary pressure support for the gas is thermal pressure, that is, that the gas is in nearly hydrostatic equilibrium (HSE). While it is true that this system is merging and highly complex (as shown in Ma et al. 2009), a comparison of the HSE mass with the lensing mass can be used to place estimates on the magnitude of non-thermal pressure support in the gas, such as bulk motions and turbulence.

We analyze public Chandra observations from a single OBS-ID (4200) with a net exposure time of 59,000 s. Gas density profiles from the ACCEPT database (Cavagnolo et al. 2008) were used to generate an enclosed gas mass profile. We also derived radial profiles based on spectra extracted from concentric annular apertures. The tool used for the HSE mass estimate is Joint Analysis of Cluster Observations (JACO; Mahdavi et al. 2007, we refer the reader to this paper for the details of the X-ray analysis procedure). The best-fit NFW parameters derived from the joint JACO fit at r₂₅₀₀ are $M_{2500} = 4.45^{+0.95}_{-0.46} \times 10^{14}\,M_\odot \, h^{-1}$, c₂₅₀₀ = 0.6 ± 0.3. The X-ray profile has a limited range $r<0.7\,{{\rm Mpc}\,h^{-1}}$.

We compare the X-ray total mass within $r<500\,{{\rm kpc}\, h^{-1}}$ with lensing-derived values at the same clustercentric radius in Table 5. The X-ray mass seems to be about ∼87% of the lensing 1D WL+SL NFW fitted value. In Figure 15, we compare the resulting total mass (M_3D < r) profiles from the X-ray fit (magenta) and the lensing 1D WL+RE NFW fit (orange). We find that the X-ray mass profile derived with the HSE assumption underestimates the lensing profile at all radii. The difference is most extreme in the core of the cluster, where the HSE X-ray mass is only 45% of the WL mass, rising to agreement with the WL mass at the limit of the X-ray data, $r=0.7\,{{\rm Mpc}\,h^{-1}}$. This inconsistency clearly stems from the departure from HSE at the center of the cluster where significant merging activity has been claimed, augmented by the highly non-spherical shape of the cluster (Meneghetti et al. 2010; Rasia et al. 2012). We enhance our discussion below by further comparing to the SZE-derived mass (see Section 9.3) which also relies on the HSE assumption.

For a wider look at the 2D distribution of the gas, we also analyze XMM-Newton observations of MACSJ0717 recently made public (P.I. Million, observations 672420101, 672420201, 672420301, totaling 145,000 s). We perform a standard reduction on the observations, removing high flare times. To achieve the best sensitivity to gas at large clustercentric radius, we summed the MOS1, MOS2, and p–n CCDs of all three observation sets. The brightest point sources were identified and excluded. Since the PSF for XMM gets fairly distorted and elongated at off-axis angles, there is incomplete removal of the halos around point sources there.

We present the logarithmic X-ray brightness map in Figure 14, where we smooth the map with a Gaussian of θ_FWHM = 05 and overlay it with logarithmic contours starting at 1.5σ_X above the background with 2σ_X intervals (solid black lines). For comparison, we overlay the mass density (2.5- and 6.5-σ_κ) contours from the Subaru lensing map (solid white line) and the galaxy distribution 2.5σ_n contour (dotted black line).

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The cluster X-ray brightness peak is clearly shifted from the mass (and galaxy) peak, at about $R=0\buildrel{\prime}\over{.} 37= 100\,{{\rm kpc}\, h^{-1}}$ north-west of the optical center. This has been noted in previous detailed analyses of the cluster center (Ma et al. 2009) and was interpreted to be due to trailing of the gas component behind the cluster as subclumps cross through the main cluster halo, because the gas and the DM have different cross-sections. In Table 1, we summarize the location of the optical center we have been using and that of the X-ray brightness peak.

With the advent of the XMM-Newton data, we can also see here the clear detection of the secondary massive component (denoted z₅ in our mass map, see Figure 10) at a 5.5σ_X level, and the third mass component (denoted z₂ in our mass map) at a 2.5σ_X level. Finally, the fourth mass component detected from lensing, z₃, is evident in the map but at a much lower significance, ∼1.6σ_X. Although lensing shows this halo to be more massive than z₂, it is hard to detect it in the X-ray image since it lies at the edge of our data where it is more prone to contamination by point sources.

Overall, it seems the gas in the outskirts (at a scale of ${\lesssim }0.7\,{{\rm Mpc}\,h^{-1}}$) is more spherically distributed around the main cluster component, but has the same substructure corresponding to high-mass peaks along the filamentary structure. The emission from the hot gas is expected to be more spherical in shape than that mapped by lensing because the gas in projection traces the gravitational potential, which is rounder than the density distribution.

We obtained SZE observations of MACSJ0717 using Bolocam at the Caltech Submillimeter Observatory. Bolocam is a 144-element bolometric array operating at 140 GHz with an angular resolution of 58'' (FWHM). The data were collected by scanning Bolocam's 8' FOV in a Lissajous pattern to produce an image with coverage extending to ≃ 10' in radius. Full details of the observations are given in Mroczkowski et al. (2012) and Sayers et al. (2013), and the data were reduced using the procedures described in Sayers et al. (2011). In addition, we note that in the multiwavelength SZE analysis of Mroczkowski et al. (2012), which used the same Bolocam SZE data as this analysis, a tentative kinetic SZE signal from subclump "B" of Ma et al. (2009) is reported at a significance of ≃ 2σ. Consequently, we subtracted the best-fit kinetic SZE template of Mroczkowski et al. (2012) from our data, although we note that Mroczkowski et al. (2012) were not able to robustly constrain a spatial template of this kinetic SZE signal, modeling it as a simple Gaussian centered on the location of "B." We then fit a spherical generalized NFW (gNFW) pressure model (Nagai et al. 2007) to our SZE data allowing both the normalization and scale radius to vary while using the best-fit slope parameters found by Arnaud et al. (2010).

We compute the mass of MACSJ0717 from this gNFW fit to the SZE data using the formalism described by Mroczkowski (2011). In particular, we assume that the cluster is spherical and in HSE, although we note that neither of these assumptions are strictly valid for MACSJ0717 due to its complex dynamical state. The resulting SZE mass profile is shown in blue in Figure 15, and we note that it is approximately ∼75% of our lensing-derived mass profile. However, the SZE mass profile is in reasonably good agreement with the X-ray derived mass profile, which also assumed HSE. Therefore, we conclude that the difference is due to the bias associated with assuming HSE. For example, even for relaxed systems, we expect the HSE-derived virial mass to be biased approximately 10%–20% lower on-average compared to the true virial mass due mainly to bulk motions in the gas (Nagai et al. 2007; Rasia et al. 2004, 2012; Meneghetti et al. 2010). Furthermore, in order to gauge the impact of the kinetic SZE signal from subclump "B," we also computed an SZE mass profile without subtracting the kinetic SZE template (shown in gray in Figure 15). As expected, the difference between the two SZE mass profiles is most significant in the inner regions of MACSJ0717 near the center of subclump "B," where the corrected mass is ∼50% lower than the uncorrected one, decreasing to only ≲ 15% difference at large radius.

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We have reliably estimated the total mass of the cluster in Sections 7.1 and 7.2 to be ${M_{\rm vir}}({\rm 1DWL+SL})=2.13\times 10^{15}\,M_\odot \, h^{-1}$ and ${M_{\rm vir}}({\rm 2DWL})=2.23\times 10^{15}\,M_\odot \, h^{-1}$, respectively, as summarized in Table 5. We note that the two masses are in excellent agreement. In Section 8.2, we derived specific masses for the individual halos comprising the cluster and its surrounding structures, in order to more accurately account for the LSS contribution to the mass. Here we use as the total mass for MACSJ0717 the sum of the virial masses of the two components that lie within the virial region of the main halo, ${M_{\rm vir}}(z_5+z_6)\approx (1.96\pm 0.28)\times {10^{15}\,M_\odot \, h^{-1}}$, as determined by multi-halo modeling (see Tables 6) which is slightly lower, but still consistent with the values found from single-halo modeling noted above.

Another total mass estimate for this cluster was previously presented in Hoekstra et al. (2012), part of a larger 50-cluster batch analysis. That measurement solely relied on WL shear measurement, and did not simultaneously constrain both ${c_{\rm vir}}$ and ${M_{\rm vir}}$, as done here, but relied on the Duffy et al. (2008) relation, which, according to their published mass of ${M_{\rm vir}}=5 \times 10^{15}\, M_\odot \, h^{-1}_{70}$, should be ${c_{\rm vir}}=3.05$. Forcing this concentration value, our mass would have been ${M_{\rm vir}}=(4.5\pm 0.6)\times 10^{15}\, M_\odot \, h^{-1}_{70}$, consistent with their mass. Since there is a strong negative correlation between the mass and concentration parameters, such an assumption of a low concentration will lead to an overestimated high mass.

We are now in the position to address the probability of finding such a massive cluster in our universe via extreme value statistics (Mortonson et al. 2011; Colombi et al. 2011; Waizmann et al. 2012a; Hotchkiss 2011; Harrison & Coles 2012). In the work of Waizmann et al. (2012a), several high-mass clusters were examined (A2163, A370, RXJ 1347−1145 and 1E0657−558), and the cumulative probability function of finding such massive systems in their given survey area was calculated using general extreme value statistics. However, they found that none of those clusters alone is in tension with ΛCDM. In another paper, Waizmann et al. (2012b) test the probability of the extremely large Einstein radius measured for MACSJ0717, previously estimated as θ_E = 55'' (for z = 2.5, Zitrin et al. 2009a) within the standard ΛCDM cosmology. Although they find this system not to be in tension with the ΛCDM expectations, the sensitivity of the Einstein radius distribution to various effects (lens triaxiality, mass–concentration, inner slope of the halo density profile, and more) implies that this comparison is much less reliable than that using a total lensing mass. To conclude, Waizmann et al. (2012b) calculate that a galaxy cluster in the redshift range 0.5 ⩽ z ⩽ 1.0 would need to have a total mass of at least M_200m = 4.5 × 10¹⁵ M_☉, where M_200m is defined with respect to the mean density of the universe at the time of collapse, in order to exclude ΛCDM at the 3σ level.

To compare with Waizmann et al.'s values, MACSJ0717 has M_200m ≈ (2.9 ± 0.5) × 10¹⁵ M_☉ from lensing. In Figure 16, we show the probability distribution function (PDF) of the most massive cluster (for details of this calculation see Davis et al. 2011; Waizmann et al. 2011, 2012a) as calculated for the MACS survey area, $A_S=22,735\deg ^2$, within the a priori redshift interval 0.5 ⩽ z ⩽ 1.0. We overlay the total mass estimate of MACSJ0717 as the blue error bar. It can be seen that the mass of MACSJ0717 falls slightly below the 95 percent quantile. In order to avoid the bias in the occurrence probabilities of rare galaxy clusters as discussed in Hotchkiss (2011), one has to set the redshift interval a priori. Since MACSJ0717 happens to fall at the lower end of the chosen redshift interval, the PDF in Figure 16 can be considered as a conservative estimate of the true rareness of the cluster such that a more thorough treatment, as presented in Harrison & Hotchkiss (2013), would yield a lower rareness.

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Therefore, we conclude that MACSJ0717's mass, being the largest above z = 0.5, does not pose any tension on the standard ΛCDM cosmology. However, the growing number of very massive clusters at high redshifts makes it advisable to study the occurrence probabilities of ensembles of massive clusters instead of single ones (see, e.g., Waizmann et al. 2013).