HUBBLE SPACE TELESCOPE DISCOVERY OF A z = 3.9 MULTIPLY IMAGED GALAXY BEHIND THE COMPLEX CLUSTER LENS WARPS J1415.1+36 AT z = 1.026^*

Surveys like SpARCS (Wilson et al. 2008), SPT (Ruhl et al. 2004), the Red-Sequence Cluster Surveys (RCS, Gladders 2004 and RCS-2, Gladders & Yee 2005; Yee et al. 2007), and the IRAC Shallow Survey (Eisenhardt et al. 2008) will discover thousands of galaxy clusters out to redshifts beyond z = 1. These large surveys will be used to probe dark energy and the underlying cosmology through direct measurements of the evolution of the cluster mass function. To fully utilize these data, it will be essential to derive reliable mass estimates from the cluster properties measured in these surveys.

Great effort has been dedicated to the development of cluster mass-observable relations in targeted cluster observations. Sunyaev–Zel'dovich (SZ) and X-ray observations probe the hot ionized intracluster gas and have been used to derive masses (LaRoque et al. 2006; Allen et al. 2008) and scaling relations that tie mass to the observed SZ quantities (Bonamente et al. 2008). Hicks et al. (2006) derive scaling relations between observed X-ray properties and the optical richness of clusters while Evrard et al. (2008) model the relationship between the velocity dispersion of cluster galaxies and cluster mass. Weak lensing measurements have been used to calibrate optical richness measurements from a large sample of clusters from the Sloan Digital Sky Survey (Koester et al. 2007; Johnston et al. 2007) and to calibrate X-ray measurements through the mass–temperature relations (Hoekstra 2007; Bardeau et al. 2007; Bergé et al. 2008). Strong lensing measurements typically have much smaller errors compared with the other methods but are restricted to the central region of clusters and are rare. Nevertheless, strong lensing systems have been studied in small samples of clusters (Comerford et al. 2006; Hennawi et al. 2008).

Large cluster surveys out to z∼ 1 have the potential to constrain the dark energy equation of state (e.g., Voit 2005), provided that the mass-observable relations are well calibrated. Full exploitation of the more distant clusters requires deep space-based observations. As a result, mass-observable relations have been studied in far fewer clusters at z > 1 relative to low-redshift clusters. In a 219-orbit program (Program number 10496, PI: Perlmutter) to search for supernovae (SNe) with the Hubble Space Telescope (HST), we observed 25 of the highest redshift galaxy clusters known at the time (Dawson et al. 2009). These images support a rich program of cluster studies including the calibration of mass proxies at z > 1. One particular cluster from this program, selected from the Wide Angle ROSAT Pointed Survey, WARPS J1415.1+3612 at z = 1.026 (Perlman et al. 2002), has already been studied in X-ray (Maughan et al. 2006; Allen et al. 2008) and SZ (Muchovej et al. 2007) observations. We now have deep images from the Advanced Camera for Surveys (ACS) and spectroscopy from the Faint Object Camera and Spectrograph (FOCAS: Kashikawa et al. 2002) on Subaru reveals a pronounced strong lensing arc of a source Lyα emitting galaxy at z = 3.90. The new data from this program combined with previous and ongoing measurements enable a multi-probe analysis of the cluster mass-observable relation for this high-redshift cluster.

Here, we present an analysis of the strong lensing and dynamical mass of WARPS J1415.1+3612. The Letter is organized as follows: we describe the observations and data in Section 2, mass estimates are derived and compared in Section 3, and the summary is found in Section 4. Throughout this Letter, we use AB magnitudes and assume a cosmology with Ω_M = 0.3, Ω_Λ = 0.7, and h = 0.7.

2.1. ACS Images

WARPS J1415.1+3612 was observed seven times with ACS from 2005 November through 2006 April for a total integration of 2425 s in the F775W filter and 9920 s in the F850LP filter, hereafter i₇₇₅ and z₈₅₀. Individual exposures were co-added using MultiDrizzle (Fruchter & Hook 2002) at a resolution of 005 pixel⁻¹. We use 25.678 and 24.867 as zero points for i₇₇₅ and z₈₅₀, respectively (Sirianni et al. 2005).

The deep ACS images revealed a complex strong lensing system near the cluster core. The composite color image from the i₇₇₅ and z₈₅₀ data is shown in Figure 1. The arc system consists of at least five images. The main arc (A) is 675 (54.4 kpc at the cluster redshift) from the center of the cluster, which we take to be the position of the brightest cluster galaxy (BCG). To the SW of the main arc, there is a triplet of arcs (B, C, and D) around a spectroscopically confirmed cluster member (no. 13). About 5'' south of the triplet, there is a fifth arc (E). The total i₇₇₅ isophotal magnitudes for the arcs A–E are 23.44, 25.75, 25.46, 25.13, and 25.62, respectively. We use the i₇₇₅ magnitudes because they suffer less contamination than the z₈₅₀ magnitudes from the much redder elliptical cluster members. The magnitudes for arcs B, C, and D are obtained after the lensing galaxy has been subtracted using the b-spline model of Bolton et al. (2006). These five images lie very close to an imaginary arc centered on the BCG that subtends slightly more than 90°. The radius of the Einstein ring for the cluster potential is taken to be the average of the two circles mentioned in Figure 1, 7.13 ± 038. The uncertainty in the radius is determined from the difference between the two circles and the average.

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The B-band luminosity for this cluster is estimated by summing up light from all the galaxies within approximately 1 Mpc of the BCG and then subtracting a background estimated from fields without clusters within the GOODS fields. We apply a K-correction to transform z₈₅₀ to rest-frame B magnitude. The total luminosity is determined to be L_B = 2.92 ± 0.88 × 10¹² L_B⊙.

2.2. Subaru Spectroscopy

The total mass inside the Einstein ring of r_E = 57.5 ± 3.1 kpc is 1.96^+0.22_−0.20 × 10¹³ M_☉ (e.g., Narayan & Bartelmann 1996). If we assume a singular isothermal sphere (SIS) profile for the central region of the cluster, this mass corresponds to a rest-frame velocity dispersion of 686⁺¹⁵₋₁₉ km s⁻¹, consistent with the value estimated from cluster member redshifts. We can estimate the magnification factor for arc A by using μ = |1/(1 − r_E/r)| (e.g., Narayan & Bartelmann 1996) for the SIS profile, where r is the distance of the image from the lens center. If we take r_E = 713 (or 57.5 kpc), μ ∼ 18 for arc A. This implies that the unmagnified i₇₇₅ magnitude for arc A is ∼ 26.6.

To get a qualitative estimate on the change in the derived strong lensing mass caused by relaxing our assumption of a spherically symmetric mass distribution, we construct elliptical Navarro–Frenk–White profile (NFW) models (Glose & Kneib 2002) with a critical curve that passes through at least part of arcs A and E and passes between arc C and the lensing galaxy (cluster member no. 13). The model with the largest ellipticity that still meets these requirements has an ellipticity of 0.1. The mass enclosed within its critical curve is 1.79 × 10¹³ M_☉, within the errors of the spherical models.

The dynamical mass is estimated from the redshifts of the 21 cluster members with Q > 1 in Table 1 using the virial scaling relation from the simulations of Evrard et al. (2008),

$$\begin{equation} \sigma _{\rm DM}(M, z)=\sigma _{\rm DM, 15} \left({h(z)M_{200}\over {10^{15}\,M_{\odot }}} \right) ^{\alpha }, \end{equation} \tag{ 1 }$$

where σ_DM(M, z) is the dark matter velocity dispersion, h(z) = H(z)/100 km s⁻¹, and M₂₀₀ is the mass within r₂₀₀ (the radius of a sphere where the mean density is 200 times the critical density at the redshift of the cluster). The constants σ_DM,15 = 1082.9 ± 4.0 km s⁻¹ and α = 0.3361 ± 0.0026 are determined from the simulations of Evrard et al. (2008). Assuming that the velocity bias b_v = σ_v,gal/σ_DM = 1, we find M₂₀₀ = 3.33^+2.83_−1.80 × 10¹⁴ M_☉ and r₂₀₀ = 0.97 ± 0.22 Mpc. Thus, the mass to light ratio is ∼114 M_☉/L_B⊙. In Figure 2, we fit an NFW profile (Navarro et al. 1997) to the total cluster mass using the strong lensing and dynamical mass estimates. The model has a concentration parameter c = 4.96^+1.81_−1.03 and a core radius r_s = 0.179^+0.078_−0.055 Mpc, where uncertainties are computed via Monte Carlo simulation.

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For a simple test of the mass-observable relation in WARPS J1415.1+36, we compare our strong lensing and dynamical estimates and a model of the mass profile to an estimate of weak lensing mass, X-ray mass, and SZ mass in Figure 2. Using the same deep ACS images, M. J. Jee et al. (2009, in preparation) derive the weak lensing mass assuming an NFW profile with a mass–concentration relation from Bullock et al. (2001). The X-ray mass M_2500(z) (Maughan et al. 2006) is determined from a best-fit two-dimensional elliptical β-model analyzed at r_2500(z). The SZ value of M_2500(z) is derived from a spherical, isothermal β-model fit to 30 GHz data from the SZ Array (Muchovej et al. 2007). In the X-ray and the SZ mass estimate, Δ(z) is a redshift-dependent density contrast as described in, e.g., Maughan et al. (2006). Both the weak lensing mass and the X-ray mass are consistent with our results. However, the SZ mass is lower than the prediction of our model by roughly a factor of 2. In Muchovej et al. (2007), it is noted that the SZ mass estimate is marginally lower than the X-ray value, likely due to low signal-to-noise ratio (S/N) in SZ measurements, uncertainties in the absolute calibration, and possible systematic errors from the model assumptions. Additional observations with the SZA at 30 GHz and 90 GHz should improve the constraints on the SZ mass estimate and shed light on the apparent discrepancy.

Using numerical simulations, Dolag et al. (2004) predict the dependence of the average halo concentration parameter on the cluster redshift and virial mass

$$\begin{equation} c(M, z) = {c_{0}\over {1+z}} \left({M\over {M_{*}}}\right)^{\gamma }. \end{equation} \tag{ 2 }$$

Shaw et al. (2006) find the best-fit parameters to be c₀ = 6.47 ± 0.03 and γ = −0.12 ± 0.03 from N-body simulations. Here, M is the virial mass and M_* = 11.0 × 10¹⁴ M_☉(Shaw et al. 2006). If we assume the dynamical mass (M₂₀₀ = 3.33 × 10¹⁴ M_☉) to be the virial mass, Equation (2) predicts the average concentration to be c = 3.70^+0.62+1.9_{−0.34 − 1.3}, where the first set of errors is from the errors in the best-fit parameters (c₀ and γ) and the second set is from the scatter about the average (Bullock et al. 2001). Our concentration of c = 4.96 is higher than the predicted value of c but is well within its errors.

We now examine the strong lensing arcs B, C, and D around cluster member no. 13. The radius of the Einstein ring for the lensing galaxy is estimated by the distance between the galaxy and arc C, 065⁺⁰³⁵₋₀₃₀. The upper and lower bounds are set by the distances from the lensing galaxy to arcs D and B, respectively. Assuming that the deflection angle due to the cluster potential does not vary appreciably for arcs B, C, and D, the mass enclosed within the Einstein radius is estimated to be 1.65^+2.25_−1.17 × 10¹¹ M_☉.

The cluster WARPS J1415+36 at z_lens = 1.026 is one of the most distant strong lensing clusters reported (Thompson et al. 2001; Gladders et al. 2003; Gilbank et al. 2008). Although the SZ mass estimate is not consistent with the rest of the data for this cluster, this work suggests that the mass-observable relations derived from numerical simulations and observations of strong lensing, weak lensing, dynamical mass, and X-ray mass still hold for clusters at redshifts at z ∼ 1.

Recently Gilbank et al. (2008) report multi-probe mass estimates for the strong lensing cluster, RCS2319, at z = 0.91. Future surveys will soon reveal many new high-redshift, strong lensing systems and provide deep, multiwavelength images of these clusters. With the corresponding improvements in mass-observable relations in the decelerating regime, galaxy clusters will soon become an even more effective tool for cosmology.

Financial support for this work was provided by NASA through program GO-10496 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. This work was also supported in part by the Director, Office of Science, Office of High Energy and Nuclear Physics, of the U.S. Department of Energy under Contract No. AC02-05CH11231, as well as a JSPS core-to-core program "International Research Network for Dark Energy" and by JSPS research grant 20040003. Additional support was provided by a scientific research grant (15204012) by the Ministry of Education, Culture, Sports, Science, and Technology of Japan. T.M. and Y.I. were financially supported by the JSPS Research Fellowship. Support for M.B. was provided by the W. M. Keck Foundation. The work of L.A.M. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.

Subaru observations were collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. The authors recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this superb mountain.