HerMES: CANDIDATE GRAVITATIONALLY LENSED GALAXIES AND LENSING STATISTICS AT SUBMILLIMETER WAVELENGTHS

Figure 1 shows Herschel SPIRE 250, 350, and 500 μm color-flux density plots for sources in HerMES blank fields. Candidate lensed SMGs presented in this paper are highlighted, and local late-type galaxies and blazars that are brighter than 80 mJy at 500 μm are also identified. As discussed in Section 2, the StarFinder+XID catalogs are used for blazars and candidate lensed galaxy flux densities, whereas the flux densities of local late-type galaxies are from the SUSSEXtractor catalog, which is more reliable for extended sources.

The principal sample of lensed SMG candidates has median S₂₅₀/S₃₅₀ = 0.90 (σ = 0.22), S₃₅₀/S₅₀₀ = 1.21 (σ = 0.24), and S₂₅₀/S₅₀₀ = 1.09 (σ = 0.51). These colors are comparable to the background SMG population (S₂₅₀/S₃₅₀ = 1.07, S₃₅₀/S₅₀₀ = 1.51, and S₂₅₀/S₅₀₀ = 1.60, with σ = 0.37, 1.02, and 1.67, respectively). There is a hint that the candidate lensed sources may be slightly redder than the background. As expected, the local spiral galaxies have significantly bluer colors than both the candidate lensed galaxies and the background SPIRE population, with median S₂₅₀/S₃₅₀ = 1.97 (σ = 0.33), S₃₅₀/S₅₀₀ = 2.08 (σ = 0.42), and S₂₅₀/S₅₀₀ = 4.14 (σ = 1.48) for the S₅₀₀ ⩾ 100 mJy subset. These colors also indicate that the candidate lensed galaxies lie at higher redshifts than local spiral galaxies with similar 500 μm flux densities.

The candidate lensed sources, local spirals, and blazars appear offset in S₂₅₀–S₂₅₀/S₃₅₀ and S₂₅₀–S₂₅₀/S₅₀₀ color-flux density spaces compared to the background of HerMES sources (Figure 1). This is because the highlighted sources are bright at 250 μm, which is a direct result of the flux selection at 500 μm. Indeed, the color–color diagram (Figure 2) shows that the lensing candidates have colors consistent with the HerMES background population, while local spiral galaxies have colors that are bluer than the majority of sources.

There are two lensed galaxy candidates that have bluer submillimeter colors than the majority. Both of these sources are known to be strongly gravitationally lensed (HBoötes03, Borys et al. 2006, Section 6.3; and HLock01, Conley et al. 2011, Section 6.7). It is possible that differential magnification could affect the submillimeter colors of these galaxies (e.g., Hezaveh et al. 2012; Serjeant 2012), although cold dust dominates the emission at 250–500 μm, so the effect is likely to be minor. We conclude that although the candidate gravitationally lensed galaxies are typically redder at submillimeter wavelengths than local late-type galaxies, there are some exceptions, and a color selection is not sufficient to identify local interlopers. Instead, the removal of interlopers requires the additional information that is provided by optical and radio data, which can be provided by existing shallow surveys (see Section 2).

We have shown that the candidate lensed SMGs have redder submillimeter colors than local spiral galaxies, which is indicative of a higher redshift population. We next consider the full redshift distributions of these sources.

There are four main ways to calculate the redshifts of SMGs. The most reliable is through the detection of submillimeter emission lines, the brightest of which are CO transitions. The second method is to calculate submillimeter photometric redshifts from the 250, 350, and 500 μm photometry and any available longer wavelength data (Table 5). Finally, optical or near-IR photometry or spectroscopy of the counterparts can be utilized. However, if an SMG is gravitationally lensed, then the foreground deflector will usually dominate the short-wavelength flux. In this case, if the foreground lens is misidentified as the SMG, then the optical redshift will be lower than the submillimeter redshift.

We are currently undertaking an extensive radio and millimeter spectroscopic follow-up campaign, targeting CO emission lines in the candidate gravitationally lensed galaxies (see Section 5.2 for details). Confirmed (multiple-line) redshifts have been obtained for five of the candidate lensed SMGs, and single-line redshifts for a further four (Table 4; D. Riechers et al. 2012, in preparation). The single-line CO redshifts are guided by the photometric redshifts in determining the most likely identification of the line emission.

Submillimeter photometric redshifts are calculated from χ² template fitting to the available submillimeter and millimeter data. The SED of SMM J2135−0102 (the Cosmic Eyelash; Ivison et al. 2010b; Swinbank et al. 2010) is used as the reference template, because Harris et al. (2012) showed that it is representative of Herschel lensed galaxies with Robert C. Byrd Green Bank Telescope (GBT) detections of CO(J = 1→0). The analysis is restricted to a single template because Harris et al. (2012) also showed that χ² fitting to the SPIRE data alone is unable to effectively select between multiple SEDs. We caution that the template choice results in a potential bias in the submillimeter photometric redshifts, due to the assumption that each source has an intrinsic SED (and dust temperature, T_D) that is similar to SMM J2135−0102. We assign each photometric redshift an error of ±0.25, which was shown empirically by Harris et al. (2012) to account for statistical errors, the uncertainty in the choice of SED template, and the implicit assumption that differential magnification between these wavelengths is unimportant. The redshift error is not required for our analysis and is only used for display purposes in Figure 4.

In Figure 3 (top panel), we show the redshift distributions of the candidate lensed galaxies, as derived from submillimeter and optical data; CO redshifts are preferred where available. The optical redshift distribution peaks at z_opt = 0.60 (median; mean z_opt = 0.72), and as expected, the submillimeter-derived redshifts peak at a higher value—z_submm = 2.8 (median and mean). Thus, on average the HerMES lensed SMGs lie at z ∼ 2.8 and are magnified by sources at z ∼ 0.7. We note that submillimeter redshifts of the supplementary sample are similar to those of the primary lensed candidates. In the inset in Figure 3 (top panel), we also show the distribution of local late-type galaxies, identified in Section 2. All of the submillimeter-luminous local galaxies are at z < 0.1, with a median of z = 0.028, confirming that they are easily distinguished from the SMGs.

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For comparison, the bottom panel of Figure 3 shows the redshift distribution of unlensed submillimeter sources in the Béthermin et al. (2011) model. Both models depend on the flux limits assumed, so we show sources with S₅₀₀ ⩾ 80 mJy and S₅₀₀ ⩾ 1 mJy separately. We note that, as observed in the HerMES data, at the bright flux limit the models contain a population of z ≪ 1 spiral galaxies in addition to the higher redshift SMGs. Figure 3 (bottom panel) also contains the redshift distribution of strongly gravitationally lensed SMGs as predicted by our model (Section 4.2). The predicted redshift distribution peaks at z ∼ 3, in broad agreement with the HerMES candidates. The redshift distribution of lensed sources is not a random sampling of the parent SMG population because the optical depth to lensing is also important.

We next consider the apparent far-IR luminosities of the HerMES candidate gravitationally lensed SMGs. In Figure 4, we show the distribution of redshift against apparent infrared (rest-frame 8–1000 μm) luminosity (i.e., assuming no lensing magnification) for the candidate gravitationally lensed sources. The infrared luminosities are calculated by fitting an optically thin modified blackbody, with fixed dust emissivity, β = 1.5, to the available submillimeter and millimeter data (Table 5).

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For comparison, we also show ∼1300 HerMES sources with optical and near-IR redshifts from a dedicated optical spectroscopic follow-up program (Casey et al. 2012) and those in the Boötes field with archival optical spectroscopic and photometric redshifts. The optical counterparts for both comparison samples are identified according to the method described in Roseboom et al. (2010), and we require that the sources are detected at >3σ in all three SPIRE bands (250, 350, and 500 μm), so that the infrared luminosities can be reliably determined.

We also show the approximate selection limits in Figure 4, which for the lensed candidate samples are calculated assuming T_D = 35 K and S₅₀₀ = 100 mJy (S₅₀₀ = 80 mJy for the supplementary sample). The selection of the comparison sources is complicated because it is driven by different wavelengths at different redshifts. In this case, we follow Casey et al. (2012) and use the minimum of three optically thin modified blackbodies—with T_D = 20 K and S₂₅₀ = 15 mJy, T_D = 30 K and S₃₅₀ = 15 mJy, and T_D = 50 K and S₅₀₀ = 15 mJy.

The candidate gravitationally lensed sources are at z ∼ 1–4 and have apparent infrared luminosities between 1.9 × 10¹³ and 1.3 × 10¹⁴ μ⁻¹ L_☉, with a median of 2.9 × 10¹³ μ⁻¹ L_☉, where μ is the magnification factor from gravitational lensing. This median infrared luminosity corresponds to a star formation rate of ∼5500 μ⁻¹ M_☉ yr⁻¹ (Kennicutt 1998), which represents some of the most extreme star formation episodes in the universe, unless the amplification from gravitational lensing is large. We note that, despite the flux selection, some of the supplementary lensed candidates are more infrared-luminous than some members of the principal sample because of the variation in T_D between the galaxies.

The comparison sample of HerMES sources with known redshifts has a median infrared luminosity of 6.9 × 10¹⁰ L_☉. However, these values are not directly comparable with the candidate lensed SMGs because 95% of the comparison sample is at z < 1. The trend to low redshift is not indicative of the redshift distribution of SPIRE-selected galaxy populations but is due to the inherent biases in archival surveys (see Casey et al. 2012 for a detailed discussion). If we only consider the 73 sources in the comparison sample with z > 1, the median infrared luminosity is 1.5 × 10¹² L_☉ (SFR ∼ 260 M_☉ yr⁻¹), which is still significantly lower than the candidate gravitationally lensed sources. As illustrated in Figure 4, this difference is a direct result of a combination of our source selection technique, which identifies candidates on the basis of bright 500 μm flux densities (Section 2), and the relatively flat K-correction for z ≳ 0.5 at 500 μm.

Existing literature discusses the details of the lensing calculations that are undertaken here (e.g., Perrotta et al. 2002; Negrello et al. 2007). Therefore, in this section we provide a summary of the calculations performed and refer to the appropriate papers for the details.

Briefly, the calculation consists of the following processes and assumptions:

• 1.  
  Foreground mass profile. Consider foreground masses with Navarro et al. (1997, NFW) or single isothermal sphere (SIS) profiles. The effect of the choice of mass profile is discussed in Section 4.2.
• 2.  
  Spatial distribution of foreground lenses. Determine the comoving number density of foreground lenses as a function of mass and redshift, using the Sheth & Tormen (1999) relation.
• 3.  
  Redshift distribution of SMGs. Use the model of Béthermin et al. (2011), with S₅₀₀ > 1 mJy, to trace the redshift distribution of the intrinsic (unlensed) population of SMGs (Figure 3; bottom panel).
• 4.  
  Strongly lensed area. Calculate the fraction of the sky (f_μ) that is strongly lensed (μ > μ_min, for μ_min = 2), using the profile and distribution of foreground masses and the redshift distribution of SMGs.
• 5.  
  Intrinsic population. Assume that the shape of the intrinsic (unlensed) number counts has the form of a Schechter (1976) function. Although other choices may be suitable, this function adequately describes the observed data with only three free parameters.
• 6.  
  Perform the magnification. Integrate and apply the lensing probability to the intrinsic flux distribution to determine the net effect of lensing. The limits of the integration are set to μ_min = 2 (for strong lensing) and μ_max = 50 (for feasible sizes of the submillimeter emission regions).
• 7.  
  Fitting. Use a Monte Carlo Markov chain (MCMC) minimization technique to fit the total HerMES counts with the four model components: unlensed SMGs, lensed SMGs, blazars, and local late-type galaxies.
• 8.  
  Predictions. Use the fitted model to predict properties of strongly lensed SMGs, including their number counts and mean magnification (see Section 4.2).

We begin by considering the properties of the foreground (lensing) structures. The effect of gravitational lensing on the submillimeter number counts can be quantified when specific assumptions about the foreground masses are made. Virialized dark matter halos have an NFW universal density (ρ) profile, which is a function of radius, r:

$$\begin{eqnarray} &&\rho (r)=\frac{\rho _{\rm s}}{(cr/r_{\rm vir})(1+cr/r_{\rm vir})^2}, \end{eqnarray} \tag{ 2 }$$

where r_vir is the virial radius and ρ_s is the characteristic density (Navarro et al. 1997). The halo concentration parameter, c, describes how centrally concentrated the mass is and can be obtained from a fit to simulations (e.g., Bullock et al. 2001):

$$\begin{eqnarray} &&c(M_{\rm vir},z)=\frac{9}{1+z}\left(\frac{M_{\rm vir}}{M_*}\right)^{-0.13}, \end{eqnarray} \tag{ 3 }$$

where M_* is the mass value such that σ(M_*) = δ_c and σ²(M) is the variance of the linear density field. M_vir is the virial mass of a dark matter halo, and δ_c is the critical density contrast for the spherical collapse model (Gunn & Gott 1972; Lacey & Cole 1993). Since δ_c has only a very mild redshift and cosmology dependence, here we take it to be fixed at the value for a matter-dominated universe, i.e., δ_c = 1.686.

While the NFW profile is the observed density profile of dark matter halos, gravitational lensing captures the total mass. Existing lensing analysis of individual galaxy- and group-scale lenses shows that the total density profile is more consistent with an SIS parameterization (e.g., Kochanek 1995; Koopmans et al. 2006, 2009; Gavazzi et al. 2007; Barnabè et al. 2010; Ruff et al. 2011; Bolton et al. 2012). Thus, as an alternative choice, we also consider the SIS density profile:

$$\begin{eqnarray} &&\rho (r)=\frac{\sigma ^2_v}{2\pi Gr^2}, \end{eqnarray} \tag{ 4 }$$

where σ²_v is the line-of-sight velocity dispersion, calculated following Perrotta et al. (2002). The SIS profile offers many advantages due to the simplicity of its form, and Perrotta et al. (2002) showed that the SIS and NFW profiles provide similar results for statistical magnifications. Indeed, as discussed in Section 4.2, we find that the uncertainties in the overall modeling are such that we cannot reliably distinguish the lensing by NFW halos and SIS spheres using the HerMES data presented here. However, detailed analysis of individual systems may be able to distinguish one profile over another on a case-by-case basis. Given the limited statistics, we do not account for sub-halo masses (e.g., Oguri et al. 2006), the effect of edge-on spirals as lenses (e.g., Blain et al. 1999a), or more complicated issues such as galaxy/dark matter halo ellipticity and external shear. Our predictions are in agreement with the current data, but in wider area surveys with more statistics it may become feasible to constrain these additional effects. We refer the reader to Oguri et al. (2006) for more detail of these effects in calculations of gravitational lensing rates.

The projected density field, Σ, around each mass profile is obtained by integrating over the parallel component, r_|| = χ, of the position vector $\bar{x}=(r_{\Vert },r_{\bot })$, where the perpendicular coordinate is r_⊥ = D_A(χ)θ, with D_A being the angular diameter distance, θ being the angular coordinate in the lens plane, and χ being the comoving radial distance. The convergence term, κ, associated with the isotropic light distortion from gravitational lensing can then be defined in terms of the critical density, Σ_crit (Lima et al. 2010a):

$$\begin{eqnarray} \kappa (\theta)&=&\frac{\Sigma (\theta)}{\Sigma _{\rm crit}}, \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} {\Sigma _{\rm crit}}&=&\frac{a}{4\pi G} \frac{D_{\rm A}(\chi _{\rm s})}{D_{\rm A}(\chi) D_{\rm A}(\chi _{\rm s} - \chi)}, \end{eqnarray} \tag{ 6 }$$

where a = (1 + z)⁻¹ is the cosmological scale factor and χ_s is the comoving radial distance to the source. The anisotropic distortion from lensing is measured by the shear, $\bm {\gamma }=\gamma _1+i\gamma _2$, where γ_i are the two components of the shear matrix. The magnitude of shear depends on the shape of the density profile of the foreground mass. For the NFW profile it is (Takada & Jain 2003)

$$\begin{eqnarray} &&\gamma _{\rm NFW}(\theta)= \frac{M_{\rm vir} f(c) c^2}{2\pi r_{\rm vir}^2}\frac{g(c\theta /\theta _{\rm vir})}{\Sigma _{\rm crit}} , \end{eqnarray} \tag{ 7 }$$

where g(x) is a function that can be calculated analytically (see Lima et al. 2010a for details) and f(c) = (ln (1 + c) − c/(1 + c))⁻¹.

For the SIS profile all the quantities can be derived analytically, and the resulting shear is

$$\begin{eqnarray} &&\gamma _{\rm SIS}(\theta)=4\pi \sigma _{v}^2\frac{D_{\rm A}(\chi _{\rm s} - \chi)}{D_{\rm A}(\chi _{\rm s})}\frac{1}{2\theta }. \end{eqnarray} \tag{ 8 }$$

Gravitational lensing causes a flux amplification due to an increase in the angular size of source galaxies. This effect is measured by the magnification factor, μ, which is given by the inverse determinant of the Jacobian matrix describing the transformation between source and image angular coordinates. In terms of the convergence and shear we have

$$\begin{eqnarray} &&\mu (\theta)=\frac{1}{\left[1-\kappa (\theta)\right]^2-|\gamma (\theta)|^2}. \end{eqnarray} \tag{ 9 }$$

A halo with mass, M, and at redshift, z_l, magnifies a source at redshift, z_s, in an elliptical region of the image plane with area, ΔΩ_μ(z_l, z_s, M, μ_min), within which the magnification is larger than μ_min:

$$\begin{eqnarray} &&\Delta \Omega _{\mu }(\mu _{\rm min}) = \int _{\mu (\theta)>\mu _{\rm min}} \frac{d\theta ^2}{\mu (\theta)}, \end{eqnarray} \tag{ 10 }$$

where we set μ_min = 2 for strong gravitational lensing.

For a known distribution of foreground masses, it is possible to define a fraction, f_μ, of the sky where μ > μ_min due to all the halos above a certain mass and in a redshift range. f_μ will therefore depend on the comoving number density of halos, defined as

$$\begin{equation} \frac{dn}{d\ln M_{\rm vir}}=\frac{\rho _m}{M_{\rm vir}}f(\nu)\frac{d\nu }{d\ln M_{\rm vir}}, \end{equation} \tag{ 11 }$$

where ν = δ_c/σ(M_vir) and σ²(M) is the variance in a top hat of radius, r. Here, we use the Sheth & Tormen (1999) relation:

$$\begin{eqnarray} &&\nu f(\nu) = A\sqrt{{2 \over \pi } a\nu ^2 } [1+(a\nu ^2)^{-p}] \exp [-a\nu ^2/2]. \end{eqnarray} \tag{ 12 }$$

We take the parameter values p = 0.3, a = 0.75, and A ≃ 0.3222 as normalization constants (Cooray & Sheth 2002). We have then

$$\begin{eqnarray} f_{\mu }&=&\int _{0}^{z_{\rm s}} dz_{\rm l} \frac{D_{\rm A}^2(z_{\rm l})}{H(z_{\rm l})} \int _{M_{\rm min}}^{M_{\rm max}} d\ln M_{\rm vir} \int _{0}^{\infty } dz_{\rm s}P(z_{\rm s})\nonumber\\ &&\times \Delta \Omega _{\mu }(z_{\rm l},z_{\rm s},M_{\rm vir},\mu _{\rm min}) \frac{dn(z_{\rm l},M_{\rm vir})}{d\ln M_{\rm vir}}, \end{eqnarray} \tag{ 13 }$$

where P(z_s) is the redshift distribution of the background SMGs, and we set M_min = 10¹² h⁻¹ M_☉ as the lower limit of the mass integral. The upper limit of the mass integral, M_max, is set to 10¹⁵ h⁻¹ M_☉, and therefore the effect of groups and clusters, including galaxies embedded in groups and clusters, is implicitly included in the calculations.

We use P(z_s) from the model of Béthermin et al. (2011) for S₅₀₀ > 1 mJy (Figure 3, bottom panel). This model, of the intrinsic HerMES SMG redshift distribution (Figure 3, bottom panel), contains faint galaxies that are mostly concentrated at z ∼ 1, with a decreasing tail thereafter. However, we note that the details of the choice of the redshift distribution of the background sources do not significantly affect our conclusions (see also Section 4.2). While the SMG population peaks at z ∼ 1–3, we note that the redshift distribution of lensed galaxies does not directly trace the background population since it is weighted by the optical depth to lensing, which is a function of redshift and increases in a nonlinear manner, so most of the SMGs that are lensed are expected to be at z ∼ 3, as is observed (Figure 3).

The lensing probability (the probability of having a magnification larger than μ) is given by (Lima et al. 2010a)

$$\begin{eqnarray} &&P({>}\mu)=1-e^{-f_{\mu }}, \end{eqnarray} \tag{ 14 }$$

from which we can calculate the probability distribution of magnification, P(μ) = −dP(> μ)/dμ, for HerMES sources.

Figure 5 presents the magnification probability distribution for foreground NFW and SIS profiles lensing a source at z = 2. This confirms that few SMGs are strongly gravitationally lensed, and those that are magnified by factors ≳ 10 are rare. As expected (see also discussion in Perrotta et al. 2002), higher magnifications are more frequent for the SIS compared to the NFW profiles. However, at lower magnifications, which are generally more likely, the SIS and NFW profiles have similar P(μ). We note that the NFW and SIS profiles do not encompass all possible galaxy mass profiles. For example, edge-on disks can significantly affect the magnification attained (Blain et al. 1999a). However, the current data are insufficient to statistically distinguish between even the simple NFW and SIS profiles (Section 4.2), and therefore further data are required to determine the distribution of mass profiles affecting strongly lensed SMGs.

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Lensing magnification increases the solid angle, Ω, and the integrated flux, S, of the lensed sources by a factor of μ. The number counts of SMGs have a steep slope at bright fluxes, so lensing magnification results in an increase in the number density of sources above a fixed flux limit. By definition, the observed and intrinsic (unlensed) quantities are related by

$$\begin{eqnarray} &&S_{\rm obs}=\mu S, \end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray} &&d\Omega _{{\rm obs}}=\mu d\Omega . \end{eqnarray} \tag{ 16 }$$

For a given magnification the intrinsic differential number density, dn/dS, is modified as (Refregier & Loeb 1997)

$$\begin{eqnarray} &&\frac{dn}{ds}\rightarrow \left. \frac{1}{\mu ^2}\frac{dn}{dS}\right|_{S=S_{\rm obs}/\mu }. \end{eqnarray} \tag{ 17 }$$

Following the formalism and the discussion of Lima et al. (2010a), the observed differential number counts for a population are then

$$\begin{eqnarray} \frac{d n_{\rm obs}(S_{\rm obs})}{d S_{\rm obs}} &=& \frac{1}{\langle \mu \rangle }\int d\mu \frac{P(\mu)}{\mu } \frac{dn}{dS}\left(\frac{S_{\rm obs}}{\mu }\right) , \end{eqnarray} \tag{ 18 }$$

where

$$\begin{eqnarray} &&\langle \mu \rangle = \int d\mu \ \mu P(\mu)\, \end{eqnarray} \tag{ 19 }$$

and the cumulative number counts are

$$\begin{eqnarray} n_{\rm obs}({>}S_{\rm obs}) &=& \frac{1}{\langle \mu \rangle }\int d\mu P(\mu) n\left({>}\frac{S_{\rm obs}}{\mu }\right) . \end{eqnarray} \tag{ 20 }$$

The limits of these integrals are set to μ_min = 2 and μ_max = 50, as previously discussed. The maximum magnification, μ_max, is determined by the size of the background source (Peacock 1982). Perrotta et al. (2002) calculated that μ_max =10–30 for 1–10 kpc sources at z = 1–4, and SMGs in lensing simulations by Serjeant (2012) are observed with μ ⩽ 33, although most have μ < 10. The star formation regions in SMGs are thought to be a few to 10 kpc in extent (e.g., Tacconi et al. 2006; Younger et al. 2008; Hailey-Dunsheath et al. 2010; Ferkinhoff et al. 2011), although some may be as small as ∼100 pc (Swinbank et al. 2010). Furthermore, the gas reservoirs in SMGs are often more extended than the star formation (Ivison et al. 2011; Riechers et al. 2011b). Therefore, the choice of appropriate maximum magnification factor is not straightforward, and μ_max = 50 is chosen as a conservative limit. We have also considered μ_max = 20 and μ_max = 30 and find that the choice of higher μ_max mainly affects the bright end of the predictions from the model, since high values of μ are required to lens SMGs to the brightest apparent fluxes. Thus, a lower value of μ_max would reduce the bright end of the mean magnification in Figure 8 (top panel) and reduce the numbers of extremely bright lensed sources (S₅₀₀ ≳ 300 mJy) such that observed sources with those flux densities are typically local late-type galaxies (top panel of Figure 10). As additional data are obtained, it is likely that μ_max will be constrained by observational results.

The intrinsic number counts of SMGs are most commonly parameterized as Schechter (1976) functions or broken power laws (e.g., Coppin et al. 2006; Weiß et al. 2009b; Lindner et al. 2011). These two forms diverge only at the faint and bright ends (see, e.g., Paciga et al. 2009) and cannot be distinguished with existing data. At the bright end the broken power law has a flatter slope than the Schechter function and allows for a higher number of intrinsically luminous sources. Consequently, models with the intrinsic number counts parameterized by a broken power law predict fewer strongly lensed sources than models that make use of the Schechter function parameterization. As current data do not allow it, we do not attempt to discriminate between these models, although we note that additional constraints may be possible as studies of the brightest submillimeter sources progress (e.g., Section 6). For simplicity, we make use of a three-parameter Schechter function, characterized by a flux density, S', beyond which the distribution is steeper and gravitational lensing is more effective at boosting the observed number of sources (Schechter 1976):

$$\begin{eqnarray} &&\frac{d n(S)}{d S}=\left(\frac{N}{S^{\prime }}\right)\left(\frac{S}{S^{\prime }}\right)^\alpha e^{-S/S^{\prime }} . \end{eqnarray} \tag{ 21 }$$

Here, α is the slope of the counts below the characteristic flux density, S', and N/S' is the normalization.

The model described above is fit to the HerMES 500 μm number counts (Figure 6). We run an MCMC code and calculate the χ² for different combinations of the Schechter distribution parameters, requiring the total 500 μm counts to fit the low flux data points (up to 45 mJy) from the P(D) analysis (Glenn et al. 2010). For bright sources, the number counts presented here are consistent with the analyses of HerMES SDP data by Oliver et al. (2010) and Glenn et al. (2010), which are also shown in Figure 6.

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To run the MCMC analysis, we used a modified version of the cosmoMC (Lewis & Bridle 2002) package, fixing the input cosmology to the WMAP-7 best fit from Komatsu et al. (2011). The convergence diagnostic is based on the Gelman and Rubin R statistic (Gelman & Rubin 1992). As described above, the minimum and maximum halo masses are fixed to 10¹² and 10¹⁵ h⁻¹ M_☉, respectively, and the minimum and maximum magnifications are set to μ = 2 and 50, respectively. Thus, N, S', and α, from the Schechter function description of the intrinsic 500 μm number counts, are the only free parameters in the model.

The model is constrained by the total number counts and the numbers of blazars and local spiral galaxies. We do not attempt to constrain the intrinsic flux densities or redshift distribution of HerMES galaxies with the lensing counts. We simply show that, down to the present accuracy, and with existing models, our predicted lensing counts are consistent with the sample of HerMES candidate lensed SMGs (Section 4.2 and Figure 6). In the future, when additional data are available and the nature of a higher fraction of candidates is confirmed, it may be possible to constrain the model further.

Unless explicitly stated, all the results presented in this paper are for NFW profiles, although in Figure 7 we also consider the effect of instead using the SIS profile.

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We next use the statistical model of galaxy–galaxy lensing, described in Section 4.1 and constrained by the observed HerMES 500 μm number counts, to make predictions about the prevalence and population of lensed HerMES SMGs.

In Figure 6 we show the model, the total observed number counts in HerMES blank fields, and the candidate strongly gravitationally lensed sources from Table 1. The contribution to the model from unlensed (intrinsic) SMGs, local late-type galaxies, and blazars is also shown in Figure 6. The model number counts for these three components are constrained by observational data, and the shaded regions represent the range of parameters that correspond to the 68% confidence limits. The blazars are modeled as a power law, and the local late-type galaxies as a power law with an exponential cutoff at 80 mJy, i.e., dN/dS∝S^αexp(− S₀/S), with S₀ = 80 mJy. The predicted distribution of strongly lensed SMGs is derived from an intrinsic Schechter function, using the model described in Section 4.1.

The model shown in Figure 6 corresponds to NFW mass profiles for the foreground lenses. If SIS profiles are used instead and the model parameters recalculated, we find that the prediction for the number counts of strongly lensed sources is comparable to the NFW result (Figure 7, dashed line). Hence, it appears that the choice between the two profiles is not important in fitting the current data. We investigate this conclusion further by using the SIS profile with parameters derived from the best-fit NFW model and show the resulting prediction for the counts of lensed sources in Figure 6. The ratio of the predictions from the NFW model and the SIS model with NFW parameters is shown in Figure 7.

There is minimal difference at the faintest flux densities: when the profiles are fit separately, we find that for S₅₀₀ ≲ 30 mJy the ratio N(> S₅₀₀)_SIS/N(> S₅₀₀)_NFW) is <1.2, and the difference between the models increases for S₅₀₀ ∼ 30 and 200 mJy, to a maximum of N(> S₅₀₀)_SIS/N(> S₅₀₀)_NFW ∼ 1.7 at S₅₀₀ ∼ 200 mJy. The increase in the ratio at bright fluxes is expected, because the difference between the two mass profiles is most pronounced at the high-magnification end (see Figure 5). The sharp cutoff in the number of sources that are intrinsically bright means that the sources with high apparent flux densities are typically subject to larger magnification factors (see Figure 8, top panel), which is where the difference in the probability of magnification between the NFW and SIS profiles is most pronounced.

There are two underlying reasons for this behavior between NFW and SIS models. NFW models underpredict the lensing cross section at the low-mass end where baryons dramatically steepen the total mass profile. SIS models overpredict the lensing cross section at the high-mass end as the velocity dispersion is based on the virial mass and not the sub-halo mass. As shown in Figure 6, current data are unable to distinguish between the two profiles. Therefore, we refer to the NFW profile for the remainder of this paper. With additional data from follow-up programs, we may eventually be able to distinguish between different foreground mass profiles, including additional profiles that are not considered here, and provide further constraints on the models. However, as discussed by Perrotta et al. (2002), the magnification distribution is dominated by foreground deflectors with a small range of masses; therefore, such effects are expected to be negligible.

In Figure 8 (top panel), we show the prediction of the mean magnification of strongly lensed sources, which increases as a function of apparent 500 μm flux density. For sources with S₅₀₀ = 100 mJy the model predicts that the mean magnification of the lensed sources is μ = 9.1 ± 2.5, where the range indicates the uncertainty in the model. For brighter sources with S₅₀₀ = 250 mJy, the calculated mean magnification is 16.9  ±  2.7. Fainter lensed SMGs, such as those in our supplementary sample (S₅₀₀ = 80–100 mJy), have lower magnifications, with μ ∼ 7 on average, although there may be individual examples with much higher amplifications. We note that the prediction of relatively low (μ ≲ 10) flux amplifications for the majority of sources is qualitatively consistent with results from the simulated lensing of individual SMGs (Serjeant 2012).

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Qualitatively, the trend of apparently brighter sources being more highly magnified is easy to understand, because intrinsically faint sources are more numerous than bright ones. Therefore, strongly lensed sources with observed flux densities S₅₀₀ ≲ 100 mJy may be the result of magnifying one of the numerous sources with intrinsic S₅₀₀ ∼ 30–50 mJy by a factor of a few. The dearth of unlensed sources with S₅₀₀ ∼ 100 mJy makes it less likely that the most apparently luminous sources will have low magnifications (see also Figure 9, top panel).

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We also consider the predicted intrinsic (i.e., before lensing amplification) 500 μm flux density distribution of strongly lensed sources that are selected with apparent flux densities above a fixed limit (S_cut). Figure 8 (bottom panel) shows that strongly lensed sources, with observed S₅₀₀ > 100 mJy (such as the candidates presented here), have a broad distribution of intrinsic 500 μm flux densities, peaking at S_intrinsic = 5 mJy, and 65% of sources have S_intrinsic < 30 mJy. The results are similar for an observed flux density cut of 80 mJy (such as our supplementary sample). The sharp turnover in the curves that occurs at S_intrinsic ≃ S_cut/2 is caused by the combination of our definition of strong lensing (μ > 2) and the steep decrease in the number counts at the bright end. The nominal HerMES detection limit is 30 mJy at 500 μm (90% completeness; L. Wang et al. 2012, in preparation), and thus ∼65% of the strongly lensed SMGs are sources that would otherwise not be detected. The amplification from gravitational lensing makes these sources ideal targets for the detailed study of high-redshift, star-forming galaxies, which would otherwise be prohibitively faint.

Within the framework of the model we can also calculate P(μ|S₅₀₀), the probability of a source with a given observed flux density being magnified by a factor, μ, as a function of S₅₀₀ (Figure 9). Indeed, P(μ|S₅₀₀) provides a measure of the predicted magnification distribution for sources with a given apparent 500 μm flux. Figure 9 (top panel) shows that for S₅₀₀ ⩽ 100 mJy, the probability of lensing decreases with increasing magnification and μ ≳ 10 is rare, having a probability of ∼10⁻³, among detected galaxies. However, at the brightest flux densities, S₅₀₀ ⩾ 150, the probability distribution is flatter, due to the rarity of intrinsically bright sources. Note that μ_max = 50 (Section 4.1), so for the purposes of calculating the predicted number counts we only consider the range μ = 2–50.

We also investigate the effect of the background (lensed) source redshift distribution on the probability of the source being magnified by μ. Figure 9 (bottom panel) shows P(μ|z) and demonstrates that for z = 2–4, the assumed redshift distribution has only a small effect on our analysis. Indeed, the prediction of the model and the results presented in this paper are insensitive to the exact form of the assumed redshift distribution of SPIRE sources. We note that if we use the redshift distribution from the Valiante et al. (2009) model instead for the Béthermin et al. (2011) model, the difference in the predicted number counts, mean magnification, and lensed fractions is within the 68% confidence limits of our results.

Figure 10 shows the predicted fraction of strongly lensed sources as a function of observed 500 μm flux density. The analysis is based on our statistical model only; in Section 4.3 we show that blending is only a minor effect.

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We first consider all the 500 μm sources and find that the strongly lensed fraction varies from <1% for S₅₀₀ < 14 mJy to a peak of 13% at S₅₀₀ = 105 mJy and then declines for the brightest fluxes (Figure 10, top panel). The decline for S₅₀₀ ≳ 100 mJy is the result of the contribution of local late-type galaxies—at these flux densities the 500 μm population is increasingly dominated by local spirals (Figure 6). Observationally, our data contain 49 local late-type galaxies, 13 lens candidates (nine confirmed; Section 6), and no blazars with S₅₀₀ > 100 mJy. Thus, 8%–23% of HerMES sources with S₅₀₀ > 100 mJy are gravitationally lensed, which is in agreement with the model.

If blazars and local spirals are excluded, then the fraction of strongly lensed sources increases from <1% for S₅₀₀ < 15 mJy to 100% for S₅₀₀ ≳ 200 mJy (Figure 10, bottom panel). A correction of <1% is required for blending (Section 4.3), so these values are applicable to HerMES lensed candidates. Smaller catalog flux limits have greater contamination from unlensed SMGs. For S₅₀₀ ⩾ 100 mJy 32%–74% of the sources are strongly lensed; for S₅₀₀ ⩾ 80 mJy (corresponding to our supplementary sources) the strongly lensed fraction is only 14%–40%. In Section 6, we show that nine of the 13 HerMES candidates are lenses, and the nature of the remaining four is unknown (Section 6). Similarly, Negrello et al. (2010) confirmed that all five H-ATLAS S₅₀₀ ⩾ 100 mJy candidates in their SDP data are gravitationally lensed. Thus, observationally, >78% of Herschel lensed galaxy candidates with S₅₀₀ ⩾ 100 mJy are bona fide lenses. These values are consistent with the predictions from our model, although the small number of sources dominates observational uncertainties.

Thus far, the model results presented for bright Herschel 500 μm sources only include individual sources and strongly lensed SMGs. It is possible that multiple faint sources could be blended in the SPIRE beam and mimic bright, gravitationally lensed SMGs. This is the same process that creates confusion noise in submillimeter data. When dealing with catalogs, it effectively shifts sources from lower to higher flux bins such that the total number of bright sources is higher than reality.

Sources that are separated by 18'' or greater are reliably deblended in the HerMES catalogs (L. Wang et al. 2012, in preparation) used here. Therefore, we consider sources that are located within 18'' of each other as blended. We use the intrinsic cumulative number counts (Figure 6) and begin by calculating the probability that two, three, or four sources of equal flux density (or greater) are located within 18'' of each other (Figure 11); in this way we are able to consider the blending rate as function of apparent (observed) flux density. We then remove the requirement for an equal flux density cutoff in the statistics and instead consider the probability that any two, three, or four sources with total flux density greater than 100 mJy are blended (Figure 12).

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The cumulative intrinsic 500 μm number counts from Figure 6 are used to calculate the Poissonian probability that randomly distributed sources of equal or greater flux density are located within 18'' of each other. The effect of the clustering of SMGs is included by using w(θ) as measured for HerMES sources with S₅₀₀ > 30 mJy; in this case w(18'') = 5.7 ± 2 (Cooray et al. 2010a). Clustering boosts the probability of blending because the sources in a clustered distribution are more likely to reside close to other sources. Indeed, Figure 11 shows that, among sources with observed S₅₀₀ > 20 mJy, blending is ∼30 times more prevalent in the clustered population.

Figure 11 shows that the probability of two 50 mJy or brighter sources being blended into a single 100 mJy or brighter source is 9.7 × 10⁻⁶. For three or four blended sources the probabilities are 2 × 10⁻⁶ and 6 × 10⁻⁷, respectively. At the S₅₀₀ ⩾ 80 mJy corresponding to our supplementary sample of lens candidates (see the Appendix), the probability is an order of magnitude higher at the level of 7 × 10⁻⁵. However, even in this case one in ∼14,000 of these candidates is expected to be blended, while for the brighter flux density cut of our primary sample, one in ∼100,000 is expected to be blended.

We also consider the possibility that galaxies of unequal flux densities are blended in the HerMES catalogs. Figure 12 shows the probability that two, three, or four sources with total S₅₀₀ ⩾ 100 mJy are blended, as a function of the flux density of the brightest component. It is apparent from Figure 12 that the blending of intrinsically bright sources (S₅₀₀ ≳ 95 mJy) with intrinsically faint sources is unlikely; this is due to the intrinsic rarity of such luminous sources. The probability of a >100 mJy source being a blend of any two fainter galaxies is always <5 × 10⁻⁵.

These results are expected since our selection limit of S₅₀₀ ⩾ 100 mJy is ∼15 × the Herschel point-source confusion noise. We note that blending contamination at a level of ≳ 1% contamination requires clustering of w(18'') ≳ 180—∼30 × higher than that extrapolated from larger scale observations. Therefore, our results are robust to the uncertainty in the SMG clustering. We conclude that the blending of sources is rare among sources selected with S₅₀₀ > 100 mJy, and none of the lens candidates presented in this paper are likely to be blends of unlensed sources.

High spatial resolution submillimeter interferometry, primarily at 880 μm, is from the Submillimeter Array (SMA). These data include multiple array configurations, from sub-compact to very extended, and the synthesized beam size ranges from ∼03 to 3'' (FWHM). The data shown here were initially taken as part of a Director's Discretionary Time follow-up program of HerMES lensed sources (PI: A. Cooray) and later as part of a large multi-semester program of lensed Herschel sources (PI: R. S. Bussmann).

SMA observing conditions were typically very good, with low atmospheric opacity (τ_225 GHz < 0.08) and good phase stability. Targets were typically observed for 1–3 hr (on-source), depending on weather conditions and the brightness of the target. We used track sharing to observe multiple targets in a given night and maximize uv coverage. All observations used an intermediate frequency coverage of 4–8 GHz and provide a total of 8 GHz bandwidth (considering both sidebands). For time-variable gain (amplitude and phase) calibration, we used the nearest quasar with S₈₈₀ > 0.5 Jy (in some cases we used the average solution provided by the two nearest quasars). We typically used either the blazar 3C 279 or 3C 84 as the primary bandpass calibrator, while a planetary moon (often Titan) was used as the absolute flux calibrator. The Multichannel Image Reconstruction, Image Analysis, and Display software (Sault et al. 1995) invert and clean tasks were used to invert the uv visibilities and deconvolve the dirty map, respectively. Natural weighting was typically chosen to obtain maximum sensitivity. Photometry is measured from SMA data using the casa ⁴⁴ task, imfit.

Two of the lensed SMG candidates were observed with the Jansky Very Large Array (JVLA; Perley et al. 2011) to obtain high-resolution radio interferometry at 1.4 and 7 GHz (Section 6). The data were taken as part of a larger follow-up program of lensed Herschel SMGs (program 11A-182; PI: R. Ivison) and were reduced using aips following the procedures described in Ivison et al. (2011), to achieve a resolution of <025 (FWHM) in both cases.

We have also obtained high-resolution near-IR imaging with the Near Infrared Camera-2 (NIRC2) and laser guide star adaptive-optics (LGSAO) system on Keck-II (Wizinowich et al. 2006), or with the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST). The latter observations are aimed at the subset of lensed candidates for which AO observations are not feasible due to the lack of nearby bright stars for tip-tilt corrections.

The Keck-II/NIRC2 LGSAO imaging (programs C213N2L, PI: H. Fu; and U034N2L, PI: A. Cooray) uses the K_s-band filter (2.2 μm) and integration times of 40 and 60 minutes per target. The resulting 5σ point-source detection limit is ∼25.6 mag for a 01 radius aperture. The estimated Strehl ratios with the LGSAO system are 15%–25% at the target positions. The images reach ∼01 spatial resolution in the best cases (Figure 13). These Keck-II/NIRC2 data are reduced following the standard procedures using a customized Interactive Data Language (idl) pipeline (see Fu et al. 2012). The image astrometry is determined relative to SDSS and Spitzer images, and the flux scale is calibrated with bright stars and galaxies detected in the Two Micron All Sky Survey.

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The candidate lensed SMGs were observed as part of an HST/WFC3 cycle 19 snapshot program (PI: M. Negrello). Data were taken with the F110W filter (1.1 μm), and on-source integration times were at least 4 minutes per target. Longer integrations of 8 minutes were used for sources with red SPIRE colors (S₅₀₀ > S₃₅₀), which indicate that they may be the highest redshift galaxies. The data were reduced with MultiDrizzle,⁴⁵ to produce images with 006 pixel⁻¹ and spatial resolution of ∼014. The typical 5σ point-source detection limit is ∼23.5 mag.

When listing the coordinates of the foreground lensing galaxy in Table 3, we make use of either HST/WFC3 or Keck-II/NIRC2 imaging. The locations of the background lensed SMG image components are from the SMA or JVLA data. The exact data used for the study of each lensed SMG candidate are discussed in Section 6.

Table 3. Confirmed HerMES Gravitationally Lensed Galaxies

Source	R.A.SMGa	Decl.SMGa	R.A.lensb	Decl.lensb	zCOc	zoptd	μe	μLIRf	TDg
	(J2000)	(J2000)	(J2000)	(J2000)				(1013 L☉)	(K)
HBoötes01	$14^{\rm h}33^{\rm m}30\mbox{$.\!\!^{\mathrm{s}}$}83$	+34°54'399	$14^{\rm h}33^{\rm m}30\mbox{$.\!\!^{\mathrm{s}}$}84$	+34°54'400	3.274	0.59 ± 0.08	≲ 5 (O)	5.6 ± 0.5	41 ± 1
HBoötes02	$14^{\rm h}28^{\rm m}25\mbox{$.\!\!^{\mathrm{s}}$}54$	+34°55'469	$14^{\rm h}28^{\rm m}25\mbox{$.\!\!^{\mathrm{s}}$}47$	+34°55'468	2.804	0.414	∼23 (R)	3.8+0.4 − 0.3	34 ± 1
	$14^{\rm h}28^{\rm m}25\mbox{$.\!\!^{\mathrm{s}}$}54$	+34°55'472	...	...	...	...	...	...	...
	$14^{\rm h}28^{\rm m}25\mbox{$.\!\!^{\mathrm{s}}$}45$	+34°55'479	...	...	...	...	...	...	...
	$14^{\rm h}28^{\rm m}25\mbox{$.\!\!^{\mathrm{s}}$}43$	+34°55'465	...	...	...	...	...	...	...
HBoötes03h	$14^{\rm h}28^{\rm m}24\mbox{$.\!\!^{\mathrm{s}}$}06$	+35°26'198	$14^{\rm h}28^{\rm m}24\mbox{$.\!\!^{\mathrm{s}}$}08$	+35°26'195	1.325	1.034	≲ 10 (O)	1.9+0.3 − 0.2	37 ± 1
HECDFS02	$03^{\rm h}37^{\rm m}32\mbox{$.\!\!^{\mathrm{s}}$}53$	−29°53'518	$03^{\rm h}37^{\rm m}32\mbox{$.\!\!^{\mathrm{s}}$}40$	−29°53'536	?	?	3.8 ± 0.02 (O)	2.6 ± 0.6	35 ± 2
	$03^{\rm h}37^{\rm m}32\mbox{$.\!\!^{\mathrm{s}}$}42$	−29°53'511	...	...	...	...	...	...	...
HLock01	$10^{\rm h}57^{\rm m}50\mbox{$.\!\!^{\mathrm{s}}$}46$	+57°30'285	$10^{\rm h}57^{\rm m}50\mbox{$.\!\!^{\mathrm{s}}$}96$	+57°30'257	2.958	0.60 ± 0.04	10.9 ± 0.7 (O)	12.6 ± 0.5	51 ± 1
	$10^{\rm h}57^{\rm m}51\mbox{$.\!\!^{\mathrm{s}}$}54$	+57°30'268	...	...	...	...	...	...	...
	$10^{\rm h}57^{\rm m}51\mbox{$.\!\!^{\mathrm{s}}$}19$	+57°30'291	...	...	...	...	...	...	...
	$10^{\rm h}57^{\rm m}50\mbox{$.\!\!^{\mathrm{s}}$}91$	+57°30'238	...	...	...	...	...	...	...
HLock03	$10^{\rm h}57^{\rm m}12\mbox{$.\!\!^{\mathrm{s}}$}26$	+56°54'587	$10^{\rm h}57^{\rm m}12\mbox{$.\!\!^{\mathrm{s}}$}22$	+56°54'586	2.771i	?	3.0+1.3 − 1.4 (O)	2.8 ± 0.2	34 ± 1
HLock04	$10^{\rm h}38^{\rm m}26\mbox{$.\!\!^{\mathrm{s}}$}60$	+58°15'426	$10^{\rm h}38^{\rm m}26\mbox{$.\!\!^{\mathrm{s}}$}76$	+58°15'423	?	0.58 ± 0.04	6.2 ± 0.1 (O)	5.2 ± 0.6	47 ± 1
							5.3+1.3 − 1.1 (D)
	$10^{\rm h}38^{\rm m}27\mbox{$.\!\!^{\mathrm{s}}$}19$	+58°15'413	...	...	...	...	...	...	...
HXMM01	$02^{\rm h}20^{\rm m}16\mbox{$.\!\!^{\mathrm{s}}$}65$	−06°01'419	$02^{\rm h}20^{\rm m}16\mbox{$.\!\!^{\mathrm{s}}$}73$	−06°01'427	2.307	0.654/0.502j	∼2.1j (O)	3.2 ± 0.3	43 ± 1
	$02^{\rm h}20^{\rm m}16\mbox{$.\!\!^{\mathrm{s}}$}58$	−06°01'443	$02^{\rm h}20^{\rm m}16\mbox{$.\!\!^{\mathrm{s}}$}40$	−06°01'423	...	...	∼1.6j (O)	...	...
HXMM02	$02^{\rm h}18^{\rm m}30\mbox{$.\!\!^{\mathrm{s}}$}67$	−05°31'315	$02^{\rm h}18^{\rm m}30\mbox{$.\!\!^{\mathrm{s}}$}69$	−05°31'319	3.395	1.35	1.5+1.0 − 0.4 (O)	3.6+0.3 − 0.2	33 ± 1

Notes. ^aSMG coordinates are the centroids of high-resolution submillimeter or radio interferometry, or optical arcs (as discussed in the text). Multiple coordinates are listed where there are multiple images. ^bCoordinates of the foreground lenses are measured from optical imaging. Multiple coordinates are listed for XMM01, where there are two deflectors. ^cz_CO is the redshift of the SMG, as traced by CO emission lines (D. Riechers et al. 2012, in preparation). ^dz_opt is the redshift of the lens, as traced by optical spectroscopic or photometric redshifts. ^eμ is the magnification factor from gravitational lensing. We denote the high-resolution image used to determine lensing magnification with R for radio (JVLA 7 GHz), O for rest-frame optical (Keck-II or HST image), or D for dust emission with SMA 880 μm. ^fμL_IR is the apparent rest-frame 8–1000 μm infrared luminosity of the SMG. ^gT_D is the dust temperature of the SMG, obtained by fitting an optically thin modified blackbody, with β = 1.5 to all the available 250–3000 μm photometry (Table 5). ^hHBoötes03 was identified as lensed by Borys et al. (2006) and has been the subject of numerous additional studies (see Section 6.3). ⁱThe CO redshifts of these sources are single-line redshifts guided by the submillimeter photometric redshift. ^jThe two z_opt values are for the two foreground galaxies. Furthermore, magnification factors for HXMM01 are given separately for the two lensed components as the source plane is made up of two merging SMGs (see Section 6.11).

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Spectroscopic redshifts of the SMGs were measured using data from multiple facilities, with the aim of observing several CO rotational transitions (e.g., Weiß et al. 2009a; Lupu et al. 2012; Scott et al. 2011; Riechers et al. 2011a) as the detection of at least two emission lines is required for a secure redshift determination. The data are primarily from a large program on the Combined Array for Research in Millimeter-wave Astronomy (CARMA; PI: D. Riechers), which is supplemented with observations from the Institut de Radioastronomie Millimtrique (IRAM) Plateau de Bure Interferometer (PdBI; PIs: A. Omont and D. Reichers) and the Zpectrometer spectrometer (Harris et al. 2007) on the 100 m diameter GBT (PI: A. Harris).

CO redshifts and 3 mm continuum photometry are adopted from D. Riechers et al. (2012, in preparation) and were obtained through "blind" detection of CO emission lines observed in wide-band frequency scans of the 3 mm atmospheric window with CARMA. Observations were predominantly taken in the compact D-array configuration, where the CARMA beam is 5'' FWHM. Therefore, the CARMA data are primarily used for spectral line identification and continuum photometry. Further observations were obtained at 1 cm and 2 mm with the GBT/Zpectrometer and the IRAM PdBI, which typically target additional CO transitions to confirm the CARMA redshifts.

In Table 4, we provide the CO redshifts and highlight SMGs with only a single millimeter emission line detection. This results in a degeneracy between the identification of the line transition and the redshift. In such cases we make use of photometric redshifts derived from submillimeter photometry (as described in Section 3.2) to determine the most likely line identification, assuming that it is a CO transition. This is a reasonable assumption because CO lines are the most luminous at the observed frequencies. Additional observations are required to confirm the redshifts of these sources.

Redshifts of the foreground lensing galaxies (Table 3 and Section 6) are primarily from the public SDSS database; spectroscopic measurements are used where available and photometric redshifts otherwise. In cases where SDSS data are unavailable, the foreground detector is undetected, or the photometry is blended, we have obtained redshifts from optical spectroscopy with the Low Resolution Imaging Spectrometer (LRIS) on Keck-I (PI: C. Bridge) and the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) on the Gran Telescopio Canarias (GTC; PI: I. Pérez-Fournon).

Spitzer/MIPS 24, 70, and 160 μm flux densities of the candidate lensed SMGs are retrieved from archival data, including the Spitzer Wide-Area Infrared Extragalactic Survey (SWIRE; Lonsdale et al. 2003) and the Spitzer Deep, Wide-Field Survey (SDWFS; Ashby et al. 2009). These are listed in Table 5, in addition to 870 μm photometry from SMA interferometry (described in Section 5.1) and millimeter continuum data from spectroscopic surveys (Section 5.2). The 2 and 2.3 mm flux densities are extracted from our PdBI data, and CARMA provides the 3 mm data. Previous studies (Conley et al. 2011; Ikarashi et al. 2011) published Caltech Submillimeter Observatory/Z-Spec 1 mm continuum flux densities for two sources (HXMM02 and HLock01), so these are also included in Table 5.

We also present 1.2 mm flux densities from the Max-Planck Millimetre Bolometer (MAMBO) instrument on the IRAM 30 m telescope (collaboration led by A. Omont and I. Pérez-Fournon). The observations are reduced and analyzed using the method described in Omont et al. (2003). The MAMBO beam is 106 (FWHM) at 1.2 mm; therefore, these data cannot be used for resolved studies, since fully sampled maps were not obtained.

HBoötes01 is the second brightest 500 μm source in our sample, with S₅₀₀ = 160 ± 33 mJy. It is a confirmed gravitationally lensed SMG and has a far-IR SED similar to M82, with T_D ∼ 40 K for fixed β = 1.5 and μL_IR ∼ 6 × 10¹³ L_☉ (Figure 14; Table 3). SMA observations in the extended and compact array configurations detect a single bright source, with S₈₇₀ = 61 ± 3 mJy. HBoötes01 has a 1.4 GHz flux density of 0.26 ± 0.04 mJy (de Vries et al. 2002), which is consistent with that expected from star formation, as calculated from the far-IR/radio correlation with the method described in Section 2.

Figure 13 shows SMA contours on HST/WFC3 F110W imaging and SDWFS 4.5 μm images. The submillimeter emission is slightly offset from a source in the HST data and coincident with an IRAC source. The HST source is also detected in the NOAO Deep Wide-Field Survey (NDWFS) (Jannuzi & Dey 1999) and SDSS. It is red in the optical and has r = 21.71 mag and z_phot = 0.59 ± 0.08 in SDSS. CO(J = 3→2) and CO(J = 4→3) are detected in our CARMA data, placing the submillimeter source at z = 3.274. Therefore, it is clear that the optical and near-IR emission and the submillimeter emission are dominated by two distinct sources at different redshifts. Despite the existence of two sources at different redshifts and the offset between the near-IR and far-IR emission, there are no arcs or other morphological indications of gravitational lensing in the SMA data. Therefore, the amplification from lensing is expected to be small: μ ≲ 5.

The configuration of HBoötes01 is similar to HXMM02 (Section 6.12; Ikarashi et al. 2011) and HLSJ091828.6+514223 (Combes et al. 2012). All three galaxies are gravitationally lensed, as determined from redshift information, and have small (≲ 1'') offsets between the submillimeter and optical sources. However, despite high-resolution submillimeter interferometry, there are no morphological indications of lensing, and we are unable to determine the precise lensing magnification.

In the HerMES SPIRE data, HBoötes02 is photometrically similar to HBoötes01, with S₅₀₀ = 157 ± 33 mJy and an SED that peaks in the 350 μm band. A single emission line is detected in CARMA observations, which is confirmed to be CO(J = 3→2) at z = 2.804 with the detection of CO(J = 1→0) by the GBT. SED fitting of the far-IR data shows that HBoötes02 has T_D = 34 ± 1 K and μL_IR = 3.8^+0.4 _{− 0.3} × 10¹² L_☉, for fixed β = 1.5 (Table 3 and Figure 14).

Optical data reveal that HBoötes02 is gravitationally lensed by the central region of an edge-on disk galaxy at z = 0.414 (Figure 13), which, due to the presence of a dust lane and its inclination angle, most likely has a higher mass density than would be estimated from its optical magnitude. The redshift of the deflector is determined from multiple emission and absorption lines observed in long-slit spectroscopy with OSIRIS on the GTC. We have also obtained a JVLA 7 GHz map of HBoötes02, which reveals four images of the background source, which are created due to gravitational lensing distortion. The images are not resolved in the 025 JVLA beam, and the total flux density is 2.3 ± 0.2 mJy at 7 GHz.

Lens modeling of the radio data indicates that the system has an Einstein radius of 080 ± 004 and is magnified by μ_JVLA ∼ 23 at 7 GHz. Thus, HBoötes02 is the most highly magnified source in our sample. The large magnification is due to the small size of the radio emission region, which is ⩽0008 (⩽65 pc at z = 2.8) in the source plane. Since the brightness temperature is much greater than 10⁴ K, these data show that an AGN is powering the radio emission.

HBoötes02 is also detected with a flux density of 12.36 ± 0.50 mJy at 1.4 GHz (de Vries et al. 2002), although its components are unresolved in those data. The observed radio spectral index between 1.4 and 7 GHz is α = −1.04. For α = −1.04 the expected flux density from star formation is only ∼0.07 mJy and ∼0.01 mJy at 1.4 and 7 GHz, respectively (based on the far-IR/radio correlation; Section 2). Therefore, the bright radio flux densities in HBoötes02 confirm that an AGN dominates the emission at these wavelengths.

HBoötes02 has also been observed with the SMA at 870 μm in extended and compact array configurations, resulting in a map with a beam of ∼07, in which a partial ring structure is resolved. Accounting for the larger SMA beam, the submillimeter emission appears to be more extended than the radio emission, and the flux ratios between the components differ between the two data sets. This suggests that differential lensing is important in HBoötes02 and that the submillimeter data trace the star formation and the radio data trace the AGN. Indeed, lens modeling of the SMA data determines that the submillimeter emission from HBoötes02 has μ_SMA = 10.1 ± 1.6 and a half-light radius of 015 ± 003 (1.2 ± 0.2 kpc at z = 2.8). Note that the submillimeter magnification (derived from the SMA data) is significantly lower than that at radio wavelengths (from the JVLA data), which is indicative of differential lensing resulting from two different emission regions.

HBoötes02 is also point-like in Keck K-band data, which indicates that the AGN may also be dominating the near-IR emission from HBoötes02. However, lens modeling is not performed on those data because the foreground deflector contains a complex dust lane. A more reliable analysis is available from the JVLA and SMA data, which are not complicated by the dust lane in the foreground galaxy. We note that the best-fit lens models based on the radio and SMA data require deflectors with a single isothermal ellipsoid profile and high ellipticity, as indicated by the near-IR imaging. A detailed analysis of the multi-wavelength observations of HBoötes02 will be presented in J. L. Wardlow et al. (2012, in preparation).

We note that there are two additional sources detected in the JVLA data, approximately 3'' and 5'' west and east of the center of the lensing galaxy, respectively. Both of these sources are resolved, although they are not detected in optical or near-IR imaging, so their nature is unclear. It is possible that they are relic jets from HBoötes02.

HBoötes03, also known as MIPS J142824.0+352619, is a gravitationally lensed source that was discovered in Spitzer MIPS imaging of the Boötes field (Borys et al. 2006). It has been subject to extensive analysis and follow-up observations, including broadband submillimeter photometry from SHARC-II (350 μm), SCUBA (850 μm; Borys et al. 2006), and SMA (890 μm) with 25 resolution (Iono et al. 2006a). Optical, near-IR, and mid-IR spectroscopy revealed the presence of a background infrared source at z = 1.325 and a foreground optical galaxy at z = 1.034 (Desai et al. 2006; Borys et al. 2006). These data confirmed the nature of HBoötes03 as a gravitationally lensed starburst galaxy, and the existing data are consistent with our new HerMES SPIRE photometry (see Figure 14). We have fit the new SPIRE and existing submillimeter photometry with an optically thin modified blackbody with fixed β = 1.5 to yield T_D = 41 ± 1 K and μL_IR = (5.6 ± 0.5) × 10¹³ L_☉.

Spitzer IRS spectroscopy shows that the mid-IR emission is dominated by star formation, with no evidence for an AGN (Desai et al. 2006). There are no morphological indicators of lensing in the submillimeter or radio data, and Borys et al. (2006) used size arguments and positional offsets between the radio/submillimeter and optical sources to estimate that the lensing magnification μ ≲ 10. We have since obtained HST/WFC3 F110W imaging of HBoötes03, in which a second, faint, near-IR source is present (Figure 13). This second source is ∼04 to the north of the z = 1.325 galaxy, and its position is consistent with it being the background SMG. The small separation between these sources, the point-like nature of the second source, and the absence of counter-images further support the hypothesis that HBoötes03 is only magnified by a small factor. near-IR integral field spectroscopy of the Hα emission does not contain AGN signatures and shows that the emission is spatially extended, although similar effects are not observed in H- or K-band continuum data (Swinbank et al. 2006). On the basis of the IFU data, Swinbank et al. (2006) argue that it is possible that HBoötes03 has μ ≫ 10 for rest-frame optical emission, although the requisite precise alignment of the system makes this unlikely.

Numerous far-IR and submillimeter emission lines have been detected in HBoötes03, including CO(J = 2→1) and CO(J = 3→2) (Iono et al. 2006b). The CO(J = 2→1) emission is not spatially extended in the 13 beam, which Iono et al. (2006b) use to argue that μ ≲ 8 for the gas-emitting region. Recently, the [C ii] 158 μm fine-structure transition was detected (Hailey-Dunsheath et al. 2010; Stacey et al. 2010), and [O i] 63 μm and [O iii] 52 μm were observed with Herschel PACS (Sturm et al. 2010). The emission-line ratios in HBoötes03 are similar to those observed in the nuclei of local starburst galaxies, indicating that HBoötes03 may be a high-redshift, high-luminosity analog of those galaxies (Hailey-Dunsheath et al. 2010; Sturm et al. 2010).

HECDFS01 is near the edge of the HerMES area, which means that it is located outside of the main ECDFS field in a region without deep data. It has not yet been observed by any of our follow-up programs, and as such the only available data are from HerMES and shallow, all-sky surveys. Therefore, we are unable to confirm whether HECDFS01 is indeed a gravitationally lensed SMG. The SPIRE colors are flat, giving a submillimeter photometric redshift of z ∼ 2.50, although this is not well constrained. We note that the galaxy 2dFGRS S401Z151 at z = 0.222 is only 32'' from the SPIRE centroid, although we cannot confirm whether it is related to the submillimeter emission.

HECDFS02, like HECDFS01, is in a region without deep archival data. However, follow-up imaging with HST/WFC3 in the F110W filter reveals gravitational arcs around a bright galaxy (Figure 13). The SPIRE fluxes of HECDFS02 peak in the 350 μm band, which indicates that it is at z ∼ 2.65. Due to the position of HECDFS02 outside of the main ECDFS area, there is inefficient data to determine a photometric redshift for the foreground lens. However, we have used the Kormendy (1977) relation for the J band (de Vries et al. 2000) to estimate that the lensing galaxy is at z ∼ 0.1. The Einstein radius is 1678 ± 0003, and modeling of the HST data shows two emitters in the source plane, which may be two star-forming regions in a single SMG or may be a merger or interaction of two galaxies. The amplification from lensing is μ_F110W = 3.79 ± 0.02 at 1.1 μm. However, differential lensing may be important, so this value may not apply to the submillimeter data.

HECDFS03 is also outside the deep survey fields, and the only follow-up data available are F110W HST/WFC3 imaging from our snapshot program. There are no arcs or other lensing features in the HST data, and although the structure of the detected sources appears to resemble a group or small cluster, we cannot verify whether HECDFS03 is gravitationally lensed. The SPIRE colors of HECDFS03 indicate that the submillimeter emission originates at z ∼ 3.20.

HLock01 is the brightest gravitationally lensed HerMES source, with 250, 350, and 500 μm flux densities of 403 ± 7, 377 ± 10, and 249 ± 7 mJy, respectively (Table 4). Due to its extreme brightness, HLock01 was subject to a significant follow-up effort, and it was the first confirmed HerMES lensed SMG (Conley et al. 2011). 880 μm SMA interferometry resolved the SPIRE source into four components (Conley et al. 2011), which were further resolved in Keck-II/NIRC2 K-band imaging. The redshift of HLock01 was established from CO emission lines as z = 2.958 (Scott et al. 2011; Riechers et al. 2011a), and Gavazzi et al. (2011) used the NIRC2 K-band data to show that the rest-frame optical emission is magnified by a factor of μ = 10.9 ± 0.7 by a small group at z ∼ 0.6. The central group galaxy has a photometric redshift of 0.60 ± 0.04 (Oyaizu et al. 2008); photometric or spectroscopic redshifts are unavailable for the remaining group members due to their faintness. Instead, the group nature of the deflector is confirmed by the Einstein radius, R_Ein = 410 ± 002, corresponding to a velocity dispersion σ_v = 483 ± 16 km s⁻¹ (Gavazzi et al. 2011).

Thorough SED fitting of HLock01 was performed by Conley et al. (2011), who find that it contains optically thick warm dust, with T_D = 88 ± 3 K for β = 1.95 ± 0.14 (note that for consistency with the rest of our sample Table 3 gives T_D for an optically thin modified blackbody with β = 1.5). Scott et al. (2011) analyzed the CO spectral line energy distribution of HLock01, including observations of the J = 1→0, 3→2, 5→4, 7→6, 8→7, 9→8, and 10→9 transitions. They found that a single warm, moderate-density gas model adequately describes the data, although a second denser component may also be present. Finally, Riechers et al. (2011a) examined the dynamics of the gas in HLock01, by studying the resolved CO lines. They showed that the CO(J = 5→4) emission exhibits resolved velocity structure, consistent with HLock01 being a gas-rich merger at z ∼ 3.

Since the publications of Conley et al. (2011), Gavazzi et al. (2011), Scott et al. (2011), and Riechers et al. (2011a), we have obtained HST WFC3 F110W and JVLA 1.4 GHz observations of HLock01, which are shown in Figure 13. The radio data have ∼11 resolution and isolate the four lensed images of HLock01 with higher accuracy than the existing SMA data (Conley et al. 2011), and they show that the central lensing galaxy is also radio-bright. The total flux density in the four radio images of HLock01 is 0.97 ± 0.05 mJy, which is ∼4 times higher than expected from the far-IR/radio correlation, if q_IR = 2.40 (Ivison et al. 2010a; see Section 2 for details). Indeed, HLock01 requires q_IR = 1.8 ± 0.4 if both the far-IR emission and the radio emission are powered by star formation. The luminous radio emission from HLock01, coupled with its warm dust temperature (T_D = 88.0 ± 2.9 K; Conley et al. 2011), suggests that HLock01 harbors both AGNs and star formation activity.

The JVLA data also reveal a radio source ∼75'' north of HLock01, which is composed of two bent lobes, indicative of an FR II source. Since bent FR II sources are most likely to be located in galaxy groups and clusters (e.g., Stocke 1979), this observation adds weight to the analysis of Gavazzi et al. (2011) that the foreground lens is a small group or cluster of galaxies.

We have obtained HST/WFC3 F110W imaging of HLock02. No lensing features are apparent in the data, and we do not have submillimeter or radio interferometry to precisely pinpoint the source of the submillimeter emission. HLock02 has red SPIRE colors, indicative of a source at z ∼ 4 (Figure 14), so the absence of lensing features in the WFC3 image may be because the SMG is below the detection threshold of these data. Therefore, we cannot determine whether or not HLock02 is gravitationally lensed.

HLock03 has S₅₀₀ = 114 ± 8 mJy with submillimeter emission peaking in the SPIRE 350 μm band. Continuum emission is detected with the SMA at 890 μm, MAMBO at 1.2 mm, and CARMA at 3mm (Figure 14). A single emission line is detected in CARMA spectroscopy, which, on the basis of the submillimeter colors, we attribute to CO(J = 3→2) at z = 2.771. If the emission is instead CO(J = 2→1), then HLock03 would be at z = 1.514, although the continuum SED makes this solution unlikely.

SMA interferometry from the compact and very extended array configurations has a combined beam of 118 × 097 and identifies HLock03 as a single submillimeter source (Figure 13). The submillimeter emission is coincident with an IRAC source, but offset by ∼05 from the galaxy that is detected in both the Keck-II/NIRC2 K_s band and HST/WFC3 F110W imaging (Table 3). The K_s-band source is faint, and therefore its redshift is unknown.

The most likely interpretation of these data is that the submillimeter and IRAC data are tracing a background source at z = 2.771 that is gravitationally lensed by the K_s-band galaxy. In this case, the absence of prominent detected lensing features means that the magnification of the SMG is likely to be small, and indeed lens modeling of the K_s-band image determines that μ = 3.0^+1.3 _{− 1.4} for rest-frame optical emission. Therefore, HLock03 is intrinsically luminous, with L_IR ∼ 10¹³ L_☉ and SFR ∼ 1700 M_☉ yr⁻¹ (Kennicutt 1998).

Gravitational lensing is confirmed in HLock04, and we have obtained extensive follow-up observations, including Keck-II/NIRC2 K_s-band and HST/WFC3 F110W imaging, SMA interferometry, and GBT and CARMA spectroscopy. Gravitationally lensed arcs are evident in the Keck-II, HST, and SMA data with an Einstein radius of 246 (Figure 13). The foreground lensing galaxy is detected in SDSS and has a photometric redshift of z = 0.60 ± 0.02 from that survey. Line emission from the lensed SMG was not detected in broadband submillimeter spectroscopy, so the redshift of the SMG is unknown, although the far-IR photometry indicates z ∼ 2.

HLock04 is unique in our sample, in that the lensing morphology is detected with high significance in both the near- and far-IR wavelength regimes, enabling separate lens modeling of both the stellar and dust emission. Serjeant (2012) showed that differential lensing can be significant for lensed SMGs, due to the irregular distribution of stars, AGNs, gas, and dust in the source plane. Indeed, differential magnification has been identified in two lensed Herschel SMGs (Gavazzi et al. 2011; Fu et al. 2012), due to source-plane offsets between the gas, dust, and stellar components.

In the case of HLock04, the SMA data at 880 μm trace the dust emission, which is magnified by μ = 5.32^+1.28 _{− 1.06}. The stellar emission (traced by the K_s-band data) is magnified by μ = 6.17 ± 0.03 and has R_eff = 0171 ± 0004 = 1.33 ± 0.03 kpc in the source plane. The SMA data constrain the size of the emitting dust to R_eff < 05 (<3.9 kpc). Therefore, the stellar and dust models are consistent, and we find no significant differential magnification in HLock04, at least for dust and stellar emission.

SMA interferometry, coupled with optical imaging, shows that HXMM01 is gravitationally lensed by two galaxies to the east and west of the submillimeter emission (Figure 13). Due to this unique configuration, we have obtained extensive follow-up observations of HXMM01, which will be published in detail in H. Fu et al. (2012, in preparation); here we summarize those results.

Keck-I/LRIS spectroscopy reveals that the eastern and western lensing galaxies are at z = 0.655 and z = 0.502, respectively, and are thus not physically associated. CO spectroscopy of the CO J =1→0, 3→2, and 4→3 transitions shows that HXMM01 is at z = 2.307. We have also observed HXMM01 with the F110W filter on HST/WFC3; these data are deeper, but lower resolution, than the Keck-I/LRIS imaging. The HST imaging is consistent with the Keck data but also reveals the presence of extended emission around the eastern lensing galaxy. This extended emission is inconsistent with being lensed emission from either of the two submillimeter sources, although it may be lensed emission from a third submillimeter-faint galaxy. It is also possible that this extended emission originates from spiral structure in the foreground galaxy.

HXMM01 is a unique case in that the existing follow-up data clearly show that it is made up of two individual, although interacting, SMGs in the source plane. For example, Hα is detected in Keck-II/NIRSPEC long-slit spectroscopy with a 700 km s⁻¹ velocity difference between the northern and southern components. The CO(J = 1→0) data also exhibit resolved velocity structure between the two components of the same velocity difference, further supporting a scenario in which the two peaks of SMA emission are two distinct sources separated by 28 (23 kpc at z = 2.3). Lens modeling with two separate sources shows that the northern source is lensed by a factor of ∼2.1 and the southern source by a factor of ∼1.6, for a total of ∼3.7. No multiple images are predicted. The optical Hα and [N ii] emission lines are broadened in both components of HXMM01 and may trace AGN emission in both galaxies.

HXMM02 is the brightest source in 1.1 mm AzTEC observations of the Subaru/XMM-Newton Deep Field (SXDF), and as such it is also known as SXDF1100.001 or Orochi (Ikarashi et al. 2011). The source is also bright at 250, 350, and 500 μm, with respective flux densities of 190 ± 7, 192 ± 8, and 132 ± 7 mJy in the three SPIRE bands.

Ikarashi et al. (2011) derived a photometric redshift of z_phot = 3.4^+0.7 _{− 0.5} for HXMM02, using continuum measurements at 880–1500 μm and in the radio at 20 and 50 cm. We have since obtained additional submillimeter spectroscopy and detected CO(J = 1→0) (GBT; H. Inoue et al. 2012, in preparation), CO(J = 3→2) (CARMA; D. Riechers et al. 2012, in preparation), CO(J = 4→3) (PdBI), and CO(J = 5→4) (CARMA; D. Riechers et al. 2012, in preparation), which pinpoint HXMM02 at z = 3.395. We note that there is an additional CO(J = 4→3) measurement obtained with the NRO 45 m telescope (Iono et al. 2012).

HXMM02 is in the SXDF region of the XMM-LSS SWIRE field, and therefore deep Subaru SuprimeCam and UKIRT WFCAM imaging is available (Furusawa et al. 2008; Warren et al. 2007). Ikarashi et al. (2011) showed that a faint optical galaxy, with z_phot = 1.39 ± 0.01, is located 05 from the submillimeter centroid. We have since obtained near-IR spectroscopy with the Infrared Spectrometer and Array Camera on the Very Large Telescope and detect Hα at z = 1.33. The positional offset between the optical and the submillimeter sources, coupled with the redshift difference, is indicative of an SMG being gravitationally lensed by the optical galaxy.

HXMM02 has also been imaged with NIRC2 and the Keck-II AO system (Figure 13). No arcs or other morphological indications of gravitational lensing are observed, which is similar to HBoötes01 and HLSJ091828.6+514223 (Combes et al. 2012). Modeling of the SMA data derives a magnification of μ = 1.5^+1.0 _{− 0.4} for HXMM02. The apparent 8–1000 μm luminosity of HXMM02 is μL_IR = (3.6^+0.3 _{− 0.2}) × 10¹³ L_☉ (Figure 14); thus, the modest amplification from lensing means that the intrinsic luminosity (magnification corrected) is L_IR = (2.4^+0.6 _{− 1.5}) × 10¹³ L_☉. HXMM02 is an extreme source, even once the effect of gravitational lensing has been accounted for. If the far-IR emission is dominated by star formation, it has intrinsic (lensing-corrected) SFR ∼ 4000 M_☉ yr⁻¹ (Kennicutt 1998).

A single line is tentatively detected in CARMA spectroscopy of HXMM03, which, due to the submillimeter photometric redshift, we consider to be CO(J = 3→2) at z = 2.72 (D. Riechers et al. 2012, in preparation). High-resolution submillimeter and radio interferometry is not available, and therefore the SMG cannot be pinpointed. No gravitational lensing features are detected in the HST/WFC3 F110W imaging, and without an accurate location for the submillimeter emission we are unable to determine whether or not HXMM03 is gravitationally lensed.

We have obtained HST/WFC3 F110W imaging of HELAISS01 (Figure 15), which reveals the presence of arc-like structures around a foreground source. No other follow-up data are available, and unfortunately, HELAISS01 is located near the edge of the field and the only archival data available are SWIRE 70 μm imaging, in which nothing is detected. The SPIRE emission from HELAISS01 has a submillimeter photometric redshift of z ∼ 2.10 (Figure 16).

Contours from SMA compact configuration observations of HLock05 are shown overlaid on HST/WFC3 F110W imaging in Figure 15. Two submillimeter sources are detected at 870 μm; one of these sources is coincident with an IRAC and F110W galaxy, whereas the other is below the detection threshold of both data sets. There is an optical source between the two SMA peaks, which may be a foreground lens, although it is faint. We have obtained CARMA spectroscopy of HLock05, in which one emission line is clearly detected, which is most likely CO(J = 4→3) at z = 3.52.

The two submillimeter sources identified with the SMA may have different colors—the southernmost source is optically bright and detected by IRAC, but the northernmost sources are undetected in the F110W data and marginally detected at 4.5 μm. If these are two images of the same lensed source, the flux ratios in the SMA data are such that a detection of the northernmost source is expected in both the HST and the IRAC data. Due to the depths of the data, the apparent color difference is marginal and insufficient to exclude a lensing origin for this source, particularly because differential magnification (e.g., Fu et al. 2012) or an SMG merger may be involved. We are therefore unable to conclusively determine the nature of HLock05. It is most likely to be a gravitationally lensed complex source at z = 3.52, although it may also be a blend of two unassociated SMGs.

We have obtained submillimeter interferometry of HXMM05 with the SMA and high-resolution F110W imaging with HST/WFC3. As shown in Figure 15, a single unresolved source is detected in the SMA data. The submillimeter source is detected in the IRAC data, and it is offset by ∼2'' from a resolved optical and near-IR galaxy. The SMG redshift is determined to be z = 2.985 with the detection of CO emission lines by CARMA and PdBI. The redshift of the optical galaxy is unknown, but the separations between the two sources and the absence of a lensed SMG counter-image are sufficient to rule out significant magnification. Therefore, we conclude that HXMM05 is a single, unlensed but intrinsically luminous SMG. It has L_IR = (3.2 ± 0.4) × 10¹³ L_☉ (SFR ∼ 5500 M_☉ yr⁻¹; Kennicutt 1998) and T_D = 45 ± 1 K, for β = 1.5.

HXMM11 is the only source in the supplementary candidate list for which we currently have evidence indicating that it is strongly gravitationally lensed. The configuration is shown in Figure 15, and the SED is in Figure 16. Two faint sources are resolved in SMA interferometric observations, the fainter of which is coincident with a faint K_s-detected source. The combined centroid of the two SMA galaxies is coincident with an IRAC source, which is most likely the foreground lens. However, the resolution of IRAC is insufficient for this interpretation to be robust. CO(J = 3→2) at z ∼ 2.18 is observed by CARMA, and corresponding CO(J = 1→0) is detected by the GBT.

Two SMGs, separated by ∼11'', are detected in SMA interferometry of HXMM12, and no central lensing galaxy is visible in the HST/WFC3 F110W imaging. On the basis of this spatial configuration we conclude that HXMM12 is most likely a blend of the two SMGs in the Herschel-SPIRE beam. No spectroscopy is available for this source, and if it is a blend of multiple SMGs, then the submillimeter photometric redshift is unreliable.