Lens Models of Herschel-Selected Galaxies From High-Resolution Near-IR Observations
We present Keck-Adaptive Optics and Hubble Space Telescope high resolution near-infrared (IR) imaging for m-bright candidate lensing systems identified by the Herschel Multi-tiered Extragalactic Survey (HerMES) and Herschel Astrophysical Terahertz Survey (H-ATLAS). Out of 87 candidates with near-IR imaging, 15 () display clear near-IR lensing morphologies. We present near-IR lens models to reconstruct and recover basic rest-frame optical morphological properties of the background galaxies from 12 new systems. Sources with the largest near-IR magnification factors also tend to be the most compact, consistent with the size bias predicted from simulations and previous lensing models for sub-millimeter galaxies. For four new sources that also have high-resolution sub-mm maps, we test for differential lensing between the stellar and dust components and find that the m magnification factor () is times higher than the near-IR magnification factor (), on average. We also find that the stellar emission is times more extended in size than dust. The rest-frame optical properties of our sample of Herschel-selected lensed SMGs are consistent with those of unlensed SMGs, which suggests that the two populations are similar.
Subject headings:submillimeter: galaxies gravitational lensing: strong emission galaxies: starburst
Dusty star-forming galaxies (DSFGs; For a recent review, see Casey et al., 2014), selected for being bright in the infrared or sub-mm regimes, are responsible for the bulk of cosmic star-formation in the early Universe (e.g. Le Floc’h et al., 2005; Takeuchi et al., 2005). Sub-millimeter galaxies (SMGs, Smail et al. 1997; Hughes et al. 1998; Barger et al. 1998 and see Blain et al. 2002 for a review), an m-bright subset of the DSFG population, present an appealing opportunity to study an important phase in galaxy evolution at the peak of cosmic star-formation. The negative -correction in the Rayleigh-Jeans tail of thermal dust emission at the (sub-)mm regime forms an approximately constant infrared (IR) luminosity limit across a wide range in redshift (). This effectively allows SMGs to be readily detected in sub-mm surveys. Since their discovery 17 years ago, we have learned that SMGs are massive ( ; Michałowski et al. 2010; Hainline et al. 2011; Bussmann et al. 2012; Targett et al. 2013), gas-rich ( ; Greve et al. 2005; Tacconi et al. 2008; Ivison et al. 2011; Bothwell et al. 2013), and metal-rich (; Swinbank et al. 2004) galaxies at a median redshift of (Chapman et al., 2005) that could be undergoing a short burst of star-formation ( Myr; Tacconi et al. 2008; Narayanan et al. 2010; Lapi et al. 2011; Hickox et al. 2012; Simpson et al. 2013). They have the most extreme star-formation rates, which can be as high as and compose of the total comoving star-formation rate density () at (Chapman et al., 2005; Wardlow et al., 2011; Casey et al., 2013). This is comparable to the total contribution of mid-IR selected galaxies at the same epoch, although SMGs are fewer in number but have larger IR luminosities (e.g. Farrah et al., 2008; Hernán-Caballero et al., 2009; Calanog et al., 2013).
From an evolutionary standpoint, it has long been proposed that ultra-luminous infrared galaxies (ULIRGs, ), which include SMGs, is an intense star-forming phase that precedes the growth of the AGN hosted by massive elliptical galaxies (Sanders et al., 1988). Multiple lines of evidence suggest that SMGs are the likely progenitors of massive elliptical galaxies (Lilly et al., 1999; Swinbank et al., 2006; Tacconi et al., 2008; Michałowski et al., 2010; Lapi et al., 2011; Hickox et al., 2012; Toft et al., 2014). For instance, of SMGs are known to harbor AGN, supporting formation scenarios in which massive elliptical galaxies evolve from a quasar-dominated phase (Alexander et al., 2003; Pope et al., 2008; Coppin et al., 2010). Furthermore, clustering analyses indicate that SMGs are hosted by dark matter halos and have space densities of , consistent with optically-selected quasars at and elliptical galaxies at (e.g. Blain et al., 2004b; Farrah et al., 2006; Hickox et al., 2012).
While our knowledge of SMGs have definitely advanced, their dominant formation mechanism is still unclear. One picture proposes that SMGs are a result of gas-rich major-mergers (Tacconi et al., 2006; Schinnerer et al., 2008; Tacconi et al., 2008; Engel et al., 2010) while another favors them as being extreme analogues of normal star-forming galaxies, fed with gas through minor mergers and smooth infall (Finlator et al., 2006; Dekel et al., 2009; Davé et al., 2010). Observational studies that focus on SMG morphologies can help clarify this issue, and would require analysis in wavelength regimes that trace the constituent gas, dust, and stars. However, SMG morphologies are difficult to study with current instruments because of poor spatial resolution, insufficient sensitivity, or both. Here, we circumvent these difficulties by studying SMGs that are strongly gravitationally lensed. The lensed background source receives a boost in apparent flux by a factor of , where is the magnification factor, enabling the study of emission that would otherwise be too faint to detect. In addition, the apparent size of the background source is increased by a factor of (Schneider 1992) – allowing high-spatial resolution studies of the lensed galaxies, even if they are at high redshift.
The obvious benefits of studying SMGs via gravitational lensing sparked interest in producing an efficient and straight-forward method to identify strong-lensing events. Efficient strong lensing event identification through bright source selection in wide-area extragalactic sub-mm/mm surveys has been long proposed (Blain, 1996; Perrotta et al., 2002; Negrello et al., 2007; Paciga et al., 2009). The idea behind this selection method exploits the fact that sources that are intrinsically sub-mm bright are also very rare (e.g. see Weiß et al., 2009). This implies that a significant fraction of the sub-mm bright population could be lensed and flatten the observed declining number counts at large flux densities. This flattening however, could also be caused by contaminants such as local late-type spiral galaxies and flat spectrum radio quasars (Negrello et al., 2007) which can be removed trivially through optical and radio surveys (e.g. SDSS, Abazajian et al. 2003; NVSS, Condon et al. 1998). Thus, after removing such contaminants, a large fraction of the brightest sub-mm sources are expected to be strongly lensed and lie at .
The launch of the Herschel Space Observatory
This paper focuses on studying the background lensed galaxies with new high-resolution near-IR data for 87 m-bright candidate lensing systems discovered by H-ATLAS and HerMES. A comprehensive analysis of the properties of the foreground lenses is deferred to a future publication (Amber et al., in prep.). Near-IR observations of Herschel-selected m-bright lensed SMGs allow one to characterize the stellar distribution at spatial resolutions that are unachievable with the current facilities. Furthermore, since classically-selected SMGs are m-bright, we can directly compare their rest-frame optical properties, such as their luminosities, against the m-bright population. This comparison can help clarify any differences between these two SMG populations, which can potentially arise from their sub-mm selections. Aside from their rest-frame optical luminosities, the morphological information recovered from reconstructing the background galaxy can also be used to compare against previous studies of unlensed SMGs (Swinbank et al., 2010; Targett et al., 2011, 2013; Aguirre et al., 2013). In this context, the morphological study of lensed SMGs at an unprecedented spatial resolution can provide observational evidence to determine the formation mechanisms that are present. Finally, these high-resolution near-IR observations compliments previous studies done on lensed SMGs using high-resolution sub-mm facilities (Bussmann et al., 2013; Weiß et al., 2013; Hezaveh et al., 2013; Vieira et al., 2013). Any sources that overlap between the near-IR and the sub-mm can be used to study the morphologies, spatial distribution, and the effects of differential magnification between the older stellar population and the dust-emitting star-forming regions of the same galaxy.
All of the candidate lensing systems in this paper have been observed using either the Hubble Space Telescope’s (HST) Wide Field Camera 3 (WFC3) in the band (F110W, =m) or Keck II Near-Infrared Camera 2 (NIRC2) with laser guide star adaptive optics system (LGS-AO, Wizinowich et al. 2006) in the (=m) band. We model the lensing in 12 galaxy-scale lensing systems with new near-IR data that have high-significance lensing morphology detections and sufficiently constrained configurations. From our lens models, we determine the magnification in the near-IR and the source-plane emission regions. Of these 12, six of the systems were also studied in the sub-mm by Bussmann et al. (2013). By comparing the lensing in the sub-mm and near-IR, we quantify the effects of differential lensing and measure the size difference of stellar and dust components. Using our near-IR data and lens models, we measure the intrinsic photometry for lensed SMGs and estimate their rest-frame absolute -band magnitudes.
This paper is organized as follows. In Section 2, we summarize the sub-mm lensed candidate selection and describe our high-resolution near-IR observations and data reduction process. Our classification of candidate lensing systems is presented in Section 3. Section 4 describes our lens modeling methodology and individual notes on each strong lensing system. We then discuss our results and compare them with previous studies of both lensed and unlensed SMGs in Section 5. Finally, we summarize our findings and conclusions in Section 6.
We adopt a CDM cosmology, with km s Mpc, , and . Unless otherwise stated, all magnitudes reported are in the AB system (Fukugita et al., 1996).
2. Lensed Candidate Selection and near-IR Observations
In this section we summarize the selection criteria used to define our sample and describe the data acquisition and reduction of our high-resolution near-IR imaging of the galaxies. A summary of all the targets observed, along with their integration times and observation dates are found on Table 1. Of the 87 near-IR targets, 49 (56%) HerMES/H-ATLAS sources are observed with Keck/NIRC2-LGS-AO, 42 (48%) HerMES sources with HST/WFC3 F110W (with 15 (17%) HerMES sources observed using both instruments).
2.1. Selection of Candidate Lensing Systems
The targets of this study are selected from the Spectral and Photometric Imaging REceiver (SPIRE, Griffin et al. 2010) maps in the HerMES (Oliver et al., 2012) and H-ATLAS (Eales et al., 2010) fields. Targets are identified in the same way in both surveys, using the SPIRE m channel to minimize the number of contaminants (Negrello et al., 2007, 2010). The Herschel-SPIRE data reduction and photometry procedures differ slightly for each survey, with the main difference being that HerMES accounts for blending from positional priors that can result in detecting fainter objects while H-ATLAS only retains sources above . Even with this difference, the m number counts appear consistent (Oliver et al., 2010; Clements et al., 2010). Full details of the H-ATLAS map-making data reduction and source extraction are presented in Pascale et al. (2011) and Rigby et al. (2011). For HerMES, see Levenson et al. (2010), Roseboom et al. (2010), and Smith et al. (2012), with updates in Viero et al. (2013) and Wang et al. (2013). Both procedures are summarized below.
For HerMES, SPIRE maps were generated using the SPIRE-HerMES Iterative Mapper (SHIM) algorithm (Levenson et al., 2010). The most updated point-source catalogues use an iterative source-detection scheme of STARFINDER (Diolaiti et al., 2000) and De-blend SPIRE Photometry (DESPHOT) algorithm (Roseboom et al., 2010, 2012; Wang et al., 2013). STARFINDER is used to detect and find the optimal positions of point sources in SPIRE maps by assuming that the observed images can be modeled as a superposition of point-response functions (PRF). These source positions are then used as inputs for DESPHOT to perform map segmentation (de-blending), source photometry, background estimation and noise (instrumental and confusion) estimation.
For sources identified by H-ATLAS fields, source extraction is performed using the Multi-band Algorithm for Source eXtraction (MADX; Maddox et al. in prep) on Herschel Interactive Processing Environment (HIPE) generated SPIRE maps (Pascale et al., 2011). MADX iteratively performs PSF fitting and subtraction to measure flux densities and positions for each band. Sources that are detected at (including confusion noise of mJy at all bands, Nguyen et al. 2010) in any of the bands are retained in the final catalogues.
|IAU Name||Short Name||Exp. Time||
|1HerMES S250 J002854.0-420457||HELAISS04|
|1HerMES S250 J002906.3-421420||HELAISS01|
|1HerMES S250 J003823.7-433705||HELAISS02|
|1HerMES S250 J021620.0-032520||HXMM26||
|1HerMES S250 J021632.1-053422||HXMM14|
|1HerMES S250 J021830.6-053125||HXMM02||,||
|1HerMES S250 J021836.7-035316||HXMM13|
|1HerMES S250 J021942.9-052433||HXMM20|
|1HerMES S250 J022016.6-060144||HXMM01||,||,|
|1HerMES S250 J022021.8-015329||HXMM04|
|1HerMES S250 J022029.2-064846||HXMM09||, ,||, ,|
|1HerMES S250 J022135.2-062618||HXMM03|
|1HerMES S250 J022201.7-033340||HXMM11||
|1HerMES S250 J022205.5-070727||HXMM23|
|1HerMES S250 J022212.9-070224||HXMM28|
|1HerMES S250 J022250.8-032414||HXMM22|
|1HerMES S250 J022515.3-024707||HXMM19|
|1HerMES S250 J022517.5-044610||HXMM27|
|1HerMES S250 J022547.9-041750||HXMM05|
|1HerMES S250 J023006.0-034153||HXMM12|
|1HerMES S250 J032434.4-292646||HECDFS08|
|1HerMES S250 J032443.1-282134||HECDFS03|
|1HerMES S250 J032636.4-270045||HECDFS05|
|1HerMES S250 J032712.7-285106||HECDFS09|
|1HerMES S250 J033118.0-272015||HECDFS11|
|1HerMES S250 J033210.8-270536||HECDFS04|
|1HerMES S250 J033732.5-295353||HECDFS02|
|1HerMES S250 J043340.5-540338||HADFS04|
|1HerMES S250 J043829.8-541832||HADFS02|
|1HerMES S250 J044154.0-540351||HADFS01|
|1HerMES S250 J044946.6-525427||HADFS09|
|1HerMES S250 J045027.1-524126||HADFS08|
|1HerMES S250 J045057.6-531654||HADFS03|
|1HerMES S250 J100030.6+024142||HCOSMOS03||
|1HerMES S250 J100057.1+022010||HCOSMOS02||,||
|1HerMES S250 J100144.2+025712||HCOSMOS01||,||
|1HerMES S250 J103330.0+563315||HLock15|
|1HerMES S250 J103618.5+585456||HLock05||,||
|1HerMES S250 J103826.6+581543||HLock04||, ,||, ,|
|1HerMES S250 J103957.8+563120||HLock17|
|1HerMES S250 J104050.6+560653||HLock02|
|1HerMES S250 J104140.3+570858||HLock11||,||,|
|1HerMES S250 J104549.2+574512||HLock06||,||,|
|1HerMES S250 J105551.4+592845||HLock08|
|1HerMES S250 J105712.2+565458||HLock03||,||,|
|1HerMES S250 J105750.9+573026||HLock01||, ,||
|1HerMES S250 J110016.3+571736||HLock12|
|1HerMES S250 J142201.4+533214||HEGS01|
|1HerMES S250 J142557.6+332547||HBoötes09|
|1HerMES S250 J142650.6+332943||HBoötes04|
|1HerMES S250 J142748.7+324729||HBoötes11|
|1HerMES S250 J142824.0+352620||HBoötes03|
|1HerMES S250 J142825.7+345547||HBoötes02||, ,||, ,|
|1HerMES S250 J143204.9+325908||HBoötes10|
|1HerMES S250 J143330.7+345439||HBoötes01|
|1HerMES S250 J143543.5+344743||HBoötes12||,||,|
|1HerMES S250 J143702.0+344635||HBoötes08|
|1HerMES S250 J144015.7+333055||HBoötes13|
|1HerMES S250 J144029.8+333845||HBoötes07|
|1HerMES S250 J161331.4+544359||HELAISN01|
|1HerMES S250 J161334.4+545046||HELAISN04|
|1HerMES S250 J170507.6+594056||HFLS07|
|1HerMES S250 J170607.7+590922||HFLS03|
|1HerMES S250 J170817.6+582845||HFLS05|
|1HerMES S250 J171450.9+592634||HFLS02|
|1HerMES S250 J171544.9+601239||HFLS08|
|1HerMES S250 J172222.3+582609||HFLS10||,||,|
|1HerMES S250 J172612.0+583743||HFLS01|
In both surveys lensing candidates are selected by applying a high flux cut at m, which for H-ATLAS is mJy (Negrello et al., 2010), where is the m flux density, and for HerMES is mJy (Wardlow et al., 2013). Sources that are not associated with local late-type galaxies or flat-spectrum radio galaxies are retained as lensing candidates. The targeted sources are presented in Table 3, along with their SPIRE 250, 350 and 500m flux densities and redshifts.
We should also clarify that our selection in HerMES at mJy was applied on an initial source catalog, extracted from blind detections using SUSSEXtractor (Savage & Oliver, 2007; Smith et al., 2012), but subsequent iterations of HerMES data products resulted in better deblending of m flux densities with m positions as a prior (Wang et al., 2013). This results in some of the sources initially categorized as candidate lensing systems (having mJy), with a final lower probability of being lensed at , based on the statistical models of Wardlow et al. (2013) that uses the foreground lensing matter distribution, unlensed SMG number counts, and an assumed SMG redshift distribution. As a result, some are confirmed as bonafide lenses and we keep them in our sample, as they have been followed-up but we exclude them for statistics involving lensed SMGs at the bright m flux densities.
Figure 1 shows as a function of the flux density ratio for the targeted candidate lensing systems with high-resolution near-IR imaging. By design, our targeted sources are biased towards those that are brightest at 500m, although they have similar 350/500m colors (with for most systems) to the bulk of the SPIRE population. This indicates that Herschel-selected lensed galaxies and the SPIRE population have similar far-IR SED shapes, dust temperatures, and redshift distribution but will have larger apparent IR luminosities due to flux boosting effects from lensing (Wardlow et al., 2013; Bussmann et al., 2013).
2.2. Keck NIRC2/LGS-AO
We have obtained Keck/NIRC2 LGS-AO imaging for Herschel-candidate lensing systems. Conditions were typically good, characterized by clear skies and seeing values of from our successful observing runs from 2011 to 2013. We observe our targets primarily using the filter (m), mainly because Keck-AO performs the best at longer wavelengths and gives the optimal sensitivity because the background is minimal at this wavelength (Simons & Tokunaga, 2002). Typical integration times for each source are minutes to acquire a point source depth of 25.7 AB using a aperture radius. We use the wide camera that has a field of view and sub-arcsecond dithering steps. The spatial resolution with AO correction reaches in the best conditions and the estimated Strehl ratios were . Some of the targets showing clear signs of lensing, are also observed in the (m) band. However, we do our lens modeling (Section 4) only in the band where the signal to noise is at its highest. We used custom IDL scripts to reduce the images, following standard procedures (Fu et al., 2012, 2013). Briefly, after bad pixel masking, background subtraction, and flat-fielding, sky background and object masks were updated iteratively. For each frame, after subtracting a scaled median sky, the residual background was removed with 2-dimensional B-spline models. In the last iteration, we discard frames of the poorest image quality and correct the camera distortion using the on-sky distortion solution from observations of the globular cluster M92
The NIRC2 images are flux calibrated against UKIDSS -band photometry, when available. Each frame is PSF matched and corrected for airmass and we use the UKIDSS aperture radius of to perform our calibration. Photometric zero points are derived by calculating the magnitude difference for overlapping sources. For NIRC2 frames that do not overlap with UKIDSS footprints, we use the night-averaged zero point and its standard deviation to account for the associated systematic error.
For the PSF used in our lens modeling analysis (Section 4), we use a nearby unsaturated point source, whenever available. Otherwise, point sources from other images observed on the same day are used, while keeping the airmass difference within 0.2 and applying the appropriate rotation.
Herschel-lensing candidates in the HerMES fields have also been observed as part of the HST WFC3 Cycle 19 snapshot program (P.I. M. Negrello). All are observed with the F110W filter (m), using a 4-point parallelogram dither pattern with point and line spacings of and , respectively. Most of the images have a total integration time of 4 minutes per target, while a few sources that have red SPIRE colors () have doubled integration times, because these sources could be at higher redshifts and thus likely fainter the in near-IR (Dowell et al., 2014).
The calwfc3 processed flat-fielded data from the HST/WFC3 pipeline are used as inputs for multidrizzle (Koekemoer et al., 2003), producing an output image with a pixel scale of 0.04 to allow adequate sampling of the PSF and to match the pixel scale of the Keck images. Due to some fields being crowded by bright sources, we turn off sky subtraction on all WFC3 frames and set the drop size parameter, “pixfrac” = 1, in order to minimize additional noise due to sky variations. We set the “bits” parameter to the value of 4608 to include pipeline-rejected pixels and dust motes, since our dithering pattern is not large enough to fill in these regions with good data. To account for the uncertainty in each pixel value, an error map is generated to account for the RMS value of the sky and the Poisson error each pixel. The resulting output images have a spatial resolution of and an average point source depth of 25.4 and 26.2 AB mag for integration times of 4 and 8 minutes, using a aperture radius.
We use a different PSF extraction method for HST/WFC3 images. Since HST/WFC3 covers a field of view of , we use starfinder to stack on unsaturated point sources within the image to generate the PSF used for our lens modeling analysis.
3. Classification of Lensing Candidates
For our 87 lensing candidates with high-resolution near-IR data, we implement a two-step grading rubric to identify sources for which we could perform our lens modeling analysis to derive magnification factors and recover the intrinsic properties of the SMG. In this section, we describe our rubric that prioritizes bonafide lensing morphologies and available redshifts for the background source. The resulting grade for each candidate lensing system is listed in Table 3 and our grading rubric is summarized in Table 2.
3.1. Visual Identification of Lensing Morphologies
For each target we assign a letter grade based on the existence and quality of any lensing features that are present in the near-IR data. Candidates that are classified as Grade A are of high-priority and are what we assume to be confirmed lensing systems. To the zeroth order, these are typically sources that show obvious lensing morphology such as rings, arcs, and counter-images, detected at high-significance. Some candidates that are more ambiguous (e.g. HLock12, HFLS08, and HECDFS05) are also classified as Grade A when a possible counter-image after subtracting the foreground galaxy is revealed and the observed lensing configuration can be successfully modeled. As an additional check to boost our confidence, we also confirm if the suspected near-IR lensing morphologies trace the observed configuration from existing high-resolution sub-mm data (Bussmann et al., 2013) or be located within the beam () of radio observations for blind spectroscopy (Riechers et al., in prep.). Grade B sources can usually be described as systems with ambiguous low signal-to-noise features surrounding a relatively brighter galaxy which could either be due to lensing or be part of the galaxy itself. Deeper high-resolution data or observations in different wavelength regimes are needed to confirm the lensing status of these systems. These sources may also be intrinsically unlensed (Dowell et al., 2014) or only moderately lensed, such is the case with HXMM01 (Fu et al., 2013). Grade C sources are assigned to candidates of lowest priority for our study. The near-IR images for these targets typically show no detections within of the measured m SPIRE position or sources with compact irregular morphologies that do not resemble any lensing morphologies. Like Grade B systems, we also interpret that our sample of Grade C sources could also include sources that are intrinsically bright in the far-IR. The near-IR lens models presented in this paper focuses on Grade A sources, which are shown in Fig. 3.
|NIR Lens Morphology||SMG and Lens Redshift||SMG Only Redshift||Lens Only Redshift||Neither|
3.2. Redshift Availability
Redshifts are needed to convert observed parameters into physical quantities. Spectroscopic followup programs at (sub)mm and optical/near-IR wavelengths are still ongoing (e.g., Harris et al., 2012; Bussmann et al., 2013, Riechers et al in prep.). The existing redshifts are presented in Table 3, and we use these data to assign a secondary letter grade from through : – redshifts available for both foreground lens and background SMG; – redshift only available for the background SMG; – redshift only available for foreground lens; – no foreground lens or background SMG redshift. Note that our focus is to study the lensed SMG, we assign a higher grade for systems with background source redshifts.
For Grade A3 and A4 systems, we estimate the lensed SMG redshifts by fitting a modified blackbody using fixed parameters of K and dust-emissivity parameter = 1.5 to the Herschel-SPIRE photometry, which is the typical average dust temperature for SMGs and dust emissivity parameter used for dusty galaxies at high-redshift (e.g. Chapman et al., 2003; Kovács et al., 2006; Wardlow et al., 2011). These far-IR photometric redshifts have a large systematic uncertainty because of redshift-temperature degeneracy effects in the far-IR SED (Blain et al., 2004a) and should therefore be used with caution. This results to a minimum uncertainty of approximately for dust temperature variation of K. Due to the inherent uncertainties associated with far-IR derived photometric redshifts, we do not use them in our analysis of the intrinsic properties of lensed SMGs (Section 5.3).
3.3. Near-IR Strong Lensing Identification Efficiency
Negrello et al. (2007) predicted that, in the regime where mJy, the surface density of unlensed SMGs is extremely low, defining a flux density cut in which a large fraction of the observed source counts are strongly lensed. Out of our 87 targets, 28 satisfy mJy and 9 of these are confirmed strong lensing events (Grade A). This yields an efficiency of at the average depth of our near-IR data (Sec. 2). The remaining could be unlensed or have faint lensing morphologies that fall below our near-IR detection limits. In addition, our near-IR sample of candidate lensing systems with mJy is incomplete and does not include SMGs from other studies observed at different depths and wavelengths (e.g., Lensed SMGs from the H-ATLAS SDP sample, Negrello et al. 2014; Dye et al. 2014). For these reasons, we conclude that is a lower limit for the near-IR lensing efficiency rate. If we also treat the 11 Grade B candidates with mJy as confirmed lensing events to determine an upper limit, the near-IR lensing efficiency rate increases to . These limits are consistent with the predicted strong lensed fraction at mJy from the statistical models of Wardlow et al. (2013). To get an idea how this efficiency can improve as a function of near-IR depth, the H-ATLAS SDP sample (Negrello et al., 2014; Dye et al., 2014), also observed using HST/WFC3 F160W with point source depths of 26.8 mag using min. integration times, confirmed lensing to be present for all 5 candidate lensing systems with mJy. For comparison, the Bussmann et al. (2013)’s sample of lensed SMGs with mJy observed with the Sub-Millimeter Array (SMA), 25 out of 30 candidates () with a depth of mJy showing evidence of moderate to strong lensing in the sub-mm maps. Of the 12 sources with high-resolution near-IR data that are confirmed to be lensed () in Bussmann et al. (2013), six are Grade A (NB.v1.78, HBoötes02, NB.v1.43, G09v1.40, HLock01, HLock04), four are Grade B (HXMM02, G09v1.97, NA.v1.195, HBoötes03), and the two remaining are Grade C (G09v1.124, G15v2.779).
The lower near-IR efficiency for identifying strong-lensing events relative to sub-mm confirmations is not surprising. If a source is detected in both the sub-mm and the near-IR has two different spectroscopic redshifts, one can use small but significant offsets between the two images as evidence for lensing. This is useful in cases for which the observed sub-mm emission does not resemble convincing lensing morphologies (e.g. HXMM02, HBoötes03). There are also different possibilities to explain the lower efficiency associated with near-IR lensing identifications, which include the background SMGs suffering from heavy dust-obscuration, being intrinsically faint in the rest-frame optical, or lying at a high redshift. A geometric argument could also be made for the cause of non-detections, in which the near-IR emission is significantly offset from the sub-mm emission and the central caustic, thus lying in regions of low magnifications on the source-plane. In all alternative cases, this could lead to the observed near-IR emission from the background SMG to fall below our detection limits despite showing a bonafide lensing morphology in the sub-mm (e.g., G15v2.779, Bussmann et al. 2012).
Figure 2 shows the cumulative frequency distribution of for all the targeted sources with high-resolution near-IR data labeled with their associated grades.
The following lists the reference key for redshifts: W13 = Wardlow et al. (2013); B13 = Bussmann et al. (2013); R14 = Riechers et al. (in prep.), M14 = Messias et al. (in prep.); O13 = Omont et al. (2013); C11 = Cox et al. (2011); H12 = Harris et al. (2012); H14 = Harris et al. (in prep.); I13 = Ivison et al. (2013); R11 = Riechers et al. (2011); S11 = Scott et al. (2011); O08 = Oyaizu et al. (2008); K14 = Krips et al. (in prep.); G13 = George et al. (2013); L14 = Lupu et al. (in prep.); and B06 = Borys et al. (2006).
The , , and are flux densities measured from SPIRE photometry. corresponds to the m flux density measured from SMA. and refer to the redshifts of the background source and foreground lens, respectively. Lens Grade is the priority value assigned to the lensed candidate, discussed in Section 3.
For comparison, we also show the SMA sample from Bussmann et al. (2013), where we convert the sub-mm grade to an equivalent near-IR grade
4. Lens Models
4.1. General Methodology
For each lensing system we use galfit (Peng et al., 2002) to model the surface brightness profile of the foreground lens and subtract it from the image. We use Sérsic profiles on foreground galaxies that resemble an elliptical morphology and edge-disk profiles for edge-on disks (G15v2.19 and HBoötes02). Foreground lens subtraction can also reveal close counter-images required to constrain the lens model (Cooray et al., 2011; Hopwood et al., 2011; Negrello et al., 2014; Dye et al., 2014). Any observed lensing features and nearby sources that are not associated with the lensing galaxy are masked out. The foreground lens subtracted image is then used as the input image for our lens modeling.
In cases where the emission from the foreground lens and background source are blended, we implement an iterative process in order to obtain an optimal lens model (Cooray et al., 2011). Using the galfit residual as the initial input, we derive a preliminary lens model. After achieving an acceptable fit ( on the order of unity), we then subtract the lensed image of the model source from the original image. For the second iteration, we then use galfit on this “lensing morphology-subtracted” image, effectively isolating the surface brightness profile of the foreground lens and eliminating the need to mask out the lensing morphology. The updated foreground lens surface brightness profile from galfit is subtracted from the original data, which will then serve as the new input for our lens modeling. This iterative method to obtain an optimal foreground lens subtracted image yields a difference from the preliminary lens model, which corresponds to a improvement. The best-fit model for these blended lensing systems typically converges after 1 or 2 iterations.
For gravitational lensing, the condition for strong lensing to occur is when the normalized surface mass density of the foreground lens, is greater than unity. In this paper, we assume a singular isothermal ellipsoid (SIE; Kormann et al., 1994) for , with the convergence at a point () in the image plane defined as:
where is the surface mass density, is the critical surface mass density, is the critical or Einstein radius and is the axis ratio. The SIE profile has been found to reproduce observed configurations of galaxy-galaxy strong lensing events (see Treu 2010 for a recent review) and has been successfully used in modeling lensed SMGs (Fu et al., 2012; Bussmann et al., 2012, 2013; Hezaveh et al., 2013). The fitting parameters we use to describe the foreground SIE profile are the Einstein radius (), distance from the measured galfit centroid () in RA and DEC, ellipticity (), and the position angle (, east of north). A parameter for the external shearing amplitude was also initially included in our analysis, but provided marginal to no improvement in the fit. In addition, our current data does not allow accurate redshift determination of any nearby foreground sources (with the exception of G12v2.30, which the effects of shear were accounted for by additional lensing profiles in Fu et al. 2012). For these reasons, we do not include shearing amplitude in our models and note that additional constraints are needed in order to properly quantify its effect on the lens models. The components of the background galaxy in the source plane are assumed to have Sérsic profiles (Sersic, 1968). While the use of Sérsic profiles may oversimplify the morphology of the high redshift star-forming population, previous studies have shown that this approach provide useful information about their morphologies, such as intrinsic size, shapes and orientations for both lensed and unlensed SMGs (Swinbank et al., 2010; Gavazzi et al., 2011; Targett et al., 2011, 2013; Aguirre et al., 2013). The fitting parameters of the background Sérsic profile are the flux (), position () from the measured foreground lens center of mass, ellipticity (), position angle (, defined east of north), effective semi-major axis (), and the Sérsic index (). For all systems, we start with the simplest model for the background galaxy (1 source) and increase the components to check if this provides a significantly better fit ().
These model parameters are all varied consistently for each lensing system. In order to take advantage of the high-resolution data, we adopt informative priors about the foreground lens, mostly given from the galfit subtraction. For the background source, we adopt uniform priors for every case. The Einstein radius is typically allowed to vary within from a circular radius that encloses the observed lensing morphology. The lensing mass is centered on the measured galfit position of the foreground lens, which is varied within an area defined by the FWHM of the PSF. The ellipticities are allowed to vary from 0.0 to 0.8, and the position angles from to , with the initial values of both set to the midpoints of these ranges. The background galaxies are initially placed in perfect alignment with the foreground lens and are allowed to explore the position space within times the Einstein radius, which is a valid assumption, since the detection of multiple counter-images is an indication that these sources are within the vicinity of the source-plane caustics. Indeed, the maximum observed offset from direct alignment between the foreground and background galaxy is 40 of the Einstein radius (HECDFS02). The effective semi-major axis length has an initial value of with a minimum value of and a maximum value of , based on half-light radii measurements of unlensed SMGs at (Chapman et al., 2003; Swinbank et al., 2010; Targett et al., 2011, 2013; Aguirre et al., 2013). Sérsic indices are allowed to vary from 0.10 to 4.00. The integrated flux in the lens model and the input image are normalized consistently before being compared and where there are multiple background components flux ratios are computed. For each lensing system, the total number of parameters is equal to , where and represent the number of lens and source components, respectively.
With a given set of initial parameters for the image and source plane, we use gravlens (Keeton, 2001) to generate a model of the lensed image. The model is convolved with the PSF to generate the expected observed image for each parameter set. This PSF-convolved model is then compared with the foreground lens subtracted image within the fitting region, shown as the green contours on Fig. 4. These fitting regions are initially hand-drawn to enclose all the suspected lensing morphologies in the data. After a preliminary lens model is derived, the fitting region is regenerated to enclose all pixels with values , measured from the data (no noise is present from the model). Defining the fitting region through this process serves three main purposes: Firstly, it helps prevent the lens model from including pixels from the background which can make the fit insensitive and degenerate from varying the input parameters. This effectively makes the model fit for shot-noise dominated pixels. Secondly, it minimizes the under or over-subtracted regions from imperfect galfit subtractions that can cause the lens model to be fixated on these unwanted features. Thirdly, it accounts for any counter-images predicted by the model but not accounted for by the data, reducing the bias in our fit.
The process of comparing the lens model to the data is iterated using the IDL routine amoebasa, which performs multidimensional minimization using the downhill simplex method with simulated annealing (Press et al., 1992) on the function, defined as:
where and is the surface brightness map of the observed and the model image, respectively, is the 1 uncertainty map for the observed image that accounts for background and shot noise, and are the pixel coordinates, and represents the number of pixels enclosed in the fitting region. Typically, for the least constrained systems (e.g., double) and for the most constrained systems (Einstein rings or giant arcs). Depending on how well constrained the lensing system is, the correct configuration for the observed lensing morphology is usually obtained after the first few iterations of amoeba_sa and the probability of accepting worse solutions decreases for each iteration due to the simulated annealing. The rest of the calls are then spent on performing an extensive search around the optimal solution with the given configuration. All parameters and calculated quantities are saved in each iteration and the confidence interval for the best fit model parameters are calculated from . We note that is renormalized to minimize correlated noise between pixels. This is done by dividing the total number of pixels of the original unbinned values from the original images by the square area of the PSF (Fu et al., 2012).
The near-IR magnification factor is calculated in the same manner as in Bussmann et al. (2013). Briefly, we integrate the model flux () within elliptical apertures with the same orientations and ellipticities as the model but with double the semi-major axis length. Then, these source plane elliptical apertures are mapped on to the image plane using the foreground lens model and the image plane flux is integrated (). The magnification factor is then simply a ratio of the two integrated fluxes, , and is representative of total from all background source components. We note that since our near-IR data is at a much higher resolution than in the sub-mm, changing the aperture size to equal the semi-major axis compared to double its value had little effect on the magnification value(within 10%).
To measure near-IR photometry, we use our fitting region to define the aperture and our results are listed in Table 6. The same aperture is also applied when measuring available multi-wavelength high-resolution near-IR data (Fig. 13). Photometric statistical errors are measured by calculating the standard deviation of the total counts from non-overlapping background-dominated fields on the data, using the same sized aperture. A simple aperture correction is calculated by measuring the ratio of total counts from the lens model with and without the aperture. We divide the integrated flux densities by for each background source to obtain a magnification-corrected value.
Note. – The following parameters discussed in Section 4.1 are used to describe the foreground lens: (RA, DEC) = centroid of light from galfit subtraction, Einstein radius, centroid position of mass relative to light, elongation, orientation of mass profile (east of north), / = value and the number of degrees of freedom.
4.2. Notes on Individual Lens Models
In this section, we provide notes on the basic characteristics for each lensing system with available lens models. We do not provide lens models for HLock01 and G12v2.30, as they have already been subjects of detailed studies from previous works (Gavazzi et al., 2011; Fu et al., 2012) and are also included in the sub-mm sample from Bussmann et al. (2013). The SMGs with lens models derived here are shown in Fig. 4. The best-fit parameters along with the errors describing the foreground lens and the background source are presented in Tables 4 and 5. As a test for differential lensing and size comparison analysis in Section 5.1, we also generate lens models for the four new sources (NB.v1.78, HBoötes02, G09v1.40, and HLock04) that overlap with Bussmann et al. (2013), using the same foreground lens parameters reported in their paper, allowing the foreground lens position to vary within to account for any astrometric offset between the near-IR and sub-mm data. The use of sub-mm derived foreground lens parameters generally yields poorer fits but is able to reproduce the observed near-IR lensing configuration. The lens models for this near-IR/sub-mm subsample are discussed on an object-by-object basis and shown in the Appendix.
NB.v1.78 (Grade A1): The -band image shows a classic configuration observed when the background source lies on top of the caustic fold, the same configuration shown by the lensing system SDSS J0737+3216 (Marshall et al., 2007). The -band image (Fig. 13) shows a consistent configuration, but the lensing morphology is fainter. The multiple, well-separated arcs, in addition to the incomplete Einstein ring strongly constrains the lens model. The best-fit lens model requires two background Sérsic profiles to account for a compact, brighter and extended, fainter, component. The best fit model shows a compact source located off-center within an extended component, indicating an asymmetric morphology. Using a single component model yields a significantly worse fit (=1.50) and fails to reproduce the extended Einstein ring. This source was also discussed in Bussmann et al. (2013), in which the SMA image reveal a similar configuration to the compact component in the -band image. We measure a marginally lower magnification factor of , compared to for the SMA data.
G15v2.19 (Grade A1): The observed lensing morphology features a quad-like configuration accompanied by an incomplete Einstein ring, observed in both -band and -band images. The background source is being lensed by an edge-on disk and has the most complicated background galaxy model in our whole sample, requiring three components. It has the poorest fit, , with both over- and under-subtracted regions that can be . Using less than 3 components resulted in . This system serves as an example in which substructure in the background source dominates, such that our assumed Sérsic profile is an inadequate description of the source. Furthermore, if all counter-images are resolved in the Keck data (as indicated by their angular sizes being larger than the Keck PSF), and if the observed emission from the individual knots are from the same source, then their surface brightnesses should be somewhat comparable, which is a property of the counter-images in the image plane (Kochanek et al., 1989). Instead, we observe the surface brightness to be significantly inconsistent relative to each other, which supports our hypothesis that the morphology of the background source is highly complex and the observed emission is due to multiple background components.
We regard our lens model as a simple solution that can serve as a basis for future analysis on this object. Our source-plane reconstruction consists of two compact objects separated by within a third extended elongated source. The positions of the two compact objects forms quads and double images in the observatations, in which one of the counter-images from each component converge at roughly the same position in the image plane to produce the brightest knot located in the northeast. The extended component straddles the caustic, causing the incomplete Einstein ring. Due to the poor fit and under-subtracted regions in the residual image, the error bars in the magnification factor we report, , are most likely underestimated, since the contribution for the complexity of the system is not included. For comparison, a more extensive analysis for this system is discussed in Messias et al. (2014), which features a semi-linear inversion (SLI) approach (Warren & Dye, 2003; Dye et al., 2008, 2014) in lens modeling multi-wavelength data simultaneously
HLock12 (Grade A1): The subtraction of the bright early-type galaxy reveals a counter-image detected at located east of the foreground lens. This constrains the lens model, which features a classic cusp configuration. The background SMG is extended with a half-light radius comparable to the foreground lens (). At , 1 is 7 kpc, so this source is larger than the average for SMGs (Aguirre et al., 2013; Targett et al., 2013, 2011; Swinbank et al., 2004; Chapman et al., 2003), although it is still consistent with other near-IR observations of SMGs at (Mosleh et al., 2011). The HST image has multiple peaks in the arc, causing the residual image to contain under-subtracted regions. This could indicate the presence of substructure in the background source or the foreground lens. It is unlikely that the most prominent under-subtracted region, south-west from the centroid of the arc emission, is associated with the background, since all variations of the lens model fail to reproduce any emission in this area, even when it is included in the fitting region and multiple components are allowed.
HLock06 (Grade A1): The lensing morphology of this source shows an arc to the west and a counter image to the east of the foreground lensing galaxy. The same features are also detected in the HST image (Fig. 13). The lens model shows that the Einstein radius of the foreground lens is very extended compared to the observed emission, which could be due to overlapping mass profiles from the neighboring galaxies. However, additional mass profiles or adding an external shearing amplitude has little effect on the derived source morphology so here we present the simplest best-fit model using a single mass component. There is significant under-subtraction in the eastern counter-image, which is not reproduced even when multiple components are used. This could primarily be due to systematic effects in the data. It is also unlikely that the residual emission northeast of the foreground lens is associated with the background galaxy since the lens model also fails to reproduce any counter-images in this region.
HBoötes02 (Grade A1): The lens model for the sub-mm emission, which shows an incomplete Einstein ring, was discussed in Bussmann et al. (2013). A multi-wavelength analysis for this object will be featured in Wardlow et al. 2014 (in prep.). The -band image shows an edge-on disk galaxy with an incomplete quad configuration, accompanied by faint, extended emission between the counter-images. The WFC3 F110W image shows no detections of the background source, while the detection in the NIRC2 -band is marginal.
To model the background source, we consider both a one component point-source (circular Gaussian profile) and a two component model with a point-source and an extended Sérsic profile. The one component fit yields a and reproduces all the observed features. However, the converged solution predicts the fourth undetected counter-image in the data to be detected at in the model. One possible explanation favoring this model would be severe obscuration from the edge-on disk. However, there is also EVLA radio observations of this system (Wardlow et al., 2013), which will not be affected by dust obscuration from the foreground lensing galaxy. In the EVLA data only the three near-IR luminous sources are detected, despite the sensitivity being high enough to detect the fourth image predicted by the single component model, if the flux ratios are as predicted. Therefore we consider it unlikely that the single component model is correct.
Furthermore, the two component model (shown in Fig. 4) has a marginally improved fit, with and has a configuration in which the fourth faint counter-image is faint and expected to be undetected (). This model also has some physically motivation, since the sub-mm data (Bussmann et al., 2013) shows an extended component, interpreted as star-forming regions, while the radio data (Wardlow et al., 2013) show a point source, indicative of an AGN. Both AGN and star-formation can be bright in the near-IR, which is supported by the faint extended emission in the observed frame -band data.
|Note. – The following parameters discussed in Section 4.1 are used to describe the background source: Flux Ratio = ratio of integrated flux, relative to the first listed component (fixed in the case of single components), background source position, relative to the the centroid of the mass profile, elongation of the background source, orientation of the background source (east of north), effective semi-major axis, Sérsic index, = near-IR magnification factor (represents the total value, with all subcomponents included).|
The center of the foreground mass profile is significantly offset from the stellar light profile ( or kpc), but this separation could be due to the dust-lane partially obscuring the true center of the stellar emission or the foreground galaxy not being perfectly edge-on. The near-IR model also predicts a smaller Einstein radius ( vs. ) and magnification factor than the sub-mm lens model ( vs. ). We note that as it currently stands, it is difficult for both lens models to account for the different observed lensing morphologies in the near-IR and sub-mm. In order to constrain the lens model, data in which the extended dusty star-forming regions and the point-source AGN component are detected at high significance is needed.
HFLS08 (Grade A1): The HST image shows an arc-like morphology east of the foreground lens. A counter-image located south-west from the foreground lens centroid is also detected at after surface brightness profile subtraction. Since there are multiple regions of emission that could all potentially be associated with the arc, we use an initial fitting region that encloses all the suspected features for our preliminary models. We also tried models in which the background galaxy is described by multiple components, or a two component mass profile. None of these solutions successfully account for the compact emission south of the foreground lens. We are unable to produce a configuration that accounts for the faint regions northeast and southeast of the foreground lens shown in the residual image. Therefore, we consider it unlikely that these features are from the lensed galaxy. Spectroscopy is required to confirm whether all the emission is associated with the background SMG. Since a single background component provides the best fit to the lensed arc, that is the model that we retain, and that is presented in Fig. 4.
NB.v1.43 (Grade A1): This object was presented in Bussmann et al. (2013) and George et al. (2013) and will be further analyzed in Fu et al. (in prep.). This object could potentially be lensed by a cluster, as discussed in Bussmann et al. (2013). The -band and -band images (Fig 13) show a much more elongated morphology than the sub-mm data, but there is little curvature. The lack of additional counter-images and a central position for the lensing mass places very weak constraints on the configuration, so we do not provide a lens model for this source.
G09v1.40 (Grade A2): The lens model for the m emission for this source was presented in Bussmann et al. (2013). The near-IR model for the background galaxy is a highly elongated, extended object with , which is roughly three times the size of the sub-mm model. In the near-IR, the background galaxy is nearly in perfect alignment with the foreground lens, producing the observed Einstein ring. This configuration shows a slight contrast with the sub-mm data, which show two peaks in the emission which could represent a double configuration, as supported by their lens model. However, the near-IR magnification is consistent with the SMA data, ), which suggests that the lensing configurations are similar and the two peaks seen in the SMA map are likely a result of having poor spatial resolution compared to Keck AO.
HCOSMOS01 (Grade A3): The -band image shows an incomplete Einstein ring in which three well-separated arcs are visible. The F110W image (Fig. 13) shows a consistent configuration but appears to be fainter. Only one component is required to reproduce the observations and using multiple components results in only a marginal improvement in the fit. The wide range of magnifications (), is due to the compact size of the background galaxy () and its location relative to the caustics. The residual image shows areas of under and over subtraction, also reflected by a relatively poor fit , indicating that the Sérsic profile could be an over-simplified model to describe the background SMG or be due to systematic effects in the data.
HLock04 (Grade A3): The double arc lensing morphology of HLock04 is detected in both the near-IR and sub-mm, which makes it ideal for multi-wavelength studies. This morphology is consistent in the , , and , but is brightest at the -band, shown in Fig. 13. We calculate a slightly higher magnification factor of compared to from Wardlow et al. (2013), but is consistent in the sub-mm ( Bussmann et al., 2013). This is likely due to the background galaxy being located outside, near the central caustic, which is a region with a steep magnification gradient (Hezaveh et al., 2012). A slight positional offset between the two lens models could then cause a significant change in magnification value.
HFLS02 (Grade A3): This object was included in the supplementary sample of Wardlow et al. (2013). The HST imaging shows an asymmetric Einstein ring lens morphology that suffers blending with the foreground lens. The residual image shows areas of under-subtraction, which could be either due to the presence of substructure in the source plane or left-over emission from the foreground lens. This is also a rare case in which the background source has a larger angular size than the foreground lens.
HECDFS05 (Grade A4): Subtracting the foreground lens emission reveals a counter-image () east of the foreground lens, exhibiting a double configuration. The residual image shows an under-subtracted region to the south of the foreground lens, which could be an arc. However, the low signal to noise feature is not reproduced in the lens modeling and may not be part of the lensed SMG. The source plane reconstruction shows a strongly magnified (), compact (), spherical () galaxy.
HECDFS02 (Grade A4): This source was discussed in Wardlow et al. (2013) and we present an updated lens model in this paper. The HST image shows an arc with two knots north-east of the foreground lens. We detect a counter-image at after subtracting the foreground lens. the best-fit lens model contains two background sources of similar size (), with their centroids separated by . The SPIRE colors suggest a redshift of 2.4, which corresponds to two kpc objects separated by kpc. Both background sources are distorted by the lensing galaxy to produce a double configuration in the image plane, where the fainter counter-image of both sources are in the same region and blended in our data. Leaving the ellipticity as a free parameter in the two-component model consistently caused it to converge to zero ( corresponds to circular symmetry), which is the lower limit, so we fix this parameter to this value in our best-fit model. The background source is reminiscent of merger-like systems presented in figure 2 of Chapman et al. (2003). A single-component model gives a slightly worse fit (), which yields a mass profile that is significantly elongated () in contrast to the rounder light profile () and a cusp configuration similar to HFLS08.
5. Results and Discussion
5.1. Differential Lensing and Source Sizes
Differential lensing is caused by spatial variations within the background galaxy, which, if they have different colors or SEDs, effectively corresponds to different wavelength regimes. This effect is more pronounced in galaxy-galaxy lensing than cluster lenses because of the steeper gradients of the magnification factors mapped onto the source plane. Recent simulations predict the effect of differential lensing in galaxy-galaxy SMG systems (Hezaveh et al., 2012; Serjeant, 2012), but few observations studies have successfully measured it (Gavazzi et al., 2011; Fu et al., 2012; Dye et al., 2014). In order to measure the effects of differential lensing, a consistent mass profile to describe the foreground galaxy must be applied on lens modeling multi-wavelength data sets of the same background source. Here, we search for evidence of differential lensing by comparing the sub-millimeter lens models (from Bussmann et al. 2013) with our near-IR lens models. Figure 5 compares with for the systems in our sample that are also in Bussmann et al. (2013), where we show both our best-fit near-IR magnifications, and the values calculated using the same foreground lens parameters from sub-mm data. To verify that the difference in lens modeling methods between the near-IR and the sub-mm is not a dominant source of error, we also model sub-mm data from Bussmann et al. (2013) and are able to recover consistent magnifications values. The results of applying sub-mm foreground lens parameters on near-IR data are summarized in Fig. 5 and Table 7. For comparison, we also show the lensed SMGs with both near-IR and sub-mm magnification measurements from Dye et al. (2014), Fu et al. (2012), Gavazzi et al. (2011), and Bussmann et al. (2013)
Lensing magnification values are generally negatively correlated to intrinsic sizes of the lensed background source. Therefore, Fig. 5 could suggest that the near-IR emission regions in lensed SMGs are larger than sub-mm emission regions in the source plane. Physically, this could imply that the lensed dusty star-forming regions have clumpier morphologies than the older stellar distribution. We further explore this, by showing in Fig. 6 the circularized effective radius (