Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). I. Automatic search for galaxy-scale strong lenses

TL;DR

This paper presents a comprehensive survey for galaxy-scale strong gravitational lenses using HSC imaging, developing and comparing three methods, and identifying numerous lens candidates with high potential for future discoveries.

Contribution

It introduces a new arc-finding algorithm, compares it with existing methods, and demonstrates their combined effectiveness in identifying strong lenses in large survey data.

Findings

15 definite lenses identified

36 highly probable lenses identified

282 possible lenses identified

Abstract

The Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) is an excellent survey for the search for strong lenses, thanks to its area, image quality and depth. We use three different methods to look for lenses among 43,000 luminous red galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS) sample with photometry from the S16A internal data release of the HSC SSP. The first method is a newly developed algorithm, named YATTALENS, which looks for arc-like features around massive galaxies and then estimates the likelihood of an object being a lens by performing a lens model fit. The second method, CHITAH, is a modeling-based algorithm originally developed to look for lensed quasars. The third method makes use of spectroscopic data to look for emission lines from objects at a different redshift from that of the main galaxy. We find 15 definite lenses, 36 highly probable lenses and 282 possible lenses. Among the three methods, YATTALENS, which was developed specifically for this problem, performs best in terms of both completeness and purity. Nevertheless five highly probable lenses were missed by YATTALENS but found by the other two methods, indicating that the three methods are highly complementary. Based on these numbers we expect to find $\sim$300 definite or probable lenses by the end of the HSC SSP.

Equations

$$I(r)=I_{0}\left\{\begin{array}[]{ll}\exp{\{-(r-r_{0})/h_{o}\}}&\rm{for}\,r>r_{0}\\ \exp{\{-(r_{0}-r)/h_{i}\}}&\rm{for}\,r<r_{0}\end{array}\right.$$

$$r^2\equiv q{x}^2+y^2/q,$$

$${\chi }^2=\sum _i\frac{(m_i-d_i{)}^2}{{\sigma }_i^2},$$

$${\chi }_{\mathrm{src}}^2=\sum _k\frac{|{\mathbf{r}}_k-{\mathbf{r}}_{\mathrm{model}}{|}^2}{{\sigma }_{\mathrm{image}}^2/{\mu }_k},$$

$${\mathbf{r}}_{\mathrm{model}}=\frac{\sum _k\sqrt{{\mu }_k}{\mathbf{r}}_k}{\sum _k\sqrt{{\mu }_k}}$$

$${\chi }_{\mathrm{c}}^2=\frac{|{\mathbf{x}}_{\mathrm{model}}-{\mathbf{x}}_{\mathrm{c}}{|}^2}{{\sigma }_{\mathrm{c}}^2},$$

$${\chi }_{\mathrm{res}}^2=\sum _{i,j}\frac{[Q(i,j)-Q^{\mathrm{P}}(i,j){]}^2}{var(i,j)},$$

Full text

1 Introduction

Strong gravitational lensing is a very powerful diagnostic tool for the study of the mass distribution in the Universe. Strong lensing by galaxies has been used to study a variety of topics in both galaxy evolution and cosmology. These include properties of the lens galaxies themselves, such as their density profile ([Treu & Koopmans (2002)], [Koopmans & Treu (2003)]) and its evolution (Ruff et al., 2011; Bolton et al., 2012a; Sonnenfeld et al., 2013b), the distribution of satellites (More et al., 2009; Vegetti et al., 2012; Nierenberg et al., 2014; Hezaveh et al., 2016), the stellar initial mass function (IMF, Treu et al. (2010), Sonnenfeld et al. (2012), Barnabè et al. (2013), Oguri et al. (2014), Schechter et al. (2014)) or the mass of the central black hole (More et al., 2008; Wong et al., 2015; Tamura et al., 2015). In addition, galaxy-scale lenses have been used to study the properties of the lensed background source (Sluse et al., 2012; Jones et al., 2013; Oldham et al., 2017) or for the measurement of cosmological parameters (Suyu et al., 2013; Collett & Auger, 2014; Suyu et al., 2017; Wong et al., 2017; Bonvin et al., 2017).

The number of currently known galaxy-scale strong lenses is a few hundred. While this number has allowed us to constrain some average properties of galaxy structure, such as the mean density profile of massive early-type galaxies (ETGs, Koopmans et al. (2006)), we are still limited by statistics once we divide the sample in subsets of different lens properties. One example is the redshift distribution: the vast majority of known lenses are at a redshift below $z=0.5$, drastically limiting our ability to constrain the evolution of the internal structure of ETGs (Sonnenfeld et al., 2015) beyond that point in cosmic history. Since galaxies are complex systems, it is important to collect lensing measurements for objects covering as wide a range in parameter space as possible.

The most straightforward way to look for gravitational lenses is to explore a large area of sky with sub-arcsecond resolution imaging. A successful example of such an effort is the Strong Lensing Legacy Survey (SL2S, Cabanac et al. (2007)). SL2S was based on the CFHT Legacy Survey (CFHTLS) data, consisting of 170 deg2 with a typical $i-$band seeing of $0.7^{\prime\prime}$. CFHTLS data was scanned both with automatic lens finding algorithms and with the contribution from citizen scientists, leading to the discovery of an order of a hundred highly probable lenses (More et al., 2012; Sonnenfeld et al., 2013a; More et al., 2016).

The Hyper Suprime-Cam Subaru Strategic Program (HSC SSP, Aihara et al. (2017)) provides a natural extension of the SL2S. With its planned 1,400 deg2 coverage in five bands, $0.6^{\prime\prime}$ seeing and $26.2$ mag depth in $i$-band, it is an excellent survey for the purpose of finding new strong lenses. In this work we apply three different lens finding methods to a sample of 43,000 massive galaxies selected from the Baryon Oscillation Spectroscopic Survey (BOSS, Schlegel et al. (2009), Dawson et al. (2013)) of the Sloan Digital Sky Survey III (SDSS-III, Eisenstein et al. (2011)) with imaging data from the S16A internal data release of the HSC SSP covering $\sim 450$ deg2 in five bands. Two of the lens finding methods are existing algorithms, while one was developed specifically for this study. The goal of this study is to explore the potential of HSC data for lens finding purposes, as well as to test the capabilities and limitations of different lens finding algorithms. We found $15$ new definite lenses and $36$ highly probable ones.

These 51 newly found lenses and lens candidates form the first sample of the Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). Since the parent sample of targets used for the search consists of massive galaxies, we refer to the corresponding sample of lenses as the SuGOHI galaxy-scale lens sample, or SuGOHI-g. In future works we will present a new sample of lenses obtained by looking at clusters of galaxies (SuGOHI-c, More et al. in prep.) as well as a sample of lensed quasars (SuGOHI-q, Chan et al. in prep.).

This paper is organized as follows. In Section 2 we present the current HSC SSP data and our target selection based on BOSS. In Section 3 we introduce our new lens finding algorithm. In Section 4 and Section 5 we describe two other lens finding methods used. In Section 6 we show the sample of newly found lenses. In Section 7 we discuss the relative performances of the three lens finders and the properties of the new lenses. We conclude in Section 8. All images are oriented with North up and East left.

2 The Data

2.1 HSC photometry

HSC (Miyazaki et al., 2012) is a 1.5 deg field of view optical camera recently installed on the Subaru Telescope. The HSC SSP survey (HSC survey, from here on) is expected to cover a 1,400 deg2 area in five bands ($g$, $r$, $i$, $z$ and $y$) to an $i$-band depth of 26.2 by its completion (see Aihara et al. (2017) for more details about the survey). We use photometric data from the S16A data release, which covers $442$ deg2 in all five bands, 178 deg2 of which to the target depth. The data is processed with the reduction pipeline hscPipe (Bosch et al. in prep.), a version of the Large Synoptic Survey Telescope stack (Ivezic et al., 2008; Axelrod et al., 2010; Jurić et al., 2015). The median seeing is $0.6^{\prime\prime}$ in $i$-band and $0.8^{\prime\prime}$ in $g$-band. The pixel scale of HSC is $0.168^{\prime\prime}$. Although data from the S16A release is not public at the time of writing of this paper, about half of the lens candidates presented in this work are also visible in the public data release 1 (PDR1, Aihara et al. (2017)).

Among the patches of sky imaged by HSC, there are three of the CFHTLS fields. This is important for the development and test of our lens finder because a large number of known lenses have been discovered in CFHTLS data.

2.2 BOSS spectroscopy and target selection

Our strong lens search is lens-based: we select objects with properties typical of lens galaxies and then look for the presence of lensed background sources. A lens-based search gives us the advantage of a better control over the selection function of lenses, with the drawback of a loss in completeness. We select lens galaxy candidates from luminous red galaxies (LRGs) in BOSS. The BOSS survey consists of two subsamples of LRGs: the LOWZ and CMASS samples. The main difference between the two samples is mostly the redshift distribution: LOWZ galaxies are mostly at $z<0.4$ while CMASS galaxies are mostly in the range $0.4<z<0.7$. The number of BOSS galaxies with photometry in all five bands the 2016A data release of HSC is $\sim 43,000$, of which $\sim 9,000$ from LOWZ and $\sim 34,000$ from CMASS.

There are two reasons for selecting lens galaxy candidates from the BOSS survey. Firstly, BOSS targeted the high mass end of the galaxy population. Since the strong lensing cross section increases with lens mass, more massive galaxies are more likely to be lenses. Secondly, optical spectroscopy data from BOSS allows us to look for signatures from strongly lensed star forming galaxies in the form of emission lines at a different redshift from the lens. The detection of emission lines from the background galaxy can add crucial information for the classification of a lens candidate. Moreover, a spectroscopic measurement of the redshift of both the lens and source galaxy allows us to convert angular measurements of the Einstein radius into mass measurements.

3 A new lens search method

We developed a new lens finding algorithm, named YattaLens. The algorithm consists of several steps, each described in detail below. The basic idea can be summarized in two key points: 1) YattaLens looks for arc-like features around massive galaxies and 2) fits simple lens models to these arcs to assess the likelihood of them being lensed galaxies. YattaLens combines in a novel way the key features of arc detection-based lens finding algorithms, such as Arcfinder (Alard, 2006; More et al., 2012) or Ringfinder (Gavazzi et al., 2014), and modeling-based algorithms (Marshall et al., 2009; Chan et al., 2015).

There are several challenges in the search for galaxy-scale lenses in ground-based imaging data. First of all, the Einstein radius (roughly the mean distance of lensed images from the center of the lens) of typical lenses is on the order of the half-light radius. This means that lensed images are often blended with the surface brightness of the foreground galaxy, making their detection more complicated. Secondly, as we will show later, many non-lenses exhibit arc-like features due to the presence of spiral arms or tangentially elongated star forming regions, increasing the risk of false positive detection. Thirdly, lens galaxies are often surrounded by satellites, companions, or unrelated objects in close proximity on the line of sight. This complicates the identification of lensed images. YattaLens is designed to tackle these challenges.

3.1 Lens Light subtraction

The first step in the search for lensed arcs consists of removing the contribution of the candidate lens galaxy from the image, to facilitate the detection of lensed images. We do this by fitting an elliptical de Vaucouleurs surface brightness profile (de Vaucouleurs, 1948) to the $i$-band data in a small ($3^{\prime\prime}$ radius) region around the center of the galaxy. We choose the $i$-band for two reasons: 1) the image quality of HSC data is best in this band, because of the requirement of using $i$-band images for weak lensing analysis, the main science driver of the survey, and 2) we expect the lens galaxy to outshine lensed background galaxies at this wavelength, since typical lens systems consist of a massive red galaxy in the foreground and a blue star-forming galaxy in the background.

This step is run for all galaxies in the parent sample, therefore it is important that it is performed in the shortest time possible. For this reason we describe the light distribution of the lens with a de Vaucouleurs profile, which provides a good descrption of the surface brightness of typical massive galaxies while having a relatively small number of free parameters. In a later step, involving only objects with potential arcs around them, the more general Sérsic profile is used. The values of the parameters of the best-fit model are found by running a short Markov Chain Monte Carlo (MCMC) with the Python package emcee (Foreman-Mackey et al., 2013), which ensures an efficient sampling of the parameter space.

We then take the best fit de Vaucouleurs model and subtract a point spread function (PSF) convolved, rescaled version of it from the $i$-band and all other bands used in the analysis (in our case the $g$-band). With this step, we are implicitly assuming that there are no color gradients in the lens galaxy.

Examples of lens-subtracted images are shown in the second column of Figure 1.

3.2 Lensed arc identification

We use SExtractor (Bertin & Arnouts, 1996) to look for objects in the lens-subtracted $g$-band image. By using the $g$-band we expect to detect lensed sources up to redshift $z\sim 4$ (Ono et al., 2017). For each object we consider their position relative to the lens light centroid, their axis ratio and orientation, and the size of their footprint.

We then apply the following series of conditions to determine whether an object can be a lensed arc or not.

A distance from the lens centroid between 3 and 30 pixels ($0.50^{\prime\prime}<R<5.04^{\prime\prime}$) 2. 2.

A minimum ratio between the major and minor axis of 1.4 3. 3.

A maximum difference of 30 degrees between the position angle of the major axis of the object and the tangential to the circle centered on the lens and passing through the object centroid. 4. 4.

A minimum angular aperture, defined as the angle subtended by the object from the lens centroid, of 25 degrees. 5. 5.

A footprint size between 20 and 500 pixels.

The minimum distance requirement in condition 1, as well as the minimum size requirement in condition 5, makes sure that the candidate arc is not just a residual from a non-perfect subtraction of the lens light. The maximum distance constraint is applied because we do not expect galaxy scale lenses to have Einstein radii larger than $5^{\prime\prime}$. Although there are lenses with larger Einstein radius, we typically refer to these as group-scale or cluster-scale lenses. Conditions 2 and 3 are applied to only select tangentially elongated objects. We add condition 4 to select objects that are elongated not just in terms of axis ratio, but that also describe a sizeable arc around the lens in angular terms. This conditions eliminates small objects far away from the lens that happen to pass the orientation and axis ratio requirement given by condition 2 and 3 but are clearly not strongly lensed. Finally, we add the maximum size requirement in condition 5 to reject catastrophic failures in the object detection process. Objects that pass all five conditions are kept as potential arcs.

3.3 Foreground model

If the object detection process described above returned at least one arc candidate, we proceed with a more accurate fit of the lens light and by modeling potential foreground objects. We turn back to the $i$-band data and fit a Sérsic profile (Sérsic, 1968) to the surface brightness distribution of the main galaxy, this time masking out any objects detected in the $g$-band image by SExtractor. We then go through non-arc-like objects detected in the $i$-band around the lens, one by one in order of decreasing $i$-band flux, and fit each one with a Sérsic profile. Each time a new object is fit, the structural parameters of the lens and previously fitted objects (i.e. centroid, effective radius, etc.) are kept fixed, as well as the relative $i$-band amplitude between the lens and any other object fit up to that point. Only the overall amplitude of all previously fit objects is varied. This prescription is adopted to reduce computation time. Only objects within $1.3$ times the distance of the farthest arc candidate of the lens are modeled. Objects farther away are simply masked out. Foreground objects other than the main galaxy are treated as massless: their constribution to the lens model, to be described in subsection 3.5, is ignored.

Although most known lenses do not have foreground objects other than the lens galaxy itself in the proximity of lensed images, accounting for the presence of foregrounds is important for the rejection of false positive candidates. An example of foreground object modeling is shown in the first row of Figure 1. After the lens light subtraction step, a galaxy is detected North of the lens and is then modeled with a Sérsic profile. The model of the lens and foreground object, together with a model for the lensed source to be described in subsection 3.5, is shown in the fourth column.

Up to this point, no color information has been used. Among the objects treated as foreground, there might be counter-images of the main arc. In the next subsection we will illustrate how we can classify images based on their color.

3.4 Multiple image set candidates

At this stage of the lens finding process, we have candidate arcs and a model for the light distribution of the lens galaxy and surrounding objects. These objects can be either foregrounds or multiple images of the arcs. We use color and position information to distinguish between the two possibilities.

First of all, we apply a color selection to the arc candidates themselves. Since we expect lensed galaxies to be relatively blue we require a $g-i$ color smaller than $2.0$. Although a $g-i$ color of $2.0$ is not a particularly strong limit, it is sufficient to eliminate a frequent source of contaminants: satellite galaxies with major axis oriented along the tangential direction. In principle, this color selection criterion could have been applied before the foreground object modeling step, in the interest of computation time. However, having an accurate model for the system is important to measure accurate colors and avoid rejecting good lenses for which the light from the arc happens to be contaminated by a foreground object. Fluxes in $i$ and $g$ band are measured by summing over pixels in the $g$-band footprint as determined by SExtractor. Although in principle we should match the PSF of the two bands for an accurate color measurement, the effect of differing PSFs is small with respect to the required precision. More important is the effect of modeling systematics from the subtraction of the light from the lens or foreground objects. To take this into account we add in quadrature to the statistical uncertainty on the flux of individual pixels a systematic uncertainty equal to 20% of the contribution from the best fit model of all light components.

We go through the blue (according to our color cut) arcs and create sets of arcs and non-arc objects with consistent $g-i$ color, which we interpret as candidate sets of multiple images of the same source. We require colors of different objects to be within 2$\sigma$ of each other in order to consider them consistent. The minimal multiple image set consists of only one arc. If other candidate arcs are present, and if they have consistent $g-i$ color, they are added to the set. An example of such a case is shown in the second row of Figure 1: two objects satisfying the definition of arc given in subsection 3.2 are found by running SExtractor on the lens-subtracted image, shown in bright green in the segmentation map panel (third column). Since they have consistent colors, they are interpreted as multiple images of the same source.

If, on the contrary, there are arc-like objects with a different color than the arc defining the set, and if they are within 1.3 times the distance of the farthest arc from the lens, they are classified as foreground and are fitted with a Sérsic profile with the same procedure described in subsection 3.3. If these arc-like objects are at a farther distance from the lens, they are simply masked out. An example of this process is shown in the third and fourth row of Figure 1. For this lens candidate, our algorithm led to the detection of two potential arcs: an extended blue arc to the North-West of the main galaxy and a redder object to the East. Both objects could be lensed sources, but since they have different colors they cannot be multiple images of the same object. Then, two different interpretations are possible. If the bluer, bigger arc is the lensed source, then the red object must be a foreground. Since this object is too far away from the lens galaxy to affect any further analysis, it is simply masked out. This scenario is shown in the third row: the candidate arc is shown in bright green and objects masked out are shown in red. In the fourth row, the second interpretation is illustrated: the redder object is considered to be the lensed source, and the bluer elongated feature is modeled as a foreground (marked in white in the segmentation map plot in addition to the main lens galaxy foreground).

Finally, we repeat the same procedure for non-arc-like objects: those with color consistent with the candidate arc(s) are assigned to a multiple image set. Objects with a different color are either modeled as foregrounds or masked out, depending on their distance from the lens galaxy. In the same system discussed above, a faint object is detected South of the lens. This is masked out in the first interpretation of the image configuration (third row of Figure 1), but is instead modeled as a foreground in the second interpretation (fourth row), because its distance from the lens is within 1.3 times that of the main arc.

In the fifth row we show an instance of a system in which a non-arc-like object with color consistent to a candidate arc is found. The object is represented in dark green in the segmentation map plot. This object was modeled as a foreground in the previous step. However, since it is now treated as a counter-image of the arc, it is removed from the model of the foregrounds.

3.5 Lens model

We proceed to fit a lens model to each set of arcs and counter-images. The lens mass model consists of a singular isothermal ellipsoid (SIE), while the source surface brightness distribution is modeled with a circularly symmetric exponential profile. The centroid of the lens mass distribution is kept fixed to the value of the lens light centroid. The free parameters of the model then are: lens angular Einstein radius $\theta_{\mathrm{E}}$, axis ratio $q$, position angle PA, source position $(s_{x},s_{y})$, source effective radius $s_{e}$, as well as the amplitude of the source, lens and foreground surface brightness components. Foreground objects are treated as massless: only their surface brightness profile is modeled.

This is clearly a simplified model compared to what is usually needed to accurately describe strong lens systems, especially with respect to the source surface brightness distribution, a choice that is motivated by the computational time required to fit the data. However, as we will show later, it is not the absolute quality of a lens model that determines the outcome of the analysis by YattaLens but rather its relative quality compared to alternative non-lens models.

We use a modified version of the lens modeling code developed by Auger et al. (2011) to find a maximum-likelihood fit to the data. We explore the parameter space defined by the six non-linear parameters $\theta_{\mathrm{E}}$, $q$, PA, $s_{x}$, $s_{y}$ and $s_{e}$ with an MCMC, where at each step of the chain we optimize for the amplitudes of the surface brightness components. As for the preliminary lens light subtraction step we use emcee to sample the posterior probability distribution of the model parameters, assuming flat priors on all of them.

This step of the algorithm is particularly slow. In order to minimize the cost in terms of time, we only run a relatively short chain, without ensuring that the MCMC has converged and that the true maximum likelihood model has been found. In order to maximize the chances of obtaining a good fit it is then important to find a reasonable starting solution. We use the following prescription to define our starting model. We set the initial mass orientation and axis ratio equal to that of the light distribution. Then, in case only one arc is present, we assume that the Einstein radius is equal to $0.7$ times the distance of the arc from the lens. In case there are two or more arcs, the Einstein radius is set to the mean distance of the arcs from the lens. Once the lens mass parameters are set, the starting position of the source is found by mapping each arc centroid to the source plane and taking the mean of their position. We use the $g$-band image to perform the fit. Although the HSC $i$-band data has better image quality, we use the $g$-band to minimize the contamination of the lensed images from the light of the lens galaxy and of foreground objects, which are typically redder than most lensed galaxies.

We then need to assess whether the best-fit lens model is a good description of the data. In principle, we could use the $\chi^{2}$ to quantify the goodness-of-fit. In practice, with our simple model it is almost impossible to fit the image of a lens down to noise level, let alone doing it automatically without human intervention. Therefore, instead of considering absolute values of the $\chi^{2}$, which have little meaning in this context, we compare the lens model $\chi^{2}$ with that obtained by fitting alternative models, described below. In principle, Bayesian evidence can be used to obtain a more accurate comparison between the different models. In practice, a simple $\chi^{2}$ analysis is sufficient for our purpose and is computationally faster than measuring the evidence.

3.6 Non-lens models

The lens candidates that have made it thus far are systems with a relatively blue, tangentially elongated object close to a massive galaxy. While some of these objects are indeed lenses, most of them are not. The two main sources of contaminants are 1) spiral arms (we will use the term spiral arm in a broad sense to indicate a mostly tangentially elongated star forming region) and 2) foreground galaxies with high ellipticity. The non-lens models that we compare against the lens model are designed to describe these two classes of systems.

The first model we consider is a “ring galaxy” model. Its surface brightness profile is defined as follows

[TABLE]

Here $r$ is the circularized radius of elliptical isophotes,

[TABLE]

and $r_{0}$, $h_{i}$ and $h_{o}$ are free parameters describing the radial position of the peak in the surface brightness distribution and an inner and outer scale radius, respectively. The other free parameters of the model are the ellipticity $q$ and the position angle of the major axis, $\rm{PA}$.

Different realizations of a ring profile are shown in the seventh column of Figure 1. While our lens model cannot produce radially elongated images, due to the upper limit on source size and the choice of a singular isothermal profile, the ring model has the ability of describing relatively large regions with approximately constant surface brightness. For example, for very large values of the inner scale radius $r_{i}$, the ring profiles reduces to a disk with approximately constant surface brightness within $r_{0}$. Although hardly any galaxy can be well described by this surface brightness profile, the ring model provides a better fit compared to a lens model for most spiral galaxies that happen to be detected by the arc-finding step described in subsection 3.2, because it can provide a very rough description of their disk. An example of a galaxy with a candidate arc for which a ring model gives a better fit compared to a lens model is shown in Figure 2.

When fitted to an actual lens, the ring model can hardly provide a reasonable fit. This is because the ring model is elliptically symmetric by construction, while the image configuration of strong lenses is not. The only case in which a ring profile could mimic a lens would be that of a perfectly circular Einstein ring. However, a perfect Einstein ring requires both a perfectly circular mass distribution and a perfect alignment between lens and source, an extremely rare circumstance.

The second non-lens model that we fit is a Sérsic profile with disky/boxy isophotes. Many arc candidates picked by the algorithm are just foreground objects with relatively high ellipticity that happen to be tangentially aligned with respect to the lens. A Sérsic profile provides a better fit with respect to a lens model for most of these systems. One such example is shown in Figure 2, while another instance appears in the fourth row of Figure 1, where the object interpreted as an arc is better fit by a Sérsic component.

In conclusion, in the analysis of a system with arc candidates, YattaLens first fits a lens model to the $g$-band image and measures the $\chi^{2}$ of the best-fit model. The $\chi^{2}$ is defined as

[TABLE]

where $m_{i}$, $d_{i}$ and $\sigma_{i}$ are the model flux, measured flux and measurement uncertainty of pixel $i$ and the sum extends over all pixels within $5^{\prime\prime}$ of the image center, excluding masked out foreground objects. The $\chi^{2}$ from the lens model is then compared to the values obtained for the best-fitting ring and Sérsic models. If the lens model $\chi^{2}$ is the lowest the candidate is selected. This procedure is carried out for each set of multiple image candidates (i.e. for each image configuration scenario). If in each scenario the lens model provides a worse fit compared to a non-lens model, the candidate is discarded.

3.7 A summary of the algorithm

We have described in detail all the steps taken by YattaLens to look for strong lenses. Let us summarize the steps of the algorithm.

Given a massive galaxy, YattaLens fits a de Vaucouleurs profile to its $i$-band surface brightness profile, then subtracts the best fit model from the $g$-band image. This step takes a few seconds on a standard machine. 2. 2.

Runs SExtractor on the lens-subtracted $g$-band image to look for tangentially elongated objects within $\sim 5^{\prime\prime}$. This step takes a fraction of a second. 3. 3.

If a candidate arc is found, YattaLens proceeds to model any object within a region where potential counter-images of the arc could be, then measures colors of arcs and other objects. This step can take from a few seconds to a few minutes, depending on how many foreground objects are present. 4. 4.

If the candidate arc is bluer than $g-i=2$, YattaLens makes sets of arcs and images of consistent color. For each multiple image set, any other object with inconsistent color is either modeled as a foreground object or masked out, depending on the ratio between its distance from the lens and the distance of the farthest candidate arc from the lens. 5. 5.

For each multiple image set, the $g$-band image is fit with a lens model, a ring model and a Sérsic model. Each model includes a model of the lens galaxy and possible foreground objects, described as the sum of Sérsic profiles with fixed relative amplitude. It takes about a minute to run this modeling step. 6. 6.

If the lens model provides a better fit, in terms of $\chi^{2}$, with respect to both the ring and the Sérsic model, the candidate is selected. Otherwise it is rejected.

In the next subsection we will show how YattaLens performs on a sample of known lenses.

3.8 Tests on known lenses

The YattaLens algorithm has been tested on a sample of known lenses that lie in the S16A data release of HSC. These are 16 galaxy-scale lenses from the SL2S survey (SL2SJ021247$-$055552, SL2SJ021411$-$040502, SL2SJ021737$-$051329, SL2SJ022357$-$065142, SL2SJ022511$-$045433, SL2SJ022610$-$042011, SL2SJ022648$-$040610, SL2SJ022708$-$065445, SL2SJ023251$-$040823, SL2SJ023307$-$043838, SL2SJ090407$-$005952, SL2SJ142003$+$523137, SL2SJ220329$+$020518, SL2SJ220506$+$014703, SL2SJ221326$-$000946, SL2SJ222148$+$011542, Gavazzi et al. (2012), Sonnenfeld et al. (2013a), Sonnenfeld et al. (2015)), plus the double source plane lens HSCJ142449$-$005322 also known as the “Eye of Horus” (Tanaka et al., 2016).

YattaLens was able to identify correctly 15 lenses out of 17. The two systems missed by YattaLens are SL2SJ022357$-$065142 and SL2SJ022708$-$065445. Both were missed during the arc detection step, the arcs being too faint to be picked out by SExtractor, which we run with a detection threshold of $2\sigma$ above the background. The images of these two lenses, which were originally discovered using Ringfinder  are shown in Figure 3.

In Figure 4 we show YattaLens’ analysis on the double source plane lens the Eye of Horus. Double source plane lenses are very interesting objects because they offer more constraints with respect to typical lenses, and can be used for detailed studies of the mass distribution of the foreground galaxy (e.g. Sonnenfeld et al. (2012)), or to infer cosmological parameters (Gavazzi et al., 2008; Collett & Auger, 2014; Schneider, 2014). Since they are also very rare, it is extremely important that lens finding algorithms do recognize them as lenses. This can be challenging for automatic algorithms because the presence of arcs from more than one source complicate their morphology. Therefore, we made sure when designing YattaLens that it could properly classify the Eye of Horus, the only spectroscopically confirmed double source plane lens in the HSC survey, as a lens.

Since most of the SL2S lenses in HSC are recovered, we can deduce that the completeness of YattaLens is comparable to that of Ringfinder. We cannot draw more quantitative statements on completeness at this stage because 1) the SL2S lenses have been used to optimize the parameters of the algorithm and 2) the SL2S sample is not a complete sample in the first place, meaning that there could be lenses missed by Ringfinder that YattaLens would be able to identify. In order to robustly determine the completeness of a lens search with YattaLens, we need to run the algorithm on realistic simulation of a large set of lenses. This is left for future work.

4 CHITAH

Chitah (Chan et al., 2015) is a lens hunter in imaging surveys, which is originally developed for lensed quasars, based on the configuration of lensed images. Not only lensed quasars, but lensed galaxies can also be captured when Chitah identifies lensed images within a lensed arc. Briefly, the procedure of Chitah is as follows:

choose two image cutouts, one from bluer bands (g/r) and one from redder bands (z/y) which have sharper PSFs. 2. 2.

match PSFs in the two selected bands. 3. 3.

disentangle lens light and lensed arc image according to color information, producing a “lens” image and a “lensed arc” image. 4. 4.

identify lens center and lensed image positions, masking out the region within $0.5^{\prime\prime}$ in radius from the lens center in the lensed arc image to prevent misidentifying lensed image positions near the lens center due to imperfect lens light separation. 5. 5.

model the lensed image configuration with an SIE lens mass distribution.

The outputs of the model are the best-fit parameters of the SIE: the Einstein radius ($\theta_{\rm E}$), the axis ratio ($q$), the position angle (PA), the lens center, and the $\chi^{2}_{\rm src}$ on the source plane, which is defined as

[TABLE]

where ${\bf r}_{k}$ is the respective source position mapped from the position of lensed image $k$ identified in the lensed arc image, $\mu_{k}$ is the magnification at the position of lensed image $k$, $\sigma_{\mathrm{image}}$ is chosen to be the pixel scale of HSC ($0.168^{\prime\prime}$) as an estimate of the uncertainty, and ${\bf r}_{\mathrm{model}}$ is the modeled source position evaluated as a weighted mean of ${\bf r}_{k}$,

[TABLE]

(Oguri, 2010). Here the index $k$ runs from 1 to 4 for quad systems. We also use the lens center from the light profile as a prior to constrain the center of the SIE lens mass model. Therefore, we define the $\chi_{\mathrm{c}}^{2}$ as

[TABLE]

where ${\bf x}_{\mathrm{c}}$ is the lens center from the light profile, and ${\bf x}_{\mathrm{model}}$ is the the lens center of the SIE model, We choose $\sigma_{\mathrm{c}}$ to be the same as $\sigma_{\mathrm{image}}$. We further take into account the residuals of the fit to the “lensed arc” image from Chitah. The difference between the lensed arc image $Q(i,j)$ and the predicted image $Q^{\rm P}(i,j)$ is defined as,

[TABLE]

where $i=1...N_{\rm x}$ and $j=1...N_{\rm y}$ are the pixel indices in the image cutout of dimensions $N_{\rm x}\times N_{\rm y}$, and $var(i,j)$ is the pixel uncertainty in $Q(i,j)$. Each image cutout is $7\arcsec\times 7\arcsec$.

The criteria of classification of lens candidates are $\chi^{2}_{\rm src}+\chi_{\mathrm{c}}^{2}<2\theta_{\rm E}$, where $\theta_{\rm E}$ is measured in arcsec, and $\chi_{\mathrm{res}}^{2}<100$. The former criterion allows Chitah to detect lens candidates covering a wide range of $\theta_{\rm E}$, since typically $\chi^{2}_{\rm src}$ scales with $\theta_{\rm E}$ and our tests with mock systems in Chan et al. (2015) show that $\chi^{2}_{\rm src}\lesssim 4$ yields a low false positive rate of $<3\%$. The latter criterion allows us to further eliminate false positives. The lens candidates are selected within $0.3\arcsec<\theta_{\rm E}<4\arcsec$.

5 Spectroscopic search

Another powerful and efficient lens search method is the spectroscopic selection technique developed by Bolton et al. (2004). This spectroscopic selection technique has lead to discoveries of almost 200 strong lenses in several dedicated lens surveys including the Sloan Lens ACS Survey (SLACS, Bolton et al. (2008)), the Sloan WFC Edge-on Late-type Lens Survey (SWELLS, Treu et al. (2011)), the SLACS for the Masses Survey (S4TM Shu et al. (2015)), the BOSS Emission-Line Lens Survey (BELLS, Brownstein et al. (2012)), and the BELLS for GAlaxy-Ly$\alpha$ EmitteR sYstems Survey (BELLS GALLERY, Shu et al. (2016a), Shu et al. (2016b)). Here we describe briefly the spectroscopic selection algorithm implemented in this work. More technical details can be found in Bolton et al. (2004) and Shu et al. (2016a).

For each observed spectrum, the best-fit galaxy template from the BOSS data reduction pipeline (Bolton et al., 2012b) is subtracted to obtain its residual spectrum. An error-weighted matched-filter search for emission-line features is performed on the residual spectrum. Note that flux errors are rescaled in this step because the BOSS pipeline-reported errors are usually underestimated at wavelengths with strong airglow lines. The rescaling process is detailed in Shu et al. (2016a). Emission-line detections with signal-to-noise ratio (SNR) greater than 4 are retained and referred to as “hits”. In previous lens surveys, galaxies with either multiple hits (SLACS, SWELLS, S4TM, BELLS) or a single hit (BELLS GALLERY) are targeted because they fall into different lens categories. The background sources are star-forming galaxies for multiple-hit systems, and Ly$\alpha$ emitters for single-hit systems. However, as the purpose of this work is to find as many strong lenses as possible, we keep all the targets with at least one hit as lens candidates. Further visual inspections on their HSC images will confirm the lens nature.

6 Results

We ran YattaLens, Chitah, and the spectroscopic search method on a sample of $\sim 43,000$ massive galaxies from the BOSS survey. A first set of $\sim 8000$ objects was used to further optimize YattaLens, in particular to improve its purity, i.e. to reduce the number of false positives. Once the algorithm was stable we applied it to the full sample. YattaLens found $1480$ lens candidates, of which 250 from the LOWZ subsample and 1230 from CMASS. Chitah found 819, while the spectroscopic method found 233. Of these candidates, 118 were common to at least two methods and 3 were found by all three.

Ten of these candidates are known lenses. They are six galaxy scale SL2S lenses (SL2SJ021411$-$040502, SL2SJ021737$-$051329, SL2SJ022346$-$053418, SL2SJ022511$-$045433, SL2SJ023307$-$043838, SL2SJ220506$+$014703), the “Eye of Horus” lens HSCJ142449$-$005321, already discussed in subsection 3.8, as well as three group scale lenses from the Strong Lensing Legacy Survey - ARCS (SARCS) sample (SL2SJ020929$-$064312, SL2SJ021408$-$053530, SL2SJ221418$+$011036, More et al. (2012)). All of these were identified by YattaLens and two of them were found by Chitah as well.

We visually inspected the remaining lens candidates and graded them according to their likelihood of being strong lenses, ${\rm P}_{\mathrm{lens}}$, using the following scheme:

• •

Grade A: definite lenses (${\rm P}_{\mathrm{lens}}>0.997$),

• •

Grade B: probable lenses ($0.5<{\rm P}_{\mathrm{lens}}<0.997$)

• •

Grade C: possible lenses ($0.003<{\rm P}_{\mathrm{lens}}<0.5$)

• •

Grade 0: non lenses (${\rm P}_{\mathrm{lens}}<0.003$)

A first classification was done using the image configuration as the only criterion to establish the likelihood of a candidate of being a lens. Typical aspects that are taken in consideration are: the curvature and orientation of the candidate arc, the presence of counter-images in the opposite position to the main arc with respect to the lens, the presence of spiral arms or a disk component (suggesting that the system is not a lens). Nine people independently graded each candidate, assigning an integer score between 0 and 3 (0 corresponding to Grade 0, 1 to Grade C, 2 to Grade B and 3 to Grade A). A first list of grade A, B and C systems is compiled, taking the average score among the graders, rounded to the nearest integer (i.e. systems with an average score strictly larger than $2.5$ are temporarily labeled as Grade A).

We then visually inspected the spectra of the grade A, B and C candidates with emission line detections, as well as the grade A and B candidates from YattaLens and Chitah, to determine whether these detections are robust and, if so, to measure the redshift of the candidate lensed source. Since we use a relatively low S/N threshold in the emission line detection algorithm, most of the candidate lines could not be confirmed by eye. The few systems with unambiguous line detections showed only one line. Roughly half of these lines showed a double peak profile typical of the [OII] doublet at 3727Å. We measured their redshift based on this interpretation. The remaining lines were all detected at a wavelength bluer than 5100Å. In those cases we assumed the line to be Ly-$\alpha$.

We found eight objects with visually confirmed emission lines from an object at a higher redshift of the source, all of which were already part of the emission line selected sample. We then discussed the grade A, B and C list in light of this additional information. Candidates HSCJ085855$-$010208 and HSCJ141815$+$015832 were upgraded from B to A, while HSCJ144307$-$004056 was upgraded from C to B. In making the final grade A list we added a unanimity requirement: all people taking part in the grading agree on the lens nature of grade A systems.