Survey of gravitationally lensed objects in HSC imaging (SuGOHI) – X. Strong lens finding in the HSC-SSP using convolutional neural networks

ABSTRACT

We apply a novel model based on convolutional neural networks (CNN) to identify gravitationally lensed galaxies in multiband imaging of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Survey. The trained model is applied to a parent sample of 2350 061 galaxies selected from the |$\sim$| 800 deg|$^2$| Wide area of the HSC-SSP Public Data Release 2. The galaxies in HSC Wide are selected based on stringent pre-selection criteria, such as multiband magnitudes, stellar mass, star formation rate, extendedness limit, photometric redshift range, etc. The trained CNN assigns a score from 0 to 1, with 1 representing lenses and 0 representing non-lenses. Initially, the CNN selects a total of 20 241 cutouts with a score greater than 0.9, but this number is subsequently reduced to 1522 cutouts after removing definite non-lenses for further visual inspection. We discover 43 grade A (definite) and 269 grade B (probable) strong lens candidates, of which 97 are completely new. In addition, we also discover 880 grade C (possible) lens candidates, 289 of which are known systems in the literature. We identify 143 candidates from the known systems of grade C that had higher confidence in previous searches. Our model can also recover 285 candidate galaxy-scale lenses from the Survey of Gravitationally lensed Objects in HSC Imaging (SuGOHI), where a single foreground galaxy acts as the deflector. Even though group-scale and cluster-scale lens systems are not included in the training, a sample of 32 SuGOHI-c (i.e. group/cluster-scale systems) lens candidates is retrieved. Our discoveries will be useful for ongoing and planned spectroscopic surveys, such as the Subaru Prime Focus Spectrograph project, to measure lens and source redshifts in order to enable detailed lens modelling.

1 INTRODUCTION

As strong gravitational lensing systems are discovered over large cosmological volume, they are powerful astrophysical tools to refine cosmological models and study the evolution of cosmic large-scale structures. Studies of strong lens systems have been successfully used to probe the total mass distribution (including both baryonic and dark matter) from galaxy (e.g. Koopmans et al. 2006; Auger et al. 2010; Sonnenfeld et al. 2015; Shajib et al. 2021) to group and cluster scales (e.g, Limousin et al. 2009; More et al. 2012; Oguri et al. 2012; Newman et al. 2013; Jauzac et al. 2021; Allingham et al. 2023), constrain dark matter substructures (e.g. Vegetti et al. 2010, 2012; Hezaveh et al. 2016; Inoue et al. 2016; Nierenberg et al. 2017; Gilman et al. 2020; Hsueh et al. 2020; Inoue et al. 2023), and study compact high-redshift objects in detail by overcoming the sensitivity and/or resolution limits of current facilities by exploiting the lensing magnification effect (e.g. Marques-Chaves et al. 2017; More et al. 2017; Jaelani et al. 2020b). Moreover, strongly lensed quasars with time delay measurements can be used to test the cosmological model by constraining cosmological parameters such as the Hubble constant (e.g. Refsdal 1964; Birrer et al. 2020; Wong et al. 2020).

In the last decade, deep learning has led to very good performance on a variety of problems, such as visual recognition, speech recognition, and natural language processing, including the application in astrophysical problems, for example, strong gravitational lensing detection. Among different types of deep neural networks, convolutional neural networks (CNNs) have been most extensively studied. Lecun et al. (1998) published the seminal paper establishing the improved modern framework of CNNs. The CNNs can learn to extract information from large amounts of labelled data without explicitly defining features, making them appealing for a wide range of physical problems where hand-crafted descriptors are typically used to analyse data. It captures the essence of images using translation-invariant sliding window filter matching algorithms. The CNNs have proven extremely efficient as ‘state of the art’ for pattern recognition tasks and have given a strong impetus to image analysis and processing. Recent studies largely demonstrate the ability of supervised CNNs to identify the rare gravitational lenses among large data sets (e.g. Jacobs et al. 2017, 2019; Petrillo et al. 2019; Cañameras et al. 2020; Huang et al. 2021; Li et al. 2021; Zaborowski et al. 2023), extending previous automated algorithms (e.g. Gavazzi et al. 2014) generally with better classification performance (Metcalf et al. 2019).

The Survey of Gravitationally lensed Objects in HSC Imaging (SuGOHI) is an ongoing lens search that aims to discover a large number of strong gravitational lens systems from the large homogeneous data of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). SuGOHI has discovered about 2000 strong gravitational lens candidates at both the galaxy-scale (SuGOHI-g; Sonnenfeld et al. 2018; Wong et al. 2018, 2022; Sonnenfeld et al. 2020 ), and the galaxy group/cluster-scale (SuGOHI-c; Jaelani et al. 2020b), including a number of lensed quasar candidates (SuGOHI-q; Chan et al. 2020, 2023; Jaelani et al. 2021 ). These lenses were discovered using a variety of search techniques, including semi-automated algorithms, visual inspection, and citizen science (see summary in Table 1). In this work, we apply a CNN to identify new strong gravitational lens systems. Cañameras et al. (2021) and Shu et al. (2022) have independently applied machine learning-based lens search algorithms with different networks to the HSC SSP Public Data Release 2 (PDR2) (Aihara et al. 2019) and published lens candidates produced by these searches. SuGOHI lens candidates, specifically galaxy-scale lenses, can be used as test samples because previous searches overlapped the sky area used in this work.

The paper is organized as follows. First, in Section 2, we provide a brief overview of the HSC-SSP PDR2 and the definition of our parent sample. In Section 3, the system of simulated lenses is described. In Section 4, we discuss the networks, training procedures, CNN’s performance, and visual inspection. Section 5 presents new lens candidates. Discussions and conclusions are presented in Section 6. Throughout this paper, we adopt a Hubble constant of |$H_0 = 72$| km  s|$^{-1}$| Mpc|$^{-1}$|⁠, and cosmological density parameters of |$\Omega _{\rm M} = 0.26$| and |$\Omega _{\Lambda } = 0.74$|⁠. The AB system is used for all magnitudes. All images are oriented with North up and East to the left.

2 THE HSC-SSP PDR2

The HSC-SSP Survey is an optical imaging survey conducted with the HSC (Coupon et al. 2018; Furusawa et al. 2018; Huang et al. 2018; Kawanomoto et al. 2018; Komiyama et al. 2018; Miyazaki et al. 2018), a |$1.7\deg ^2$| field-of-view optical camera on the 8.2-m Subaru telescope, which has a pixel scale of 0.168 arcsec pixel^-1. In this work, we use data products from the HSC-SSP PDR2 Wide covering |$\sim$| 800 deg|$^2$| (Aihara et al. 2019) in gri bands out of a final survey area of 1400 deg|$^2$|⁠. The median |$5\sigma$| depths (for point sources) in |$gri$| filters for the PDR2 Wide layer are 26.6, 26.2, and 26.2 mag, while the median seeings are 0.77, 0.76, and 0.58 arcsec, for |$gri$|⁠, respectively. The PDR2 data is processed with hscPipe version 6 (Bosch et al. 2018). Aihara et al. (2019) use a variety of aperture sizes for PDR2 photometric measurements, but a small aperture (e.g. 1.5 arcsec) is recommended to avoid blending with nearby sources. They note that the aperture corrections (Bosch et al. 2018) based on unresolved point sources have been applied to those aperture fluxes, allowing users to obtain meaningful colours. The combination of a large area and observation depth makes the data from the HSC-SSP Survey ideal for discovering new or unusual strong gravitational lenses (e.g. HSC J090429.75-010228.2; Jaelani et al. 2020a).

The photometric redshifts used in this work are determined using the mizuki algorithm (Tanaka 2015). The robustness of the photometric redshifts is a function of galaxy redshift and brightness, and is quantified in terms of |$\Delta z/(1 + z_{\rm ref})$|⁠, where |${\rm {\Delta }}z\equiv | z-{z}_{\rm ref}|$| and |$z_{\rm ref}$| is a reference redshift. The mizuki’s photometric redshifts measurement are most accurate at |$0.2 \lesssim z_{\rm phot}\lesssim 1.5$|⁠. A thorough explanation of mizuki’s application to the HSC-SSP data is presented in Tanaka et al. (2018). Since the HSC-SSP Survey footprint overlaps with the Sloan Digital Sky Survey (SDSS), we collect spectroscopic redshifts, whenever available, from the SDSS Data Release 16 (Ahumada et al. 2020) catalogues.

For our strong lens search, we select to be our parent sample galaxies in PDR2 Wide retrieved from the HSC CAS Search service¹ based on their magnitude limit, stellar mass, and star formation rate. To be more specific, we select objects from tables that satisfy the following criteria:

• for pdr2_wide.forced

  • isprimary is True

  • [grizy]_pixelflags_edge is False

  • [grizy]_pixelflags_interpolatedcenter is False

  • [grizy]_pixelflags_crcenter is False

  • [grizy]_cmodel_flag is False

  • i_extendedness_value > 0.9

  • ([ri]_cmodel_mag|$-$|a_[ri]) < 28.0

  • (z_cmodel_mag|$-$|a_z) < 23.0

• for pdr2_wide.forced2

  • i. [grizy]_sdsscentroid_flag is False

• pdr2_wide.meas

  • j. [grizy]_inputcount_value > 0

• pdr2_wide.masks

  • k. i_mask_pdr2_bright_objectcenter is False

• pdr2_wide.photoz_mizuki

  • l. 0.2 < photoz_median < 1.2

  • m. stellar_mass > 5.0e10

  • n. (sfr/stellar_mass) < 1.0e-10.

We remove objects with saturated pixels and unreliable photometry, as well as probable stars, using criteria 2–11. We concentrate on finding lensed features among a set of galaxies based on the properties that make them possible lenses, as defined by criteria 12–14. The upper redshift and lower stellar mass bounds are a compromise between obtaining a sample of lenses as complete as possible and the need to find lenses with Einstein radius smaller than 1 arcsec. The lower redshift cut is introduced to avoid dealing with galaxies that are too bright for the detection of lensed features, which are typically faint. This query returns a total of 2350 061 unique HSC objects. We use HSC |$gri$| cutouts (64 |$\times$| 64 pixel² corresponding to 10.752|$\times$| 10.752 arcsec², which is sufficient for galaxy-scale lenses) centred on the parent objects, which are retrieved from the PDR2 Image Cutout service²

3 SIMULATED GALAXY-SCALE LENSES

In order to train the network on a large sample of realistic galaxy-scale lenses, we use the simct³ pipeline (detailed in More et al. 2016). With this pipeline, we superpose a set of simulated lensed galaxies on the real image cutouts of massive galaxies from the multiband HSC imaging (see Section 2). This ensures that most of the features and properties in the training images will statistically be similar to the real survey images which will be classified. The methodology of simct is summarized below.

The mass model of the lens galaxies is assumed to follow singular isothermal ellipsoid (SIE, Kormann, Schneider & Bartelmann 1994) and the contribution from an external shear is also included in the model (see Table 2). We start with the position, photometric magnitudes, photometric redshifts, and ellipticity of the massive galaxies to convert their light parameters into the SIE model mass parameters. Thus, following the |$L{-}\sigma _v$| scaling relation (Parker et al. 2005), we obtain the velocity dispersion. Similarly, assuming mass follows light, we obtain the position of the lens potential and the ellipticity parameters. We use adaptive moments (which use an elliptical Gaussian weighting function) from the PDR2 catalogue to measure lens ellipticities and position angles (PAs). Then, the Einstein radius, |$\theta _E$|⁠, with an axis ratio, |$q=1-e$|⁠, and its dependence on the velocity dispersion of the SIE is given by

where |$D_{\rm ls},\ D_{\rm s}$|⁠, and c are the angular diameter distance between the lens and the source, the angular diameter distance between the observer and the source, and the speed of light, respectively.

The i-band magnitude and the redshift of the background galaxies are drawn from the source counts and redshift distribution as prescribed in Faure et al. (2009). Faure et al. assumed that the number density of sources at redshift |$z_s$| brighter than the apparent magnitude threshold of |$m_{\rm lim}\sim 26$| [mag] in the F814W filter band. Each galaxy is parameterized with a Sersic profile for a fixed Sersic index of 1 corresponding to an exponential profile. The ellipticity and PA are drawn randomly from a uniform distribution within the range indicated in Table 2. The colours of the galaxy are extracted from the photometric CFHTLenS catalogue (Hildebrandt et al. 2012; Erben et al. 2013). The effective radius of the galaxy is estimated from the luminosity|$-$|size (⁠|$L{-}r_{\rm eff}$|⁠) relation (Bernardi et al. 2003, with a redshift scaling to account for size evolution) given by

where |$L_r=L_{\rm s}/10^{10.2}\,{\rm L}_{\odot }$| and |$L_{\rm s}$| is the luminosity of background source.

Given the source and the lens population properties, as above, we compute the probability of lensing by following (More et al. 2016, see their section 3.1.1) which accounts for the lensing cross-section, their number densities and magnification bias. Here, we limit a massive galaxy to act as a lens and accept a background source if the Einstein radius falls within the range given in Table 2 and the magnitude of the second brightest lensed image is above the limiting magnitude of the HSC Survey. Once all of the parameters for the lens and source models have been determined, we use gravlens (Keeton 2001) to generate simulated lensed images. After accounting for the shot noise in the lensed images and convolving them with the seeing in each of the filters. The simulated lensed image is added to the real HSC image centred on the galaxy selected to act as a lens (see the left panel in Fig. 1). Fig. 2 shows the distributions of the Einstein radius, redshifts, i-band magnitude, and ellipticity for both lens and the source of the simulated galaxy-scale lenses. We also show the distribution of colour–colour (⁠|$m_r-m_i$| versus |$m_g-m_r$|⁠) diagram of the lens galaxies and the sources (see Fig. 3) with selection effect tend to bluer sources.

From a total of about 22  000 simulated lens systems, we exclude about 3000 systems located within GAMA09H field which is used for a comparison analysis in More et al. (2024). We also exclude tens of simulated lens galaxies whose centres have been identified as known lens galaxies in previous studies (e.g. More et al. 2012; Sonnenfeld et al. 2018, 2020). We then end up with 18 660 simulated lens systems.

4 CONVOLUTIONAL NEURAL NETWORK

4.1 Training data set

The data set for training the CNN is divided into two subsets of equal number of members: one containing the 18 660 simulated lenses simulated with 64 |$\times$| 64 pixel (corresponding to 10.752 |$\times$| 10.752 arcsec²) cutouts from Section 3, and the other containing the 18 660 non-lens objects that were not used to generate simulated lenses. These cutouts are large enough to capture galaxy-scale lenses and yet small enough for fairly quick training and searching.

The data set is split into 80 per cent for training and 20 per cent for validation (see Table 3). We select non-lens objects for the negatives, which contains: 55 per cent galaxies that are randomly selected from the parent catalogue; 34 per cent spiral galaxies from Tadaki et al. (2020); 5 per cent stars from the SDSS spectroscopic star catalogue (Ahumada et al. 2020); 4 per cent galaxy groups or ‘crowded’ galaxies like LRG + egde-on galaxy (or arc-like feature); and 2 per cent dual point-like, tricky spiral or merger galaxies that are visually inspected from the parent catalogue (see the right panel in Fig. 1).

In order to identify blue sources, we select HSC |$gri$|-band images due to their excellent depth and quality. The FITS images in three bands are converted to RGB images scaled with an arcsinh stretch using HumVI⁴ (Marshall et al. 2016) and supplied to the CNN as vectors of 12 288 (64 |$\times$| 64 |$\times$| 3) floating-point numbers. To ensure that the colour-composite images contain no missing information regarding the colour of the sources/arcs, we explore the optimal configuration of contrast, colour balance, and brightness parameters when combining the three new images into an RGB colour composite. Before the CNN’s training stage, we preprocess our data by normalizing each image brightness to be between 0 and 1. This normalization can help improve the network’s performance and training efficiency by enhancing numerical stability, promoting faster convergence, aiding with generalization, preventing saturation of activation functions, and optimizing the training process. In general, data augmentation is a common practise in machine learning; it is used to expand the training set in order to prevent overfitting and teach the network rotational, translational and scaling invariance. Here, we use in-place data augmentation to make sure that, when the network is trained, it sees new variations of our data set at each and every epoch. This augmentation method is done at training time and not an ‘additive’ operation which is transforming the original data in the batch by a series of random transformation, then returning the randomly transformed into network for training. We investigate the optimal values for random values of the augmentation criteria while keeping the network architecture the same. We augment our data set applying the following transformations to the simulated and non-lens galaxy sample: (i) a random rotation in the range [–30 deg, 30 deg]; (ii) a random resizing by a factor in the range [0.8, 1.2]; (iii) a random flip along the horizontal axis; and (iv) and a random channel_shift_range⁵|$= 0.9$|⁠.

4.2 CNN architecture

The CNN architecture is inspired by LeNet (Lecun et al. 1998) and Jacobs et al. (2017), with modifications displayed in Table 4. The CNN consists of five convolutional layers followed by four fully connected hidden layers. Five dropout regularizations (Srivastava et al. 2014) are added to the network at intervals between layers to minimize the likelihood of overfitting by dropping 20 per cent of the output neurons at random during training with rectified linear unit (ReLU; Nair & Hinton 2010) non-linear activations. The output layer consists of a single neuron with sigmoid activation. Three Maxpooling layers with |$2 \times 2$| kernel sizes and stride 2 are inserted between the convolutional layers to make the CNN invariant to local translations of the relevant features in gri image cutouts while reducing the network parameters. The network has a total of 6441 985 trainable parameters upon completion. In order to investigate the hyperparameters, we train different CNN architectures with random configurations over several cycles. We explore the models with 4–7 convolutional layers, different kernel sizes, 3–5 dropout layers, batchsizes ranging from 64 to 512, and dense units of 2–5. We also test the effect of different learning rates, in the range of |$10^{-2}$|–|$10^{-5}$|⁠, and dropout rates of 0.1–0.5. Our best network is summarized in Table 4.

We use the Adam optimization algorithm (Kingma & Ba 2014) to minimize the cross-entropy error function over the training data with a learning rate of 0.000 05. The CNN is trained for the maximum allowed 100 epochs using mini-batch stochastic gradient descent with 128 images per batch. If the network does not provide improved accuracy or loss after five consecutive epochs, we terminate the training early. This network is implemented utilizing the python neural network library Keras (Chollet & others 2018) with the TensorFlow backend (Abadi et al. 2016). The CNN is trained on an NVIDIA RTX 3070 8GB. On average, network training requires less than an hour for a training data set like the one we used.

Completeness is measured on spectroscopically confirmed or grade A or B SuGOHI galaxy-scale lenses (Sonnenfeld et al. 2018; Wong et al. 2018; Sonnenfeld et al. 2020). We rejected a few lenses with large image separations |$\gtrsim 3\,{\rm arcsec}$|⁠, indicating significant perturbation from the lens environment, as we have no intention of recovering such configurations. As test lenses, we use 220 SuGOHI-g lens systems. We collect the 78 665 non-lenses, including random galaxies from a parent catalogue; spiral galaxies from Tadaki et al. (2020); and stars from the SDSS spectroscopic star catalogue (Ahumada et al. 2020).

4.3 CNN performance

The CNN provides a score, |$p_{\rm CNN}$|⁠, ranging from 0 to 1, with 1 for lenses and 0 for everything else (non-lenses). The evolution of the training loss for the network with optimized hyperparameters until epoch 52 (see Fig. 4) corresponds to the validation set’s minimum binary cross-entropy loss without overfitting. The network achieved a training (validation) accuracy of 0.986 (0.981) and a loss of 0.041 (0.059). The small difference between the two curves (generalization gap) indicates that the model’s predictions on new data with similar properties to the training set are relatively stable. Using the test set, the final network performance was characterized. In Fig. 5, we show the probabilities predicted by the model for all lens and non-lens test examples. When |$p_{\rm CNN}\gt 0.9$|⁠, the distribution is dominated by lenses.

To evaluate the number of lenses correctly identified, we use a receiver operating characteristic (ROC) curve which compares the true positive rate (TPR) to the false positive rate (FPR) as functions of the decision threshold applied to the score and precision–recall (PR) curves for the trained CNN showing the precision as function of the recall or TPR. We use the following definitions of TPR or recall, FPR, and precision:

where TP, FP, TN, and FN are true positive, false positive, true negative, and false negative, respectively. In general, the excellent performance are shown by the ROC and PR curves in Fig. 6. The ROC curve illustrates the performance of a binary classifier in distinguishing between the two classes as the decision threshold is altered. The Area Under the ROC Curve (AUC) of our CNN are 0.976 and 0.971, for imbalanced (0.3–99.7) and balanced (50–50) test sample, respectively. For balanced test sample, the PR curve shows that the network can classify all objects as lens sample would yield a precision (purity) of 97.3 per cent at a recall (completeness) of 82.3 per cent of SuGOHI-g lenses in the test set with an FPR of 1.3 per cent for |$p_{\rm CNN}=0.5$| as the threshold; and a precision of 98.8 per cent at a recall of 72.3 per cent of SuGOHI-g lenses with an FPR of 0.49 per cent for |$p_{\rm CNN}=0.9$| as a threshold (see Table 5). We find that the misclassified test lenses (see Fig. 7) contain compact or fainter lens galaxies, lensed sources with redder colours, stronger blending with lens light or companion galaxies, or lower source-to-lens flux ratios, or lensed by group/cluster. Our simulations include fewer examples of each of these configurations.

4.4 Visual inspection

We applied the trained CNN to the |$gri$| cutouts of all 2.4 million galaxies in order to determine their score |$p_{\rm CNN}$|⁠. The CNN identifies 55 469, 20 241, and 1830 as candidate lenses with |$p_{\rm CNN}\gt 0.5$|⁠, |$p_{\rm CNN}\gt 0.9$|⁠, and |$p_{\rm CNN}=1.0$|⁠, respectively. About 0.86 per cent of the parent sample has |$p_{\rm CNN}\gt 0.9$|⁠. We note that several candidates have a blue feature close to a red galaxy with a very faint or no counter blue image. This is possibly due to our training data set being sensitive to small Einstein radii. After an initial visual inspection performed by a single inspector (ATJ) to remove definite non-lenses, a ‘good’ sample of 1522 potential lens candidates is determined.

We inspect RGB images of these candidates using custom written, java-based application called visapp (More et al. 2016), which displays PNG images made with |$gri$| imaging. visapp utilizes capabilities of the invert, zoom, contrast, and brightness adjustment features, as well as the remark area. Fig. 8 shows a snapshot of the classification interface from the visapp with an inverted and zoomed image. We assign each candidate a grade between 0 and 3, using the grading convention from Sonnenfeld et al. (2020), where 0 means ‘almost certainly not a lens’, 1 means ‘possibly a lens’, 2 means ‘probably a lens’, and 3 means ‘almost certainly a lens’. There are comment columns for the candidates that require further discussion. It is possible to invert the images’s colour, zoom in or out and shift it. The grades used throughout the paper are the mean grade, |$\langle Gr\rangle$|⁠, assigned by authors ATJ, AM, KTI, DCYC, KCW, and PWP.

Next, we implemented the scheme outlined below (Sonnenfeld et al. 2018):

• A: |$\langle Gr\rangle \gt 2.5$|⁠,

• B: |$1.5\lt \langle Gr\rangle \le 2.5$|⁠,

• C: |$0.5\lt \langle Gr\rangle \le 1.5$|⁠, and

• Not a lens: |$\langle Gr\rangle \le 0.5$|⁠.

Then, the grades were compiled and averaged, and each grader’s scores were revealed and compared. Graders were then allowed to adjust their scores, particularly for contentious objects with disparate scores or scores close to the grade thresholds, which were probably due to personal grading experience or human fatigue. During this stage, we also used the HSC PDR2 map⁶ for additional inspection, if necessary.

5 RESULTS

In total, we discover 43 grade A, 269 grade B, and 880 grade C candidates. The results are summarized in Table 5, which include the number of parent sample, lens candidates, purity, and completeness. The full list of the grade A and some examples of grade B candidates are given in Table 6. We note that the nearby lensed arcs could affect the i-band magnitude and photometric redshift. We show colour composite images of the grade A candidates in Fig. 9 and of the grade B candidates in Fig. A1. The lens redshift distribution of the grade A and grade B candidates is shown in Fig. 10 with the peak at |$z_{\ell ,\ \rm {phot}}\sim 0.7$| and |$z_{\ell ,\ \rm {spec}}\sim 0.6$|⁠. While some lens candidates which were grade C from previous SuGOHI publications have been upgraded to a higher grade in recent references, we list the grade C lens candidates in the Appendix. The fraction of grades A and B with |$\langle Gr\rangle \gt 1.5$| among CNN recommendations, decreases rapidly when lowering the threshold |$p_{\rm CNN}$|⁠. We estimate that 85.9 per cent of the highest scores |$0.95 \lt p_{\rm CNN}\le 1.00$| which has |$\langle Gr\rangle \gt 1.5$|⁠, and about 14.1 per cent for |$0.90 \lt p_{\rm CNN}\le 0.95$|⁠. After final visual inspection, taking |$\langle Gr\rangle \gt 0.5$| to be TP and |$\langle Gr\rangle \le 0.5$| to be FP, the purity is 78.32 per cent. In general, we find that the majority of lensed sources have a blue colour, which is due to the selection effect from our training sample.

Separately from this work, Cañameras et al. (2021) and Shu et al. (2022) have recently applied machine-learning-based lens search algorithms to the HSC-SSP PDR2 (Aihara et al. 2019) and have published lens candidates from these searches. Our parent sample and training set have smaller number of galaxies compared to Cañameras et al. (2021) and Shu et al. (2022), however, we still are able to discover a comparable number of lenses (see details in More et al. 2024). We note that about 51 per cent of our parent sample and the parent sample from Cañameras et al. (2021) overlap. There is some overlap in the candidates we discovered as we used the HSC-SSP data set. Recently, More et al. (2024) presented a systematic comparison of neural network performance that included results from Cañameras et al. (2021), Shu et al. (2022), this work, and Ishida et al., in preparation. They provided an analysis of several neural networks with different training data sets and/or parent catalogues, and evaluated the networks’ performance on common test samples, performance when trained on interchanged data sets, and performance on SuGOHI lenses. Figs 1–3, as well as section 5.3 of More et al. (2024), show full examples of lens systems that were missed in this work but retrieved by others. Fig. 11 shows a subset of confirmed lenses and lens candidates from the common test samples in More et al. (2024). Previous studies by Cañameras et al. (2021) and Shu et al. (2022) have successfully classified some lens systems, denoted by C21 and S22 on the top of each cutout in Fig. 11. Some lens systems are still not classified by all networks, which suggests that we should improve and investigate hyperparameters in the training data sets.

We have identified and cross-matched previous candidates with our candidates and listed the relevant references in Table 6. We find 504 overlapping candidates with 215 and 289 candidates from grade A or B, and grade C, respectively. We find that 143 of 289 overlapping grade C have a higher grade in previous searches. There are 207 and 160 candidates from all grades that overlap with the findings from Cañameras et al. (2021) and Shu et al. (2022), respectively. Our CNN also recovers 32 group- and cluster-scale lens candidates, although it is not optimized for these systems. Many candidates with a blue arc feature near a red galaxy have a lower grade, as seen in Table B1. Rojas et al. (2023) found that is difficult for experts to recover candidates with Einstein radius less than 1.2 times the seeing during visual inspection.

6 SUMMARY

We present new candidates for galaxy-scale strong gravitational lenses from the HSC-SSP PDR2, covering 800 deg|$^2$| in the |$gri$| bands, using a CNN as part of the SuGOHI project. In order to identify possible galaxy-scale lenses, we use strict pre-selection criteria, such as multiband magnitudes, stellar mass, star formation rate, extendedness limit, and photometric redshift range, resulting in about 2.4 million galaxies of parent sample. By initially adopting a conventional threshold, |$p_{\rm CNN}\gt 0.9$|⁠, we find 20 241 candidates which are then refined to 1522 systems with lensing features for further inspection.

On the basis of visual inspections of the cutouts, six authors independently graded the strong lens candidates. According to the average visual inspection scores, 312 candidates identified by the CNN are considered grade A or B (i.e. definite or probable), and 880 are grade C (possible) strong-lens candidates. This list was cross-referenced with our extensive compilation of strong gravitational lenses previously published as confirmed systems or candidates in order to identify duplicates. Among the candidates, there are 97 new discoveries (3 from grade A and 94 from grade B, respectively). We find that 143 grade C candidates were graded as A or B in previous literature. The (photometric) redshift of the candidate lens galaxies range from 0.2 to 1.2. Follow-up spectroscopy will confirm these lenses and measure source redshifts so that detailed lens modelling can yield scientific results.

ACKNOWLEDGEMENTS

We are also grateful to Honoka Murakami and Sherry H. Suyu for their valuable contributions and fruitful discussions, which have significantly improved the quality of this manuscript. We also thank the anonymous referee for useful comments on the paper. This research is supported by Program Riset Unggulan Pusat dan Pusat Penelitian (RU3P) 2023 which is funded by Direktorat Penerapan Ilmu dan Teknologi Multidisiplin (DPITM) Insitut Teknologi Bandung. This work also is supported Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number JP20K14511. RC thanks the Max Planck Society for support through the Max Planck Research Group for S.H.S. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (LENSNOVA: grant agreement No 771776).

The Hyper Suprime-Cam (HSC) collaboration includes the astronomical communities of Japan and Taiwan, and Princeton University. The HSC instrumentation and software were developed by the National Astronomical Observatory of Japan (NAOJ), the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High Energy Accelerator Research Organization (KEK), the Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was contributed by the FIRST program from the Japanese Cabinet Office, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the Japan Society for the Promotion of Science (JSPS), Japan Science and Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University.

This paper is based on data collected at the Subaru Telescope and retrieved from the HSC data archive system, which is operated by Subaru Telescope and Astronomy Data Center (ADC) at NAOJ. Data analysis was in part carried out with the cooperation of Center for Computational Astrophysics (CfCA) at NAOJ. We are honored and grateful for the opportunity of observing the Universe from Maunakea, which has the cultural, historical and natural significance in Hawaii. This paper makes use of software developed for Vera C. Rubin Observatory. We thank the Rubin Observatory for making their code available as free software at http://pipelines.lsst.io/. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

This research made use of Astropy⁷ (Astropy Collaboration et al. 2013, 2018), numpy (Harris et al. 2016), matplotlib (Caswell et al. 2019), simct (More et al. 2016), and tensorflow (Developers 2022).

DATA AVAILABILITY

The basic information of the lens candidates can be browsed or downloaded from the SuGOHI online database http://www-utap.phys.s.u-tokyo.ac.jp/~oguri/sugohi/ and imaging data from the HSC-SSP Public Data Release 2 https://hsc-release.mtk.nao.ac.jp/doc/. The lens and non-lens test data sets are available upon reasonable request to the authors.

Footnotes

REFERENCES

APPENDIX A: IMAGES OF 269 GRADE B CANDIDATE

APPENDIX B: IMAGES OF 143 GRADE C CANDIDATE

The full list of 880 grade C is also available at http://www-utap.phys.s.u-tokyo.ac.jp/ oguri/sugohi/. Here, we show 143 grade C candidates which had higher grade in previous references.