Identification of GalaxyGalaxy Strong Lens Candidates in the DECam Local Volume Exploration Survey Using Machine Learning

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Identiﬁcation of Galaxy–Galaxy Strong Lens Candidates in the DECam Local Volume

Exploration Survey Using Machine Learning

E. A. Zaborowski

1,2,3

, A. Drlica-Wagner

3,4,5

, F. Ashmead

,J.F.Wu

6,7

, R. Morgan

, C. R. Bom

, A. J. Shajib

3,5,70

S. Birrer

10,11

, W. Cerny

3,5,12

, E. J. Buckley-Geer

3,4

, B. Mutlu-Pakdil

, P. S. Ferguson

, K. Glazebrook

S. J. Gonzalez Lozano

, Y. Gordon

, M. Martinez

, V. Manwadkar

,J.O’Donnell

, J. Poh

3,5

, A. Riley

17,18,19

J. D. Sakowska

, L. Santana-Silva

, B. X. Santiago

22,23

, D. Sluse

, C. Y. Tan

3,25

, E. J. Tollerud

, A. Verma

J. A. Carballo-Bello

, Y. Choi

, D. J. James

, N. Kuropatkin

, C. E. Martínez-Vázquez

, D. L. Nidever

J. L. Nilo Castellon

, N. E. D. Noël

, K. A. G. Olsen

, A. B. Pace

, S. Mau

10,36

, B. Yanny

, A. Zenteno

T. M. C. Abbott

, M. Aguena

, O. Alves

, F. Andrade-Oliveira

, S. Bocquet

, D. Brooks

, D. L. Burke

10,11

A. Carnero Rosell

23,41,42

, M. Carrasco Kind

43,44

, J. Carretero

, F. J. Castander

46,47

, C. J. Conselice

M. Costanzi

49,50,51

, M. E. S. Pereira

, J. De Vicente

, S. Desai

, J. P. Dietrich

, P. Doel

, S. Everett

I. Ferrero

, B. Flaugher

, D. Friedel

, J. Frieman

3,4,5

, J. García-Bellido

, D. Gruen

, R. A. Gruendl

43,44

G. Gutierrez

, S. R. Hinton

, D. L. Hollowood

, K. Honscheid

1,2

, K. Kuehn

59,60

, H. Lin

, J. L. Marshall

18,19

P. Melchior

, J. Mena-Fernández

, F. Menanteau

43,44

, R. Miquel

45,62

, A. Palmese

, F. Paz-Chinchón

43,64

A. Pieres

23,65

, A. A. Plazas Malagón

, J. Prat

3,5

, M. Rodriguez-Monroy

, A. K. Romer

, E. Sanchez

, V. Scarpine

I. Sevilla-Noarbe

, M. Smith

, E. Suchyta

,C.To

, and N. Weaverdyck

38,69

(DELVE & DES Collaborations)

Department of Physics, The Ohio State University, Columbus, OH 43210, USA; zaborowski.11@osu.edu

Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, OH 43210, USA

Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA

Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, USA

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Physics Department, 2320 Chamberlin Hall, University of Wisconsin-Madison, 1150 University Avenue Madison, WI 53706-1390, USA

Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil

Kavli Institute for Particle Astrophysics & Cosmology, P.O. Box 2450, Stanford University, Stanford, CA 94305, USA

SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA

Department of Astronomy, Yale University, New Haven, CT 06520, USA

Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA

Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

Centre for Astrophysics & Supercomputing, Swinburne University of Technology, VIC 3122, Australia

Santa Cruz Institute for Particle Physics, Santa Cruz, CA 95064, USA

Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK

George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA

Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA

Department of Physics, University of Surrey, Guildford, GU2 7XH, UK

NAT-Universidade Cruzeiro do Sul/Universidade Cidade de São Paulo, Rua Galvão Bueno, 868, 01506-000, São Paulo, SP, Brazil

Instituto de Física, UFRGS, Caixa Postal 15051, Porto Alegre, RS—91501-970, Brazil

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STAR Institute, Quartier Agora—Allée du six Aout, 19c B-4000 Liége, Belgium

Department of Physics, University of Chicago, Chicago, IL 60637, USA

Sub-department of Astrophysics, University of Oxford, Denys Wilkinson Building, Oxford, OX1 3RH, UK

Instituto de Alta Investigación, Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren 2477, Iquique, Chile

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NSF’s National Optical Infrared Astronomy Research Laboratory, 950 N. Cherry Avenue, Tucson, AZ 85719, USA

McWilliams Center for Cosmology, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA

Cerro Tololo Inter-American Observatory, NSF’s National Optical-Infrared Astronomy Research Laboratory, Casilla 603, La Serena, Chile

Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA

University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, D-81679 Munich, Germany

Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK

Instituto de Astroﬁsica de Canarias, E-38205 La Laguna, Tenerife, Spain

Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife, Spain

Center for Astrophysical Surveys, National Center for Supercomputing Applications, 1205 West Clark Street, Urbana, IL 61801, USA

Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA

Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona)Spain

Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193 Bellaterra (Barcelona), Spain

Institut d'Estudis Espacials de Catalunya (IEEC), E-08034 Barcelona, Spain

Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road, Manchester,M13 9PY, UK

Astronomy Unit, Department of Physics, University of Trieste, via Tiepolo 11, I-34131 Trieste, Italy

The Astrophysical Journal, 954:68 (24pp), 2023 September 1 https://doi.org/10.3847/1538-4357/ace4ba

INAF-Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34143 Trieste, Italy

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Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg, Germany

Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain

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Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain

Department of Astronomy, University of California, Berkeley, 501 Campbell Hall, Berkeley, CA 94720, USA

Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK

Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ—20921-400, Brazil

Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton, BN1 9QH, UK

School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

Received 2022 November 11; revised 2023 July 1; accepted 2023 July 3; published 2023 August 23

Abstract

We perform a search for galaxy–galaxy strong lens systems using a convolutional neural network (CNN)applied to

imaging data from the ﬁrst public data release of the DECam Local Volume Exploration Survey, which contains ∼520

million astronomical sources covering ∼4000 deg

of the southern sky to a 5σpoint–source depth of g=24.3,

r=23.9, i=23.3, and z=22.8 mag. Following the methodology of similar searches using Dark Energy Camera data,

we apply color and magnitude cuts to select a catalog of ∼11 million extended astronomical sources. After scoring

with our CNN, the highest-scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (not a

lens)to 3 (very probable lens). We present a list of 581 strong lens candidates, 562 of which are previously unreported.

We categorize our candidates using their human-assigned scores, resulting in 55 Grade A candidates, 149 Grade B

candidates, and 377 Grade C candidates. We additionally highlight eight potential quadruply lensed quasars from this

sample. Due to the location of our search footprint in the northern Galactic cap (b>10 deg)and southern celestial

hemisphere (decl. <0deg), our candidate list has little overlap with other existing ground-based searches. Where our

search footprint does overlap with other searches, we ﬁnd a signiﬁcant number of high-quality candidates that were

previously unidentiﬁed, indicating a degree of orthogonality in our methodology. We report properties of our

candidates including apparent magnitude and Einstein radius estimated from the image separation.

Uniﬁed Astronomy Thesaurus concepts: Strong gravitational lensing (1643)

Supporting material: machine-readable table

1. Introduction

Strong gravitational lensing results from the general-

relativistic deﬂection of light caused by the inhomogeneous

distribution of matter along the line of sight. Since the ﬁrst

observations of a doubly imaged lensed quasar (Walsh et al.

1979)and giant arcs of lensed galaxies near the center of

galaxy clusters (Lynds & Petrosian 1986; Paczynski 1987;

Soucail et al. 1987,1988), strong lensing has grown into an

important tool for constraining astrophysics and cosmology

(see Treu 2010, for a review).

Strong lens systems provide a wealth of astrophysical

information that is difﬁcult or unfeasible to obtain with

traditional analysis. The magnifying effect of strong lensing

can enable detailed study of the internal morphologies of

background source galaxies down to scales of tens of parsecs

for galaxies that are too distant or faint to study under normal

circumstances (e.g., Bayliss et al. 2014; Livermore et al. 2015;

Johnson et al. 2017; Cornachione et al. 2018; Ritondale et al.

2019a; Rivera-Thorsen et al. 2019; Ivison et al. 2020; Florian

et al. 2021; Khullar et al. 2021). Strong lensing can be used to

measure the distribution of both dark and luminous matter in

galaxies, which provides essential information for modeling

galaxy formation, constraining the stellar initial mass function,

and understanding the baryonic processes that drive galaxy

evolution (e.g., Treu & Koopmans 2002; Czoske et al. 2008;

Barnabè et al. 2011; Leier et al. 2016; Nightingale et al. 2019;

Sonnenfeld et al. 2019; Shajib et al. 2021).

Strong lensing also provides a critical test of the cold dark

matter paradigm by probing the distribution of dark matter in

galaxies and galaxy clusters. At large scales, strong lensing

constrains the shape and content of dark matter halos (e.g.,

Kochanek 1991; Koopmans & Treu 2002; Bolton et al.

2006,2008; Koopmans et al. 2006; Bradačet al. 2008; Grillo

et al. 2015; Shu et al. 2016; Shajib et al. 2021). On small scales,

strong lensing probes the properties of the small dark matter

halos that reside in lens substructure and as ﬁeld halos along

the line of sight (e.g., Vegetti & Koopmans 2009; Vegetti et al.

2010,2012; Hezaveh et al. 2013,2016; Birrer et al. 2017;

Gilman et al. 2018,2020; Hsueh et al. 2019; Ritondale et al.

2019b; Meneghetti et al. 2020; Sengül et al. 2022).

NHFP Einstein Fellow.

Original content from this work may be used under the terms

of the Creative Commons Attribution 4.0 licence. Any further

distribution of this work must maintain attribution to the author(s)and the title

of the work, journal citation and DOI.

The Astrophysical Journal, 954:68 (24pp), 2023 September 1 Zaborowski et al.

Measurements of strongly lensed sources that are variable in

time, such as supernovae and quasars, provide exceptional

information about the expansion history of the Universe

(Refsdal 1964; Oguri & Marshall 2010; Treu 2010). Time-

delay measurements from multiply imaged supernovae (e.g.,

Goldstein & Nugent 2017; Goldstein et al. 2018; Shu et al.

2018; Pierel & Rodney 2019; Suyu et al. 2020; Huber et al.

2021)and lensed quasars (e.g., Suyu et al. 2010,2013,2017;

Treu & Marshall 2016; Bonvin et al. 2017; Birrer et al. 2020;

Millon et al. 2020; Shajib et al. 2020; Wong et al. 2020)

provide independent measurements of the Hubble Constant,

, that complement measurements from the local distance

ladder (e.g., Freedman et al. 2019,2020; Riess et al.

2019,2021)and the Cosmic Microwave Background (CMB;

e.g., Planck Collaboration et al. 2020). Constraints on H

from

time-delay cosmography using strongly lensed quasars are

competitive with other methods (Wong et al. 2020)and are

expected to improve as more suitable lens systems are

discovered (Shajib et al. 2018), while observations of strongly

lensed supernovae may provide a powerful probe in the future

(e.g., Suyu et al. 2020). Time-delay cosmography can be used

to constrain the expansion history of the Universe and probe

the equation of state of dark energy (e.g., Treu 2010; Treu &

Marshall 2016; Treu et al. 2018; Birrer & Treu 2021; Sharma &

Linder 2022).

The population of candidate strong lens systems has

increased rapidly with the advent of deep, wide-ﬁeld, digital

sky surveys. Lens searches with the Sloan Digital Sky Survey

(SDSS; e.g., Allam et al. 2007; Estrada et al. 2007; Bolton et al.

2008; Hennawi et al. 2008; Belokurov et al. 2009; Diehl et al.

2009; Kubo et al. 2009,2010; Lin et al. 2009; Stark et al. 2013;

Shu et al. 2017), the CFHTLS Strong Lensing Legacy Survey

(e.g., Cabanac et al. 2007; More et al. 2012; Gavazzi et al.

2014; Marshall et al. 2016; More et al. 2016), the Hyper

Suprime-Cam Subaru Strategic Program (HSC-SSP; e.g.,

Sonnenfeld et al. 2018; Jaelani et al. 2020), the Kilo Degree

Survey (KiDS; e.g., Petrillo et al. 2017,2019; Li et al. 2020),

Pan-STARRS-1 (PS1; e.g., Berghea et al. 2017; Cañameras

et al. 2020), and Gaia (e.g., Lemon et al. 2017; Agnello et al.

2018; Krone-Martins et al. 2018; Delchambre et al. 2019)have

yielded thousands of lens candidates and hundreds of

conﬁrmed lens systems.

The Dark Energy Camera (DECam; Flaugher et al. 2015)on

the 4 m Blanco Telescope at Cerro Tololo Inter-American

Observatory in Chile provides one of the premier wide-area

imaging systems in the Southern Hemisphere. Searches for

strong lenses with DECam have already resulted in thousands

of new lens candidates discovered in data from the Dark

Energy Survey (DES; e.g., Agnello et al. 2015b; Nord et al.

2016; Diehl et al. 2017; Agnello & Spiniello 2019; Jacobs et al.

2019a,2019b;O’Donnell et al. 2022; Rojas et al. 2022)and the

Dark Energy Camera Legacy Survey (DECaLS; e.g., Huang

et al. 2020,2021; Dawes et al. 2022; Stein et al. 2022; Storfer

et al. 2022). However, these searches cover only a fraction of

the sky area that DECam has observed, and many more

discoveries are expected. Furthermore, searches for strong lens

systems with DECam are an excellent precursor for the

upcoming Rubin Observatory Legacy Survey of Space and

Time (Ivezićet al. 2019), which will cover a similar sky area

with much increased sensitivity.

The rapidly increasing quantity and quality of imaging data

from current and future surveys continues to provide new

opportunities and challenges for strong lens searches. Current

ground-based imaging surveys produce catalogs of hundreds of

millions of objects, while the relative occurrence rate of strong

lensing is ∼10

−5

(e.g., Jacobs et al. 2019b). At the same time,

the complex morphology of lens systems and the multi-

dimensional information content of astronomical imaging (i.e.,

ﬂux, color, and morphology)makes strong lens searches

challenging to automate. Visual searches by groups of experts

continue to ﬁnd hundreds of strong lens candidates (e.g., Diehl

et al. 2017;O’Donnell et al. 2022); however, some amount of

automation is necessary to fully leverage future large data sets.

One attempt to tackle these challenges is by “crowdsourcing”

strong lens searches to a large number of human inspectors

(e.g., Marshall et al. 2016; Garvin et al. 2022). However,

because human visual inspection is subjective, it is often

desirable to combine scores in a way that accounts for varying

preferences. Intrinsic lens candidate properties may be

decoupled from human preferences by using statistical

techniques such as matrix factorization (e.g., Mnih &

Salakhutdinov 2007).

Another approach to tackle these large data sets is through

the adoption of image-based deep-learning algorithms, which

have proliferated across astronomy (e.g., Dieleman et al. 2015;

Hezaveh et al. 2017; Pasquet et al. 2019; Wu & Boada 2019;

Wu et al. 2022). Convolutional neural networks (CNNs; e.g.,

Lecun et al. 1998; Krizhevsky et al. 2012)in particular have

seen much success in recent lens searches (e.g., Agnello et al.

2015a; Bom et al. 2017; Jacobs et al. 2019a,2019b; Petrillo

et al. 2019; Cañameras et al. 2020; Huang et al. 2020,2021;Li

et al. 2020; Dawes et al. 2022; Rojas et al. 2022; Stein et al.

2022; Storfer et al. 2022). The need for automation motivated

the community to engage in competitive data challenges to

design optimal strong lens-ﬁnding algorithms (Metcalf et al.

2019; Bom et al. 2022). Among the lessons learned in the

competitions is the fact that human inspection achieved lower

performance in huge data sets (Metcalf et al. 2019)compared

to CNNs, and that lensing features can be subtle even for visual

inspection (Bom et al. 2022). However, when transitioning

from simulated data sets to real data, in which there are many

orders of magnitudes more nonlenses than lenses, all searches

require a ﬁnal visual inspection for validation (e.g., Huang et al.

2020,2021; Rojas et al. 2022; Stein et al. 2022), effectively

reducing, but not eliminating, the “human in the loop.”Thus, it

is important to understand both the human and machine biases

in lens search procedures.

Here, we present a CNN-based search for gravitational lens

systems using DECam data assembled and processed by the

DECam Local Volume Exploration Survey (DELVE; Drlica-

Wagner et al. 2021). Our search covers a region of the sky that

is largely outside of previous strong lens searches using data

from DES (DES Collaboration et al. 2021)and DECaLS (Dey

et al. 2019), and is largely unexplored by previous deep,

ground-based imaging surveys. We speciﬁcally target galaxy–

galaxy strong lens systems when training our CNN; however,

our search also has some sensitivity to lensed quasars and

group-scale lenses. Starting from an initial target list of ∼11

million sources, our CNN reduces the candidate list to ∼50,000

candidates. We execute a visual inspection campaign to further

reﬁne our list to 581 candidate lens system, which we classify

The Astrophysical Journal, 954:68 (24pp), 2023 September 1 Zaborowski et al.

using the ratings assigned during visual inspection. Of these

581 lens candidates, we recover 562 previously undiscovered

lenses and 19 previously reported candidates.

The structure of this paper is as follows. In Section 2,we

describe the DELVE data products, our creation of image

cutouts, and our pre-processing of those cutouts. In Section 3,

we describe the design of our CNN, the generation of our

training data, and our training procedure. We present some

quantitative evaluations of our CNN performance on both

simulated data and previously known lenses. Furthermore, we

describe the visual inspection campaign that led to our ﬁnal

ranked candidate list. In Section 4, we describe our sample of

581 candidate strong lens systems and compare to other

existing catalogs. Finally we conclude and provide some future

outlook in Section 5.

2. Data Set

The DELVE data were assembled from multiband imaging

by DECam (Flaugher et al. 2015)on the 4 m Blanco Telescope

at Cerro Tololo Inter-American Observatory in Chile. DELVE

contributes new observations covering a large area of the sky

that had not previously been surveyed with DECam.

Furthermore, DELVE processes all publicly available DECam

data with the DES Data Management pipeline (Morganson

et al. 2018), thereby providing uniform multiﬁlter imaging of

the sky in the griz bands to a limiting magnitude of ∼23.5 mag

(Drlica-Wagner et al. 2021). The ﬁrst DELVE data release

(DELVE DR1; Drlica-Wagner et al. 2021)provides a catalog

of ∼520 million unique astronomical sources assembled from

∼5000 deg

of the high-Galactic-latitude sky in the northern

Galactic cap (b>10 and decl. <0). This region is distinct from

the DES footprint and overlaps with DECaLS only in the

region with decl. >−7(Figure 1).

We begin our search by selecting astronomical objects that

conform to a set of color–magnitude cuts developed by Jacobs

et al. (2019a)for their strong lens search of the DES data:

16 22

17.2 22

15 21

0.2 1.75.

<-<

-<-<

()

Using a sample of simulated lenses, Jacobs et al. (2019a)

estimate that these cuts contain 98.7% of true lenses while

signiﬁcantly reducing the target sample size (and thus the

number of false positives). We note that, among the inputs used

to create this estimate, the mock deﬂector galaxies are early-

type galaxies with masses drawn from the Hyde & Bernardi

(2009)fundamental plane of SDSS elliptical galaxies, and the

mock source galaxies are elliptical exponential disks with

properties drawn from the Cosmic Evolution Survey (COS-

MOS)sample (Ilbert et al. 2009). Applying these cuts to the

∼520 million objects in DELVE DR1, in addition to requiring

full coverage of the cutout image in each band, griz, results in a

data set of ∼49 million objects. We apply a cut on the star–

galaxy classiﬁcation (at least one of EXTENDED_CLASS_

[GRIZ] 2)to select a catalog of extended sources, resulting

in a data set of ∼11 million objects. The color–magnitude cuts

simulated lens systems around early-type lens galaxies, which

are generally massive and have a relatively high lensing cross

section. We expect that applying the same color cuts will select

a similarly massive set of target galaxies. As a check, we cross-

match the galaxies in our target data set against a catalog of

Figure 1. Locations of strong lens candidates from this work (red)and previous searches (black)collected in the Master Lens Database (Moustakas et al. 2012)

augmented by the results from recent searches using DECaLS (Huang et al. 2020,2021; Dawes et al. 2022; Storfer et al. 2022), the extended Baryon Oscillation

Spectroscopic Survey (eBOSS; Talbot et al. 2021), and HSC (Sonnenfeld et al. 2018,2020; Chan et al. 2020; Jaelani et al. 2020,2021; Cañameras et al. 2021; Shu

et al. 2022; Wong et al. 2022). Lens candidates are overplotted on the DELVE DR1 griz footprint (blue). The DELVE DR2 griz footprint (turquoise)is shown for

reference, but the search was conducted only on the DR1 data set. The DES footprint is outlined with solid blue lines (DES Collaboration et al. 2021), while the

DECaLS region is outlined with solid green lines (Dey et al. 2019). The Galactic plane (b=0°)is shown as a solid black curve, while the two dashed black curves

show b=±10°. The sky map is shown using an equal-area Thomas–McBryde ﬂat polar quartic projection in celestial equatorial coordinates.

Lens candidates listed in an updated version of the Master Lens Database

(Moustakas et al. 2012)augmented with the results from recent searches using

DECaLS (Huang et al. 2020,2021; Dawes et al. 2022; Storfer et al. 2022),

eBOSS (Talbot et al. 2021), and HSC (Sonnenfeld et al. 2018,2020; Chan

et al. 2020; Jaelani et al. 2020,2021; Cañameras et al. 2021; Shu et al. 2022;

Wong et al. 2022).

The Astrophysical Journal, 954:68 (24pp), 2023 September 1 Zaborowski et al.

stellar mass and photometric redshift for galaxies in DECaLS

DR9 (Zou et al. 2022). Figure 2shows that our target galaxies

tend to be more massive and lie at lower redshift relative to the

full distribution of galaxies in DECaLS DR9. These conditions

indicate a relatively higher lensing cross section, and thus we

validate the effectiveness of the color–magnitude cuts.

For each object in our initial target list, we determine the best

observation of that object in each band. Following the

convention deﬁned in Drlica-Wagner et al. (2021), we select

the observation with the largest effective exposure time,

eff exp

´, where t

eff

is the effective exposure timescale factor

derived from the full-width at half maximum (FWHM)of the

point-spread function (PSF), sky brightness, and extinction due

to clouds (Neilsen et al. 2016), and Texp is the shutter-open time

of the observation. After identifying the best image in each

band, we create 45 ×45 pixel (11 8×11 8)cutout images in

each band around each of the sources passing our initial set of

photometric selection criteria. We convert the image pixel

values, f, into ﬂux units, F, via the transformation

Ff T100.4 30 ZP exp

=´ -() as described in Marshall et al.

(2016), where ZP is the zero point derived from the

photometric calibration of the image (Drlica-Wagner et al.

2021). It has been shown that rescaling the image data

improves network performance (Jacobs et al. 2019b). There-

fore, we apply the transformation XXm

¢= -()

to each

image, where μand σare the mean and standard deviation of

the image, respectively, and then we rescale each image to the

interval [0, 1]. It should be noted that the DELVE DR1 imaging

data cover a wide range of exposure times (30–350 s)and PSF

image quality (PSF FWHM between 0 7 and 2 0; Drlica-

Wagner et al. 2021). We show the distributions of PSF FWHM

and exposure time for our target data set in Appendix A.We

found that it was important to capture this variation when

constructing the training sample for our CNN-based search

described in the next section.

The preceding fully describes the data processing used for

CNN training. However, when displaying the images for

human visual inspection, we perform the following additional

processing. We take our rescaled image data in the griz bands

and create composite PNG-format images as follows. The

channels red (R), green (G), and blue (B)are assigned the bands

i+z,r, and g, respectively. For each channel, we estimate the

mean sky value, μ, and sky standard deviation, σ, using

iterative sigma clipping to select mostly sky pixels. Once μand

σare determined, we ﬁrst subtract μfrom each channel, then

we clip the maximum pixel value at 100σand the minimum

pixel value at zero, and we ﬁnally rescale each channel to

integer values in the range 0–255. We ﬁnd that, to adequately

visualize all images, two different “scalings”are useful:

1. Scaling 1: we take the base scaling as described above,

and then use the PIL package

increase the saturation

with an enhancement factor of 1.25. This scaling works

well to see features in the vicinity of bright objects.

2. Scaling 2: we take the base scaling as described above,

and further apply a logarithmic stretch with a stretch

factor of 50. We then use the PIL package to increase the

brightness with an enhancement factor of 1.25. This

scaling works well for identifying very faint features.

An example image in both scalings is shown in Figure 3.

During visual inspection of the candidates (Section 3.4),we

present both scalings side-by-side. Throughout this paper,

Scaling 2 is generally used.

3. Methods

In this section, we describe our search for strong lens

systems in data from DELVE DR1 using a combination of

automated and visual inspection techniques. We trained a

simple CNN to search for strong lens systems in cutouts created

from a sample of ∼11 million astronomical objects. Our CNN

was trained on actual DELVE observed images of galaxies

from this same data set (negative sample)and the same galaxies

with simulated lensing superimposed (positive sample),

including training on a false-positive sample (see

Section 3.2). We perform visual inspection of the 50,000

highest ranked targets output by the CNN. This visual

inspection results in 581 candidates, which are subdivided into

three grades. In this section, we describe the construction of our

CNN and our visual inspection campaign in more detail.

3.1. Convolutional Neural Networks

We rely on a CNN to perform an initial identiﬁcation of lens

candidates from image data. The core operation in a CNN is a

Figure 2. Distributions of stellar mass and photometric redshift for both the

target data set in this work and the full sample of galaxies in DECaLS DR9,

based on the Zou et al. (2022)catalog. Galaxies in our target data set are

generally more massive and lie at lower redshift relative to the full distribution

of galaxies in DECaLS DR9.

Figure 3. Composite PNG image, shown in the two scalings used in this work

(Section 2). Left: scaling 1, useful to visualize features near bright objects.

Right: scaling 2, useful to visualize very faint features. Both scalings were

shown side-by-side during visual inspection of the candidates. Scaling 2 is

generally shown in this paper.

http://pil.readthedocs.io

The Astrophysical Journal, 954:68 (24pp), 2023 September 1 Zaborowski et al.

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IdentiﬁcationofGalaxy–GalaxyStrongLensCandidatesintheDECamLocalVolumeExplorationSurveyUsingMachineLearningE.A.Zaborowski1,2,3,A.Drlica-Wagner3,4,5,F.Ashmead4,J.F.Wu6,7,R.Morgan8,C.R.Bom9,A.J.Shajib3,5,70,S.Birrer10,11,W.Cerny3,5,12,E.J.Buckley-Geer3,4,B.Mutlu-Pakdil13,P.S.Ferguson14,K.Glazebrook15,S...

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Identification of GalaxyGalaxy Strong Lens Candidates in the DECam Local Volume Exploration Survey Using Machine Learning

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