# A Spitzer survey of Deep Drilling Fields to be targeted by the Vera C. Rubin
Observatory Legacy Survey of Space and Time

M. Lacy,1 J.A. Surace,2 D. Farrah,3,4 K. Nyland,5 J. Afonso,6,7 W.N.
Brandt,8,9,10 D.L. Clements,11 C.D.P. Lagos,12,13,14 C. Maraston,15 J.
Pforr,16 A. Sajina,17 M. Sako,18 M. Vaccari,19,20 G. Wilson,21 D.R.
Ballantyne,22 W.A. Barkhouse,23 R. Brunner,18 R. Cane,18 T.E. Clarke,24 M.
Cooper,25, A. Cooray,25 G. Covone,26 C. D’Andrea,18 A.E. Evrard,27,28 H.C.
Ferguson,29 J. Frieman,30,31 V. Gonzalez-Perez,15,32 R. Gupta,18 E.
Hatziminaoglou,33 J. Huang,34,35,36 P. Jagannathan,37 M.J. Jarvis,19,38 K.M.
Jones,39 A. Kimball,37 C. Lidman,40, L. Lubin41 L. Marchetti,42,19,20P.
Martini,43,44R.G. McMahon,45 S. Mei,46,47 H. Messias,48 E.J. Murphy,1 J.A.
Newman,49 R. Nichol,15 R.P. Norris,50 S. Oliver,51 I. Perez-Fournon,52,53 W.M.
Peters,24M. Pierre,54 E. Polisensky,24 G.T. Richards,55 S.E. Ridgway,56 H.J.A.
Röttgering,57 N. Seymour,58 R. Shirley,51,52 R. Somerville,59 M.A. Strauss,60
N. Suntzeff,61 P.A. Thorman,62 E. van Kampen,33 A. Verma,38 R. Wechsler,63
W.M. Wood-Vasey64

###### Abstract

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will
observe several Deep Drilling Fields (DDFs) to a greater depth and with a more
rapid cadence than the main survey. In this paper, we describe the “DeepDrill”
survey, which used the Spitzer Space Telescope Infrared Array Camera (IRAC) to
observe three of the four currently defined DDFs in two bands, centered on 3.6
$\mu$m and 4.5 $\mu$m. These observations expand the area which was covered by
an earlier set of observations in these three fields by the Spitzer
Extragalactic Representative Volume Survey (SERVS). The combined DeepDrill and
SERVS data cover the footprints of the LSST DDFs in the Extended Chandra Deep
Field–South field (ECDFS), the ELAIS-S1 field (ES1), and the XMM-Large-Scale
Structure Survey field (XMM-LSS). The observations reach an approximate
$5\sigma$ point-source depth of 2 $\mu$Jy (corresponding to an AB magnitude of
23.1; sufficient to detect a 10${}^{11}M_{\odot}$ galaxy out to $z\approx 5$)
in each of the two bands over a total area of $\approx 29\,$deg2. The dual-
band catalogues contain a total of 2.35 million sources. In this paper we
describe the observations and data products from the survey, and an overview
of the properties of galaxies in the survey. We compare the source counts to
predictions from the SHARK semi-analytic model of galaxy formation. We also
identify a population of sources with extremely red ([3.6]$-$[4.5] $>1.2$)
colours which we show mostly consists of highly-obscured active galactic
nuclei.

###### keywords:

surveys – infrared: general – infrared:galaxies – catalogues

††pubyear: 2019††pagerange: A Spitzer survey of Deep Drilling Fields to be
targeted by the Vera C. Rubin Observatory Legacy Survey of Space and Time–B

##  1 Introduction

Surveys by the Spitzer Space Telescope have proved extremely valuable for
finding and characterizing distant galaxies. The redshifting of the peak of
stellar emission at $1.6\,\mu$m into the Spitzer bands makes them especially
sensitive to high-redshift galaxies (e.g. Berta et al., 2007; Stefanon et al.,
2015; Cecchi et al., 2019). Spitzer data thus provide a very useful complement
to deep surveys in the optical, where the surface density of galaxies is
higher, but intrinsically luminous, high-redshift galaxies that are either
quiescent or dust-reddened can be outnumbered by lower-redshift, lower
luminosity blue galaxies. The Vera C. Rubin Observatory Legacy Survey of Space
and Time (LSST; Ivezić et al., 2019) will observe the Southern sky in six
optical bands ($u,\,g,\,r,\,i,\,z$ and $y$) in about 800 passes (summed over
all bands) over ten years, to a co-added 5$\sigma$ depth of $AB\approx
24.4-27.1$, depending on band. Within the survey area, there will be several
Deep Drilling Fields (DDFs) where observations are repeated more frequently,
resulting in both a better sampled cadence, and a deeper coadded final image
($AB\approx 26.2-28.7$, depending on band; Brandt et al., 2018; Scolnic et
al., 2018). The DDFs will thus become important reference fields for both time
domain and ultra-deep imaging studies.

We therefore proposed to observe the DDFs that had already been defined by the
LSST team in the near-infrared with the Spitzer Space Telescope during its
post-cryogenic mission (after the liquid helium cryogen supply for the
telescope was exhausted in May 2009). Although only the two shortest
wavelength bands of the Infrared Array Camera (IRAC; Fazio et al., 2004a;
Carey et al., 2010), at 3.6 and 4.5 $\mu$m, continued in operation following
the exhaustion of the cryogenic coolant in Spitzer in 2009, their sensitivity
was almost unchanged, as was the optical behaviour of the telescope and
instrument.

The observations described in this paper supplement an earlier set of
observations over smaller areas in these three fields by the Spitzer
Extragalactic Representative Volume Survey (SERVS; Mauduit et al., 2012), for
which images and catalogs are available from the Infrared Science Archive
(IRSA) (a second data release of SERVS, including the data fusion of Vaccari
(2015) and deeper Spitzer catalogs is planned). The DeepDrill images are of
similar depth to those from SERVS (a $5\sigma$ depth of $\approx 2\,\mu$Jy in
both bands), but cover more than twice the area ($\approx$ 27 deg2 compared to
12 deg2 in these fields covered by SERVS (see Table 1), though SERVS also
includes a further 6 deg2 in the Lockman and ELAIS-N1 fields). We also note
that deeper warm Spitzer data in the ECDFS field were taken recently as part
of the “Cosmic Dawn Survey" (principal investigator P. Capak). Figure 1 shows
the SERVS-DeepDrill survey in the context of other surveys at $\approx$3.6
$\mu$m. The IRAC image and catalog data on the three DDFs described in this
paper will be made available though the Infrared Science Archive (IRSA).

Figure 1: Depth versus area for extragalactic surveys at 3.6 $\mu$m. Red
crosses indicate surveys taken during the post-cryogenic phase of Spitzer as
Exploration Science or Frontier Legacy surveys (surveys which incorporate
previous efforts in the same fields have been combined). For comparison, we
show surveys taken during the cryogenic mission of Spitzer as cyan circles,
WISE mission in magenta, and two Guaranteed Time/Early Release (GTO/ERS)
surveys planned for the James Webb Space Telescope in grey. References (top to
bottom): AllWISE: Wright et al. (2010); Mainzer et al. (2011); SpIES: Timlin
et al. (2016); SSDF: Ashby et al. (2013a); SWIRE: Lonsdale et al. (2003);
SERVS$+$DeepDrill: this paper; SHELA: Papovich et al. (2016); COSMICDAWN Capak
et al. (2016); SDWFS Ashby et al. (2009); SHIRAZ: Annunziatella et al. in
preparation; SPLASH: Steinhardt et al. (2014); SCOSMOS: Sanders et al. (2007);
COMPLETE: Labbe et al. (2016); SpUDS Kim et al. (2011); SEDS: Ashby et al.
(2013b); SCANDELS Ashby et al. (2015); SIMPLE: Damen et al. (2011); GOODS:
Dickinson et al. (2003); JWST ERS/GTO surveys: Rieke et al. (2019).

The scientific motivation for this survey closely followed that for SERVS,
namely the study of galaxy evolution as a function of environment from $z\sim
5$ to the present, but with the additional feature of the deep and multi-epoch
LSST DDF data. The DDFs are expected to be observed throughout the ten year
duration of the LSST survey, with a cadence as frequent as once every two
nights at times of year when the fields are available for observation (Brandt
et al., 2018; Scolnic et al., 2018). The time domain adds the ability to
detect and obtain light curves of supernovae in distant galaxies (of which we
expect $\sim 10^{4}$ in the DDFs; LSST Science Collaboration et al., 2009),
and to allow the study of AGN flares, tidal disruption events, and other
variable phenomena. The Spitzer data provide information on the properties of
host galaxies of supernovae and other transients and help to identify and
classify AGN, and, indeed, SERVS has already proved useful for these types of
investigations (Lunnan et al., 2014; Falocco et al., 2015; Chen et al., 2018).
In conjunction with other data at optical and shorter near-infrared
wavelengths, the Spitzer survey in these fields will enhance the study of the
host galaxies of supernovae and AGN through improved estimates of stellar
mass, star formation history and reddening (Pforr et al., 2013).

Medium-depth surveys with warm Spitzer covering areas $\sim 10-100$ deg2 have
proven very valuable for both studies of individual rare objects (with
comoving densities $\sim 10^{-5}$ to $10^{-8}$ Mpc-3), and statistical studies
of populations including luminous AGN and quasars ($\sim 100$ deg-2 in such
surveys), galaxy clusters ($\sim 10$ deg-2) and ultraluminous dusty star-
forming galaxies ($\sim 1000$ deg-2). Examples from SERVS include
gravitational lenses, Lyman-$\alpha$ nebulae (Marques-Chaves et al., 2018,
2019) and galaxy clusters at $z\sim 0.3-2$ (Nantais et al., 2016, 2017;
Delahaye et al., 2017; Foltz et al., 2018; Chan et al., 2019; Pintos-Castro et
al., 2019; Old et al., 2020; van der Burg et al., 2020).

SERVS has proven particularly valuable for the identification of the host
galaxies of radio sources. These galaxies typically have high stellar masses,
and are bright in the IRAC bands, with $>95$% of faint radio sources
identified in SERVS (e.g. Luchsinger et al., 2015; Whittam et al., 2015;
Mahony et al., 2016; Ocran et al., 2017; Singh et al., 2017; Cotton et al.,
2018; Prandoni et al., 2018; Ocran et al., 2020a; Ishwara-Chandra et al.,
2020). The small population of infrared-faint radio sources (IFRS) that are
unidentified, or very faint, in the IRAC bands seem to represent a population
of dust-reddened, high-$z$ radio-loud AGN (Norris et al., 2011; Herzog et al.,
2014; Maini et al., 2016).

Dusty star-forming galaxies detected in the mm/submm with positions from ALMA
can often be identified with faint IRAC sources, allowing better understanding
of their stellar masses and extinctions (Simpson et al., 2014; Gómez-Guijarro
et al., 2019; Leung et al., 2019; Patil et al., 2019; Dudzevičiūtė et al.,
2020; Ocran et al., 2020a; Ocran et al., 2020b). Other uses include obtaining
constraints on stellar masses and ages of galaxies in overlapping deep
spectroscopic surveys (Calabrò et al., 2017; Thomas et al., 2017; Khusanova et
al., 2019), studying cosmic background radiation (Mitchell-Wynne et al., 2016)
and exploiting fields suitable for deep multi-conjugate adaptive optics
observations of distant galaxies (Lacy et al., 2018).

The DDFs have garnered significant observational resources from other
telescopes, from the radio and far infrared through to the X-ray. A list of
the large area ($>1\;{\rm deg}^{2}$) surveys in the DDFs may be found in Table
2 (see also Table 1 of Chen et al., 2018), and their coverages are illustrated
in Figures 2, 3 and 4. In the X-ray, the XMM-SERVS survey (Chen et al., 2018)
is covering the original SERVS areas in ES1, XMM-LSS and ECDFS. The optical
data are less homogeneous, including data from Hyper Suprime-Cam (HSC) (Aihara
et al., 2018; Ni et al., 2019), the Dark Energy Survey (DES; Abbott et al.,
2018), and the ESO ESIS and VOICE surveys (Berta et al., 2006; Vaccari et al.,
2016), however, as all three fields will be targeted for deep LSST
observations this is not a major concern. In the near-infrared, the VISTA
VIDEO survey (Jarvis et al., 2013) covers the whole SERVS area, and is
supplemented by VEILS (Hönig et al., 2017) which covers the DES fields that
are repeatedly observed to find supernovae and other time-domain phenomena
(hereafter the DES DDFs). The fields are covered by the SWIRE survey in the
mid-infrared (Lonsdale et al., 2003), and the HerMES survey in the far-
infrared (Oliver et al., 2012). In the radio, existing deep surveys from the
ATCA (ATLAS) (Franzen et al., 2015), GMRT (Smolčić et al., 2018) and LoFAR
(Hale et al., 2019) cover a significant fraction of the fields. The MIGHTEE
survey with MeerKAT, currently underway, will image the inner regions of all
three fields even more deeply at 0.9–1.7 GHz (Jarvis et al., 2016).

Vaccari (2015) combined SERVS data with catalogues of optical and near-
infrared photometry that were available at the time in all five SERVS fields,
and Pforr et al. (2019) used these catalogues to derive photometric redshifts
for $\approx 4$ million galaxies. Furthermore, the Herschel Extragalactic
Legacy Project has incorporated SERVS data within their workflows to produce
multi-wavelength catalogues and extract more accurate FIR/SMM fluxes to study
the dust properties of infrared galaxies over cosmic time (Vaccari, 2016;
Hurley et al., 2017; Małek et al., 2018; Shirley et al., 2019). For very
challenging applications, such as identifying rare sources, and obtaining
photometric redshifts accurate enough to study environments, more accurate
photometry that allows for the difference between the relatively large Spitzer
point spread function and overlapping ground-based surveys in the near-
infrared or optical is needed. This more refined photometry requires the
application of forced photometry techniques such as The tractor (Lang et al.,
2016), and has been successfully used in the XMM-LSS field (Nyland et al.,
2017), with the remaining SERVS/DeepDrill fields to follow. The improved
photometry and photometric redshifts from it enable the accurate estimation of
environmental parameters for galaxies out to at least $z\sim 1.5$ (Krefting et
al., 2020). The tractor photometry in XMM-LSS was also used to obtain
photometric redshifts for X-ray AGN in the XMM-SERVS survey (Chen et al.,
2018).

This paper is structured as follows: Section 2 describes the observations,
Section 3 the processing of the image data and tests to assess the quality of
the astrometric and photometric calibration. Section 4 describes the image and
catalogue data products to be included in the release. In Section 5, we
present an overview of the galaxy population in DeepDrill, including colours
and source counts, and also highlight sources with very red [3.6]$-$[4.5]
colours found in the survey. Section 6 contains a short summary.

Table 1: Spitzer/IRAC DeepDrill Observations

Field Name | DeepDrill Field Centre | SERVS Area∗ | DeepDrill | Total Area† 3.6 $\mu$m | Total Area† 4.5 $\mu$m | Total Area† Both
---|---|---|---|---|---|---
| (J2000) | (deg2) | Observation dates | (deg2) | (deg2) | (deg2)
ES1 | 00:37:48 $-$44:01:30 | 3 | 2015-09-27 to 2016-10-24 | 9.2 | 9.0 | 8.6
XMM-LSS | 02:22:18 $-$04:49:00 | 4.5 | 2015-10-21 to 2016-11-25 | 9.2 | 9.4 | 8.9
ECDFS | 03:31:55 $-$28:07:00 | 4.5 | 2015-05-04 to 2016-12-26 | 9.1 | 9.4 | 8.8

∗ The SERVS field centres differ slightly from the DeepDrill ones, but the
SERVS fields are entirely encompassed by the DeepDrill survey.

† Total areas are those covered by the SERVS and DeepDrill data combined.

Table 2: Other surveys ($>1$deg2) in the DeepDrill fields.

Survey | Field(s) | Bands/Wavelengths/Energies | Overlap Area |  Depth‡ | Reference
---|---|---|---|---|---
|  |  |  (deg2) |  |
XMM-SERVS |  ECDFS, XMM-LSS, ES1 | 0.5-10 keV | 13 |  $1.7\times 10^{-15}{\rm erg\;cm^{-2}s^{-1}}$ (0.5-2 keV) | Chen et al. (2018)
XXL |  XMM-LSS | 0.5-10 keV | 8 |  $5\times 10^{-15}{\rm erg\;cm^{-2}s^{-1}}$ (0.5-2 keV) | Pierre et al. (2016)
DEVILS |  ECDFS, XMM-LSS | 3750-8850Å | 4 |  Spectroscopic, $Y<21.2$ | Davies et al. (2018)
ESIS | ES1 | $B,~{}V,~{}R$ | 4.5 |  Vega magnitude $\approx 25$ | Berta et al. (2006)
VOICE | ECDFS | $u,~{}g,~{}r,~{}i$ | 8 |  $AB$ magnitude $\approx 26$ | Vaccari et al. (2016)
DES (DR1) |  ES1, XMM-LSS, ECDFS | $g,~{}r,~{}i,~{}z$ | 28 | $AB=25.1,\,24.8,\,24.2,\,23.4,\,22.2^{{\ddagger}{\ddagger}}$ | Abbott et al. (2018)
HSC (DR1) |  XMM-LSS | $g,~{}r,~{}i,~{}z,~{}y$ | $\approx 6$ | $i_{AB}\approx 26.5-27.0^{\S}$ | Aihara et al. (2018)
HSC (Ni et al.) | ECDFS | $g,~{}r,~{}i,~{}z$ | 5.7 | $AB\approx 25.9,~{}25.6,~{}25.8,~{}25.2$ | Ni et al. (2019)
SWIRE |  ECDFS, XMM-LSS, ES1 |  3.6, 4.5, 5.8, 8.0, 24, 60, 160 $\mu$m | 27 | various depths | Lonsdale et al. (2003)
OzDES |  ES1, XMM-LSS, ECDFS | Spectroscopic; 370-880 nm | 17 | $r_{AB}\approx 23$ | Childress et al. (2017)
PFS | XMM-LSS | Spectroscopic; 380-1260 nm | 6 | $J_{AB}\approx 23.4$ | Takada et al. (2014)
VIDEO |  ECDFS, XMM-LSS, ES1 | $(Z)^{*},(Y)^{*},J,H,K_{s}$ | 13 | (25.7), (24.6), 24.5, 24.0, 23.5 | Jarvis et al. (2013)
VEILS |  ECDFS, XMM-LSS, ES1 | $J,\,K_{s}$ | $\approx 6$ | 25.5, 24.5 | Hönig et al. (2017)
HerMES |  ECDFS, XMM-LSS, ES1 |  250, 350, 500 $\mu$m | 27 |  $\sim 25$mJy${\S}$ | Oliver et al. (2012)
ATLAS | ECDFS, ES1 | 1.4 GHz | 6.3 |  14-17$\mu$Jy | Franzen et al. (2015)
GMRT |  XMM-LSS | 610 MHz | 8 |  $\approx 1\;$mJy | Smolčić et al. (2018)
LoFAR |  XMM-LSS | 120–168 MHz | 9 | 1.4 mJy | Hale et al. (2019)
MIGHTEE |  ECDFS, XMM-LSS, ES1 |  900-1670 GHz∗∗ | 16.6 |  2$\mu$Jy | Jarvis et al. (2016)

‡ Typical source detection limit ($\approx 5\sigma$).

∗ ECDFS was only observed in $J,H$ and $K_{s}$.

∗∗ A smaller area survey (4 deg2) will also be carried out at 2-4 GHz in
ECDFS.

§ The XMM-LSS field of the HSC survey contains one ultradeep pointing and
three deep ones, so the depth varies with position.

‡‡ 10$\sigma$ magnitude limits from Abbott et al. (2018) $+0.75$ to convert to
$5\sigma$; note that there is significant overlap between DeepDrill and the
DES Deep Drilling fields (see Figures 2-4, which, when the data are co-added,
will be significantly deeper than the main survey).

§ Hurley et al. (2017)

##  2 Observations

We were awarded time to perform a survey of three of the four LSST DDFs that
have been defined at the time of writing:
111https://www.lsst.org/scientists/survey-design/ddf the ELAIS-S1 field (ES1),
the XMM-Large-Scale Structure Survey field (XMM-LSS) and the Extended Chandra
Deep Field-South field (ECDFS). The fourth DDF identified by LSST, the COSMOS
field, has deep coverage (to $5\sigma$ depth of $\approx 0.3\,\mu$Jy in both
bands) in the inner 2 deg2 from several Spitzer surveys (Sanders et al., 2007;
Steinhardt et al., 2014; Ashby et al., 2018). There is also a wider survey
(SHIRAZ; Annunziatella et al. 2020 in preparation), to a similar depth as
SERVS/DeepDrill that covers an additional $\approx$ 2 deg2 outside of the
central area to overlap with the Hyper Suprime-Cam Deep Survey (Aihara et al.,
2018).

The central areas of all three of our fields were observed as part of SERVS
(Mauduit et al., 2012) during the early months of the post-cryogenic Spitzer
mission (2009-07-28 to 2011-03-06). The DeepDrill Survey (Program ID 11086,
P.I. Lacy) was observed between 2015-05-04 and 2016-12-26 (Table 1). The
DeepDrill observations followed the SERVS Astronomical Observation Request
(AOR) construction, with each AOR making up a square tile of nine pointings,
each pointing consisting of six repeats of 100s frames dithered using the IRAC
small cycling dither pattern.222See the IRAC Instrument Handbook
https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/
The use of Fowler sampling in the IRAC detectors (Fazio et al., 2004b) means
that the 100s frame time corresponds to a little less than 100s integration on
sky: 93.6s at 3.6 $\mu$m and 96.8s at 4.5 $\mu$m. The fields were imaged in
two epochs to facilitate rejection of asteroids, with a targeted depth of 12
frames. Due to scheduling constraints, the time separation of the two epochs
was non-uniform, ranging from a few weeks to $\sim 1$ year. The spatial
coverage is also non-uniform. Areas around the edges of the SERVS fields in
particular received additional coverage, and some outlying regions did not
receive the full coverage. Figure 5 shows the distribution of coverage in each
field. The area in each band with a coverage of 9 or more 100-second frames
(i.e. with $>$87% of the sensitivity of the nominal coverage of 12 frames),
and the area with coverage of 9 or more in both bands at the same position are
listed in Table 1 (the area with both bands is slightly smaller as the two
IRAC detectors are offset). We encourage users with a need for uniformity in
depth to make use of the supplied coverage maps.

The survey was designed such that source confusion only becomes significant
near the nominal flux density limit of the survey, where there are about 30
beams per source, the typical value at which source confusion becomes
significant (Condon et al., 2012). In Appendix A, we show how the confusion
noise is expected to vary with depth of coverage in the survey, including both
confusion from randomly-distributed sources and an additional term due to
galaxy clustering. To more accurately extract faint source parameters from the
deepest parts of the survey we recommend PRF fitting of sources and their
near-neighbors, which can be further improved by using a prior from a higher
resolution survey of similar or greater depth.

##  3 Data analysis

###  3.1 Image processing

Data processing of the DeepDrill data was similar to that carried out for the
SERVS dataset (Mauduit et al., 2012), using a data cleaning pipeline derived
from processing SWIRE and COSMOS data (Lonsdale et al., 2003; Sanders et al.,
2007). The processing began with the Corrected Basic Data (CBCD) frames from
the Spitzer Science Center (basic calibrated data frames with corrections for
common artifacts, see Lowrance et al., 2016). A refined dark frame for each
AOR was constructed after identifying and masking astronomical sources in the
data and subtracted from each individual frame in the AOR. Hot pixels in the
4.5$\mu$m data were masked, and the column pulldown correction provided in the
CBCD was improved (see Lowrance et al., 2012). The images were then rectified
to a common background level corresponding to the mean background during the
observations. Further corrections were made for latent images on a frame-by-
frame basis, as these are particularly prevalent in warm mission data. The
data were then mosaicked using mopex (Makovoz et al., 2006) (see table 3 of
Mauduit et al., 2012, for the parameters used).

A pointing issue was found and corrected in the ES1 field, where the pointing
refinement task in the Spitzer data processing pipeline failed for four of the
AORs in the South of the field. We also found that we needed to correct the
photometric calibration of the SERVS data in ES1, which was taken early in the
post-cryogenic mission, while the instrument performance was still being
characterized and before the final array temperatures had been set. This was
done by comparing the fluxes of sources in the overlap between the SERVS and
DeepDrill datasets, and applying the measured offsets to the SERVS data (1.04
at [3.6] and 0.98 at [4.5]). The ES1 data are thus all on the final warm
mission calibration. Following Mauduit et al. (2012), the $\approx 1$ deg2 in
the Southwestern part of the XMM-LSS field that was taken during the cryogenic
mission as part of the SpUDS programme (Kim et al., 2011) was included in the
final images. The calibrations of these data are the same as those of the
DeepDrill data to within 1%, but the SpUDS data are significantly deeper.
Similarly, the central $\approx 0.5$ deg2 of the ECDFS field contains data
from the much deeper cryogenic SIMPLE (Damen et al., 2011) and GOODS
(Dickinson et al., 2003) programmes. However, in this case we used only a
depth of $\approx 12$ frames per sky position to obtain an approximately
uniform depth for the survey of that field.

###  3.2 Astrometric accuracy

We matched the DeepDrill catalogs to Gaia Data Release 2 (DR2; Lindegren et
al., 2018). The IRAC pointing is calibrated using 2MASS (Skrutskie et al.,
2006), and the pointing refinement pipeline now includes proper motion
information to provide positions for epoch J2000 (Lowrance et al., 2016). We
therefore used the proper motion information in Gaia to derive positions
appropriate for the year 2000 to match to the Spitzer positions. We matched
the dual-band DeepDrill catalogues to Gaia using a
1$\aas@@fstack{\prime\prime}$0 match radius. 3% of sources in the DeepDrill
survey have counterparts in Gaia DR2. The results are shown in Table 3, where
we list the mean systematic offset between Spitzer and Gaia DR2 positions
$\Delta$(R.A.) and $\Delta$(Decl.), along with the scatter $\sigma$(R.A.) and
$\sigma$(Decl.), representing the positional accuracy of a typical source in
the survey. This scatter is independent of source flux, and is thus probably
dominated by the scatter in the pointing refinements of individual frames,
which is $\approx$0$\aas@@fstack{\prime\prime}$3 on an individual CBCD frame
(Lowrance et al., 2016). All systematic offsets when averaged over a mosaic
are $<0.1$ arcsec.

Figure 2: The footprints of multi-wavelength surveys on the ELAIS-S1 field (see Table 2 for survey references), superimposed on a greyscale of the IRAC 4.5 $\mu$m coverage. Upper left: optical surveys (the DES DDFs are shown in cyan with rectangles indicating the individual chips, the ESIS survey in mauve with cross-hatches, and the LSST footprint is shown as a black circle), upper right, near-infrared surveys (VIDEO in red, left hatched and VEILS in orange, right-hatched), lower left, 24 $\mu$m coverage from SWIRE in magenta and far-infrared coverage in HerMES in green (the L4 data is deeper than the hatched L6 data), and lower right the X-ray XMM-SERVS coverage in yellow, cross-hatched and the ATLAS radio survey in red, with circular hatches. Figure 3: The footprints of multi-wavelength surveys on the XMM-LSS field (see Table 2 for survey references), superimposed on a greyscale of the IRAC 4.5 $\mu$m coverage. Upper left: optical surveys (the LSST footprint is shown as a black circle, the DES DDFs are in cyan with rectangles indicating the individual chips, the HSC-deep survey is in green with left hatches, the HSC-ultradeep in blue with cross-hatching). Upper right: near-infrared surveys (VIDEO in red, left hatched and VEILS in orange, right-hatched), lower left: 24 $\mu$m coverage from SWIRE in magenta and far-infrared coverage from HerMES in green (the L3 data is the deepest, L4 less deep and L6 the shallowest). Bottom right: X-ray surveys - the XXL survey coverage is shown in light yellow, left-hatched and the XMM-SERVS survey in dark yellow, cross-hatched). The position of the infrared-bright, variable star Mira ($K\approx-2.2$) is indicated with the black star symbol. Figure 4: The footprints of multi-wavelength surveys on the ECDFS field (see Table 2 for survey references), superimposed on a greyscale of the IRAC 4.5 $\mu$m coverage. Upper left: optical surveys (the LSST footprint is shown as a black circle, the DES DDFs are in cyan with rectangles indicating the individual chips, the HSC-deep survey in is green with left hatches, and the VOICE survey is in blue with circular hatches). Upper right: near-infrared surveys (VIDEO in red, left hatched and VEILS in orange, right-hatched), lower left, 24 $\mu$m coverage from SWIRE in magenta and far-infrared coverage in HerMES in green (the L2 data is deeper than the hatched L6 data), and lower right the X-ray XMM-SERVS coverage in yellow, cross-hatched and the ATLAS radio survey in red, with circular hatches. Figure 5: Area of each field as a function of coverage in units of IRAC image frames of 100s duration. The distribution for the 3.6 $\mu$m band is shown as the blue dotted line, and that for the 4.5 $\mu$m band as the continuous red line. The small areas of very high ($>50$) frame coverage in XMM-LSS and ECDFS result from the inclusion of data from earlier deep surveys in these fields, as detailed in Section 3. Table 3: IRAC source matches in Gaia DR2: number of matches, mean position offsets and scatter. Field | Matches |  $\Delta$(R.A.) |  $\Delta$(Dec.) |  $\sigma$(R.A.) |  $\sigma$(Dec.)
---|---|---|---|---|---
|  | (arcsec) | (arcsec) | (arcsec) | (arcsec)
ES1 | 24375 | 0.07 | 0.00 | 0.24 | 0.22
XMM-LSS | 19712 |  $-$0.04 | 0.02 | 0.23 | 0.21
ECDFS | 23946 |  $-$0.02 | 0.02 | 0.20 | 0.21

###  3.3 Photometric accuracy

The photometric calibration history of IRAC is given in Carey et al. (2012).
The post-cryogenic mission calibration factors were obtained by matching the
fluxes of the standard stars to the cryogenic observations, and have an
absolute accuracy $\approx 3$%. Some scatter is to be expected, as the
$\approx 1\aas@@fstack{\prime\prime}8$ IRAC PSF is undersampled by the
1$\aas@@fstack{\prime\prime}$2 pixels, and the sensitivity across each pixel
varies as a function of position within the pixel. As most of the sources in
DeepDrill are slightly extended, and because any given point in the sky is
covered by a large number of observations, this intrapixel sensitivity
variation is assumed to average out. Aperture corrections were applied as
described in Mauduit et al. (2012), using the values in Table 2 of that paper.

As noted in Section 3, some SERVS fields (including ES1) were taken early in
the Spitzer warm mission, before the calibration factors were finalized. In
SERVS, this issue was dealt with by forcing the flux densities to the same
scale as SWIRE. The SWIRE flux densities were based on an early calibration of
IRAC, and thus there are significant differences between the calibration of
the DeepDrill data (which are based on the final Spitzer post-cryogenic
mission calibration) and the original SERVS data in the same fields. Table 4
gives the ratio of the calibration factors derived from comparing the
DeepDrill to the SERVS Aperture 2 (3$\aas@@fstack{\prime\prime}$9 diameter)
flux densities for sources $>10\,\mu$Jy in the same field. The more accurate
DeepDrill calibration is preferred.

Table 4: Differences in the photometic calibration between SERVS and DeepDrill (the DeepDrill calibration is preferred.) Field | DeepDrill/SERVS flux ratio
---|---
| 3.6 $\mu$m | 4.5 $\mu$m
ES1 | 0.95$\pm 0.01$ | 0.96$\pm 0.01$
XMM-LSS | 0.96$\pm 0.01$ | 0.98$\pm 0.01$
ECDFS | 0.95$\pm 0.01$ | 0.97$\pm 0.01$

##  4 Data products

This section briefly describes the data products from DeepDrill that are
available in the data release. These consist of images and two sets of
catalogues, single-band catalogues and dual-band catalogues.

###  4.1 Images

Images were made at a pixel scale of 0$\aas@@fstack{\prime\prime}$60 per pixel
(oversampling the PSF width of 1$\aas@@fstack{\prime\prime}$8), and are
calibrated in MJy sr-1. This results in a conversion factor from pixel values
to $\mu$Jy of 8.46. Coverage images were made, in units of 100-second IRAC
frames, along with uncertainty images. Finally, mask images, showing the
location of bright stars in the fields are included, made using the methods
described in Mauduit et al. (2012).

###  4.2 Catalogues

Single-band (3.6$\;\mu$m and 4.5$\;\mu$m) catalogues were produced using
SExtractor (Bertin & Arnouts, 1996). Parameters used are shown in Table 5,
note some of these differ from Mauduit et al. (2012), principally to improve
background filtering: the background mesh size was changed from 32 to 16
pixels, and the filtersize from five to three. These changes improved the
background estimates in regions of scattered light around bright objects. The
default convolution filter (2-pixel [1$\aas@@fstack{\prime\prime}$2] FWHM) was
used for source detection, along with a weight map (the depth of coverage map
was used). Photometric apertures labelled 1–5 corresponded to the SWIRE
(Lonsdale et al., 2003) standard apertures with radii
1$\aas@@fstack{\prime\prime}$4, 1$\aas@@fstack{\prime\prime}$9,
2$\aas@@fstack{\prime\prime}$9, 4$\aas@@fstack{\prime\prime}$1 and
5$\aas@@fstack{\prime\prime}$8, respectively, with aperture corrections
applied per Mauduit et al. (2012). Uncertainties in the flux densities are
from SExtractor, adjusted to allow for the effects of pixel resampling and
detector gain. An additional 3% error is added in quadrature to account for
the systematic error in the IRAC flux density scale. The raw output from
SExtractor was filtered to output sources with a signal-to-noise ratio $>5$ in
the SWIRE aperture 2 (3$\aas@@fstack{\prime\prime}$9 diameter). The flag
column in the catalogue is a bitwise flag that takes the first and second bit
of the SExtractor flag (bit 1: photometry may be affected by neighbours or bad
pixels, and bit 2: the source was blended with a neighboring object), and adds
a further flag bit (3) to indicate that the source is either a bright ($K<12$)
star, or within the region affected by the halo of a bright star according to
the rules in Mauduit et al. (2012). The catalog columns are listed in Table 6.
The star masks used to create this flag are included in the data delivery to
the Infrared Science Archive (IRSA). The 3.6$\;\mu$m and 4.5$\;\mu$m
catalogues contain 2.7 and 2.5 million sources, respectively, summed over all
three fields.

Table 5: Source extraction parameters used in SExtractor Parameter | Value
---|---
DETECT_MINAREA | 5
DETECT_THRESH | 1.0
DETECT_MINCONT | 0.0005
ANALYSIS_THRESH | 0.4
BACK_SIZE | 16
BACK_FILTERSIZE | 3
BACKPHOTO_TYPE | LOCAL
Table 6: Single band catalogue columns Column(s) | Description | Units
---|---|---
1 | Name (J2000 coordinates prefixed by DD1) | -
2 | Right Ascension (ICRS) | Degrees
3 | Declination (ICRS) | Degrees
4-8 | Aperture corrected flux densities in apertures 1-5 |  $\mu$Jy
9 | Isophotal flux density |  $\mu$Jy
10 | SExtractor Auto flux density |  $\mu$Jy
11-17 | Uncertainties on columns 4-10 |  $\mu$Jy
18 | Kron radius | 0$\aas@@fstack{\prime\prime}$6 pixels
19 | Signal-to-noise ratio | -
20 | Local RMS noise |  $\mu$Jy
21 | Coverage | 100s frames
22 | Flag (see text) | -
Table 7: Dual band catalogue columns Column(s) | Description | Units
---|---|---
1 | Name (J2000 coordinates prefixed by DD1) | -
2 | Right Ascension (ICRS) | Degrees
3 | Declination (ICRS) | Degrees
4-8 | Aperture corrected flux densities at 3.6$\mu$m in apertures 1-5 |  $\mu$Jy
9-13 | Aperture corrected flux densities at 4.5$\mu$m in apertures 1-5 |  $\mu$Jy
14-23 | Uncertainties in columns 4-13 |  $\mu$Jy
24-25 | Isophotal flux densities at 3.6 and 4.5$\mu$m |  $\mu$Jy
26-27 | Uncertainties in columns 24-25 |  $\mu$Jy
28-29 | SExtractor Auto flux densities at 3.6 and 4.5$\mu$m |  $\mu$Jy
30-31 | Uncertainties in columns 28-29 |  $\mu$Jy
32-33 | Kron radii at 3.6 and 4.5$\mu$m | 0$\aas@@fstack{\prime\prime}$6 pixels
34-35 | Signal-to-noise ratios at 3.6 and 4.5$\mu$m | -
36-37 | Coverage | 100s frames
38-39 | Flags at 3.6 and 4.5$\mu$m (see text) | -

Dual-band catalogues were created by matching the two single-band catalogues
produced by SExtractor with a 0$\aas@@fstack{\prime\prime}$6 matching radius
(before applying the $5\sigma$ cut) and then applying a 3$\sigma$ cut for the
signal-to-noise ratio of the detection in a 3$\aas@@fstack{\prime\prime}$9
diameter at both 3.6 $\mu$m and 4.5$\mu$m. (We considered using the dual-image
capability of SExtractor, but we found that the approach of performing two
independent source detection rounds on the individual channels and then
merging the results in catalogue space resulted in a more reliable catalogue.)
There will thus be objects present in the merged catalogue that are not
present in the single-band catalogues (and vice-versa). The 3.6 $\mu$m
positions are given in the catalog as these correspond to the smallest PSF.
Columns are listed in Table 7. The dual-band catalogues in each field contain
approximately 800,000 sources, giving a total of 2.4 million sources.

Multiwavelength catalogues in the center 3–5 deg2 of each of the DeepDrill
fields are in the process of construction (Nyland et al., in preparation,
Nyland et al., 2017). These employ forced photometry with the tractor (Lang et
al., 2016), using the ground-based near-infrared VIDEO data as a prior to
overcome source blending issues. Recovered IRAC magnitudes from this technique
are a good match to the aperture magnitudes in SERVS/DeepDrill (Nyland et al.,
2017). These catalogues are not part of the initial DeepDrill data release,
but will form part of a subsequent data release.

Figure 6: [3.6]$-$[4.5] colours of galaxies as a function of redshift (cf.
Papovich, 2008). The grey dots show the galaxies with photometric redshifts in
the XMM-LSS field (Krefting et al., 2020), spectroscopic galaxy targets from
the OzDES survey (Childress et al., 2017) (OzDES LRG, ClusterGalaxy, RedMaGiC,
BrightGalaxy, Emission Line Galaxy and Photo-z types) are shown as orange
dots, AGN_monitoring targets from OzDES are shown as cyan crosses, and A2SUDS
submm galaxies with photometric redshifts as magenta crosses. The lines
indicate various color cuts; the “Blue cut” (blue dotted line) is the line
below which the blue population of Figure 8 (d) is selected; “red cut” (red
dotted line) the line above which the red population of Figure 8 (d) is
selected. We also include the [3.5]$-$[4.6] color cut of Stern et al. (2012)
(“AGN cut”; cyan dashed line), above which candidate AGN dominate in the much
shallower WISE survey. Three models based on Maraston (2005) evolutionary
synthesis models (see Guarnieri et al., 2019) are shown, a 3 Gyr old dusty
star-forming galaxy, a 3 Gyr passive galaxy and a 100 Myr galaxy. (Note that
the 3 Gyr models do not extend beyond $z=2.17$, where the age of the Universe
is 3 Gyr.) We also plot the composite SED of the A2SUDS submm galaxies from
Dudzevičiūtė et al. (2020).

##  5 Analysis and results

###  5.1 [3.6]–[4.5] colour as a function of redshift

To show the variation of galaxy colour with redshift in DeepDrill we use the
photometric redshifts in XMM-LSS from Krefting et al. (2020). These use
tractor-based forced photometry (Nyland et al. 2020, in preparation, see also
Nyland et al., 2017; Cotton et al., 2018) to obtain redshift estimates for
690,000 sources in the overlap between SERVS and DeepDrill. These photometric
redshifts have an uncertainty in $z/(1+z)\approx 0.03$ and outlier fraction
1.5% in the redshift range $0<z<1.5$. To supplement these photometric
redshifts with a smaller, but more accurate, sample of spectroscopic redshifts
we matched to the OzDES Data Release 1 (Childress et al., 2017), finding 9623
matches within 1${}^{{}^{\prime\prime}}$ of the DeepDrill positions
(corresponding to $\approx 0.4$% of the galaxies in DeepDrill). The OzDES AGN
were specially targeted for monitoring programmes.

In the absence of photometric redshifts (still the case over much of the
DeepDrill survey), the [3.6]$-$[4.5] colour can be used as a crude redshift
indicator (Papovich, 2008). Figure 6 shows this colour as a function of
redshift. The models (based on Maraston, 2005) show that the dip in the
[3.6]$-$[4.5] colour at $z\approx 0.6$–$0.8$ is a strong function of the shape
of the spectral energy distribution in the near-infrared, which is itself a
strong function of the age and nature of the stellar population. Nevertheless,
the spectroscopic and photometric redshifts show that most galaxies follow a
fairly tight trend in [3.6]$-$[4.5] colour as a function of redshift. Galaxies
with blue colours (bluer than the blue dotted line at [3.6]$-$[4.5]$=-0.3$ in
Figure 6) are at $z\approx 0.5$–$0.9$, and galaxies with red colours (redder
than the red dotted line corresponding to [3.6]$-$[4.5]$=$0.1) are at
$z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1.3$. Also shown in Figure 6 is the
boundary color commonly used to select AGN candidates from WISE data (Stern et
al., 2012) : [3.5]$-$[4.6]$>$0.8 in the Vega system, corresponding to
[3.6]$-$[4.5]$>$0.16 in AB. We also plot the colours and photometric redshifts
of submm-selected galaxies from the A2SUDS sample of Dudzevičiūtė et al.
(2020) and the locus of the [3.6]$-$[4.5] colour from their composite SED. The
very red colour of the A2SUDS SED in the range
$0.3\stackrel{{\scriptstyle<}}{{{}_{\sim}}}z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}0.5$
is due to the strong 3.3$\mu$m Polycyclic Aromatic Hydrocarbon (PAH) feature
passing through the [4.5] band.

In Figure 7 we plot the [4.5] magnitude against redshift for the sample
matched to OzDES, the A2SUDS sample and the galaxies with photometric
redshifts (note that the “banding” in the distribution of photometric
redshifts is an artifact of the photometric redshift algorithm). Most of the
galaxies in the survey have stellar masses between $10^{10}$ and
$10^{11}M_{\odot}$, and galaxies with masses of 10${}^{11}M_{\odot}$ can be
detected out to $z\approx 5$. As expected, the AGN are red and bright, though
it should be noted that around the AllWISE limit of $AB\,\approx\,19.5$ the
counts of red galaxies begin to rapidly exceed those of AGN, making selection
of AGN based on [3.6]$-$[4.5] colour alone highly contaminated at faint
magnitudes.

Figure 7: Magnitude versus redshift in [4.5] (symbols as for Figure 6). Also
plotted are two instances of the 3 Gyr old dusty star-forming galaxy model in
Figure 6 with stellar masses of 10${}^{10}M_{\odot}$ and 10${}^{11}M_{\odot}$,
and a 1 Gyr dusty galaxy model with 10${}^{11}M_{\odot}$ from the same
library, along with the composite submm galaxy SED from A2SUDS.

###  5.2 Source counts

Source counts from Spitzer surveys have been presented in Fazio et al.
(2004b), Mauduit et al. (2012), Ashby et al. (2013a), Ashby et al. (2015) and
Ashby et al. (2018). We compare the differential counts (number per square
degree per magnitude) in the DeepDrill fields (Tables 8, 9) to the S-CANDELS
counts of Ashby et al. (2015) (the deepest of the currently-published post-
cryogenic misson counts) in Figure 8. Completeness estimates from Mauduit et
al. (2012) were used to correct the counts at AB magnitudes $<21.25$; at
fainter magnitudes we ran a new set of simulations (6000 simulated point
sources in each half-magnitude bin) on the DeepDrill ES1 field to improve our
estimates of completeness (Figure 8 (c)). These simulations involved scaling
point sources extracted from the mosaics to a known flux density corresponding
to the mid-point of the magnitude bin, adding a grid of 6000 of these sources
at known positions to the mosaic, and rerunning SExtractor. The resulting
catalogues were then matched to the known positions within
1$\aas@@fstack{\prime\prime}$2, and the fraction of recovered sources noted as
the completeness value for that bin. These extractions also allowed us to
examine possible biases in the recovered flux densities near the flux density
limit from both Eddington bias (Eddington, 1940) and biases from source
confusion resulting in an oversubtracted background. We find significant
biases only at the faintest magnitudes – at $AB=22.75$ (2.9 $\mu$Jy) the
recovered flux densities are higher than those input by 3% at [3.6] and 5% at
[4.5], however, this rises to 15% at [3.6] and 24% at [4.5] at $AB=23.25$ (1.8
$\mu$Jy), consistent with Eddington bias dominating. We thus do not list the
counts below $AB=22.75$.

The DeepDrill counts agree well with the deeper counts from the literature,
starting to diverge slightly at $AB\approx 22$, probably due to differences in
the photometric algorithms used when the significance of the DeepDrill
detections drops below $\approx 10\,\sigma$, and the source confusion limit is
approached. We also constructed counts from the deeper data in the $\approx
0.45\,$deg2 of the XMM-LSS field that uses images from the SpUDS survey,
verifying that the counts in that area have the same shape as the overall
counts to $AB\approx 22.5$, beyond which they are more complete, as expected.

To measure the counts in DeepDrill, we used the flux densities within the
3$\aas@@fstack{\prime\prime}$8 diameter aperture (with an aperture correction
of 0.736 at [3.6] and 0.716 at [4.5]). This will slightly underestimate the
fluxes (and hence the counts) at bright magnitudes ($AB\sim 16-18$), where the
galaxies may be resolved on scales larger than the aperture (at brighter
magnitudes the counts are dominated by stars). A comparison to the counts made
with the 8$\aas@@fstack{\prime\prime}$2 diameter aperture (with aperture
corrections of 0.920 and 0.905 at [3.6] and [4.5], respectively) shows that
the counts in this range are about $\approx 0.1$ dex higher in both bands.
Over other magnitude ranges the differences are less than 0.1 dex (except at
$AB\stackrel{{\scriptstyle>}}{{{}_{\sim}}}21$, when the higher noise results
in more incompleteness in the larger aperture). It is also the case that the
aperture corrections are derived from point sources, so both the fluxes and
the completeness corrections are strictly incorrect for marginally-resolved
galaxies. However, the good agreement between the counts from the two
apertures with very different aperture corrections argues against this being a
significant problem. The counts of Ashby et al. (2015) used a point-source
fitting method and agree with ours to within 0.1 dex over the whole magnitude
range. The point-source fitting method works better on blended objects, but
also can be affected by flux boosting from very low level cosmic rays, whereas
our use of SExtractor will probably lead to slight undercounting at faint
magnitudes due to blending near the confusion limit.

Figure 8: DeepDrill source counts. (a) the 3.6 $\mu$m counts: the three sets
of points show the completeness-corrected counts from each DeepDrill field.
The dot-dashed magenta line shows the mean counts from the S-CANDELS fields
(Ashby et al., 2015). The magenta dotted line shows star counts from the UDS
field (which is within the DeepDrill XMM-LSS field) from Ashby et al. (2015),
using the model from Wainscoat et al. (1992) as refined by Cohen (1993, 1994,
1995) and Arendt et al. (1998). (As all three fields have Galactic latitudes
of $-60^{\circ}\pm 15^{\circ}$ these will be representative of the survey as a
whole.) The dashed black and green lines show the galaxy counts from the Shark
(Lagos et al., 2018; Lagos et al., 2019) and GALFORM semi-analytic
simulations, respectively, and the dotted red line those from the EAGLE
hydrodynamic simulations. (b) the same for the 4.5 $\mu$m counts. (c) the
survey completeness as a function of magnitude. (d) counts for red
([3.6]$-$[4.5]$>$0.1) and blue ([3.6]$-$[4.5]$<$-0.3) sources separately, with
the total [4.5] counts also shown, along with model counts from Shark, GALFORM
and EAGLE. Table 8: Counts at 3.6 $\mu$m and their uncertainties for the three
DeepDrill fields, the mean, and those from the simulations.

AB Mag | Completeness | ES1 | Error |  XMM-LSS | Error | ECDFS | Error | Mean | Error | Shark | GALFORM | EAGLE
---|---|---|---|---|---|---|---|---|---|---|---|---
14.25 | 1.0 | 1.586 | 0.032 | 1.4 | 0.04 | 1.331 | 0.044 | 1.453 | 0.02 | 0.444 | 0.521 | -
14.75 | 1.0 | 1.928 | 0.022 | 1.883 | 0.023 | 1.91 | 0.022 | 1.907 | 0.013 | 0.785 | 0.656 | -
15.25 | 1.0 | 2.024 | 0.02 | 2.068 | 0.019 | 2.098 | 0.018 | 2.065 | 0.011 | 1.09 | 0.889 | -
15.75 | 1.0 | 2.185 | 0.016 | 2.157 | 0.017 | 2.229 | 0.016 | 2.191 | 0.009 | 1.387 | 1.164 | -
16.25 | 1.0 | 2.304 | 0.014 | 2.314 | 0.014 | 2.371 | 0.013 | 2.331 | 0.008 | 1.666 | 1.403 | -
16.75 | 1.0 | 2.428 | 0.012 | 2.447 | 0.012 | 2.508 | 0.011 | 2.462 | 0.007 | 1.986 | 1.675 | -
17.25 | 1.0 | 2.613 | 0.01 | 2.611 | 0.01 | 2.675 | 0.009 | 2.634 | 0.005 | 2.282 | 2.023 | 1.642
17.75 | 1.0 | 2.811 | 0.008 | 2.825 | 0.008 | 2.857 | 0.008 | 2.831 | 0.004 | 2.576 | 2.337 | 2.318
18.25 | 1.0 | 3.088 | 0.006 | 3.089 | 0.006 | 3.111 | 0.006 | 3.096 | 0.003 | 2.878 | 2.658 | 2.853
18.75 | 1.0 | 3.427 | 0.004 | 3.42 | 0.004 | 3.425 | 0.004 | 3.424 | 0.002 | 3.170 | 3.018 | 3.320
19.25 | 0.98 | 3.736 | 0.003 | 3.734 | 0.003 | 3.731 | 0.003 | 3.733 | 0.002 | 3.448 | 3.332 | 3.668
19.75 | 0.96 | 3.973 | 0.002 | 3.966 | 0.002 | 3.969 | 0.002 | 3.97 | 0.001 | 3.699 | 3.613 | 3.915
20.25 | 0.95 | 4.132 | 0.002 | 4.13 | 0.002 | 4.132 | 0.002 | 4.131 | 0.001 | 3.917 | 3.846 | 4.111
20.75 | 0.94 | 4.24 | 0.002 | 4.241 | 0.002 | 4.242 | 0.002 | 4.241 | 0.001 | 4.086 | 4.058 | 4.238
21.25 | 0.91 | 4.342 | 0.008 | 4.344 | 0.008 | 4.345 | 0.008 | 4.344 | 0.008 | 4.216 | 4.237 | 4.338
21.75 | 0.87 | 4.433 | 0.008 | 4.429 | 0.008 | 4.435 | 0.008 | 4.432 | 0.008 | 4.323 | 4.404 | 4.417
22.25 | 0.83 | 4.522 | 0.009 | 4.529 | 0.009 | 4.523 | 0.009 | 4.525 | 0.009 | 4.422 | 4.562 | 4.494
22.75 | 0.76 | 4.652 | 0.010 | 4.650 | 0.010 | 4.646 | 0.010 | 4.649 | 0.009 | 4.524 | 4.701 | 4.580

Counts and errors are expressed as log${}_{10}(N)$, where $N$ is the count per
square degree per magnitude. The errors are based on Poisson statistics,
combined with the uncertainty in the completeness estimates (which dominate at
fainter magnitudes).

Table 9: Logarithmic counts at 4.5 $\mu$m and their uncertainties for the
three DeepDrill fields, the mean, and those from the simulations.

AB Mag | Completeness | ES1 | Error |  XMM-LSS | Error | ECDFS | Error | Mean | Error | Shark | GALFORM | EAGLE
---|---|---|---|---|---|---|---|---|---|---|---|---
14.25 | 1.0 | 1.419 | 0.04 | 1.289 | 0.045 | 1.332 | 0.043 | 1.35 | 0.022 | 0.297 | 0.085 | -
14.75 | 1.0 | 1.761 | 0.027 | 1.825 | 0.024 | 1.859 | 0.023 | 1.817 | 0.014 | 0.604 | 0.521 | -
15.25 | 1.0 | 1.886 | 0.023 | 1.876 | 0.023 | 1.908 | 0.022 | 1.89 | 0.013 | 0.930 | 0.706 | -
15.75 | 1.0 | 2.016 | 0.02 | 2.037 | 0.019 | 2.079 | 0.018 | 2.045 | 0.011 | 1.24 | 0.919 | -
16.25 | 1.0 | 2.201 | 0.016 | 2.176 | 0.016 | 2.252 | 0.015 | 2.211 | 0.009 | 1.545 | 1.225 | -
16.75 | 1.0 | 2.338 | 0.014 | 2.341 | 0.013 | 2.387 | 0.013 | 2.356 | 0.007 | 1.831 | 1.457 | -
17.25 | 1.0 | 2.5 | 0.011 | 2.508 | 0.011 | 2.577 | 0.01 | 2.53 | 0.006 | 2.149 | 1.803 | 1.370
17.75 | 1.0 | 2.69 | 0.009 | 2.722 | 0.009 | 2.762 | 0.008 | 2.726 | 0.005 | 2.423 | 2.149 | 2.015
18.25 | 1.0 | 2.965 | 0.007 | 2.972 | 0.006 | 2.995 | 0.006 | 2.978 | 0.004 | 2.717 | 2.453 | 2.642
18.75 | 1.0 | 3.258 | 0.005 | 3.263 | 0.005 | 3.269 | 0.005 | 3.263 | 0.003 | 3.012 | 2.776 | 3.097
19.25 | 0.98 | 3.607 | 0.003 | 3.604 | 0.003 | 3.608 | 0.003 | 3.606 | 0.002 | 3.298 | 3.116 | 3.517
19.75 | 0.96 | 3.919 | 0.002 | 3.927 | 0.002 | 3.926 | 0.002 | 3.924 | 0.001 | 3.577 | 3.450 | 3.811
20.25 | 0.95 | 4.131 | 0.002 | 4.131 | 0.002 | 4.137 | 0.002 | 4.133 | 0.001 | 3.829 | 3.755 | 4.025
20.75 | 0.93 | 4.263 | 0.002 | 4.269 | 0.002 | 4.268 | 0.002 | 4.267 | 0.001 | 4.054 | 4.015 | 4.195
21.25 | 0.92 | 4.347 | 0.008 | 4.347 | 0.008 | 4.356 | 0.008 | 4.35 | 0.008 | 4.223 | 4.224 | 4.311
21.75 | 0.89 | 4.424 | 0.008 | 4.419 | 0.008 | 4.427 | 0.008 | 4.423 | 0.008 | 4.331 | 4.394 | 4.394
22.25 | 0.85 | 4.513 | 0.009 | 4.524 | 0.009 | 4.517 | 0.009 | 4.518 | 0.009 | 4.415 | 4.546 | 4.466
22.75 | 0.76 | 4.639 | 0.01 | 4.604 | 0.01 | 4.631 | 0.01 | 4.625 | 0.009 | 4.509 | 4.665 | 4.551

Counts and errors are expressed as log${}_{10}(N)$, where $N$ is the count per
square degree per magnitude. The errors are based on Poisson statistics,
combined with the uncertainty in the completeness estimates (which dominate at
fainter magnitudes).

We also compare our source counts to two semi-analytic simulations, GALFORM
and Shark, and to the Evolution and Assembly of GaLaxies and their
Environments (EAGLE) hydrodynamic simulations. Semi-analytic simulations can
generate large samples for easy comparison to surveys like DeepDrill, but
require some assumptions to be made regarding the effects of dust attenuation
in relation to the geometry of disks and bulges to compute observed fluxes,
compared to hydrodynamical simulations, which use 3D radiative transfer to
calculate these effects directly.

The GALFORM simulated counts are based on a lightcone specifically built for
SERVS. This SERVS lightcone of model galaxies was constructed using the Lagos
et al. (2012) GALFORM model variant using the techniques described in Merson
et al. (2013). 333The data are available from
https://zenodo.org/record/3568147#.X2utDC9h2L6 The lightcone covers the
redshift range $0<z<6$, has a sky coverage of $18.09$ deg2 and contains model
galaxies with apparent, dust attenuated magnitudes in the [3.6] band down to 2
$\mu$Jy (see also Krefting et al., 2020). The Shark simulated lightcone was
built from the Shark semi-analytic model of galaxy formation and evolution
(Lagos et al., 2018; Lagos et al., 2019) to compare with the DeepDrill survey.
This lightcone has an area of $\approx 107.9$ deg2, and a flux selection at
the [3.6] band $>0.575\,\mu$Jy (equivalent to an AB magnitude of $24.5$), with
the same redshift range of $0\leq z\leq 6$.

We computed the predicted number counts from the EAGLE hydrodynamical
simulations (Schaye et al., 2015; Crain et al., 2015) by extracting all
galaxies at $0<z<8$ from their public database (McAlpine et al., 2016), and
particularly their redshift, and apparent [3.6] and [4.5] flux densities (see
Camps et al. (2018) for details of how these were computed). To calculate the
number counts at a given band, we first calculated the area spanned by the box
size of $100\,\rm Mpc$ projected in the sky (we assume that the width of the
box is negligible with respect to the luminosity distance and hence we can
assume all galaxies in the box to be at the same redshift). We then calculate
the number of galaxies per unit area at each redshift and apparent magnitude
bin. We then integrate the latter over redshift to obtain a total number per
unit area in each magnitude bin, which we then divide by the width of the
magnitude bin to compare to our other measurements. We do this at $3.6\mu$m,
$4.5\mu$m and for subsamples of red and blue IRAC galaxies.

Overall, there is a fair agreement between the models and theobservations in
the regime where galaxies dominate the observed counts
($AB\stackrel{{\scriptstyle>}}{{{}_{\sim}}}18$). At intermediate magnitudes,
$\approx 18$-$21$, the semi-analytic models underpredict the number of
galaxies compared to both our counts and those in the literature (by up to a
factor of 1.8 in the [3.6] band and 2.2 in the [4.5] band for Shark), but the
EAGLE hydrodynamic simulation does better. At the faint end ($AB\approx 22$)
the GALFORM model does best, with both Shark and EAGLE underpredicting the
counts. All lightcones contain only the stellar emission of galaxies in the
IRAC bands, neglecting warm dust emission from AGNs. Including this may
improve the agreement between some of the models and the data.

We also examine the source counts as a function of colour, using the red and
blue colour cuts described above to isolate intermediate- ($z\approx 0.7$) and
high-redshift ($z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1.3$) galaxies. Figure
8 (d) shows these counts, again compared to the model galaxies. Both the blue
and red counts start well above all the model counts (in the case of the blue
counts at $AB<18$ this is due to stars), with EAGLE producing the largest
fraction of blue galaxies, and Shark the smallest. Both sets of observed
counts converge to near-agreement with the Shark simulation at the faint end,
but the other models do less well, with both EAGLE and GALFORM overpredicting
the blue counts, and GALFORM also overpredicting the red counts. This suggests
that the redshift distribution of the sources is quite different in the three
simulations. With increasing number of photometric and spectroscopic redshift
for SERVS and DeepDrill, we will be able to compare the redshift distributions
of the data and the simulations, which will add another dimension to the tests
shown here. A detailed discussion of the galaxy luminosity function and
stellar mass function using DeepDrill data will also be presented in future
papers.

###  5.3 Very red objects in [3.6]–[4.5]

In this section, we investigate the population of objects in DeepDrill at
extreme red [3.6]$-$[4.5] colours. Such objects are of interest for both
Galactic astronomy, where late-type dwarf stars with strong molecular bands
can have extreme [3.6]$-$[4.5] colours (Leggett et al., 2010), and for
extragalactic astronomy, where such [3.6]$-$[4.5] colours are sometimes found
for highly obscured, highly luminous AGNs (Tsai et al., 2015). In Table 10 we
list the 19 objects detected in both IRAC bands with a signal-to-noise ratio
$>3$ ([3.6]$-$[4.5]$>$1.2) that also have 24 $\mu$m coverage in SWIRE
(3$\sigma$ depth $\approx 100\mu$Jy; total area of overlap $\approx$ 30 deg2).
16 of the objects have detections at 24 $\mu$m, implying their SEDs continue
to rise rapidly in the mid-infrared. These are good candidates for dusty
high-$z$ AGN. In Figure 9 we plot the logarithm of the flux density ratio
between 3.6 and 5.8‘$\mu$m, $S_{5.8}/S_{3.6}$, versus the logarithm of the
flux density ratio between 4.5 and 8.0‘$\mu$m, $S_{8.0}/S_{4.5}$ for the 15 of
these objects that are covered by the SWIRE IRAC 5.8 $\mu$m and 8.0 $\mu$m
observations, and compare to the colours of spectroscopically-confirmed AGNs
from Lacy et al. (2013). Our very red IRAC objects are redder than nearly all
of the confirmed AGNs, but follow the extrapolation of the colour trend of AGN
to the red (though fall a little below the selection area of Donley et al.,
2012). A few of the very red objects have faint detections in VIDEO (Table
10), for these objects the $K_{s}-$[4.5] colours of the sources detected at
24$\mu$m are also consistent with AGNs (Messias et al., 2012).

The very red AGNs that are detected at 24 $\mu$m have some similarities to
objects selected on the basis of extremely red $R-24\,\mu$m colours in surveys
with Spitzer (dust-obscured galaxies or “DOGs"; Dey et al., 2008), very red
$r-22\,\mu$m colours between the Sloan Digital Sky Survey and WISE (Ross et
al., 2015) and objects with very red colours between the WISE bands themselves
(“Hot DOGs"; Tsai et al., 2015). These sets of objects are also dominated by
AGN emission in the mid-infrared. However, we emphasize that the [3.6]$-$[4.5]
colours of the very red objects presented here are typically more extreme.
None of the DOGs, only 11/77 of the red AGN in Ross et al. (2015) and 5/20 of
the Hot DOGs have [3.6]$-$[4.5] colours as red as the very red objects
described here.

Three sources are not detected at 24 $\mu$m, and are thus less likely to be
AGN. One of these (DD J033258.19$-$274143.8) is in the much deeper coverage of
S-CANDELS, and has faint detections at 5.8 and 8.0 $\mu$m (Figure 9). This
object was also detected in multiple epochs of archival Hubble Space Telescope
(HST) coverage (2004-08-13 using the ACS instrument through the F850LP filter
for proposal ID 9500 and 2011-12-30 through F814W for the CANDELS
observations, proposal ID 12060). We downloaded the relevant data from the HST
archive, and noted that the object has a significant proper motion, moving
approximately 0.7 arcsec in R.A. and 0.5 arcsec in Decl. between the two
epochs. We therefore tentatively identify this object as a brown dwarf star.
With a [3.5]$-$[4.6] colour of 1.6 in AB magnitudes (2.2 in Vega magnitudes),
this places the star in a spectral class approximately at the transition
between T and Y-dwarfs (Leggett et al., 2017). We speculate that the remaining
two objects that lack a 24 $\mu$m detection may also be brown dwarfs.

To further investigate the possibility of an AGN origin for the majority of
the very red sources we searched for serendipitously available mid-infrared
spectroscopy as well as deep radio continuum data in the DeepDrill fields. For
one of the very red sources, DD J022050.38$-$053714.1 (5MUSES-033), the
Spitzer IRS spectrum from the CASSIS database (Lebouteiller et al., 2011)
shows a strong mid-infrared continuum and spectral features consistent with an
AGN at its photometric redshift (derived from SWIRE data) of 2.02 (Rowan-
Robinson et al., 2013). This source is also detected in the VLA Sky Survey
(VLASS; Lacy et al. 2020) with a 3 GHz flux density $S_{\mathrm{3GHz}}=2.0\pm
0.2\,$mJy. The correspondingly high radio luminosity of
$L_{\mathrm{3GHz}}=5\times$10${}^{25}\,{\rm W\;Hz^{-1}}$ is much more
consistent with the radio emission being powered by an AGN rather than by star
formation (e.g. Kimball et al., 2011). One further source, DD
J022008.87-041819.0 is also detected in VLASS with $S_{\mathrm{3GHz}}=0.54\pm
0.2\,$mJy. Its photometric redshift is 2.01, which implies
$L_{\mathrm{3GHz}}=1.3\times$10${}^{25}\,{\rm W\;Hz^{-1}}$, also more likely
to be powered by an AGN than by star formation. In addition to VLASS, we also
searched for counterparts in the deep radio surveys with published source
catalogs listed in Table 4 (LOFAR, GMRT, and ATLAS). None of the very red
sources is detected in these radio surveys. We also searched for counterparts
in deep (sub-mJy beam-1 rms sensitivity) commensal 340 MHz data from the VLA
Low-band Ionosphere and Transient Experiment (VLITE444VLITE provides data at
340 MHz from a subset of the VLA antennas during regular VLA observations
above 1 GHz over a field-of-view (measured at the full-width at half power of
the primary beam) of 5.5 deg2 and a maximum resolution of $\sim
5^{\prime\prime}$ in the VLA A configuration.; Clarke et al. 2016; Polisensky
et al. 2016) that were observed during an ultra-deep, single-pointing VLA
imaging campaign centered on the Hubble Ultra Deep Field (HUDF) within CDFS at
3 GHz (Abrahams et al. 2020, submitted). Of the 12 very red sources in CDFS
that fall within the currently imaged portion (spanning a width of 2 deg) of
the deep VLITE data, one source (DD J033401.66$-$265017.0) has a compact
counterpart in VLITE with a primary-beam-corrected flux of 1.0$\pm$0.3 mJy at
a SNR of 4.8. The lack of detection in VLASS implies a moderately-steep
spectral index, $\alpha^{0.34\,\mathrm{GHz}}_{3.0\,\mathrm{GHz}}<-0.9$.
Unfortunately, the source currently lacks a photometric redshift, though
assuming it is at $z>1$ it is also more likely to be powered by an AGN. Full
details on the deep VLITE imaging centered on the HUDF will be presented in a
forthcoming study (Polisensky et al., in preparation).

Figure 9: The distribution of the objects with very red [3.6]$-$[4.5] colours
in mid-infrared color space for all objects with detections in all four IRAC
bands. The black crosses indicate probable AGNs, and the brown dot the likely
brown dwarf (DD J033258.21$-$274143.7). The cyan dots represent the
spectroscopically-confirmed Spitzer-selected AGNs from Lacy et al. (2013),
with the selection criteria of AGN candidates for that paper shown as the blue
dotted line. We also show the AGN selection criterion of Donley et al. (2012)
as the red dot-dash line. Both infrared AGN selection techniques shown here
rely on the warm dust emission from the AGN outshining the stellar emission
from the host galaxy, see Lacy & Sajina (2020) for a detailed discussion.
Table 10: Mid-infrared and radio photometry of the very red sources from
DeepDrill with 24 $\mu$m coverage in SWIRE. Infrared photometry is from either
the Spitzer source list (SSTSL2; Teplitz et al., 2010), this paper, or
S-CANDELS, as noted in the Notes column.

Name | $K_{s}$ | $S_{3.6}$ | $S_{4.5}$ | $S_{5.8}$ | $S_{8.0}$ | $S_{24}$ | $S_{\rm 3GHz}$ | Photometric | Notes
---|---|---|---|---|---|---|---|---|---
| (AB) |  ($\mu$Jy) |  ($\mu$Jy) |  ($\mu$Jy) |  ($\mu$Jy) |  ($\mu$Jy) | (mJy) | Redshift |
DD J003136.66$-$432234.9 | - |  1.2$\pm 0.7$ |  6.3$\pm 0.7$ |  $<$20 | $<20$ |  $<$100 | - | - |
DD J003441.85$-$423119.9 | - |  3.8$\pm 0.5$ |  15.2$\pm 0.4$ |  81$\pm 4$ |  250$\pm 6$ |  1710$\pm 80$ | - | - | SSTSL2
DD J003449.14$-$422934.8 | - |  2.0$\pm 0.6$ |  6.4$\pm 0.5$ |  42$\pm 7$ |  104$\pm 7$ |  230$\pm 30$ | - | - | This paper
DD J003723.88$-$432554.7 | - |  1.8$\pm 0.6$ |  6.9$\pm 0.5$ |  27$\pm 7$ |  87$\pm 7$ |  290$\pm 30$ | - | - | This paper
DD J003831.45$-$440045.2 |  22.39$\pm 0.06$ |  3.0$\pm 0.7$ |  10.7$\pm 0.6$ |  21$\pm 3$ |  70$\pm 6$ |  390$\pm 80$ | - | - | SSTSL2
DD J004411.11$-$442448.7 | - |  2.9$\pm 0.4$ |  9.3$\pm 0.4$ |  $<$20 | - |  577$\pm 30$ | - |  | This paper
DD J021821.44$-$053101.5 | - |  6.9$\pm 0.5$ |  21.4$\pm 1.0$ |  125$\pm 7$ |  248$\pm 7$ |  1430$\pm 30$ | $<0.4$ | 2.02 |
DD J022008.87$-$041819.0 |  21.04$\pm 0.02$ |  107.6$\pm 3.7$ |  337.9$\pm 5.3$ |  997$\pm 30$ |  2330$\pm 70$ |  6010$\pm 30$ |  0.54$\pm 0.12$ | 2.01 |
DD J022017.88$-$045753.3 | - |  4.8$\pm 0.7$ |  15.4$\pm 1.2$ |  28$\pm 4$ |  90$\pm 8$ |  290$\pm 60$ | $<0.4$ | - | SSTSL2
DD J022050.38$-$053714.1 | - |  37.0$\pm 1.3$ |  122.9$\pm 2.5$ |  380$\pm 10$ |  1090$\pm 30$ |  5000$\pm 200$ |  2.0$\pm 0.12$ | 2.05 | 5MUSES-033; This paper
DD J022228.02$-$034235.3 | - |  43.1$\pm 1.8$ |  143.6$\pm 4.2$ |  320$\pm 10$ |  870$\pm 30$ |  1094$\pm 240$ | $<0.4$ | 2.34 | This paper
DD J032727.28$-$270621.9 | - |  1.8$\pm 0.9$ |  9.7$\pm 0.6$ |  $<$20 | $<20$ |  $<$100 | $<0.15$ | - |
DD J032857.12$-$284111.8 |  22.80$\pm 0.06$ |  16.0$\pm 1.2$ |  56.6$\pm 2.2$ |  173$\pm 3$ |  443$\pm 5$ |  1730$\pm 90$ | $<0.15$ | - | SSTSL2, This paper
DD J033029.88$-$293445.5 | - |  4.5$\pm 0.5$ |  14.5$\pm 0.7$ |  59$\pm 7$ |  198$\pm 7$ |  680$\pm 30$ | $<0.15$ | - | SSTSL2, This paper
DD J033053.41$-$274717.8 |  22.41$\pm 0.06$ |  11.9$\pm 0.8$ |  46.7$\pm 2.0$ |  150$\pm 5$ |  480$\pm 10$ |  2010$\pm 40$ | $<0.15$ | - | SSTSL2
DD J033258.19$-$274143.8 |  22.93$\pm 0.06$ |  1.7$\pm 0.5$ |  7.3$\pm 0.9$ |  5.3$\pm 2.2$ |  6.1$\pm 1.8$ |  $<$100 | $<0.15$ | - | S-CANDELS
DD J033400.05$-$283001.9 | - |  2.7$\pm 0.5$ |  9.2$\pm 0.8$ |  47$\pm 3$ |  80$\pm 8$ |  200$\pm 40$ | $<0.15$ | - | SSTSL2
DD J033401.66$-$265017.0 | - |  24.4$\pm 1.0$ |  76.3$\pm 1.7$ |  176$\pm 2$ |  227$\pm 7$ |  1000$\pm 50$ | $<0.15$ | - |  $S_{\mathrm{340MHz}}=$1.2 mJy; SSTSL2, This paper
DD J033602.31$-$284944.2 | - |  3.6$\pm 0.4$ |  12.8$\pm 1.0$ |  33$\pm 2$ |  87$\pm 5$ |  490$\pm 50$ | $<0.15$ | - | SSTSL2

† Photometric redshifts are from Rowan-Robinson et al. (2013) except for DD
J021821.44$-$053101.5 which is from Williams et al. (2009).

##  6 Summary

We describe the DeepDrill survey, which images $\approx 27\,$deg2 in three of
the four pre-defined LSST Deep Drilling fields to a depth of $\approx
2\,\mu$Jy. Accuracy in photometric and astrometric calibration is described.
We illustrate the use of the [3.6]$-$[4.5] colour to divide objects into high
($z>1.3$) and low ($z\sim 0.7$) redshift bins. This property of the
[3.6]$-$[4.5] colour will be particularly valuable for breaking degeneracies
in photometric redshift estimates obtained from LSST optical data alone in
regions of the DDFs not covered by other deep near-infrared data (e.g. Pforr
et al., 2013).

We show that source count data at [3.6] and [4.5] alone can provide useful
comparisons to models of galaxy formation. The model and observed counts
generally agree well, but a small discrepancy observed at intermediate
magnitudes warrants further investigation. These comparisons will be further
enhanced when the Spitzer data are fully combined with the other
multiwavelength data in the LSST Deep Drilling fields. We are currently
working on completing multi-band 0.4-4.5$\mu$m catalogs using forced
photometry in the centers of the fields (defined by the overlap between the
DeepDrill and VIDEO surveys). We show that most objects with extremely red
[3.6]$-$[4.5] colours are mostly identifiable as dusty AGNs at $z>1$, but we
also find one likely T or Y brown dwarf star and two further brown dwarf
candidates. Future papers will discuss the stellar masses of galaxies in
DeepDrill (Maraston et al. 2020, in preparation) and their clustering (van
Kampen et al. 2020 in preparation).

The 3-5 $\mu$m region in the near-infrared is uniquely useful for capturing
light from the peak in the stellar SED at rest frame $\approx 1\mu$m at $z\sim
1-4$. Although new surveys with Spitzer are no longer possible, we expect that
the legacy value of the existing survey datasets will last well into the
future. When combined with the existing and planned multiwavlength datasets in
these fields, the DeepDrill data will be able to help answer fundamental
questions about the nature of AGN and galaxy evolution, and its dependence on
environment from before Cosmic Noon to the present.

## Data Availability

The data products from the post-cryogenic Spitzer surveys of the three LSST
DDFs described here (images, coverage maps, uncertainty images, bright star
masks and single and dual-band catalogues) are available from IRSA
(https://irsa.ipac.caltech.edu/data/SPITZER/DeepDrill). These include mosaic
images, coverage maps, uncertainty images and bright star masks. Each field
has two single-band catalogues cut at $5\sigma$, and a dual-band catalogue
requiring a detection at $>3\sigma$ at both 3.6 and 4.5$\mu$m. The simulated
lightcone catalogue from SHARK is also included in the release, its columns
are described in Table 11.

Table 11: Columns in the SHARK simulated lightcone catalogue. Column(s) | Description | Units
---|---|---
1 | ID | -
2 | Right Ascension | Degrees
3 | Declination | Degrees
4 | Redshift | -
5 | Log10(Stellar Mass) | Solar masses
6 | Log10(Star Formation Rate) | Solar masses/year
7 | Half-light radius | Kpc
8 | Bulge-to-Total ratio | -
9-13 | Apparent mag. in $u,g,r,i,z$ | AB
14-17 | Apparent mag. in $Y,J,H,K$ (VISTA) | AB
18 | Apparent mag. in WISE [3.4] | AB
19-20 | Apparent mag. in IRAC [3.6] and [4.5] | AB
21 | Apparent mag. in WISE [4.6] | AB
22-34 | Absolute mag. in the above bands | AB

## Acknowledgements

We would like to thank the referee for a thorough review that significantly
improved the paper. We also thank the contributors to the original DeepDrill
proposal not listed as coauthors on this paper, including M. Dickinson, I.
Prandoni and L. Spitler, and especially I. Smail for helpful comments and
suggestions. This work is based on observations made with the Spitzer Space
Telescope, which was operated by the Jet Propulsion Laboratory, California
Institute of Technology under a contract with NASA. Support for this work was
provided by NASA through an award issued by JPL/Caltech. The National Radio
Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. WNB
acknowledges support from NASA grant 80NSSC19K0961. GW acknowledges support
from the National Science Foundation through grant AST-1517863, by HST program
number GO-15294, and by grant number 80NSSC17K0019 issued through the NASA
Astrophysics Data Analysis Program (ADAP). Support for program number GO-15294
was provided by NASA through a grant from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Incorporated, under NASA contract NAS5-26555. IRS acknowledges
support from the United Kingdom Science and Technology Funding Council
(ST/P000541/1). Basic research in radio astronomy at the Naval Research
Laboratory is funded through 6.1 Base funding. This research has made use of
the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This work made extensive
use of topcat (Taylor, 2011) for catalog matching and analysis.

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##  Appendix A Source confusion in the DeepDrill survey

To better understand how source confusion affects the DeepDrill survey as a
function of depth, and in the presence of source clustering, we make use of
some results from studies at other wavelengths. The analytic approach
described here, although only approximate, allows us to predict trends in the
noise in the survey as a function of depth, and to compare the contributions
of random and clustered sources to the confusion noise.

Source confusion and its contribution to flux and number count uncertainties
has been investigated by several authors (e.g. Scheuer, 1957; Condon, 1974;
Hacking & Houck, 1987; Condon et al., 2012; Vernstrom et al., 2016). Hacking &
Houck (1987) show that the confusion noise in the absence of clustering,
$\sigma_{\mathrm{random}}$, obeys:

$\sigma_{\mathrm{random}}^{2}=\frac{\alpha}{2-\alpha}\Omega_{\mathrm{e}}AD_{\mathrm{c}}^{2-\alpha},$
(1)

where $\alpha$ is the slope and $A$ the normalization of the integrated source
counts $n(>S)=AS^{-\alpha}$ near the survey limit, $D_{\mathrm{c}}$ is the
cutoff in the “deflection” - the deviation of flux density, $S$ from the mean
background - at the survey limit, and the effective source area
$\Omega_{\mathrm{e}}$ is given by:

$\Omega_{\mathrm{e}}=\int
h(\boldsymbol{x})^{\alpha}{\mathrm{d}}\boldsymbol{x},$ (2)

where $h(\boldsymbol{x})$ represents the response of the instrument to a
typical source near the survey limit as a function of position vector
$\boldsymbol{x}$. For IRAC, we use the extended Point Response Functions
(PRFs) from the Spitzer Science
Center555https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/calibrationfiles/psfprf/
as an empirical $h(\boldsymbol{x})$. The slope of the integrated source counts
close to the flux density limit in both [3.6] and [4.5] is $\alpha\approx
0.5$. The non-Gaussian wings of the IRAC PRF, which are further amplified
relative to the core by taking the PRF to the 0.5 power in Equation 2, means
that the integral is slow to converge, and we chose to limit the integration
to the inner 1/4 of the IRAC array where the bulk of the contributions will
occur. This integration results in effective area at [3.6] of
$\Omega_{e}=1.82\times 10^{-9}$sr, and at [4.5] of $\Omega_{e}=1.86\times
10^{-9}$sr. These values are much larger than that of the
1$\aas@@fstack{\prime\prime}$8 FWHM Gaussian that corresponds to the core of
the IRAC PRF at these wavelengths ($\Omega_{\mathrm{e}}=1.7\times
10^{-11}$sr), and are also much larger than the solid angle of the
1$\aas@@fstack{\prime\prime}$9 radius aperture through which the source counts
are measured ($\Omega_{\mathrm{e}}=2.7\times 10^{-10}$sr).

Galaxy clustering also adds to confusion noise. The effects of clustering on
the distribution of deflections, $P(D)$, have been discussed by Barcons
(1992), Takeuchi & Ishii (2004) and Argüeso et al. (2019), and a full
treatment requires complicated mathematics outside the scope of this paper.
Here, we adopt the approach of Barcons (1992), where we sum the confusion
noise contribution from unclustered sources and a term due to clustering in
quadrature to estimate the total confusion noise $\sigma_{\mathrm{conf}}$:

$\sigma^{2}_{\mathrm{conf}}=\sigma^{2}_{\mathrm{random}}+<I>^{2}\Xi,$ (3)

where $<I>$ is the mean intensity per beam area, $\Omega_{\mathrm{b}}$, and

$\Xi=\frac{1}{\Omega_{\mathrm{b}}^{2}}\int_{\Omega_{\mathrm{b}}}d\boldsymbol{x_{1}}\int_{\Omega_{\mathrm{b}}}w(|\boldsymbol{x_{1}}-\boldsymbol{x_{2}}|)\mathrm{d}\boldsymbol{x_{2}}$

where w($\theta$) (and $\theta=|\boldsymbol{x_{1}}-\boldsymbol{x_{2}}|$) is
the two-point correlation function. Measurements of the two-point correlation
function in DeepDrill (van Kampen et al. in preparation) show that
$w(\theta)=(\theta/\theta_{0})^{-\delta}$ where $\delta\approx 0.68$, and the
correlation length, $\theta_{0}\approx 0\aas@@fstack{\prime\prime}2$.

We next approximate the total noise $\sigma_{\mathrm{T}}$ as the contribution
of instrumental noise, $\sigma_{\mathrm{I}}$ (obtainable from the Spitzer
Performance Estimation Tool
666https://irsa.ipac.caltech.edu/data/SPITZER/docs/dataanalysistools/tools/pet/senspet/index.html)
and confusion noise,
$\sigma_{\mathrm{T}}=\sqrt{\sigma_{\mathrm{I}}^{2}+\sigma_{\mathrm{conf}}^{2}}$.
(With the caveat that the distribution of deflections $P(D)$ is not Gaussian;
Herranz et al. (2004).) By setting $D=\sigma_{\mathrm{T}}$ in Equation 1 and
solving numerically, we recover $\sigma_{\mathrm{T}}=0.41$ $\mu$Jy at [3.6]
and $0.51$ $\mu$Jy at [4.5] at the nominal survey depth of 12$\times$100s
frames, close to the empirical result from SERVS of
$\sigma_{\mathrm{T}}\approx 0.4\;\mu$Jy in both the [3.6] and [4.5] bands
found from measuring the RMS variation in randomly-placed
1$\aas@@fstack{\prime\prime}$9 radius empty apertures (Mauduit et al., 2012).
Table 12 shows that, as the depth of the survey is increased beyond the
nominal depth of 12 frames, $\sigma_{\mathrm{T}}$ decreases, but by factors
less that the square root of the number of frames, and the contribution of
confusion noise becomes dominant. The contribution from clustering is small,
but almost constant with depth as it is dominated by bright sources well above
the survey limit, so becomes more significant in deeper surveys. Source
confusion in very deep IRAC images can be effectively mitigated by PRF
subtraction or forced photometry techniques (e.g. Ashby et al., 2015; Nyland
et al., 2017) that remove the PRF wings from the images, reducing
$\Omega_{\mathrm{e}}$ and $\Omega_{\mathrm{b}}$.

Positional accuracy is also affected by source confusion (Hogg, 2001). In the
case of DeepDrill, however, the low value of $\alpha$ results in the effect of
centroid errors due to source blending at the measured $\approx 30$ beams per
source being
$\stackrel{{\scriptstyle<}}{{{}_{\sim}}}$0$\aas@@fstack{\prime\prime}$1 (Hogg,
2001, their Figure 2).

Table 12: Calculated noise as a function of depth in DeepDrill Depth | $\sigma_{\mathrm{I}}$ | $\sigma_{\mathrm{random}}$ | $<I>\sqrt{\Xi}$ | $\sigma_{\mathrm{conf}}$ | $\sigma_{\mathrm{T}}$
---|---|---|---|---|---
(100s | ($\mu$Jy) | ($\mu$Jy) |  $(\mu$Jy) |  $(\mu$Jy) | ($\mu$Jy)
frames) | [3.6] | [4.5] | [3.6] | [4.5] | [3.6] | [4.5] | [3.6] | [4.5] | [3.6] | [4.5]
6 | 0.35 | 0.51 | 0.33 | 0.41 | 0.15 | 0.13 | 0.36 | 0.43 | 0.51 | 0.67
9 | 0.29 | 0.42 | 0.30 | 0.36 | 0.15 | 0.13 | 0.34 | 0.38 | 0.45 | 0.57
12 | 0.25 | 0.36 | 0.28 | 0.33 | 0.15 | 0.14 | 0.32 | 0.36 | 0.41 | 0.51
24 | 0.18 | 0.25 | 0.25 | 0.28 | 0.16 | 0.14 | 0.30 | 0.31 | 0.34 | 0.41
48 | 0.13 | 0.18 | 0.23 | 0.24 | 0.16 | 0.14 | 0.28 | 0.28 | 0.30 | 0.33
96 | 0.09 | 0.13 | 0.21 | 0.22 | 0.16 | 0.14 | 0.27 | 0.26 | 0.28 | 0.29

##  Appendix B Author affiliations

1National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA
22903, USA
2Infrared Processing and Analysis Center, MS 100-22, California Institute of
Technology, Pasadena, CA 91125, USA
3Department of Physics and Astronomy, University of Hawaii, 2505 Correa Road,
Honolulu, HI 96822,USA
4Institute for Astronomy, 2680 Woodlawn Drive, University of Hawaii, Honolulu,
HI 96822, USA
5National Research Council, resident at the Naval Research Laboratory,
Washington, DC 20375, USA
6Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, OAL,
Tapada da Ajuda, PT1349-018 Lisboa, Portugal
7Departamento de Física, Faculdade de Ciências, Universidade de Lisboa,
Edifício C8, Campo Grande, PT1749-016 Lisbon, Portugal
8Department of Astronomy and Astrophysics, 525 Davey Lab, The Pennsylvania
State University, University Park, PA 16802, USA
9Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA
10Department of Physics, 104 Davey Lab, The Pennsylvania State University,
University Park, PA 16802, USA
11Astrophysics Group, Imperial College London, Blackett Laboratory, Prince
Consort Road, London SW7 2AZ, UK
12International Centre for Radio Astronomy Research (ICRAR), University of
Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia.
13ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)
14Cosmic Dawn Center (DAWN), Copenhagen, Denmark
15Institute of Cosmology and Gravitation, Dennis Sciama Building, Burnaby
Road, Portsmouth PO1 3FX, UK
16ESA/ESTEC Keplerlaan1, 2201 AZ, Noordwijk, The Netherlands
17Department of Physics and Astronomy, Tufts University, 212 College Avenue,
Medford, MA 02155, USA
18Department of Physics and Astronomy, University of Pennsylvania,
Philadelphia, PA 19104, USA
19Department of Physics and Astronomy, University of the Western Cape, Private
Bag X17, Bellville 7535, South Africa.
20INAF - Istituto di Radioastronomia, via Gobetti 101, I-40129 Bologna, Italy
21Department of Physics and Astronomy, University of California, Riverside,
900 University Avenue, Riverside, CA 92521, USA
22Center for Relativistic Astrophysics, School of Physics, Georgia Institute
of Technology, 837 State Street, Atlanta GA 30332-0430, USA
23Department of Physics and Astrophysics, University of North Dakota, Grand
Forks, ND 58202-7129, USA
24Naval Research Laboratory Remote Sensing Division, Code 7213, 4555 Overlook
Avenue SW, Washington, DC 20375, USA
25Department of Physics and Astronomy, University of California, 4129 Reines
Hall, Irvine, CA 92697, USA
26Department of Physics, University of Napoli "Federico II", via Cinthia 9,
80126 Napoli, Italy
27Department of Physics and Michigan Center for Theoretical Physics,
University of Michigan, Ann Arbor, MI 48109, USA
28Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
29Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA
30 Kavli Institute for Cosmological Physics, University of Chicago, Chicago,
IL 60637, USA
31 Fermi National Accelerator Laboratory, PO Box 500, Batavia, IL 60510, USA
32Astrophysics Research Institute, Liverpool John Moores University, 146
Brownlow Hill, Liverpool L3 5RF, UK
33 European Southern Observatory, Karl-Schwarzschild-Str 2, D-85748 Garching
bei München, Germany
34 National Astronomical Observatories of China, Chinese Academy of Sciences,
Beijing 100012, China
35 China-Chile Joint Center for Astronomy, Chinese Academy of Sciences, Camino
El Observatorio, 1515 Las Condes, Santiago, Chile
36 Center for Astrophysics $\mid$ Harvard and Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA
37 National Radio Astronomy Observatory, 1003 Lopezville Road, Socorro, NM
87801, USA
38Astrophysics, Department of Physics, Keble Road, Oxford OX1 3RH, UK
39 University of Kansas, Department of Physics and Astronomy, 1082 Malott,
1251 Wescoe Hall Drive, Lawrence, KS 66045
40Australian Astronomical Observatory, North Ryde, NSW 2113, Australia
41 Department of Physics, University of California-Davis, One Shields Avenue,
Davis, CA 95616, USA
42 Department of Astronomy, University of Cape Town, Private Bag X3,
Rondebosch 7701, Cape Town, South Africa
43 Center for Cosmology and Astro-Particle Physics, The Ohio State University,
Columbus, OH 43210, USA
44 Department of Astronomy, The Ohio State University, Columbus, OH 43210, USA
45Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK
46Université de Paris, F-75013, Paris, France, LERMA, Observatoire de Paris,
PSL Research University, CNRS, Sorbonne Université, F-75014 Paris, France
47 Jet Propulsion Laboratory, Cahill Center for Astronomy & Astrophysics,
California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
48 Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura 763-0355,
Santiago, Chile
49 Department of Physics and Astronomy and the Pittsburgh Particle Physics,
Astrophysics and Cosmology Center (PITT PACC), University of Pittsburgh,
Pittsburgh, PA 15260, USA
50 Western Sydney University, Locked Bag 1797, 1797, Penrith South, NSW,
Australia
51 Astronomy Centre, Department of Physics and Astronomy, University of
Sussex, Brighton BN1 9QH, UK
52 Instituto de Astrofísica de Canarias (IAC), Calle Vía Lactea s/n, E-38205
La Laguna, Tenerife, Spain
53 Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife,
Spain
54 AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne
Paris Cité, 91191, Gif-sur-Yvette, France
55Department of Physics, Drexel University, 32 S. 32nd Street, Philadelphia,
PA 19104 USA
56NSF’s National Optical-Infrared Astronomy Research Laboratory, 950 N. Cherry
Avenue, Tucson, AZ 85719, USA
57Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the
Netherlands
58International Centre for Radio Astronomy Research, Curtin University,
Bentley, WA 6102, Australia
59Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue,
New York, NY 10010, USA; Department of Physics and Astronomy, Rutgers, The
State University of New Jersey, 136 Frelinghuysen Rd, Piscataway, NJ 08854,
USA
60Department of Astrophysical Sciences, Princeton University, Princeton, New
Jersey 08544, USA
61George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and
Astronomy, Department of Physics and Astronomy, Texas A & M University, 4242
TAMU, College Station, TX 77843, USA
62Haverford College, Departments of Physics and Astronomy, 370 Lancaster
Avenue, Haverford, PA 19041, USA
63Kavli Institute for Particle Astrophysics and Cosmology and Department of
Physics, Stanford University, Stanford, CA 94305, USA; Department of Particle
Physics and Astrophysics, SLAC National Accelerator Laboratory, Stanford, CA
94305, USA
64Pittsburgh Particle Physics, Astrophysics, and Cosmology Center (Pitt-PACC),
University of Pittsburgh, Pittsburgh, PA 15260, USA