#  Hubble Space Telescope Imaging of Luminous Extragalactic Infrared
Transients and Variables from the SPIRITS Survey111Based in part on
observations and archival data from the NASA/ESA Hubble Space Telescope
obtained at Space Telescope Science Institute, operated by Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
Also in part on observations and archival data made with the Spitzer Space
Telescope, operated by the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with NASA.

Howard E. Bond Department of Astronomy & Astrophysics, Pennsylvania State
University, University Park, PA 16802, USA  Space Telescope Science Institute,
3700 San Martin Dr., Baltimore, MD 21218, USA  Jacob E. Jencson Steward
Observatory, University of Arizona, 933 N Cherry Ave., Tucson, AZ 85721-0065,
USA  Patricia A. Whitelock South African Astronomical Observatory, P.O. Box 9,
7935 Observatory, South Africa  Department of Astronomy, University of Cape
Town, Private Bag X3, Rondebosch 7701, South Africa  Scott M. Adams Cahill
Center for Astronomy & Astrophysics, California Institute of Technology,
Pasadena, CA 91125, USA  Present address: Orbital Insight, 1201 N Wilson
Blvd., Suite 2100, Arlington, VA 22209, USA  John Bally Center for
Astrophysics & Space Astronomy, Astrophysical & Planetary Sciences Department,
University of Colorado, UCB 389, Boulder, CO 80309, USA  Ann Marie Cody SETI
Institute, 339 Bernardo Ave., Suite 200, Mountain View, CA 94043, USA  Robert
D. Gehrz Minnesota Institute for Astrophysics, School of Physics & Astronomy,
University of Minnesota, 116 Church St. SE, Minneapolis, MN 55455, USA  Mansi
M. Kasliwal Cahill Center for Astronomy & Astrophysics, California Institute
of Technology, Pasadena, CA 91125, USA  Frank J. Masci IPAC, California
Institute of Technology, 1200 E California Blvd., Pasadena, CA 91125, USA
Howard E. Bond<EMAIL_ADDRESS>
###### Abstract

SPIRITS—the SPitzer InfraRed Intensive Transients Survey—searched for luminous
infrared (IR) transients and variables in nearly 200 nearby galaxies from 2014
to 2019, using the warm Spitzer telescope at 3.6 and 4.5 µm. Among the SPIRITS
variables are IR-bright objects that are undetected in ground-based optical
surveys. We classify them as (1) transients, (2) periodic variables, and (3)
irregular variables. The transients include “SPRITE”s (eSPecially Red
Intermediate-luminosity Transient Events), having maximum luminosities fainter
than supernovae, red IR colors, and a wide range of outburst durations (days
to years). Here we report deep optical and near-IR imaging with the Hubble
Space Telescope () of 21 SPIRITS variables. They were initially considered
SPRITE transients, but many eventually proved instead to be periodic or
irregular variables as more data were collected. images show most of these
cool and dusty variables are associated with star-forming regions in late-type
galaxies, implying an origin in massive stars. Two SPRITEs lacked optical
progenitors in deep pre-outburst images; however, one was detected during
eruption at $J$ and $H$, indicating a dusty object with an effective
temperature of $\sim$1050 K. One faint SPRITE turned out to be a dusty
classical nova. About half the targets proved to be periodic variables, with
pulsation periods of 670–2160 days; they are likely dusty asymptotic-giant-
branch (AGB) stars with masses of $\sim$5–$10\,M_{\odot}$. A few of them were
warm enough to be detected in deep frames, but most are too cool. Out of six
irregular variables, two were red supergiants with optical counterparts in
images; four were too enshrouded for detection.

††facilities: HST (ACS, WFPC2, WFC3), IRSA, Spitzer

##  1 SPIRITS: Searching for Extragalactic Infrared Transients and Variables

Several classes of luminous variable stars and optical transients (OTs) have
been known for many decades—most famously supernovae (SNe), classical novae
(CNe), and luminous blue variables (LBVs). In recent years, wide-field optical
imaging surveys have been finding OTs in increasingly large numbers, and the
discovery rates are now becoming enormous. However, optical surveys are
relatively insensitive to objects that are intrinsically cool, dusty, or
located in obscured regions. Thus our knowledge of variable and transient
phenomena occurring primarily at infrared (IR) wavelengths has, until fairly
recently, been limited.

In 2014, our team started a systematic search for luminous IR transients and
variables in nearby galaxies, called SPIRITS (SPitzer InfraRed Intensive
Transients Survey). Our survey used the Infrared Array Camera (IRAC; Fazio et
al. 2004) on the warm Spitzer Space Telescope to search for variable
extragalactic objects at wavelengths of 3.6 and 4.5 µm. From 2014–2016, our
target list contained $\sim$190 galaxies, consisting of about 37 galaxies
within 5 Mpc, 116 luminous galaxies with distances of about 5 to 15 Mpc, and
the 37 most luminous galaxies in the Virgo cluster at 17 Mpc. From 2017
through the end of the survey in 2019 December, we reduced our target list to
a subset of the 105 galaxies of the original sample most likely to host new
transients, including the most luminous and actively star-forming galaxies,
and the 58 galaxies that had previously hosted an IR transient candidate.
Observing cadences ranged from a few weeks to several years, augmented with
additional data available in the Spitzer
archive.222https://irsa.ipac.caltech.edu/Missions/spitzer.html The nominal
$\rm S/N=5$ limiting magnitudes for isolated objects in our exposures are
$[3.6]=20.0$ and $[4.5]=19.1$ (Vega scale). These correspond to absolute
magnitudes of $-8.5$ and $-9.4$ at 5 Mpc, and $-10.9$ and $-11.8$ at 15 Mpc.
However, in practice the limiting magnitudes are affected by our ability to
remove the background in image subtraction, and the detection limits can be
substantially brighter than the nominal values.

Details of the SPIRITS image-processing and variable-identification pipeline
are given in Kasliwal et al. (2017, hereafter K17). The pipeline includes
subtraction of template reference images, for which we used available archival
frames, the Post-Basic Calibrated Data (PBCD)-level mosaics, including Super
Mosaics333Super Mosaics are available as Spitzer Enhanced Imaging Products
through the NASA/IPAC Infrared Science Archive:
https://irsa.ipac.caltech.edu/data/SPITZER/Enhanced/SEIP/overview.html, or
images from the Spitzer Survey of Stellar Structure in Galaxies (S4G; PID
61065; PI K. Sheth). Where Super Mosaics or S4G mosaics were not available, we
used stacks of archival BCD-level images. For all “saved” sources, those
vetted by human scanners and given a SPIRITS designation, we performed
aperture photometry on the difference images using a 4 mosaicked-pixel
($2\farcs 4$) aperture and background annulus from 4–12 pixels ($2\farcs
4$–$7\farcs 2$). The extracted flux is multiplied by aperture corrections of
1.215 for [3.6] and 1.233 for [4.5], as described in the IRAC Instrument
Handbook,444https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/
and converted to Vega-system magnitudes using the Handbook-defined zero-
magnitude fluxes for both IRAC channels. The final photometry that we employ
places a grid of apertures near each individual source position to robustly
estimate the uncertainties and upper limits, as described in Jencson (2020,
hereafter J20). For non-transient, variable sources (where the difference flux
measured may be negative; see our definitions below in §2), if there is a
plausible, identifiable counterpart source in the reference images, we add the
flux of the source from aperture photometry on the reference images to our
difference photometry. Otherwise, we offset the difference-flux measurements
of a given light curve to bring the minimum, negative value to zero before
converting to magnitudes. All photometry presented in this work is provided in
an electronic format as “data behind the figures.” Full details of the SPIRITS
survey and initial discoveries are presented in K17, and updated overviews are
given by Jencson et al. (2019b) and J20.

##  2 SPIRITS Variables and “SPRITE”s

Based on what was known about OTs at the beginning of the SPIRITS survey, we
anticipated at a minimum that we would discover members of known classes of
dusty transients, as well as heavily optically obscured SNe. The category of
dusty OTs includes eruptive events with peak luminosities between those of SNe
and CNe, which appear to fall into two main groups:

(1) “Intermediate-luminosity red transients” (ILRTs), typified by NGC 300
OT2008-1 (Bond et al., 2009) and SN 2008S in NGC 6946 (Szczygieł et al.,
2012). The progenitors of both of these events were detected in archival
Spitzer images as luminous mid-IR sources (Prieto, 2008; Prieto et al., 2008),
which were heavily obscured at optical wavelengths. The outflows from ILRTs
form substantial dust, and they are bright IR sources at late times after
their optical light has faded (e.g., Kochanek, 2011, and references therein).
ILRTs are strongly associated with spiral arms, indicating that they arise
from fairly massive stars. The origin of ILRT outbursts is debated: proposed
mechanisms include electron-capture SNe, low-mass core-collapse SNe, events
related to LBV eruptions, and binary interactions (see discussion and
references in Adams et al., 2016; Cai et al., 2018, 2019, 2021). A recently
discovered likely member of this class, M51 OT2019-1 (AT 2019abn), had a
massive, self-obscured progenitor similar to the two class prototypes, and it
was shown to be variable in the 12 years of available pre-outburst archival
imaging with Spitzer/IRAC (Jencson et al., 2019a). An extended phase of early
circumstellar dust destruction observed during the rise of this transient
disfavors a terminal-explosion scenario, strengthening the connection between
ILRTs and giant eruptions of LBVs (Jencson et al., 2019a; Williams et al.,
2020).

(2) “Luminous red novae” (LRNe), a lower-luminosity class of dust-forming
transients, generally (but not always) associated with older populations.
Examples include M31 RV and V4332 Sgr (Bond, 2011, 2018, and references
therein) and V838 Mon (Sparks et al., 2008; Woodward et al., 2021). These
events are probably the result of common-envelope interactions and stellar
mergers (e.g., Pastorello et al., 2019; Howitt et al., 2020); this was
definitely the case for the LRN V1309 Sco, which was shown to have been a
close binary with a rapidly decreasing orbital period before its eruption
(Tylenda et al., 2011).

As reported by K17, our initial analysis of the SPIRITS data indeed revealed
numerous IR transients and variables. An unexpected finding was a new class of
IR transients that lack counterparts in deep optical imaging during
outburst—unlike the ILRTs and LRNe described above—and have maximum IR
luminosities lying between those of CNe and SNe. We refer to these objects as
“SPRITE”s (eSPecially Red Intermediate-luminosity Transient Events). These
events were defined in K17 as transients with absolute magnitudes at maximum
in the range $-14<M_{[4.5]}<-11$, IR colors in the range
$0.3<[3.6]-[4.5]<1.6$, and having no optical counterparts detected during the
outbursts in deep ground-based images.

A second surprise emerged as the SPIRITS program continued to collect data.
Several luminous stars initially considered to be transients based on a small
number of observations showing a rising brightness, including several of the
candidate SPRITEs, were found to be periodic variables when more Spitzer data
became available. In fact, it is striking how many luminous variable stars are
conspicuous in late-type galaxies, when Spitzer frames taken over several
years are blinked. The contrast with what is seen at optical wavelengths,
where bright variables are rare, is remarkable. These objects are most likely
pulsating cool and dusty stars, with very long periods, up to several years.
Most of them are probably dust-obscured AGB stars, similar to, but more
luminous than, those found in the Large Magellanic Cloud and other nearby
galaxies, as described by Whitelock et al. (2003), Goldman et al. (2017),
Whitelock et al. (2018), and Menzies et al. (2019). They may be analogs of the
OH/IR stars found close to the plane in our own Galaxy (e.g., Epchtein &
Nguyen-Quang-Rieu, 1982; Jones et al., 1982).

These IR-luminous pulsators have been discussed by Karambelkar et al. (2019,
hereafter K19), who present a catalog of over 400 periodic or suspected
periodic variables found in the SPIRITS survey. Another recent study of
pulsating IR variables, based in part on SPIRITS data for galaxies in the
Local Group, has been presented by Goldman et al. (2019). However, we cannot
rule out that some of these apparently periodic objects may actually be
massive binaries with very long orbital periods, rather than pulsators. For
example, Williams et al. (2012) have described a binary system containing a
carbon-rich Wolf-Rayet (WC) star, which periodically forms dust during
periastron passage when its wind collides with the outflow from a companion
star. Recently, we reported six extragalactic WC Wolf-Rayet binary candidates
displaying such dust-formation episodes as mid-IR SPIRITS variables, including
the mid-IR counterpart to the recently discovered colliding-wind WC4+O binary
candidate, N604-WRXc, in M33 (Lau et al., 2021).

A few of the SPIRITS transients are so luminous that they are very likely to
be obscured SNe (Jencson et al., 2017, 2019b). In a few cases these objects
did prove to have detectable optical counterparts. An example is SPIRITS 16tn
in NGC 3556, at a distance of only 8.8 Mpc, which reached at least
$M_{[4.5]}=-16.7$ (Jencson et al., 2018). It had been missed in optical SN
surveys, but following the SPIRITS discovery it was detected in deep Hubble
Space Telescope () and ground-based images at $I$ and JHK. Its optical
extinction is estimated to be $A_{V}\simeq 8$–9. This event raises the
possibility that some of the SPIRITS transients with relatively few
observations could have been obscured SNe that happened not to be imaged
around their times of maximum light.

Young stellar objects (YSOs) are another potential source of transient
phenomena at IR wavelengths. Some low- to moderate-mass YSOs experience sudden
$\sim$5 to 10 magnitude increases at visual wavelengths, followed by a gradual
decline lasting years to decades. These “FU Orionis” outbursts are thought to
be triggered by enhanced accretion from a circumstellar disk onto the YSO
(e.g., Hartmann & Kenyon, 1996). The Spitzer YSOVAR project (Rebull et al.,
2014) found that most YSOs are variable in the IR, and some experience
luminous outbursts. In 2015, two massive YSOs underwent $\sim$$4\times
10^{4}~{}L_{\sun}$ IR flares (Hunter et al., 2017; Caratti o Garatti et al.,
2017). More luminous events are thought to be associated with explosions such
as the $\sim$550-yr-old BN/KL outflow in Orion OMC1 (Bally et al., 2020).
Bally & Zinnecker (2005) proposed that mergers of the most massive stars can
produce IR flares with luminosities comparable to those of SNe. Numerical
simulations show that in dense cloud cores, orbital decay can induce massive
stars and binaries to migrate rapidly to the core’s center to form non-
hierarchical systems. Such systems are unstable. $N$-body interactions tend to
rearrange them into hierarchical configurations, compact binaries, and ejected
stars (e.g., Reipurth & Mikkola, 2015). In sufficiently dense sub-groups,
$N$-body interactions may lead to YSO mergers. In a molecular cloud, dust
shifts the UV and visual light from major accretion events and stellar mergers
into the IR or sub-mm. The resulting luminous IR flares are expected to be
similar to some SPIRITS IR transients.

##  3 HST Follow-up of SPIRITS Variables

In the present paper we report results of follow-up optical and near-IR
imaging observations of SPRITEs and other SPIRITS transients and variables,
made with and its Wide Field Camera 3 (WFC3). We received allocations of two
orbits for an initial Director’s Discretionary program in Cycle 21
(GO/DD-13935, PI H.E.B.), and eight orbits for a regular Cycle 23 program
(GO-14258, PI H.E.B.). Two observing programs from another team (GO-14463 in
Cycle 23, GO-14892 in Cycle 24, both with PI B. McCollum) were devoted to
imaging of two further SPIRITS transients; we have obtained these data from
the public archive555http://archive.stsci.edu/ and include analyses of them in
this paper. In addition to our newly obtained WFC3 images from these programs,
we downloaded frames of the sites from the archive; these had been secured
with the Wide Field Planetary Camera 2 (WFPC2) and the Advanced Camera for
Surveys (ACS), as well as WFC3.

The main goals of our imaging were: (1) deep searches for optical/near-IR
counterparts of SPRITEs while the events were underway; (2) characterization
of their stellar environments; and (3) identification of (or limits on)
progenitor objects by comparison of our new images with pre-outburst archival
images.

Our primary considerations for target selection were: (1) the outburst event
appeared to satisfy the photometric criteria for SPRITEs outlined above, and
was expected to be underway during the observation666Our observations were
“non-disruptive targets of opportunity,” meaning that the observations were to
be obtained no less than 3 weeks after activation. As discussed below, in a
few cases of fast transients, the IR outbursts had already ended by the time
of the observation.; (2) there was no detected optical counterpart in
concomitant optical ground-based imaging with moderate-aperture telescopes (to
rule out ordinary CNe, SNe, LBVs, and other known types of OTs); and (3) the
site of the SPRITE had been imaged previously by at the F814W band (or
longward in a few cases). As noted by K17, SPRITEs appear to have a wide
duration of outburst timescales, ranging from fast events to long-duration
eruptions. We attempted to sample transients spanning this range.

Table 1 lists the SPIRITS targets that were observed in the four programs.
Columns 1 and 2 list the object designations and host galaxies, and column 3
gives the date of the observation. Column 4 contains the program ID number.
Our WFC3 observations were made in the UVIS-channel F814W bandpass, and the
IR-channel F110W and F160W filters (although in one case we omitted the F110W
image). Hereafter in this paper we denote these filters as $I$, $J$, and $H$,
respectively, but we emphasize that these should not be confused with the
ground-based bandpasses with the same designations.

Table 1:  Wide Field Camera 3 Observing Log SPIRITS | Host | Observation | Program | Total Exposure Time [s] | Other SPIRITS
---|---|---|---|---|---
Designations | Galaxy | Date | IDaaPI for 13935 and 14258 was H.E.B. PI for programs 14463 and 14892 was B. McCollum. In the 14463 program there were also exposures in F625W, F606W, F125W, and F140W; in 14892 there were also exposures in F105W. | F814W | F110W | F160W | Variables in Field
14aje | M101 | 2014-09-22 | 13935 | 1575 | 738 | 177 | $\dots$
14axa | M81 | 2014-09-26 | 13935 | 1659 | 671 | 155 | $\dots$
14qb | NGC 4631 | 2015-11-02 | 14258 | 1575 | 738 | 177 | $\dots$
15nz | M83 | 2016-01-18 | 14463 | 584 | $\dots$ | 796 | 14akj, 14atl
15qo, 15aag | NGC 1313 | 2016-02-11 | 14258 | 1500 | 553 | 317 | $\dots$
15ahg, 14al, 14dd | NGC 2403 | 2016-03-07 | 14258 | 1500 | 553 | 317 | 15ahp
15afp | NGC 6946 | 2016-03-19 | 14258 | 1320 | 484 | 317 | $\dots$
15wt, 14bbc | NGC 7793 | 2016-04-18 | 14258 | 1290 | 484 | 317 | 14th, 17fe
16aj | NGC 2903 | 2016-05-23 | 14258 | 1425 | 738 | 177 | $\dots$
15mr, 15mt | NGC 4605 | 2016-06-14 | 14258 | 1575 | $\dots$ | 684 | $\dots$
16tnbbSPIRITS 16tn has been analyzed in detail by Jencson et al. (2018), and interpreted as a heavily obscured core-collapse SN. Tabulated here for completeness, but not discussed in this paper. | NGC 3556 | 2016-09-25 | 14258 | 1425 | 738 | 403 | $\dots$
16ea | NGC 4214 | 2017-05-17 | 14892 | $\dots$ | 2385 | 2385 | $\dots$

For most of the observations we used small subarrays, rather than read out the
entire detector, in order to obtain more exposure time during the visits. In
four cases, we adjusted the pointing, and used a larger subarray, so as to
include one or two additional interesting SPIRITS variables in the WFC3 field
of view (FOV), as indicated by the multiple entries in column 1. All exposures
were taken at three dither positions, and we downloaded the default pipeline
drizzle-combined images from the archive. Columns 5 through 7 in Table 1 list
the total exposure times in each filter, which varied slightly due to
visibility constraints. For nominal exposure times of 1500, 600, and 300 s,
the limiting ($\rm S/N=5$) Vega-scale IJH magnitudes are 26.2, 25.2, and 23.4,
respectively, based on the WFC3 exposure-time calculators
(ETCs).777http://etc.stsci.edu/etc/input/wfc3uvis/imaging; the listed values
are optimistic and only approximate because they neglect possible background
light from the host galaxy and confusion in crowded star fields.

Our final observation in GO-14258 was actually made on the obscured SN SPIRITS
16tn, rather than a candidate SPRITE. As noted above, this target is discussed
in detail by Jencson et al. (2018); it will not be considered further in the
present paper.

We also searched the SPIRITS archive for additional variable objects that
happened to fall within the FOVs of our images, but had not been the primary
targets. Five of them proved interesting enough to include in the analyses in
this paper. The final column in Table 1 lists these additional “serendipitous”
IR variables.

##  4 IR Light-Curve Classification

Table 2 lists information on the SPIRITS variables targeted in the
observations discussed in this paper. For each pointing in the table, a header
gives the host galaxy and its distance modulus, from the literature sources
cited in a footnote. Column 1 gives the SPIRITS designations, and columns 2
and 3 the J2000 coordinates. The final column gives our classification of each
object’s light curve, as described in this section.

Table 2:  Targets and Light-Curve ClassificationsaaThe distance moduli adopted for the host galaxies are from these sources: M101: Jang & Lee (2017); NGC 6946: Pejcha & Prieto (2015); NGC 2903: Tully et al. (2016); all others: Tully et al. (2013). SPIRITS | R.A. | Decl. | Light-Curve
---|---|---|---
Designation | (J2000) | (J2000) | Classification
Field of 14aje in M101, $m-M=29.16\pm 0.02$
14aje | 14:02:55.51 | +54:23:18.5 | SPRITE (fast)
Field of 14axa in M81, $m-M=27.79\pm 0.06$
14axa | 09:56:01.52 | +69:03:12.4 | TransientbbProbably a classical nova; see §6.3.
Field of 14qb in NGC 4631, $m-M=29.33\pm 0.10$
14qb | 12:41:57.50 | +32:32:06.7 | Irregular
Field of 15nz in M83, $m-M=28.34\pm 0.07$
15nz | 13:37:08.37 |  $-29$:50:19.7 | Periodic
14akj | 13:37:03.59 |  $-29$:50:57.4 | Irregular
14atl | 13:37:07.96 |  $-29$:50:41.3 | Irregular
Field of 15qo in NGC 1313, $m-M=28.14\pm 0.08$
15qo | 03:18:15.26 |  $-66$:30:03.4 | Periodic
15aag | 03:18:23.63 |  $-66$:30:24.2 | Periodic
Field of 15ahg in NGC 2403, $m-M=27.51\pm 0.06$
15ahg | 07:36:37.40 | +65:38:02.6 | Periodic
14al | 07:36:32.38 | +65:37:26.1 | Periodic?
14dd | 07:36:30.04 | +65:37:57.8 | Periodic
15ahp | 07:36:35.68 | +65:37:47.2 | Irregular
Field of 15afp in NGC 6946, $m-M=28.27\pm 0.07$
15afp | 20:34:59.65 | +60:11:18.1 | Periodic?
Field of 15wt in NGC 7793, $m-M=27.77\pm 0.07$
15wt | 23:57:43.38 |  $-32$:35:03.1 | Periodic
14th | 23:57:46.32 |  $-32$:34:41.3 | Irregular
14bbc | 23:57:46.28 |  $-32$:35:20.6 | Periodic
17fe | 23:57:44.77 |  $-32$:34:58.4 | SPRITE (slow)
Field of 16aj in NGC 2903, $m-M=29.82\pm 0.45$
16aj | 09:32:11.64 | +21:30:03.0 | Irregular
Field of 15mr in NGC 4605, $m-M=28.72\pm 0.10$
15mr | 12:39:54.87 | +61:36:46.3 | Periodic
15mt | 12:40:06.94 | +61:36:22.3 | Periodic?
Field of 16ea in NGC 4214, $m-M=27.34\pm 0.08$
16ea | 12:15:38.61 | +36:19:46.9 | Periodic?

At the time the prime targets in each field were selected for imaging, they
were all candidate SPRITE transients. However, with the accumulation of
substantial additional Spitzer data since the dates of the observations, we
are able to refine our variability information beyond what was available at
the time of selection. In particular (see §2), it became apparent that many of
the candidate SPRITEs are actually not transients, but pulsators with very
long periods—likely mass-losing intermediate-mass stars approaching the end of
their AGB evolution. For the purposes of this paper, we have used the
following classification scheme for transients, periodic variables, and
irregular variables:

(1) Transients and SPRITEs. These are sources that were undetected, brightened
once, and then declined below detectability, and for which there are
sufficient data before and/or after the outburst to rule out the categories
below. Specifically, we use the criteria outlined in §1.3 of J20 to select
bona fide transients. Transients falling within the absolute-magnitude and
color ranges given in §2, which were not detected from the ground at optical
wavelengths, are called SPRITEs. We subdivide them into “fast” SPRITEs (having
outburst durations of less than one typical Spitzer visibility window of
$\lesssim$6 months) and “slow” SPRITEs (having outburst durations extending
over more than one visibility window).

(2) Periodic and likely periodic variables. As discussed above, K19 identified
a set of SPIRITS variables with sufficient data to show that they were varying
periodically, most likely due to long-period pulsations. We call the targets
in the present study “periodic variables” if we have seen at least one and a
half cycles of variation. If there is less time coverage, but the available
light-curve shape is similar to those of the known periodic variables, we call
the object “periodic?”.

(3) Irregular variables. These objects vary irregularly, in a fashion
inconsistent with either of the above classes. Specifically, they do not show
obvious periodicity, nor an outbursting transient behavior as described above.

##  5 Astrometric Registration

In order to search for optical counterparts of SPIRITS variables and
transients in images, it is necessary to carry out a precise astrometric
registration of the Spitzer and frames. This task is complicated by the fact
that a large fraction of stars and background galaxies that are prominent at
3.6 and 4.5 µm are faint or invisible at optical wavelengths—and vice versa.
In addition, sources that are isolated at resolution (the WFC3 plate scales
are $0\farcs 0396$ and $0\farcs 128\,\rm pixel^{-1}$ in the UVIS and IR
channels, respectively) are often blended at Spitzer IRAC resolution ($0\farcs
6\,\rm pixel^{-1}$). These considerations make it necessary to blink the IRAC
and WFC3 frames visually in order to select a sample of isolated objects
common to both images—many of which are either foreground stars or compact,
IR-luminous background galaxies.

In many cases, the SPIRITS variables were seen to lie in crowded locations in
their host galaxies, including clusters, associations, and H II regions. In
these instances, we first subtracted a reference Spitzer image, in which the
variable was faint or absent, from a frame showing the variable in a bright
phase. We then used these “difference” images to determine the positions of
the variables in the same astrometric framework as the reference objects in
the direct frames.

We employed standard tasks in IRAF and STSDAS888The Image Reduction and
Analysis Facility (IRAF) was distributed by the National Optical Astronomy
Observatory, which was operated by the Association of Universities for
Research in Astronomy (AURA) under a cooperative agreement with the National
Science Foundation. The Space Telescope Science Data Analysis System (STSDAS)
was distributed by the Space Telescope Science Institute, which is operated by
AURA for NASA. to determine centroid locations for the reference stars and
galaxies in the frames. Then we used the geomap task to map the coordinate
system of the Spitzer frame to the image, followed by the geoxytran task to
determine the $(x,y)$ position of the Spitzer variable in the frame. The
precision of the registrations varied depending on the number and quality of
the reference objects, but generally ranged from an rms of about 0.1 to 0.3
Spitzer/IRAC pixels ($0\farcs 06$ to $0\farcs 18$), or about 1.5 to 4.5
WFC3/UVIS pixels in the $x$ and $y$ directions. Depending on the quality of
the target’s image in the Spitzer frames, the uncertainty of its position
could be somewhat larger than for the reference-frame stars.

##  6 Infrared Transients and SPRITEs

With the accumulation of Spitzer observations and other information, only
three of our targets chosen for follow-up have remained classified as
transients. We discuss them in this section. Their IR light curves are shown
in the three panels of Figure 1. In this figure, and in subsequent light-curve
plots in this paper, the epochs of observations are marked with vertical black
or gray arrows, marking the dates of our triggered observation or of the
archival observations, respectively. Since our targets are faint and extremely
red, we generally only consider archival images taken in broad-band filters at
$I$ (F814W) or longer wavelengths.

For the transients and SPRITEs, we also include optical constraints from wide-
field, untargeted surveys, namely the intermediate Palomar Transient Factory
(iPTF; Cao et al., 2016) and the Asteroid Terrestrial-impact Last Alert System
(ATLAS; Tonry et al., 2018; Smith et al., 2020). The iPTF constraints,
originally reported in Appendix 2 of J20, consist of forced-photometry
measurements on the $g$\- and Mould $R$-band difference images at the
locations of our transients using the PTF IPAC/iPTF Discovery Engine (PTFIDE)
tool (Masci et al., 2017), stacked in 10-day windows to provide deeper limits.
ATLAS constraints were obtained from forced photometry999ATLAS forced-
photometry server: https://fallingstar-data.com/forcedphot/ on the available
ATLAS-c (“cyan”) and ATLAS-o (“orange”) difference images, again stacked in
10-day windows.

Figure 1:  Spitzer IRAC light curves of two SPRITEs and a transient. In all of
the light-curve figures in this paper, Vega-scale magnitudes are plotted for
IRAC measurements, with red squares indicating [4.5] magnitudes, and blue
circles [3.6] magnitudes. Error bars are shown when they are larger than the
plotting symbols. Open symbols with down arrows indicate upper luminosity
limits for non-detections. Open downward triangles represent optical limits
(AB magnitudes) in ATLAS-$c$ (turquoise) and -$o$ (light orange) for SPIRITS
17fe and iptf-$g$ (green) and -$R$ (dark orange) for SPIRITS 14aje and SPIRITS
14axa. The detection of an optical counterpart of SPIRITS 14axa reported by
Hornoch & Kucakova (2014) at $R=18.9$ mag (Vega) is also shown as the orange
diamond. The epochs of our triggered observations are indicated at the top of
each frame by black arrows, and the epochs of available archival broad-band
images ($I$ band or longward) by gray arrows. Left frame: 14aje in M101, a
luminous, very fast, and very red SPRITE, detected in only two observations;
middle frame: 17fe in NGC 7793, a slow SPRITE, which brightened suddenly and
then declined over at least the subsequent 2.7 years; right frame: 14axa in
M81, a likely classical nova caught in a dusty phase.

Table 3 summarizes several properties of the light curves of the three
transients, including information on the dates they were detectable, dates of
maximum light, their apparent and absolute magnitudes at peak, and the
$[3.6]-[4.5]$ color at peak.

Table 3: Properties of Transients SPIRITS |  $t_{0}$aaTime of the first Spitzer/IRAC detection. | Max. AgebbMaximum age of transient at the time of discovery, i.e., time between first detection and the previous non-detection |  $\Delta t_{\mathrm{LC}}$ccTime between first and last detections. | $t_{\mathrm{peak}}$ | $[4.5]_{\mathrm{peak}}$ | $M_{[4.5],\mathrm{peak}}$ |  $[3.6]-[4.5]$ddMeasured at the time of the light-curve peak, $t_{\mathrm{peak}}$.
---|---|---|---|---|---|---|---
Designation | [MJD] | [days] | [days] | [MJD] | [mag] | [mag] | [mag]
14aje | 56742.84 | 694.45 | 28.98 | 56742.84 | $15.52\pm 0.03$ | $-13.6$ | $1.7\pm 0.1$
14axa | 56821.90 | 122.43 |  $<$258.75 | 56821.90 | $16.28\pm 0.08$ | $-11.5$ | $0.5\pm 0.1$
17fe | 57800.71 | 127.04 | 957.17 | 57828.22 | $15.83\pm 0.04$ | $-10.9$ | $0.69\pm 0.06$

###  6.1 14aje: Fast SPRITE

The Spitzer light curves of SPIRITS 14aje in M101 ($d\simeq 6.8$ Mpc) are
shown in the left-hand panel of Figure 1. This transient was first detected on
2014 March 26, at an apparent magnitude $[4.5]=15.52\pm 0.03$. This
corresponds to an absolute magnitude of $M_{[4.5]}\simeq-13.6$ at the distance
of M101, well above the brightest IR luminosities observed for CNe (see §6.3).
Its color was extremely red, $[4.5]-[3.6]=1.73$. The transient had been
undetected in an archival Spitzer observation at $4.5\,\mu$m in 2012 and is
not present in available Super Mosaic images (2004–2007 stack; see below for
more details). 14aje faded quickly, dropping by $\sim$0.6 mag on 2014 April
24. It was below detection at our next visit on 2014 September 2, and at all
of our Spitzer observations since then. As presented in Appendix 2 of J20,
limits from iPTF constrain any transient optical emission during the IR
outburst to $r\gtrsim 21$ mag. We classify 14aje as a fast SPRITE, confirming
the initial classification by K17.

We triggered our first SPIRITS follow-up observations on this transient,
obtaining WFC3 frames on 2014 September 22. In addition to our data, there was
subsequent archival imaging in an unrelated program in 2017 (GO-14678, PI B.
Shappee); both dates are marked with arrows in the light-curve figure. An
earlier archival observation was obtained in 2003 (GO-9492, PI F. Bresolin),
outside the plotted time interval. Our observations were discussed briefly by
K17, but are updated here.

As the light curve shows, the 14aje event was so fast that the IR outburst
unfortunately appears to have ended at an uncertain date before the epoch of
our triggered observations. We registered Spitzer frames showing 14aje at
maximum with the ACS images taken in 2003 and 2017, in order to determine its
location in the frames. (We chose the ACS frames because of their large FOVs,
providing more astrometric reference sources than our own WFC3 images obtained
with smaller subarrays.) The top panel in Figure 2 shows a color rendition of
the SPRITE’s environment, taken from the Hubble Legacy
Archive101010http://hla.stsci.edu/hlaview.html (HLA). The site lies in a
spiral arm of M101, with several young associations nearby containing blue
supergiants and a few red supergiants. The transient is located in a dark dust
lane, but does not appear to lie within a rich association. The bottom three
panels in Figure 2 zoom in on the site in the WFC3 images we obtained several
months after the outburst in, from left to right, $I$, $J$, and $H$. The green
circles show the 3$\sigma$ error locations from the astrometric registration.
There are several faint stars within the error circle in the $I$ frame, the
brightest of which is more conspicuous in the $J$ and $H$ images. The apparent
magnitudes (Vega scale) of this star are $I=25.8$, $J=23.3$, and $H=22.2$,
according to photometry from the Hubble Source Catalog
(HSC),111111http://archive.stsci.edu/hst/hsc . In this paper we frequently
give photometry for sources detected in images; in many cases these values are
quoted from the HSC (see Whitmore et al., 2016, for an overview). HSC
magnitudes are on the AB scale, and are determined using small photometric
apertures. Throughout this paper we have corrected the HSC magnitudes to
infinite apertures, using the values at
https://archive.stsci.edu/hst/hsc/help/HSC_faq/ci_ap_cor_table_2016.txt. Where
appropriate, we then converted the AB magnitudes to the Vega scale, using the
zero-points for the WFC3 camera available at
http://www.stsci.edu/hst/instrumentation/wfc3/data-analysis/photometric-
calibration , and for the ACS camera from Sirianni et al. (2005). available
from the HLA display of the field. However, none of the stars within the error
circle varied significantly in the $I$-band frames taken in 2003, 2014, and
2017. Thus we conclude that we did not detect the transient with a few months
after its IR eruption had ended. Moreover, aside from the possibility that the
object was able to return to essentially the same quiescent level it had
before outburst, we have no compelling identification of an optical
progenitor. These observations, along with the rapidity of the IR transient,
make this SPRITE event qualitatively different from ILRTs like NGC 300
OT2008-1, SN 2008S, and M51 OT2019-1, which would have been detected easily by
a few months after their outbursts at $I$, $J$, and $H$.

There is also no pre-eruption IR counterpart detected in the available
archival Spitzer/IRAC imaging. We examined the location of the event in the
SHA Super Mosaics in all four IRAC channels, which consist of stacks of images
taken between 2004–2007, and derived $5\sigma$ limiting magnitudes based on
the faintest detected sources within a $40^{\prime\prime}$ radius in PSF-
photometry catalogs constructed for M101 by K19. Our limiting (and absolute)
magnitudes of $[3.6]>19.7$ ($-9.5$), $[4.5]>19.2$ ($-10.0$), $[5.8]>16.9$
($-12.3$), and $[8.0]>15.9$ ($-13.3$) are sufficient to rule out an obscured
progenitor as luminous and massive as those observed for the ILRTs mentioned
in the previous paragraph. All of them had $M_{[4.5]}<-10$ before their
outbursts.

One possibility is that SPIRITS 14aje was a heavily obscured core-collapse SN,
similar to those presented in Jencson et al. (2017, 2018, 2019b), but for
which the luminous IR peak was missed during the gap in Spitzer/IRAC coverage
between 2012 and the start of the SPIRITS survey in 2014. The red
$[3.6]-[4.5]$ color would not be unusual for a late-phase core-collapse SN
(see, e.g., Tinyanont et al., 2016; Szalai et al., 2019; Jencson et al.,
2019b). The deep optical limits from iPTF shown in Figure 1 to $R\gtrsim 21$
mag would then imply many magnitudes of extinction ($A_{V}\gtrsim 9$ mag for
an SN peaking at $M_{R}=-16$ mag). Such high obscuration, perhaps by a dense
molecular cloud, would explain the lack of a conspicuous progenitor star in
the archival HST imaging. Still, given our relatively weak constraints on the
timescale and peak brightness of 14aje, we are unable to confirm this
scenario, and its definite nature thus remains elusive.

Figure 2:  images of the site of the fast SPRITE SPIRITS 14aje in M101. Top:
color rendition of the site, from $B$, $V$, and $I$ images in the Hubble
Legacy Archive. The frame is $29^{\prime\prime}$ high ($\sim$950 pc at the
distance of M101). The site of 14aje, marked with a red cross, lies in a dust
lane in a spiral arm of M101, with several rich young associations in the
vicinity. Bottom row: zooms in on frames we obtained several months after the
outburst, in $I$, $J$, and $H$. The site of 14aje from astrometric
registration of the Spitzer and frames is marked with green 3$\sigma$ error
circles. None of the optical stars detected within the error circles in these
frames appear to have varied in archival images taken at an epoch before, and
an epoch after, the outburst (see text). Each frame is $5^{\prime\prime}$
high. All images presented in this paper have north at the top, east on the
left.

###  6.2 17fe: Archetypal Slow SPRITE

The Spitzer IR light curves of SPIRITS 17fe in the Sculptor-group galaxy NGC
7793 ($d\simeq 3.6$ Mpc) are shown in the middle panel of Figure 1. We caught
it rising in brightness on 2017 February 16, and it had brightened another 0.8
mag on 2017 March 16. At that date, marking the maximum brightness seen in our
data, it had apparent magnitudes of $[3.6]=16.52$ and $[4.5]=15.83$,
corresponding to absolute magnitudes of $-11.3$ and $-11.9$, respectively.
Subsequently, 17fe slowly faded until going below our detection limit in our
final Spitzer observations on 2019 November 1. Thus the outburst duration was
at least 988 days. There were no detections of this object prior to the 2017
outburst throughout the available Spitzer imaging at 3.6 and 4.5 $\mu$m, as
shown by the upper limits in the middle panel of Figure 1. Also shown are the
optical limits derived from the ATLAS forced-photometry light curves in the
ATLAS-c and -o bands, which constrain the presence of an optical counterpart
to $\gtrsim$19–20 AB mag in both bands for nearly the entire duration of the
IR transient. We thus classify 17fe as a prototypical slow SPRITE—luminous in
the IR, undetected in ground-based optical data.

The site of 17fe serendipitously lies within the field that we imaged for
SPIRITS 15wt (discussed below in §7.5), for which our triggered observations
were obtained on 2016 April 18. This was 304 days before our first Spitzer
detection of the 17fe event. We astrometrically registered a Spitzer 4.5
$\mu$m difference-image frame, taken at 17fe’s maximum light, with an archival
ACS $I$-band frame obtained in 2003 (GO-9774, PI S. Larsen). (The 2003 frame,
rather than our 2016 image obtained with a WFC3 subarray, was chosen for the
registration because of its larger FOV.) The top picture in Figure 3 shows a
color rendition of the site from the HLA. Like the fast SPRITE 14aje, the 17fe
event occurred in a spiral arm of its host galaxy, with numerous young blue
stars, red supergiants, and dust lanes in its vicinity. The frames in the
middle row of Figure 3 zoom in on images of the site, with green circles
marking the 3$\sigma$ location from the astrometric registration. From left to
right, these frames show $I$ in 2003, and $J$ and $H$ from our own pre-
outburst observation in 2016. In addition to these frames, there are archival
images in the $I$ band obtained in 2001 (two epochs: GO-8599, PI T. Boeker;
and GO-9042, PI S. Smartt) and in 2014 (GO-13364, PI D. Calzetti). There were
no changes in brightness of any objects inside the error circle in all of
these pre-outburst images. Outside the error circles on the southwest side is
a bright red star, which is a high-amplitude variable in the frames; however,
it is too far outside the circle to be related to 17fe.

In addition to the pre-outburst images, there are fortuitous archival WFC3/IR
frames obtained in the $J$ and $H$ bandpasses on 2018 January 16 (GO-15330, PI
D. Calzetti), 306 days after the date of the IR maximum. The IR outburst was
still underway at this epoch. Cutouts from these frames are shown in the
bottom row of Figure 3. A faint, very red object has appeared near the center
of the astrometric error circle at both wavelengths, making it a very likely
near-IR counterpart of the SPRITE in outburst. Based on aperture photometry
relative to HSC stars in the nearby field, we find Vega-scale magnitudes for
this star of $J=24.2$ and $H=21.4$. There is a hint that this object is
present in our 2016 pre-outburst $J$ and $H$ frames, but the field is crowded
with overlapping faint stars. There is no convincing progenitor in the pre-
outburst $I$ frames; there is a partially resolved star inside the error
circle in the 2003 $I$-band image just southwest of the center, with a Vega-
scale magnitude of $I\simeq 27.1$. However, this star does not coincide with
the object that appeared in the 2018 frames.

In Figure 4, we show the spectral-energy distribution (SED) of 17fe,
constructed from the 2018 January 16 WFC3/IR detections and interpolations of
the Spitzer/IRAC [3.6] and [4.5] light curves to the same epoch, 333 days
after the first detection of the event with Spitzer. The SED is very red,
appearing to peak in the IR around 3 $\mu$m, at a band luminosity of $\lambda
L_{\lambda}\sim 10^{4}~{}L_{\odot}$. The near- to mid-IR SED can be
approximated by a blackbody spectrum of temperature $T_{\mathrm{BB}}\simeq
1050$ K. We also tried fitting the HST and Spitzer points with two separate
blackbodies. In this case, the data alone indicate a slightly warmer
temperature of $T_{\mathrm{BB}}\simeq 1290$ K; however, there is not strong
evidence for two components. These values are near the temperatures for dust
condensation (e.g., Ney & Hatfield, 1978; Gehrz et al., 1980a), suggesting the
presence of newly formed, warm dust.

A stellar merger is a compelling scenario for the origin of LRNe and at least
some slow SPRITEs. For SPRITEs like 17fe, early dust formation is required to
obscure or dramatically shorten the associated OT. In models by Pejcha et al.
(2016a, b), elaborated by Metzger & Pejcha (2017), the secondary light-curve
peak seen in many LRNe can be explained by the shock-interaction of the
dynamical merger ejecta with equatorially concentrated material ejected from
the binary during the pre-dynamical in-spiral phase. The dense, rapidly
cooling regions behind radiative shocks are favorable locations for dust
formation. Metzger & Pejcha (2017) find that, for certain binary
configurations, namely those involving giant stars and having long phases of
pre-merger mass loss, dust may form early enough to completely obscure the
associated shock-powered transient at optical wavelengths.

For a similar, but more luminous, slowly evolving IR transient, SPIRITS 19fi,
an associated faint, short-duration ($\approx$10 day), red OT was detected in
stacked observations from the Zwicky Transient Facility (see J20). For two
other slow SPRITES, SPIRITS 17ar and SPIRITS 18nu, their near-IR outburst
spectra show strong molecular absorption features akin to those of a late M
giant (Jencson et al., in prep.). These features are also seen in late-time
spectra of several optically bright LRNe (e.g., Kamiński et al., 2015;
Blagorodnova et al., 2017, 2020). These observations, together with the late-
time SED of SPIRITS 17fe suggestive of warm dust, lend credence to a stellar
merger accompanied by early dust formation as a viable origin of many slow
SPRITEs.

Figure 3:  images of the site of the slow SPRITE SPIRITS 17fe in NGC 7793.
Top: color rendition of the environment, created in the Hubble Legacy Archive
from $B$, $V$, and $I$ frames. Frame is $30^{\prime\prime}$ high ($\sim$525 pc
at the distance of NGC 7793). The site of 17fe, marked with a red cross, lies
in a spiral arm, with dust lanes and numerous young blue stars and red
supergiants in the vicinity. Middle row: zooms in on frames taken before the
outburst, in $I$, $J$, and $H$. The $I$ frame was taken 13.2 yr before the
eruption, and $J$ and $H$ 0.8 yr before. The site of 17fe from astrometric
registration of the Spitzer and frames is marked with green 3$\sigma$ error
circles. Each frame is $2\farcs 4$ high. Bottom row: frames taken in $J$ and
$H$ 0.8 yr after the maximum of the IR outburst, while the eruption was still
underway. A near-IR counterpart is detected at $J$ and is bright at $H$.
Figure 4:  SED of the slow SPRITE, SPIRITS 17fe, constructed from photometry
of the HST WFC3/IR F110W, F128N, and F160W images taken on 2018 January 16.2
(blue diamonds), and from the Spitzer/IRAC [3.6] and [4.5] light curves
interpolated to the same epoch (orange squares). Blackbody fits to only the
HST points (blue dashed curve), only the Spitzer points (orange dotted curve),
and all points together (black solid curve) are shown with their corresponding
temperatures, $T_{\mathrm{BB}}$, given in the legend in the upper-left corner.

###  6.3 14axa: Classical Nova?

SPIRITS 14axa in M81 ($d\simeq 3.6$ Mpc) was initially classified by us (K17)
as a fast SPRITE. We detected it with Spitzer at only one epoch, 2014 June 13,
as shown by its light curve in the right-hand panel of Figure 1. There were
Spitzer non-detections 122 days before this observation (2014 February 11),
and 239 days afterward (2015 February 7). Our triggered observations on 2014
September 26 were obtained between the dates of the Spitzer detection and the
subsequent non-detection, so it is unknown whether the IR event was still
underway. The absolute magnitude at the single Spitzer detection was
$M_{[4.5]}\simeq-11.5$.

We learned later that this event had also been detected at optical wavelengths
and reported as a CN, designated PNV J09560160+6903126.121212We are grateful
to D. Bishop for maintaining a website devoted to extragalactic novae, at
https://www.rochesterastronomy.org/novae.html, which alerted us to this
optical detection. The apparent coincidence of 14axa with the nova was also
noted by Oskinova et al. (2018). The initial discovery was by Hornoch &
Kucakova (2014), who reported an unfiltered (approximately $R$) optical
magnitude of 18.9, on 2014 May 21.9. The transient had been fainter than
magnitude 21.7 two nights earlier, demonstrating an extremely fast rise time.
Five nights later, Hornoch et al. (2014) observed the object with a wide-field
camera on the 2.5-m Isaac Newton Telescope. A narrow-band filter confirmed
strong emission at H$\alpha$, and yielded a Sloan $r^{\prime}$ magnitude of
19.6. All of this information is consistent with the transient being a CN,
although to our knowledge there is no direct spectroscopic confirmation of
this conclusion. Our detection with Spitzer suggests that the nova was in a
dust-forming post-maximum phase at the time of our observation.

The site of 14axa lies between two spiral arms of M81, in a crowded sheet of
stars which appears to lack a young population (in contrast to most of the
SPIRITS IR transients, which strongly tend to be associated with spiral arms,
young associations, and dusty environments). There are three available
$I$-band images of the site, two obtained with ACS in 2002 and 2004 (GO-9353,
PI S. Smartt, and GO-10250, PI J. Huchra), and our triggered WFC3 observation
in 2014. We performed an astrometric registration of the Spitzer 4.5 $\mu$m
image showing 14axa with the 2004 ACS image, in order to locate the site in
the frames. Figure 5 shows renditions of the three $I$-band frames, with green
circles marking the 3$\sigma$ error positional locations. Not far from the
centers of the circles is a faint star that noticeably brightened in the 2014
image. Approximate $I$ magnitudes (AB scale), determined from aperture
photometry relative to nearby stars with HSC magnitudes, are 25.2 in 2002,
25.8 in 2004, and 24.7 in 2014. (In our 2014 $J$ and $H$ frames, the object is
badly blended with the neighboring star to the northeast.) The $I$-band
luminosity at the 2014 observation is consistent with a CN about four months
past maximum; see, for example, the $I$-band and near-IR light curves of T Pyx
presented by Walter et al. (2012) and Evans et al. (2012). However, the pre-
outburst object is unusually luminous compared to the progenitors of typical
CNe. Unless it is a chance superposition, the pre-outburst detection suggests
that the binary system has a red-giant donor star, similar to Galactic
(recurrent) novae such as T Pyx and RS Oph (e.g., see the reviews of Schaefer,
2010; Mukai, 2015). The object was below detection in archival pre-outburst
images at the $V$ band, showing that it was indeed red.

Figure 5: False-color renditions of $I$-band images of the site of SPIRITS
14axa in M81. Top: ACS image from 2002; middle: ACS image from 2004; bottom:
WFC3 image taken by us on 2014 September 26, triggered by the Spitzer
discovery 3.5 months earlier. Each frame is $1\farcs 6$ high. The green
circles show the 3$\sigma$ positional error circles, based on an astrometric
registration of the 2004 image with a Spitzer image showing the transient. A
faint star inside the error circle, seen in 2002 and 2004, had brightened in
the 2014 image, and is likely to be the optical counterpart of this probable
classical nova.

As discussed in J20, the majority of SPIRITS transients fainter than
$M_{[4.5]}\simeq-12.5$ at peak are similar to 14axa: that is, they were
detected only within a single Spitzer visibility window—implying an
evolutionary timescale $\lesssim$6 months. At their peak they have red IR
colors of $[3.6]-[4.5]$ between 0.5 and 1.2. Two events, SPIRITS 15bb and
SPIRITS 15bh, were also preceded by short ($\lesssim$2 months), faint
($M_{g}\approx-8$) optical outbursts recovered in stacked, archival iPTF
images. All 15 of these fast and faint IR transients in SPIRITS were found in
just seven galaxies within $\approx$5 Mpc, and nearly half of them were in
M81. This high rate from a small number of the nearest galaxies suggests they
are common events. CNe are thus an attractive scenario for their origin; the
rate in large galaxies like the Milky Way is estimated to be $\approx$40–80
yr-1 (e.g., Shafter, 2017; De et al., 2021). As with 14axa, the optical
precursors detected for 15bb and 15bh were in the luminosity range typical of
novae, further supporting this hypothesis. Some novae, namely those of the DQ
Her class, such as NQ Vul (Ney & Hatfield, 1978), LW Ser (Gehrz et al.,
1980a), and V705 Cas (Gehrz et al., 1995a; Evans et al., 1997, 2005), form
optically thick dust shells, while others that form optically thin shells
still produce strong IR emission, peaking on a timescale of $\approx$50–80
days at $M_{\mathrm{[4.5]}}\approx-11$ to $-12.5$ (e.g., V1668 Cyg; Gehrz et
al., 1980b). These properties are generally consistent with the fast and faint
IR transients discovered by SPIRITS (J20). Further study on the implications
of this population for the rate of strongly dust-forming novae and their
impact on the chemical enrichment and dust budget of galaxies (e.g., Gehrz,
1988, 1999; Evans et al., 2012) is thus warranted. A less likely alternative
is that this was the coronal-emission phase of an ONe nova such as QU Vul
(Greenhouse et al., 1988, 1990). These novae appear to be several absolute
magnitudes fainter at $4.5\,\micron$ during maximum light than dusty novae
(see, e.g., Gehrz et al. 1995b).

##  7 Luminous Periodic Infrared Variables

As noted above (§2), a significant fraction of the suspected transients
discovered early in the SPIRITS survey proved eventually to be periodic, or
likely periodic, variables when more Spitzer data, over longer time baselines,
had accumulated. The periods associated with these sources are nearly all
longer than 1000 days. This led to us triggering observations of variables
that were only recognized as being periodic later on. In typical cases, the
objects were in the rising phase of their light curves during the first few
SPIRITS observations, leading to our initial classifications of them as
candidate SPRITEs.

In view of the importance of the periodicity to understanding these sources,
we first summarize our analysis of the Spitzer photometry and the consequent
insight into the nature of this sample of periodic sources. We then describe
the observations of individual objects and the additional understanding they
provide.

Characteristics of the periodic and likely periodic variables that we observed
with are summarized in Table 4. We derived the periods given in column 2 from
the Spitzer light curves using the procedure described in K19 (which in turn
follows VanderPlas & Ivezić 2015), allowing the [3.6] and [4.5] magnitudes to
be analyzed simultaneously. Two of the variables have periods quoted as lower
limits, because there is Spitzer photometry covering only about a single
cycle. Coverage of the other sources is rather better than for most of the
variables discussed by K19, although few have complete coverage for as much as
two cycles. Given that Mira light curves are known not to repeat exactly from
cycle to cycle, our derived periods can only be good to about 5–10%, and are
best judged by examining the individual light curves. The mean apparent
magnitudes (denoted [3.6] and [4.5]) are given in columns 3 and 5, the peak-
to-peak amplitudes ($\Delta[3.6]$ and $\Delta[4.5]$) in columns 4 and 6, and
the mean colors ($[3.6]-[4.5]$) in column 7. Columns 8 and 9 give the the mean
absolute magnitudes at [3.6] and [4.5], calculated using the distance moduli
in Table 2. The absolute magnitudes cover the range $-11.07>M_{[4.5]}>-12.31$,
except for one unusually luminous variable, 15mr, at $M_{[4.5]}\simeq-13.76$.

Table 4: Properties of Periodic and Suspected Periodic Variables SPIRITS | Period | [3.6]aa[3.6] and [4.5] denote the mean apparent magnitudes of the variables, and $\Delta[3.6]$ and $\Delta[4.5]$ denote the peak-to-peak amplitudes of their variations. |  $\Delta[3.6]$aa[3.6] and [4.5] denote the mean apparent magnitudes of the variables, and $\Delta[3.6]$ and $\Delta[4.5]$ denote the peak-to-peak amplitudes of their variations. | [4.5]aa[3.6] and [4.5] denote the mean apparent magnitudes of the variables, and $\Delta[3.6]$ and $\Delta[4.5]$ denote the peak-to-peak amplitudes of their variations. |  $\Delta[4.5]$aa[3.6] and [4.5] denote the mean apparent magnitudes of the variables, and $\Delta[3.6]$ and $\Delta[4.5]$ denote the peak-to-peak amplitudes of their variations. | $[3.6]-[4.5]$ | $M_{[3.6]}$ | $M_{[4.5]}$
---|---|---|---|---|---|---|---|---
Designation | [days] | [mag] | [mag] | [mag] | [mag] | [mag] | [mag] | [mag]
15nzbbInsufficient data at [3.6] to determine mean magnitude, amplitude, and absolute magnitude over the pulsation cycle (see text). The approximate color given in column 7 is based on an estimate of the likely mean [3.6] magnitude. | 1614 | $\dots$ | $\dots$ | 16.66 | 1.07 | 1.5 | $\dots$ |  $-$12.17
15qo | 1232 | 16.69 | 1.37 | 16.11 | 1.43 | 0.58 |  $-$11.45 |  $-$11.68
15aag | 1233 | 18.10 | 1.63 | 17.07 | 1.55 | 1.04 |  $-$10.04 |  $-$11.07
15ahgcc15ahg, 15wt, 14bbc, 15mr, and 15mt had detected or suspected optical/near-IR counterparts in imaging (see text). 16ea is equivocal (see §7.7). The others had no convincing counterparts at $I$, $J$, or $H$ in images. | 1163 | 16.49 | 0.93 | 16.13 | 1.16 | 0.36 |  $-$11.02 |  $-$11.38
14al |  $\sim$2160 | 16.60 | 0.96 | 15.20 | 0.82 | 1.40 |  $-$10.91 |  $-$12.31
14dd | 1418 | 16.89 | 0.95 | 15.92 | 1.11 | 0.97 |  $-$10.62 |  $-$11.59
15afp | ¿1650 | 17.63 | 0.79 | 16.87 | 1.13 | 0.76 |  $-$10.64 |  $-$11.40
15wtcc15ahg, 15wt, 14bbc, 15mr, and 15mt had detected or suspected optical/near-IR counterparts in imaging (see text). 16ea is equivocal (see §7.7). The others had no convincing counterparts at $I$, $J$, or $H$ in images. | 1188 | 16.55 | 0.90 | 16.03 | 0.94 | 0.53 |  $-$11.22 |  $-$11.75
14bbccc15ahg, 15wt, 14bbc, 15mr, and 15mt had detected or suspected optical/near-IR counterparts in imaging (see text). 16ea is equivocal (see §7.7). The others had no convincing counterparts at $I$, $J$, or $H$ in images. | 1498 | 16.29 | 1.12 | 15.57 | 1.13 | 0.71 |  $-$11.48 |  $-$12.20
15mrcc15ahg, 15wt, 14bbc, 15mr, and 15mt had detected or suspected optical/near-IR counterparts in imaging (see text). 16ea is equivocal (see §7.7). The others had no convincing counterparts at $I$, $J$, or $H$ in images. | 1113 | 15.71 | 1.37 | 14.96 | 1.32 | 0.76 |  $-$13.01 |  $-$13.76
15mtcc15ahg, 15wt, 14bbc, 15mr, and 15mt had detected or suspected optical/near-IR counterparts in imaging (see text). 16ea is equivocal (see §7.7). The others had no convincing counterparts at $I$, $J$, or $H$ in images. | ¿1800 | 16.86 | 1.67 | 16.69 | 2.16 | 0.17 |  $-$11.86 |  $-$12.03
16eab,cb,cfootnotemark:  |  $\sim$670 | $\dots$ | $\dots$ | 16.51 | 1.11 | 1.6 | $\dots$ |  $-$10.83

A similar class of luminous periodic IR variables discovered in nearby
galaxies by SPIRITS was discussed by K19; they suggested that some of these
objects are related to the dusty OH/IR stars (intermediate-mass, oxygen-rich
Mira variables) found in our Galaxy and the LMC. In Figure 6 we plot the
period-luminosity relation for our variables, using filled grey circles for
objects with one variation cycle or less, and filled black circles for those
with more. Also plotted are the data from K19 for SPIRITS periodic variables
in nearby galaxies (filled red circles), and for LMC OH/IR stars from Goldman
et al. (2017) (filled cyan squares). All but one of our variables fall on, or
close to, the clump of variables that K19 identify with intermediate-mass AGB
stars ($1000<P<2000$ days and $-11>M_{[4.5]}>-13$), and which itself falls
close to the extrapolated period-luminosity relation found for Mira variables
in the LMC (Riebel et al., 2015; Whitelock et al., 2017). These sources have
large variation amplitudes (e.g., K19, their Figure 4), as do our sources
which are in the approximate range $0.8<\Delta[4.5]<2.2$ mag. The range of
colors, $0.17<[3.6]-[4.5]<1.5$, is also comparable to the values discussed by
K19 (cf. their Figure 5). Footnotes in column 1 of Table 4 mark the five
variables with detections or possible detections, as we discuss later in this
section.

Figure 6:  Mean [4.5] absolute magnitude versus pulsation period for the
periodic and suspected periodic variables from this paper, shown as black
points, or grey points if only one pulsation cycle or less has been covered.
Red points mark the periodic variables from K19, and cyan squares the LMC
OH/IR stars from Goldman et al. (2017). The isolated and unusually luminous
black point is SPIRITS 15mr (see §7.6).

Most of these variables have extremely red Spitzer colors, indicating very low
effective temperatures and circumstellar dust, a consequence of high mass-loss
rates. For example, colors of $[3.6]-[4.5]\simeq 0.6$, 1.0, and 1.5 correspond
to blackbody temperatures of $\sim$1000, 800, and 500 K, respectively (cf.
Figure 7 in K19).

At such very low effective temperatures, we generally would not expect to
detect these objects with our one-orbit observations. In a typical case of a
variable with an apparent IRAC channel 2 magnitude of $[4.5]\simeq 16.5$, and
the nominal exposure times we used for our observations (§3), the WFC3 ETC
indicates that the source would not be detected ($\rm S/N<5$) in the /WFC3
$I$, $J$, or $H$ bandpasses if its blackbody temperature were below $\sim$750
K. Above 750 K it would be detectable only at $H$. For a temperature above 850
K, it would be detected also at $J$. For detection at $I$, a source with
$[4.5]=16.5$ would have to be hotter than $\sim$1275 K. However, the use of
blackbodies in these estimates is only a rough approximation, since OH/IR
stars have strong molecular absorptions, due to H2O and CO in particular,
which influence the $[3.6]-[4.5]$ and other colors. Moreover, these estimates
are optimistic, since they neglect background light and dust extinction.

It is also possible to estimate the anticipated magnitudes, using what is
known about the LMC OH/IR stars that are illustrated in Figure 6, and assuming
that our variables are similar. We use the $JHK(L)$ lightcurves for these
OH/IR stars from Whitelock et al. (2003) and $I$-band light curves from
Soszyński et al. (2009); note, however, that the very reddest LMC sources were
not detected in the ground-based $I$\- or $H$-bands. Unfortunately there is
only single-epoch Spitzer photometry for these, so we do not have mean Spitzer
magnitudes or colors. The single-epoch colors are in the range
$0.3<[3.6]-[4.5]<0.8$ for the AGB stars, and $[3.6]-[4.5]=0.9$ for the single
supergiant. The AGB amplitudes are in the ranges $1.5<\Delta H<1.9$ and
$2.8<\Delta I<4.0$, while the supergiant has $\Delta H=0.4$ and $\Delta
I=1.5$. The very large amplitudes of the AGB variables, particularly at the
shortest wavelengths, complicates any predictions of flux. Furthermore the
Goldman et al. (2018) comparison of the SMC with the LMC suggests that the
mass-loss rates of these O-rich stars are a function of metallicity; therefore
it seems likely that the AGB stars under discussion will have thicker shells
than similar stars in the LMC and thus fainter magnitudes at wavelengths.
Nevertheless, these provide a useful comparison and the following ranges of
colors found for the LMC sources are used to estimate the expected magnitudes
for our sources: $7.6<[I-4.5]<10.7$ and $2.6<H-[4.5]<4.8$. However, additional
dust extinction is possible and will make the magnitudes even fainter than
these values would predict.

We also note that there are significant differences between the bandpasses of
the ground-based $IJHK$ filters and the similar filters used by . Although
these differences are potentially problematic, particularly for cool stars
with extended atmospheres where strong molecular absorption dominates the
colors, they are not important for the comparisons made here, where the large-
amplitude variations dominate.

We now discuss the individual periodic and likely periodic variables that we
imaged with . Their Spitzer light curves are collected in Figure 7.

Figure 7:  Spitzer IRAC light curves of periodic and suspected periodic
variables from difference imaging. Plotting symbols as in Figure 1. Baseline
magnitudes (aperture photometry on reference images) are shown as open
symbols, where the dashed horizontal bars indicate the range of epochs that
were included in the reference image stacks.

###  7.1 15nz

SPIRITS 15nz was announced by Jencson et al. (2015) as a possible IR transient
in M83 ($d\simeq 4.7$ Mpc), based on our initial few SPIRITS observations.
These data showed a slowly rising [4.5] luminosity during 2014 and early 2015.
In response to this announcement, a separate team (GO-14463, PI B. McCollum)
obtained imaging of the site. Since 2015 we have accumulated additional IR
observations, and there are also archival Spitzer data obtained in 2010. The
IR light curves of 15nz are shown in the top-left panel of Figure 7. The data
at [4.5] indicate a period close to 1600 days. There are insufficient [3.6]
detections to analyze for periodicity, but they can be used for an estimate of
the color, which at $[3.6]-[4.5]\simeq 1.5$ makes 15nz the reddest of the
periodic variables discussed in this section.

As noted in the introduction to this section, detection of a source as cool as
15nz at wavelengths is not expected. We registered a Spitzer frame taken at
maximum brightness with frames to find the precise location of the variable in
the latter. At this site in the disk of M83 there is a dense sheet of faint
stars. There are several faint objects within a 3$\sigma$ error circle, but
comparing $I$-band frames taken at three epochs (2009, 2010, 2016), we see no
significant variation of any of these stars. Only two epochs of imaging at $J$
and $H$ are available (2009, 2016), but again we see no variation of any
detected stars within the error circle. It thus appears that, as was expected,
15nz has no optical or near-IR counterpart at $I$, $J$, and $H$. From a
comparison with the OH/IR stars in the LMC, we would expect 15nz to have
$I>27.4$ and $H>21.5$, or probably much fainter given how red it is.

###  7.2 15qo and 15aag

SPIRITS 15qo was likewise announced by Jencson et al. (2015) as an IR
transient, lying in NGC 1313 ($d\simeq 4.2$ Mpc). A second transient or
variable in the same galaxy, SPIRITS 15aag, was announced by Jencson et al.
(2016a); it lies only $54^{\prime\prime}$ away from 15qo. We adjusted our
pointing so as to capture both of these objects in the same image frames.

The Spitzer light curves of these two variables are shown in the top-middle
and top-right frames of Figure 7. As in the case of 15nz, both objects were
caught in rising phases in the first few SPIRITS observations, and were
announced as transients. However, as the light curves show, they later proved
to be periodic variables. Curiously, their pulsation periods are nearly the
same, both being about 1230 days, and they are also nearly in phase. They are,
however, definitely distinct objects.

We registered a Spitzer image showing both objects near maximum light with
archival images as well as the new images obtained in our program. At the site
of 15qo there is an extremely rich star field, lying in an actively star-
forming region in NGC 1313. Several faint stars fall within a 3$\sigma$ error
circle, including a bluish star near the center. None of these stars appear to
be significantly variable in $I$-band frames taken in 1994, 2003, 2004 (two
epochs), and 2016. Our $J$ and $H$ frames show no very red star at the site.
We conclude that there is no detectable optical/near-IR counterpart.

The results are similar for 15aag, which is significantly redder than 15qo. It
also lies in a rich field, not far from several H II regions. There is again a
faint star within the 3$\sigma$ error circle, which showed no significant
variability in $I$-band frames taken in 2001, 2003, 2004 (two epochs), and
2016. This star is detected in our $J$ and $H$ observations, but the source is
not extremely red; unfortunately these are the only frames in $J$ and $H$ in
the archive. As in the case of 15qo, we find no convincing optical/near-IR
counterpart.

###  7.3 15ahg, 14al, and 14dd

SPIRITS 15ahg is another object announced as an IR transient by Jencson et al.
(2016a), lying in the M81-Group spiral galaxy NGC 2403 ($d\simeq 3.2$ Mpc).
Two previously identified variables in the SPIRITS database, 14al and 14dd,
lie close to the position of 15ahg, and we adjusted the telescope pointing so
that we could include all three in the frames. The site of these variables
lies near a spiral arm on the northwest side of NGC 2403, in an extremely rich
star field. Several giant H II regions are nearby.

The Spitzer light curves of 15ahg are shown in the left panel in the second
row of Figure 7. Its period is about 1160 days and it is relatively blue, with
a mean $[3.6]-[4.5]=0.36$ There are two $I$-band observations of this site in
the archive, one taken in 2005 (GO-10402, PI R. Chandar), and the other our
frame obtained in 2016. We registered these images with a Spitzer IRAC channel
2 frame from the SPIRITS program, taken near maximum brightness of 15ahg.
Inside the 3$\sigma$ error circle in the $I$-band frames is a faint star that
brightened significantly from 2005 to 2016, consistent with the phasing of the
IR variability shown in Figure 7. In the 2005 image, the variable lies in a
blended clump of several faint stars, which is possibly a compact sparse
cluster. In 2016 it had risen to an $I$ magnitude of about 24.5 (Vega scale,
based on aperture photometry relative to several HSC stars in the field). This
star is optically very red, and is well detected in our $J$ and $H$ frames.
The HSC Vega-scale $J$ and $H$ magnitudes for the object are 20.79 and 18.94,
respectively. Thus there is little doubt that this object is the optical/near-
IR counterpart of the Spitzer variable. The four panels in Figure 8 show small
postage stamps from the two $I$-band frames (top row), and from our $J$ and
$H$ images (bottom row). The astrometric 3$\sigma$ error circle is shown in
green in the top two frames.

A comparison with the LMC OH/IR stars (see introduction to this section) would
predict $18.7<H<20.9$ and $1.1<(J-H)<2.0$ for 15ahg. These are consistent with
the measured $H\simeq 18.9$ and $J-H\simeq 1.8$ and support our suggestion
that this object is a pulsating AGB variable.

Figure 8:  False-color renditions of images of the site of the periodic
variable SPIRITS 15ahg in the nearby galaxy NGC 2403. Top row: $I$-band frames
taken in 2005 (left) and 2016 (right). The green circles mark 3$\sigma$ error
positions of the Spitzer variable. Just north of the center is a star that
brightened significantly and is a likely optical counterpart of 15ahg. Bottom
row: images of the site in 2016, taken in $J$ (left) and $H$ (right). The
candidate counterpart is bright at $J$ and very bright at $H$. Height of each
frame is $3\farcs 6$.

The light curves of 14al and 14dd are shown in the second and third panels in
the second row of Figure 7. 14al is extremely red, with a mean
$[3.6]-[4.5]=1.4$, and its approximate period, 2160 days (5.9 years), is the
longest of any of the periodic variables. Its peak-to-peak amplitudes,
$\Delta[3.6]\simeq 1.0$ and $\Delta[4.5]\simeq 0.8$ mag, although slightly
less than those of the other periodic variables, are still large. 14al lies in
a rich star field. There are several faint stars at the site, but none varied
significantly in the $I$ frames from 2005 and 2016. None of them are bright at
$J$ and $H$. We conclude there is no convincing optical/near-IR counterpart.

14dd is another likely periodic variable, with a period of 1420 days and a red
color of $[3.6]-[4.5]\simeq 1.0$. As in the case of the nearby 14al, there are
no variable objects at the site in the two available $I$-band frames, nor any
conspicuous objects within the error circle at $J$ and $H$. Again, we find no
credible optical/near-IR counterpart of this very cool object.

###  7.4 15afp

The IR light curves of SPIRITS 15afp are shown in the left-hand panel in the
third row of Figure 7. This object rose by over one magnitude from the first
SPIRITS observation in 2014 to a peak in late 2015, leading us to announce it
as a candidate transient (Jencson et al., 2016a). We triggered our imaging in
2016 March. 15afp lies in a spiral arm of the face-on and actively star-
forming galaxy NGC 6946 ($d\simeq 4.5$ Mpc). This variable could be periodic,
but our observations cover less than one cycle of a period of around 1650
days. We also note our photometry is likely contaminated by another nearby,
but unrelated, variable source. The amplitudes and color are similar to the
other periodic variables discussed in this section. However, we cannot rule
out that the object is a slow SPRITE transient, based on our relatively
limited data.

We registered a Spitzer image taken at the maximum brightness of 15afp with an
ACS $I$-band frame obtained in 2016 October (GO-14786, PI B. Williams). The
site lies in a dense sheet of stars, with moderately high extinction. There
are several faint stars within a 3$\sigma$ error circle. None of them appeared
to vary between the ACS frame and our own WFC3 $I$-band frame taken 7 months
earlier, nor in comparison with a shallow ACS frame obtained in 2004 (GO-9788,
PI L. Ho). There are no conspicuous sources at the site in our $J$ and $H$
frames. On the basis of these fairly limited data, we see no convincing
evidence of an optical or near-IR counterpart.

###  7.5 15wt and 14bbc

The Spitzer light curves of SPIRITS 15wt are plotted in the middle panel in
the third row of Figure 7. 15wt rose by nearly 1 mag over the first two years
of SPIRITS observations of the host galaxy, NGC 7793 in the nearby Sculptor
Group ($d\simeq 3.6$ Mpc). This slow eruption of an apparent transient
prompted us to trigger our imaging, obtained on 2016 April 18. However, our
subsequent observations, as well as archival data, clearly reveal that 15wt is
actually a periodic variable of the type discussed by K19, with a well-
determined period of 1190 days. It is relatively “blue,” with a mean color of
$[3.6]-[4.5]\simeq 0.5$.

We registered an archival /ACS $I$-band image of NGC 7793 obtained on 2003
December 10 (GO-9774, PI S. Larsen) with a Spitzer frame taken near maximum
brightness of 15wt, in order to locate the site in the frames. We then
registered the ACS frame with WFC3 $I$-band frames taken on 2014 January 18
(GO-13364, PI D. Calzetti) and on 2016 April 18 in our own program. Just
inside the 3$\sigma$ registration error circle is a star that was not detected
in 2003 and 2014, but had brightened in 2016. This object is very bright in
the $J$ and $H$ frames that we obtained at the same time as our $I$ image in
2016, and the date of the imaging is close to the time of maximum brightness
in the Spitzer frames. Thus we conclude that the optical/near-IR object is the
counterpart of the IR variable. In confirmation, there are also archival
WFC3/IR frames of the site taken on 2018 January 16 in $J$ and $H$ (GO-15330,
PI D. Calzetti), when the IR variable was near minimum light, as shown in
Figure 7. The counterpart is significantly fainter in these frames than in
2016.

Figure 9 presents false-color renditions of the $I$-band frames from 2014 and
2016 in the top row, revealing the star just inside the error circle that
brightened in 2016. The bottom row shows that this star is very bright in $J$
and $H$, in the WFC3 frames taken during our same visit in 2016. The HSC gives
the following magnitudes (Vega scale) for this object at the 2016 epoch:
$I=24.23$, $J=20.25$, and $H=18.70$. The LMC OH/IR stars (see introduction to
this section) would have $26.7>I>23.6$ and $20.8>H>18.6$ at this distance,
consistent with our suggestion that the Spitzer variable and its optical/near-
IR counterpart is a pulsating AGB star.

Figure 9:  False-color renditions of WFC3 images of the site of the periodic
IR variable SPIRITS 15wt in the nearby galaxy NGC 7793. Top row: $I$-band
frames taken in 2014 (left) and 2016 (right). The green circles mark 3$\sigma$
error positions of the Spitzer variable. Inside the circles is a star that
brightened significantly around the time of maximum IR luminosity, and is a
likely optical counterpart of 15wt. Bottom row: near-IR images of the site in
2016, taken in $J$ (left) and $H$ (right). The counterpart is bright at $J$
and very bright at $H$. Height of each frame is $2\farcs 4$.

Another IR variable, 14bbc, had been discovered earlier during the SPIRITS
program. It lies close to the position of 15wt, and we adjusted the pointing
for our triggered observation in 2016 so as to include both 15wt and 14bbc in
the images. The Spitzer light curves of 14bbc are shown in the right-hand
panel in the third row of Figure 7. This is another periodic variable, which
has undergone two full cycles during the archival and SPIRITS Spitzer
observations (plus an earlier observation in 2004). Its period is 1500 days,
and its color is ($[3.6]-[4.5]\simeq 0.7$).

The site of 14bbc lies in an extremely dense star field in a spiral arm of NGC
7793. We located the site in the available images through astrometric
registration, as just described for 15wt. As shown in the $I$-band frame in
the left panel of Figure 10, there are several faint stars inside the
3$\sigma$ error circle. None of them varied between archival frames obtained
in 2003, 2014, and our own frames from 2016, and we believe the variable was
not detected in the $I$ band. However, as shown in the figure, a blended
source does appear in the $J$ frame, and it is bright at $H$; the HSC gives a
Vega-scale magnitude for this object of $H=19.42$. In the archival frames
obtained on 2018 January 16 used for 15wt, the candidate has faded
significantly at both $J$ and $H$, consistent with the phasing of 14bbc seen
in Figure 7. Based on its extremely red optical color, location near the
center of the error circle, and variability at $J$ and $H$, we conclude that
this star is the near-IR counterpart of the Spitzer variable. Its magnitude is
consistent with the $20.4>H>18.2$ anticipated for an AGB variable at the
distance of NGC 7793, using the LMC OH/IR star colors (see introduction to
this section).

Figure 10:  False-color renditions of WFC3 images of the site of the periodic
IR variable SPIRITS 14bbc in NGC 7793, obtained on 2016 April 18. From left to
right the frames were taken in $I$, $J$, and $H$. The green circle in the $I$
image is the 3$\sigma$ error position of the Spitzer variable. As discussed in
the text, here is no obvious counterpart of 14bbc in the $I$ frame (none of
the faint stars inside the circle varied across several epochs), but it is
detected at $J$ and is bright at $H$. Height of each frame is $2\farcs 4$.

###  7.6 15mr and 15mt

The IR variability of SPIRITS 15mr was reported by Jencson et al. (2015), who
suggested it as a transient and possible SPRITE. It belongs to the star-
forming barred spiral galaxy NGC 4605 ($d\simeq 5.5$ Mpc). Another SPIRITS
variable, 15mt, lies nearby, and for our triggered observation on 2016 June 14
we adjusted the telescope pointing to include both objects. The Spitzer light
curves of both variables are plotted in the bottom-left and bottom-middle
panels in Figure 7. As the figure shows, both objects were rising in
brightness up to the date of our 2016 imaging, leading at that time to our
classification of both as possible transients. However, our subsequent
observations show that 15mr is a periodic variable that has gone through two
cycles, with a period of 1110 days.

The position of 15mr in the period-luminosity relation (Figure 6) shows it to
be about 2 mag brighter than the other sources with similar periods. However,
its color, $[3.6]-[4.5]\simeq 0.8$, and peak-to-peak amplitudes,
$\Delta[3.6]=1.4$ and $\Delta[4.5]=1.3$, are very similar to those of the
other pulsators. As Figure 6 shows, a few of the variables in K19 also lie in
this region of the period-luminosity relation. The nature of these luminous
variables is unclear, although this is where we expect to find mass-losing red
supergiants. The LMC OH/IR supergiant, IRAS 04553$-$6825, the most luminous
source from Goldman et al. (2017), is an example of this population.

15mt is also an apparent periodic variable with a longer period ($\sim$1800
days), but the classification is less certain because it has only gone through
a single cycle in the available Spitzer data. It has a very “blue” IR color,
$[3.6]-[4.5]\simeq 0.2$, and especially large peak-to-peak amplitudes,
$\Delta[3.6]\simeq 1.7$ and $\Delta[4.5]\simeq 2.2$.

We registered a Spitzer IRAC 4.5 $\mu$m frame from 2016 April, showing both
15mr and 15mt near maximum brightness, with an archival WFC3 $I$-band image
obtained in 2013 (GO-13364, PI D. Calzetti), and we compared the 2013 image
with our triggered frame taken in 2016. 15mr lies in a rich star field with
moderate extinction, with several young associations in the vicinity. As shown
in the top left image of Figure 11, inside the 3$\sigma$ registration error
circle are several resolved stars and numerous, partially resolved fainter
objects. The site lies near or within a rich young association to the
southwest, from which it is separated by a dark dust lane. The brightest star
within the error circle is also bright in $H$, as shown in the top right image
in Figure 11, making it a candidate counterpart of 15mr. However, this star is
not especially red at optical wavelengths, and is even detected in the $u$
band (F336W filter); the HSC gives magnitudes (Vega scale) of $u=23.39$,
$B=24.12$, $V=23.70$, and $I=22.99$. Yet the object also has a near-IR excess,
as shown by the HSC Vega-scale magnitude of $H=20.36$. By comparing the two
available $I$-band images from 2013 and 2016, we see no significant variation
of this star. Without further information, it remains unclear whether the
bluish star represents a binary companion of (or a chance alignment with) the
IR variable, or whether the situation is more complicated. The LMC OH/IR
supergiant mentioned above, IRAS 04553$-$6825, has $I-[4.5]\simeq 8.7$ and
$H-[4.5]\simeq 3.8$, so 15mr would be expected to have $I\simeq 23.7$ and
$H\simeq 18.8$. Taking into account the limited information we have on
supergiant colors and 15mr’s large amplitude, the measured $H=20.36$ cannot be
used to rule out the possibility that it is an OH/IR supergiant. The shorter-
wavelength magnitudes may be too bright for the OH/IR-supergiant
interpretation, but, as already noted, they could plausibly originate from a
chance alignment in this rich star field, or conceivably a binary companion.

15mt also lies in a rich field, overlain with clumpy dust absorption, as shown
in the $I$-band image in the bottom left frame in Figure 11. There are several
resolved stars inside the 3$\sigma$ error circle, and a brighter star on the
northeast side just outside the circle. The $H$-band image in the lower right
panel in the figure shows two partially resolved bright stars, one
corresponding to the bright $I$-band star just outside the circle. This bright
star is extremely red; its Vega-scale HSC magnitudes are $V=25.18$, $I=22.47$,
and $H=19.44$, making it a plausible optical/near-IR counterpart of
15mt—especially since the variable’s $[3.6]-[4.5]$ color is relatively “blue.”
However, we see no significant variation of this star in the $I$ band between
2013 and 2016. The second $H$-band star, just inside the error circle, appears
to be undetected in the $I$ frame. An LMC OH/IR AGB star (see introduction to
this section) would have $27.4>I>24.3$ and $21.5>H>19.3$, so it seems possible
that the star measured is the Spitzer source, but that it is confused at
shorter wavelengths by bluer stars. Alternatively the second $H$-band star may
be the Spitzer source. 15mt is discussed further in the summary below.

Figure 11:  False-color renditions of WFC3 images of the site of the periodic
IR variables SPIRITS 15mr and 15mt in NGC 4605. Top row: the site of 15mr in
$I$\- and $H$-band frames taken in 2016. The green circle in the $I$ frame
marks the 3$\sigma$ error position of the Spitzer variable. The brightest star
inside the circle is bright at $H$, and may be a counterpart of 15mr. Bottom
row: $I$ and $H$ frames from the same two images, showing the site of 15mt. A
bright star just outside the northeast edge of the error circle is much
brighter in $H$ and might be a counterpart of the Spitzer variable. However,
there is also a source just inside the circle on the northeast side that is
bright at $H$ but undetected at $I$, making it another candidate counterpart.
Height of each frame is $3\farcs 6$.

###  7.7 16ea

SPIRITS 16ea was announced by Jencson et al. (2016b) as a possible IR
transient in the nearby starburst irregular galaxy NGC 4214 ($d\simeq 2.9$
Mpc). In response to this publication, a separate team (GO-14892, PI B.
McCollum) obtained imaging observations of the site of 16ea with WFC3.

The Spitzer light curves of 16ea are plotted in the bottom-right panel of
Figure 7. Unfortunately, the quality of the light curves is relatively poor
and difficult to interpret. This is due to the presence of many image and
subtraction artifacts in the vicinity of 16ea in our difference images,
leading to large uncertainties and numerous nondetections. Still, the handful
of detections at [4.5] shows evidence of multiple peaks, consistent with a
periodic variable. Hence we classify it as probably periodic, although the
properties listed in Table 4 should be viewed with caution. The inferred color
(from the limited [3.6] detections) is very red at $[3.6]-[4.5]=1.6$ mag. The
observations in GO-14892 were obtained on 2017 May 17 and 21; unfortunately
this imaging was done only in the WFC3 IR channel. The status of the variable
at this epoch is uncertain, but it appears to have been near a minimum in the
pulsation cycle.

We astrometrically registered a Spitzer 4.5 µm difference image with an
archival WFC3 $I$-band frame obtained on 2009 December 23 (GO-11360, PI R.
O’Connell). Images in the WFC3 IR channel $J$ and $H$ bandpasses were obtained
at the same time in the O’Connell program. Figure 12 shows false-color
renditions of the 16ea site from these $IJH$ frames, with the 3$\sigma$
registration error circle shown in the left panel. Inside the circle is a
bright star, which is very red, making it a plausible optical and near-IR
counterpart of 16ea. The HSC gives magnitudes (adjusted to Vega scale) for
this star of $I=22.30$, $J=20.75$, and $H=19.88$. In comparison with an ACS
$I$-band image of the site obtained on 2004 October 24 (GO-10332, PI H. Ford),
we see no significant change in brightness of this candidate. Comparing the
2009 and 2017 frames in $J$ and $H$, there is again no compelling evidence for
variability. Given the fragmentary data from both and Spitzer, it is difficult
to reach firm conclusions about this object, beyond our identification of a
probable optical/near-IR counterpart.

Figure 12:  False-color renditions of WFC3 images of the site of the IR
variable SPIRITS 16ea in NGC 4214, obtained in 2009. From left to right the
frames were taken in $I$, $J$, and $H$. The green circle in the $I$ image is
the 3$\sigma$ error position of the Spitzer object in the WFC3 frame. A
bright, very red star inside the southwestern edge of the circle, which is
also detected at $J$ and $H$, is a likely optical and near-IR counterpart of
the Spitzer variable. Height of each frame is $3\farcs 3$.

###  7.8 Periodic Variables: Discussion

The analysis of the Spitzer data for the periodic variables suggests that the
majority (at least nine) of them are highly evolved AGB stars, similar to
those discussed by K19 and to the OH/IR AGB variables in the Galaxy and LMC.
Where we have detections they support this conclusion. These stars are
important in several respects. Their progenitors must have had intermediate
masses (approximately 5 to $10\,M_{\odot}$), and they represent a brief and
poorly understood phase of late stellar evolution dominated by convection and
mass loss. They are among the most significant dust producers in their
respective galaxies, returning significant quantities of processed material to
the interstellar medium. Intermediate-mass AGB variables, such as these, will
be among the most distant individual stars observable with the James Webb
Space Telescope (JWST), and are likely to be important probes of their
respective populations.

It is not surprising that the four variables that we detected at wavelengths,
and identified as possible AGB stars, are among the bluest objects, lying in
the range $0.17<[3.6]-[4.5]<0.76$ in Table 4. 15qo is the bluest
($[3.6]-[4.5]=0.58$) variable that was not detected by ; however, its host
galaxy is 0.4 mag more distant than that of 14bbc, the reddest object that was
detected. Thus the detections, or lack thereof, are consistent with our
conclusion that these sources are AGB variables.

The fifth variable that was also also detected by , but does not appear to be
an AGB star, is 15mr. As discussed above, it is more luminous than the AGB
variables, and is possibly a red supergiant. However, as discussed by K19 for
variables in this part of the period-luminosity relation, it could
alternatively be a dust-producing binary system.

One source that lies in a position in the period-luminosity consistent with
the AGB variables, but may be something else, is 15mt. Its blue Spitzer colors
and very large variation amplitudes are not typical, and alternative
explanations should be considered. While we might speculate that its
periodicity could be due to orbital motion in a binary, we would expect an IR-
luminous binary to be dusty and thus have red colors. We observed only a
single cycle of variation, so it remains possible that 15mt is actually a
transient. Unfortunately we have insufficient information to be confident one
way or the other.

14al is a better candidate for an AGB variable, but its period, estimated to
be longer than 2160 days, is poorly defined because of insufficient time
coverage. There are only a few pulsating stars known with primary periods
above 2000 days. If confirmed as a pulsating AGB star, 14al is potentially
very interesting. It may be a candidate super-AGB star, i.e., a star with a
progenitor mass of about $10\,M_{\odot}$ that could become an electron-capture
SN (Siess, 2007; Doherty et al., 2015, 2017). It is well worth a more detailed
study with JWST.

##  8 Luminous Irregular Infrared Variables

Several classes of stars may produce irregular, or non-periodic, variability
in the IR. These include LBVs, which may undergo repeated outbursts or
eruptive mass-loss events capable of forming copious dust, though the
mechanism driving such outbursts is not well understood. In Jencson et al.
(2019b), we presented discoveries of two such sources, SPIRITS 17pc and
SPIRITS 17qm, which underwent multiple, extremely red outbursts over the
course of several years, and for which we identified luminous counterparts in
archival HST imaging, likely to be LBVs. Dust-forming, colliding-wind WC
binaries, like the SPIRITS sources presented in Lau et al. (2021), are in fact
periodic, but may be classified as irregular variables under our definition
presented in §2 if their orbital periods are longer than the available Spitzer
coverage. In this section, we discuss the six SPIRITS variables that we
classify as irregular, and for which we have imaging. Their Spitzer light
curves are shown in Figure 13. Table 5 gives details of the Spitzer
photometry.

Table 5: Properties of Irregular Variables SPIRITS |  $t_{\mathrm{peak}}$aaTime of the observed light curve peak (Vega magnitudes) at either [3.6] or [4.5]. |  $[3.6]$bbMeasured at time $t_{\mathrm{peak}}$. | $\Delta[3.6]$ |  $[4.5]$bbMeasured at time $t_{\mathrm{peak}}$. | $\Delta[4.5]$ |  $[3.6]-[4.5]$bbMeasured at time $t_{\mathrm{peak}}$. |  $M_{[3.6]}$bbMeasured at time $t_{\mathrm{peak}}$. |  $M_{[4.5]}$bbMeasured at time $t_{\mathrm{peak}}$.
---|---|---|---|---|---|---|---|---
Designation | [MJD] | [mag] | [mag] | [mag] | [mag] | [mag] | [mag] | [mag]
14qb | 58619.73 | $15.91\pm 0.07$ | 1.4 | $14.80\pm 0.02$ | 1.0 | $1.11\pm 0.07$ | $-13.4$ | $-14.5$
14th | 56715.49 | $17.11\pm 0.07$ | 1.2 | $15.51\pm 0.05$ | 1.0 | $1.60\pm 0.09$ | $-10.7$ | $-12.3$
14akj | 54695.30 | $14.96\pm 0.03$ | 0.7 | $13.82\pm 0.01$ | 0.5 | $1.14\pm 0.03$ | $-13.4$ | $-14.5$
14atl | 58277.58 | $15.84\pm 0.02$ | 1.3 | $15.69\pm 0.07$ | 1.0 | $0.15\pm 0.07$ | $-12.5$ | $-12.7$
15ahp | 57388.85 | $15.47\pm 0.01$ | 0.4 | $15.56\pm 0.03$ | 0.2 | $-0.09\pm 0.03$ | $-12.0$ | $-12.0$
16aj | 57425.97 | $16.84\pm 0.34$ | 0.8 | $15.94\pm 0.27$ | 1.3 | $0.90\pm 0.43$ | $-13.0$ | $-13.9$

Figure 13:  Spitzer IRAC light curves of six irregular variables. Plotting
symbols as in Figure 1.

###  8.1 14qb

IR variability of SPIRITS 14qb in the actively star-forming galaxy NGC 4631
($d\simeq 7.3$ Mpc) was discovered at our first two epochs of SPIRITS
observations. Comparison of IRAC frames obtained in 2014 March and April, with
archival images from 2004, showed that 14qb had risen $\sim$1.1 and 0.8 mag at
3.6 and 4.5 µm, respectively, as shown in the Spitzer light curve in the top
left panel of Figure 13. The source was luminous ($M_{[4.5]}\simeq-14.5$ in
2014 March) and extremely red ($[3.6]-[4.5]\simeq 1.1$). At our observation a
year later, in 2015 March, 14qb had faded about 0.2 mag at both wavelengths,
and was still fainter 5 months later. At that point, we considered it to be a
“slow” SPRITE transient, and triggered our observations; these were obtained
in 2015 November. Since then, however, 14qb did not continue to fade like a
transient; instead, it slowly brightened, up to our most recent, and final,
Spitzer observations in 2019 October. Thus it cannot be considered to be a
SPRITE, nor is it periodic, and we classify 14qb as irregular.

In addition to our triggered WFC3 observations in 2015, there are archival
frames obtained with ACS in 2004 (GO-9765, PI R. de Jong). We astrometrically
registered the ACS $I$-band frame with a Spitzer 4.5 µm difference image
showing 14qb at maximum brightness. 14qb is located in an extremely crowded
star-forming region southwest of the nucleus of NGC 4631, with numerous young
stars and dust lanes. Figure 14 shows a color rendition of the location,
created in the HLA from ACS frames in $V$ and $I$. The vicinity of 14qb
exhibits fairly high and spatially variable extinction, and the object lies
near the northern edge of a rich young association.

There are a few faint stars within a 3$\sigma$ astrometric error circle in the
$I$ frame, none of which varied significantly from 2004 to 2015. None of these
stars are conspicuous in the 2015 $J$ and $H$ frames. We conclude that there
is no credible counterpart at $I$, $J$, and $H$ to this bright and very cool
IR variable. Based on the limited information available for this source, we
cannot conclusively determine its nature. Its high IR luminosity could be
consistent with dust formation by an LBV, for example, but the star must be
heavily enshrouded to explain the lack of a detectable optical or near-IR
counterpart.

Figure 14:  Color rendition of the site of the irregular variable SPIRITS 14qb
in the star-forming galaxy NGC 4631, from $V$ and $I$ frames in the Hubble
Legacy Archive. Frame is $18^{\prime\prime}$ high ($\sim$640 pc at the
distance of NGC 4631). The site of 14qb is marked with a red cross. It lies in
a region of intense star formation, with dust lanes and young associations in
the vicinity.

###  8.2 14akj and 14atl

As noted in the last column of Table 1, SPIRITS 14akj and 14atl are two IR
variables that serendipitously lie near the primary target 15nz (a periodic
variable discussed above in §7.1). These two objects belong to the actively
star-forming spiral galaxy M83 ($d\simeq 4.7$ Mpc). Their Spitzer light curves
are shown in the top-middle and top-right panels of Figure 13.

We classify both variables as irregular. 14akj slowly and irregularly declined
in brightness over the duration of the Spitzer imaging. However, we cannot
completely rule out that it might be a periodic variable with a very long
period, of order 8 years. It is extremely red, with a color of
$[3.6]-[4.5]\simeq 1.1$; it is also luminous, having fallen from
$M_{[4.5]}\simeq-14.5$ to $-14.0$ from 2008 to 2019. 14atl differs from 14akj
in several respects. It slowly rose from 2010 to mid-2018 by about one
magnitude, but with two dips in brightness. Our final observations showed that
another dip was underway. 14atl is relatively quite “blue,” with
$[3.6]-[4.5]\simeq 0.15$, and it is less luminous than 14akj, with an absolute
magnitude averaging about $M_{[4.5]}\simeq-12.5$ over the final few years of
our monitoring.

We astrometrically registered a Spitzer IRAC channel 2 image showing both
14akj and 14atl with an /WFC3 $I$-band image obtained in 2009 (GO-11360, PI R.
O’Connell), in order to determine their locations in the frame. The site of
14akj lies in a very active star-forming region. Inside a 3$\sigma$ error
circle there are three fairly bright stars, and several fainter ones, forming
a small cluster, as shown in the top two panels of Figure 15. The top left
panel shows a false-color rendition of the $I$-band image with a 3$\sigma$
error circle marking the position of 14akj. None of the three bright stars
varied significantly between the two available $I$-band frames (the other
being a 2016 image from program GO-14059, PI R. Soria). None of these stars
are prominent in the one available $J$ frame nor the two archival $H$ frames.
The top right panel is a color rendition of the field, obtained from the HLA
and created from WFC3 frames obtained in 2016 in $u$, $B$, and $I$. The image
shows several rich young stellar associations in the vicinity of 14akj. All of
the stars inside the error circle are seen to be quite blue. It could be that
the counterpart to 14qkj was not detected in the optical or near-IR images, in
which case it is likely to be a heavily enshrouded, and fairly massive young
object. Alternatively, this source could be consistent with a WC colliding-
wind binary system, where one of the bright blue stars detected with HST is,
in fact, the counterpart. Optical spectroscopy to search for WC features, as
presented for other SPIRITS sources in Lau et al. (2021), could test this
scenario.

.

Figure 15:  images of the sites of the irregular variables SPIRITS 14akj (top)
and 14atl (bottom) in star-forming regions of M83. The left-hand frames depict
the $I$-band frames of the sites, with green circles marking the 3$\sigma$
astrometric locations of the irregular IR variables. The right-hand pictures
are color renditions of the sites, from the Hubble Legacy Archive. At the
location of 14akj there are no convincing optical counterparts; all of the
candidate stars are blue and not conspicuously variable. However, 14atl has a
bright, optically variable, and extremely red and luminous counterpart. Height
of frames is $12^{\prime\prime}$ ($\sim$275 pc at the distance of M83).

The site of 14atl was also astrometrically localized in the same $I$ frame as
described above. The bottom two pictures in Figure 15 depict the $I$ frame and
the 3$\sigma$ location (left panel), and the HLA color rendition (right
panel). Inside the error circle is an optically bright star, and the color
rendition shows that this object is extremely red. This star is very bright in
a single available $J$ frame and two $H$ frames. Between 2009 and 2016 the
star brightened in $I$ by about 0.5 mag, and in $H$ by 0.6 mag. These are in
accordance with a similar brightening seen in the Spitzer data. There is thus
little doubt that this star is the optical and near-IR counterpart of 14atl.

Because the HSC magnitudes are averaged over widely separated epochs, we
performed aperture photometry on the available individual WFC3 frames. We used
the zero-points and corrections to infinite aperture from the site referenced
in footnote 10. Table 6 gives our results. The uncertainties in the
magnitudes, including systematics from the camera calibrations, are generally
about $\pm$0.02–0.03 mag.

Table 6:  WFC3 Photometry (AB Magnitudes) of Irregular Variable SPIRITS 14atl in M83  Filter | 2009 Aug 26aaGO-11360, PI R. O’Connell. | 2016 Jan 18-19bbGO-14463, PI B. McCollum. | 2016 Jan 21ccGO-14059, PI R Soria.
---|---|---|---
F555W | 23.70 | $\dots$ | 23.45
F606W | $\dots$ | 22.46 | $\dots$
F625W | $\dots$ | 22.13 | $\dots$
F814W | 20.70 | 20.20 | 20.17
F110W | 19.42 | $\dots$ | $\dots$
F125W | $\dots$ | 18.61 | $\dots$
F140W | $\dots$ | 18.48 | $\dots$
F160W | 19.01 | 18.41 | $\dots$

We show the 2009 and 2016 SEDs of 14atl in Figure 16, constructed from our HST
aperture photometry of the optical/near-IR counterpart and linear
interpolations of the [3.6] and [4.5] magnitudes to the corresponding epochs.
The SEDs at both epochs are similar, peaking between $\approx$1–2$\,\mu$m at
band luminosities of $\lambda L_{\lambda}\simeq 10^{5}~{}L_{\odot}$. In
comparison with PHOENIX model photospheres (non-rotating, solar metallicity;
Kučinskas et al., 2005, 2006), the SEDs appear consistent with a luminous red
supergiant with an effective temperature of $T_{\mathrm{eff}}\approx 3500$ K
and bolometric luminosities of $\log\,L_{\mathrm{bol}}/L_{\odot}\simeq
5.24$–$5.47$. We note an excess of mid-IR flux at [3.6] and [4.5] compared to
the stellar models. Interestingly, the mid-IR color is redder when the star is
fainter. Together, these facts likely point to emission from warm dust that
condenses in a stellar wind. The observed variability is likely associated
with semiregular variations arising from pulsational instabilities, which are
common in cool supergiants (e.g., Yoon & Cantiello, 2010; Yang & Jiang, 2011).

Figure 16:  Left: SED of the irregular variable SPIRITS 14atl in M83,
constructed from /WFC3 photometry (Table 6) of the optical and near-IR
counterpart obtained in 2009 August (orange circles) and 2016 January (red
circles). The Spitzer [3.6] and [4.5] measurements are interpolated to the
same two epochs. PHOENIX model stellar photospheres (nonrotating, solar-
metallicity) with $T_{\mathrm{eff}}=3500$ K, scaled to luminosities of
$\log(L/L_{\odot})=5.24$ and $5.47$) provide reasonable approximations to both
data epochs. They are superposed in the corresponding colors. Right: SED of
the irregular variable SPIRITS 15ahp in NGC 2403, constructed from HSC
magnitudes from 2005 March (orange circles) and 2016 March (red circles),
along with [3.6] and [4.5] estimates from interpolations of the Spitzer light
curves to the corresponding dates. A PHOENIX model photosphere with
$T_{\mathrm{eff}}=3300$ K, scaled to a luminosity of $\log(L/L_{\odot})=5.11$,
is superposed, again providing a reasonable approximation to the data.

###  8.3 15ahp

The IR variable SPIRITS 15ahp is another serendipitous target, lying by chance
in the field of our observations of the periodic variables 15ahg, 14al, and
14dd, which were discussed above (§7.3). This field is in the M81 Group galaxy
NGC 2403, and the site of 15ahp lies in a star-forming spiral arm of the host
galaxy. The IR light curves of 15ahp are shown in the bottom-left panel of
Figure 13. This object varies in IR brightness by about 0.2 mag peak-to-peak,
on a fairly short timescale of a few months. We classify it as an irregular
variable. Its IR color also appears to vary.

The astrometric registration of Spitzer frames with images of this site was
described in §7.3. The top two panels in Figure 17 show the 3$\sigma$
astrometric error circles for the location of 15ahp in two of the three
available $I$-band images, an archival one from 2005 (GO-10402, PI R. Chandar)
and the other our frame obtained as a result of our triggered 2016 March 7
observation. A third $I$-band image from 2019 is available (GO-15645, PI D.
Sand) but not illustrated. Inside the error circle is a prominent star, which
rose in $I$-band brightness by about 0.25 mag between 2005 and 2016. This is
qualitatively consistent with the brightening at [3.6] and [4.5] over the same
interval, as seen in Figure 13. 15ahp then faded by 0.17 mag at the 2019
observation. The star is very bright at $J$ and $H$, as shown in the bottom
two panels in Figure 17. There is thus little doubt that this object is the
optical/near-IR counterpart of SPIRITS 15ahp. The HSC gives magnitudes (AB
scale) of this star from the 2005 ACS frames of $\rm F658N=21.74$ and
$I=20.25$, and from the 2016 WFC3 frames of $I=20.07$, $J=18.63$, and
$H=18.17$.

The multi-epoch SED, constructed in a similar manner to that of 14atl, is
shown in the right panel of Figure 16. As with 14atl, the star appears
consistent with a red supergiant, though perhaps a bit cooler and less
luminous ($T_{\mathrm{eff}}\approx 3300$ K;
$\log\,L_{\mathrm{bol}}/L_{\odot}\approx 5.1$), based on our comparisons with
PHOENIX models. We again note a mid-IR excess compared to the photospheric
models and that the mid-IR color is slightly redder when the star is fainter,
likely indicating the presence of circumstellar dust.

Figure 17:  False-color renditions of images of the site of the irregular
variable SPIRITS 15ahp in the nearby galaxy NGC 2403. Top row: $I$-band frames
taken in 2005 (left) and 2016 (right). Green circles mark 3$\sigma$ error
positions of the Spitzer variable. A conspicuous optical counterpart of 15ahp
lies within the error circle, and brightened by $\sim$0.25 mag from 2005 to
2016. Bottom row: images of the site in 2016, taken in $J$ (left) and $H$
(right). The counterpart is very bright at $J$ and $H$. Height of each frame
is $4\farcs 8$.

###  8.4 14th

SPIRITS 14th is yet another serendipitous target, which happens to lie in the
field of 15wt and 14bbc in the nearby galaxy NGC 7793, which we imaged with as
described above (§7.5) on 2016 April 18. The bottom-middle panel in Figure 13
shows the Spitzer light curves, which we classify as that of an irregular
variable. 14th brightened by about 1 mag from late 2011 to a peak in early
2014, and then declined by nearly the same amount over the next two years.
Since then it has remained nearly constant at [4.5] but somewhat “noisy” at
[3.6], with our most recent and final observation showing it quite faint at
[3.6]. This variable is extremely red, with a typical color of
$[3.6]-[4.5]\simeq 1.5$. It is not extremely luminous; the absolute magnitude
at our final observation was about $M_{[4.5]}\simeq-11.5$.

We registered a Spitzer frame showing 14th near maximum brightness with
$I$-band images, as discussed for 15wt and 14bbc in §7.5. The site is in a
very rich star field. There are a few resolved stars within a 3$\sigma$
registration error circle, on top of an unresolved or partially resolved
background. Comparing $I$ frames obtained in 2003, 2014, 2016 (our triggered
observation), and 2017 shows no significant variations of any of these stars.
Moreover, none of them are conspicuous at $J$ and $H$, nor varied between $JH$
images obtained in 2016 and 2018. We conclude that 14th is undetected in the
optical and near-IR images, which is consistent with its extremely red IR
color. Again, without an obvious counterpart detection in the optical or near-
IR, it is difficult to draw strong conclusions about the nature of the source,
other than that it is likely a young, fairly massive, and heavily enshrouded
object.

###  8.5 16aj

SPIRITS 16aj was announced as a possible transient by Jencson et al. (2016b).
It lies in the actively star-forming barred spiral NGC 2903, the most distant
of the galaxies discussed in this paper ($d\simeq 9.2$ Mpc). The Spitzer light
curves of 16aj are shown in the bottom-right panel of Figure 13. This object
rose in brightness by about 1 mag over the first two years of SPIRITS
monitoring (early 2014 to early 2016), leading us to consider it a slow
SPRITE; at that point we triggered imaging of the site, which was obtained on
2016 May 23. However, since early 2016 the object has remained at a nearly
constant magnitude, although with possible short-term variations of a few
tenths of a magnitude. Thus we now classify 16aj as an irregular variable,
rather than a true transient. It is fairly red ($[3.6]-[4.5]\simeq 0.9$) and
of relatively high luminosity ($M_{[4.5]}\simeq-13.9$).

We astrometrically registered Spitzer frames, including a difference image
showing 16aj, with an ACS $I$-band image taken in 2004 (GO-9788, PI L. Ho) and
with our own $I$ frame obtained in 2016. At the site there are a few resolved
faint stars, lying on a sheet of unresolved starlight. We see no $I$-band
variations between 2004 and 2016, and the $J$ and $H$ frames we obtained on
the same date in 2016 reveal no extremely red stars. The site lies on the edge
of a rich young association and H II region, and there are numerous dark dust
lanes in the vicinity. We conclude that 16aj lacks a detectable optical or
near-IR counterpart. Similarly to 14qb, 14th, we conclude only that the star
is likely to be relatively young, massive, and heavily enshrouded.

##  9 Summary

SPIRITS was the first large-scale monitoring survey of nearby galaxies, using
the warm Spitzer telescope to search for luminous variable stars and
transients at IR wavelengths. In the work described here, we employed new and
archival optical and near-IR images to study the sites of 21 SPIRITS
variables. The selected targets were of special interest because they were
undetected or very faint in ground-based optical surveys. Our aims were to
search for progenitors, attempt to detect the sources during outburst using
deep imaging, and characterize their environments.

We classify the SPIRITS variables into three groups based on their photometric
behavior: SPRITEs and transients; periodic variables; and irregular variables.
Our main results from the imaging are as follows.

  1. 1.

“SPRITEs” are a new class of intermediate-luminosity IR transients that lack
counterparts in deep ground-based optical imaging. They are defined as objects
having absolute magnitudes at maximum in the range $-14<M_{[4.5]}<-11$. We
investigated images of three SPRITEs, two of them with fast outburst
timescales of a few days to a few weeks, and one with a slow timescale of
nearly three years. Like most SPRITEs, two of the three occurred in dusty,
star-forming regions, consistent with an origin from massive stars. No
progenitors were found in deep pre-outburst archival images for the two
objects in young regions. We did detect one of them—the slowly evolving
17fe—during outburst at $J$ and $H$. This allowed us to construct an SED,
indicating that 17fe during eruption was a dusty object with a temperature of
about 1050 K. Unusually, the third SPRITE candidate, the very fast 14axa,
occurred in the old bulge of M81 rather than in a star-forming region. It
appears to have been a dusty classical nova. Some, or many, of the fast
SPRITEs at the low end of the luminosity range are likely to be classical
novae, instead of arising from massive stars. Most SPRITEs, however, are
events of an uncertain nature—possibly a mixture of massive stellar mergers,
dust-obscured core-collapse supernovae, and eruptions of massive stars related
to those of luminous blue variables.

  2. 2.

Variable stars are much more conspicuous among the brightest members of
stellar populations in the IR than they are in the optical, particularly in
late-type galaxies. More than half of our SPIRITS targets, although initially
considered to be transients, proved to be periodic variables. Their pulsation
periods are long, ranging from $\sim$670 to over 2100 days. These objects are
likely to be highly evolved, dusty AGB stars, similar to OH/IR objects known
in the Galaxy and Magellanic Clouds. The pulsators found by SPIRITS are
strongly associated with star-forming regions in nearby spirals and irregular
galaxies, and they likely arise from intermediate-mass stars
($\sim$5–$10\,M_{\odot}$). Out of the 12 periodic variables for which we have
images, only five were warm enough to be detected with at $I$, $J$, and/or
$H$, along with one uncertain case.

  3. 3.

Six SPIRITS variables did not fit our definitions for transients or (likely)
periodic variables, and we classify them as irregular. Two of these sources,
14atl and 15ahp, had relatively blue IR colors
($-0.1\lesssim[3.6]-[4.5]\lesssim 0.2$ ) and had bright, red counterparts in
HST imaging. Their optical–near-IR SEDs are consistent with those of luminous,
pulsating red supergiants. The remaining four irregular variables are much
redder at IR wavelengths ($[3.6]-[4.5]\gtrsim 0.9$) and, not surprisingly, we
did not identify convincing optical or near-IR counterparts in deep images.
These objects may be consistent with eruptive, dust-forming mass-loss events,
like those of LBVs, but their massive stellar counterparts are likely heavily
enshrouded. For the case of 14akj, however, we noted a possible association
with several luminous blue stars. 14akj could therefore instead correspond to
a dust-forming colliding-wind Wolf-Rayet (WC type) binary. Optical
spectroscopy to search for prominent WC emission features would test this
possibility.

  4. 4.

None of the SPIRITS transients observed by appear to be flares associated with
YSOs. Although some lie in the dust lanes of the host galaxies, none of the
investigated transients are directly associated with star-forming complexes.
However, future IR observations with facilities such as JWST and the Nancy
Roman Space Telescope may reveal YSO transients in star-forming regions.

The SPIRITS project was the first systematic time-domain reconnaissance of
stellar variability among IR-luminous stars in nearby galaxies. It revealed
several new classes of extremely cool and dusty transients and pulsating or
irregular variables. An understanding of the nature of these diverse objects
will require more intensive time coverage of their variations and outbursts
than was possible with Spitzer. Infrared spectroscopy would be a key new
element in such investigations. Considerable progress will be possible with
the powerful IR capabilities of JWST and the Roman Space Telescope.

Support for HST Program numbers GO-13935, GO-14258, and AR-15005 was provided
by NASA through grants from the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy,
Incorporated, under NASA contract NAS5-26555. Support for this work was also
provided by NASA through awards issued by JPL/Caltech. P.A.W. acknowledges a
research grant from the South African National Research Foundation and is
grateful to John Menzies (SAAO) for the use of his period-finding software.
J.B. is supported by NSF grant AST-1910393. R.D.G. was supported in part by
the United States Air Force. Some of the data presented in this paper were
obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space
Telescope Science Institute. Our work is also based in part on data obtained
from the Hubble Legacy Archive, which is a collaboration between the Space
Telescope Science Institute (STScI/NASA), the Space Telescope European
Coordinating Facility (ST-ECF/ESAC/ESA), and the Canadian Astronomy Data
Centre (CADC/NRC/CSA). This research has made use of the NASA/IPAC Infrared
Science Archive, which is operated by the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National
Aeronautics and Space Administration.

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