# A MIRI Search for Planets and Dust Around WD 2149+021

Sabrina Poulsen Homer L. Dodge Department of Physics and Astronomy, University
of Oklahoma, 440 W. Brooks St, Norman, OK 73019, USA  John Debes AURA for ESA,
Space Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD 21218,
USA  Misty Cracraft Space Telescope Science Institute, 3700 San Martin Dr,
Baltimore, MD 21218, USA  Susan E. Mullally Space Telescope Science Institute,
3700 San Martin Dr, Baltimore, MD 21218, USA  William T. Reach Stratospheric
Observatory for Infrared Astronomy, Universities Space Research Association,
NASA Ames Research Center, Moffett Field, CA 94035  Mukremin Kilic Homer L.
Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W.
Brooks St, Norman, OK 73019, USA  Fergal Mullally Constellation, 1310 Point
Street, Baltimore, MD 21231  Loic Albert Institut Trottier de recherche sur
les exoplanètes and Département de Physique, Université de Montréal, 1375
Avenue Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Katherine Thibault
Institut Trottier de recherche sur les exoplanètes and Département de
Physique, Université de Montréal, 1375 Avenue Thérèse-Lavoie-Roux, Montréal,
QC, H2V 0B3, Canada  J. J. Hermes Department of Astronomy, Boston University,
725 Commonwealth Avenue, Boston, MA 02215, USA  Thomas Barclay NASA Goddard
Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA  Elisa V.
Quintana NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD
20771, USA

###### Abstract

The launch of JWST has ushered in a new era of high precision infrared
astronomy, allowing us to probe nearby white dwarfs for cold dust, exoplanets,
and tidally heated exomoons. While previous searches for these exoplanets have
successfully ruled out companions as small as 7-10 Jupiter masses, no
instrument prior to JWST has been sensitive to the likely more common sub-
Jovian mass planets around white dwarfs. In this paper, we present the first
multi-band photometry (F560W, F770W, F1500W, F2100W) taken of WD 2149+021 with
the Mid-Infrared Instrument (MIRI) on JWST. After a careful search for both
resolved and unresolved planets, we do not identify any compelling candidates
around WD 2149+021. Our analysis indicates that we are sensitive to companions
as small as $\sim$0.34 MJup outwards of 1$\farcs$263 (28.3 au) and $\sim$0.64
MJup at the innermost working angle (0$\farcs$654, 14.7 au) with 5$\sigma$
confidence, placing significant constraints on any undetected companions
around this white dwarf. The results of these observations emphasize the
exciting future of sub-Jovian planet detection limits by JWST, which can begin
to constrain how often these planets survive their host stars evolution.

††facilities: JWST, Spitzer, WISE, GALEX

##  1 Introduction

The majority of observed white dwarfs have hydrogen-dominated atmospheres that
are expected to be nearly pure, as heavier elements gravitationally settle
below the photosphere and out of our view. Despite this, 25-50% of isolated,
hydrogen-dominated white dwarfs are “polluted” with trace elements such as
calcium and iron, forming the DAZ spectral class (Zuckerman et al., 2003;
Koester et al., 2014). Given that these elements sink out of the atmosphere on
timescales ranging from thousands of years to a few days (Koester, 2009),
these metals must have recently been accreted onto the white dwarf. The origin
of these accreted elements has been theorized for decades- Previously this
pollution was attributed to the interstellar medium (Dupuis et al., 1992,
1993; Hansen & Liebert, 2003), yet compelling evidence has accumulated which
instead points to asteroids and other rocky planetesimals for the origin of
these metals (Jura, 2008, 2014). While the mechanics of this are not well
constrained by current observations, one widely accepted hypothesis to explain
this phenomenon is the presence of giant planets in wide-orbits around the
polluted white dwarf (Alcock et al., 1986; Debes & Sigurdsson, 2002; Jura,
2003).

In this scenario, massive planets that survive the red-giant phase
occasionally perturb the orbits of asteroids and other bodies, which are then
dynamically scattered towards the white dwarf. When these objects pass within
the Roche limit of the star, they disintegrate into a cloud of dust and gas
which then accretes onto the white dwarf. This scenario was shown to be viable
by Debes et al. (2012), who used numerical simulations to show that a single
giant planet is capable of perturbing planetesimals into highly eccentric
orbits which can then create a steady stream of material to be accreted onto
the star. This model predicts that many polluted white dwarfs may host a
planetary system containing a Jovian analog, although dynamical simulations
have shown less massive planets are also capable of efficient scattering
(Frewen & Hansen, 2014).

While there are theories of second-generation planets born of mass lost on the
asymptotic giant branch, white dwarfs may come to host planetary systems via
first-generation planets which survive their hosts’ evolution. The orbital
evolution of a planet depends almost entirely on its mass and initial semi-
major axis, as more massive planets in tighter orbits suffer strong tidal
forces which pull the planet towards engulfment faster than the effects of
stellar mass loss release the planet to wider orbits. When investigating red
giants, Wolthoff et al. (2022) finds the global occurrence rate of planetary
systems with at least one giant planet (M $>$ 0.8 MJup) to be 10.7%, with a
maximum occurrence rate reached at a stellar mass of 1.68 $M_{\odot}$. We can
also look to white dwarf progenitors (A and F stars), as we would expect the
occurrence rate of giant planets in wide orbits to be similar. While the exact
occurrence rates are not yet well constrained, recent results from transit and
radial velocity surveys from 10 to 100 au (Fernandes et al., 2019) show that
26% of G and K stars between 0.1 and 100 au have a giant planet larger than
0.1 MJup and 6% have a giant planet larger than Jupiter. Direct imaging
surveys (Nielsen et al., 2019) indicate that giant planets are even more
common around A and F stars than G and K stars. For a 1.5 $M_{\odot}$ star
(the estimated progenitor mass of the star discussed in this paper), Mustill &
Villaver (2012) show that a 1 MJup planet contacts the stellar envelope during
the AGB phase for initial circular orbits within $\sim$3.2 au. While this
radius increases for larger planets, a sufficiently massive planet may survive
the common envelope phase and be found interior to this limit (Bear & Soker,
2012).

The search for giant planets around white dwarfs has been challenging due to
limitations in the methods commonly used to detect exoplanets. Transit
surveys, such as TESS, are designed to detect short-period objects (Ricker et
al., 2015) and are not well-suited for detecting wide-orbit planets that are
of interest in this context. Vanderburg et al. (2020) did succeed in using
TESS to find a $\sim$13 MJup companion orbiting its white dwarf, however its
orbital period is unusually short at 1.4 days and raises questions as to how
this planet migrated or survived so close to its host. Radial velocity
methods, which rely on detecting shifts in spectral lines, are also not ideal
for white dwarfs due to their lack of prominent spectral lines for high-
precision analysis. Astrometry measures the tiny movements of stars caused by
the gravitational pull of orbiting planets, however Gaia is limited to closer
orbits and may not be sensitive enough to detect a significant number of wide-
orbit planets around white dwarfs (Sanderson et al., 2022). Additionally,
direct detection of planets from the ground is challenging due to absorption
of infrared light in the Earth’s atmosphere, making it difficult to directly
observe cool companions.

Investigators have historically turned to space-based searches to attempt to
take advantage of the low star-planet contrast. Debes et al. (2005) used HST
to search for companions orbiting seven of the nearest DAZs and ruled-out
companions down to 10-18 MJup in orbital separations greater than 30 au.
Mullally et al. (2007) surveyed 124 white dwarfs to look for infrared excess
and placed limits on companions larger than 10 MJup less than 30 au from the
star (see also Kilic et al., 2009). Brandner et al. (2021) searched seven
white dwarfs in the Hyades cluster with NICMOS and found no companions larger
than 7 MJup beyond 10 au. There have also been successful hunts for these
elusive planets- Luhman et al. (2012), using Spitzer IRAC, found a cool, low-
mass, brown dwarf with common proper motion to a white dwarf, while Blackman
et al. (2021) was able to use micro-lensing to find a giant planet around a
white dwarf.

While these massive planets have been proven difficult to find in the past,
JWST gives us the opportunity to look for sub-Jovian-mass companions around
white dwarfs for the first time. JWST’s aperture size, coupled with its mid-
infrared capabilities, provides the necessary tool to look for planets with
masses $<$7 MJup, which are predicted to be more common and could determine
whether the polluted atmospheres are truly linked to planetary systems. The
cycle 1 JWST program “A Search for the Giant Planets that Drive White Dwarf
Accretion” (GO 1911: PI, S. Mullally) observed four nearby, young, polluted
white dwarfs in uncrowded fields.

The first target observed in this program was WD 2149+021, which was first
noted in 1961 as a ‘white dwarf suspect’ in a paper on Lowell proper motions
(Giclas et al., 1961) where they were cataloging stars with a proper motion of
more than 0.27 arcsec/year. WD 2149+021 was listed in that paper as G93-48. In
1965, in a paper characterizing 166 white dwarfs, it was listed as a DA white
dwarf (Eggen & Greenstein, 1965). In 1983, it was listed among the UBVRI
Photometric standard stars around the celestial equator by Arlo Landolt
(Landolt, 1983) and as one of the Hubble UV spectrophotometric, optical
spectrophotometric and optical polarimetric standard calibration objects in
1990 (Turnshek et al., 1990) and listed as a DA3 spectral type star. Later
Koester et al. (2005) discovered a narrow Ca K line from UVES echelle
spectroscopy taken in 2002 and 2003 in the photosphere and found an abundance
of [Ca/H]=$-$7.7, confirming it as an actively accreting DAZ. Further
monitoring of the white dwarf has taken place, as recently as 2016 with
Keck/HIRES (NASA/Keck Program N171b; PI: Redfield), where archival visible
echelle spectra still show the presence of the Ca K line. This implies at
least 14 years of accretion. WD 2149+021 was observed by both the Hipparcos
and Gaia missions, which means that any residual acceleration detected in its
astrometry could reveal the presence of a substellar companion (Kervella et
al., 2019; Brandt, 2021; Kervella et al., 2022). Kervella et al. (2022) found
no significant acceleration, limiting planets with masses $<$0.7 MJup between
3-10 au.

This paper presents the limits on planet and dust detection from our
observation of WD 2149+021. We describe the methods used to obtain our
observations, followed by the modeling of the white dwarf’s photometry based
on previous observations. We then discuss our limits to detecting resolved
planets, an analysis of background objects in the MIRI field of view, the
limits to detecting unresolved planets, cold dust, and finally tidally heated
exomoons. We conclude by discussing our primary findings, as well as
discussing some considerations to keep in mind.

##  2 Description of Observations

WD 2149+021 was observed by MIRI in four broadband filters centered on 5.6,
7.7, 15.0, and 21.0 µm. This multi-filter approach allows us to employ two
different methods for planet detection: searching for resolved planets using
direct imaging, and unresolved planets using infrared excess. At 15 µm, most
Jovian analog planets will have contrasts of $\sim$100:1, which MIRI is able
to spatially resolve beyond $\sim$15 au (1.5$\times$ the FWHM of the 15 µm
filter). To directly image exoplanets we focus on the 15 µm filter, as these
observations have the longest exposure time and provide the deepest mass
limits. However, we also rely on the other filters to look for evidence that a
source is a background star or galaxy. Planets should be dimmer and redder
than stars, and should be shaped like a point source while typical galaxies
are extended.

To detect unresolved planets, we now focus on the 21 µm filter as the white
dwarf flux is lower than in the 15 µm filter. We compared the photometry of
the white dwarf against predicted spectral energy distributions (SEDs) of the
photosphere, allowing us to search for infrared excesses in the longer
wavelength bands. By modeling planet flux and adding that to the predicted
flux of WD 2149+021 with no companion, we find that planets close to $\sim$5
MJup would show a strong excess in the 21 µm filter, while planets close to
$\sim$3 MJup would still exceed a 3$\sigma$ significant excess (Figure 1).
These limits will continue to improve as MIRIs absolute flux calibration
improves.

Figure 1: The expected flux for WD 2149+021 with varying mass companions,
normalized to the expected flux of WD 2149+021 with no companions, for each of
the four MIRI filters used. From left to right, these filters are F560W
(purple), F770W (blue), F1500W (green), and F2100W (yellow). With current
absolute flux calibration reported to be 3$\%$ or better in all filters, the
dotted and dashed horizontal lines denote a 3$\sigma$ and 5$\sigma$
confidence, respectively. Companions above 2MJup were modeled using cloudless
Sonora-Bobcat grid models (Marley et al., 2021), and companions below
2MJupwere modeled using cloudless Bex models (Linder et al., 2019).

JWST targeted WD 2149+021 with the mid-infrared instrument (MIRI) in imaging
mode with four different broadband filters: F560W, F770W, F1500W, F2100W (Tab.
1). The object was targeted by JWST on 2022 October 13 and the data are
located on MAST: https://doi.org/10.17909/kj1r-9e95 (catalog
https://doi.org/10.17909/kj1r-9e95). Each image, grouped by filter, was
composed of many exposures dithered using the Cycling dither pattern with the
FASTR1 readout pattern. The exposure times and observing parameters are shown
in Table 1. Build 9.3 of the JWST Calibration pipeline was used to process the
data starting from the uncal files. Each image was processed through stage one
and two of the imaging pipeline using mostly default parameters as defined in
the parameter reference files, only setting the jump detection threshold to
5$\sigma$. After the stage two pipeline was run, a mean background image was
created for each filter and subtracted from each cal file. Lastly, the level
three imaging pipeline was run on the background subtracted files and combined
with the resample kernel set to ‘gaussian’, the weight type set to ‘exptime’,
and doubling the outlier detection scale parameter to ‘1.0 0.8’, but using the
parameter reference files in CRDS for all other parameter settings. These
background subtracted cal and i2d files were used for all subsequent analyses.

Table 1: Observing parameters of WD 2149+021. NGroups is the number of groups up the ramp per integration, and NInts is the number of integrations taken for each exposure. Filter | $\lambda_{0}$ | NGroups | NInts | Dithers | Exp time
---|---|---|---|---|---
| ($\mu$m) |  |  |  | (s)
F560W | 5.635 | 27 | 2 | 4 | 610
F770W | 7.639 | 10 | 2 | 4 | 233
F1500W | 15.064 | 90 | 5 | 12 | 15118
F2100W | 20.795 | 33 | 8 | 8 | 6016

Figure 2 shows a color image of WD 2149+021, created by stacking the F770W
(blue), F1500W (green), and F2100W (red) exposures. The white dwarf is in the
center of the image, surrounded by background sources that are both unresolved
and extended. A faint false positive, the closest source to WD 2149+021, is
excluded as it is not consistent with a planetary SED and the FWHM along the
sources major axis is twice the PSF FWHM for the F1500W filter (and is hence
resolved). We assume point sources will have a FWHM $\pm$20% from the nominal
PSF.

Figure 2: Color image of WD 2149+021 created by combining the F770W, F1500W,
and F2100W filters. Visible directly above the white dwarf is a false positive
candidate, eliminated due to its extended shape and incorrect color.

##  3 White Dwarf Modeling and Photometry

In order to determine if WD 2149+021 is orbited by unresolved planets or dust,
we must first accurately model the white dwarf spectral energy distribution
based on available photometry. We then remove the white dwarf flux at the
infrared wavelengths to see if there is any contribution from a much cooler
counterpart. We first gather and fit against observed UV/Vis/NIR/Mid-IR
photometry. For UV/Vis we convolve the HST CALSPEC spectrum of WD 2149+021
that should have $\sim$1% absolute flux accuracy (Bohlin et al., 2001) with
the GALEX FUV/NUV and Sloan $griz$ filter profiles via the Spanish Virtual
Observatory SPECPHOT tool111http://svo2.cab.inta-csic.es/theory/specphot/. For
the NIR we use the 2MASS Point Source Catalog, and for the mid-IR we use a
combination of ALLWISE W1, W2, and Spitzer SEIP flux values for IRAC2 and
IRAC4 (Wright et al., 2010; Mainzer et al., 2014; SSC/IRSA, 2013). Table 2
gives the measured photometry for WD 2149+021. We then utilize the
grid222https://www.astro.umontreal.ca/b̃ergeron/CoolingModels/ of publicly
available cooling models for hydrogen dominated atmosphere white dwarfs
(Bergeron et al., 1995; Holberg & Bergeron, 2006; Kowalski & Saumon, 2006;
Tremblay et al., 2011; Bédard et al., 2020) to minimize a chi-square metric
assuming the Gaia DR3 distance (Gaia Collaboration et al., 2016, 2023a,
$d$=22.4 pc) and estimate the 95% confidence interval for $T_{\mathrm{eff}}$
and log g. We find, from the photometric fitting,
$T_{\mathrm{eff}}$=17840$\pm$100 K and log g=8.01$\pm$0.01.

Table 2: Photometry of WD 2149+021 Filter | Central Wavelength | Fν | $\sigma_{\nu}$
---|---|---|---
|  $\mu$m | (mJy) | (mJy)
GALEX FUV | 0.1530 | 39.0 | 0.4 |
GALEX NUV | 0.2353 | 50.0 | 0.5 |
Johnson B | 0.4384 | 33.0 | 1.2 |
Johnson V | 0.5480 | 28.2 | 1.7 |
Sloan g | 0.4747 | 32.3 | 0.3 |
Sloan r | 0.6188 | 23.8 | 0.2 |
Sloan i | 0.7544 | 18.2 | 0.2 |
Sloan z | 0.8791 | 13.8 | 0.1 |
2MASS J | 1.2391 | 8.4 | 0.2 |
2MASS H | 1.6487 | 5.0 | 0.2 |
2MASS K | 2.1634 | 2.9 | 0.1 |
WISE 1 | 3.4655 | 1.37 | 0.03 |
WISE 2 | 4.6443 | 0.76 | 0.02 |
IRAC 2 | 4.5024 | 0.79 | 0.02 |
IRAC 4 | 7.8556 | 0.27 | 0.01 |
F560W | 5.6173 | 0.49 | 0.02 |
F770W | 7.6523 | 0.26 | 0.01 |
F1500W | 15.1003 | 0.071 | 0.002 |
F2100W | 20.8471 | 0.042 | 0.001 |
Figure 3: Probabilty distributions for the age, initial mass, and final mass
of WD 2149+021 derived using wdwarfdate (Kiman et al., 2022). The values
$T_{\mathrm{eff}}$=17753$\pm$72 K and log g=8.01$\pm$0.01 were used for input
values. The DA cooling model (Bédard et al., 2020), MIST based IFMR (Cummings
et al., 2018), and [Fe/H]=0.0, v/vcrit=0.0 (Choi et al., 2016; Dotter, 2016)
were chosen for the model WD, model IFMR, and isochrone of the progenitor star
respectively.

This is similar to inferred values from McCleery et al. (2020), who find
$T_{\mathrm{eff}}$=17876$\pm$188 K and log g=8.01$\pm$0.01 and Kilic et al.
(2020) who find $T_{\mathrm{eff}}$=17753$\pm$72 K and log g=8.06$\pm$0.004.
All three of these results have consistent resulting temperatures and we agree
with the surface gravity determined by McCleery et al. (2020). All three
methods are similar: using a Gaia-derived parallax and photometry. While we
use a larger number of filters, Kilic et al. (2020) used Pan-STARRs photometry
and McCleery et al. (2020) used Gaia DR2 photometry. The reported Pan-STARRS
photometry appears to be fainter than would be expected from our Calspec
spectrum, implying the possibility of slight saturation being present in the
Pan-STARRS images, making this photometry unreliable for fitting purposes.
Thus, we will assume a log g=8.01 for calculations of the total age of the
system. The mass and cooling age are then inferred from the cooling models and
the WD mass-radius relationship using $T_{\mathrm{eff}}$=17753$\pm$72 K and
log g=8.01$\pm$0.01 (Fig 3). This implies a mass of 0.62 $M_{\odot}$ and a
white dwarf cooling age of 114 Myr.

To measure the photometry of WD 2149+021 in the four MIRI filters, we
conducted aperture photometry using the recommended CRDS aperture radii and
background apertures for each filter in the MIRI aperture correction file
(jdo, 2016). We chose photometric apertures that correspond to 80% of the
total flux of the target. We utilized the recommended color corrections for a
Rayleigh-Jeans flux distribution, which correspond to 1.011, 1.021, 1.013, and
1.017 for F560W, F770W, F1500W, and F2100W respectively. Additionally, F1500W
and F2100W have recently been reported to have experienced drops in
sensitivity between commissioning and July 2023 of 3% and 12%,
respectively333https://www.stsci.edu/contents/news/jwst/2023/miri-imager-
reduced-count-rate.html, with updates to the relevant calibration files now
available. We have included the updated calibrations, as well as improvements
to the absolute flux calibration for F560W and F770W, with expected
uncertainties of 3%. A comparison between the MIRI photometry of WD 2149+021
and the expected photospheric photometry is given in Figure 4.

Figure 4: (above) The measured spectral energy distribution of WD 2149+021
(black squares) compared to a DA cooling model with $T_{\mathrm{eff}}$=17480 K
and $\log{g}$=8.01 (red squares). Overplotted is the CALSPEC spectrum for WD
2149+021 (black line). The observed JWST MIRI photometry is shown with the
blue squares and matches the expected photospheric flux to within the three
times the absolute flux calibration uncertainties (dashed lines) of $\sim$3%.

To predict the expected flux of the white dwarf for each filter, we
interpolated the existing models to the reference wavelengths of the four MIRI
filters. The resulting MIRI photometry is listed in Table 2. We found that the
MIRI photometry is consistent with the predicted white dwarf fluxes, and thus
there is no evidence for a significant IR excess around WD 2149+021.

##  4 Results

In the following section, we demonstrate that our observations are sensitive
to a variety of measurable signatures of planetary systems due to MIRI’s
sensitivity, stable PSF and the absolute flux calibration. Cool giant planets
can be detected either through infrared excess (e.g., Ignace, 2001) or by
direct detection via high contrast imaging (e.g., Burleigh et al., 2002; Debes
et al., 2005). Additionally, warm dust within the tidal disruption radius of
the WD can be detected as an infrared excess (Jura, 2003). Other more exotic
signatures include infrared excess due to highly irradiated sub-Jovian planets
(Sandhaus et al., 2016) or the direct imaging of tidally heated exo-moons
(Peters-Limbach & Turner, 2013).

###  4.1 Limits to direct detection

In order to determine our sensitivity to resolved companions, the contrast
between a circular aperture located at the center of the white dwarf (the
central aperture) can be compared against multiple equally sized apertures
located at a fixed distance away from the central aperture. The optimal
aperture radius to maximize the SNR was determined to be 67% (Naylor, 1998;
Masci, 2008) of the FWHM of MIRI’s PSF444https://jwst-docs.stsci.edu/jwst-mid-
infrared-instrument/miri-observing-modes/miri-imaging for each filter.

To obtain a meaningful contrast close to the WD and out to $\sim$10″, we
constructed reference PSFs and subtracted them from the white dwarf in order
to gain contrast interior to $\sim$1″ in each filter. The MIRI PSF wings for
the white dwarf at wavelengths shorter than 15 µm are detected beyond the
first Airy ring, which is field dependent and for the F560W filter also
includes the cruciform feature (Wright et al., 2023).

For the F560W and F770W filters, we utilized the PSFs of two of our other
targets: WD 2105-820 and WD 1620-391. We combined the two PSFs for each filter
together and calculated offsets and scalings relative to WD 2149+021 based on
the measured stellar centroids and aperture photometry. However, the F1500W
and F2100W exposures were much longer for WD 2149+021 than for the other white
dwarfs in our program, making it difficult to use our other targets for PSF
subtraction. Instead, we used a bright star in the field of view to determine
the shape of the PSF. Subtracting this PSF does not perform as well close to
the star, but does perform better in the wings. Figure 5 shows our PSF
subtraction for F560W and F1500W.

Figure 5: (top left) F560W image of WD 2149+021. (top right) F560W with a
reference PSF scaled and subtracted from the image. (bottom left) F1500W image
of WD 2149+021. (bottom right) F1500W image with a reference PSF scaled and
subtracted from the image. Our observations nearly hit the background
sensitivity limit close to the star in both filters.

After calculating the flux in the central aperture using the non-PSF
subtracted image, a ring of non-overlapping apertures is placed around the
white dwarf on the PSF subtracted image. The aperture-to-aperture standard
deviation was then measured for each ring, allowing us to calculate the
5$\sigma$ contrast for each radii as:

$\text{Contrast}(r)=\frac{5.0*\sigma(r)}{\text{sum}_{\text{WD}}}$ (1)

where $\text{sum}_{\text{WD}}$ is the total flux in the central aperture. Due
to other objects in the immediate field around WD 2149+021, it was necessary
to remove outlier apertures before taking their standard deviation. This
process was automated based on the median absolute deviation (MAD) with a
5$\sigma$ rejection limit, such that an aperture would be rejected if:

$\frac{\text{sum}_{aper}-\text{median}_{ring}}{\text{MAD}}>5.0$ (2)

However, apertures close to the white dwarf (within the first 2 rings) were
not allowed to be rejected. This process consistently rejected apertures
clustered near the false positive marked on Figure 2, as well as the suspected
background galaxy above it, with few other apertures being rejected. The
contrast was calculated using this method for multiple distances in order to
create the 5$\sigma$ contrast curve shown in Figure 6.

A grid search of the PSF subtracted image was also performed, where an
aperture was placed at each integer pixel within 2$\farcs$5 of the central
source in order to probe for outlier sources. Of these apertures (also sized
at 67% the FWHM of MIRI’s PSF $\approx$ 0$\farcs$32 = 2.97 pixels), none had a
sum above 5$\sigma$ significance.

Filter | Inner Contrast | Inner Radius | Median Contrast | Median Contrast Radius
---|---|---|---|---
F560W | 6.1$\times$10-2 | 0$\farcs$277 (6.2 au) | 8.1$\times$10-4 | 1$\farcs$06 (23.8 au)
F770W | 2.2$\times$10-2 | 0$\farcs$360 (8.1 au) | 2.5$\times$10-3 | 1$\farcs$38 (30.9 au)
F1500W | 1.1$\times$10-2 | 0$\farcs$654 (14.7 au) | 6.0$\times$10-3 | 1$\farcs$26 (28.3 au)
F2100W | 6.8$\times$10-2 | 0$\farcs$903 (20.2 au) | 4.6$\times$10-2 | 1$\farcs$46 (32.8 au)
Table 3: Contrast values for each filter at the inner most radius, as well as
the median contrast. The inner most radius and the median contrast radius (the
radius at which the contrast hits the median contrast) are listed in both
arcseconds and au. Figure 6: This contrast curve reports the flux ratio of our
central aperture relative to the standard deviation of the background at
varying radial distances for two of our filters, F550W (top) and F1500W
(bottom). The blue dashed lines are located at the median contrast level for
each filter, and are reported as the associated limiting mass by interpolating
the 3 Gyr Bex model. On the F1500W contrast curve, an additional line in green
has been added to show the contrast level expected for a 1 Jupiter mass
companion, also based on the 3 Gyr Bex model. Finally, the red dashed line
shows the contrast level for our own Jupiter (4.6 Gyr) based on synthetic
spectra generated using the Planetary Spectrum Generator (Villanueva et al.,
2018), which has been scaled to the distance of WD 2149+021.

In order to convert the sensitivity of our observations given in Table 3 to
planetary masses, we used cloudless Sonora-Bobcat grid models (Marley et al.,
2021) above 2 MJup and cloudless Helios grid models (Linder et al., 2019)
below 2 MJup. We first calculated the proper $T_{\mathrm{eff}}$, $\log{g}$
combinations for a given age corresponding to various substellar companion
masses from the Sonora-Bobcat grid. We then interpolated JWST fluxes from the
grids of predicted fluxes for ages between 1.5-10 Gyr. For the Helios grid,
fluxes for specific ages for 0.3, 0.5, 1, and 2 MJup were pre-calculated. We
then converted the predicted fluxes or magnitudes to apparent fluxes
accounting for the distance to WD 2149+021, 22.4 pc.

###  4.2 Analysis of Background Objects

Since the contrast curve is consistent with hitting the limiting background
sensitivity at radii beyond 1$\farcs$2, we also investigated the possible rate
of contamination from both resolved and unresolved sources in the field. We
conducted a search for significantly detected sources above the background
with the DAOFIND equivalent IDL astrolib routine FIND.pro, using the following
parameters for our F1500W image: We searched for objects with a peak flux of
10 nJy/pixel, default roundness and sharpness criterion, and an assumed PSF
FWHM of 4.4 pixels (0$\farcs$48). We avoided the “bonus region” in the upper
left of the detector and masked out edges where only one or two dithers
contributed to the image to cut down on spurious detected sources. This left a
total detector area of 9237 arcsec2.

Each detection was vetted to determine if it was consistent with a resolved or
unresolved source by fitting the detection with a 2-D Gaussian. The core of
the JWST PSF is reasonably approximated by a Gaussian out to $\sim$1-FWHM, and
in general the morphology of extended sources is smooth enough to also be
approximated by Gaussian shapes.

Spurious sources with excessively small FWHM values, offsets from flux peaks,
or extremely large FWHM values were filtered out, leaving a total of 119
sources besides the WD present in F1500W. We determined a rough cutoff between
resolved and unresolved sources by looking at the population of all detections
and noting that the width of the distribution centered around 4.4 pixels (the
FWHM of the PSF core) varied by $\sim$20%. Nearly all of the proposed point
sources below this cut-off (27) also had F560W detections which were visually
inspected, with only 3 sources being resolved at the shorter, higher spatial
resolution filter. We flagged those as extended and removed them as point
sources, leaving 24 point source objects and 84 extended objects in the field.

Aperture photometry encompassing 60% of a point source flux was measured for
each detected object in the four filters. In most cases significant
(SNR$\sim$5) detections were present in all filters. Figure 7 shows the field
point sources as a function of their F1500W flux and their F2100W/F560W
colors. Unfortunately, exoplanet isochrones relevant to white dwarfs show that
substellar objects overlap with background sources no matter what combination
of colors is used for these four filters.

In the case of WD 2149+021, only a couple of objects are consistent, within
the uncertainties, to predicted SEDs of cool Jupiter-mass planets. As
mentioned above, however, there is still little observational constraint of
what planets should look like beyond Jupiter and thus there is an inherent
systematic uncertainty in our true sensitivity. Even so, it is clear that our
observations at F1500W were more than sufficient to detect sub-Jovian mass
planets, provided estimates of the F1500W flux are reasonably correct. One
such object in Figure 7, which resides in between the two model isochrones and
would be consistent with a 0.5-10 MJup companion, is also detected in an
archival Spitzer IRAC2 image from 2009 (AOR: 35007232 PI: Burleigh). It is
consistent with having zero proper motion and is thus firmly ruled out as a
co-moving companion to WD 2149+021, which would have traveled $\sim$4″ over
the past 13 yr. A full common proper motion search for co-moving companions is
beyond the scope of this paper.

Given these results, we can estimate the probability that a background object
will appear close enough to a white dwarf to potentially contaminate the
star’s flux or pose as a spurious planetary companion. First, we take the
generic probability that any source will be present: in that case there are
0.01 sources per arcsec2. Within the PSF FWHM at F1500W, the probability that
there is a spurious IR excess due to a background object is just 0.8%. For a
search for planets within 100 au of the WD (4$\farcs$5), the probability of
background contmination is 73%.

However, JWST is able to resolve most sources. In that case, the probability
that a point source might be an interloper within 5″ is 16%, which can can be
dependent on galactic latitude. Stellar objects typically have F1500W/F560W
flux ratios of $<$0.3 under the assumption of a Rayleigh-Jeans flux
distribution, which should not be the case for cooler planet mass candidates
and extra-galactic objects. If we also filter-out objects with F1500W/F560W
flux ratios $>$0.3, then the probability that a red point source will be
within 5″ to WD 2149+021 is 11%. Red point sources at separations of between
0$\farcs$5 and 1$\farcs$5 are highly likely to be physically bound to the WD,
since the probability there is between 0.1-1.3%. Larger imaging surveys should
expect to find significant contamination from extended sources beyond a few
arcseconds. Companions detected at smaller separations may be difficult to
disentangle from resolved galaxies due to PSF subtraction residuals, although
the overall probability that this will happen for the range of contrasts
expected for planetary companions is fairly low. It is clear that any large
surveys will be required to test for common proper motion, as is typical for
direct imaging surveys at other wavelengths.

Figure 7: F1500W flux vs. F2100W/F560W flux ratio for all point sources
detected in the WD 2149+021 field. Overplotted is a 0.1 Gyr and 10 Gyr
isochrone constructed from a combination of Sonora-Bobcat and BEX models,
bracketing planets formed during post-main Sequence evolution to the upper
limit to the total age uncertainty (6.5 Gyr, Figure 3) of WD 2149+021.

###  4.3 Limits to unresolved companions

After plotting the CALSPEC spectrum on top of our observed flux (Figure 4), we
see that the observed JWST MIRI photometry matches the expected photospheric
flux to within the absolute flux calibration uncertainties. The current
accuracy of the MIRI flux calibration is 3%. Assuming the 5-$\sigma$ upper
limits of 15% to the presence of unresolved companions, we can convert those
upper limits to mass sensitivities to unresolved companions that are only
emitting thermal emission with orbital radii of $<$0$\farcs$5 (11.2 au). Using
the isochrones for a total WD age of 1.5, 3, 8 Gyr, corresponding to the
youngest, most probable, and oldest total WD ages, we find limits of 2, 4, 7
MJup respectively. Even at ages as old at 10 Gyr (the maximum age of the
theoretical isochrones), the mass limit is 8 MJup.

Interior to $\sim$0.3-1 au, the insolation from the host WD becomes important
and contributes to the total luminosity of a companion, making it brighter
than it otherwise would appear. Calculating an equilibrium temperature and a
surface area under the assumption of blackbody emission allows us to place
upper limits to the radius of objects that might be heated sufficiently close
to the WD that might be detectable.

To estimate our radius limits, we calculated the maximum emitting area allowed
by our 21 µm 3$\sigma$ upper limits to the flux for WD 2149+021, following a
similar procedure outlined in Farihi et al. (2014). Using our flux limit
($F_{\mathrm{limit}}$) and distance to the WD ($d_{\mathrm{WD}}$) where we
estimate the total emitting area ($A_{\mathrm{heated}}$) for blackbody
emission $B(21~{}\micron,T_{\mathrm{eq}})$ with an equilibrium temperature
($T_{\mathrm{eq}}$):

$A_{\mathrm{heated}}=\frac{F_{\mathrm{limit}}d_{WD}^{2}}{\pi
B(21~{}\micron,T_{\mathrm{eq}})}$ (3)

with $T_{\mathrm{eq}}$:

$T_{\mathrm{eq}}=T_{\mathrm{eff}}\left(1-\alpha\right)^{0.25}\sqrt{\frac{R_{\mathrm{WD}}}{2~{}a}}$
(4)

where $\alpha$=0.3 is the planetary albedo and $a$ is the semi-major axis of
the planet. We set R${}_{\mathrm{WD}}=0.0127~{}R_{\odot}$. We assume a
circular orbit. True planets’ spectral energy distributions are modified from
a pure blackbody by either their surface or atmospheric composition (e.g.
Figure 6 from Limbach et al. 2022) and thus our true sensitivity is dependent
on the properties of a given planet. We find that irradiated planets will be
detectable if they range from 1-12 R⊕ if they have orbital separations between
the Roche radius and 0.3 au respectively. We can estimate the mass from the
limiting radii, assuming the approximate relationship of 0.39
MJup$\times(R_{pl}/12.1~{}R_{\oplus})^{1.8}$ (Bashi et al., 2017).

Figure 8 shows a combination of the unresolved irradiated, unresolved
thermally emitting, and direct imaging sensitivity limits from our MIRI
observations as a function of orbital radius. We compare this to the confirmed
exoplanet population known as of 1 Sep 2023, but with a modified semi-major
axis for each planet. If every planet were to survive post-main sequence
evolution and its orbit evolved adiabatically, its final semi-major axis would
be a factor of 2.4 larger due to the mass loss of the host star as shown on
our plot. For planets beyond $\sim$3 au, tidal effects from the red giant and
asymptotic giant phases evolution are not strong enough to plunge the planet
into the star.

JWST observations can directly test the minimum survivable mass and semi-major
axis of planetary companions in post-main sequence systems. As with post-
common envelope binaries that have undergone common envelope evolution, we
expect that some fraction of planets within 3 au to survive and migrate to
small semi-major axes, where they are then irradiated by the white dwarf.
Planets that survive this process move outwards and become amenable to direct
imaging with JWST. Gaia and JWST will likely be sensitive to a wide range of
planets down to $\sim$1 MJup that orbit between 1-10 au, though we expect most
inner planets to be destroyed during post-main sequence evolution. For WD
2149+021, we would be sensitive to nearly 50% of all currently known
exoplanets with current orbital semi-major axes $>$3 au. In particular, we
also show that our WD direct imaging is significantly more sensitive to
intermediate and widely separated Jovian and sub-Jovian analogs than current
direct imaging surveys in the NIR with ground-based AO.

Figure 8: JWST/MIRI mass sensitivity for WD 2149+021. The solid red line
denotes our mass sensitivity for WD 2149+021 from unresolved IR-excesses and
directly imaged companions. The dashed line represents IR-excess mass
sensitivity assuming that close-in planets are irradiated by the WD. The
orange lines are the IR-excess limits from previous Spitzer and HST direct
imaging observations of other WDs. Symbols in blue represent planets with
initial semi-major axes $>$3 au, the approximate orbital radius where planets
are expected to survive post-main-sequence evolution (Mustill & Villaver,
2012). Planet Semi-major axes are expanded to account for adiabatic mass loss
without tidal effects. Our observations would be sensitive to 55% of these
known planet companions, if they were present in orbit around WD 2149+021. We
also overplot the two known WD exoplanet candidates with semi-major axes $<$
10 au. Exoplanet data provided by https://doi.org/10.26133/NEA12 (catalog
https://doi.org/10.26133/NEA12).

###  4.4 Limits to unresolved cold dust

Most WDs that accrete rocky material do not show evidence for thermal emission
from the dust that may be present. The current picture of this accretion
requires rocky bodies that tidally disrupt, with constituent disruption
products ground down into small dust which sublimates into the gas that
eventually accretes onto the surface of the white dwarf. If there is
sufficient material an optically thick disk could form, creating warm dust
near the sublimation radius of dust within a few WD radii (Jura, 2003). This
picture is consistent with the roughly 1-4% of metal-polluted WDs that show
significant Mid-IR emission at or within the tidal disruption radius (Debes et
al., 2011; Barber et al., 2014; Rocchetto et al., 2015). If the accretion is
dominated by the Poynting-Robertson drag of dust, then certain dust accretion
rates can account for sufficient mass in the disk to be observable (Rafikov,
2011; Metzger et al., 2012; Kenyon & Bromley, 2017a). Such disks are very easy
to detect unless they are nearly edge-on.

If the dust is not optically thick, the sublimation radius of dust for WDs
like WD 2149+021 moves outwards to roughly the Roche tidal disruption radius
and can have much lower luminosities– while an optically thick disk could
reprocess up to a few percentage of the WD luminosity, optically thin dust
akin to a debris disk can have orders of magnitude lower luminosity and remain
undetectable to previous surveys of WDs.

However, colder or lower luminosity dust disks are amenable to detection with
JWST. It is likely that there exists a larger number of low luminosity or cold
disks around WDs with lower accretion rates. For example, recent work has
shown that tidally disrupting rocky bodies do not form geometrically flat
disks as originally envisioned by Jura (2003) but rather can be vertically
extended due to the lack of significant collisional damping (hereafter K17
Kenyon & Bromley, 2017b). Such optically thin disks tend to be less massive
while still consisting of a fairly large emitting area from small dust
(Ballering et al., 2022). This would be consistent with existing circumstellar
gas measurements that put the outer ranges of the gas at around the tidal
disruption radius, since optically thin dust will sublimate further out
(Manser et al., 2016; Steele et al., 2021). So far only one accreting WD has
been probed for additional cold dust beyond $\sim$10 µm – G29-38, which was
probed both by ALMA and Herschel and showed no additional dust components
(Farihi et al., 2014).

JWST photometry of nearby WDs at wavelengths beyond 15 µm probes for very
small amounts of warm and cool dust and start to constrain the details of dust
accretion. WD 2149+021 is sufficiently luminous to heat dust close to the
tidal disruption radius, but significantly beyond that radius such that one
would expect all planetesimals to be fully evaporated if they tidally disrupt
(Steckloff et al., 2021). In fact, if the scenario of K17 is correct, that
tidally disrupted bodies relax into quasi-circular swarms that collisionally
evolve, JWST is sensitive to the predicted dust disks present for a large
fraction of accreting white dwarfs. K17 predicts that steady-state dust disks
formed from the regular injection of 1-100 km planetesimals result in a dust
disk with an equilibrium mass of collision products of 1014-1020 g for
accreting WDs.

In the case of WD 2149+021, the Ca abundance inferred by Koester (2009)
implies a mass accretion rate $\dot{M}$=2$\times 10^{7}g\ s^{-1}$ assuming a
bulk earth composition. K17 found that the equilibrium mass ($M_{d,eq}$) for a
collisional cascade at the tidal disruption radius ($a$) of a WD should be:

$\displaystyle M_{d,eq}$ $\displaystyle\approx$ $\displaystyle 7\times
10^{18}\ \mathrm{g}\left(\frac{\dot{M}}{10^{10}\mathrm{g\
s}^{-1}}\right)^{\frac{1}{2}}\left(\frac{0.6M_{\odot}}{M_{\mathrm{WD}}}\right)^{\frac{9}{20}}$
$\displaystyle\times\left(\frac{r_{\mathrm{o}}}{1\mathrm{km}}\right)^{1.04}\left(\frac{\rho}{3.3\mathrm{g\
cm^{-3}}}\right)^{\frac{9}{10}}$
$\displaystyle\times\left(\frac{0.01}{e}\right)^{\frac{4}{5}}\left(\frac{\Delta
a}{0.2a}\right)^{\frac{1}{2}}\left(\frac{a}{R_{\odot}}\right)^{\frac{43}{20}}r_{\mathrm{o}}\geq
1~{}\mathrm{km}$

where $r_{\mathrm{o}}$ is the characteristic size of the input bodies, $\rho$
is the average density, and $e$ is the eccentricity of the disk. The output
gas accretion onto the WD is then equivalent to the influx of mass into the
disk in a steady state (Kenyon & Bromley, 2017a). For a collisional ring of
bodies roughly at the tidal disruption radius $M_{d,eq}$=7$\times 10^{17}$ g
assuming ro=1 km. Interestingly, this also corresponds to just above the
accretion rate predicted to show IR excess assuming late stage dust accretion
from highly eccentric asteroids, an extension of the simulations done in K17
(Brouwers et al., 2022).

Similar to Equation 3, we can estimate limits to unresolved dust emitting
areas ($A_{\mathrm{dust}}$) where we calculate a new equilibrium temperature
for dust grains instead of planetary surfaces.

We assume any dust present is primarily made up of silicates, and we use an
empirically derived set of optical constants for galactic dust often used to
model debris disks (Draine, 2003). We assume all the dust has a singular size
$r_{g}$= 1 µm. We use the Planck-averaged estimates for an emission cross-
section $Q_{abs}(T,a)$ given by Draine (2003) for the relevant grain size and
we assume a density ($\rho$) of 3.3 g cm-3. Between dust temperatures of 100 K
and 1300 K $Q_{abs}(T,a)$ ranges from $\sim$0.1-0.4 respectively, while
$Q_{abs}(T,a)\sim 0.1$ for 10 µm grains. These quantities allow us to
calculate an upper limit to the dust mass ($M_{\mathrm{dust}}$):

$M_{\mathrm{dust}}=\frac{4}{3Q_{abs}(T)}\rho A_{\mathrm{dust}}$ (6)

Figure 9 shows our inferred dust mass upper limits with the above assumptions
compared to a few different scenarios. First, we compare to the predicted
equilibrium disk masses predicted by K17 (solid lines) in Equation 4.4
assuming disk radii from 1 RWD to several tens of R⋆, well outside the
expected Roche radius ($\sim$R⊙).

If K17’s predictions were correct, then we should have easily detected the
dust with our MIRI observations. One caveat is that this assumes the dust is
primarily in small grains, rather than locked up in larger bodies. To account
for this effect we can modify the mass limits by the mass ratio of small dust
grains to larger dust grains/bodies assuming a pure collisional size
distribution, which is
$\sim(\frac{r_{g,\mathrm{m}ax}}{r_{g,\mathrm{m}in}})^{0.5}$, where we assume
$r_{g,\mathrm{m}in}$=1 µm and $r_{g,\mathrm{m}ax}$ is either 1 km or 100 km.
In this case, the total mass in 1 µm grains is small enough to remain
undetectable by MIRI exterior to 10 and 2 R⊙ for cascades fed by 1 and 100 km
bodies, respectively.

We also compare our expected mass limits if we assume that the total amount of
mass in 1 µm grains is equivalent to the last 14 years of accretion (orange
line in Figure 9). This is the total length of time that WD 2149+021 has been
observed to be actively accreting rocky material. Again, we would have easily
detected that amount of dust, as our limits are a factor of $>$20 more
sensitive interior to the Roche disruption radius.

Our MIRI observations demonstrate that a large survey of DAZ, DBZ, or DZ stars
should be sensitive to very small amounts of dust, and that for accretion
rates $>$108 g s-1, JWST is very sensitive to low luminosity dust excesses.

Figure 9: Dust emission limits estimated for WD 2149+021. The solid black line
shows the estimated MIRI dust mass limit assuming a mass in 1 µm grains,
derived from the F2100W upper limits to a flux excess. The yellow line
corresponds to the total mass accreted by WD 2149+021 in the time it’s been
known to possess Ca metal absorption lines. The solid blue and red lines
represent the expected equilibrium disk mass of dust assuming a steady state
collisional cascade (See Equation 4.4) for typical planetesimal sizes of 100
km (blue) and 1 km (red). The dashed lines are the expected masses in 1 µm
grains only.

###  4.5 Limits to Tidally Heated ExoMoons

We also consider the detectability of tidally heated exomoons that orbit giant
planets around WD 2149+021 and how that might impact candidate companions.
Analogs to the Jovian moon Io might be tidally heated by very cool giant
planets(Peters-Limbach & Turner, 2013). In this scenario, the moon has some
fraction of its surface covered by volcanic activity at high Teff, with
potentially enough short wavelength emission that it appreciably modifies the
F2100W/F560W color of a planetary companion.

In Section 4.1, we relied on the very red predicted colors of giant planets to
help identify possible planet candidates. We show below that this might be
complicated if large tidally heated moons are common around WDs. Predicted
emission of tidally heated exomoons is presented in other works that consider
both the possible average luminosity from tidal heating or fractional coverage
by hot spots (Peters-Limbach & Turner, 2013) with a longevity that in
principle could last for billions of years (Rovira-Navarro et al., 2021),
depending on the moon’s size and orbital configuration.

Recently, Io was observed with JWST/NIRSPEC and the mid-IR emission was
consistent with a combination of temperatures and emitting areas ranging from
T=1500 K and 2$\times$108 cm2 to T=300 K and 1.6$\times 10^{14}$ cm2 (de Pater
et al., 2023). The combination of all the components creates a spectrum that
peaks at 17 µm, approximating a single blackbody spectrum with a
T${}_{\mathrm{eff}}\sim$320 K and emitting area with an equivalent area of
1.5$\times 10^{14}$ cm2. At 22.4 pc, Io would have a flux density in F1500W of
$\sim$0.02 nJy, four orders of magnitude below our F1500W detection limits. At
the given temperature and distance of WD 2149+021, detectable moons would need
emitting areas 5 times larger than the radius of Io, and equivalent to a moon
with R=1.36 R⊕.

Since the population of exo-moons is poorly known, we take a simple approach
that qualitatively illustrates the issue that a warm or hot exomoon poses: we
calculate the emission of an Earth-radius moon with a fractional coverage of
1500 K hot spots relative to the WD 2149+021 field point sources, and combine
its mid-IR emission with two 3 Gyr planets with different masses, one with 2
MJup, and the other with 5 MJup. We then determine how much of the surface
must be covered in hot spots to appreciably alter the color of these planets
in the observed MIRI filters.

Figure 10: F1500W flux vs. F2100W/F560W flux ratios for the field point
sources in the field surrounding WD 2149+021. We compare these objects to the
expected colors and fluxes for two planets (2 MJup and 5 MJup) that have 1 R⊕
tidally heated exo-Moons with varying coverage fractions of 1500 K hot spots.
Significantly heated moons can potentially change the observed position of a
Jovian planet candidate in this plot by having an excess of shorter wavelength
emission.

The effect of a giant planet having a moon with significant short wavelength
emission is to make the apparent flux ratio of F2100W/F560W less red,
complicating the exclusion of sources with F560W detections. Whether large,
tidally heated moons are common enough to significantly contaminate planetary
searches around WDs is an open question, but the fact that these systems must
be experiencing some dynamical perturbations suggest that it might be more
frequent than around main sequence stars. Our deep MIRI observations,
particularly at F1500W, are sensitive enough to start placing upper limits on
the presence of large tidally heated moons in orbit around giant planets and
reinforces the need for common proper motion tests to identify bound
companions to WDs in the mid-IR.

##  5 Conclusion

We have presented the first multi-band photometry of WD 2149+021 taken with
the MIRI imager early in JWST’s operational lifetime. To search for resolved
sources we performed a grid search within 2$\farcs$5 of WD 2149+021, and to
search for extremely widely separated candidates DAOFIND was used to detect
round, resolved sources over the entire detector. To search for unresolved
companions, we compared against available UV/Vis/NIR/Mid-IR photometry to
determine if our observations show an infrared excess. This analysis did not
identify any compelling candidates, placing limits on resolved companions of
$\sim$0.34 MJup outwards of 1.263′′ and $\sim$0.64 MJup at the innermost
radius (0.654′′). Limits on unresolved companions were found to be 2, 4, 7
MJup, corresponding to the youngest, most probable, and oldest total WD ages,
respectively.

This is the most sensitive search for cold planets around white dwarfs ever
conducted, reaching sub-Jupiter sensitivities for the first time. While recent
discoveries of white dwarf exoplanets (Sigurdsson et al., 2003; Luhman et al.,
2011; Gänsicke et al., 2019; Vanderburg et al., 2020; Gaia Collaboration et
al., 2023b) demonstrates that some planets are in close orbit and thus may
survive their hosts’ evolution, more observations are necessary to constrain
the occurrence rate of these planets as well as their properties. It should be
noted that improvements to the absolute flux calibration of the MIRI detector
(we assume 3%, but eventually it may reach 2%) will improve our unresolved
mass limits. Finally, the accuracy of planet mass sensitivities reported in
this paper is limited by the accuracy of current exoplanet models, which do
not focus on modeling at cold effective temperatures. Comparing against solar
system objects such as Jupiter is a useful check for these planet models, but
does not account for our system being $\sim$1.6 Gyrs younger.

Based on observations with the NASA/ESA/CSA James Webb Space Telescope
obtained from the Mikulski Archive for Space Telescopes at the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Incorporated, under NASA contract NAS5-03127. Support
for Program number 1911 was provided through a grant from the STScI under NASA
contract NAS5-03127. MK acknowledges support by the NSF under grant
AST-2205736 and NASA under grant 80NSSC22K0479. This publication makes use of
data products from the Wide-field Infrared Survey Explorer, which is a joint
project of the University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, and NEOWISE, which is a project
of the Jet Propulsion Laboratory/California Institute of Technology. WISE and
NEOWISE are funded by the National Aeronautics and Space Administration.

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