# WD 0141$-$675: A case study on how to follow-up astrometric planet
candidates around white dwarfs

Laura K. Rogers,1 John Debes,2 Richard J. Anslow,1 Amy Bonsor,1 S. L.
Casewell,3 Leonardo A. Dos Santos,2 Patrick Dufour,4 Boris Gänsicke,5 Nicola
Gentile Fusillo,6 Detlev Koester,7 Louise Dyregaard Nielsen,8 Zephyr Penoyre,9
Emily L. Rickman,10 Johannes Sahlmann,11 Pier-Emmanuel Tremblay,5 Andrew
Vanderburg,12 Siyi Xu (许bsmi偲gbsn艺),13 Erik Dennihy,14 Jay Farihi,15 J. J.
Hermes,16 Simon Hodgkin,1 Mukremin Kilic,17 Piotr M. Kowalski,18 Hannah
Sanderson19 and Silvia Toonen20
1Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge,
CB3 0HA, UK
2Space Telescope Science Institute, Baltimore, MD, USA
3Centre for exoplanet research, School of Physics and Astronomy, University of
Leicester, University Road, Leicester, LE1 7RH, UK
4 Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-
Ville, Montréal, Québec H3C 3J7, Canada
5 Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
6 European Space Agency, European Space Astronomy Centre (ESAC)
7 Institut f$\ddot{u}$r Theoretische Physik und Astrophysik,
Universit$\ddot{a}$t Kiel, 24098 Kiel, Germany
8 Karl-Schwarzschild-Straße 2, 85748 Garching bei M$\ddot{u}$nchen, Germany
9 Leiden Observatory, Leiden University, PO Box 9513, 2300 RA, Leiden, The
Netherlands
10 European Space Agency (ESA), ESA Office, Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218, USA
11 RHEA Group for the European Space Agency (ESA), European Space Astronomy
Centre (ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada,
Madrid, Spain
12 Department of Physics and Kavli Institute for Astrophysics and Space
Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
13 Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, HI 96720, USA
14 Rubin Observatory Project Office, 950 N. Cherry Ave., Tucson, AZ 85719, USA
15 Department of Physics and Astronomy, University College London, London,
WC1E 6BT, UK
16 Department of Astronomy & Institute for Astrophysical Research, Boston
University, 725 Commonwealth Avenue, Boston, MA 02215, USA
17 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma,
440 W. Brooks St., Norman, OK 73019, USA
18 Institute of Energy and Climate Research (IEK-13), Forschungszentrum
J$\ddot{u}$lich, Wilhelm-Johnen-Straße, J$\ddot{u}$lich 52425, Germany
19 Department of Earth Sciences, University of Oxford, South Parks Road,
Oxford OX1 3AN, UK
20 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science
Park 904, 1098 XH Amsterdam, Netherlands
E-mail<EMAIL_ADDRESS>
(Accepted 2023 October 6. Received YYY; in original form ZZZ)

###### Abstract

This work combines spectroscopic and photometric data of the polluted white
dwarf WD 0141$-$675 which has a now retracted astrometric super-Jupiter
candidate and investigates the most promising ways to confirm Gaia astrometric
planetary candidates and obtain follow-up data. Obtaining precise radial
velocity measurement for white dwarfs is challenging due to their intrinsic
faint magnitudes, lack of spectral absorption lines, and broad spectral
features. However, dedicated radial velocity campaigns are capable of
confirming close in giant exoplanets (a few M${}_{\textrm{Jup}}$) around
polluted white dwarfs, where additional metal lines aid radial velocity
measurements. Infrared emission from these giant exoplanets is shown to be
detectable with JWST MIRI and will provide constraints on the formation of the
planet. Using the initial Gaia astrometric solution for WD 0141$-$675 as a
case study, if there were a planet with a 33.65 d period or less with a nearly
edge on orbit, 1) ground-based radial velocity monitoring limits the mass to
$<$ 15.4 M${}_{\textrm{Jup}}$, and 2) space-based infrared photometry shows a
lack of infrared excess and in a cloud-free planetary cooling scenario, a sub-
stellar companion would have to be $<$ 16 M${}_{\textrm{Jup}}$ and be older
than 3.7 Gyr. These results demonstrate how radial velocities and infrared
photometry can probe the mass of the objects producing some of the astrometric
signals, and rule out parts of the brown dwarf and planet mass parameter
space. Therefore, combining astrometric data with spectroscopic and
photometric data is crucial to both confirm, and characterise astrometric
planet candidates around white dwarfs.

###### keywords:

stars: individual: WD 0141$-$675 – white dwarfs – planets and satellites:
composition – planets and satellites: detection – planets and satellites:
dynamical evolution and stability – techniques: radial velocities

††pubyear: 2023††pagerange: WD 0141$-$675: A case study on how to follow-up
astrometric planet candidates around white dwarfs–WD 0141$-$675: A case study
on how to follow-up astrometric planet candidates around white dwarfs

##  1 Introduction

Exoplanets are known to be ubiquitous, with over 5000 discovered around main
sequence stars; however, few planets have been confirmed around white dwarf
stars. White dwarfs are the final products of stellar evolution for low- and
intermediate- mass stars with an initial main sequence mass less than 9–12 M⊙
(e.g. Lauffer et al., 2018; Althaus et al., 2021); roughly 97 percent of the
stars in the Milky Way will evolve to white dwarfs (Fontaine et al., 2001).
The accurate Gaia parallax measurements for stars in the Milky Way has enabled
the number of white dwarfs discovered to increase by an order of magnitude,
with the most recent catalogue reporting 359,000 high-confidence white dwarf
candidates (Gentile Fusillo et al., 2021).

There is an ever-increasing number of remnant planetary systems discovered
around white dwarf stars. The most common observations are metal pollution in
the white dwarfs’ photosphere which is attributed to the accretion of
planetesimals that have been tidally disrupted when on star-grazing orbits.
This is observed in 25–50 percent of white dwarfs cooler than 25,000 K, where
radiative levitation effects are negligible so the pollution source must be
external (Zuckerman et al., 2003, 2010; Koester et al., 2014; Wilson et al.,
2019). Observations of the circumstellar environment reveal: infrared excesses
from circumstellar dust in 1.5–4 percent of white dwarfs (e.g. Wilson et al.,
2019), double peaked gaseous emission features in 0.067 percent of white
dwarfs (Manser et al., 2020), and transiting debris around of order 10 white
dwarfs (e.g. Vanderburg et al., 2015). However, there are still very few
confirmed planets around white dwarfs, and they are either inferred to be
present, or remain unconfirmed (Sigurdsson et al., 2003; Gänsicke et al.,
2019; Blackman et al., 2021). The most notable candidate is WD 1856+534b, a
giant transiting planet candidate found from TESS data on an orbit of 1.4 d
(Vanderburg et al., 2020). The tidal disruption scenario as the origin of the
observed metal pollution requires the presence of surviving large planets in
the outer system, capable of scattering smaller rocky bodies within the tidal
disruption radius of the white dwarf (e.g. Debes & Sigurdsson, 2002). In order
for 25–50 percent of white dwarfs to be polluted, surviving giant planets must
therefore be relatively common. However, planets around white dwarfs remain
difficult to detect due to, for example, low transit probabilities or few/no
narrow absorption lines for precise radial velocity measurements (e.g. Faedi
et al., 2011; Maxted et al., 2000; Belardi et al., 2016).

There are more detections of white dwarfs with sub-stellar companions than
there are detections of planets around white dwarfs, however, these are still
rare with estimates of an occurrence rate of approximately 0.5 percent (Steele
et al., 2011). This low number is partly as a result of sub-stellar companions
not surviving the evolution of the host star due to their masses and orbital
locations (Nelemans & Tauris, 1998; Nordhaus et al., 2010; Mustill et al.,
2013). The commonly accepted origin of close white dwarf-sub stellar binaries
is post common-envelope evolution, where one star in a binary system evolves
to a red giant and overflows its Roche lobe forming a common envelope around
the binary (e.g. Lagos et al., 2021). Drag causes orbital angular momentum to
be lost, resulting in the binary separation decreasing. If the envelope is
ejected, this leaves a white dwarf in a binary with a close companion (e.g.
Maxted et al., 2006). It is unknown whether pollution is correlated or
uncorrelated with the presence of a close sub-stellar companion. Only one
white dwarf-brown dwarf system shows metal pollution; Farihi et al. (2017)
reported a white dwarf-sub stellar binary, where a circumbinary dust disc
orbiting a polluted white dwarf (SDSS J155720.77+091624.6) was identified with
a brown dwarf companion on a 2.27 hour orbit.

The exquisite astrometric capabilities of Gaia opens a new window of
opportunity to discover planets around white dwarfs; with the release of Gaia
DR5 around 10 gas giants on wide orbits (0.03$-$13 M${}_{\textrm{Jup}}$ with
semi-major axes 1.6$-$3.91 au) are expected to be discovered around white
dwarfs (Perryman et al., 2014; Sanderson et al., 2022). The first astrometric
orbital solutions were released as part of the Gaia DR3 (Gaia Collaboration et
al., 2023a). This presented the first astrometric planet candidate around a
white dwarf (Gaia Collaboration et al., 2023b), a super-Jupiter around Gaia
DR3 4698424845771339520 (WD 0141$-$675). Due to its proximity to the Sun (9.72
pc) and its brightness, WD 0141$-$675 is a well studied white dwarf with
archival photometric and spectroscopic data covering the ultraviolet through
to mid-infrared wavelengths. It was first classified as a DA white dwarf in
Hintzen & Jensen (1979), and high-resolution spectra later revealed the
presence of calcium H and K lines, a sign that this white dwarf is polluted
with heavy metals (Debes & Kilic, 2010). Both accretion from the ISM and
intermediate absorption from the ISM are unlikely to explain the pollution as
WD 0141$-$675 is 9.72 pc away and lies within the local bubble. As it is
nearby, bright, and polluted it was included in the search for astrometric
companions with Gaia DR3 (Holl et al., 2023). The astrometric data was better
fitted by including a companion instead of a single star. The Gaia DR3 non-
single star orbital solution had a companion mass of 9.26 M${}_{\textrm{Jup}}$
and a period of 33.65 d, see Table 1 for further details. In May 2023 it was
announced that there were false positives in the Gaia astrometric solutions,
and WD 0141$-$675 no longer has a non-single star astrometric solution
111https://www.cosmos.esa.int/web/gaia/dr3-known-issues.

This work presents a case study using the nearby polluted white dwarf WD
0141$-$675 to place constraints on the planetary material being accreted by
the white dwarf and investigate how to follow-up astrometric candidate planets
to confirm and characterise them. This paper presents a detailed photometric
and spectroscopic analysis of WD 0141$-$675 to probe what could be done to
confirm and characterise astrometric planet candidates given an astrometric
solution similar to that originally posed with a planetary mass of 9.26
M${}_{\textrm{Jup}}$ and a period of 33.65 d. Section 2 reports the optical
and ultraviolet spectroscopic observations that were used to obtain the
abundance of the material polluting the white dwarf, constrain the accretion
rate onto the white dwarf, and put limits on the composition of the parent
body accreted, as derived in Section 5. Section 3 reports the full spectral
energy distribution (SED) with details on how to calculate limits to emission
from planetary companions calculated using planetary cooling models. Radial
velocities were calculated using the optical spectra to put constraints on the
mass of the planet candidate, as described in Section 4. Section 6
investigates the origin of the pollutant material in the photosphere of the
white dwarf. Finally, the discussions and conclusions on how to use this work
to follow up astrometric planet candidates are presented in Sections 7 and 8.

Table 1: Properties of WD 0141$-$675 from Gaia DR3 and the astrometric orbital
solution for the (now retracted) candidate planet.

Gaia DR3 Number: | 4698424845771339520
---|---
RA | 01:43:00.98
DEC |  $-$67:18:30.35
D (pc) | 9.72
G band (mag) | 13.69
G${}_{\textrm{BP}}$ band (mag) | 13.94
G${}_{\textrm{RP}}$ band (mag) | 13.29
SpT | DAZa
RUWE | 1.049
Subasavage et al. (2017)b: |
T${{}_{\textrm{eff}}}$ (K) | 6380 (120)
$\log(g)$ (cm s-2) | 7.97 (0.03)
$\tau_{\textrm{cool}}$ (Gyr) | 1.94 ${}^{+0.13}_{-0.12}$d
Total age (Gyr) | 8.02 ${}^{+3.62}_{-2.99}$d
M (M⊙) | 0.58 (0.02)d
log(q)c |  $-$7.59
Spectroscopic method (this work): |
T${{}_{\textrm{eff}}}$ (K) | 6421 (90)
$\log(g)$ (cm s-2) | 8.10 (0.04)
$\tau_{\textrm{cool}}$ (Gyr) | 2.30 ${}^{+0.27}_{-0.18}$d
Total age (Gyr) | 4.03 ${}^{+2.38}_{-0.59}$d
M (M⊙) | 0.65 (0.03)d
log(q)c |  $-$7.80
Photometric method (this work): |
T${{}_{\textrm{eff}}}$ (K) | 6321 (50)
$\log(g)$ (cm s-2) | 7.97 (0.03)
$\tau_{\textrm{cool}}$ (Gyr) | 1.98 ${}^{+0.10}_{-0.09}$d
Total age (Gyr) | 8.06 ${}^{+3.64}_{-2.98}$d
M (M⊙) | 0.57 (0.02)d
log(q)c |  $-$7.55
Planet Period (d) | 33.65 $\pm$ 0.05e
Planet Mass (M${}_{\textrm{Jup}}$) | 9.26${}_{-1.15}^{+2.64}$e
Inclination (deg) | 87.0 $\pm$ 4.1e

Notes:

aSpT from Debes & Kilic (2010).

bWhite dwarf parameters from Subasavage et al. (2017) derived using
photometry.

c $\textrm{q}=log_{\textrm{10}}(M_{\textrm{CVZ}}/M_{\textrm{WD}})$, the mass
ratio of the convective zone of the white dwarf, $M_{\textrm{CVZ}}$, to the
total mass of the white dwarf, $M_{\textrm{WD}}$.

d Total age, cooling age ($\tau_{\textrm{cool}}$), and mass are calculated
using wdwarfdate (Kiman et al., 2022).

ePlanet parameters from Gaia Collaboration et al. (2023b), inferred from
Monte-Carlo resampling, the median of the Planet Mass is 9.26
M${}_{\textrm{Jup}}$, and the mode is 8.3 M${}_{\textrm{Jup}}$. The posterior
distribution on the mass overlaps into the brown dwarf mass regime.

##  2 Spectroscopic Observations

###  2.1 MIKE/Magellan

WD 0141$-$675 was observed five times with the Magellan Inamori Kyocera
Echelle (MIKE) spectrograph (Bernstein et al., 2003) on the 6.5 m Magellan
Clay Telescope at Las Campanas Observatory between 2008 – 2010 (PI: Debes).
The MIKE spectrograph is a double echelle spectrograph with two arms covering
wavelengths of 3350–5000 Å (blue) and 4900–9500 Å (red). The data were
obtained under varying atmospheric conditions with the 0.7 $\times$ 5" slit.
This gave a spectral resolution of $\sim$ 35,000 for the red arm and 46,000
for the blue arm. The spectra were binned at 2 $\times$ 2 and had a slow
readout speed. The data were reduced with the standard Carnegie Python MIKE
pipeline included extraction, flat-fielding and wavelength calibration (Kelson
et al., 2000; Kelson, 2003). Due to the conditions, this gave a signal-to-
noise ratio (S/N) per pixel of 8–43, as reported in Table 2. To determine the
pollutant abundance, these data were stacked together, weighted by their S/N,
to achieve a final stacked spectrum with a S/N of 50–60 at the continuum
around the calcium K line (3933 Å). These data were corrected for radial
velocity shifts before they were stacked.

###  2.2 VLT X-shooter

WD 0141$-$675 was observed with the echelle spectrograph X-shooter (Vernet et
al., 2011) on Unit Telescope 3 of the Very Large Telescope (VLT) at Paranal
Observatory, Chile. X-shooter enables simultaneous observations in the 3 arms:
UVB (3000–5595 Å), VIS (5595–10240 Å) and NIR (10240–24800 Å). Observations of
WD 0141$-$675 have been taken in two modes: STARE, where a spectrum is taken
using a fixed point on the sky, and NOD mode, where the telescope is nodded
between two positions to reduce the affect of the sky background, important
for NIR observations. The NOD mode observations were taken on 2017-07-27 with
run ID 099.D-0661 (PI: Gänsicke) with a nodding throw length of 5 arcsecs, and
the STARE mode observations were taken on 2019-12-05 with run ID 1103.D-0763
(PI: Gänsicke). For all observations a 1.0, 0.9 and 0.9 arcsec slit width are
used for the UVB, VIS and NIR arms, this gives an optimal resolution
($\lambda/\Delta\lambda$) of 5400, 8900, and 5600 respectively. The data
reduction was performed using the standard procedures within the Reflex
reduction tool222http://www.eso.org/sci/software/esoreflex/ developed by ESO
with minor changes adopted to optimise the spectral extraction (Freudling et
al., 2013). Telluric line removal was performed on the reduced spectra using
Molecfit (Smette et al., 2015; Kausch et al., 2015). This gave a S/N per pixel
of 170 and 120, as reported in Table 2.

###  2.3 Hubble STIS

WD 0141$-$675 was observed with the Space Telescope Imaging Spectrograph
(STIS) on the Hubble Space Telescope on 2016 May 04 (PI: Gänsicke). The G230L
grating was used with a central wavelength of 2376 Å, this gives wavelength
coverage of 1570–3180 Å and a resolving power of 500. The exposure time was
2293 s giving a S/N of 70.

##  3 SED and Spectral Modelling

###  3.1 White dwarf parameters

Two methods were used to derive the white dwarf parameters: the first fitted
white dwarf models to the pressure broadened hydrogen spectral lines (the
spectroscopic method), and the second fitted white dwarf models to broad band
photometry (the photometric method). A description of these techniques, the
models, and minimisation methods used are discussed in detail in Bergeron et
al. (2019); Genest-Beaulieu & Bergeron (2019). The spectroscopic fit to the
hydrogen absorption lines is shown in Fig. 1, with an effective temperature of
6421 $\pm$ 90 K and $\log(g)$ of 8.10 $\pm$0.04. The adopted uncertainties are
from Liebert et al. (2005), giving 1.4 percent in effective temperature and
0.04 dex in $\log(g)$; this does not take into account systematic errors from
the model atmospheres. For the photometric method, GALEX NUV, SkyMapper
$uvgriz$ (Wolf et al., 2018) and 2MASS $JHK$ photometry (Cutri et al., 2003)
were fitted. Parallaxes from Gaia were required to obtain $\log(g)$ and
evolutionary models described in Bédard et al. (2020) were used to derive the
mass of the white dwarf. Reddening is not considered as it only becomes
important for objects $>$ 100 pc. The best fitting photometric effective
temperature and $\log(g)$ were 6321 $\pm$ 50 K and 7.97 $\pm$ 0.03
respectively (Table 1), with 1 $\sigma$ errors calculated separately using a
reduced $\chi^{2}$ analysis. The derived values for the spectroscopic and
photometric methods are reported in Table 1. Previously derived photometric
parameters from Subasavage et al. (2017) are reported for reference; it should
be noted that these parameters were derived prior to the Gaia parallax
measurements. The total ages derived from the photometric and spectroscopic
parameters are different by a factor of two, this has a significant impact on
the detectability and properties of planets around these stars.

Figure 1: Normalised sections of the X-shooter spectrum for WD 0141$-$675
showing the Balmer lines vertically offset from one another. The best fitting
white dwarf model from the spectroscopic method (see Section 3.1 for further
details) is over-plotted in red with an effective temperature of 6421 K and
$\log(g)$ of 8.10.

###  3.2 Spectral Energy Distribution

In order to assess the Spectral Energy Distribution (SED) of WD 0141$-$675,
photometry was collated from GALEX in the NUV band, SkyMapper in the optical
($uvgriz$), 2MASS for the near-infrared photometry $JHK$ bands, and Spitzer
for the mid infrared Kilic et al. (2008). The Kilic et al. (2008) data were
used for all Spitzer bands except for the 4.5 $\mu$m band, where data from
programme 60161 (PI: Burleigh) was used due to the higher S/N. The IRAC
channel 2 (4.5 $\mu$m) had 20 frames taken, each with an exposure time of 30
s. These data were reduced using the Mopex pipeline, and aperture photometry
performed using Apex and using the recommended pixel to pixel and array
location corrections for the IRAC warm mission, resulting in a S/N of 210.

The full SED including the spectra from VLT X-shooter and HST STIS, and the
photometry as outlined above is shown in Fig. 2. The white dwarf model over-
plotted on the data assumes the photometric temperature and $\log(g)$. The
STIS and GALEX data in the NUV lie systematically above the white dwarf
models. Different white dwarf models were tested in an attempt to reproduce
the observed ultraviolet-excess including: models at higher effective
temperature, atmospheric models which included He and metal pollutants (Dufour
et al., 2012), models which included 3D effects (Tremblay et al., 2013), and
independent models that previous work used to successfully reproduce NUV
through IRAC spectra of cool (T${}_{\textrm{eff}}$ $<$ 5600 K) white dwarfs
(Saumon et al., 2014). None of the models reproduce the ultraviolet-excess.
This may point to some minor problems with the existing models, however, this
is not important for the analysis performed in this paper.

Figure 2: SED of WD 0141$-$675\. The spectra are from HST STIS (orange), and
VLT X-shooter (blue) which has been smoothed for clarity. The ultraviolet
photometry is from the GALEX NUV band, the optical photometry is from
SkyMapper, the near-infrared photometry ($JHK$) is from 2MASS, and the mid-
infrared photometry from Spitzer is taken from Kilic et al. (2008). The white
dwarf model assumes the parameters derived in Section 3 using the photometric
method, with a temperature of 6321 K and $\log(g)$ of 7.97, and is overlaid as
a grey dashed line. The spectra are scaled to this model to account for slit
losses.

###  3.3 Photometric limits to the candidate companion

Assuming the Gaia astrometric solution for WD 0141$-$675 with the planet
candidate having a period of 33.65 d, the companion is an unresolved source
that could cause an infrared excess (e.g. Steele et al., 2011), if bright
enough. Previous studies which assessed the SED of WD 0141$-$675 reported no
excess infrared emission (Mullally et al., 2007; Kilic et al., 2006). This
work corroborates these claims with neither the Spitzer photometry, nor the
near-infrared X-shooter arm displaying excess infrared emission above what is
expected from an isolated white dwarf. Therefore, strong constraints can be
put on the emission from a candidate cool companion.

Planetary cooling models are used to place photometric limits on a sub-stellar
companion with the properties identified by the Gaia astrometric solution. It
is difficult to precisely predict the spectra of planets around white dwarfs
as the age is unknown, the upper atmosphere may have been altered during post-
main-sequence evolution, or the companion could have gained significant mass
during common envelope evolution with the host star. When assessing emission
from planets around white dwarfs it is therefore crucial to consider a range
of potential ages. The following considers two bounding cases in order to help
place constraints on what might be possible to detect with existing
observatories and to check for upper limits to existing mid-infrared
photometry of this object from Spitzer and WISE (Mullally et al., 2007; Kilic
et al., 2006, 2008). The first bounding case is that the object was
rejuvenated by the post-main sequence (e.g. Spiegel & Madhusudhan, 2012) (or
formed during the start of the post main sequence), and therefore for this
case study of WD 0141$-$675 it would have a planetary cooling age of 2 Gyr.
This corresponds to the average cooling age of the white dwarf from the three
sets of white dwarf parameters in Table 1 calculated from wdwarfdate (Kiman et
al., 2022) using cooling models from Bédard et al. (2020). The second bounding
case is that it formed in the protoplanetary disc and has been untouched by
the stellar evolution of its host and it consequently has a cooling age
equivalent to the total age of the system (equal to the white dwarf cooling
age plus the time on the main sequence). The total age was calculated with
wdwarfdate using the Cummings et al. (2018) initial-final mass relation. Given
the uncertainties on total age from different white dwarf parameters and that
the initial-final mass relation is less reliable for the mass range of WD
0141$-$675 (Heintz et al., 2022), a conservative bounding case of 10 Gyr is
used. To calculate the predicted planetary emission, Sonora-Bobcat cloud-free,
sub-stellar atmosphere models were used (Marley et al., 2021). In the
following analysis it is assumed that the object has both a solar metallicity
and C/O ratio.

The optimistic case is first considered where the companion accreted a
significant amount of material during post-main sequence evolution such that
it has a young cooling age. For this case study, at the best fit mass of 9.26
M${}_{\textrm{Jup}}$, a 2 Gyr cooling age implies a T${}_{\textrm{eff}}$=370 K
and $\log(g)$=4.3. For these objects, the companion is brightest in the mid-
infrared at Spitzer IRAC2 and WISE W2, with an expected flux of 0.2 mJy. As
seen in Fig. 3, there is high quality photometry of Spitzer IRAC2 and WISE W2
bands for WD 0141$-$675 and these observations would have detected excesses
above the photosphere at 3 $\sigma$ significance for fluxes of 0.15 and 0.11
mJy respectively. Therefore, these limits are below the expected flux for a
young companion with a mass of 9.26 M${}_{\textrm{Jup}}$, so a 2 Gyr old
planet with this mass is ruled out. The Spitzer and WISE upper limit
corresponds to an upper mass limit of 7 M${}_{\textrm{Jup}}$ for a 2 Gyr
planet cooling age assuming a T${}_{\textrm{eff}}$=330 K and a $\log(g)$=4.3.

Next, the case where the planet was unaffected by post main sequence evolution
and matches the total age of the host white dwarf is considered. In this case
for WD 0141$-$675, a 10 Gyr cooling age for a 9.26 M${}_{\textrm{Jup}}$
companion implies a T${}_{\textrm{eff}}=250$ K and $\log(g)$=4.4. Again, the
companion is brightest at IRAC2 and W2, with predicted fluxes of 0.026 and
0.024 mJy respectively, well below the upper limits and not detectable at
these wavebands as seen in Fig. 3. The upper limits from Spitzer and WISE
correspond to a 16 M${}_{\textrm{Jup}}$ companion for a 10 Gyr planet age,
assuming T${}_{\textrm{eff}}$=330 K and $\log(g)$=4.5. Therefore, if the
planet has a clear atmosphere, this rules out companions more massive than 16
M${}_{\textrm{Jup}}$. However, if the planet were cloudy, which would suppress
the infrared flux, then no mass limits can be placed.

Assuming the case study where WD 0141$-$675 has a 9.26 M${}_{\textrm{Jup}}$
planetary mass companion, the Spitzer and WISE 3 $\sigma$ upper limits
corresponds to an age of 3.7 Gyr, implying the planet candidate must be at
least 3.7 Gyr old. Figure 3 demonstrates that JWST is capable of detecting
infrared emission from a 9.26 M${}_{\textrm{Jup}}$ planet of any age around WD
0141$-$675\. The 21 $\mu$m JWST 3 $\sigma$ limit is equivalent to a planet
just 16 percent brighter than Jupiter, when scaled to the distance of WD
0141$-$675 (9.72 pc). Therefore, as shown by this case study, JWST is
sensitive enough to detect infrared emission from giant planets around white
dwarf stars.

Figure 3: The expected emission from a 9.26 M${}_{\textrm{Jup}}$ planetary
companion using Sonora-Bobcat models for planetary cooling ages between 2–10
Gyr as a function of wavelength for WD 0141$-$675\. The dashed black line
shows the 3 $\sigma$ upper limits from Spitzer/WISE photometry of WD
0141$-$675; any models that lie above this should have been detected and can
therefore be ruled out. From these limits, a companion temperature down to 330
K is ruled out, equivalent to planetary cooling ages of up to 3.7 Gyr. The
predicted JWST 3 $\sigma$ infrared excess limits (6 percent) are additionally
shown as a black line; above 12 $\mu$m JWST MIRI can detect infrared emission
from a 9.26 M${}_{\textrm{Jup}}$ cloud-free planet, regardless of whether it
was 2 or 10 Gyr old.

###  3.4 Photometric variability limits from existing surveys

Photometric surveys conducted in optical and infrared wavebands can produce
key information on the orbit of candidate companions. Optical photometric
surveys can put constraints on transiting planets, and if detected can place
stringent limits on planetary radius and period. This can enable follow-up
spectroscopic observations of the transit or eclipse of the companion to
constrain the structure and composition of the atmosphere. Infrared surveys
may provide information on the emission from the planet (Limbach et al.,
2022), and time series data may detect variability in the planetary emission.
This can be used to constrain the albedo of the companion.

For the case study of WD 0141$-$675, assuming the Gaia astrometric orbital
solution and the errors associated with this, the candidate companion would
have a 2.7 percent transit probability. The Transiting Exoplanet Survey
Satellite (TESS, Ricker et al. 2015) obtained data of WD 0141$-$675 in Sectors
1 and 2 (with a cadence of 2 min); and Sector 29 (with a cadence of 20 s),
with each sector lasting approximately 27 d. Lightkurve (Lightkurve
Collaboration et al., 2018) was used to assess whether any optical variability
was observed that could be due to a transiting companion, or transiting
tidally disrupted material. Lomb-Scargle periodograms were constructed which
found no coherent, periodic variability (on any timescale ranging from minutes
– days) to a limit of at least 0.02 percent amplitude, and as each sector
spans most of the planet period (each sector is 27 d and the companion period
was 33.65 $\pm$ 0.05 d). There is a 99.3 percent likelihood that a transit
should have been observed with TESS, this likelihood takes into account the
gaps in the middle of the sectors. Including
ASAS3333http://www.astrouw.edu.pl/asas/?page=asas3,
ASASSN444https://www.astronomy.ohio-state.edu/asassn/, and ATLAS (Tonry et
al., 2018) ground-based data, this increases to 99.5 percent. If the candidate
planet were transiting the host star, an inclination of at least 89.8 degrees
would be required (R=1 R${}_{\textrm{Jup}}$). Therefore, with 99.5 percent
confidence, an inclination of 89.8–90.2 degrees can be ruled out for the
candidate companion. Therefore, photometric surveys can rule out a range of
inclinations that would otherwise be compatible with the Gaia astrometric
solution.

Wide-field Infrared Survey Explorer (WISE) and NEOWISE observations from
2010–2020 were investigated using the unTimely catalogue from Meisner et al.
(2023) to investigate whether the mid-infrared fluxes varied over this
baseline. There are 16 detections of WD 0141$-$675 in each of the 3.4 and 4.6
$\mu$m bands taken over 4000 d. The resulting mid-infrared lightcurves were
found to be consistent with a straight line within the errors, so over 4000 d
there were no changes detected in the mid-infrared flux for WD 0141$-$675.

##  4 Radial Velocities

For main sequence stars, radial velocities are crucial to detect exoplanets
and determine their masses (e.g. Mayor & Queloz, 1995). This is more difficult
for white dwarfs as some white dwarfs have no spectral features (DCs) and if
they do, the features are pressure broadened, making it difficult to obtain
precise radial velocities. However, the astrometric candidates that Gaia will
identify around white dwarfs are in the gas giant regime (massive planets with
large radial velocity amplitudes), and therefore, for some candidates they may
show detectable radial velocity signatures. Additionally, if these planets are
discovered around polluted white dwarfs, the metal lines tend to be narrower
enabling increased radial velocity precision.

WD 0141$-$675 is both bright and polluted with narrow metal lines, therefore,
it is an ideal target for precision radial velocities. Radial velocities were
calculated for the available mid and high-resolution optical spectra of WD
0141$-$675 as described in Section 2. The radial velocities were calculated by
fitting a Gaussian profile to the core of the narrowest lines: the H $\alpha$
Balmer line, and the Calcium H and K metals lines from the polluted material.
For each spectrum these lines were first measured to ensure they were detected
at the 3 $\sigma$ level before it was used for the radial velocity
calculation. A Gaussian profile was fitted to the core of these lines using
the Idl programme Gaussfit which gave the position of the center of the line
and the estimated uncertainty on the fit parameters. From this, the weighted
average of the line centers was found using the estimated uncertainties as the
weights, and these were converted to a radial velocity per spectrum and are
reported in Table 2. Figure 4 shows five epochs of radial velocities derived
from photospheric calcium lines and hydrogen lines taken with the MIKE
spectrograph between 2008–2010 and two epochs with the X-Shooter spectrograph
in 2017 and 2020. The uncertainties are dominated by the stability of the
instruments and for MIKE this is estimated by observations of another nearby
white dwarf (1 $\sigma=$ 0.50 km s-1). For X-shooter, Parsons et al. (2017)
report that the velocity precision is approximately 1 km s-1; measurements of
sky emission lines in the VIS arm for WD 0141$-$675 corroborates this
precision. The rms of the radial velocities including the X-shooter and MIKE
data for WD 0141$-$675 is 0.94 km s-1, and excluding the X-shooter data is
0.47 km s-1. Therefore, using the MIKE data the rms of the radial velocity
data is 0.47 $\pm$ 0.50 km s-1 and there is no evidence that the MIKE radial
velocities have an additional radial velocity component due to a planetary
companion. Taking this rms value as 1 $\sigma$, the 3 $\sigma$ upper limit for
a companion is 15.4 M${}_{\textrm{Jup}}$; this upper limit assumes the Gaia
orbital period (33.65 $\pm$ 0.05 d), Gaia inclination (87.0 $\pm$ 4.1 deg),
and that these data are sampling the full period. Therefore, at the 3 $\sigma$
limit, companions more massive than 15.4 M${}_{\textrm{Jup}}$ could be ruled
out for this case study, shown as the shaded grey region in Fig. 4.

Monte Carlo models were used to show the range of parameter space of planets
that can be ruled out based on a radial velocity campaign using MIKE data that
sampled the period five times. The aim was to calculate the probability of
detecting a planet with a particular mass and period on a circular orbit
around a white dwarf of mass 0.6 $M_{\odot}$ using the MIKE observations as
the basis for the observing strategy. Two models were conducted, as shown in
Fig. 5, the first assuming an inclination of $i=87.0\,\pm\,4.1$ deg, and the
second assuming no prior information on the inclination. For each mass and
period, 5000 simulated observations were constructed, the first model drew
random inclinations from a Gaussian distribution centered on 87.0 deg with a
standard deviation of 4.1 deg, and the second drew random orbital inclination
from a uniform distribution between 0 and 90 deg. This produced a radial
velocity curve that was sampled five times, with each radial velocity
measurement being drawn from a Gaussian centered on that velocity and a
standard deviation given by the median radial velocity error from MIKE (0.5 km
s-1). This data was then fitted with a radial velocity curve and if the signal
could be detected at $>$ 3 $\sigma$, where $\sigma$ is the spread in radial
velocities expected for WD 0141$-$675 (0.47 km s-1), then it is characterised
as a planet detection. Figure 5 shows the results of the Monte Carlo models.
If the orbital inclination were close to edge on, companions of mass $>$ 15
M${}_{\textrm{Jup}}$ with periods of $<$ 15 d and $>$ 6.5 M${}_{\textrm{Jup}}$
with periods of $<$ 1 d can be ruled out confidently. However, if the
astrometric signal resulted in an unconstrained inclination then none of the
parameter space can be ruled out with certainty.

Table 2: Radial velocities (RV) from MIKE and X-shooter. S/N measured per pixel at the continuum around the calcium K line (3933Å).  Instrument | MJD (d) | S/N | RV (km s-1)
---|---|---|---
MIKE | 54698.691 | 43.0 | 63.19 $\pm$ 0.19
MIKE | 55119.604 | 8.0 | 63.78 $\pm$ 1.05
MIKE | 55363.876 | 10.0 | 64.23 $\pm$ 1.17
MIKE | 55410.775 | 14.5 | 62.98 $\pm$ 0.50
MIKE | 55412.774 | 35.0 | 62.51 $\pm$ 0.28
X-shooter | 57961.8453 | 170.0 | 64.60 $\pm$ 0.55
X-shooter | 58822.5208 | 120.0 | 66.39 $\pm$ 0.85
Figure 4: Seven radial velocity measurements of WD 0141$-$675 taken between
2008–2020 with MIKE (blue circle data points) and X-Shooter (orange triangle
data points). For the MIKE and X-Shooter radial velocities separately, the
weighted mean has been subtracted from each. Assuming a companion on a close
to edge-on orbit, 87 deg, with a period of 33.65 d and that the five MIKE data
points are sampling the full period, companions more massive than 15.4
M${}_{\textrm{Jup}}$ are ruled out for this case study and the grey regions
represent radial velocity signatures that would result in a companion mass
above this mass limit.

(a) $i=87.0\,\pm\,4.1$ deg (b) $0<i<90$ deg

Figure 5: Contour plots showing Monte Carlo models that calculate the
probability of detecting a planet around WD 0141$-$675 of a particular mass on
an orbit with period, P, assuming that five spectra were taken that sample the
period with the radial velocity precision taken as the median of that of the
MIKE datasets (0.5 km s-1). (a) Model assuming the inclination from the
astrometric orbit $i=87.0\,\pm\,4.1$ deg, and (b) model assuming no prior
information is known about the inclination. See Section 4 for further details.

##  5 Abundance Analysis

Figure 6: White dwarf model fits (red lines) to the calcium H and K lines from
the MIKE data (left and middle), and the calcium K line from the X-shooter
data (right). The abundance was calculated per line, with the fitted log(Ca/H)
abundance labelled at the bottom of each panel. These values assume the
spectroscopic temperature and $\log(g)$ reported in Section 3.1. Figure 7:
Accretion rate as a function of effective temperature for white dwarfs between
4000 and 8000 K from Blouin & Xu (2022), calculated assuming the white dwarf
is accreting material with bulk Earth-like abundances. WD 0141$-$675 is over-
plotted as a black diamond and sits at the lower end of the distribution.

Using the new white dwarf parameters derived in Section 3.1, the stacked
spectra from the five sets of Magellan MIKE observations, and the VLT
X-shooter spectra introduced in Section 2 were fitted separately to obtain the
abundance of the polluting planetary material. The [Ca/H] abundance was
measured for the stacked MIKE data, and the X-shooter data following methods
in Dufour et al. (2012). The spectra were divided into regions of 5–15 Å
around the calcium H and K absorption lines. The white dwarf effective
temperature and $\log(g)$ were inputted using the spectroscopic and
photometric temperature and $\log(g)$ from Table 1, and the best-fitting
abundance for that spectral line was found; model fits to the data are shown
in Fig. 6. Table 3 reports the average abundances calculated using the
spectroscopic and photometric temperatures. The reported uncertainties contain
contributions from the abundance spread from measuring multiple calcium lines
including with two instruments, the propagated error in the equivalent width
measurements, and error induced from differing white dwarf parameters. Updated
diffusion timescales from Koester et al. (2014); Koester et al. (2020) were
used to derive the calcium accretion rate using the spectroscopic and
photometric temperature and $\log(g)$, reported in Table 3. The total
accretion rate was calculated, assuming that calcium makes up 1.6 percent of
the mass of the body as in Bulk Earth (Allègre et al., 1995). Figure 7 shows
the accretion rate as a function of effective temperature for white dwarfs
between 4000 and 8000 K from Blouin & Xu (2022). The accretion rate of WD
0141$-$675 is low compared to the population of polluted white dwarfs of this
temperature range.

The spectra are found to be consistent with the accretion of material of
either bulk Earth, as may be expected for rocky asteroids, or Solar
composition, as may be expected from comets or the outer layers of gas giants.
The [Ca/H] abundance was used to scale to Bulk Earth (McDonough, 2003) and
Solar (Grevesse et al., 2007) abundance, and models were computed for these
abundances assuming the spectroscopic temperature and $\log(g)$. The models
were compared to the data, and no further features that should have been
detected were observed in the data. From the models, the next strongest lines
in the spectra are the Mg I and II lines around 2790–2850 Å. Figure 8 shows
the predicted models convolved to the resolution of STIS. No detection of Mg
II is made in the STIS data, and the spectra are consistent with bulk Earth
and Solar-like compositions. Magnesium abundances are similar for bulk Earth
and Solar compositions, so to differentiate them the detection of more
volatile species such as oxygen or carbon would be required. Additionally, to
determine the phase of accretion: build-up, steady-state or declining phase,
at least three elements are required covering a range of elemental sinking
timescales. Therefore, higher resolution or higher S/N data would be required
to confirm whether the pollutant composition was bulk Earth or Solar like, and
the phase of accretion.

Table 3: Abundance of the pollutant of WD 0141$-$675, and inferred accretion rates from calcium, and a total accretion rate assuming a bulk Earth composition (where calcium makes up 1.6 percent of the mass of the body). | Spec: | Phot:
---|---|---
Average [Ca/H]: |  $-$10.72$\pm$0.10 |  $-$10.82$\pm$0.10
log($\tau_{\textrm{Ca}}$) (yrs): | 3.94 | 4.24
$\dot{M}_{\textrm{Ca}}$ (g s-1): | 5.0$\times 10^{4}$ | 3.6$\times 10^{4}$
$\dot{M}_{\textrm{Total}}$ (g s-1): | 3.1$\times 10^{6}$ | 2.2$\times 10^{6}$
Figure 8: Non detection of Magnesium in the HST STIS data. After the calcium
lines, assuming either Bulk-Earth or Solar abundances in build-up accretion
phase, the next strongest lines in the spectra are Mg I and II lines around
2790–2850 Å. No detection of Mg II is made in the STIS data, however, the data
are consistent with the models.

##  6 Origin of Calcium in the white dwarf

The case study system, WD 0141$-$675, is a polluted white dwarf, meaning
planetary material must have arrived in the photosphere of the white dwarf.
This section models WD 0141$-$675 with a planet on the astrometric orbit and
investigates the origin of calcium in the white dwarf, and whether pollution
in white dwarfs with close-in astrometric planet candidates is a positive
indication that the planet is real.

###  6.1 Mass loss from close-in planets

Atmospheric mass loss, or escape, has been extensively detected in short-
period transiting exoplanets (e.g., Vidal-Madjar et al., 2003; Fossati et al.,
2010; Ehrenreich et al., 2015; Allart et al., 2018; Spake et al., 2018; Sing
et al., 2019). Most of these are observed in hot gas giants that receive
extreme levels of high-energy irradiation, which drives mass loss rates
$>10^{9}$ g s-1 (e.g., Erkaev et al., 2015; Salz et al., 2016b). Gänsicke et
al. (2019) inferred a gas giant planet around WD J091405.30+191412.25, this
has an expected mass loss rate which matches that of the white dwarf accretion
rate, highlighting this scenario as a plausible pollution mechanism in the
post main sequence. The energy-limited mass loss formulation (see, e.g., Salz
et al., 2016a) predicts that the escape rate $\dot{M}$ of a planet with a
H/He-dominated atmosphere is given by:

$\dot{M}=\frac{\epsilon\pi R_{\rm p}^{3}F_{\rm XUV}}{KGM_{\rm p}}\mathrm{,}$
(1)

where $\epsilon$ is the efficiency of converting irradiation into an outflow,
$F_{\rm XUV}$ is the incident XUV flux, $K$ is a correction factor that takes
into account the tidal effects (Erkaev et al., 2007), $R_{\rm p}$ is planetary
radius and $M_{\rm p}$ is the planetary mass. For the test case system of WD
0141$-$675, a planet mass of 9.26 M${}_{\textrm{Jup}}$, radius of 1.0
R${}_{\textrm{Jup}}$, semi-major axis of $0.172$ au, and an XUV spectral
energy distribution as estimated in Section 3.2, gives a photoionisation
escape rate of just 15 g s-1. In addition, it is unlikely that the planet is
losing significant amounts of mass from Jeans escape due to its inferred high
gravity and low temperature. Thus, photoionisation and thermal escape from the
planet are unlikely to be the cause of the pollution observed in the host
star. These models show that for cooler white dwarfs
(T${}_{\textrm{eff}}<7,000\,$K), mass loss from close-in giant planets cannot
cause significant atmospheric pollution, such as is observable for WD
0141$-$675, due to the low incident XUV flux. However, for hotter white dwarfs
with close-in planets, this effect can explain the accretion rate (Gänsicke et
al., 2019), so must be considered as a potential source of the pollution.

###  6.2 Can scattering supply the observed pollution?

A standard pathway for white dwarf pollution involves planetesimals scattered
inwards by planets. The following work considers whether scattering is a
viable option to explain the observed accretion. The scenario is considered
that the white dwarf is orbited by a close-in giant planet and there is an
unseen reservoir of planetesimals in the outer white dwarf planetary system,
similar to an asteroid belt that has survived the star’s evolution. The
material from this outer belt would either be directly scattered by the
candidate planetary companion (e.g. Bonsor et al., 2011; Debes et al., 2012)
or scattered inwards towards the observed planetary companion by further
undetected planets (e.g. Bonsor et al., 2012; Marino et al., 2018).

To determine the likelihood of planetesimals being scattered towards the white
dwarf and making it past the planet, simulations were conducted using the
REBOUND N-body code (Rein & Liu, 2012). The MERCURIUS integrator was used
(Rein et al., 2019), which uses the high-order adaptive integrator IAS15
during close encounters (Rein & Spiegel, 2015) and otherwise the symplectic
integrator WHFAST (Wisdom & Holman, 1991; Rein & Tamayo, 2015). In this work
mass-less test-particles were injected at a constant rate,
R${}_{\textrm{in}}$, into the chaotic region, $\delta a_{\mathrm{chaos}}$, of
the planet, where the chaotic region is defined as $\delta
a_{\mathrm{chaos}}=1.3a_{\mathrm{pl}}\left(\frac{M_{\mathrm{pl}}}{M_{\ast}}\right)^{2/7}$
(Wisdom, 1980), and then scattered from this region. The number of particles
ejected from the system, and collided with the white dwarf or the planet was
tracked, as shown in Fig. 9. The criterion for a particle to hit the white
dwarf is taken to be when it enters the Roche sphere (approximately 1.0 R⊙),
the criterion for a particle to collide with the planet is when it enters the
physical radius of the planet (1.0 R${}_{\textrm{Jup}}$), and particles are
removed from the simulation when the semi-major axis exceeds 150 au, thus
ensuring that all particles on extreme eccentric orbits can still return and
interact with the system.

Figure 9 shows that across the wide range of initial particle eccentricities,
few particles make it past the planet and hit the white dwarf. Given a
constant input rate of particles with a specific orbital eccentricity, the
simulations demonstrate that there is an almost constant ratio of particles
that are ejected from the system, collide with the Super-Jupiter, and are
accreted by the white dwarf, compared to the total number of particles
scattered. These scattering rates are determined by the relative probability
of each outcome, which is found to be dependent on the eccentricity of the
planetesimal belt. The corresponding probability of each scattering outcome
are given in Table 4. The few particles that do make it past the planet may be
sufficient to supply the observed accretion. Given the accretion rate of
3.1$\times$106 g s-1 (assuming the spectroscopic white dwarf parameters), over
a cooling time of 2.3 Gyrs, an efficiency of 1 percent (for the $e=$ 0 case),
2.3$\times$1025 g in small bodies must enter the chaotic zone of the inner
planet over the cooling age of the white dwarf. This is equivalent to 0.4
percent of Earth’s mass or 10 asteroid belts (0.06 Kuiper belts). This assumes
that accretion began as the white dwarf formed and continued accreting at the
same rate in steady state. However, in reality, this would not be the case,
given the stochastic nature of white dwarf planetary systems (Wyatt et al.,
2014), it is likely that there were periods of enhanced or no accretion. The
most massive observed debris discs contain hundreds of Earth masses (Krivov &
Wyatt, 2021), thus, it remains plausible that the observed accretion for this
case study was supplied by the scattering of small bodies.

Table 4: Scattering outcomes from the N body simulations described in Section 6.2. The table gives the fraction of the different scattering outcomes compared to the total number of particles scattered from the chaotic zone ($\textrm{N}_{\textrm{Scat}}$) across the total time of the simulations. These outcomes are that the particles: (1) get ejected from the system ($\textrm{N}_{\textrm{esc}}$), (2) collided with the Super-Jupiter ($\textrm{N}_{\textrm{SJ}}$), and (3) collided with the white dwarf ($\textrm{N}_{\textrm{WD}}$); these are shown for different eccentricities ($e$) of the disc. Given the accretion rate onto the white dwarf using the spectroscopic and photometric white dwarf parameters (see Table 1), the total mass scattered from the disc over the cooling time was calculated (2.3 Gyrs and 1.95 Gyrs for the spectroscopic and photometric white dwarf parameters respectively) using M${}_{\textrm{$\tau_{\textrm{cool}}$}}=\tau_{\textrm{cool}}\dot{M}_{\textrm{WD}}\frac{\textrm{N}_{\textrm{Scat}}}{\textrm{N}_{\textrm{WD}}}$, where $\dot{M}_{\textrm{WD}}$ is the derived accretion rate onto the white dwarf from Section 5. $e$ | $\frac{\textrm{N}_{\textrm{esc}}}{\textrm{N}_{\textrm{Scat}}}$ | $\frac{\textrm{N}_{\textrm{SJ}}}{\textrm{N}_{\textrm{Scat}}}$ | $\frac{\textrm{N}_{\textrm{WD}}}{\textrm{N}_{\textrm{Scat}}}$ | Spec M${}_{\textrm{$\tau_{\textrm{cool}}$}}$ (g) | Phot M${}_{\textrm{$\tau_{\textrm{cool}}$}}$ (g)
---|---|---|---|---|---
0.00 | 0.42 | 0.56 | 0.01 | 2.3$\times$1025 | 1.4$\times$1025
0.25 | 0.47 | 0.49 | 0.03 | 7.5$\times$1024 | 4.5$\times$1024
0.50 | 0.62 | 0.30 | 0.06 | 3.8$\times$1024 | 2.3$\times$1024
0.75 | 0.52 | 0.13 | 0.32 | 7.0$\times$1023 | 4.2$\times$1023
Figure 9: Results from the N body simulations described in Section 6.2. The
number of particles ejected from the system, accreted onto the super-Jupiter,
and accreted onto WD 0141$-$675 are plotted as a function of time, normalised
to the total number of scattered particles. The fractions are plotted for four
separate simulations in which test-particles are injected at a constant rate
into the chaotic region, $\delta a_{\mathrm{chaos}}$, of the super-Jupiter
with initial eccentricities 0.0, 0.25, 0.50, 0.75 respectively. This behaviour
represents the evolution at any time period when particles enter the planet’s
chaotic zone as the fraction remains unchanged, and Table 4 reports the
fractions ejected from the system, accreted onto the super-Jupiter, and
accreted onto the white dwarf.

The eccentricity of the disc affects the fraction of bodies that collide with
the white dwarf and planet. As the eccentricity increases, the fraction of
bodies that collides with the white dwarf increases, whereas the fraction that
collides with the planet decreases, as seen in Fig. 9 and Table 4. It is only
at an eccentricity of 0.75 that the fraction of particles colliding with the
white dwarf is greater than the fraction of particles colliding with the
planet. These findings agree with previous works on the importance of highly
eccentric belts to pollute white dwarfs. From Table 4 it is shown that the
planet would also accrete a significant mass of small bodies. Over the cooling
age of the white dwarf the planet will accrete 0.01 percent of its mass (9.26
$M_{\textrm{Jup}}$) in small bodies for the $e=0$ case down to 0.000001
percent of its mass for the $e=0.75$ case. This may result in detectable
metallicity enhancements to the atmosphere of the gas giant planet.

Whilst the models reported in Section 6.1 indicate that mass loss directly
from the atmospheres of close-in giant planets is unlikely to lead to
atmospheric pollution for this case study, scattering can continue to supply
pollution in systems with close-in planets, given a sufficiently massive
reservoir of material. Thus, whilst pollution may not be the natural companion
to close-in giant planets (for full details see Sanderson et al., 2022), this
work shows that pollution in the atmosphere of a white dwarf with an
astrometric planet detection does not suggest that the signal is not real,
rather that the white dwarf is orbited by a massive active outer planetary
system.

##  7 Discussion

Over the lifetime of Gaia, it is expected to increase the total number of
detected exoplanets by a factor of 14 (Perryman et al., 2014). These
astrometric detections provide the full orbital solutions as well as the mass
of the exoplanet (Holl et al., 2023). However, to get down to planetary
masses, high precision astrometry is required and even then, binaries with two
similar stellar components can mimic these astrometric signals (Marcussen &
Albrecht, 2023). Therefore, follow-up observations are crucial to confirm the
planetary nature of these astrometric signals. This work presents a case study
using the nearby polluted white dwarf WD 0141$-$675, which had a Gaia
astrometric planet candidate (now retracted) of mass 9.26 M${}_{\textrm{Jup}}$
on a period of 33.65 d. The posterior distribution of masses for this
companion overlapped into the brown dwarf mass regime, therefore, in order to
confirm an astrometric planet candidate it is crucial to obtain follow-up data
to place tighter constraints on the mass of the companion. This work collated
spectroscopic and photometric observations of WD 0141$-$675 with an aim of
demonstrating how to follow-up astrometric companions to confirm their
planetary nature.

###  7.1 Confirming the Planetary Nature of a Companion

One potential false-positive for astrometric planet candidates is a binary,
where the two stars are similar - a double degenerate binary with two nearly
equal-brightness white dwarfs (Gaia Collaboration et al., 2023b; Marcussen &
Albrecht, 2023). Using the case study of WD 0141$-$675, this can be ruled out.
Firstly, no secondary lines are observed in the high-resolution spectra.
Additionally, two independent methods are used to find the best fitting white
dwarf parameters, the photometric and spectroscopic methods. If there were two
white dwarfs, a larger radii would be needed to explain the luminosity, which
would give a much lower $\log(g)$ than a 0.13 dex difference for the
photometric method. The radial velocities can provide further constraints on
the candidate mass which rules out white dwarf masses on a period of 33.65 d
with an inclination of 87.0 deg. However, caution should be taken as there
could be a blend in lines where two stars have overlapping lines and this can
create the illusion of no net radial velocity shift (Torres et al., 2004).
This can lead to asymmetric line profiles, so to rule this out the shape of
the absorption feature should be studied over time. For WD 0141$-$675 no
asymmetric shifts are observed in the absorption line profiles. The re-
normalised unit weight error (RUWE) measured from Gaia can indicate the
presence of close binary companions (e.g. Belokurov et al., 2020) by
introducing excess scatter into astrometric solutions. Stars with high excess
scatter would have RUWE values $>$ 1.25 (if using Gaia DR3), and those with
average excess scatter would have a RUWE value closer to 1 (Penoyre et al.,
2022). For WD 0141$-$675, the RUWE is 1.049 implying no excess scatter, this
means that if there were a companion it only causes a very slight perturbation
to the single body fit. The Gaia RUWE value is consistent with a single body
astrometric solution, implying no large deviation from a massive close-in ($<$
30 yr orbit) tertiary companion. As demonstrated by this case study, by
collating spectroscopic and photometric data, this false-positive scenario can
be ruled out for astrometric planets around white dwarfs.

Radial velocities provide a powerful tool to constrain the mass of the object
inducing the astrometric signals, if the orbital inclination is favourable.
For the case study of WD 0141$-$675, using sparsely sampled, archival low- and
medium-resolution spectra, assuming a nearly edge on orbit from the
astrometric signature allows close in (P $\sim$ days) planets $>$ 6
M${}_{\textrm{Jup}}$ to be ruled out (Fig. 5a). However, with no prior
information on the inclination, it is not viable to confidently constrain the
mass of a planetary companion (Fig. 5b). There are significant radial velocity
shifts between instruments, as seen from Table 2, making the use of archival
data with multiple instruments more challenging. Additionally, using
instruments that are not designed for precise radial velocity precision means
that for this case study, only companions with orbits that produce signals $>$
1.41 km s-1 are detectable. However, with dedicated radial velocity campaigns
using a high-resolution stable spectrograph such as VLT ESPRESSO (R$=$140,000
with radial velocity noise floor of 0.5 m s-1), constraining companion masses
for white dwarf stars is possible (Pasquini et al., 2023). The typical
ESPRESSO radial velocity uncertainty was assessed by scaling the errors from
X-shooter and MIKE with the expected S/N, spectral resolution, and number of
useful spectral lines across the wide ESPRESSO wavelength coverage. Here, the
increase in spectral resolution is predominantly taken into account as an
improved sampling of each spectral line (resulting in a higher S/N). Error-
bars of 125$-$250 m s-1 are achievable with ESPRESSO in 1 hr exposures. The
observation campaign simulated covers a baseline of 90 d (2.5 planetary
orbits) where WD 0141$-$675 is observed with a 5-night cadence, with some
randomness added to the sampling to avoid aliases. Figure 10 shows 18
simulated radial velocities for ESPRESSO, and the Lomb-Scargle periodogram of
this simulated data which clearly shows a detection of a planet with period
33.65 d. It should be noted, however, that even though the metal lines are
narrower than the hydrogen and helium features, broadening effects are still
present which give a limit to the radial velocity precision that is
independent from the instrument’s limit.

With the successful launch of JWST, highly sensitive photometric measurements
are possible beyond 10 µm with the MIRI imager, where the emission of the
white dwarf is significantly fainter but still easily detected at high S/N in
a reasonable integration time. Using WD 0141$-$675 as a case study, Fig. 3,
especially at F1500W, F1800W, and F2100W, the predicted emission from the
companion will be 15, 27, and 47 percent of the white dwarf’s emission, while
the expected absolute flux calibration accuracy is approximately 2 percent.
Therefore, JWST is an invaluable tool to help confirm the presence and
properties of a planet candidate around a white dwarf.

Figure 11 shows the probability of astrometrically detecting a planet around
WD 0141$-$675 of a given mass and semi-major axes with Gaia. If no astrometric
signals are observed, planets greater than 7 $M_{\textrm{Jup}}$ can be ruled
out, out to a few au, and outside of 1 au planets down to 0.5
$M_{\textrm{Jup}}$ can be ruled out. If an astrometric signal is detected,
JWST MIRI could detect infrared emission from the companion which can confirm
the planetary nature, and targeted radial velocity campaigns can further
constrain the mass. For this case study, combining the radial velocity limits
with the infrared emission limits, if a cloud-less planet had a 33.65 d period
with an inclination of 87 degrees, the planet would be less than 15.4
$M_{\textrm{Jup}}$. This is approximately in the planetary mass regime.
However, if the planet were further from the white dwarf than predicted, on a
less inclined orbit, or has a cloudy atmosphere, this could result in a
significant reduction in the strength of the infrared emission of the
companion and the amplitude of the radial velocity signature.

(a)  (b)

Figure 10: (a) A comparison between the radial velocities presented in this
paper, and simulated radial velocities with increased numbers of observations
taken at a higher frequency with VLT ESPRESSO. The MIKE and X-Shooter radial
velocities phase folded on a 33.65 d period, where the weighted mean values
have been subtracted to illustrate the relative radial velocity shift and take
any absolute radial velocity shift between the two instruments into account.
The black opaque solid line is the Gaia best-fit model. The translucent lines
are 1000 randomly chosen models from the re-sampled posterior solution of the
original astrometric solution. The red triangles are simulated data for a
high-resolution stable spectrograph such as VLT ESPRESSO. (b) The Lomb-Scargle
periodogram of the 18 simulated ESPRESSO radial velocities. The planet signal
is recovered with better than 0.1 percent False Alarm Rate (FAR).  Figure 11:
Probability of an astrometric planet detection as a function of mass and semi-
major axis for WD 0141$-$675 using Sanderson et al. (2022). The white hatched
region highlights semi-major axes with periods longer than the Gaia mission
length. The regions where the detectability drops below one above the yellow
boundary are numerical, see Sanderson et al. (2022) for further details.

###  7.2 WD 0141$-$675 Pollution

Previous works using the 2017 X-shooter data derived a [Ca/H] abundance of
$-$10.96 $\pm$ 0.11 for WD 0141$-$675 using a temperature of 6150 K and
$\log(g)$ of 7.58 (Kawka et al., 2019). This is consistent within errors to
the abundance derived in this work, with the differences likely due to the
differing white dwarf parameters used to fit the [Ca/H] abundance.

Based on abundance estimates from the spectra, a total accretion rate of 106 g
s-1 was inferred, the equivalent of a small asteroid’s worth of material
accreted each year. This is not enough to expect a bright and warm infrared
excess due to dust (Rafikov, 2011a, b), especially given that dust discs
around cool white dwarfs are rare, and is consistent with the lack of an
infrared excess as seen in Fig. 2.

###  7.3 Is atmospheric pollution expected for white dwarfs with close-in
giant planets?

Spectroscopic observations, such as those described in Section 2, can indicate
whether metals are present in the atmosphere of these white dwarfs. These
metals are generally associated with the presence of an outer planetary
system. However, in the case of close-in giant planets, it is crucial to
consider whether atmospheric pollution is an indicator that supports the
presence of the planet.

Sanderson et al. (2022) shows that it is harder to scatter material onto star-
grazing orbits in the presence of a close-in giant planet due to the likely
dynamical gaps in the planetary system following mass-loss on the giant
branch. In Section 6.2, this work shows that whilst this is the case, in the
scenario that sufficient material is present in the outer planetary system,
the relatively low levels of metals observed in the atmosphere of WD
0141$-$675 could be supplied by scattering, whilst the star was orbited by a
planet on the original Gaia astrometric solution (see Table 1 for details). On
the other hand, atmospheric pollution from photoionisation atmospheric mass
loss and Jeans escape were both found to be implausible to explain the level
of accretion onto the white dwarf (see discussion in Section 6.1). Thus,
whilst the conclusion remains that on a pollution level, there is unlikely to
be as high levels of pollution in white dwarf planetary systems with close-in
giant planets compared to those with only lower mass (rocky) planets, it is
not possible to use atmospheric pollution to rule out the presence of close in
giant planets in an individual white dwarf planetary system.

##  8 Conclusions

Gaia is expected to astrometrically reveal of order 10 planets orbiting white
dwarfs (Perryman et al., 2014; Sanderson et al., 2022). This work shows that
follow-up observations, notably photometric and spectroscopic observations are
crucial to confirm the planetary nature of such companions. This work focuses
on the retracted astrometric planet candidate orbiting WD 0141$-$675 with
planetary mass of 9.26 M${}_{\textrm{Jup}}$ on an orbit with a period of 33.65
d as a case study. The main conclusions are as follows:

  1. 1.

Infrared observations from Spitzer and WISE can be used to rule out young,
massive planets. JWST MIRI is the only infrared instrument with the
sensitivity to detect close-in, giant planets of any age orbiting white
dwarfs.

  2. 2.

Archival low- and medium-resolution spectra can be used to obtain radial
velocities if the signal is $\gg 1$ km s-1. However, short cadence radial
velocity time series using high-resolution stable instruments such as VLT
ESPRESSO have the power to detect planetary mass objects on close-in orbits
around white dwarfs with radial velocity signatures $\ll 1$ km s-1. This is
however very costly in terms of telescope time, and thus most useful for
systems with robust companions.

  3. 3.

Double degenerates with nearly equal-brightness companions are a false
positive for astrometric planet signals. This is ruled out as an explanation
of the astrometric signal for the case study: the lack of spectral features
detected from the secondary, radial velocities constrain the binary mass to be
much less than a typical white dwarf mass, and fitting the white dwarf
parameters with the spectroscopic and photometric method separately reveal
consistent parameters. For future detections this kind of analysis will allow
the double degenerate false positive to be ruled out.

  4. 4.

N body simulations showed that atmospheric pollution from inwards scattering
of small asteroids is unlikely, but not impossible in white dwarf planetary
systems with close-in giant planets. Therefore, when planets are found around
polluted white dwarfs, it should be considered whether it is dynamically and
physically feasible to pollute the white dwarf with small bodies.

  5. 5.

WD 0141$-$675 is being polluted at a rate of 106 g s-1 the equivalent of a
small asteroid’s worth of material accreted each year. Scaling the calcium
abundance ([Ca/H] = $-$10.72) to bulk-Earth and Solar abundances, no
additional features should have been detected, meaning the spectra are
consistent with both bulk-Earth and Solar. Additional high-S/N and high-
resolution data would be required to determine further details on the
composition of the pollutant.

Given that so few planet candidates are known around white dwarfs, every
confirmation gives crucial insights into these evolving planetary systems and
the future of planetary systems. In particular, which planets survive post-
main sequence evolution and which ones do not; this provides information on
the efficiency of common envelope evolution for low mass companions, impacting
both occurrence rates of sub-stellar objects as well as binary evolution at
high mass ratios. Therefore, following up astrometric planet candidates
identified with Gaia around white dwarfs is crucial.

## Acknowledgements

We thank the referee for helpful comments that improved the manuscript. LR
acknowledges support of an ESA Co-Sponsored Research Agreement No.
4000138341\22\NL\GLC\my = Tracing the Geology of Exoplanets. AB and LR
acknowledge support of a Royal Society University Research Fellowship,
URF\R1\211421. RJA is grateful for a PhD Studentship from the Science and
Technology Facilities Council (STFC). SLC acknowledges support from an STFC
Ernest Rutherford Fellowship: ST\R003726\1. ZP acknowledges that this project
has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (Grant
agreement No. 101002511 - VEGA P). SX is supported by the international Gemini
Observatory, a program of NSF’s NOIRLab, which is managed by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation, on behalf of the Gemini partnership of
Argentina, Brazil, Canada, Chile, the Republic of Korea, and the United States
of America. This project has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (Grant agreement No. 101020057). MK acknowledges support by the
National Science Foundation under grant AST-2205736 and NASA under grant
80NSSC22K0479.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research made use of
pystrometry, an open source Python package for astrometry timeseries analysis
(Sahlmann, 2019).

## Data Availability

VLT X-shooter data available from the ESO archive
(http://archive.eso.org/eso/eso_archive_main.html). Magellan MIKE spectra are
available on reasonable request. The TESS data are available from the Mikulski
Archive for Space Telescopes (https://archive.stsci.edu/tess/). Spitzer data
available from the NASA/IPAC Infrared Science Archive
(https://irsa.ipac.caltech.edu/Missions/spitzer.html). HST STIS data are
available from the Mikulski Archive for Space Telescopes
(https://mast.stsci.edu/search/ui/#/hst).

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