A Giant Planet Candidate Transiting a White Dwarf
Andrew Vanderburg, Saul A. Rappaport, Siyi Xu, Ian Crossfield, Juliette C. Becker, Bruce Gary, Felipe Murgas, Simon Blouin, Thomas G. Kaye, Enric Palle, Carl Melis, Brett Morris, Laura Kreidberg, Varoujan Gorjian, Caroline V. Morley, Andrew W. Mann, Hannu Parviainen, Logan A. Pearce, Elisabeth R. Newton, Andreia Carrillo, Ben Zuckerman, Lorne Nelson, Greg Zeimann, Warren R. Brown, René Tronsgaard, Beth Klein, George R. Ricker, Roland K. Vanderspek, David W. Latham, Sara Seager, Joshua N. Winn, Jon M. Jenkins, Fred C. Adams, Björn Benneke, David Berardo, Lars A. Buchhave, Douglas A. Caldwell, Jessie L. Christiansen, Karen A. Collins, Knicole D. Colón, Tansu Daylan, John Doty, Alexandra E. Doyle, Diana Dragomir, Courtney Dressing, Patrick Dufour, Akihiko Fukui, Ana Glidden, Natalia M. Guerrero, Xueying Guo, Kevin Heng, Andreea I. Henriksen, Chelsea X. Huang, Lisa Kaltenegger, Stephen R. Kane, John A. Lewis, Jack J. Lissauer, Farisa Morales, Norio Narita, Joshua Pepper, Mark E. Rose, Jeffrey C. Smith, Keivan G. Stassun, Liang Yu
AA Giant Planet Candidate Transiting a White Dwarf
Andrew Vanderburg , , , Saul A. Rappaport , Siyi Xu , Ian Crossfield , Juliette C. Becker , ,Bruce Gary , Felipe Murgas , , Simon Blouin , Thomas G. Kaye , , Enric Palle , , CarlMelis , Brett M. Morris , Laura Kreidberg , , Varoujan Gorjian , Caroline V. Morley , An-drew W. Mann , Hannu Parviainen , , Logan A. Pearce , , Elisabeth R. Newton , AndreiaCarrillo , , Ben Zuckerman , Lorne Nelson , Greg Zeimann , Warren R. Brown , Ren´eTronsgaard , Beth Klein , George R. Ricker , Roland K. Vanderspek , David W. Latham ,Sara Seager , , , Joshua N. Winn , Jon M. Jenkins , Fred C. Adams , , Bj ¨orn Benneke , ,David Berardo , Lars A. Buchhave , Douglas A. Caldwell , , Jessie L. Christiansen , KarenA. Collins , Knicole D. Col´on , Tansu Daylan , , John Doty , Alexandra E. Doyle , DianaDragomir , Courtney Dressing , Patrick Dufour , , Akihiko Fukui , , Ana Glidden , , Na-talia M. Guerrero , Xueying Guo , Kevin Heng , Andreea I. Henriksen , Chelsea X. Huang , ,Lisa Kaltenegger , , Stephen R. Kane , John A. Lewis , Jack J. Lissauer , Farisa Morales , ,Norio Narita , , , , , Joshua Pepper , Mark E. Rose , Jeffrey C. Smith , , Keivan G.Stassun , , Liang Yu , Department of Astronomy, University of Wisconsin-Madison, Madison, WI 53706, USA Department of Astronomy, The University of Texas at Austin, Austin, TX 78712, USA NASA Sagan Fellow Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139,USA NSFs NOIRLab/Gemini Observatory, 670 N. Aohoku Place, Hilo, Hawaii, 96720, USA Dept. of Physics and Astronomy, University of Kansas, 1251 Wescoe Hall Dr., Lawrence, KS 66045, USA Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA
51 Pegasi b Fellow Hereford Arizona Observatory, Hereford, AZ 85615, USA Instituto de Astrof´ısica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain Dept. Astrof´ısica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain Los Alamos National Laboratory, P.O. Box 1663, Mail Stop P365, Los Alamos, NM 87545, USA Raemor Vista Observatory, 7023 E. Alhambra Dr., Sierra Vista, AZ 85650, USA Laboratory for Space Research, The University of Hong Kong, Pokfulam, Hong Kong, China Center for Astrophysics and Space Sciences, UCSD, CA 92093-0424, USA Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, CH-3012, Bern, Switzerland Max Planck Institute for Astronomy, K¨onigstuhl 17, 69117 Heidelberg, Germany Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA 02138, USA NASA Jet Propulsion Laboratory, 4800 Oak Grove Dr, Pasadena, CA 91109, USA Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA Steward Observatory, University of Arizona, Tucson, AZ 85721, USA NSF Graduate Research Fellow Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA Large Synoptic Survey Telescope Corporation Data Science Fellow Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1562, USA Department of Physics and Astronomy, Bishops University, Sherbrooke, QC J1M 1Z7, Canada Hobby Eberly Telescope, University of Texas, Austin, Austin, TX, 78712, USA DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 328, DK-2800 Kgs. Lyngby, Denmark Department of Earth and Planetary Sciences, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA NASA Ames Research Center, Moffett Field, CA, 94035, USA Physics Department, University of Michigan, Ann Arbor, MI 48109, USA Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA D´epartment de Physique, Universit´e de Montr´eal, Montr´eal, QC H3C 3J7, Canada Institut de Recherche sur les Exoplan`etes (iREx), Universit´e de Montr´eal, Montr´eal, QC H3C 3J7, Canada SETI Institute, Mountain View, CA 94043, USA Caltech/IPAC-NASA Exoplanet Science Institute, Pasadena, CA 91106, USA NASA Goddard Space Flight Center, Exoplanets and Stellar Astrophysics Laboratory (Code 667), Greenbelt, MD 20771, USA Kavli Fellow a r X i v : . [ a s t r o - ph . E P ] S e p Noqsi Aerospace, Ltd., 15 Blanchard Avenue, Billerica, MA 01821, USA Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, Los Angeles, CA, USA Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA Department of Astronomy, University of California - Berkeley, Berkeley, CA, 94720, USA Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,Japan Juan Carlos Torres Fellow Cornell University, Astronomy and Space Sciences Building, Ithaca, NY 14850, USA Carl Sagan Institute, Space Science Building 311, Ithaca, NY 14850, USA Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA Department of Physics and Astronomy, Moorpark College, 7075 Campus Road, Moorpark, CA 93021, USA Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan JST, PRESTO, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Komaba Institute for Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan Department of Physics, Lehigh University, 16 Memorial Drive East, Bethlehem, PA 18015, USA Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 USA Department of Physics, Fisk University, Nashville, TN 37208, USA ExxonMobil Upstream Integrated Solutions, Spring, TX 77389, USA
Astronomers have discovered thousands of planets outside the solar system , most of whichorbit stars that will eventually evolve into red giants and then into white dwarfs. Duringthe red giant phase, any close-orbiting planets will be engulfed by the star , but more dis-tant planets can survive this phase and remain in orbit around the white dwarf
3, 4 . Somewhite dwarfs show evidence for rocky material floating in their atmospheres , in warm debrisdisks , or orbiting very closely , which has been interpreted as the debris of rocky plan-ets that were scattered inward and tidally disrupted . Recently, the discovery of a gaseousdebris disk with a composition similar to ice giant planets demonstrated that massive plan-ets might also find their way into tight orbits around white dwarfs, but it is unclear whetherthe planets can survive the journey. So far, the detection of intact planets in close orbitsaround white dwarfs has remained elusive. Here, we report the discovery of a giant planetcandidate transiting the white dwarf WD 1856+534 (TIC 267574918) every 1.4 days. Theplanet candidate is roughly the same size as Jupiter and is no more than 14 times as mas-sive (with 95% confidence). Other cases of white dwarfs with close brown dwarf or stellarcompanions are explained as the consequence of common-envelope evolution, wherein theoriginal orbit is enveloped during the red-giant phase and shrinks due to friction. In thiscase, though, the low mass and relatively long orbital period of the planet candidate makecommon-envelope evolution less likely. Instead, the WD 1856+534 system seems to demon-strate that giant planets can be scattered into tight orbits without being tidally disrupted,and motivates searches for smaller transiting planets around white dwarfs. WD 1856+534 (hereafter, WD 1856 for brevity) is located 25 parsecs away in a visual triplestar system. It has an effective temperature of ± Kelvin and became a white dwarf 5.9 ± TESS ), in order to search forany periodic dimming events caused by planetary transits. A statistically significant transit-likeevent was detected by the
TESS
Science Processing Operations Center (SPOC) pipeline based2n 28 days of data acquired between 18 July and 14 August, 2019. The signal was rejected byan automated classification system designed to identify planets around main-sequence stars. Wenoticed the signal in a visual inspection of all possible transit-like events detected around whitedwarfs. As usual, caution is required when interpreting
TESS data because of the relatively coarseangular resolution; in this case, the white dwarf was blended together with several much brighterstars in the
TESS images. However, the signal’s duration of ≈ (cid:38)
30 minutes for the transit of a main-sequence star, strongly suggesting that thetransit signal originates from the white dwarf and not the other stars.To better characterize the transit signal, we obtained data with higher angular resolution.On 2019 October 10 and 17, we observed transits with three small privately-operated telescopes,revealing that the white dwarf dims by up to 56% for eight minutes. On 2019 October 22, weobserved a transit with two larger telescopes, the Telescopio Carlos S´anchez and Gran TelescopioCanarias (Figure 1). Together, these data show that a Jupiter-sized object transits the white dwarfin a grazing configuration (that is, the companion only occults part of the much smaller star).Jupiter-sized objects can have a wide range of masses, ranging from giant planets (withmasses as low as ∼ M J ) to low-mass stars ( ∼ M J ). Determining the mass is usuallyachieved through precise Doppler monitoring of the primary star. However, the spectrum of WD1856 is classified as type DC , a featureless continuum with no strong optical absorption or emis-sion features. Optical and near-infrared spectra from the MMT Telescope, Lick Shane Telescope,Gemini-North telescope, and Hobby Eberly Telescope confirmed this classification (Figure 2). Thelack of strong spectroscopic absorption features precludes precise Doppler observations.Instead, we constrained the mass of the transiting body based on the lack of any detectablethermal emission. We observed a transit on 2019 December 16 with NASA’s Spitzer
Space Tele-scope operating at wavelengths between 4 and 5 microns. At these infrared wavelengths, thethermal emission from a low-mass star or brown dwarf would make a larger fractional contributionto the total light than at the optical wavelengths of our other observations. This, in turn, wouldcause the fractional loss of light during transits to be smaller at infrared wavelengths than at op-tical wavelengths (absent slight differences in the stellar limb darkening profile between the twobands). Figure 1 compares the infrared and optical light curves. There is no discernible differencein the fractional loss of light; any thermal flux from the transiting body can be no more than 6.1%of the flux from the white dwarf (with 95% confidence).Such a faint object can only be a planet or a very low-mass brown dwarf, based on theoreticalmodels of brown dwarf evolution and atmospheres . Figure 3 shows the resulting constraintson the mass of the transiting companion as a function of the system age. A mass exceeding 13.8 M J is ruled out regardless of age (95% confidence), and the constraints for younger systems areeven stronger. The system’s motion through space suggests it is a member of the Galaxy’s thindisk, implying an age less than about 10 Gyr and a mass less than 11.7 M J (95% confidence).3 R e l a t i v e B r i gh t ne ss GTC (0.48 µ m) Depth = 56.65% ± -6 -4 -2 0 2 4 6Minutes from Midtransit0.20.40.60.81.01.2 R e l a t i v e B r i gh t ne ss -6 -4 -2 0 2 4 6Minutes from Midtransit Spitzer (4.5 µ m) Depth = 56.3% ± -6 -4 -2 0 2 4 6Minutes from Midtransit Figure 1: Transit observations of WD 1856. a , Optical transit observations with the Gran Telesco-pio Canarias and b , infrared transit observations with the Spitzer
Space Telescope. The red curvesare the best-fitting models. The horizontal colored shaded regions (light blue for GTC, light red for
Spitzer ) show the 68% confidence interval for the maximum loss of light. Any thermal emissionfrom the transiting body would have led to a smaller loss of light at infrared wavelengths. The lackof any observed difference implies that the transiting body has a mass smaller than 13.8 Jupitermasses (with 95% confidence). Each
Spitzer point is an average of five exposures (each with a twosecond exposure time), and the error bars show the 1 σ error on the mean. The uncertainties on theGTC points are smaller than the size of the symbols.Therefore, the transiting body almost certainly has a mass in the planetary regime .Most or all of the usual circumstances that sometimes result in “false positive” transitingexoplanet detections can be ruled out, given the data at hand. The ground-based transit observationsconfirm that the TESS signal is not an instrumental artefact or contamination from a differentsource. The transit duration is too long for the companion to be another white dwarf in either a 1.4or 2.8-day period orbit. There is no evidence for unresolved blended sources in archival images orin the astrometric data from ESA’s
Gaia mission. Even if there were a faint undetected companion,the transits are deep enough ( > >
50% transit depth implies that the signal also cannot be primary and secondary eclipses of anequal-temperature white dwarf/white dwarf binary. We conclude that WD 1856 is orbited by eithera giant planet or a very low-mass brown dwarf, which we designate WD 1856 b.To avoid destruction when WD 1856’s progenitor evolved into a red giant, WD 1856 b musthave been farther than about 1 AU from its host star, raising the question of how it arrived inthe close orbit we observe today. Most short-period white dwarf binaries, including the handful4
Wavelength ( Å ) N o r m a li z e d F l u x ( F ) HET/LRS2Gemini/GNIRSLick/KastMMT/Blue Channel
Figure 2: Spectroscopic observations of WD 1856. We show spectra from four observatories(the HET, the Gemini-North telescope, the Lick Shane telescope, and the MMT observatory) thathave been scaled to remove offsets in their absolute flux calibrations. The optical spectra show apure continuum, confirming the DC spectral classification, while the near infrared spectrum fromGemini-North shows only spurious features due to imperfect correction of the telluric absorptionand sky emission from Earth’s atmosphere.of known white dwarf/brown dwarf pairs , are believed to have formed via common envelopeevolution . In this theory, an expanding giant star grows large enough to engulf a lower-massbinary companion. Friction from the giant star’s gaseous envelope causes the companion to rapidlyspiral inward towards the giant’s dense core, depositing its orbital energy into the envelope. Ifthe companion and core have enough gravitational potential energy, the envelope can be ejected,halting the companion’s orbital evolution and resulting in a binary system with an orbital periodranging from hours to days. If there is not enough gravitational potential energy to unbind theenvelope, then the companion continues spiraling inward towards the giant star’s core until theymerge.It is difficult to explain WD 1856 b’s current orbit with standard common envelope theory.Compared to a list of known close white dwarf/brown dwarf binaries that were thought to haveformed via common envelope evolution, WD 1856 b has by far the combination of lowest mass andlongest orbital period of any similar system. This implies that the gravitational potential energyreleased during the common envelope phase is very small, which in turn makes it difficult tosuccessfully eject the envelope of the WD progenitor. The amount of gravitational potential energy5 System Age (Gyr) M a ss o f W D b ( M J ) P l a n e t s B r o w n D w a r f s % ( ) % ( ) . % ( ) J y J y J y . J y . J y . J y Figure 3: Allowed mass range for WD 1856 b as a function of the system age. Giant planetsand brown dwarfs cool and contract as they age, so higher masses are allowed by our
Spitzer observations for older systems. The masses and ages comprising the greyed-out region at the topof the plot (high masses) are excluded by the lack of any detectable thermal emission with
Spitzer .The blue and red regions are the allowed ranges for planet and brown dwarf solutions, respectively,and are separated by the traditional 13 M J deuterium burning limit. The 1 σ (68% confidence), 2 σ (95%), and 3 σ (99.7%) regions are shaded with darker regions representing increasingly unlikelysolutions. Several additional contours of constant brightness in the Spitzer µm band are shownand labeled. To convey that the system’s most likely age is (cid:46)
10 Gyr, the background has beenshaded darker for much older ages.to be released is ∆ φ (cid:39) − GM wd M com a = (cid:18) πGP (cid:19) / M wd M com ( M wd + M com ) / ∝∼ M com ( M wd /P ) / (1)where M wd , M com , a , and P are the WD mass, companion mass, orbital separation, and orbitalperiod, respectively, after the common envelope. The brown dwarfs in the systems compiled inref tend to have masses of at least 50-60 M J and orbital periods in the range of ∼ (cid:46) M J ) and long orbital period ( ∼
34 hr) could therefore have released only ∼
15 times less gravitational potential energy than the other systems listed in ref . More formally,we calculated that throughout most of the progenitor’s giant phases, WD 1856 b’s gravitationalpotential energy release was insufficient to eject the progenitor giant star’s envelope and avoidmerging with its core (see Methods ). Some groups have suggested that the envelopes own internalenergy could contribute to its ejection , but even this extra energy source appears insufficientfor WD 1856 b to have ejected the envelope. WD 1856 b can likely only have formed by this6echanism if the common envelope phase began after much of the envelopes mass had alreadybeen lost. Given the difficulty in forming WD 1856 b via common envelope evolution and thedegree to which it stands out from the population of known post-common envelope binaries, weconclude that the system’s current configuration most likely formed via some other mechanism.Instead, a more likely formation history is that WD 1856 b was a planet that underwent dy-namical instability. It is well established that when stars evolve into white dwarfs, their previouslystable planetary systems can undergo violent dynamical interactions
13, 25 that excite high orbitaleccentricities. We have confirmed with our own simulations that WD 1856 b-like objects in multi-planet systems can be thrown onto orbits with very close periastron distances. If WD 1856 b wereon such an orbit, the orbital energy would have rapidly dissipated due to tides raised on the planetby the white dwarf
26, 27 . The final state of minimum energy would be a circular short-period orbit.WD 1856’s advanced age ( ≈ ∼ Gyr) dy-namical processes to take place. In this case, it is no coincidence that WD 1856 is one of the oldestwhite dwarfs observed by
TESS .Future observations should be able to confirm the planetary nature of WD 1856 b or (lesslikely) show that it is a low-mass brown dwarf. The amplitude of features in a planet’s transmissionspectrum depend inversely on the strength of its surface gravity. If WD 1856 b has a mass closeto that of Jupiter, its spectral features could have amplitudes of about 1%. However, weak spectralfeatures do not necessarily imply a large mass for WD 1856 b, because spectral features can bemuted by high altitude clouds or hazes . Another path to measuring WD 1856 b’s mass would beto replicate our Spitzer observations with the upcoming
James Webb
Space Telescope (
JWST ).With its much larger collecting area, a single
JWST transit observation should either detect thermalemission from WD 1856 b or place a strong enough constraint on its mass to solidify its planetarynature.WD 1856 b will be a focus of future observational and theoretical studies. If the object’s massis low enough for it to cool to its equilibrium temperature (about 165 K), transmission spectroscopyobservations could probe species like methane and ammonia in the atmosphere of one of the coldestknown transiting planets . If instead WD 1856 b has a higher mass and has retained some ofits primordial heat, the white dwarf’s low luminosity means infrared observations with JWST could reveal WD 1856 b’s thermal emission spectrum with unusual detail. Regardless of its exactmass, WD 1856 b demonstrates that low-mass objects can migrate into close orbits around whitedwarfs while avoiding total tidal disruption. Unlike common envelope evolution, which predictsthat low-mass objects will merge with their host star’s core, there is no reason why the dynamicalmechanisms we invoke to explain WD 1856 b’s formation could not also be applied to even smallerplanets, similar in size to Earth .1. Akeson, R. L. et al. The NASA Exoplanet Archive: Data and Tools for Exoplanet Research.Publ. Astron. Soc. Pacif. , 989 (2013).2. Villaver, E. & Livio, M. The Orbital Evolution of Gas Giant Planets Around Giant Stars.7 able 1: Summary of parameters for WD 1856+534 system.
Parameter Value Value (Eccentric Fit) Source
Other Designations
TIC 267574918TOI 1690LP 141-142MASS J18573936+5330332
Gaia
DR2 2146576589564898688
Astrometric parameters
Right Ascension 18:57:39.34
Gaia
Declination +53:30:33.3
Gaia
Right ascension proper motion 240.759 ± Gaia
Declination proper motion -52.514 ± Gaia
Parallax 40.3983 ± Gaia
Distance to Star 24.754 ± Gaia
Literature and New Photometric measurements g ± r ± i ± z ± y ± G ± Gaia B P ± Gaia R P ± Gaia J ± H ± K ± W ± W ± W > σ ) ALLWISE W > σ ) ALLWISEIRAC 4.5 µm ± White Dwarf Stellar Properties
Mass ( M (cid:63) ) 0.518 ± M (cid:12) this workRadius ( R (cid:63) ) 0.0131 ± R (cid:12) this workRadius ( R (cid:63) ) 1.429 ± R ⊕ this workSurface Gravity ( log g cgs ) 7.915 ± T eff ) 4710 ±
60 K this workCooling Age ( t cool ) 5.85 ± log Ca / (H + He) ) < − . this workIron abundance ( log Fe / (H + He) ) < − . this workMagnesium abundance ( log Mg / (H + He) ) < − . this workSodium abundance ( log Na / (H + He) ) < − . this workSulphur abundance ( log S / (H + He) ) < − . this work Planet Candidate Properties
Orbital Period ( P ) ∗ ± ± t t ) 2458779.3750828 ± ± R p /R (cid:63) ) 7.28 ± +3 . − . this workScaled semimajor axis ( a/R (cid:63) ) 336 ±
14 325 ±
18 this workSemimajor axis ( a ) 0.0204 ± ± i ) 88.778 ± +1 . − . deg this workOrbital eccentricity ( e ) 0 < σ ) this workTransit Duration ( t ) 7.998 ± ± R p ) 10.4 ± R ⊕ +5 . − . R ⊕ this workTransit impact parameter ( b ) 7.16 ± +3 . − . this workIncident Flux ( S ) 0.181 ± S ⊕ +0 . − . S ⊕ this workEquilibrium Temperature ( T eq ) ∗∗ +14 − K 164 +14 − K this work
Spitzer
Dilution Parameter ( d ) 0.004 ± ± µm magnitude > σ ) > σ ) this workAbsolute IRAC 4.5 µm magnitude > σ ) > σ ) this workThe reported uncertainties represent 68% confidence intervals (1 σ ) unless stated otherwise.*The reported orbital period is the value measured by observers in our Solar System’s barycentric frame (i.e. slightly Doppler shifted from the orbitalperiod in the WD 1856 system’s rest frame).**Equilibrium temperature T eq calculated assuming an albedo α uniformly distributed between 0 and 0.7 and perfect heat redistribution. T eq = T eff (1 − α ) / (cid:113) R (cid:63) a . , L81–L85 (2009).3. Luhman, K. L., Burgasser, A. J. & Bochanski, J. J. Discovery of a Candidate for the CoolestKnown Brown Dwarf. Astrophys. J. , L9 (2011).4. Marsh, T. R. et al. The planets around NN Serpentis: still there. Mon. Not. R. Astron. Soc. , 475–488 (2014).5. Jura, M. A Tidally Disrupted Asteroid around the White Dwarf G29-38. Astrophys. J. ,L91–L94 (2003).6. Kilic, M., von Hippel, T., Leggett, S. K. & Winget, D. E. Excess Infrared Radiation from theMassive DAZ White Dwarf GD 362: A Debris Disk? Astrophys. J. , L115–L118 (2005).7. Becklin, E. E. et al.
A Dusty Disk around GD 362, a White Dwarf with a Uniquely HighPhotospheric Metal Abundance. Astrophys. J. , L119–L122 (2005).8. G¨ansicke, B. T., Marsh, T. R., Southworth, J. & Rebassa-Mansergas, A. A Gaseous MetalDisk Around a White Dwarf.
Science , 1908 (2006).9. Wilson, T. G., Farihi, J., G¨ansicke, B. T. & Swan, A. The unbiased frequency of planetarysignatures around single and binary white dwarfs using Spitzer and Hubble. Mon. Not. R.Astron. Soc. , 133–146 (2019).10. Vanderburg, A. et al.
A disintegrating minor planet transiting a white dwarf. Nature ,546–549 (2015).11. Manser, C. J. et al.
A planetesimal orbiting within the debris disc around a white dwarf star.
Science , 66–69 (2019).12. Vanderbosch, Z. et al.
A White Dwarf with Transiting Circumstellar Material Far Outside ItsTidal Disruption Radius. arXiv e-prints arXiv:1908.09839 (2019).13. Debes, J. H. & Sigurdsson, S. Are There Unstable Planetary Systems around White Dwarfs?Astrophys. J. , 556–565 (2002).14. G¨ansicke, B. T. et al.
Accretion of a giant planet onto a white dwarf star. Nature , 61–64(2019).15. McCook, G. P. & Sion, E. M. A Catalog of Spectroscopically Identified White Dwarfs.Astrophys. J. Suppl. , 1–130 (1999).16. Nelson, L., Schwab, J., Ristic, M. & Rappaport, S. Minimum Orbital Period of Precata-clysmic Variables. Astrophys. J. , 88 (2018).17. Marley, M., Saumon, D., Morley, C. & Fortney, J. Sonora 2018: Cloud-free, solarcomposition, solar C/O substellar atmosphere models and spectra (2018). URL https://doi.org/10.5281/zenodo.1309035 .98. Spiegel, D. S., Burrows, A. & Milsom, J. A. The Deuterium-burning Mass Limit for BrownDwarfs and Giant Planets. Astrophys. J. , 57 (2011).19. Casewell, S. L. et al.
WD0837+185: The Formation and Evolution of an Extreme Mass-ratioWhite-dwarf-Brown-dwarf Binary in Praesepe. Astrophys. J. , L34 (2012).20. Littlefair, S. P. et al.
The substellar companion in the eclipsing white dwarf binary SDSSJ141126.20+200911.1. Mon. Not. R. Astron. Soc. , 2106–2115 (2014).21. Rappaport, S. et al.
WD 1202-024: the shortest-period pre-cataclysmic variable. Mon. Not.R. Astron. Soc. , 948–961 (2017).22. Parsons, S. G. et al.
Two white dwarfs in ultrashort binaries with detached, eclipsing, likelysub-stellar companions detected by K2. Mon. Not. R. Astron. Soc. , 976–986 (2017).23. Paczynski, B. Common Envelope Binaries. In Eggleton, P., Mitton, S. & Whelan, J. (eds.)
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IAU Symposium , 75 (1976).24. Xu, X.-J. & Li, X.-D. On the Binding Energy Parameter λ of Common Envelope Evolution.Astrophys. J. , 114–121 (2010).25. Veras, D. & G¨ansicke, B. T. Detectable close-in planets around white dwarfs through lateunpacking. Mon. Not. R. Astron. Soc. , 1049–1058 (2015).26. Goldreich, P. & Soter, S. Q in the Solar System. Icarus , 375–389 (1966).27. Veras, D. & Fuller, J. Tidal circularization of gaseous planets orbiting white dwarfs. Mon.Not. R. Astron. Soc. , 2941–2953 (2019).28. Kreidberg, L. et al. Clouds in the atmosphere of the super-Earth exoplanet GJ1214b. Nature , 69–72 (2014).29. Agol, E. Transit Surveys for Earths in the Habitable Zones of White Dwarfs. Astrophys. J. , L31 (2011). 10 ethods
TESS
Target Selection and Observations:
We discovered the transits of WD 1856 b in datafrom NASA’s
TESS mission . TESS is a satellite which observes a 96 ◦ by 24 ◦ region of sky withfour 10 cm optical cameras. TESS observes the same region of sky continuously for approximately28 days at a time; each 28 day observation is called a sector. Over the course of its two-year primemission,
TESS will observe 26 sectors, covering over 70% of the sky.
TESS collects and down-loads images of its entire field of view with 30-minute exposure times, but
TESS also observes20,000 carefully chosen targets each month with shorter (two minute) exposure times. Becausetransits of white dwarf stars typically have durations much shorter than the 30-minute cadence of
TESS ’s full frame image downloads, we proposed for two-minute-cadence observations of knownand candidate white dwarf stars.We first proposed
TESS observations of white dwarf stars in the Southern ecliptic hemi-sphere in late 2017, before the second data release (DR2) from ESA’s
Gaia mission enabled thediscovery of hundreds of thousands of new white dwarf candidates. We proposed two-minute ca-dence observations of white dwarfs in the Montreal White Dwarf Database (MWDD) brighterthan a magnitude of 17.5 in either V , I , or TESS bands and which are more than 20 (cid:48)(cid:48) from anybrighter stars which would contaminate the TESS photometric apertures. We also performed ourown search (using the same V or I or TESS ≤ . We used proper motions from the Hot Stuff for One Year catalog , Gaia G -band magnitudes, and 2MASS J -band magnitudes to calculate each stars RPM. We defined cutsin color/RPM space to select likely white dwarfs. A total of 615 unique white dwarf candidatesfrom our program were observed during TESS ’s first year of operations.For the second year of
TESS observations of the Northern ecliptic hemisphere, we identifiedtargets from a catalog of candidate white dwarfs based on Gaia
DR2. We proposed two-minuteobservations of all white dwarf candidates brighter than Gaia G -band magnitude of 17 with agreater than 75% probability of being a true white dwarf, and removed white dwarfs less than 20 (cid:48)(cid:48) from any brighter stars which would contaminate the TESS photometric apertures. Thanks to Gaia
DR2, our Northern target list was much more complete than our Southern list. So far (throughSector 19), a total of 1189 unique Northern white dwarf candidates from our program have beenobserved.Once the
TESS data on these targets were collected and downlinked from the spacecraft, theywere processed by the Science Processing Operations Center (SPOC) pipeline
35, 36 based at NASAAmes Research Center. The SPOC pipeline performed pixel-level calibrations, identified optimalphotometric apertures, extracted light curves, corrected for systematic errors and diluting flux fromnearby stars
37, 38 , and searched for periodic transit signals . The SPOC pipeline’s periodic transitsearch algorithm detected a convincing, 1.4 day period, short-duration transit signal around WD1856 (listed in the TESS
Input Catalog as TIC 267574918). The transits were first detected in
TESS ’s Sector 14 observations, but the signal was rejected by an automatic classification algorithm11esigned to separate viable planet candidates from false positives . We noticed WD 1856 in avisual inspection of all possible transit-like signals around white dwarfs identified by the SPOCpipeline (including those rejected by the automatic classifier), and initiated follow-up observations.Subsequently, WD 1856 was also observed in TESS
Sector 15 and Sector 19 (and will be observedagain in Sector 22 and 26). The transits were re-detected in a combined analysis of the Sector 14-15 data and in the Sector 19 data. After being rejected by the automatic classifier in Sectors 14 and15, WD 1856 b’s transit signal was promoted to the status of “planet candidate” in the Sector 19observations and was given the designation
TESS
Object of Interest (TOI) 1690.01.Though the
TESS data confidently revealed the presence of 6-8 minute long, 1.4 day periodtransits, and tests performed by the SPOC pipeline showed that the signal likely originated onWD 1856 (and not on some other nearby star), the
TESS light curve data were challenging tointerpret. Compared to many other ground-based or space-based telescopes,
TESS has relativelypoor spatial resolution.
TESS ’s optics focus about 50% of a given star’s light into one of its 20 (cid:48)(cid:48) pixels, and the wings of the point spread function (PSF) extend several pixels farther. This poseschallenges for observations of faint stars like WD 1856, especially since it is only about 40 (cid:48)(cid:48) (2pixels) away from a pair of physically associated M-dwarf stars (see below). The M-dwarfs areabout 100 times brigher than WD 1856 in the
TESS bandpass and contribute a significant amountof flux into WD 1856’s photometric aperture. In situations like this, the dilution correction appliedby the SPOC pipeline to the WD 1856 light curve is fairly uncertain given the difficulty in preciselymeasuring the wings of the
TESS
PSF. This uncertainty in the SPOC dilution correction translatedto a substantial uncertainty in the true depth of WD 1856 b’s transits.WD 1856 stands out among the stars targeted in our
TESS sample as one of the coolest, andtherefore oldest, white dwarfs we observed. Among the 1724 white dwarfs in our sample observedby
TESS in Sectors 1-19 with catalog reported effective temperatures , only 8 white dwarfs arecooler than WD 1856. Archival Imaging and Search for Companions
We searched for both wide and close stellarcompanions to WD 1856 in archival survey data. WD 1856 was previously believed to be partof a visual triple star system with a pair of M-dwarfs called G 229-20. G 229-20 consists oftwo nearly equal-brightness M-dwarf stars separated by about 2.3 arcseconds ( ≈ AU projectedseparation). The M-dwarf pair is located approximately 43 (cid:48)(cid:48) away from WD 1856 ( ≈ Gaia
DR2 show that G 229-20 A/B have nearly identical propermotions and parallaxes to WD 1856, confirming the three stars are physically associated. Fromhere on, we refer to the Northern component of the binary as G 229-20 A since it is slightly brighterin resolved photometry from
Gaia
DR2.We searched for additional co-moving companions in the
Gaia archive. We queried all starsin
Gaia
DR2 within 600 (cid:48)(cid:48) of WD 1856 (approximately 15000 AU projected separations) and lookedfor proper motions similar to WD 1856 and G 229-20 A/B. We found no stars with remotely similarspace motions to the WD 1856 system. 12e also checked to see if the
Gaia observations showed any evidence for close, unresolvedcompanions to either WD 1856 or G 229-20 A/B. Sometimes, close binary companions can intro-duce excess scatter into the
Gaia astrometric observations
41, 42 . This excess scatter is parameterizedin a statistic called the Renormalized Unit Weight Error (RUWE ). Solutions with low astrometricscatter have RUWE values close to 1, while stars whose astrometric solutions show anomalouslyhigh scatter (perhaps due to astrometric motion from an unresolved binary companion) tend tohave RUWE values greater than about 1.4. None of the members of the WD 1856 system showevidence for excess astrometric scatter that might reveal close companions; the RUWE values forWD 1856, G 229-20 A, and G 229-20 B are 1.04, 1.01, and 0.94 respectively.Finally, we searched for background stars at the present-day position of WD 1856 in archivalimaging. WD 1856 was observed in the Palomar Observatory Sky Survey (POSS) on 27 July1952 with a photographic plate with a blue sensitive emulsion. Due to its high proper motion,WD 1856 has moved over 16 arcseconds since being imaged by POSS, making it possible tosearch for background stars at WD 1856’s present-day position. There are no possible backgroundcontaminants at WD 1856’s current position brighter than the POSS image’s limiting magnitude(approximately 21 st magnitude in blue ). Extended Data Figure 1 shows the POSS image of WD1856 along with modern images from Pan-STARRS and TESS . Ground-based Transit Follow-up
Based on the orbital period and time of transit inferred fromthe
TESS observations of WD 1856, we planned ground-based transit observations to confirm thetransit signal and measure its true depth. We observed transits of WD 1856 b on 10 October 2019and 17 October 2019 (UTC) with three small privately owned ground-based telescopes in Arizona:a 16-inch telescope at the Hereford Arizona Observatory (operated by Bruce Gary), a 16 inchtelescope at Raemor Vista Observatory, and a 32-inch at Junk Bond Observatory (both operatedby Thomas G. Kaye). We observed in white optical light without any color filter; our effectivebandpass was defined by the telescope systems’ throughput and the CCDs’ quantum efficiency.Weather conditions on both nights were clear and stable. The data were reduced following standardprocedures for these telescopes . All three telescopes confidently detected the transit signal with aconsistent ≈
60% depth on both nights.The data showed that the depths of odd and even numberedtransits are indistinguishable and both greater than 50% of the total brightness, so WD 1856 mustnot be a nearly equal-brightness eclipsing binary star with a true orbital period of 2.8 days (sincethe sum of the depths of a binary’s primary and secondary eclipse cannot exceed 100%).After confirming the transits and determining the depth, we observed another transit of WD1856 b with two larger telescopes to more precisely determine the transit shape and attempt to de-tect or rule out any color dependence in the transit depth. We observed a transit of WD 1856 on 22October 2019 with the MuSCAT2 instrument on the 1.52 meter Telescopio Carlos S´anchez andwith the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy(OSIRIS) imager/spectrograph on the 10.4 meter Gran Telescopio Canarias (GTC). MuSCAT2provides simultaneous multi-color images of a 7 . (cid:48) × . (cid:48) g , r , i , and z s . We reduced the observations with the stan-dard MuSCAT2 pipeline and detected the transit with the same depth in each of the four MuSCAT213 OSS I Blue: 1952 ′′ WD 1856
Pan−STARRS g: 2011 ′′ WD 1856
Pan−STARRS g: 2011 ′ WD 1856G 229−20
TESS Sector 14: 2019 ′ Extended Data Figure 1: Archival imaging of WD 1856. a , From the Palomar Observatory SkySurvey on a photographic plate with a blue-sensitive emulsion. b , From the Panoramic SurveyTelescope and Rapid Response System (Pan-STARRS) survey in g band. c , From the Pan-STARRSsurvey in g band, zoomed out to show the co-moving M-dwarf pair (labeled G 229-20). d , Co-added TESS image from Sector 14. The photometric apertures for the three sectors of TESSobservations (14, 15, and 19) are shown as red, purple, and blue colored outlines, respectively. Thepresent-day location of WD 1856 is shown with a red cross in all images.14ands. Our GTC observations used OSIRIS as an imager to obtain a precise g (cid:48) -band light curve ofWD 1856. We obtained 10-second exposures of WD 1856 and read out the detector in frame trans-fer mode, which allowed us to observe nearly continuously (one frame was being read out whilethe next was exposing). We reduced the observations using standard IRAF scripts to calibrate theimages and extract light curves for both WD 1856 and comparison stars. We experimented withdifferent sized photometric apertures, and found that a 6 pixel aperture minimized the scatter in thelight curve. The resulting light curve was extremely precise (0.5% scatter per 10 second exposure)and revealed a smooth, symmetric 56% deep transit.Our follow-up light curves are shown in Extended Data Figure 2, compared to the TESS discovery light curve (corrected for the dilution from nearby stars).
Spectroscopy of WD 1856
A previous study assigned WD 1856 the spectral type classificationof DC, indicating a continuum dominated spectrum with very few weak absorption features . Wesought to confirm this classification and detect any weak absorption features by collecting ourown optical spectroscopic observations. We observed WD 1856 on 5 October 2019 with the BlueChannel spectrograph on the 6 meter MMT telescope at Fred L. Whipple Observatory. We usedthe 500 line/mm grating and achieved 3.8 ˚A spectral resolution over a bandpass from 3700-6800˚A. A 10 minute exposure yielded a signal-to-noise ratio of about 50 per pixel or 80 per resolutionelement. The resulting spectrum confirmed the DC spectral classification.We continued searching for features in WD 1856’s spectrum by extending our wavelengthcoverage beyond the red limits of our MMT Blue Channel observations. We obtained 60 minuteexposures of WD 1856 on both 11 October 2019 and 12 October 2019 with the Kast DoubleSpectrograph on the 3 meter Shane Telescope at Lick Observatory. On both nights, we configuredthe blue arm of the spectrograph to yield spectra with a resolving power R = λ/ ∆ λ = ) on the 10 meter Hobby Eberly Telescope at McDonald Observatory.LRS2 is a combination of two integral field dual-channel spectrographs: one operating in the blue(3700 to 7000 ˚A) and one operating in the red (6500 to 10500 ˚A). We observed WD 1856 with thetwo blue channels of LRS2 with a spectral resolving power of R = λ/ ∆ λ = R = . The pipeline performs basicCCD reduction tasks, wavelength calibration, fiber extraction, sky subtraction, and flux calibration.We used the flux-calibrated, fiber extracted spectra for the UV and orange channels to construct asingle data cube correcting for differential atmospheric refraction and the small 0 . (cid:48)(cid:48) R e l a t i v e B r i gh t ne ss + O ff s e t TESS
SpitzerGTCGary/Kaye oddGary/Kaye evenMuSCAT2 gMuSCAT2 rMuSCAT2 iMuSCAT2 z s -5 0 5Minutes from Mid-transit01234567 R e l a t i v e B r i gh t ne ss + O ff s e t Extended Data Figure 2: All transitobservations of WD 1856. From topto bottom, we show the light curves(arbitrarily offset for visual clarify)from
TESS ; data from several pri-vate telescopes in Arizona (operatedby Gary and Kaye) with odd andeven-numbered transits shown sepa-rately; simultaneous light curves infour colors from MuSCAT2; a lightcurve from the GTC, and a light curvefrom
Spitzer . The individual two-minute-cadence
TESS flux measure-ments are shown as grey points, andthe rose-colored points are averagesof the brightness in roughly 30 sec-onds in orbital phase. The
TESS datahave been corrected for dilution fromnearby stars so that the transit depthmatches that of the GTC data.LRS2 spectra had the highest signal-to-noise ratio of all of our observations, but still showed nocompelling evidence for any spectral features. In particular, the LRS2 spectra rule out any H α absorption feature deeper than about 1%.Finally, we observed WD 1856 on 21 November 2019 with the Gemini Near InfraRed Spec-16rograph (GNIRS
33, 51 ) on the 8.1m Gemini-North telescope (program ID GN-2019B-DD-107) atMaunakea Observatory in Hawaii. The 32 l/mm grating was used in the cross-dispersed mode,which provides continuous wavelength coverage from 1.0-2.5 micron. A slit width of 1 . (cid:48)(cid:48) R ≈ ∼ . (cid:48)(cid:48)
35 in H band around the target. Data reductionwas performed using the XDGNIRS pipeline v2.2.6. The correction for sky emission featuresand absorption due to Earth’s atmosphere was imperfect and introduced some artefacts into thedata, but we saw no evidence that any of the features in the data are actually spectral lines fromWD 1856’s atmosphere.Our spectra of WD 1856 are shown in Figure 2. Spectroscopy of G 229-20 A/B
We also obtained ground-based optical spectra of G 229-20 A/B,the co-moving pair of companions to WD 1856. We observed G 229-20 A and B with the KastDouble Spectrograph on the 3 meter Shane Telescope at Lick Observatory. These observationswere conducted on 11 October 2019, the same night as the first of our two Kast observations ofWD 1856, and were taken with an identical instrument setting (R = 1300 from 3420-5480 ˚A andR = 3500 in the red from 5570 to 7860 ˚A). Seeing conditions were good enough to resolve the twostars, so we observed them simultaneously by rotating the spectrograph slit to the position angle ofthe binary and placing both stars on the slit. We extracted spectra of the two stars using standardIRAF routines. While the stars were resolved, there was still some blending along the spatial axis.We obtained medium-resolution spectra of G 229-20 A/B with two different echelle spec-trographs. One spectrum came from the FIbre-fed Echelle Spectrograph (FIES ) on the NordicOptical Telescope (NOT) on the island of La Palma, Spain on 2020 February 18. We used FIESin high-efficiency mode, in which the spectrogaph is fed with a 2 . (cid:48)(cid:48) . We obtainedthe second spectrum with the Tillinghast Reflector Echelle Spectrograph (TRES ) on the 1.5 me-ter telescope on Mt. Hopkins, Arizona on 2020 February 24. We used the standard instrumentalsetup with the spectrograph fed by a 2 . (cid:48)(cid:48) . We cross-correlated thespectra with an archival observation of Barnard’s Star and found that the absolute radial velocityof G 229-20 A/B is 17.9 ± km s − (on the IAU standard system ). We also inspected the H α line for G 229-20 A/B from the FIES spectrum. G 229-20 A/B have H α in absorption, with anequivalent width of -0.32 ˚A (where equivalent width is defined to be positive for emission features).We also used an archival spectrum of G 229-20 A published in a previous work . Theobservation was made on 25 August 2006 with the MkIII spectrograph on the McGraw-Hill 1.3meter telescope at MDM Observatory and covered the wavelength range of 62008700 ˚A. Theauthors assigned the star a spectral type of M3.5.17 pitzer Observations
We observed a transit of WD 1856 b with the InfraRed Array Camera(IRAC) on NASA’s
Spitzer
Space Telescope on 2019 December 16. We observed in IRAC Chan-nel 2, the reddest possible channel (sensitive to wavelengths of light between 4 and 5 microns) tobest constrain the thermal flux from a faint, cool companion. We followed standard procedures forprecise photometric observations with IRAC. We began with a 30-minute long “burn-in” periodwhere we obtained dithered images of WD 1856 to allow both the spacecraft and detector to settleinto equilibrium prior to the actual transit observations. We then observed WD 1856 for approx-imately two hours surrounding the predicted time of transit from our ground-based observations.These observations were conducted in “peak-up” mode, where WD 1856 was carefully placed ona well-characterized pixel known to have minimal sensitivity variations. Images from a 32 × Spitzer data with the Photometry for Orbits, Eclipses, and Transits (POET)pipeline . POET extracts raw light curves from the images and optimizes a transit model whilesimultaneously modeling and removing spacecraft systematic errors. We investigated differentsizes for the photometric aperture and found the best results with a relatively small 1 pixel radius(as expected for a star as faint as WD 1856). We optimized the transit and systematics model usingMarkov Chain Monte Carlo (MCMC). The transit of WD 1856 was clearly detected in the Spitzer observations with nearly identical characteristics to the optical transit observations.We also used the out-of-transit
Spitzer observations to measure the combined flux of WD1856 and WD 1856 b in IRAC Channel 2. We measured the flux using standard aperture pho-tometry as done in previous
Spitzer observations of white dwarfs
60, 61 using a 2 pixel (1.2 arcsec)aperture (while applying a correction for any flux lost outside the aperture). We determined thetotal combined flux from WD 1856 and WD 1856 b in IRAC band 2 to be 173 ± µ Jy . Wealso searched for other faint red companions in the Spitzer observations. We coadded the individ-ual
Spitzer subarray observations to yield a deep (cid:48)(cid:48) × (cid:48)(cid:48) image of the region surrounding WD1856 b. We detected one faint source (at RA=18:57:39.9, Dec= +53:30:48.9), with a measuredflux of 27 ± µ Jy without an optical counterpart. Given its distance from WD 1856 (16 (cid:48)(cid:48) or 400AU projected separation) and the M-dwarf companions (30 (cid:48)(cid:48) or 750 AU projected separation), webelieve the source is more likely to be a background star or galaxy than a bound companion (sincethe probability of a chance alignment is high). Otherwise, we find no additional sources near WD1856 with flux greater than 16 µ Jy (3 σ confidence), which at the distance of the WD 1856 systemcorresponds to brown dwarfs with mass m > M J (for ages up to 13.8 Gyr). White Dwarf Stellar Properties
We determined fundamental stellar parameters for WD 1856 us-ing archival photometric observations and our high signal-to-noise optical spectra from the HET.We followed the procedure of Blouin et al. (2019) and fit cool white dwarf spectral and evolu-tionary models to broad-band photometry from the Pan-STARRS and 2MASS surveys and thetrigonometric parallax from Gaia
DR2. We modeled WD 1856’s SED/spectra with atmosphereswith a variety of different compositions ranging between H / He = 10 − and H / He = 10 . We18ompared the predicted depth of the H α absorption feature from the different models with the ob-served HET spectrum (Extended Data Figure 4); pure helium and most hydrogen/helium mixturesare consistent with our observed spectrum, but if WD 1856 b had a pure hydrogen atmosphere (ornearly so), we likely would have seen an H α absorption feature in our HET spectra. The mod-els with at least some helium also were a better match to the observed SED; a pure hydrogenmodel over-predicts WD 1856’s NIR flux, while models with at least some helium better matchthe observations (see Extended Data Figure 3).We derived the white dwarf’s fundamental stellar parameters from the results of our fits tothe model atmospheres with varying ratios of hydrogen and helium. We found that a model withequal quantities of hydrogen and helium (50%/50% H/He) gave the best fit to the data. The result-ing stellar parameters for some of the models we evaluated are given in Extended Data Table 1.The fits to pure hydrogen and 50%/50% H/He mixture yielded fairly consistent stellar parameters,while the pure helium atmosphere gave a significantly larger white dwarf and lower stellar mass.This discrepancy is due to the effects of He-He-He collision-induced absorption (CIA) in a purehelium atmosphere, which absorbs a significant fraction of a white dwarf’s infrared flux . How-ever, the efficiency of this opacity source is fairly uncertain, and it is plausible that its effects areoverestimated in the pure He model.We adopt the stellar parameters from the 50%/50% H/He model that best matched our ob-servations and use them throughout the rest of the paper. However, since WD 1856’s atmosphericcomposition is not well constrained, we adopted conservative uncertainties on our stellar parame-ters. We inflated the formal uncertainties on the mass and radius from our model fits by adding a10% and 3.3% uncertainty in quadrature, respectively. Our final, adopted values for the star’s massand radius are: M (cid:63) = ± M (cid:12) and R (cid:63) = ± R (cid:12) .We tested how much our results depend on the specific white dwarf models used by rederiv-ing WD 1856’s stellar parameters using alternate methods. We fit WD 1856’s spectral energydistribution (SED) with a simple blackbody curve and found a best-fit temperature of T eff = 4720 ±
50 Kelvin, a bolometric flux F bol = 3.93 × − ± × − erg s − cm − , and a stellar ra-dius of R (cid:63) = 0.01298 ± R (cid:12) . Using an approximate fitting formula designed to mimicthe mass/radius relation from simple zero-temperature (black dwarf) models and assuming a 2:1oxygen/carbon ratio, we calculated a mass of M (cid:63) = 0.54 ± M (cid:12) . We also estimated WD 1856’scooling age using analytic relations and found t cool ∼ . All of these values are in good agreement with our adopted values, indicating that ourresults are fairly robust to different model assumptions.Finally, we used the non-detection of spectroscopic features to place upper limits on theabundance of other elements in WD 1856’s atmosphere. With our HET spectrum, we place stronglimits on the presence of Ca, Fe, Mg, Na. When found in the atmospheres of white dwarfs, theseelements are usually attributed to accretion from tidally disrupted rocky bodies like asteroids orsmall planets. Since WD 1856 b is roughly the size of Jupiter, we also searched for elementsmore consistent with the composition of a giant planet’s atmosphere, like those recently found in19he atmosphere of WD J0914+1914 . It is harder to constrain the abundances of these elementsbecause they show few spectral features at wavelengths covered by our spectroscopy. We can ruleout sulphur abundances greater than log ( S/H ) = − . , but this limit is weaker than the measuredsulphur abundance on WD J0914+1914. Future observations with higher spectral resolution andsignal-to-noise will test whether WD 1856 shows evidence of accretion from its companion. F ν ( µ Jy ) PanSTARRS 2MASS WISE SpitzerPure Hydrogen50% Hydrogen, 50% HeliumPure HeliumBlackbody
Extended Data Figure 3: Spectral energy distribution of WD 1856. Photometric measurementsfrom Pan-STARRS , 2MASS , WISE , and Spitzer , are shown as blue, orange, dark red, andpink points. The formal 1 σ (standard deviation) photometric uncertaitines on the Pan-STARRSand WISE points are smaller than the symbol size. Three different SED models are shown as solidcurves: a pure hydrogen atmosphere model (red), a 50% hydrogen, 50% helium model (blue), anda blackbody curve (black). None of the three SED models capture all of the SED’s features, but allthree yield relatively consistent effective temperatures and stellar parameters. M-dwarf Stellar Properties
We determined the masses of G 229-20 A/B using broadband pho-tometry and their
Gaia
DR2 trigonometric parallax measurements. In most photometric surveys(including 2MASS and Pan-STARRS), G 229-20 A and B are not well resolved and only have com-bined flux measurements. The two stars are, however, resolved in
Gaia
DR2 and have individuallyreported flux measurements. We converted the flux ratio of A/B from
Gaia
DR2 to a flux ratio in2MASS K -band using spectrophotometric standards from Mann et al. (2015 ). We then estimatedthe mass of each star using the M K S − M ∗ relation from Mann et al. (2019 ), forcing the total K S -band flux to match the unresolved measurement. This yielded masses of 0 . ± . M (cid:12) and . ± . M (cid:12) for A and B, respectively. The unresolved 2MASS K S measurement has a pho-tometric quality flag indicating a very poor profile fit (as expected for a close visual binary), so we20
30 640 650 660 670 680Wavelength (nm)0.960.981.001.021.04 N o r m a li z ed F l u x Pure Hydrogen Model50% Hydrogen/50% Helium ModelPure Helium ModelHET LRS2 Spectrum
Extended Data Figure 4: Spectrum of WD 1856 near the H α line. Our summed HET/LRS2 spec-trum (black connected points) is shown in comparison with three atmosphere models: a pure hy-drogen model (red), a 50% hydrogen, 50% helium model (blue), and a pure helium model (gold).We likely rule out a pure hydrogen atmosphere based on our non-detection of an H α feature inour LRS2 spectra, but otherwise remain uncertain about the precise composition of WD 1856’senvelope.also derived masses using the same method but without using the 2MASS measurement (and onlythe Gaia G -band magnitude), which yielded more conservative mass estimates of . ± . M (cid:12) and . ± . M (cid:12) . We choose to adopt these more conservative estimates to avoid any possiblesystematics associated with the 2MASS data.We checked these results for consistency by fitting the SED of the two stars instead ofempirical relations. Here, we fit only the resolved Gaia G , B P , and R P magnitudes. We fixed theeffective temperature of each M-dwarf to the values determined in the TICv8 ( T eff , A = 3521 Kand T eff , B = 3513 K) since those were already based on the resolved Gaia G BP − G RP colors,and determined the bolometric flux of the two stars using the Gaia parallax. We determined theradii of the two stars to be R (cid:63),A = 0 . ± . R (cid:12) , and R (cid:63),B = 0 . ± . R (cid:12) . Converting fromradii to masses using relations between the mass/radius of M-dwarfs and their absolute K-bandmagnitudes
74, 76 yields M (cid:63),A = 0 . ± . M (cid:12) , and M (cid:63),B = 0 . ± . M (cid:12) . These resultsare in good agreement with our adopted masses. Triple System Orbit Analysis
We investigated the orbits of the three stellar components in theWD 1856 system of WD 1856 and G 229-20 A/B about the system’s center of mass.
Gaia
DR221easured highly precise positions and proper motions for the three stars, so we used the Linear Or-bits for the Impatient (LOFTI ) algorithm to derive orbital constraints from these observations.Given input proper motions, positions, radial velocities (if available), and masses of the stellarcomponents, LOFTI uses rejection sampling to determine probability distributions for differentorbital parameters.We ran LOFTI to determine parameters for the orbit of WD 1856 and G 229-20 A/B aboutthe system’s center of mass. For the latter, we approximated G 229-20 A/B as a point mass. Weused the masses determined in our earlier analysis, and ran LOFTI until the rejection samplingalgorithm had accepted 50,000 possible orbits. We found that the outer orbit is likely viewedclose to face on (inclination i = 22 +11 − degrees) and may be modestly eccentric ( . +0 . − . ). Thesemimajor axis is a = 1500 +700 − AU, and the separation between WD 1856 and the center of massof G 229-20 at closest approach is a (1 − e ) = 1030 +130 − AU.We also ran LOFTI to determine parameters for the orbit of G 229-20 A and B about eachother. Again, we ran the rejection sampler until we accumulated 50,000 samples in our posteriorprobability distribution. G 229-20 A and B orbit with a semimajor axis a = 58 +54 − AU and have aseparation of a (1 − e ) = 39 +27 − AU at their closest approach. The eccentricity of the orbit is notwell constrained, with e < . (95% confidence) and the posterior probability distribution for theinclination peaks near 50 degrees ( i = 51 +11 − degrees). Transit Analysis
We determined the best-fit values and uncertainties on the transit parametersand the flux of WD 1856 b at 4.5 microns with a simultaneous MCMC analysis of the GTC and
Spitzer light curves. We first selected a small portion of both the
Spitzer and GTC light curves nearthe observed transits; we used
Spitzer data collected at times . ≤ BJD ≤ . and GTC data from . ≤ BJD ≤ . (after converting the GTC timestampsto BJD TDB ). For convenience, we down-sampled the two-second-cadence Spitzer light curveby a factor of 5 to match the 10-second cadence of the GTC light curve points. We divided the
Spitzer and GTC data by the median out-of-transit flux measurement to set the out-of-transit fluxlevel to 1. We estimated uncertainties on each point in the light curves by multiplying a value forthe out-of-transit scatter (from the standard deviation of the normalized out-of-transit points) bythe square root of each flux value.We fit the transits with exact analytic transit light curve models for stars with quadraticlimb darkening laws coupled to a code for solving Kepler’s equation (for fits with nonzero ec-centricity). We oversampled the model light curves by a factor of 6 and integrated to account forthe 10-second exposure time of both the GTC observations and our binned Spitzer observations.We fixed the limb darkening parameters for the white dwarf to values calculated from model atmo-spheres. For our GTC g (cid:48) -band observation we used coefficients specifically calculated for whitedwarfs by Gianninas et al. (2013 ). The Gianninas coefficients ( u = 0 . , u = 0 . ) closelymatch coefficients independently calculated by Claret et al. (2019 , u = 0 . , u = 0 . ). Forour Spitzer observation we used coefficients from models of main sequence stars with the sameeffective temperature ( u = 0 . , u = 0 . ). We modeled WD 1856 b’s flux contribution (if any)22 − − . . . . . . . . . . . − . − . . . . − − . . . . . .
300 320 340 360 380 − . − .
05 0 0 .
05 0 . . Extended Data Figure 5: Posterior probability distributions of transit parameters. This “corner-plot” shows correlations between pairs of parameters in our MCMC transit fit (with circular orbitsenforced) and histograms of the marginalized posterior probability distributions for each parameter.For clarity, we have plotted correlations with the inclination angle i instead of the fit parameter cos i and subtract the median time of transit ( t t ). The orbital inclination i , scaled semimajor axis a/R (cid:63) , and planet/star radius ratio R p /R (cid:63) are strongly correlated due to the grazing transit geometrybut constrained by the prior on stellar density. We do not include rows for the GTC and Spitzer photometric jitter terms because these are nuisance parameters which showed no correlations withthe other physical parameters. 23o the
Spitzer light curve by fitting for a dilution term d ≡ F WD 1856 b /F WD 1856 . We calculated andre-normalized the
Spitzer transit model M S ( t ) from the un-diluted transit model M ( t ) : M S ( t ) = M ( t ) + d d (2)At each MCMC link, we subtracted the transit models from the GTC and Spitzer light curves,fit a quadratic polynomial to the residual light curves, and added this polynomial curve to the transitmodel. This step marginalizes over any possible trends and normalization errors in the two lightcurves. We fit for two additional photometric error terms (one for GTC and one for
Spitzer ) addedin quadrature to our calculated uncertainties and imposed a Gaussian prior on the density of WD1856 centered at 324,000 g cm − with a width of 54,000 g cm − based on our stellar parameters.Our knowledge of the stellar density lets us calculate WD 1856 b’s average orbital speed viaKepler’s third law (see Seager & Mall´en-Ornelas 2003 ) and link the transit duration (a directobservable quantity) to the planet candidate’s radius. This information, along with a constraint onthe transit impact parameter from the maximum depth of the transit, helps the MCMC converge toa well-behaved solution.The transit of WD 1856 is grazing, so even when imposing a prior on the white dwarf’sstellar density, the radius of the transiting object is almost completely degenerate with the object’sorbital speed at the time of transit. We therefore performed one fit assuming a circular orbit andanother fit allowing for orbital eccentricity. When we assumed circular orbits, we fit for 10 freeparameters: orbital period, time of transit, cosine of the orbital inclination ( cos i ), scaled semimajoraxis ( a/R (cid:63) ), planet/star radius ratio ( R p /R (cid:63) ), photometric jitter terms for both the Spitzer and GTClight curves, and the
Spitzer dilution parameter d . Other than our prior on stellar density (whichmostly affects a/R (cid:63) ), we used uniform priors with bounds ( −∞ , ∞ ) on all parameters except forthe jitter terms, a/R (cid:63) , R p /R (cid:63) , which we restricted to [0 , ∞ ) , and cos i , which we restricted to [0 , . We did not impose a prior to force the dilution parameter to be positive to avoid a Lucy-Sweeney-like bias. We explored parameter space with an affine invariant MCMC sampler with50 walkers evolved for 200,000 steps (discarding the first half for burn-in).For our fits allowing eccentric orbits, we changed our parameterization to speed the MCMCconvergence. Instead of exploring parameter space in cos i , we defined a new parameter δ ≡ R p /R (cid:63) − b , where b = a/R (cid:63) cos i is the transit impact parameter to avoid a strong correlationbetween R p /R (cid:63) and b . We also fit for combinations of eccentricity e and argument of periastron ω ( √ e sin ω and √ e cos ω ) for a similar reason. We imposed a physical cutoff for high eccentricityorbits; at each link, we calculated WD 1856 b’s instantaneous Roche lobe radius at periastron R L : R L ≈ .
46 (1 − e ) a (cid:18) M p M (cid:63) (cid:19) / (3)assuming a planet mass M p = 15 M J (see below). We discarded any links where the planet’s sizeexceeded this radius, which prevented the fit from diverging towards high eccentricities and large24ompanion radii. Even with these modifications, the eccentric fit was much slower to converge; weevolved 50 walkers for 8,000,000 links, discarding the first 5,000,000 to remove the burn-in phaseand save disk space. Correlations between selected parameters for both the circular and eccentricfits are shown in Extended Data Figures 5 and 6.Both fits showed that WD 1856 b is a roughly Jupiter-sized object. If its orbit is circular, WD1856 b has a radius R p = 10.4 ± R ⊕ ; if eccentric orbits are allowed, the uncertainty on the radiusis significantly larger: R p = 15.4 +5 . − . R ⊕ . Radii smaller than about 7 R ⊕ are strongly ruled out inboth cases, so the companion cannot be another white dwarf. Our fits also revealed that the transitdepth at 4.5 micron wavelengths is nearly identical to the optical transit depth. We measure the Spitzer dilution parameter d = 0 . ± . . Evidently, the flux of WD 1856 b is only a smallfraction of the white dwarf itself at 4.5 microns. This places strong constraints on the temperature(and therefore mass) of WD 1856 b, as described below.In principle, using inaccurate limb darkening coefficients in our fits can adversely affectour measurement of the dilution coefficient and planet radius. We tested the robustness of ourresults to such errors by running additional MCMC fits where the limb darkening coefficients werefree parameters constrained by basic physical priors . We ran three separate fits: one where the Spitzer limb darkening coefficients were restricted to likely values ( u < . , u < . ) and theGTC coefficients were fixed to model values; one with the Spitzer coefficients free and the GTCcoefficients fixed to the model values; and one where both the GTC and
Spitzer limb darkeningcoefficients were free. Our results are insensitive to the limb darkening coefficients; our fit withthe
Spitzer coefficients restricted to ( u < . , u < . ) and GTC coefficients fixed to modelvalues gave statistically identical results to our baseline fit. Even when both the Spitzer and GTCcoefficients were allowed to freely vary, the dilution parameter and R p /R (cid:63) shifted by only 0.2 σ and 0.4 σ , respectively. Companion Mass Limit
We quantified the constraints placed by our
Spitzer observations usingbrown dwarf/giant planet evolutionary and atmosphere models. From our measurement of d = F WD 1856 b /F WD 1856 at 4.5 microns from our transit fits, and our measured total flux of WD 1856and WD 1856 b at 4.5 microns (173 ± µ Jy ), we calculate the flux of WD 1856 b at 4.5 microns: F WD 1856 b = d F WD 1856 = F total / d = 0 . ± . µ Jy (4)When we exclude all unphysical solutions where d < , we calculate 68%, 95% and 99.7% upperlimits on F WD 1856 b at 4.5 microns that are 5.2, 10.2, and 15.5 µ Jy , respectively. We emphasizethat this limit on WD 1856 b’s flux at 4.5 microns is model independent and does not rely on ourwhite dwarf stellar parameters or SED fit.We used the Sonora grid of cloud-free solar metallicity brown dwarf/giant planet modelsto relate the thermal flux at 4.5 microns to atmospheric parameters like effective temperature andsurface gravity. We interpolated the predicted thermal flux in IRAC Channel 2 from the Sonora at-mosphere models onto two sets of evolutionary models: the underlying models used in the Sonora25 − . . . . −
100 0 100
84 86 88
250 300 350
Extended Data Figure 6: Posterior probability distributions of transit parameters when eccentric or-bits are allowed. This “corner-plot” shows correlations between pairs of parameters in our MCMCtransit fit (allowing eccentric orbits) and histograms of the marginalized posterior probability dis-tributions for each parameter. This plot shows a subset of the parameters that correlate with theorbital eccentricity. For clarity, we have plotted correlations with the eccentricity e , argument ofperiastron w and orbital inclination i instead of the fit parameters √ e cos ω , √ e sin ω , and δ .atmosphere calculations, and a more densely-sampled grid of models produced using the Modu-lar Experiments in Stellar Evolution (MESA) code. We found that the two evolutionary grids gavenearly identical results, and adopted the MESA models given their denser sampling.The MESA brown dwarf models predict the properties of objects with masses from 2.1 M J to 104 M J over 20 Gyr of evolution and are sampled at a total of 329,732 points in the mass/ageplane. We compared the predicted 4.5 micron flux for each of these model points to determine theallowed brown dwarf masses given our constraints. We assume that WD 1856 b must be at leastas old as the white dwarf’s cooling age (roughly 5.85 Gyr) and cannot be older than the age of the26niverse (13.8 Gyr), so we ignore any model points outside this age range. We found that for theoldest (13.8 Gyr) possible brown dwarfs/giant planets, we constrain the mass to be less than 11.1 M J at 68% confidence (1 σ ), 13.8 M J at 95% confidence (2 σ ), and 16.1 M J at 99.7% confidence(3 σ ). The object’s temperature must be below (250 K, 290 K, 320 K) at (1 σ , 2 σ , 3 σ ) confidence.The tail of WD 1856 b’s allowed mass distribution straddles the 13 M J deuterium burninglimit traditionally used to distinguish giant planets and brown dwarfs . However, using thedeuterium burning limit to distinguish planets from brown dwarfs is imprecise. There is likelyno specific mass above which deuterium burning takes place in brown dwarfs; instead the limitlikely spans a range from about 11-16 M J (depending on the object’s composition and how onedefines the onset of deuterium burning). It may also be more appropriate to divide planets andbrown dwarfs by their formation histories
94, 95 . Given the lack of a clear division between planetsand brown dwarfs, we refer to WD 1856 b as a planet candidate until future observations can placestronger constraints on its mass.These upper limits on WD 1856 b’s mass are model dependent, so we tested how they changewhen we use different model grids and assumptions. We repeated our calculation using the newATMO 2020 evolutionary and atmospheric models . Since these models were only calculatedto an age of 10 Gyr, we compared the 1 σ , 2 σ , and 3 σ upper mass limits with those for for 10Gyr objects with the Sonora/MESA models. We found good agreement in the mass upper limitsbetween the two models (within about 2 M J , with ATMO 2020 models yielding a lower 1 σ masslimit and a higher 3 σ mass limit due to stronger dependence of 4.5 µm flux on mass). We alsotested the effects of non-equilibrium chemistry, which can be important for cold brown dwarfs ,using the ATMO 2020 models. Even strong disequilibrium chemistry ( log K zz ∼ . ) had aminimal effect on our mass limits.The effect of clouds on our mass limits is more difficult to quantify. In general, the presenceof clouds slows the cooling of brown dwarfs and giant planets, so objects with clouds shouldgenerally remain hotter and more luminous throughout their evolution . However, when cloudsare present, they can significantly change the object’s spectrum and tend to decrease the flux inthe 4.5 µm band . Water clouds are expected to form in giant planets and brown dwarfs coolerthan about 375 K , so in the case of WD 1856 b, these two effects will likely compete. Futuremodeling should more fully reveal which effect dominates. Age of the WD 1856 system
Because giant planets and brown dwarfs cool as they age, our masslimits are stronger for younger systems. We therefore attempted to place additional constraints onthe total system age in addition to the white dwarf cooling age (age (cid:38) . Gyr) and the age ofthe universe (age < . Gyr) . One possible way to measure the age of a white dwarf is to addthe white dwarf’s cooling age to the estimated main sequence lifetime of its progenitor star usinga white dwarf initial/final mass relation. Unfortunately, two factors make it difficult to estimate theprogenitor’s age. First, the white dwarf initial/final mass relations assume the star evolved as anisolated single star and did not undergo mass/transfer or a common envelope phase. As we showbelow, though it is difficult, it is perhaps not impossible that WD 1856 b reached its current orbit27y this mechanism. Second, a white dwarf progenitor’s lifetime is a sensitive function of the whitedwarf’s final mass; a 50% increase in a white dwarf’s mass from 0.5 M (cid:12) to 0.75 M (cid:12) correspondsto a 275% increase in the progenitor’s mass from 0.8 M (cid:12) to 3 M (cid:12) and a corresponding factor of ∼
20 decrease in the star’s main sequence lifetime (from ∼
10 Gyr to ∼ Myr). With a massof 0.52 M (cid:12) , the white dwarf initial/final mass relation favors a long-lived progenitor with a massless than that of the Sun and a total system age at least 15 Gyr, older than the age of the universe.Since our white dwarf model spectra struggle to describe our observations (see above), we suspectthat systematic errors in our estimate of WD 1856’s mass likely explain the system’s apparentlyunphysical age. If the true mass were closer to 0.6 M (cid:12) (only ≈ . σ away given our conservativeuncertainties), this tension would disappear. We conclude that given these uncertainties, estimatingWD 1856’s progenitor’s lifetime cannot give a reliable system age.Extended Data Figure 7: H α equivalent width for G 229-20 A/B compared to other nearby M-dwarfs. The histogram shows the H α equivalent widths for large sample of M-dwarfs with similarspectral types from the Sloan Digital Sky Survey . G 229-20 A/B (shown as a blue arrow) havelower than average H α equivalent width, but fall well within the distribution of field M-dwarfs.We then shifted our attention to the binary M-dwarf pair G 229-20 A/B. Presumably thesestars formed together with WD 1856’s progenitor, and therefore should be the same age as WD1856’s planet candidate. It is notoriously difficult to determine the age of old ( (cid:38) α in emission, and light curves of the two stars from TESS , the ASAS-SN survey, and28he SuperWASP survey show no evidence for a rotational variability. This is unsurprising since weassume G 229-20 A and B must have formed before WD 1856 became a white dwarf about 5.85Gyr ago. However, we also saw no evidence that G 229-20 A/B are particularly old. Like mosttypical field age M-dwarfs, the spectra G 229-20 A/B show a band of prominent Calcium Hydride(CaH) and Titanium Oxide (TiO) absorption features often characterized using the ζ T iO/CaH parameter ; if G 229-20 A/B were old sub-dwarfs, we would expect ζ T iO/CaH < . , but thevalue is 0.93, consistent with most Solar-metallicity M dwarfs. G 229-20 A/B’s H α equivalentwidth (a proxy for magnetic activity and therefore age ) is lower than average, but still wellwithin typical ranges for field M-dwarfs (see Extended Data Figure 7). We also investigatedthe system’s galactic kinematics. Using the system’s position, proper motion, and parallax from Gaia
DR2 along with our measured radial velocity (with an inflated uncertainty to account for theM-dwarfs’ motion about the system barycenter), we calculated the system’s 3D space motion to be(U,V,W) = (8.65 ± ± ± km s − with respect to the Local Standard of Rest(LSR ). We calculated the relative probabilities that the WD 1856 system is a member ofthe galactic thin disk, thick disk, or halo, and found that WD 1856 is most likely (93%) a memberof the thin disk, with only about a 7% chance that it is part of the thick disk. Halo membershipis strongly disfavored (4000:1 odds against). The mean age for stars in the thin disk is about 7-8Gyr (with large spread), and the oldest stars in the thin disk are probably around 8-10 Gyr inage . Thick disk stars are about 1.5-2 Gyr older on average than thin disk stars, with a meanage of ≈ .All in all, these lines of evidence point to a system that is fairly old, but not likely to be mucholder than about 10 Gyr. If we assume the system is no older than 10 Gyr, WD 1856 b’s mass mustbe less than (9.4 M J , 11.9 M J , 13.6 M J ) at (1 σ , 2 σ , 3 σ ) confidence. Common Envelope Evolution
When WD 1856’s progenitor star was on the main sequence, thecompanion WD 1856 b must have orbited farther from the progenitor than it does today, or it couldnot have survived the progenitor’s red giant evolutionary phase. Here, we consider how WD 1856b might have reached its current orbit close to WD 1856. One obvious possibility for placinga massive planetary object in a relatively close orbit with a white dwarf is common envelopeevolution
23, 112, 113 . Nelson et al. (2018) investigated the likelihood that short-period, detachedbinaries containing a brown dwarf (or low-mass M-dwarf) companion in orbit with a white dwarf(or hot subdwarf) could have been formed via a common envelope (‘CE’) phase of evolution. Theycompiled a table of 25 binaries with orbital periods between 68 min and 4 hours and showed thatthe measured masses of the companions, which typically fall in the range of 50100 M J , are notinconsistent with the predictions of CE evolution. There are some detached systems having orbitalperiods longer than 4 hours with companion masses in this range, but none that we are aware ofwith periods as long as that of WD 1856 (1.4 days). Nonetheless, we will now examine whetherit is possible for a 15 M J object (at the upper end of our allowed mass distribution) to eject theenvelope of a low-mass giant and end up in an orbit as long as 1.4 days.There are a number of different ways to formulate the initial-final orbital separation ( a f − a i )during a CE phase based on conservation of energy. The basic idea is to determine the final binary29rbital separation once the low-mass companion has ejected the CE of the progenitor, in termsof the initial orbital separation of the primordial binary and its constituent masses. More recenttreatments of the energy formulation take into account the fraction of the internal energy used toeject the envelope, for example the recombination energy
24, 114–116 . Conservation of energy relates a f to a i as follows: GM p M e λr L a i = α (cid:20) GM c M s a f − GM p M s a i (cid:21) , (5)where M p and M s are the masses of the primordial primary (the WD progenitor) and the primordialsecondary star (in this case the massive planet), respectively, and M c and M e are the masses ofthe core and envelope of the primary star . The parameter λ − is a measure of the totalgravitational binding energy of the envelope to itself and to the core of the primary star in units of − GM p M e /R p , while α is an energy efficiency parameter for ejecting the common envelope. Thefactor r L ≡ R L /a i is the dimensionless radius of the Roche lobe of the primary star when masstransfer commences. If the internal energy (e.g., electron recombination) is taken into account,then either α or λ may be considered to be larger than unity
24, 116, 119 .Extended Data Figure 8: Theoretical relationships between the a star’s radius and the mass ofits core. We show MIST evolution tracks in the radius–core-mass plane for solar compositionmodels with masses ranging from 1-2.8 M (cid:12) . The RGB phase is clearly identifiable for core massesbetween 0.2 and 0.47 M (cid:12) , while the thermal pulses on the AGB are readily recognized at highercore masses of (cid:38) . M (cid:12) . The lime green curve is the analytic expression given by Eqn. (8). Thevertical lines for each star mark the point where the envelope has been exhausted by the AGB wind.For the masses and separations relevant to the formation of the WD 1856 system, the secondterm in square brackets in Eqn. (5) is negligible compared to the first term (see Rappaport et al.,30015 for a more detailed analysis). Upon dropping that term, we find: a f a i (cid:39) λαr L (cid:18) m c m s m e m p (cid:19) . (6)where lower-case masses are implicitly expressed in solar units. In turn, this can be expressed asthe ratio of final to initial orbital periods: P f P i (cid:39) (cid:18) λαr L (cid:19) / (cid:18) m c m s m e m p (cid:19) / (cid:18) m p + m s m c + m s (cid:19) / . (7)Since the mass of the degenerate core of low-mass stars is closely related to the radius of the giant,it also follows that there is a relation between the orbital period and giant’s core mass when masstransfer commences.We illustrate the R ( M c ) relation in Extended Data Figure 8. Here we show MIST evolu-tion tracks for solar metallicity stars in the radius–core mass plane. These are for 7 different initialstellar masses covering the range of 1.0 to 2.8 M (cid:12) . On the first red giant branch there is a commonlocus of upper limits to the radius, while on the Asymptotic Giant Branch (AGB) the same is true,with the main difference being the thermal pulses during which the radius varies substantially. Thelime green curve superposed on the plot is an analytic expression that represents fairly well thelocus of upper limits – which is where mass transfer to a companion star would first occur. Theexpression R ( m c ) (cid:39) . × m / c m c + 10 m c + 4 R (cid:12) (8)(for 0.7 (cid:38) M c (cid:38) . M (cid:12) ) is modeled after Eqn. (5) in Rappaport et al. (1995 ) and inferredfrom Eqn. (12) in Kalomeni et al. (2016 ), with some minor modifications.The orbital period that corresponds to a primary with core mass m c and which is just fillingits Roche-lobe with the secondary star is: P i (cid:39) . × f ( m c ) / r / L √ m p + m s days (9) with : f ( m c ) ≡ m / (1 + 20 m + 10 m ) + f where f = 7 . × − . Here r L has the same meaning as in Eqns. (6) and (7).We now combine Eqns. (7) and (9) into a single equation for the post-common envelopeperiod, P pce , and associate the system masses in Eqn. (7) with those we observe in WD 1856: m c ≡ m wd , m s ≡ m com , and m e ≡ m p − m c , where the subscript “com” stands for the current31ompanion to the WD which we believe is a gas-giant planet: P pce (cid:39) . × ( λα ) / f / ( m wd )( m wd + m com ) / (cid:20) m wd m com ( m p − m wd ) m p (cid:21) / days . (10)Note that the period of the post-CE system is a function only of the masses of the companion, thewhite dwarf, and its progenitor.For the WD 1856 system we know P f = 1 . d, M wd = 0 . M (cid:12) , and we will take M com (cid:39) . M (cid:12) as an upper limit on the mass of the current companion object. Thus, wecan use Eqn. (10) to find the required value of αλ as a function of the primary mass (progenitor ofthe WD): αλ (cid:39) . × − P / f ( m wd ) − ( m wd + m com ) / ( m p − m wd ) m p m wd m com . (11)Finally, in Extended Data Figure 9 we plot Eqn. (11) as a function of the mass of the primaryprogenitor star of the current WD. From this figure we can see that for progenitor masses of 1, 2,and 3 M (cid:12) , values of the parameter αλ = 2 . , , and 38 would be required to unbind the envelopes.According to Xu et al. (2010 ), the calculated values of αλ , including internal energies are (cid:46) . , (cid:46) , and (cid:46) , respectively (when the stellar radii are in the relevant range of 100–250 R (cid:12) ),considerably less than the values required for WD 1856 b to eject the primary star’s envelope.Without invoking internal energy, it appears even more improbable that a 15 M J object couldunbind the common envelope of the white dwarf’s progenitor.We explored whether WD 1856 b could have plausibly ejected a common envelope at anypoint in its progenitor’s evolution by calculating the required αλ value from the MIST tracksdirectly. At each point in the MIST tracks where the primary star was expanding to engulf newregions of its solar system, we calculated the required αλ assuming an orbit for WD 1856 b suchthat the primary star was just filling its Roche lobe. We calculated the minimum αλ during threedifferent intervals in the progenitor star’s evolution: before the star reached the thermally pulsatingAGB phase and began rapidly losing mass, before 30% of the progenitor’s envelope mass had beenlost, and at any point in the star’s evolution. Our values for αλ as a function of stellar mass andat different points in the progenitor’s evolution are also shown in Extended Data Figure 9. Ourcurve of the minimum αλ prior to the AGB confirms the results from our analytic study: it isenergetically difficult for WD 1856 b to eject the envelope while most of its mass is still in place.Even once 30% of the envelope’s mass is lost, it is still difficult to eject the envelope; typical αλ values of 1-10 indicate that WD 1856 b’s gravitational potential energy is insufficient, but theenvelope perhaps could be ejected if a large fraction of the envelope’s internal energy contributedto its ejection. By the very end of the AGB phase, once about 50%-60% of the envelope’s masshas been lost, the minimum αλ values become less than unity. The observed population of postcommon envelope binaries suggests that towards the end of the AGB phase, λ could be as highas 10, so it is possible that WD 1856 b could eject its progenitor’s envelope (though the population32lso favors values of α (cid:46) . ). However, given the relatively small region of parameter space inwhich this mechanism could produce WD 1856 b’s current orbit, we consider common envelopeevolution less likely than the dynamical explanation outlined below. O • )0.11.010.0100.01000.0 α λ S ys t e m A ge > . G y r Analytic: Prior to any mass lossAnalytic: After 0.1 M O • lostMIST: Prior to AGB phaseMIST: Prior to 30% of envelope lostMIST: Any point in evolution O • )0.11.010.0100.01000.0 α λ Extended Data Figure 9: The minimum value of the efficiency parameter αλ required for WD1856 b to form via common envelope as a function of the progenitor stellar mass. The two dashedcurves show the minimum αλ values from our analytic calculation (Equation 11) required for a15 M J object to eject the primary star’s envelope. The purple dashed curve is taken directly fromEquation 11, while the brown dashed curve results if the progenitor star has lost 0.1 M (cid:12) in a stellarwind by the time of the common envelope. The three solid curves curves show the minimum αλ computed directly from MIST tracks in three different situations: before the star reaches the AGB(red), before more than 30% of the star’s envelope mass has been lost (black), and at any point inthe star’s evolution, regardless of the mass lost (blue). Stars in the grey region at low masses evolvetoo slowly for the system to have left the main sequence more than 5.85 Gyr ago and are not viablesolutions. For values of αλ > (horizontal grey line), one must invoke the internal energy of thestar to help unbind the envelope during the common envelope phase. Before mass is lost duringthe AGB phase, it is difficult for WD 1856 b to eject the common envelope, but it is possible WD1856 b could have ejected its progenitor’s envelope if the common envelope phase began after theprogenitor reached the AGB. We have smoothed the lower two curves to remove some unphysicalscatter likely due to numerical artefacts in the model grids.For planets that might manage to eject the envelope of the WD progenitor, at least in princi-33le, there are some other perils that may await it. Passy et al. (2012 ) examined whether planetsand brown dwarfs would be disrupted by ram pressure during their passage through the dense innerenvelopes of the giant during the common envelope phase. They conclude that brown dwarfs andJovian-mass objects (including a M J planet) are not likely to lose significant mass during theirpassage, whereas lower-mass planets could well be destroyed. Bear & Soker (2011 ) studied themass loss of planets that might survive the common envelope, only to find themselves in the intenseradiation of the nascent white dwarf (see also Schreiber et al. 2019 ). Bear & Soker (2011 )concluded that, while lower mass planets might be obliterated by evaporation, Jovian planets andthose of higher mass might well survive to the point where the WD has cooled sufficiently forplanetary evaporative losses to become insignificant. Thus, if WD 1856 b had somehow been ableto successfully eject the envelope of its progenitor, it might then survive the subsequent heating bythe very hot white dwarf. However, we caution that these conclusions are very dependent on theassumed input physics of the models. Dynamical Formation
Given the difficulty explaining WD 1856 b’s current orbit with commonenvelope evolution we investigated other ways to form the system. Here, we consider whether WD1856 b could have reached its current orbit as a result of dynamical scattering after WD 1856’sprogenitor evolved into a white dwarf. This framework has two main components: (i) perturbingWD 1856 b into a high-eccentricity orbit with a close periastron passage and (ii) dissipating theorbital energy to shrink the planet’s semimajor axis and shorten the orbital period to 1.4 days. Weconsider these two processes separately.
Generating a short periastron distance for WD 1856 b:
Since WD 1856 b must have formedand evolved far away ( (cid:38) -Lidov effect . We ran a small set of N-body simulationsusing
Mercury6 with the four known bodies in the WD 1856 system, initialized with WD 1856b in a circular orbit with a distance of 1-2 AU about WD 1856, and with G 229-20 A/B orbiting ata distance of about 1000 AU, consistent with the result of our LOFTI orbit fits (described above).Under these conditions (and when the mutual inclination between the orbits of WD 1856 b and G229-20 A/B is large enough), G 229-20 A/B do induce Kozai-Lidov cycles in WD 1856 b’s orbit,but the timescales are slow ( (cid:38)
100 million years) and the amplitudes of the eccentricity oscillationare low (e ∼ e (cid:38) . eccentricity and close periastron passages.Even if G 229-20 A/B could not have decreased WD 1856 b’s periastron distance by excit-ing its eccentricity, it is possible that additional (undiscovered) bodies in the system could have.Previous work
13, 25 has shown that systems of multiple planets residing exterior to the red giant ex-pansion radius (but in a relatively well-packed configuration) can remain dynamically stable until34fter the WD has formed and begun cooling, then experience potentially violent instabilities. Veras& Gansicke (2015 ) found that increasing the number of planets in their simulations resulted inmore extreme dynamical evolution, including periastron passages as close as that of WD 1856 b.We ran an additional set of N-body simulations to confirm that the pattern seen by Veras & Gan-sicke (2015) holds true for systems with giant planets like WD 1856. Again, we used Mercury6 to calculate the evolution of multi-planet systems. We initialized our simulations with up to fourplanets in closely packed orbits, with equal masses to WD 1856 b. Though our simulations are notan exhaustive exploration of parameter space, they do confirm that in multi-planet systems, vio-lent dynamical instabilities can lead to planets being ejected from the system, sent onto a collisioncourse with the white dwarf, or into orbits with small periastron distances.
Dissipating orbital energy and shrinking the semimajor axis:
If WD 1856 b had been per-turbed into a highly eccentric orbit with a close periastron passage, it must have dissipated much ofits orbital energy to end up with a 1.4 day period like we see today. We investigated whether tidaleffects could dissipate WD 1856’s orbital energy quickly enough to nearly circularize the planet’sorbit in the roughly 5.85 Gyr cooling age of the white dwarf. Because WD 1856 is very small anddense, any tides raised on the white dwarf by the planet will be small and have negligible dissipa-tive effects. Instead, any tidal dissipation in WD 1856 b’s orbit must be due to tides raised on theplanet by its star.The problem of tidally dissipating orbital energy for planets in highly eccentric orbis aroundwhite dwarfs has previously been studied by Veras and Fuller (2019a and 2019b ). They cal-culated the total time needed to circularize a highly eccentric orbit as the sum of two differenttidal regimes: a chaotic tidal regime at high eccentricities (e (cid:38) . ), where dissipation is domi-nated by the exchange in energy between the orbit and internal modes, and a classic tidal regime,at e (cid:46) . , where dissipation is dominated by equilibrium tides. Veras and Fuller calculatetimescales for the completion of the chaotic tidal regime for gas giant planets and find typicalvalues between 1 and 100 million years – we conservatively choose a timescale at the high-endof their estimates for the WD 1856 system. We then estimated the time needed for the system tocircularize from e ≈ . via equilibrium tides with: t circ = 6 a Q p m p n p k p m ∗ R p , (12)where a is the planetary semimajor axis, Q p is the planetary tidal quality factor, m p the planetarymass, n p the planetary mean motion (related to the orbital period P by n = 2 π/P ), k p the planetaryLove number, m ∗ the stellar mass, and R p the planetary radius . Plugging in parameters for theWD 1856 system, and assuming WD 1856 b has Jupiter’s mass, radius, and Q/k p (estimated to be Q J /k p,J ≈ ), we estimate a tidal circularization timescale of about 2 Myr. Larger planetmasses (5-10 M J ) and more conservative estimatates of Q/k p up to should still circularizewithin the white dwarf’s cooling age. All together, the timescale for tidal circularization of WD1856 b’s orbit is comfortably less than the system’s age.We note that these processes could just as easily be applied to smaller planets than WD 185635. Packed systems of Earth-mass planets should exhibit the same dynamical instabilities that candrive close periastron distances for giant planets , and tidal circularization should be even moreefficient for rocky Earth-sized planets than gas giants like WD 1856. We estimate that tides raisedon an Earth-sized planet should dissipate its orbital eccentricity within about 500,000 years. Thisformation pathway could potentially lead to the production of habitable-zone rocky planets . Oldwhite dwarfs cool slowly and could provide a relatively stable radiation environment for billions ofyears ; we estimate that WD 1856 b’s current orbital location was in the circumstellar habitablezone for almost 3 Gyr. WD 1856 b may demonstrate a mechanism that can lead to a secondgeneration of habitability in a planetary system. Other theories
We also explored other mechanisms that might be able to lead to WD 1856 b’s cur-rent orbital configuration. We consider these other mechanisms less likely since they require eitherfinely-tuned or a priori unlikely initial conditions to succeed, but mention them for completeness.
Close Stellar Encounters:
WD 1856 may have been perturbed from its initial, long-periodorbit by a close flyby with another star. We estimated the most likely distance of closest approach D closest between WD 1856 and another star during its 5.85 Gyr cooling age: D closest ∼ ( π v t cool n ) − / (13)where v is the typical stellar velocity in WD 1856’s vicinity ( ≈ km s − ), t cool is the cooling age(5.85 Gyr), and n is the number density of stars in WD 1856’s vicinity. We estimated n using thefact that there are about 6000 stars within 25 parsecs of the sun from Gaia
DR2, giving a densityof about 0.1 star per cubic parsec. We find D closest ∼ AU, so likely within its cooling lifetime,another star has passed by within the orbit of G 229-20 A/B. However, a much closer approachthan 600 AU would be required to perturb WD 1856 b from a ∼ p of such a close approach decreases as p ∝ D − . Dynamical Instabilities from Galactic Tides:
Bonsor & Veras (2015 ) suggested that galac-tic tides could perturb the orbit of a wide white dwarf binary and lead to a close approach billionsof years after the system’s formation. This mechanism could provide a trigger for dynamical in-stabilities in old white dwarf systems. In principle, such a mechanism could be important to theformation of WD 1856 b given the old system age and the presence of wide visual companions.Bonsor & Veras (2015 ) calculate that for galactic tides to be important on timescales of a fewGyr, the semimajor axis must be greater than about a few thousand AU and the wide binary orbitmust be highly inclined with respect to the galactic plane (that is, the the pole of the orbit mustbe near the plane). Our fit to the WD 1856/G 229-20 orbit with LOFTI gives a semimajor axis ofabout 1500 AU with a tail out beyond 4000 AU. We constrained the inclination of the orbit withrespect to the galactic plane, i b , by calculating the location of the orbital pole for each poste-rior sample from our fit. In particular, we used the equations on page 13 of Chang (1929 ), aftercorrecting an error in the second equation on page 13 that should read sin i sin Ω = m sin M (seeHeintz 1969 ). The probability distribution for i b is strongly peaked towards high inclinations,36ith the greatest probability at 90 ◦ . At 68% and 95% confidence, i b must be greater than 60 ◦ and41 ◦ , respectively. Therefore, the galactic tide mechanism could plausibly operate in at least part ofallowed orbital parameter space. Tidal dissipation during the giant phase:
Previously, Adams & Bloch (2013 ) calcu-lated the orbital evolution of exoplanets orbiting near expanding giant stars (see also Rasio etal. 1996 ). The orbits of these planets evolve due to two competing factors: mass loss (whichdrives orbits outwards) and tidal dissipation (which drives orbits inwards). Planets which orbitnear an equilibrium radius where these two effects are nearly equal in strength can in some casesmigrate inwards due to tidal evolution but avoid engulfment by the red giant host. This requiresextremely finely-tuned initial parameters to have a chance of forming WD 1856 b’s present-dayconfiguration. Computing the exact location of this radius (which is likely somewhere around 1-2AU) is difficult as the radius depends on the starting angular momentum, mass loss rate, dissipationcoefficients, and other parameters that are difficult to constrain; however, it could be plausible thatfinely tuning the initial parameters of the planetary orbit and stellar properties could shrink theorbit of WD 1856 b to its current semimajor axis.
Dynamical interactions near periastron:
If two planets happened to be scattered into closeperiastron passages at the same time and had a close scattering event near periastron, one planetcould have been ejected, leaving the other planet in a short-period orbit around WD 1856. Thelikelihood of such an encounter is fairly low; events which can excite high eccentricities and closeperiastron distances are already rare (happening perhaps once in the lifetime of a white dwarf plan-etary system ), so the probability of two planets having close periastron passages simultaneouslyis even lower. Another related mechanism involves a proto-WD 1856 b with a massive moon(or a binary planet) on a highly eccentric orbit with a close periastron passage. The moon/binarycompanion could be ejected in a similar way to how hypervelocity stars are ejected binary mem-bers perturbed by the Galaxy’s central black hole , shedding enough orbital energy to leave WD1856 b in a nearly circular orbit. Again, this mechanism is a priori unlikely, since we have yet todiscover a binary planet. Partial Tidal Disruption:
If WD 1856 b reached a periastron distance slightly closer to WD1856 than the Roche limit, it could have been partially tidally disrupted, losing enough mass todissipate its orbital energy, while remaining at least somewhat intact . This process has alsobeen studied in the case of the tidal disruption of a star by a supermassive black hole . If thisprocess happened recently and material from the planet was still accreting onto the white dwarf,the elements might be visible in the planet’s spectrum. This motivates more sensitive spectroscopyof WD 1856.
Expected amplitude of spectral features in transmission
Due to the small radius of the whitedwarf host star, the spectral features expected from transmission spectroscopy are much largerthan they would be around a main sequence star. We estimated the amplitude of spectral featuresas follows: 37raditionally the amplitude of spectral features in transmission is proportional to the annulusof the planet’s terminator region . However, that approximation does not apply to the case of agrazing transit where the star is smaller than the planet. To account for the grazing geometry forWD 1856, we assumed that the atmosphere covers a slice of the star with width equal to the stellardiameter and height equal to the scale height. In this case, the amplitude A of spectral features is A ≈ nHπR (cid:63) (14)where n is the number of scale heights typically crossed by atmospheric features (usually n = 2 for cloud-free gas giant exoplanets ) and H is the atmospheric scale height: H = kTµg (15)where k is Boltzmann’s constant, T is the planet’s temperature, µ is the mean molecular weight inthe atmosphere, and g is the planet’s surface gravity. To calculate the scale height, we assumed asolar composition atmosphere ( µ = 2.3 amu) and assumed planet properties for two cases:1. Mp = 10 Mjup, T = 280 K (a reasonable internal temperature for an object of this mass)2. Mp = 1 Mjup, T = 165 K (the equilibrium temperature)For case 1, the scale height H = 4 km and the amplitude of spectral features is 0.1%. Forcase 2, the scale height H = 12 km and the amplitude of spectral features is 0.7%.We note that our assumption that the atmosphere covers a slice of the star with width equalto the stellar diameter is an approximation for nearly 50% deep transits of planets that are muchlarger than their stars. A more general expression (valid for | − Rp/R (cid:63) | < b < Rp/R (cid:63) ) forthe expected height of transmission features for grazing transits is A ≈ snHπR (cid:63) (16)where s = 2 R p R (cid:63) cos − b − (cid:16) R p R (cid:63) (cid:17) b R p R (cid:63) (17)For cases like WD 1856, where the planet is much larger than the star and blocks close to 50% ofthe stellar disk, s ≈ , and the expression reduces to to Equation 14. For WD 1856 b’s particulartransit parameters, s = 2 . . 38 xpected amplitude of Doppler boosting signal WD 1856 b’s mass could be measurable viasmall variations in the host star’s brightness caused by Doppler boosting . The semi-amplitude A b of the Doppler boosting signal is A b = (3 − α ) Kc (18)where K is radial velocity semiamplitude induced by the planet, c is the speed of light, and α isthe average logarithmic derivative of flux with respect to frequency. For a blackbody spectrum, α is approximately α (cid:39) − xe x e x − (19)and x = hνkT eff (20)where h is Planck’s constant, ν is the frequency of light in the observed bandpass, k is Boltzmann’sconstant, and T eff is the blackbody temperature. Assuming a mass of 14 M J for WD 1856 b, theDoppler boosting amplitude is about 50 parts per million (ppm) in the TESS bandpass, about 100ppm in blue optical light, and about 30 ppm in near infrared light around 1.5 microns.It will be difficult to detect these signals because of WD 1856’s intrinsic faintness and con-tamination from G 229-20 A/B. We fit the out-of-transit
TESS light curve (with a dilution correc-tion applied) with a sine/cosine model and found a boosting semiamplitude of − ± ppm– far too uncertain to detect an orbiting planet. If the PLATO mission observes WD 1856 nearthe center of its field of view for two years, it may come close to a tentative detection of a 14 M J planet, depending on how much starlight from G 229-20 A/B contaminates WD 1856’s aperture.With their large apertures and high spatial resolution, JWST and
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We thank Sebastian Lepine for providing the archival spectrum of G 229-20 A, andPerry Berlind and Jonathan Irwin for collecting and extracting velocities from the TRES spectrum. Wethank Brice-Olivier Demory for helpful comments on the manuscript and Fred Rasio, Dimitri Veras, PeterGao, Benjamin Kaiser, Willie Torres, Jonathan Irwin, JJ Hermes, Jason Eastman, Avi Shporer, and KeithHawkins for helpful conversations. A.V.’s work was performed under contract with the California Instituteof Technology (Caltech)/Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan FellowshipProgram executed by the NASA Exoplanet Science Institute. I.J.M.C. acknowledges support from the NSFthrough grant AST-1824644, and from NASA through Caltech/JPL grant RSA-1610091. TD acknowl-edges support from MITs Kavli Institute as a Kavli postdoctoral fellow. D. D. acknowledges support fromNASA through Caltech/JPL grant RSA-1006130 and through the TESS Guest Investigator Program Grant80NSSC19K1727. S.B. acknowledges support from the Laboratory Directed Research and Developmentprogram of Los Alamos National Laboratory under project number 20190624PRD2. Resources supportingthis work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced upercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products.This work is partially based on observations made with the Nordic Optical Telescope, operated by the NordicOptical Telescope Scientific Association at the Observatorio del Roque de los Muchachos, La Palma, Spain,of the Instituto de Astrofisica de Canarias. This article is partly based on observations made with the MuS-CAT2 instrument, developed by ABC, at Telescopio Carlos S´anchez operated on the island of Tenerife bythe IAC in the Spanish Observatorio del Teide. This work is partly supported by JSPS KAKENHI GrantNumbers JP17H04574, JP18H01265 and JP18H05439, and JST PRESTO Grant Number JPMJPR1775.This research has made use of NASA’s Astrophysics Data System, the NASA Exoplanet Archive, which isoperated by the California Institute of Technology, under contract with the National Aeronautics and SpaceAdministration under the Exoplanet Exploration Program, and the SIMBAD database, operated at CDS,Strasbourg, France. This work is based in part on observations made with the Spitzer
Space Telescope,which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract withNASA. This work is partially based on observations obtained at the international Gemini Observatory, aprogram of 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 Gem-ini Observatory partnership: the National Science Foundation (United States), National Research Council(Canada), Agencia Nacional de Investigaci´on y Desarrollo (Chile), Ministerio de Ciencia, Tecnolog´ıa e In-novaci´on (Argentina), Minist´erio da Ciˆencia, Tecnologia, Inovac¸ ˜oes e Comunicac¸ ˜oes (Brazil), and KoreaAstronomy and Space Science Institute (Republic of Korea). The authors wish to recognize and acknowl-edge the very significant cultural role and reverence that the summit of Maunakea has always had within theindigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observationsfrom this mountain.
Contributions
A.V. led the
TESS proposals, identified the planet candidate, organized observations, per-formed the transit and flux limit analysis, and wrote most of the manuscript. S.A.R helped organize obser-vations, performed independent data analysis, and wrote portions of the manuscript. S.X. helped organizeobservations, obtained and analyzed the Gemini data, measured fluxes from the
Spitzer data, and helpedguide the strategy of the manuscript. I.J.M.C, La.K, V.G., B.B., D.B., J.L.C., D.D., C.D., S.R.K., Fa.M., andL.Y acquired and produced a light curve from the
Spitzer data. S.A.R., J.C.B., L.N., B.Z., F.C.A., and J.J.Linvestigated the formation of the WD 1856 system. B.G, Fe.M, T.G.K., E.P., H.P., A.F., and N.N. acquiredfollow-up photometry. S.B., P.D., and K.G.S. determined the parameters of the white dwarf, while A.W.M.and E.R.N. studied the M-dwarf companions. C.M., G.Z., W.R.B., R.T., L.A.B., A.E.D., and A.I.H. acquiredspectra of the white dwarf and/or M-dwarf companions. B.M., K.H., and T.D. performed an independentanalysis analysis of the
TESS data, and J.A.L. performed an independent analysis of the white dwarf SED.C.V.M. provided valuable expertise on brown dwarf models, and Li.K. investigated the system’s implica-tions. L.A.P. determined parameters for the binary M-dwarf orbits and white dwarf/M-dwarf orbits, andA.C. investigated the system’s galactic kinematics. G.R.R., R.K.V., D.W.L., S.S., J.N.W., J.M.J., D.A.C.,K.A.C., K.D.C., J.D., A.G., N.M.G., C.X.H., J.P., M.E.R., and J.C.S. are members of the
TESS missionteam.
Data Availability
We provide all reduced light curves and spectra as supplementary data products to themanuscript.
Competing Interests
The authors declare that they have no competing financial interests. orrespondence Correspondence and requests for materials should be addressed to A.V. (email: [email protected]).
Code availability
Much of the code used to produce these results is publicly available and linked through-out the paper. We wrote custom software to analyze the data collected in this project. Though this code wasnot written with distribution in mind, we will make our custom analysis code available online via github fortransparency. xtended Data Table 1: Comparison of White Dwarf Parameters from Different Atmo-sphere Models. Parameter 100% H 100% He 50%/50% H/HeMass ( M (cid:63) ) 0.537 ± M (cid:12) ± M (cid:12) ± R (cid:63) ) 0.0131 ± R (cid:12) ± R (cid:12) ± log g cgs ) 7.931 ± ± ± T eff ) 4785 ±
60 K 4430 ±
60 K 4710 ± t cool ) 5.7 ± ± ±0.5 Gyr