A Backward-Spinning Star with Two Coplanar Planets Downloaded by Guest on September 30, 2021 Downloaded by Guest on September 30, 2021 I.S4 Fig

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Downloaded by guest on September 30, 2021 mlKnudstrup Emil ie hc a edtce ietyo sa paetredshift apparent an as blue or the directly on detected deficit be small can stellar a ordinarily with which show would associated side, lines that effect absorption light Doppler The the the the rotation. to of of half due some approaching blueshifted blocks the be of it absorption front star’s star, in the is rotating stel- in planet the the distortion of When a portion this lines. to a of leading blocks planet photosphere, basis transiting lar the the physical a via that as The star is method the planets, effect. of both (RM) obliquity of sky-projected Rossiter–McLaughlin the transits measuring the of spanning way intervals A time K2-290 of over spectroscopy optical high-resolution performed System We A K2-290 the “warm in Obliquity a Stellar is radius “c” d, planet 48.4 outer period mass The orbital sub-Neptune.” with “hot Jupiter” orbital a an it has of radius “b” ing a and planet d inner away, 9.2 of The farther period planets. located transiting dwarf two M bors of another projected separation projected is a a C, with with dwarf K2-290 M star, an tiary of is separation B, K2-290 orbital star, secondary The (M masses solar T formation system a from can torque star. gravitational disks the neighboring the protoplanetary to due provides and misaligned grossly system stars become of The that capable disk. demonstration is by protoplanetary that clearest tilted the companion is stellar tilted wide-orbiting A having a K2-290 has be star and to ets the known that rotation stellar compan- show 124 the suitable we is a Here, coplanar nor has retrograde. a identified, case been in two neither star star in ion are misaligned misalign- but a There primordial system, of multiplanet a perturbations. examples from postformation known obtain previously from to than easier ment a is star, that backward-rotating condition a of events—with system are postformation dis- coplanar scenario other ruptive a or scattering this combine planet–planet out of would planets—ruling multiple example examples ideal definite wide-orbiting An no a known. of but torque In star, dur- gravitational the turbulence companion explanations. or from leading formation result star the ing can are misalignments star/disk planet theory, isolated effects wider-orbiting secular involve or a scattering misalignments from planet–planet formation. which known grav- for planet previously usual Jupiters, by after hot the the upset place of planet, was took Most a alignment that initial of the perturbations the motion itational to that disk orbital between parallel is protoplanetary the misalignment interpretation equator and its a stellar reveal rotation and observations stellar the star When with a plane. 2020) disk aligned, that 18, August initially review assumed for (received are widely 2020 22, December is approved and It NJ, Princeton, University, Princeton Bahcall, A. Neta by Edited e Japan; 152-8551, Tokyo Technology, d of Institute Tokyo Sciences, a planets coplanar Hjorth two Maria with star backward-spinning A PNAS exoplanets aainIsiuefrTertclAtohsc,Uiest fTrno oot,O 5 H,Canada 3H8, M5S ON Toronto, Toronto, of University Astrophysics, Theoretical for Institute Denmark; Canadian C, Aarhus DK-8000 University, Aarhus Astronomy, and Physics of Department Centre, Astrophysics Stellar eateto srnm srpyis etrfrEolnt n aial ols h enyvnaSaeUiest,Uiest ak A182 and 16802; PA Park, University University, State Pennsylvania The Worlds, Habitable and Exoplanets for Center Astrophysics, & Astronomy of Department ◦ 220A salt-yeFsa ihams of mass a with star F late-type a star, is primary The A, stars. three K2-290 of consists (1) system K2-290 he ± 01Vl 1 o e2017418118 8 No. 118 Vol. 2021 246 6 ◦ ± | oprdwt h riso oho t nw plan- known its of both of orbits the with compared rmrilinclination primordial 15 a,1 at ass(M masses Earth

io Albrecht Simon , a n aisof radius a and ) n u’iSato Bun’ei and , 113 ± 2 3.06 2467 srnmcluis(u.Teter- The (au). units astronomical | ⊕ iayhost binary ). ± a,1,2 −155 +177 1.51 0.16 b u h rmr trhar- star primary The au. ± euuiHirano Teruyuki , at ai (R radii Earth | 0.07 obliquity 11.3 oa ai (R radii solar ± 0.6 | 1.19 c eateto srpyia cecs rneo nvriy rneo,N 08544; NJ Princeton, University, Princeton Sciences, Astrophysical of Department ⊕ R ,mak- ), ⊕ ± and , b 0. ohaN Winn N. Joshua ,

07 ). ,w n h k-rjce biut obe to obliquity sky-projected the find we Appendix), Appendix). (SI provide transit datasets Telescope 8.1-h two the Subaru of these coverage Disper- 8.2-m Together, phase High Hawaii. complete the in the on Kea used Mauna (3)] we For on 2019, Islands. [HDS June Canary Spectrograph 12 the sion on Telesco- in transit, Palma 3.6-m second La the the on on Galileo (2)] Nazionale [HARPS-N Radial-Velocity pio Accuracy first North High the Searcher the based observed with Planet are 2019 We April data transits. 25 ret- The on different transit is rotation. two orbit star’s of planet’s observations the on the to that respect implies with rograde (RVs) 1, velocities (Fig. radial K2-290 of of planet outer the c. Planet sec- anomalous the an as during observed blueshift. star be a would by the followed This redshift transit transit. of the the side of of half half (receding) ond first redshifted the the during star and the blueshifted the of blocks side planet planet’s (approaching) the the then and aligned, rotation are distor- stellar motion the orbital spectral if example, stellar the For sky-projected (λ). obliquity of the on evolution (v depends velocity time rotational transit The a throughout line. tions entire the of doi:10.1073/pnas.2017418118/-/DCSupplemental at online information supporting contains article This 2 (1). spectrum from stellar independently the of determined broadening was line that observed the value the with sistent 8 ulse eray1,2021. 15, February Published 1 the under Princeton Published Submission.y with Direct PNAS affiliated a is both article This are N.A.B. collaborated.y not and have paper.y J.N.W. They the University. wrote statement: B.S. and interest E.K., Competing J.J.Z., R.I.D., analyzed R.I.D., E.K. J.N.W., J.N.W., and T.H., T.H., J.J.Z., S.A., R.I.D., S.A., M.H., J.N.W., T.H., and M.H., S.A., data; M.H., research; research; performed designed E.K. S.A. and J.J.Z., and M.H. contributions: Author owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To ..adSA otiue qal oti work. this to equally contributed S.A. and M.H. ◦ et h trrttsbcwr,adacmainsa with star companion identified. been a has and misalign- properties backward, suitable primordial rotates a star such The for to ment. candidate shown is best-known surrounded system still the K2-290 is the be the Here, star been upsets disk. the protoplanetary star while have a stage, by companion reasons early distant an possible a at alignment theory, many one and In misalign- of offered. known, drastic feature many are universal false: ments a proved This be systems. to planetary planets alignment the astronomers their source: spin-orbit Most cloud. and same expected planets. molecular the a stars the of from collapse that of momentum gravitational theory orbits angular the their the inherit with supports up fact lines This equator Sun’s The Significance eas find also We . yfitn aaeeie oe oteR iesre (SI series time RV the to model parameterized a fitting By hsi h poieo h atr htwsosre for observed was that pattern the of opposite the is This c eea .Dawson I. Rebekah , NSlicense.y PNAS v sin sin i ? https://doi.org/10.1073/pnas.2017418118 6 = i ? n h k rjcino h stellar the of projection sky the and ) .9 −0.6 +0.5 b eateto at n Planetary and Earth of Department d km . y y .Teosre pattern observed The Left). .J Zanazzi J. J. , https://www.pnas.org/lookup/suppl/ s −1 Fg ) hc scon- is which 1), (Fig. e λ c , 153 = | f6 of 1 ◦ ±

ASTRONOMY Fig. 1. The RM effect for both of the planets in the K2-290 system. (Left) Data for the outer, larger planet c. Gray circles are RV data obtained with HARPS-N on 25 April 2019. White circles show HDS RVs obtained on 12 June 2019. The error bars indicate the internal uncertainties as derived for the RV data points ◦ ◦ by the Data Reduction Software of the spectrographs. The solid gray line is the best-fitting model, which has a projected obliquity of λc = 153 ± 8 . Lower shows observed minus calculated (O − C) between the data and the best-fitting model. The dashed gray line is a model in which λc is zero and all of the other parameters are the same as in the best-fitting model. The horizontal bars denote the time intervals from first to fourth contact (light gray) and second to third contact (dark gray). (Right) Same as Left but for the smaller, inner planet b. These RVs were obtained on 20 July 2019 with ESPRESSO. We find +45 ◦ λb = 173−53 . The shaded gray area shows the time interval when our view of K2-290 was blocked by clouds.

Planet b. What about the orbital orientation of the inner planet? collisions with the star or tidal disruption. We display these The observation of the RM effect for the inner planet is more limits in Fig. 2. challenging because of the planet’s smaller size. One might We also tested how different values of the planetary masses expect the orbits of the two planets to be closely aligned, based and orbital eccentricities influence these stability zones. The on prior observations and statistical analyses of the Kepler mul- most significant influence is from the orbital eccentricity of tiplanet systems (4–6), but K2-290 is unusual in having a giant planet c. For example, taking the eccentricity to be 0.144, we planet. Furthermore, the statistical studies could not tell whether found that the unstable range of mutual inclinations is enlarged the planets always orbit in the same direction or if they could to 59◦ to 136◦. The best-available constraint on the orbital sometimes orbit in opposite directions (an admittedly speculative eccentricity based on RV data is a 3-σ upper limit of 0.24 (1). possibility). In summary, we found that nearly perpendicular configura- Limits on mutual orbital inclinations from long-term dynami- tions can be ruled out, but mutual inclinations near 0◦ and 180◦ cal simulations. We performed numerical integrations of the are both viable. gravitational dynamics of the two-planet system in order to Spectroscopic transit observations—planet b. To decide between check on the long-term stability of the system for different these possibilities, we observed a transit of the inner planet choices of the mutual orbital inclination. We used the mer- with the newly commissioned Echelle Spectrograph for Rocky cury6 code (7), including the effects of general relativity. We Exoplanets and Stable Spectroscopic Observations [ESPRESSO assumed both orbits to be initially circular. This is a conserva- tive assumption in that sense that any initial eccentricity would extend the range of unstable mutual inclinations. The coplanar configuration is stable for at least 2.8 Gy, the maximum time span that was simulated. An antialigned configuration, with a mutual inclination of 180◦, is also stable over the same time span. We tried a configuration in which planet c’s orbit is misaligned relative to the star by the observed amount and planet b is aligned with the stellar equator. This configuration is also stable for at least 2.8 Gy, although both planets do not often transit at the same time. When one planet transits, the other planet also transits about 15% of the time. Based on these integrations, we calculated the expected level of transit timing variations (TTV) and transit duration variations (TDVs) using the code described in ref. 8. In both scenarios, the expected level of TTVs is too small to be detectable using the currently available dataset. The TTVs are on the order of 0.1 min for the inner planet and 0.01 to 0.1 min for the outer planet (depend- ing on the mass of the inner planet). For the case in which the inner planet is aligned with the stellar spin, the TDVs of the inner Fig. 2. Results for the projected obliquities of K2-290 with respect to both planet are on the order of 10 min over 3 y. Our simulations also of the known planets. Upper shows the posterior for the projected obliquity showed that values of the mutual orbital inclinations between of planet c, based on the RM measurements shown in Fig. 1. Lower shows ◦ ◦ 74 and 112 are unstable, as Lidov–Kozai cycles of planet b’s the same for the smaller planet b (black). The orange posterior also takes orbit drive up its eccentricity. This makes the planet prone to into account the constraints from our orbital stability calculations.

2 of 6 | PNAS Hjorth et al. https://doi.org/10.1073/pnas.2017418118 A backward-spinning star with two coplanar planets Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 i.S4 Fig. Appendix, (SI and data deformation the the of time of ratio the strength signal-to-noise expected in the the eye nondetection with visual by consistent This detected is 2) functions. be cross-correlation cannot the of shadow” series during “planet lines the ( stellar shadow) 1) the Doppler of the deformations (i.e., transit as detected be can few orbits. a antialigned of of possibility order exotic case, the Based more aligned (on even 13. the probability the for small favor is percent) a data freedom allow the do of that they with degrees conclude although fit we of poorer tests, number these a the on is cases, model both antialigned In the a has while model 13, aligned The of point. zero velocity the from 180 AF,aogwt ierfi.Tesoeo hsln stknt eterotation the be to taken is function line A. this autocorrelation K2-290 of Locations slope of the The period (Bottom) in fit. linear peaks lag. a with autocorrelation of along (ACF), of function sequence a the time as the of in Autocorrelation gaps the (Middle) across interpolation series. linear including curve, light Kepler 3. Fig. aligned exactly are planets two the which in (λ one models: ent in parameters free few effectively a are only of model The parame- amplitude the (10). an those has second of anomaly per knowledge RV meters the prior that Our guarantees detected. ters was b tran- and planet time, the midtransit of the knowledge parameter, prior v impact precise transit the have depth, already sit not did measure we cannot if signal-to- we lower The means planet. ratio outer noise the for obtained value the with data. HARPS-N the the for for used coefficients were limb-darkening that used data the We ESPRESSO on analysis. planet constraints previous for same the as the on approach based obliq- on same parameters projected priors the darkening setting the followed time of we this b, c, determination planet the of 1, For Paranal uity Fig. 2). at in (Fig. shown Telescopes orbits data Large The Very Appendix). 8.4-m Right (SI Chile the in of Observatory one and (9)] akadsinn trwt w olnrplanets coplanar two with star backward-spinning A al. et Hjorth Flux sin b sacnitnycek eas netgtdi h Meffect RM the if investigated also we check, consistency a As o nee ipe et efitdtedt ihtodiffer- two with data the fitted we test, simpler even an For is result The Autocorrelation 0.9994 0.9996 0.9998 1.0000 1.0002 1.0004 1.0006 ◦ = Location of peak in ACF [days] −0.2 0.0 0.2 0.4 0.6 0.8 i 10 15 20 25 30 + ueotataindobt n r ossetwt aligned with consistent are and orbits antialigned out rule ? 0 5 λ 0 ecudnthv encndn htteR fetfor effect RM the that confident been have not could we , Detrended (Top) period. rotation stellar the of Determination c λ n h te nwihte r nilge (λ antialigned are they which in other the and ) 3160 0 c .Teeaen reprmtr nete oe apart model either in parameters free no are There ). λ λ b b 10 n h eoiyzr point. zero velocity the and 173 = 1 3180 −53 +45 ◦ 20 v ,wihi compatible is which Appendix), (SI 2 Cycle number sin Lag [days] Days 3200 i ? .W on that found We Appendix). SI n h elrbn limb- Kepler-band the and λ 3 30 b swl as well as 3220 4 40 λ χ c 2 Indeed, . χ statistic 2 A–C). 3240 26. = b 5 = 50 velocity systematic for 13). account the (12, to rotation enlarged differential 10% we to to due although errors 1 A, from K2-290 uncertainty of fractional period 3, rotation be (Fig. the to number for slope to cycle the function vs. linear found a location we fitting peak By displays measured peaks. which spaced the lag, The regularly of of function interpolation. series a a linear as 3, strength with Fig. autocorrelation in gaps the shown is the curve time in light uniform resulting filling with auto- curve by the light compute a sampling to created width prepare we a To function, d). with correlation (20.8 filter samples median time high-pass 1,000 a of applying downward- photometric overall by an the trend removed the We of sloping (11). version A on K2-290 “K2SFF” for series the time based with determi- this began For we period telescope. Kepler 80-day nation, the the with rotation in observed seen series are time stellar that fluctuations the brightness quasiperiodic determined We Inclination Stellar and Period Rotation Stellar analysis the shadow. than Doppler simpler the is of method the because RVs anomalous Appendix, (SI signal S4 shadow Fig. RM/planet the of strength expected measured we a which λ detected from characteristics, we expected observations, the ESPRESSO with the signal of all stacking By 3) sin where used have we where obnn h otroso hs w ouin ihequal with solutions two these for posterior the of including and weight posteriors There the stellar for velocity. Combining the solutions rotation possible of projected two combination and are the radius, on period, based rotation obliquity stellar large rota- projected measured the velocity, than larger tion is velocity rotation the ae asadobtldsac fK-9 (0. B K2-290 of and distance finding orbital and signals acceleration, mass mated planetary be constant to the long-term acceleration modeled possible the We a d. with have 500 along we over (1), extending previously data obtained measurements HARPS-N of entries the two in last HARPS-N (the with 2019 taken summer observations RV new two combining By Bodies Wide-Orbiting on Limits RV is obliquity stellar the for result the be to taken was function likelihood The parameters model The 14. were ref. in advocated technique star, inference the of obliquity the and of line independent obliquity. an stellar large here a have for we evidence transits, of detection the of Since unity. than less b edtrie h nlnto nl fteselrrtto axis rotation stellar the of angle inclination the determined We ae pnti au,w acltdteeutra rotation equatorial the calculated we value, this upon Based 157 = i ? 113 L R 0 = = ? v D–F , v ± ◦ . P ≡ 63 ne h supino nfr rotation: uniform of assumption the under ± rot 2 R 2π .W aemr ofiec nteaayi fthe of analysis the in confidence more have We ). 34 ± ? u,w ol xett e ailacceleration radial a see to expect would we au), and , + v /R R hs efudidpneteiec o a for evidence independent found we Thus, 0.09 ◦ sin ? ossetwt h Vbsdrsl n the and result RV-based the with consistent , 0. v

/P = 075 P cos − i ? rot rot 2π sin P 1.511 6 = R i − rot ? ? d 1 γ R ˙ and i o hc nfr roswr adopted. were priors uniform which for , 1 = .9 9 = orb ? 6. 6. 11.2 = 3d 63 ± .511 63 skont ecoet nt because unity to close be to known is 2 ± ψ 0.5 u sn aito fteBayesian the of variation a using , i ± 5 ≡ ? https://doi.org/10.1073/pnas.2017418118 hc r near are which , 2 ± m km 0.06 √ ± + 0.075 1 124 s 1. with S1) Table Appendix, SI −1 − s λ ms km 1 −1 .W dpe hsvalue this adopted We d. vu i.3, Fig. Top. b ◦ cos y ae nteR effect, RM the on based ± mligthat implying , km/s 0.5 R −1 − 2 6

i km/s 6.9 ae nteesti- the on Based . ◦ ? −1 1.Ti au for value This (1). h eutwas result The . Tbe1). (Table , 368 39 Middle PNAS ± ◦ 0. and 2 Bottom), , 021 sin | shows 141 f6 of 3 i M ? [2] [1] ◦

is .

ASTRONOMY −1 −1 M (t) on the order of 5 m s y . Therefore, the observed long- Σ(r, t) ' d , [3] term acceleration is compatible with zero (within 2-σ) and is 2πroutr also compatible with the expected contribution from the nearby where M dwarf. There is no evidence for any other wide-orbiting Md0 Md(t) = [4] bodies. 1 + t/tv

is the disk mass, tv = 0.5 My. is the viscous timescale, and M = Discussion d0 0.1 M is the initial disk mass. Although modifying the disk Systems similar to K2-290, with coplanar planetary orbits and a properties does modify the likelihood of secular resonance cross- grossly misaligned host star (Fig. 4), had been predicted to exist ing, we find a secular resonance occurs over a wide swath of as a consequence of the tidal torque on a protoplanetary disk reasonable disk parameters for this system (SI Appendix). from a neighboring star (15, 16). Another possible explanation The model assumes that the two planets form within the disk for such systems is the tilting torque exerted on the inner system at the locations we observe them today. Our model does not take of planets by a massive planet on a wide and highly inclined orbit. into account the effects of planet migration or photoionization The Kepler-56 system features two planets on coplanar orbits of the disk as previous work has shown that these effects tend and a misaligned star (17), and in that case, a wider-orbiting to lead to even greater excitation of the stellar obliquity dur- third planet was detected through long-term RV monitoring ing the disk-hosting phase (25). The mass of the outer planet (18). Based on the mass and orbital distance of the third planet, is set equal to its currently observed value, while the mass of it is possible or even probable that the planet was responsible for planet b is set equal to 21.1 M⊕, the 3-σ upper limit that was tilting the orbital plane of the inner two planets long after the derived from RV observations (1). In general, smaller values of planets formed (19). Likewise, the HD 3167 multiplanet system Mb increase the chance of large star–disk misalignments occur- was recently found to have a misaligned star (20), but there is ring. The model also includes a companion star of mass MB in not yet any evidence for either a wider-orbiting planet or a com- a circular and inclined orbit with radius aB. We assumed the panion star. Turbulence (21) and disk torquing (22) can lead to binary’s semimajor axis is greater than the observed projected misaligned protoplanetary disks. However, retrograde orbits, as separation [aB > 113 au (1)]. We used the secular equations from observed for K2-290 A, are difficult to achieve via turbulence, ref. 25 for the dynamical evolution of planet-forming star–disk– and late infall of material will lead to a further reduction of any binary systems. To these, we added the gravitational influence of 0 0 misalignment (23). planets b and c on the star–disk ω˜sd and disk–star ω˜ds precession The unique aspect of K2-290 is that a companion star has been frequencies (equations 65 and 66 in ref. 25): detected (K2-290 B) with properties that make it a good candi- 0 date for the misalignment of the protoplanetary disk. There is no ω˜sd =ω ˜sd + ωsb + ωsc, [5] evidence for a wider-orbiting massive planet: the upper limit on 0 any long-term radial acceleration is about 10 times smaller than ω˜ds =ω ˜ds + (Lb/Ld)ωbs + (Lc/Ld)ωcs, [6] the acceleration that was observed for Kepler-56. In addition, √ where L ' (2/3)M GM?rout is the total disk orbital angu- star/disk misalignment is an attractive explanation for K2-290 d d √ because it can easily produce retrograde orbits (24, 25). This lar momentum, Li = Mi GM?ai are the planets’ orbital angu- is because the orientation of the orbital plane of a wide binary lar momenta (where i is either b or c), and the precession star may have only a weak correlation with the orientation of the frequencies are protoplanetary disk around either star (26, 27). In contrast, pro- p 3 ducing a retrograde system through the action of a wide-orbiting 3kq ¯ Mi GM?R? ωsi = Ω? 3 , [7] planet requires invoking an unseen third planet with an unusu- 2k? M? ai ally high orbital inclination, which would be difficult to achieve through planet–planet interactions (28). 2s 3kq ¯ 2 R? GM? ωis = Ω? 3 . [8] 2 ai ai Primordial Disk/Star Misalignment Scenario In Eqs. 5 and 6, we use the notation of ref. 25, where preces- The originally proposed mechanism for star/disk misalignment sion frequencies with tildes are averaged (integrated) over the was nodal precession of the disk around the angular momentum radial extent of the disk. We assumed the primary star to have vector of the binary orbit (15). It was later recognized that the moment-of-inertia constants of k? = 0.2 overall and kq = 0.1 for gravitational coupling between the star and disk is also important the rotational bulge, as appropriate for the premain sequence and that misalignments are more likely to arise from secular res- phase (24). We neglected the torque on the planets from star B onances between spin and nodal precession (16). Furthermore, (ω˜0 ' ω˜ ). the magnetic fields of stars as massive as K2-290 A are probably dB dB Fig. 5 displays the main result: the time evolution and excita- too weak to have enforced star–disk alignment (29). tion of primordial misalignments or mutual star–disk inclinations To demonstrate that this scenario is plausible for the case −1 ˆ of K2-290, we calculated the system’s secular evolution due to θsd = cos (ˆs · ld) excited by the binary companion for differ- −1 ˆ ˆ mutual gravitational torques between the rotational bulge of the ent initial disk-binary mutual inclinations θdb = cos [ld(0) · lB] host star, the protoplanetary disk, and the companion star K2- (where ˆs is the host star’s stellar spin axis, ˆld is the disk’s orbital 290 B. We employed the model described in ref. 25. In this model, there is a star of mass M?, radius R?, and rotation frequency Ω?. To represent the pre-main sequence phase of stellar Table 1. Selected parameters of the K2-290 system evolution, the stellar radius is set equal to R? = 2 R , and the Parameter Value p 3 rotation rate is set such that Ω¯ ? = Ω?/ GM?/R? = 0.1. Includ- Stellar rotation period, Prot (d) 6.63 ± 0.66 ing contraction of the stellar radius and evolution of the stellar ◦ Stellar inclination angle, i? ( ) 39 ± 7 spin during the disk-hosting phase does not have a significant −1 Projected stellar rotation velocity, v sin i? (km s ) 6.9 ± 0.5 impact on the ensuing star–disk–binary dynamics (16). The star ◦ +45 Projected obliquity with respect to planet b, λb ( ) 173−53 is surrounded by a circular flat disk with an inner radius of ◦ Projected obliquity with respect to planet c, λc ( ) 153 ± 8 rin = 4 R? and an outer radius of rout= 50 au. The disk’s surface Obliquity with respect to planet c, ψ (◦) 124 ± 6 density profile is c

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Fig. akadsinn trwt w olnrplanets coplanar two with star backward-spinning A ( SI al. present et Hjorth still is disk original gaseous the the cases, such while all occurs in but misalignment crossing, resonance precession nodal another through or the Appendix ), after (SI planets disappears two the disk of gaseous plane orbital the reorient to (30). continues cluster masses Lupus (16, the disk in My rates protostellar 1 accretion of and star host 0.05 measurements and between with timescales consistent the over as 25), mass long its as occurs Previous loses crossing orbit. disk resonance binary secular the vec- that and of found momentum momentum work vector angular angular momentum disk’s the around the angular tor of disk’s frequency the stel- precession around the the one-to-one of axis a frequency spin model, precession lar our the between In occurs resonance. the resonance main is secular misalignment The a star/disk 5). of large occurrence (Fig. a measurements producing the the for for can obliquity requirement with values stellar consistent of the range of made value plausible be final a the for distance, orbital and binary orbit binary the and observed. dissi- been disk not knowledge the [< our if compact (< extremely averted fast system were be extremely this were only for timescale would pation occur inner misalignment not A the by would (25). misalignments took planets primordial massive we of short-period, suppression Since the values. (1), 3-σ the surements parameter be to of mass obliquity planet’s range stellar a measured over the with consistent ω c ˜ dB nasbe ftemdl ecniee,tecmainstar companion the considered, we models the of subset a In disk the between angle the for possibilities of range wide a For ,lrepioda iainet r eeae,wihare which generated, are misalignments primordial large ), a B lutaino h rhtcueo 220Aadistokonplan- known two its and A K2-290 of architecture the of Illustration fe eua eoac cusi h ytm( system the in occurs resonance secular a After . pe ii bandfo Vmea- RV from obtained limit upper 3 u(5] n uhdsshv to have disks such and (25)], au σ ofiec nevl o h stel- the for intervals confidence ˆ l B 0.05 stebnr’ orbital binary’s the is b y ri h disk the if or My) ψ c 124 = ◦ ω ˜ ± sd 0 6 ∼ ◦ h nl ewe h nua oetmvcoso h otstar host the of vectors momentum (θ angular nation disk the the between and angle planets). the embedded (with actions 5. Fig. shapes line stellar the of rely not deformation they do rather, the transit; techniques in during These contained observed 4). RVs information spec- and anomalous the on the 3 for of sections use techniques Appendix, RVmake analysis results (SI exact these alternative the data supplement on employed troscopic To depend have supplied. critically we information not further, parameters, prior do and model, results setup our of model that choice confirm our to in tests detail pro- information host We the prior their determine K2-290. and to of of observations, front obliquity these in from jected in derived planets RVs, detailed two apparent are the of observations for transits obtained These during data star. system spectroscopic high-resolution K2-290 analyze the we article, this In Methods and Materials solar the to similar system. more planets, exoplane- wider-orbiting of with explorations systems future It tary for (34). expectations set Jupiters to hot helps the also systems other especially of misalignments, reinterpretation observed a with to lead For always may are (33). This disks aligned. protoplanetary cannot them well their we and of that stars shows one that system assume with K2-290 safely the misaligned of architecture be the obvi- must now, and misaligned, star are the disks some outer are ously, and inner There 1/3 the configurations. which that in nonaligned evidence cases had found sample which are 32, their there yet ref. of however, from not star; limited, way have misaligned albeit disks a one hints, of imaged than examples directly more any of up be Studies turned may disk. scenario there a this misalign that mea- frequently to mind similar how in perform see keeping to to occurs, interesting systems be other prop- of observed will the surements It for K2-290. explanation of plausible erties a provide to nario now are stars. that single systems as in observed even mechanism operated disk-torquing have might the here Therefore, a described after (31). companions years retained their million has lose K2-290 few systems while many that companion, note stellar also a We S7). 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ASTRONOMY during planetary transits. Our analysis of these deformations is consistent Archive: http://archive.eso.org/cms.html. The Kepler light curve of the K2- with our earlier analysis of the RVs. SI Appendix, section 5 details the setup 290 system from the K2 mission reported in this paper is archived in Mikulski of our calculations, which explore possible postformation secular resonance Archive for Space Telescopes: https://archive.stsci.edu. scenarios. The HARPS-N data reported in this paper are archived in the INAF ACKNOWLEDGMENTS. M.H., S.A., and E.K. acknowledge support from the Danish Council for Independent Research through DFF (Danmarks Frie (Istituto Nazionale di Astrofisica) Science Archive (https://www.ia2.inaf.it/) Forskningsfond) Sapere Aude Starting Grant 4181-00487B and the Stellar under program identification A39TAC 2. The HDS data reported in this Astrophysics Center, which is funded by Danish National Research Foun- paper are archived in the SMOKA (Subaru Mitaka Okayama Kiso Archive) dation Grant DNRF106. This work was supported by JSPS (Japan Society Archive (https://smoka.nao.ac.jp) under program identification S19A122. for the Promotion of Science) KAKENHI Grants16K17660 and 19K14783. The ESPRESSO data reported in this paper are archived in the ESO (European Work by J.N.W. was supported by the Heising-Simons Foundation and NASA Southern Observatory) Science Archive (http://archive.eso.org/cms.html) Award 80 NSSC18K1009. R.I.D. is supported in part by NASA XRP (Exo- under program identification 2103.C-5041(A). The Kepler light curve of the planets Research Program) Grant NNX16AB50 G. We thank Akito Tajitsu K2-290 system from the K2 mission reported in this paper is archived in the and Sanghee Lee for assisting with the Subaru observations. We acknowledge the very significant cultural role and reverence that the summit of Mikulski Archive for Space Telescopes (https://archive.stsci.edu/). Maunakea has always had within the indigenous Hawaiian community. We This paper also includes data collected by the K2 mission, which was are most fortunate to have the opportunity to conduct observations from funded by the NASA Science Mission directorate. This research made use this mountain. The data analyzed in this paper were obtained with the of Lightkurve, a Python package for Kepler and TESS (Transiting Exoplanet Italian Telescopio Nazionale Galileo operated on the island of La Palma Survey Satellite) data analysis (Lightkurve Collaboration). by the Fundacion´ Galileo Galilei of the Istituto Nazionale di Astrofisica at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias as part of Program A39TAC 2; the Subaru Telescope, Data Availability. Stellar spectra and derived data products (e.g., RVs) have which is operated by the National Astronomical Observatory of Japan as been deposited. The HARPS-N data reported in this paper are archived in part of Program S19A122; and the Very Large Telescope with data collected the INAF Science Archive: https://www.ia2.inaf.it. The HDS data reported at the European Organisation for Astronomical Research in the South- in this paper are archived in the SMOKA Archive: https://smoka.nao.ac.jp. ern Hemisphere under ESO DDT (Director’s Discretionary Time) Program The ESPRESSO data reported in this paper are archived in the ESO Science 2103.C-5041(A).

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