Further Observations of the Tilted Planet XO-3: A New Determination of Spin-Orbit Misalignment, and Limits on Differential Rotation
Teruyuki Hirano, Norio Narita, Bun'ei Sato, Joshua N. Winn, Wako Aoki, Motohide Tamura, Atsushi Taruya, Yasushi Suto
aa r X i v : . [ a s t r o - ph . E P ] O c t PASJ:
Publ. Astron. Soc. Japan , 1– ?? , c (cid:13) Further Observations of the Tilted Planet XO-3: A New Determinationof Spin-Orbit Misalignment, and Limits on Differential Rotation ∗ Teruyuki
Hirano , Norio
Narita , Bun’ei
Sato , Joshua N.
Winn , Wako
Aoki , Motohide
Tamura , Atsushi
Taruya and Yasushi Suto [email protected] Department of Physics, The University of Tokyo, Tokyo, 113-0033, Japan Department of Physics, and Kavli Institute for Astrophysics and Space Research,Massachusetts Institute of Technology, Cambridge, MA 02139, USA National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA (Received 2011 August 7; accepted 2011 September 29)
Abstract
We report on observations of the Rossiter-McLaughlin (RM) effect for the XO-3 exoplanetary system.The RM effect for the system was previously measured by two different groups, but their results werestatistically inconsistent. To obtain a decisive result we observed two full transits of XO-3b with theSubaru 8.2-m telescope. By modeling these data with a new and more accurate analytic formula for theRM effect, we find the projected spin-orbit angle to be λ = 37 . ◦ ± . ◦ , in good agreement with theprevious finding by Winn et al. (2009). In addition, an offset of ∼
22 m s − was observed between thetwo transit datasets. This offset could be a signal of a third body in the XO-3 system, a possibility thatshould be checked with future observations. We also attempt to search for a possible signature of thestellar differential rotation in the RM data for the first time, and put weak upper limits on the differentialrotation parameters. Key words: stars: planetary systems: individual (XO-3) — stars: rotation — techniques: radialvelocities — techniques: spectroscopic —
1. Introduction
Since the discovery of the first transiting planet, manygroups have been studying the stellar obliquities (spin-orbit angles) of planet-hosting stars through measure-ments of the Rossiter-McLaughlin (RM) effect. The RMeffect is a distortion of stellar spectral lines that occursduring transits, originating from the partial occultation ofthe rotating stellar surface. It is often manifested as a pat-tern of anomalous radial velocities (RVs) during a plane-tary transit (Queloz et al. 2000; Ohta et al. 2005; Winnet al. 2005; Narita et al. 2007; Triaud et al. 2010). Bymodeling the RM effect, one can determine the angle λ between the sky projections of the stellar rotational axisand the orbital axis. The statistics of the spin-orbit angle λ should provide a clue to the formation and evolutionof close-in giant planets (hot-Jupiters and hot-Neptunes).Since 2008, many transiting systems with significant spin-orbit misalignments have been reported (e.g. H´ebrardet al. 2008; Narita et al. 2009b; Pont et al. 2010). Thishas attracted much attention to the importance of dy-namical mechanisms for producing close-in planets, aswell as tidal evolution of planets and their host stars(Fabrycky & Tremaine 2007; Wu et al. 2007; Nagasawa et * Based on data collected at Subaru Telescope, which is operatedby the National Astronomical Observatory of Japan. al. 2008; Chatterjee et al. 2008; Triaud et al. 2010; Winnet al. 2010).In this paper, we present the measurement of the RMeffect for the XO-3 system. The XO-3 system was discov-ered by Johns-Krull et al. (2008). Photometric follow-upsby Winn et al. (2008) allowed the system parameters tobe refined. The large mass of the planet ( M p = 11 . ± . M Jup ) and its eccentric orbit ( e = 0 . ± . λ = 70 ◦ ± ◦ ,suggesting a significant spin-orbit misalignment for thefirst time among the known planetary systems. Onthe other hand, Winn et al. (2009) independently mea-sured the RM effect with the High Resolution EchelleSpectrometer (HIRES) installed on the Keck I telescope,and found λ = 37 . ◦ ± . ◦ , which differs by more than 2 σ from the former result.The reason for the discrepancy was unclear, but it mayindicate the presence of unknown systematic errors in oneof the datasets, or even in both. It is equally possible thatthe discrepancy should be ascribed to the different tech-niques adopted in modeling the RM effect. H´ebrard et al.(2008) and Winn et al. (2009) both used analytic formu-lae to compute the anomalous RVs, but the former groupused a formula that was based on a calculation of the first [Vol. ,moment of the distorted line profile, while the latter groupused a formula that was calibrated by numerical analysisof simulated RM spectra. Recently Hirano et al. (2011)presented a new and more accurate analytic formula forthe RM effect, showing in particular that the RM velocityanomaly depends on many factors such as the rotationalvelocity of the star, the macroturbulent velocity, and eventhe instrumental profile (IP) of the spectrograph, not allof which were considered in the previous literatures.Specifically, for rapidly rotating stars like XO-3, thevelocity anomaly calculated by Hirano et al. (2011) dif-fers strongly from the simpler, previous analytic descrip-tions based on the first-moment approach (Ohta et al.2005; Gim´enez 2006). When the incorrect relation is usedbetween the RM velocity anomaly and the position of theplanet, the results for λ may be biased.In order to resolve the disagreement, and obtain a de-cisive result for the angle λ with fewer systematic errors,we observed another two full transits of XO-3b with theHigh Dispersion Spectrograph (HDS) on the Subaru 8.2-m telescope. We also applied the new analytic formula byHirano et al. (2011) to model the RM effect with greateraccuracy. We find that the best-fit value for λ based onour new measurements is very close to that reported byWinn et al. (2009).We describe the detail of the observation in Section 2.The data analysis procedure and the derived parametersare presented in Section 3. Section 4 discusses the compar-ison with the previous results, and considers the possibleeffect of the stellar differential rotation.
2. Observations
We observed two complete transits of XO-3b withSubaru/HDS on November 29, 2009 and February 4, 2010(UT). We also obtained several out-of-transit spectra oneach of those two nights as well as on January 15, 2010(UT). The out-of-transit spectra were obtained in orderto help establish the Keplerian orbital parameters of thesystem. We adopted a typical exposure time as 600-750seconds, and chose the slit width as 0.4 ′′ , correspondingto the spectral resolution of ∼ , ∼
100 per pixel in the 1D spectra. Wethen processed the reduced spectra with the RV analysisroutines for Subaru/HDS developed by Sato et al. (2002).Table 1 gives the resulting RVs (corrected for the motionof the Earth) and the associated errors, which are com-puted from the dispersion of RVs that were determinedfrom individual 4 ˚A segments of the spectrum (Sato et al.2002). We obtained a typical RV precision of 11-14 m s − .
3. Analysis and Results
We determined the projected spin-orbit angle λ in sev-eral steps. First, in order to provide an independent de- Table 1.
Radial velocities measured with Subaru/HDS.
Time [BJD (TDB)] Relative RV [m s − ] Error [m s − ]2455164.703174 523.9 13.42455164.711814 514.4 13.52455164.719564 497.3 13.42455164.727304 457.9 13.12455164.735054 404.1 11.52455164.742804 358.9 13.52455164.750544 333.2 12.82455164.758275 277.8 13.02455164.766005 232.3 12.72455164.773745 198.3 12.52455164.781485 195.7 13.12455164.789205 149.4 12.92455164.796945 111.1 12.82455164.804675 112.2 12.22455164.812405 109.7 13.02455164.820135 130.9 11.92455164.827875 157.7 12.72455164.835605 124.0 12.42455164.839555 166.4 21.82455211.720046 766.1 14.52455211.729516 774.0 13.72455211.738975 844.1 14.22455231.709440 492.8 14.02455231.718219 524.8 13.32455231.725949 506.8 13.92455231.733688 480.2 13.32455231.741418 427.6 13.52455231.749157 444.2 13.12455231.756887 416.1 12.52455231.764636 356.7 13.82455231.772366 283.6 14.92455231.780095 308.1 14.22455231.787834 220.1 13.02455231.795574 183.6 12.22455231.803313 179.2 13.42455231.811063 132.0 12.82455231.818802 127.6 12.82455231.826532 70.5 12.32455231.834271 72.9 12.02455231.842001 122.6 13.22455231.849740 139.6 13.12455231.857469 110.5 13.2termination, we use only the transit data from our newSubaru observations. Since those data alone are insuffi-cient to determine all the Keplerian orbital parameters ofthe system, we also use the out-of-transit RV data pointsfrom OHP/SOPHIE (H´ebrard et al. 2008). This essen-tially provides an independent determination of λ since wedo not use the in-transit RV data from OHP/SOPHIE.Our model for the RVs is similar in some respectsto the previous analyses by Narita et al. (2009a) andNarita et al. (2010). Each RV data set (Subaru/HDS andOHP/SOPHIE) is modeled as V model = K [cos( f + ̟ ) + e cos( ̟ )] + ∆ v RM + γ offset , (1)o. ] 3where K is the orbital RV semi-amplitude, f is the trueanomaly, e is the orbital eccentricity, ̟ is the angle be-tween the direction of the pericenter and the line of sight,and finally γ is a constant offset for the data from a givenspectrograph.The RM velocity anomaly ∆ v RM is modeled withEquation (16) of Hirano et al. (2011). In order to compute∆ v RM , we adopt the following values for the basic spectro-scopic parameters; the macroturbulence dispersion ζ = 6 . − , the Gaussian dispersion (including the instrumen-tal profile) β = 3 . − , and the Lorentzian dispersion γ = 1 . − . These values are taken from Gray (2005)and from the comparison with the numerical simulationsby Hirano et al. (2011). Also, we assume the quadraticlimb darkening law with u = 0 .
32 and u = 0 .
36 followingClaret (2004).We fit the two RV data sets (Subaru and OHP) by min-imizing χ = X i " V ( i )obs − V ( i )model σ ( i ) , (2)where V ( i )obs is the observed RV value labeled by i while V ( i )model corresponds to Equation (1). The uncertainty foreach RV point is expressed by σ ( i ) . Since we do nothave any new photometric observations of the transit,we fix the photometrically measured parameters to be R p /R s = 0 . a/R s = 7 .
07, and i o = 84 . ◦ from therefined parameter set by Winn et al. (2008). The remain-ing parameters are K , e , ̟ , γ offset (for each data set),the rotational velocity of the star v sin i s , and the spin-orbit angle λ . We allow all the parameters to vary freelyto minimize χ , using the AMOEBA algorithm. We addthe stellar jitter of σ jitter = 13 . − in quadrature tothe RV uncertainties in Table 1 so that the reduced χ inthe global RV fitting becomes unity (after adding an ad-ditional parameter to allow for an offset between the twoSubaru transits, as explained below). This jitter is ac-counted for in estimating the uncertainty for the systemparameters in Table 2.By fitting the Subaru/HDS data along with the out-of-transit OHP/SOPHIE data, we find the spin-orbit angleto be λ = 36 . ◦ ± . ◦ . This is in agreement with the pre-vious finding by Winn et al. (2009), and in disagreementwith the previous finding by H´ebrard et al. (2008). Thereduced chi-squared is ˜ χ = 1 .
14. Interestingly, when weplot the residuals between the Subaru/HDS data and thebest-fit model, we find a small negative trend as a functionof time over the 67-day span of the observations. To showthis, we plot our new out-of-transit
RV data as a functionof BJD in the upper panel of Figure 1, along with thebest-fit curve (red). The residuals from the best-fit curveare shown at the bottom. This trend cannot be corrobo-rated or refuted by the previously published observations;the RV precision obtained by Johns-Krull et al. (2008)and H´ebrard et al. (2008) was insufficient, and the preciseRV measurements of Winn et al. (2009) did not cover asufficiently long observation period. -100-50 0 50 100 160 170 180 190 200 210 220 230 R e s i dua l [ m s - ] BJD - 2455000-1000-500 0 500 1000 1500 2000 2500 R V [ m s - ] Subaru out-of-transitbest-fit model-100-50 0 50 100 -0.4 -0.2 0 0.2 0.4 R e s i dua l [ m s - ] Orbital Phase-1000-500 0 500 1000 1500 2000 R V [ m s - ] OHPSubarubest-fit model
Fig. 1. (Upper) New RV data outside of transits, obtainedwith Subaru/HDS. (Lower) The orbit of XO-3b based on themeasurements with Subaru/HDS (blue), and the previouslypublished RVs obtained with OHP/SOPHIE (black). For thisfigure, a linear RV trend ( ˙ γ ) was fitted to the data and thensubtracted. For each of the figures above, the best-fit modelis shown as a red curve and the RV residuals from the best-fitmodel are plotted at the bottom. [Vol. , Table 2.
The best-fit parameter sets.
Parameter (A) Subaru (B) Subaru + Keck K [m s − ] 1499.5 ± ± e . +0 . − . . ± . ω [ ◦ ] 347 . ± . . +1 . − . v sin i s [km s − ] 17 . ± . . ± . λ [ ◦ ] 37 . ± . . ± . γ [m s − day − ] − . ± . − . ± . χ γ , representing a constant radial acceleration.We then refitted the Subaru RV data. The results fromthis fit are given in column (A) in Table 2. The uncer-tainty for each parameter is derived by the criteria that∆ χ becomes unity. The inclusion of the constant ac-celeration improves the reduced chi-squared significantly( ˜ χ = 0 .
91 from 1.14 in the absence of ˙ γ ) and the best-fitRV acceleration is ˙ γ = − . ± .
088 m s − day − , indi-cating a 3 . σ detection. Since the two transit observationsare separated by 67 days, the RV offset between the twotransits is estimated as ∼
22 m s − . The resultant RVsas a function of the orbital phase are shown in the lowerpanel of Figure 1. Now that we have seen that our new results bySubaru/HDS support the previous RM measurement byKeck/HIRES (Winn et al. 2009), we would like to try tocombine the two independent measurements (Subaru andKeck) and carry out a joint analysis in order to derive theparameters with greater precision.We fit all of the transit data from Subaru/HDSand Keck/HIRES, and also the out-of-transit data fromOHP/SOPHIE. We allow for a constant RV acceleration˙ γ , as before. We estimate the best-fit values for K , e , ̟ , v sin i s , λ , and ˙ γ as in Section 3.1. The results aresummarized in the column (B) of Table 2. Most of thevalues are very close to the best-fit values in case (A).The projected rotation rate of v sin i s = 18 . ± . − is in good agreement with the spectroscopically measuredvalue ( v sin i s = 18 . ± .
17 km s − , Johns-Krull et al.2008). The resulting phase-folded RV anomalies duringtransits are plotted in Figure 2, in which the Keplerianmotion and the linear RV trend are subtracted from thedata. The RV data taken by Subaru/HDS are indicatedin blue for the first transit and purple for the second tran-sit, and those by Keck/HIRES are shown in green. Thered solid curve is the best-fit curve based on the analyticformula of Hirano et al. (2011). -80-60-40-20 0 20 40 60 80-0.03 -0.02 -0.01 0 0.01 0.02 0.03 R e s i dua l [ m s - ] Orbital Phase-200-150-100-50 0 50 100 ∆ v [ m s - ] KeckSubaru 1st visitSubaru 2nd visit
Fig. 2.
RV data spanning the transit, after subtracting theorbital contributions to the velocity variation, and also a lin-ear function of time. The plotted data includes the newSubaru/HDS data (blue for the fist transit on UT 2009 Nov.29 and purple for the second transit on UT 2010 Feb. 4) andthe previously published Keck/HIRES data taken on UT 2009Feb. 2 (green). The RV residuals are plotted at the bottom.
4. Discussion and Summary
We have investigated the RM effect for the XO-3 sys-tem, which was the first confirmed system with a signifi-cant spin-orbit misalignment (H´ebrard et al. 2008). Thenew spectroscopic measurements including two full tran-sits taken by Subaru/HDS and the new analysis methodusing the analytic formula for the RM effect by Hirano etal. (2011), found the spin-orbit angle of λ = 37 . ◦ ± . ◦ ,supporting the result by Winn et al. (2009) based on themeasurement with Keck/HIRES. The joint analysis of allthe RV data sets covering three transits with Subaru/HDSand Keck/HIRES have shown that the projected stellarspin velocity estimated by the RM analysis well agreeswith the spectroscopically measured value.Our analysis also detected an RV trend, or at least RVoffsets, among the three epochs of the Subaru/HDS obser-vations. The cause of the extra RV variation is not clear.It is possibly an indication of a third body in the sys-tem: a stellar companion (binary), or an additional mas-sive planet. Nevertheless it should be noted that this staris known to have a high “RV jitter” of around 15 m s − ,and the precise physical causes and timescales of the jitterare not known. It is possible for starspots or other surfaceinhomogeneities being carried around by stellar rotationto produce a systematic offset in RV observations con-ducted on a single night. Since the rotational velocityof the star is large for a planet-hosting star, even a rela-tively small spot could cause an apparent RV anomaly ino. ] 5a similar manner as the RM effect. For example, the RVacceleration of 22 m s − could be caused by a very darkspot whose size is only 0.002 of the total stellar disk area.The best way to investigate these possibilities is with ad-ditional measurements of the out-of-transit RV variation,with a precision better than 15 m s − .As for the results for λ , we would like to understand thereason for the discrepancy between the OHP/SOPHIE re-sults, and the Subaru/HDS + Keck/HIRES results. Tothis end we try several additional tests. As we havepointed out, H´ebrard et al. (2008) employed the analyticformula based on the first moment of the distorted lineprofiles to describe the RM effect (Ohta et al. 2005). Forrapidly rotating stars, however, the RM velocity anomalycomputed from the first moment significantly deviatesfrom that based on the cross-correlation method (Hiranoet al. 2010). Therefore, we reanalyze the OHP data usingthe new analytic formula by Hirano et al. (2011) to see ifthe original estimate for the spin-orbit angle λ was biased.Instead of fixing the stellar spin velocity v sin i s as doneby H´ebrard et al. (2008), we allow it to be a free param-eter, and fit all the OHP RV data (H´ebrard et al. 2008).The resulting spin-orbit angle is λ = 58 . ◦ ± . ◦ and thestellar spin velocity of v sin i s = 15 . ± . − . The cen-tral value for λ approaches our new results (37 . ◦ ± . ◦ ),but they still disagree with each other with > σ . Thisshows that a biased model played only a minor role in thediscrepancy. The major reason seems to have been sys-tematic effects in the OHP/SOPHIE dataset, perhaps dueto the short-term or long-term instrumental systematics(instability) for fainter objects as reported by Husnoo etal. (2011).Incidentally, with only a small modification, the ana-lytic formula by Hirano et al. (2011) can also be used tocalculate the RM velocity anomaly in the presence of dif-ferential rotation (DR). The detection of DR would be ofgreat interest for understanding the convective/rotationaldynamics of the host star. Furthermore, it allows a possi-bility to break the degeneracy between the projected andthe real three-dimensional spin-orbit misalignment angleby inferring the inclination angle of the stellar spin axiswith respect to the line of sight ( i s ), an angle that is or-dinarily not measurable with the RM observations (if thestar is a solid rotator).Since XO-3 has a comparably large v sin i s , our new datamay provide a good opportunity to search for the signa-ture of DR, or at least to put constraints on the degree ofDR quantitatively.To model DR, we introduce two major parameters: thestellar inclination i s and the coefficient of DR, α . Thestellar angular velocity Ω as a function of the latitude l on the stellar surface is written as Ω( l ) = Ω eq (1 − α sin l ),where Ω eq is the angular velocity at the equator (Reiners2003b). We step through a two-dimensional grid in α andcos i s , and for each grid point we fit the RVs with the sixparameters listed in Table 2. We compute the resulting χ at each point ( α , cos i s ). We note here that the DRof our Sun is well described by α ≃ .
2. This also seemsto be a typical value of other stars based on the spectral c o s i s α∆χ = 1.0 ∆χ = 0.0 Fig. 3.
Contour plot of ∆ χ in the space of the DR parame-ters α and i s . The confidence region where ∆ χ ≤ . χ = 2 .
30 by the black dashed line, which de-termines the 1 σ region in a two-dimensional parameter space. line analysis of (Reiners & Schmitt 2003a), although thoseauthors also point out that some stars may have “anti-solar” like differential rotations in which α <
0. Thus, ourgrid extends from − . ≤ α ≤ . ≤ cos i s ≤ . i s > .
95 is very unlikely because thestar would need to be rotating unrealistically rapidly togive the observed value of v sin i s .Figure 3 shows contours of ∆ χ ≡ χ − χ in the ( α ,cos i s ) plain. The location of the best-fit model (definingthe condition ∆ χ = 0 .
0) is plotted with a black cross.This figure shows that with the current RV data, we areonly able to provide fairly weak constraints on the param-eters. We are able to rule out the far upper left and rightcorners of this parameter space, corresponding to Solar-like DR viewed at low inclinations. We can rule out muchstronger levels of DR ( | α | > ∼ .