Determination of the inclination of the multi-planet hosting star HR8799 using asteroseismology
Duncan Wright, André-Nicolas Chené, Peter De Cat, Christian Marois, Philippe Mathias, Bruce Macintosh, Josh Isaacs, Holger Lehmann, Michael Hartmann
aa r X i v : . [ a s t r o - ph . S R ] J a n To appear in ApJ Letters
Determination of the inclination of the multi-planet hosting starHR8799 using asteroseismology D. J. Wright
Koninklijke Sterrenwacht van Belgi¨e, Ringlaan 3,B-1180 Brussel, Belgium
A.-N. Chen´e
Canadian Gemini Office, HIA/NRC of Canada,5071, West Saanich Road, Victoria (BC), V9E 2E7, CanadaDepartamento de Astronom´ıa, Casilla 160-C, Universidad de Concepci´on, ChileDepartamento de F´ısica y Astronom´ıa, Facultad de Ciencias,Universidad de Valpara´ıso, Av. Gran Breta˜na 1111, Playa Ancha,Casilla 5030, Valpara´ıso, Chile [email protected]
P. De Cat
Koninklijke Sterrenwacht van Belgi¨e, Ringlaan 3,B-1180 Brussel, Belgium [email protected]
C. Marois
National Research Council Canada, Herzberg Institute of Astrophysics,5071 West Saanich Road, Victoria, BC V9E 2E7, Canada
P. Mathias
Laboratoire d’Astrophysique de Toulouse-Tarbes, Universit´e de Toulouse, CNRS, 57 avenued’Azereix, F-65000 Tarbes, France [email protected]
B. Macintosh
Lawrence Livermore National Laboratory,7000 East Avenue, Livermore, CA 94550, USA [email protected]
J. Isaacs
Lawrence Livermore National Laboratory,7000 East Avenue, Livermore, CA 94550, USADepartment of Physics, University of Wisconsin,Madison, WI, 53706, USA [email protected] andH. Lehmann and M. Hartmann
Th¨uringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenburg, Germany [email protected]; [email protected]
ABSTRACT
Direct imaging of the HR8799 system was a major achievement in the study ofexoplanets. HR8799 is a γ Doradus variable and asteroseismology can provide anindependent constraint on the inclination. Using 650 high signal-to-noise, highresolution, full visual wavelength spectroscopic observations obtained over twoweeks at Observatoire de Haute Provence (OHP) with the SOPHIE spectrographwe find that the main frequency in the radial velocity data is 1.9875 d − . Thisfrequency corresponds to the main frequency as found in previous photometricobservations. Using the FAMIAS software to identify the pulsation modes, wefind this frequency is a prograde ℓ =1 sectoral mode and obtain the constraintthat inclination i & ◦ . Subject headings: stars: oscillations — stars: variables: other — stars: individual(HR 8799) 3 –
1. Introduction
The imaging discovery of the three (Marois et al. 2008), and now four (Marois et al.2010) planets around HR 8799 is a significant achievement in the search for and study ofplanets orbiting other stars. For the first time, the thermal emission of planets in orbitaround another star has been unambiguously detected.The dynamical evolution of a planetary system is complex. From the basic planet forma-tion assumption that planets form by the core accretion or disk instability scenario in a diskalong the star’s equatorial plane, systems can suffer drastic changes; planet-planet perturba-tions, interactions with a disk or stellar encounters can change a planet’s orbital inclination,its semi-major axis, its orbital eccentricity or even eject it (Raymond, Armitage & Gorelick2010). In the case of HR 8799, it is not impossible that a close encounter occurred priorto planet formation, since its relatively high galactic velocity compared to the Columba as-sociation and its far distance away from the other association members (Hinz et al. 2010)are suggesting that it may have been kicked out and is probably moving quickly away fromits birth place. Such an encounter could have tilted a disk relative to the star’s equatorialplane and induce perturbations that may have led to planet formation where planets wouldhave a non-negligible orbital inclination relative to the star. Radial velocity searches haveconfirmed such chaotic behaviors by detecting systems where planets are orbiting well awayfrom the star’s equatorial plane (Triaud et al. 2010 and references therein), although forclose-in extrasolar planets this misalignment could also be caused by the Kozai mechanism(e.g. Wu, Murray & Ramsahai 2007; Fabrycky & Tremaine 2007; Winn et al. 2009). Forthe wide HR8799 planets the Kozai mechanism is not operational (even if the system hada stellar companion in the past); finding a misalignment between the star and the planet’sorbital plane would be a sign of a significant dynamical interaction in the system past.Marois et al. (2008) have suggested that the HR 8799 planets are in a similar orbitalplane with a low inclination and have mostly circular orbits. This is because the detectedorbital motions are close to their expected face-on circular orbit values, the orbital motion ismainly in azimuth and the star is known to be a slow rotator (thus it would be viewed mainlypole-on). Dynamical analyses (e.g. Reidemeister et al. 2009; Fabrycky & Murray-Clay2010; Moro-Mart´ın, Rieke & Su 2010; Marshall, Horner & Carter 2010) have confirmedthat the planets are mostly in the same plane with small eccentricities, although such fitsare still very uncertain due to the limited amount of orbital coverage available. In addi-tion, the planets also all orbit in the same counter-clockwise orientation, further support- Based on observations obtained at the Observatoire de Haute-Provence which is operated by the InstitutNational des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France. i ∼ ◦ –23 ◦ ; while attempting a co-herent analysis of various portions of observational data on known components of the sys-tem, Reidemeister et al. (2009) concluded that i should range between 20 ◦ and 30 ◦ . Also,Spitzer observations of HR 8799’s complex debris disk suggest that any inclination anglelarger than ∼ ◦ should be excluded (Su et al. 2009). Using a statistical distribution ofstar’s rotation speed (Royer, Zorec & G´omez 2007), HR 8799 with its 37.5 ± − V sin i (Kaye & Strassmeier 1998) would be consistent with an inclination of ∼ . ◦ if it is an A5star or ∼ . ◦ if it is an F0 star (HR 8799 spectral classification is uncertain mainly dueto its low metallicity that is affecting it’s broad band colors). Such a determination is ofcourse statistical and a direct star’s inclination determination is required for a meaningfulcomparison with the estimated planet orbital plane inclination.HR 8799 is an intrinsic photometric and spectroscopic variable (Rodriguez & Zerbi1995; Mathias et al. 2004). It has also been confirmed as a γ Doradus (Dor) variable(Zerbi et al. 1999). The γ Dor stars are late A to early F stars whose pulsations are drivenby a flux-blocking mechanism at the base of their convective envelope (e.g. Dupret et al.2004). The γ Dor nature of HR 8799 offers a unique opportunity to estimate its inclinationvia an asteroseismic analysis of the observed g -modes. In a previous asteroseismic analysisusing photometric frequencies Moya et al. (2010) has shown that an age determination forthe system, which allows to discriminate between planets and brown dwarfs, is a difficult taskwith the current information and discussed the importance of an inclination determinationsince the equatorial rotational velocity can be used in constraining the age of the system.In this letter, we present a spectroscopic asteroseismic analysis and also obtain limits forHR 8799’s stellar inclination. The data have been acquired from an extensive multi-siteground-based high-resolution spectroscopy campaign. Section 2 describes that data used inthis letter. Section 3 discusses the pulsation mode identification and the determination ofthe stellar inclination and Section 4 describes the conclusions.
2. Observations
In this letter we examine data collected from Observatoire de Haute Provence (OHP)using the SOPHIE spectrograph. We have 650 SOPHIE observations taken from 28/09 -12/10/2009. They cover a wavelength range between 3875–6940˚A with a spectral resolutionof R ∼
75 000. These data are the largest single-site subset of more than 2000 observationstaken during an intensive spectroscopic multi-site campaign devoted to this star. Only theOHP spectra will be examined in this publication as study of the complete combined data 5 –set of observations will be left until the detailed publication.The data were treated using the local reduction packages written specifically for theSOPHIE spectrograph data. This produced reduced, merged and automatically continuumnormalized 1-D spectra which were further manually normalized using a synthetic spectrumfor guidance.Instead of using single spectral lines, we examined the cross-correlation profile (CCP).This profile is obtained using the normalised 1-D spectra cross-correlated with a line mask.The line mask was produced with the SYNSPEC software (Hubeny & Lanz 1995) using aT eff =7500 K, log( g ) = 4 . − and 1.7475 d − (shown in Figure1: right). These frequencies by themselves produce a good fit to the observed radial velocityvariations. They closely correspond with those found in photometry by both Zerbi et al.(1999) and Cuypers et al. (2006).
3. Pulsation mode identification
It is possible to identify further frequencies present in the data but upon examinationit is observed that extraction of any combination of the other frequencies present does notalter the results for the 1.98 d − frequency. The focus for this letter is on the inclinationrestrictions possible from the 1.98 d − frequency, hence we will continue without examiningany further frequency information, and leave that for the detailed publication based on thewhole dataset of the campaign.To determine the degree ℓ and azimuthal order m of the pulsation mode using theFAMIAS software (Zima 2008) we extract the Fourier parameters, i.e. the zero point,the amplitude and the phase distributions across the CCPs, for the two frequencies. The − and 1.7475 d − fit for the first half ofthe OHP data (left). Frequency analysis of the radial velocity of the OHP data (right) withlines marking the frequencies determined.Fourier parameters of 1.9875 d − are shown as a solid line in the panels of Figure 2. TheFourier parameters of 1.7475 d − were not sufficiently well matched by the FAMIAS softwareto consider this pulsation mode identified or constrained. This is probably a result of otherpulsation frequencies present in the data that have not been detected or removed, and thathave sufficient amplitude to affect the parameters of the 1.7475 d − mode.The FAMIAS software uses a first order Coriolis force approximation, limiting the pul-sation models that can be used to fit the Fourier parameters to those respecting ν ≤
1, where ν is the so-called “spin-parameter”. This parameter is defined as ν = 2 f Ω /f corot , where f Ω is the rotation frequency and f corot is the pulsation frequency in the corotating frame. f corot is connected to the observed pulsation frequency f obs through: f corot = f obs - m f Ω and, hence,changes for different values of m of the model being fitted. As for f Ω , its changes dependon the inclination used by the model. On the other hand, one could wonder how significantis the effect of stellar rotation when ν > n ) low degree ( ℓ ) gravity-modes (see Figure 1 of Townsend2003) and found that prograde modes ( m >
0, this paper; m < ν limitations for the FAMIAS models of the 1.9875 d − frequency. For the valuesof m =-3:3, limits of ν ≤ m =3, ν ≤ m =2, ν ≤ m =1 and ν ≤ m ≤ ν limitations and the estimated stellar parameters R ∗ =1.5 R ⊙ (Gray & Kaye 1999), V sin i =39.5 km s − (i.e. a value within the uncertainties given bythis study and by Kaye & Strassmeier 1998) we can place restrictions on the inclination forwhich the FAMIAS models are valid for each value of m , they are i = 60 ◦ , 37 ◦ , 32 ◦ , 32 ◦ , 15 ◦ , 7 –0 ◦ and 0 ◦ for m = 3, 2, 1, 0, -1, -2 and -3, respectively.These model limits imply that we cannot test all the inclinations between 0 ◦ and 90 ◦ .However, one has to consider that an inclination lower than 5 ◦ is physically impossible, sinceit would imply an equatorial rotation velocity higher than the break-up velocity when usingan estimated mass of M ∗ =1.5 M ⊙ (Gray & Kaye 1999). Moreover, models with m =1, 2 and3 are limited to i > ◦ , 33 ◦ and 54 ◦ respectively to be physically possible (f corot > m and inclinationthat we are unable to test due to the FAMIAS model restrictions. However, these “holes” canbe mitigated by the fact that at lower inclinations than those imposed by the model limits,the ν value, and hence the Coriolis force, becomes large enough that the pulsations surfacedeformations begin to be limited to an equatorial waveguide (Townsend 2003). In these casesjust the regions about the equator are varying, but we would be viewing the star from lowinclinations. This means that only a small area of the visible surface would be experiencingpulsation and the radial velocity amplitude would be expected to be low when compared withobserved radial velocity amplitudes in other γ Dor stars. To give an example of this, if i =20 ◦ and the mode was m =0 then approximately one quarter of the full surface variability is visiblesince more than half the pulsation amplitude is constrained to within 35 ◦ of the equator.In contrast, the 1.98 d − frequency in question has an amplitude of 1.09 km s − which iscomparable to the radial velocity amplitudes of the strongest mode in other γ Dor stars e.g.1.3 km s − in γ Doradus (Balona et al. 1996), 0.35 km s − in HD49434 (Uytterhoeven et al.2008), 1.45 km s − in HD189631 and 0.49 km s − in HD40745 (Maisonneuve et al. 2010).Therefore, it is unlikely that we are dealing with a strong Coriolis force and hence a high ν value for a given m value. Because of this the inclination “holes” mentioned previously,which are associated with high ν values, can be considered as unlikely solutions.Table 1: Table of constraints on the inclination from both the model limitations and physicalconstraints m value 3 2 1 0 -1 -2 -3model i limits ( ◦ ) > > > > > > > i limits ( ◦ ) > > > > > > > ℓ and m combinations from ℓ =0 to ℓ =3 were tested keeping in mind the restrictionsfrom Table 1. Higher values of ℓ were not considered because the 1.9875 d − is a strongphotometric frequency found in the data of Zerbi et al. (1999) and modes with ℓ > ℓ and m values obtained with FAMIAS are shown in Figure2. The dashed-dotted line corresponds to an ℓ =1 m =1 mode with χ red =30.0 and the dottedline to an ℓ =2 m =-2 mode with χ red =43.9. This figure confirms that the best fitting mode isthe ℓ =1 sectoral mode as the ℓ =2 m =-2 solution does not match the shape of the amplitudedistribution well. The extremely small uncertainties in the zero point distribution causeany deviation from a perfect fit to rapidly increase the χ red value. Hence, the value of χ red =30.0 should be considered as a very good fit. On examination of the amplitude andphase distributions across the profile for all of the modes tested, only the ℓ =1 m =1 modedemonstrates a good match in shape for both and is considered conclusively the best solutionfor this pulsation frequency. The values for the input parameters to FAMIAS resulting fromthis mode are given in the last column of Table 2. The errors are estimated based on anexamination of the χ red results.Table 2: Table of parameters for genetic algorithm search. Both the allowed range and bestfit results, an ℓ =1 m =1 mode, are shown. Uncertainties are estimated based on χ red resultsParameters Allowed ranges Best fitmin : maxM ∗ (M ⊙ ) 1.2 : 1.8 1.5 ± ∗ (R ⊙ ) 1.2 : 1.8 1.5 ± ◦ ) 5 : 90 65 ±
25V sin i (km s − ) 36 : 46 39.8 ± − ) 5 : 15 8.3 ± − ) 0.1 : 10 0.659 ± π ) 0 : 1 0.95 ± ℓ =1 m =1 mode. Based on Table 1 we can confidently use the FAMIAS results for i ≥ ◦ . The best fit inclination has i =65 ◦ . For i = 35 ◦ , 40 ◦ and 90 ◦ , we find χ red = 37.2, 32.9and 31.07, respectively. It is obvious from Figure 3 that the χ red does not change much inthe range i = 40 ◦ to 90 ◦ but it rises quickly at lower inclinations. From this we obtain ourresult i & ◦ .The FAMIAS software assumes that pulsation axis is aligned with the rotational axis,but this is not necessarily the case in all stars. However, such misalignment is unlikely in thecase of HR 8799 because, in that case, some modulation of the pulsation properties by therotational period would have been observed. In addition, it would have led to more complexamplitude and phase across the profile, and the fits that we have achieved would not havebeen as good. 9 – Z e r o p t. A m p l . ( k m s − ) −70 −60 −50 −40 −30 −20 −10 0 10 20 30 40−0.500.5 Velocity (km s −1 ) P ha s e ( π r ad ) Fig. 2.— Zero point profile (top), amplitude distribution (middle) and phase distribution(bottom) for the frequency 1.98 d − is the solid line. The best fit ℓ =1 m =1 mode is thedashed-dotted line with a χ red of 30.0. The next best fitting mode of those tested is the ℓ =2 m =-2 mode shown as a dotted line with χ red =43.9.
10 20 30 40 50 60 70 80 9010 Inclination (deg) χ
30 40 50 60 70 8025303540
Fig. 3.— The inclination dependence of the genetic algorithm search for the best fitting ℓ =1 m =1 mode. The inset figure is a zoom in on the region of low χ red . For inclinations i & ◦ the differences in χ red is small.It is worth noting that no planetary reflex velocity is identified. This was expectedsince the amplitudes of the quite distant and low orbital inclination exo-planets would beonly fractions of a meter per second which would be masked by the much larger (km s − )pulsational velocities and is also beyond the precision attainable by our observations. 10 –
4. Conclusions
We conclude that the stellar rotational inclination axis has a value i & ◦ based onidentification of the 1.98 d − frequency as an ℓ =1 m =1 mode. This is the strongest pulsa-tion in both photometry (Zerbi et al. 1999; Cuypers et al. 2006) and spectroscopic radialvelocities. Through dynamical analyses it is suspected that the planets are mostly in thesame plane with small eccentricities and that the planets orbit inclination axis is ∼ ◦ ± ◦ (Reidemeister et al. 2009; Lafreni`ere et al. 2009). The current data suggests a misalign-ment of ∆ i & ◦ between the stellar rotational inclination and planetary orbit axes, thoughmore detailed pulsational analyses and better orbital fits are needed before this can be con-firmed.We thank A. Moya for helping discussion and useful advices. Wright acknowledgessupport from the Belgian Federal Science Policy (project MO/33/021). ANC acknowledgessupport from Comit´e Mixto ESO-GOBIERNO DE CHILE and from BASAL/ FONDAPproject. PDC acknowledges financial support from the Fund for Scientific Research - Flanders(FWO; project G.0332.06). Portions of this work were performed under the auspices of theU.S. Department of Energy by Lawrence Livermore National Laboratory under ContractDE- AC52-07NA27344. Facilities:
OHP-1.93m (SOPHIE)
REFERENCES
Balona, L. A., B¨ohm, T., Foing, B. H. et al. 1996, MNRAS 281, 1315Cuypers, J., Aerts, C., De Cat, P. et al. 2006, A&A, 499, 967Dupret, M.-A., Thoul, A., Scuflaire, R., Daszy´ska-Daszkiewicz, J., Aerts, C., Bourge, P.-O.,Waelkens, C. & Noels, A. 2004, A&A 414, L17Fabrycky, D. C. & Murray-Clay, R. A. 2010, ApJ, 710, 1408Fabrycky, D. & Tremaine, S. 2007, ApJ, 669, 1298Go´zdziewski, K. & Migaszewski, C. 2009, MNRAS, 397L, 16Gray R. O. & Kaye A. B. 1999, AJ, 118, 2993Hinz, P. M., Rodigas, T. J., Kenworthy, M. A., Sivanandam, S., Heinze, A. N., Mamajek,E. E. & Meyer, M. R. 2010, ApJ, 716, 417 11 –Hubeny, I., Lanz, T. 1995 ApJ, 439, 875Kaye, A. B., Strassmeier, K. G. 1998 MNRAS, 294L, 35Lafreni`ere, D., Marois, C., Doyon, R. & Barman, T. 2009, ApJ, 694, L148Maisonneuve, F., Pollard, K. R., Cottrell, P. L. et al. 2010, MNRASMathias, P., Le Contel, J.-M., Chapellier, E. et al. 2004, A&A 417, 189Marois, C., Macintosh, B., Barman, T. et al. 2008, Sci 322, 1348Marois, C.; Zuckerman, B.; Konopacky, Q. M.; Macintosh, B.; Barman, T.; 2010 arXiv1011.4918Marshall, J., Horner, J. & Carter, A. 2010, IJAsB, 9, 259Moro-Mart´ın, A., Rieke, G. H. & Su, K. Y. L. 2010, ApJ, 721, L199Moya, A., Amado, P. J.; Barrado, D., Garc´ıa Hern´andez, A., Aberasturi, M., Montesinos,B. & Aceituno, F. 2010, MNRAS, 405L, 81Raymond, S. N., Armitage, P. J. & Gorelick, N. 2010, ApJ,711, 772Reidemeister, M., Krivov, A. V., Schmidt, T. O. B., Fiedler, S., M¨uller, S., L¨ohne, T. &Neuh¨auser, R. 2009, A&A, 503, 247Rein, H., Papaloizou, J. C. B. & Kley, W. 2010, A&A, 510, 4Rodriguez, E. & Zerbi, F. M. 1995, IBVS, 4170, 1Royer, F., Zorec, J. & G´omez, A. E. 2007, 463, 671Su, K. Y. L., Rieke, G. H., Stapelfeldt, K. R. et al. 2009, ApJ, 705, 314Triaud, A. H. M. J., Collier Cameron, A., Queloz, D. et al. 2010, A&A 524A, 25Townsend, R. H. D., 2003, MNRAS 343, 125Uytterhoeven, K., Mathias, P., Poretti, E. et al. 2008, A&A, 489, 1213Winn, J. N., Johnson, J. A., Albrecht, S., Howard, A. W., Marcy, G. W., Crossfield, I. J. &Holman, M. J. 2009, ApJ, 703L, 99Wu, Y., Murray, N. W., Ramsahai, J. M. 2007, ApJ, 670, 820 12 –Zerbi, F. M., Rodrigez, E., Garrido, R., et al. 1999, MNRAS 303, 275Zima, W. 2008, CoAst, 155