High surface magnetic field in red giants as a new signature of planet engulfment?
Giovanni Privitera, Georges Meynet, Patrick Eggenberger, Cyril Georgy, Sylvia Ekström, Aline A. Vidotto, Michele Bianda, Eva Villaver, Asif ud-Doula
AAstronomy & Astrophysics manuscript no. 29142˙ap c (cid:13)
ESO 2018June 20, 2018
High surface magnetic field in red giants as a new signature ofplanet engulfment?
Giovanni Privitera , , Georges Meynet , Patrick Eggenberger , Cyril Georgy , Sylvia Ekstr¨om , Aline A. Vidotto ,Michele Bianda , Eva Villaver , Asif ud-Doula Geneva Observatory, University of Geneva, Maillettes 51, CH-1290 Sauverny, Switzerland Istituto Ricerche Solari Locarno, Via Patocchi, 6605 Locarno-Monti, Switzerland School of Physics, Trinity College Dublin, The University of Dublin, Ireland Department of Theoretical Physics, Universidad Aut´onoma de Madrid, M´odulo 8, 28049 Madrid, Spain Penn State Worthington Scranton, Dunmore, PA 18512, USAReceived / Accepted
ABSTRACT
Context.
Red giant stars may engulf planets. This may increase the rotation rate of their convective envelope, which could lead tostrong dynamo-triggered magnetic fields.
Aims.
We explore the possibility of generating magnetic fields in red giants that have gone through the process of a planet engulfment.We compare them with similar models that evolve without any planets. We discuss the impact of magnetic braking through stellarwind on the evolution of the surface velocity of the parent star.
Methods.
By studying rotating stellar models with and without planets and an empirical relation between the Rossby number and thesurface magnetic field, we deduced the evolution of the surface magnetic field along the red giant branch. The e ff ects of stellar windmagnetic braking were explored using a relation deduced from magnetohydrodynamics simulations. Results.
The stellar evolution model of a red giant with 1.7 M (cid:12) without planet engulfment and with a time-averaged rotation velocityduring the main sequence equal to 100 km s − shows a surface magnetic field triggered by convection that is stronger than 10 Gonly at the base of the red giant branch, that is, for gravities log g >
3. When a planet engulfment occurs, this magnetic field canalso appear at much lower gravities, that is, at much higher luminosities along the red giant branch. The engulfment of a 15 M J planet typically produces a dynamo-triggered magnetic field stronger than 10 G for gravities between 2.5 and 1.9. We show thatfor reasonable magnetic braking laws for the wind, the high surface velocity reached after a planet engulfment may be maintainedsu ffi ciently long to be observable. Conclusions.
High surface magnetic fields for red giants in the upper part of the red giant branch are a strong indication of a planetengulfment or of an interaction with a companion. Our theory can be tested by observing fast-rotating red giants such as HD31993,Tyc 0347-00762-1, Tyc 5904-00513-1, and Tyc 6094-01204-1 and by determining whether they show magnetic fields.
1. Introduction
The tidal forces between star and planets change the planetaryorbit and may sometimes produce the engulfment of the planetby the star. A number of past studies (Soker et al. 1984; Siess& Livio 1999a,b; Villaver & Livio 2007, 2009; Nordhaus et al.2010; Kunitomo et al. 2011; Villaver et al. 2014) have shownthat the possible impact of an engulfment, planetary or other-wise, leads to changes in the stellar luminosity and radii for ashort period of evolutionary time, to modifications of the surfaceabundances, in particular to an increase in lithium abundance(Alexander 1967; Fekel & Balachandran 1993; Sandquist et al.1998, 2002; Carlberg et al. 2010; Adam´ow et al. 2012), and tochanges in the surface velocity (Carlberg et al. 2009; Carlberg2014).Our team focused on this last consequence in two previ-ous papers referred to here as Papers I and II (Privitera et al.2016a,b). To explore this e ff ect, we used stellar rotating modelswhere the rotation in the whole star can be followed consistentlyaccording to the shellular theory by Zahn (1992) and a ff ected bytidal interaction when an external convective zone appears (Zahn1977, 1989). Papers I and II showed that the observed surface ve- locities of some stars can only be explained by some interactionwith a planet or a brown dwarf.In this letter we study to which extent such tidal interac-tions and engulfment processes may trigger a magnetic field andalso whether this planet-induced magnetic field might be strongenough to slow down the stellar rotation through the process ofwind magnetic braking (ud-Doula & Owocki 2002; ud-Doulaet al. 2008). Section 2 briefly recalls the main ingredients of themodels. The evolution of the Rossby number for di ff erent stellarmodels is discussed in Sect. 3. Planet-induced magnetic fieldsand their possible consequences on the evolution of the stellarrotation are presented in Sect. 4, and conclusions are drawn inSect. 5.
2. Physics of the models
To study the problem addressed here, we need to understandstellar and planetary models whose evolutions are closely inter-linked through five di ff erent processes: (a) the evolution of theplanetary orbit that accounts for the evolution of the star, (b) thechanges in angular momentum of the star that are due to changesin planetary orbit, (c) the physics of the engulfment, (d) the linkbetween the engulfment and the generation of a surface mag- a r X i v : . [ a s t r o - ph . S R ] S e p rivitera et al.: High surface magnetic field in red giants as a new signature of planet engulfment? netic field, and (e) the impact of the generated magnetic field onthe rotational evolution of the red giant star. The first three pro-cesses were extensively discussed in Papers I and II. Here wefocus on the last two, which involve magnetic fields. Red giantsare characterized by a deep convective envelope in slow rota-tion, therefore tidal dissipation can be introduced by taking intoaccount only the equilibrium tide (see e.g. Ogilvie 2014; Villaveret al. 2014). The impact of inertial waves in the convective en-velope (see e.g. Bolmont & Mathis 2016) and dynamical tidesin the radiative envelope of main-sequence models (Zahn 1975)can be safely neglected in the present computations because theconvective envelope of red giants rotate slowly and the separa-tion between the planet and the star (initial semi-major axis of0.5 au) is relatively large.As shown in Sect. 4, a planet engulfment may strongly ac-celerate the convective envelope of a red giant. When rotationis high enough, it may, through Coriolis acceleration, create dif-ferential rotation and helical turbulence in the convective zone,which is required for a dynamo process (the so-called α and ω e ff ects, respectively) (see e.g. Sect. 3.2.2 in Charbonneau 2013).To determine whether Coriolis acceleration is strong enoughto create di ff erential rotation, a dimensionless number calledRossby number can be defined asRo ≡ P rot / t tov , (1)where P rot is the stellar spin period and t tov the convective turn-over time. In general, Ro < B ) of red giants increases when the Rossby num-ber decreases has recently been found for solar-type and low-mass stars (Vidotto et al. 2014; Auri`ere et al. 2015). We hereuse the relation given by Auri`ere et al. (2015) for red-giant stars:lg( B ) = − . ∗ lg(Ro) + . ffi ciently strong surface magnetic field is gener-ated, it may force the stellar wind to co-rotate with the star. Thisin turn may lead to a torque on the convective envelope. This isthe essence of wind magnetic braking. The loss of angular mo-mentum by this process is first estimated following ud-Doula &Owocki (2002) and ud-Doula et al. (2008),d J d t =
23 ˙ M Ω R [0 . + ( η ∗ + . / ] , (2)where J is the angular momentum of the convective envelope,˙ M the mass-loss rate given by Reimers (1975), Ω , the angu-lar surface velocity, R the stellar radius, and η ∗ the magneticconfinement parameter (ud-Doula & Owocki 2002) defined by η ∗ ≡ B R / ˙ M υ ∞ , where B is the surface magnetic field at theequator and υ ∞ the terminal wind velocity. Winds of red giantstars are expected to be slow, with observed terminal wind ve-locities of between 30 and 70 km s − (Robinson et al. 1998). Forour models here, we chose υ ∞ =
50 km s − . Except for υ ∞ , theother quantities were taken from stellar evolution models.Equation (2) was deduced for hot massive stars from 2DMHD simulations of magnetic wind confinement models wherea rotation-aligned dipole magnetic field is considered. In the caseof red giants, one notable di ff erence, however, is the ionizationfraction of the wind, which is of course much lower for red giantsthan for the hot stars. The lower the ionization fraction, the lower the coupling between the wind and the magnetic field, probably,and thus the weaker the wind braking. To account for this ef-fect, we computed the loss of angular momentum in our model(d L / d t ) using a parametric approach by introducing a wind brak-ing e ffi ciency factor f ≤ L / d t = f d J / d t , where d J / d t is given by Eq. (2).Because Eq. (2) was deduced for hot massive stars, the ques-tion is whether it can be used for red giants with an externalconvective envelope. In principle, this can be the case if theformalism is not too sensitive to the wind-driving mechanism.To check this point, we also used the formalism of Matt et al.(2012), which has been obtained for solar-type stars. The loss ofangular momentum according to Matt et al. (2012) is then givenbyd J d t = K (2 G ) m B ˙ M − R + M m Ω ( K + . s (cid:63) ) m , (3)where K = . K = . G is the gravitational constant, m = . M is the mass of the star, and s (cid:63) = Ω R / ( GM ) − / (see Matt et al. 2012, for more details). For Eq. (2) an e ffi ciencyfactor f is used to change the braking e ffi ciency.
3. Evolution of the Rossby number
Planet engulfment has a very significant impact on the surfacerotation of red giants. We show this in the left panel of Fig. 1,where we plot the evolution of surface rotation velocities as afunction of surface gravity for 1.7 M (cid:12) stellar models with var-ious initial rotation rates, as indicated in the caption. It thencompares what happens when a 15 M J planet is engulfed (ata log g of around 2.2) by an initially slowly rotating 1.7 M (cid:12) star.Clearly, the engulfment leads to a spin-up at a level that cannotbe reached by single-star models regardless of their initial rota-tion rates (Paper II). If a lower mass planet is considered, thenthis will change the time at which the engulfment occurs, shift-ing it to lower gravities, which will produce a lower increase inthe surface velocity (see Paper II). The same occurs when themass of the planet is kept constant but the initial distance to thestar is increased.The right panel of Fig. 1 shows the evolution of the Rossbynumber for the same models. Models without engulfment have aphase where Ro < ffi ciently fast for Ro to decrease below 1. Morequantitatively, when we initially consider the fastest rotatingmodel, Ro < ff erent evolution of Ro is evident. At the time ofengulfment, the Rossby number becomes suddenly smaller than1. After the engulfment, the star continues to expand and themagnetic braking causes the Rossby number to increase again.When we compare models with and without engulfment, themost striking di ff erence is that models with planet engulfmentproduce Ro < < . This suggests that such amodel can hardly produce an observable magnetic field.
4. Planet engulfment and surface magnetic field
We now study the magnetic field generation for our models. Theleft panel of Fig. 2 shows the predicted evolution of the sur-face magnetic field as a function of the surface gravity for 1.7
Fig. 1:
Left panel:
Predicted evolution of the surface velocity as a function of the surface gravity for 1.7 M (cid:12) stellar models alongthe red giant branch with and without planet engulfment. Di ff erent initial rotations on the ZAMS are considered for models withoutengulfment: Ω ini / Ω crit = − . The model with planet engulfment(blue continuous line, the dotted blue line is the model without engulfment) initially had Ω ini / Ω crit = J planet orbitingat a distance equal to 0.5 au. The engulfment occurs when the surface gravity of the star is around 2.2. Right panel:
Evolution of theRossby number as a function of the surface gravity for the same stellar models along the red giant branch with and without a planetengulfment.M (cid:12) stellar models with and without planet engulfment. Surfacemagnetic fields of up to a few tens of Gauss could be triggeredby an engulfment at surface gravities where such fields are other-wise not expected. Even for the initially faster rotating stars thatevolved in isolation, no significant magnetic field is expected forlog g <
2. Thus, a strong magnetic field at low gravities togetherwith a high surface velocities are strong signs of a past engulf-ment. Of course, a planet with too low a mass or a planet initiallyorbiting the star at too large a distance will only lead to a weakmagnetic field that will not be observable.The question here might be asked whether the strong mag-netic field linked to the fast rotation might prevent the star fromkeeping trace of the past engulfment high rotation rate for a suf-ficiently long time to be an observable feature. When our 1.7M (cid:12) reaches its peak surface velocity at the time of engulfment,the surface magnetic field is around 20 G. With such a strongfield, the shortest wind magnetic braking timescale (obtainedusing f =
1) is 20 Myr. Since the duration from the engulfmentto the tip of the red giant branch is about 34 Myr, wind mag-netic braking is expected to significantly a ff ect the evolution ofthe surface velocity (of course, a value of f = ff erent windbraking e ffi ciencies f , as indicated in the caption. The wind mag-netic braking was applied only to the case with engulfment.The magnetic braking does not change the maximum ve-locity reached by the engulfment. The rise is too short for thisbraking to have any e ff ect. After the engulfment, the strongerthe braking, the more rapidly the decrease in surface velocity.Without magnetic braking, the star retains a surface velocityabove 10 km s − for 29 Myr. When f equals 0.2, 0.5, or 0.8, thisduration reduces to 25, 20, and 16 Myr, respectively. Comparedto the whole red giant branch lifetime, which is about 181 Myr,these values correspond to fractions equal to 16% ( f = f = f = f = ff ect of the engulfment on the surface veloc-ities, planet engulfment remains a strong candidate for explain-ing the observed fast-rotating red giants.All these results were obtained by using the magnetic brak-ing formalism of ud-Doula & Owocki (2002) and ud-Doula et al.(2008) (Eq. (2)). A model computed with the formalism of Mattet al. (2012) (Eq. (3)) is shown by the red dotted line in the rightpanel of Fig. 2. A value of f equal to 0.5 was used in this case.The two braking formalisms lead to very similar results (onlya slight increase of the global e ffi ciency of the braking is seenwhen Eq. (3) is used). This can be understood by comparing forinstance the expressions for the Alfv´en radius in the two cases(Eq. (19) in ud-Doula et al. (2008) and Eq. (6) in Matt et al.(2012)): for red giants, the term related to the magnetic confine-ment parameter dominates and the dependence of the Alfv´en ra-dius on this term is nearly identical in both formalisms (a valueof m of 0.2177 for Matt et al. (2012) and 0.25 for ud-Doula et al.(2008)).Wind magnetic braking would also a ff ect the evolution ofthe surface velocities of our models with no engulfment. Thesestars, as shown above, may also develop a surface magnetic fieldat the base of the red giant branch (see right panel of Fig. 1 andthe left panel of Fig. 2), which, at its turn, may drive some windmagnetic braking. This would shift the curves corresponding tono engulfment in the surface velocity downward compared tothe surface gravity plots (see the left panel of Fig. 1 and the rightpanel of Fig. 2), but would not much a ff ect what occurs duringthe engulfment. For the case considered here, the quantity ofangular momentum added by the planet is so large that the initialsurface rotation of the star has little influence.Wind magnetic braking during the red giant phase wouldchange the interpretation of the observed surface rotations of redgiants stars. Wind magnetic braking would shift to lower val- Fig. 2:
Left panel:
Predicted evolution of the surface magnetic field as a function of the surface gravity for 1.7 M (cid:12) stellar modelsalong the red giant branch with and without planet engulfment. The models are the same as in Fig. 1. Above the horizontal dashedline, Ro <
1. The two empty stars are observations from Auri`ere et al. (2015). The other points correspond to the star HD232862observed on four consecutive days by L`ebre et al. (2009) (the triangle is the first observation, then the square, pentagon, and thecircle).
Right panel:
Evolution of the surface rotation as a function of the surface gravity for the same models as shown in Fig. 1,with in additional cases where magnetic braking laws with various e ffi ciencies have been accounted for after the engulfment. Thedashed blue, magenta, and red curves correspond to values of f equal to 0.2, 0.5, and 0.8 using Eq. (2) (see text). The red dotted lineis obtained using Eq. (3) with f = .
5. The continuous blue curve corresponds to the case f =
0. We have indicated how the durationof the period during which the surface velocity is above 10 km s − varies as a function of the strength of the magnetic braking. Thesame three observations as those indicated in the left panel are shown. The dots show the observations by Carlberg et al. (2012), theblack circles show the stars with a υ sin i <
10 km s − , the filled red- and blue-circled magenta points have υ sin i >
10 km s − . Theblue-circled magenta points correspond to stars (HD31993, Tyc 0347-00762-1, Tyc 5904-00513-1, and Tyc 6094-01204-1) whosesurface velocity cannot be explained by any reasonable model for single stars (Paper II).ues the maximum surface velocity that can be reached at a givensurface gravity by an initial mass model that evolves without in-teraction (tides or engulfment). The maximum surface velocityis obtained by considering the highest possible initial rotationon the ZAMS and assuming solid-body rotation. Any stars pre-senting higher surface rotations than this limit are very strongcandidates for having experienced planet engulfment (see morein Paper II). Since wind magnetic braking would lower this limit,it would allow more observed stars to lie above it and thus, as in-dicated above, would enlarge the size of stars whose surface ro-tation needs an interaction to be explained. A too e ffi cient mag-netic braking would probably increase the number of candidatesthat would have had to experience such interactions by too much.This point will be discussed in a more extended future work.Although it is beyond the scope of the present work to makedetailed comparisons with observations, we discuss below threestars that are interesting candidates for having engulfed a planet,and that have masses around 1.7 ± . (cid:12) , that is, they are sim-ilar to the models discussed here. The positions of these stars inthe magnetic field versus log g and in the surface velocity ver-sus log g plots are indicated in Fig. 2. The daily variation ofthe magnetic field of HD232862 may be due to the change ofthe viewing angle when the star rotates. These three stars havesurface magnetic fields and rotations that are high enough for be-ing good candidates for a planet engulfment. Two of them (HD31993 and 232862) might also be explained by assuming ini-tially very fast-rotating stars, but the probability of such extremeinitial conditions is quite low so that an interaction remains amore reasonable explanation for the currently observed proper-ties. For these two stars, the engulfment of a 15 M J planet that began orbiting the star at 0.5 au occurs at a gravity that is too lowto explain their properties. This would indicate a higher massplanet or a shorter initial distance between planet and star. Themagnetic field of HD9746 may well be explained by the case ofengulfment shown in the figures. Its υ sin i is equal to 9 km s − (Balachandran et al. 2000). Our models would predict a value υ around 30 km s − . Planet-induced magnetic field theory mightbe tested by checking whether those stars whose high surfacevelocities cannot be explained by stellar models evolving in iso-lation truly present measurable magnetic fields. Typically, starssuch as HD31993, Tyc 0347-00762-1, Tyc 5904-00513-1, andTyc 6094-01204-1 (the blue-circled magenta points in Fig. 2)are interesting candidates.
5. Conclusion
A planet engulfment can increase stellar rotation to such an ex-tent that an observable surface magnetic field can develop. Planetengulfment might explain the strong magnetic field in the upperpart of the red giant branch, where stars without interaction ro-tate too slowly to allow a dynamo t o create such strong fields.Some good candidate stars show both high surface rotation ratesand high surface magnetic fields that are compatible with an en-gulfment. Likewise, some fast-rotating red giants may be foundto show some surface magnetic fields if our present models arecorrect (for instance HD31993, Tyc 0347-00762-1, Tyc 5904-00513-1, and Tyc 6094-01204-1).The planet-induced magnetic fields are strong enough toslow the star down by wind magnetic braking. This will reducethe time that the surface velocity of a star can be maintained above a given limit. However, for moderate couplings, the windmagnetic braking e ff ect does not disrupt the production of ob-servable ( i.e. su ffi ciently long-lasting) fast-rotating red giants byplanet engulfment. This seems compatible with recent resultsthat suggested a low e ffi ciency of surface magnetic braking forstars more evolved than the Sun (van Saders et al. 2016).The increased stellar rotation and magnetic field generationlinked to planet engulfment can in principle operate on the windand might increase the mass loss. Whether this mechanism canexplain the high mass-loss rates needed to form hot subdwarfstars that are singles is an interesting question that needs to beexplored in the future. Acknowledgements.
We would like to thank St´ephane Mathis for his valuablecomments and suggestions. The project has been supported by Swiss NationalScience Foundation grants 200021-138016, 200020-160119 and 200020-15710.E.V. acknowledges support from the Spanish Ministerio de Economa yCompetitividad under grant AYA2014-55840P. AuD acknowledges support byNASA through Chandra Award numbers GO5-16005X, AR6-17002C and G06-17007B issued by the Chandra X-ray Observatory Center which is operated bythe Smithsonian Astrophysical Observatory for and behalf of NASA under con-tract NAS8- 03060.
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