arXiv subjects

Patrick Eggenberger

Publications and source records attributed to Patrick Eggenberger.

At least 37 records · Page 2Linked to original sources

arXiv2022

Backtracing the internal rotation history of the $β$ Cep star HD 129929

HD 129929 is a slowly-rotating $β$ Cephei pulsator with a rich spectrum of detected oscillations, including two rotational multiplets. The asteroseismic interpretation revealed the presence of radial differential rotation in this massive star of $\sim$9.35 M . The stellar core is indeed estimated to spin $\sim$3.6 times faster than the surface. The surface rotation was consequently derived as $\sim$2 km/s. This massive star represents an ideal counter-part to the wealth of space-based photometry results for main-sequence and evolved low-mass stars. Those latter have revealed a new, and often unexpected, picture of the angular momentum transport processes acting in stellar interiors. We investigate in a new way the constraints on the internal rotation of HD 129929, focusing on their interpretation for the evolution of the internal rotation during the main sequence of a massive star. We test separately hydrodynamic and magnetic instability transport processes of angular momentum. We used the best asteroseismic model obtained in an earlier work. We calibrated stellar models including rotation, with different transport processes, to reproduce that reference model. We then looked whether one process is favoured to reproduce the rotation profile of HD 129929, based on the fit of the asteroseismic multiplets. The impact of the Tayler magnetic instability on the angular momentum transport predicts a ratio of the core-to-surface rotation rate of only 1.6, while the recently revised prescription of this mechanism predicts solid-body rotation. Both are too low in comparison with the asteroseismic inference. The models with only hydrodynamic processes are in good agreement with the asteroseismic measurements. Strikingly, we can also get a constraint on the profile of rotation on the zero age main sequence: likely, the ratio between the core and surface rotation was at least $\sim$1.7.

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arXiv2022

Grids of stellar models with rotation VI: Models from 0.8 to 120 $M_\odot$ at a metallicity Z = 0.006

Context: Grids of stellar models, computed with the same physical ingredients, allow one to study the impact of a given physics on a broad range of initial conditions and are a key ingredient for modeling the evolution of galaxies. Aims: We present a grid of single star models for masses between 0.8 and 120 $M_\odot$, with and without rotation for a mass fraction of heavy element Z=0.006, representative of the Large Magellanic Cloud (LMC). Methods: We used the Geneva stellar evolution code. The evolution was computed until the end of the central carbon-burning phase, the early asymptotic giant branch phase, or the core helium-flash for massive, intermediate, and low mass stars, respectively. Results: The outputs of the present stellar models are well framed by the outputs of the two grids obtained by our group for metallicities above and below the one considered here. The models of the present work provide a good fit to the nitrogen surface enrichments observed during the main sequence for stars in the LMC with initial masses around 15 $M_\odot$. They also reproduce the slope of the luminosity function of red supergiants of the LMC well, which is a feature that is sensitive to the time-averaged mass loss rate over the red supergiant phase. The most massive black hole that can be formed from the present models at Z=0.006 is around 55 $M_\odot$. No model in the range of mass considered will enter into the pair-instability supernova regime, while the minimal mass to enter the region of pair pulsation instability is around 60 $M_\odot$ for the rotating models and 85 $M_\odot$ for the nonrotating ones. Conclusions: The present models are of particular interest for comparisons with observations in the LMC and also in the outer regions of the Milky Way. We provide public access to numerical tables that can be used for computing interpolated tracks and for population synthesis studies.

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arXiv2022

Grids of stellar models with rotation VII: Models from 0.8 to 300 M$_\odot$ at super-solar metallicity (Z = 0.020)

We present a grid of stellar models at super-solar metallicity (Z = 0.020) extending the previous grids of Geneva models at solar and sub-solar metallicities. A metallicity of Z = 0.020 was chosen to match that of the inner Galactic disk. A modest increase of 43% (=0.02/0.014) in metallicity compared to solar models means that the models evolve similarly to solar models but with slightly larger mass loss. Mass loss limits the final total masses of the super-solar models to 35 M$_\odot$ even for stars with initial masses much larger than 100 M$_\odot$. Mass loss is strong enough in stars above 20 M$_\odot$ for rotating stars (25 M$_\odot$ for non-rotating stars) to remove the entire hydrogen-rich envelope. Our models thus predict SNII below 20 M$_\odot$ for rotating stars (25 M$_\odot$ for non-rotating stars) and SNIb (possibly SNIc) above that. We computed both isochrones and synthetic clusters to compare our super-solar models to the Westerlund 1 (Wd1) massive young cluster. A synthetic cluster combining rotating and non-rotating models with an age spread between log10 (age/yr) = 6.7 and 7.0 is able to reproduce qualitatively the observed populations of WR, RSG and YSG stars in Wd1, in particular their simultaneous presence at log10(L/L$_\odot$) = 5-5.5. The quantitative agreement is imperfect and we discuss the likely causes: synthetic cluster parameters, binary interactions, mass loss and their related uncertainties. In particular, mass loss in the cool part of the HRD plays a key role.

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arXiv2021

Asteroseismology of $β$ Cephei stars: The stellar inferences tested in hare and hound exercises

The $β$ Cephei pulsators are massive main-sequence stars, presenting low radial-order modes. These modes probe in particular the chemical gradient at the edge of the convective core. They hence give constraints on macroscopic processes, such as hydrodynamic or magnetic instabilities. Yet, it is not clear to what extent the seismic inferences depend on the physics employed for the stellar modelling or on the observational dataset. We investigate the observational constraints which are necessary to provide accurate constraints on the mixing processes in $β$ Cephei stars. We explore the importance of the identification of the angular degree of modes. Depending on the quality of the seismic dataset and the classical constraints, we estimate the precision achievable with asteroseismology. We propose a method extending the forward approach classically used to model $β$ Cephei stars The probability distributions of the asteroseismic-derived stellar parameters are obtained. With these distributions, we provide a systemic way to estimate the errors of the modelling. A particular effort is made to also include the theoretical uncertainties of the models. We then estimate the accuracy and precision of asteroseismology for $β$ Cephei stars in a series of hare and hound exercises. The exercises show that a set of four to five oscillation frequencies with an identified angular degree already leads to accurate inferences on the stellar parameters. Without the identification of the modes, the addition of other classical observational constraints allow to succeed the seismic modelling. When the micro-physics of the star and stellar models used for the modelling differ, the constraints derived on the internal structure remain valid if expressed in terms of acoustic variables. The characterisation of the mixing processes at the boundary of the convective core remain model-dependent.

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arXiv2021

Angular momentum distributions for observed and modeled exoplanetary systems

The distribution of angular momentum of planets and their host stars provides important information on the formation and evolution of the planetary system. However, mysteries still remain, partly due to bias and uncertainty of the current observational datasets and partly due to the fact that theoretical models for the formation and evolution of planetary systems are still underdeveloped. In this study, we calculate the spin angular momenta of host stars and the orbital angular momenta of their planets using data from the NASA Exoplanet Archive, together with detailed analysis of observation dependent biases and uncertainty ranges. We also analyze the angular momenta of the planetary system as a function of star age to understand their variation in different evolutionary stages. In addition, we use a population of planets from theoretical model simulations to reexamine the observed patterns and compare the simulated population with the observed samples to assess variations and differences. We found the majority of exoplanets discovered thus far do not have the angular momentum distribution similar to the planets in our Solar System, though this could be due to the observation bias. When filtered by the observational biases, the model simulated angular momentum distributions are comparable to the observed pattern in general. However, the differences between the observation and model simulation in the parameter (angular momentum) space provide more rigorous constraints and insights on the issues that needed future improvement.

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arXiv2021

Standard solar models: a perspective from updated solar neutrino fluxes and the gravity-mode period spacing

Context: The Sun is by far a privileged target for testing stellar models with unique precision. A recent concern appeared with the progress in the solar surface abundances derivation that has led to a decrease of the solar metallicity. While the ancient high-metallicity models were in fair agreement with other solar observational indicators, it is no longer the case for low-metallicity models. Recent collection of data are however promising to shed a new light on it. For instance, the Borexino collaboration released in 2020 the first-ever complete estimate of neutrinos emitted in the CNO cycle. It has reaffirmed the role of the neutrino constraints in the solar modelling process and its associated issues. In parallel, newly claimed detection of solar gravity modes of oscillations offers another opportunity of probing the stratification in the Sun's central layers. Aims: We propose to combine the diagnoses from neutrinos and helioseismology, both from pressure and gravity modes, for assessing the predictions of solar models. We compare in detail the different physical prescriptions currently at disposal for stellar model computations. Results: The CNO neutrino flux confirms a preference for high-metallicity models. Nevertheless, we found that mild modification of the nuclear screening factors can re-match low-metallicity model predictions to observed fluxes, although it does not restore the agreement with the helioseismic frequency ratios. Neither the high-metallicity or low-metallicity models are able to reproduce the gravity-mode period spacing. The disagreement is huge, more than 100$σ$ to the reported value. Reversely, the family of standard models narrows the expected range of the Sun's period spacing: between $\sim$2150 to $\sim$2190~s. Moreover, we show this indicator can constrain the chemical mixture, opacity, and to a lower extent nuclear reactions in solar models.

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arXiv2021

Star-planet interactions VI. Tides, stellar activity and planet evaporation

Tidal interactions and planet evaporation processes impact the evolution of close-in star-planet systems. We study the impact of stellar rotation on these processes. We compute the time evolution of star-planet systems consisting of a planet with initial mass between 0.02 and 2.5 M$_{ Jup}$ (6 and 800 M$_{ Earth}$), in a quasi-circular orbit with an initial orbital distance between 0.01 and 0.10 au, around a solar-type star evolving from the Pre-Main-Sequence (PMS) until the end of the Main-Sequence (MS) phase. We account for the evolution of: the stellar structure, the stellar angular momentum due to tides and magnetic braking, the tidal interactions (equilibrium and dynamical tides in stellar convective zones), the mass-evaporation of the planet, and the secular evolution of the planetary orbit. We consider that at the beginning of the evolution, the proto-planetary disk has fully dissipated and planet formation is complete. Both a rapid initial stellar rotation, and a more efficient angular momentum transport inside the star, in general, contribute toward the enlargement of the domain which is devoid of planets after the PMS phase, in the plane of planet mass vs. orbital distance. Comparisons with the observed distribution of exoplanets orbiting solar mass stars, in the plane of planet mass vs. orbital distance (addressing the "Neptunian desert" feature), show an encouraging agreement with the present simulations, especially since no attempts have been made to fine-tune initial parameters of the models to fit the observations. We also obtain an upper limit for the orbital period of bare-core planets, that agrees with observations of the "radius valley" feature in the plane of planet radius vs. orbital period. The two effects, tides and planet evaporation, should be accounted for simultaneously and in a consistent way, with a detailed model for the evolution of the star.

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arXiv2021

HAYDN -- High-precision AsteroseismologY of DeNse stellar fields (ESA Voyage 2050 White Paper)

In the last decade, the Kepler and CoRoT space-photometry missions have demonstrated the potential of asteroseismology as a novel, versatile and powerful tool to perform exquisite tests of stellar physics, and to enable precise and accurate characterisations of stellar properties, with impact on both exoplanetary and Galactic astrophysics. Based on our improved understanding of the strengths and limitations of such a tool, we argue for a new small/medium space mission dedicated to gathering high-precision, high-cadence, long photometric series in dense stellar fields. Such a mission will lead to breakthroughs in stellar astrophysics, especially in the metal poor regime, will elucidate the evolution and formation of open and globular clusters, and aid our understanding of the assembly history and chemodynamics of the Milky Way's bulge and few nearby dwarf galaxies.

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arXiv2020

Grids of stellar models with rotation: V. Models from 1.7 to 120 Msun at zero metallicity

Understanding the nature of the first stars is key to understanding the early universe. With new facilities such as JWST we may soon have the first observations of the earliest stellar populations, but to understand these observations we require detailed theoretical models. Here we compute a grid of stellar evolution models using the Geneva code with the aim to improve our understanding of the evolution of zero-metallicity stars, with particular interest in how rotation affects surface properties, interior structure, and metal enrichment. We produce a range of models of initial masses (Mini) from 1.7 Msun to 120 Msun, focusing on massive models of 9 Msun < Mini < 120 Msun. Our grid includes models with and without rotation, with rotating models having an initial velocity of 40% of the critical velocity. We find that rotation strongly impacts the evolution of the first stars, mainly through increased core size and stronger H-burning shells during core He-burning. Without radiative mass loss, angular momentum builds at the surface in rotating models, thus models of initial masses Mini > 60 Msun reach critical rotation on the main sequence and experience mass loss. We find that rotational mixing strongly affects metal enrichment, but does not always increase metal production as we see at higher metallicities. This is because rotation leads to an earlier CNO boost to the H shell during He-burning, which may hinder metal enrichment depending on initial mass and rotational velocity. Electronic tables of this new grid of Population III models are publicly available.

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arXiv2020

Reinvestigating $α$ Cen AB in light of asteroseismic forward and inverse methods

The $α$ Cen stellar system is the closest neighbour to our Sun. Its main component is a binary composed of two main-sequence stars, one more massive than the Sun and one less massive. The system's bright magnitude led to a wealth of astronomical observations over a long period, making it an appealing testbed for stellar physics. In particular, detection of stellar pulsations in both $α$ Cen A and B has revealed the potential of asteroseismology for determining its fundamental stellar parameters. Asteroseismic studies have also focused on the presence of a convective core in the A component, but as yet without definitive confirmation. Progress in the determination of solar surface abundances and stellar opacities have yielded new input for stellar theoretical models. We investigate their impact on a reference system such as $α$ Cen AB. We seek to confirm the presence of a convective core in $α$ Cen A by analysing the role of different stellar physics and the potential of asteroseismic inverse methods. We present a new series of asteroseismic calibrations carried out using forward approach modelling and including updated chemical mixture and opacities in the models. We then complement our analysis with help of recent asteroseismic diagnostic tools based on inverse methods developed for solar-like stars. The inclusion of an updated chemical mixture -- that is less metal-rich -- appears to reduce the predicted asteroseismic masses of each component. Neither classical asteroseismic indicators such as frequency ratios, nor asteroseismic inversions favour the presence of a convective core in $α$ Cen A. The quality of the observational seismic dataset is the main limiting factor to settle the issue. Implementing new observing strategies to improve the precision on the pulsation frequencies would certainly refine the outcome of asteroseismology for this binary system.

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arXiv2019

Grids of stellar models with rotation IV. Models from 1.7 to 120 Msun at a metallicity Z = 0.0004

The effects of rotation on stellar evolution are particularly important at low metallicity, when mass loss by stellar winds diminishes and the surface enrichment due to rotational mixing becomes relatively more pronounced than at high metallicities. Here we investigate the impact of rotation and metallicity on stellar evolution. Using a similar physics as in our previous large grids of models at Z=0.002 and Z=0.014, we compute stellar evolution models with the Geneva code for rotating and nonrotating stars with initial masses (Mini) between 1.7 and 120 Msun and Z=0.0004 (1/35 solar). This is comparable to the metallicities of the most metal poor galaxies observed so far, such as I Zw 18. Concerning massive stars, both rotating and nonrotating models spend most of their core-helium burning phase with an effective temperature higher than 8000 K. Stars become red supergiants only at the end of their lifetimes, and few RSGs are expected. Our models predict very few to no classical Wolf-Rayet stars as a results of weak stellar winds at low metallicity. The most massive stars end their lifetimes as luminous blue supergiants or luminous blue variables, a feature that is not predicted by models with higher metallicities. Interestingly, due to the behavior of the intermediate convective zone, the mass domain of stars producing pair-instability supernovae is smaller at Z=0.0004 than at Z=0.002. We find that during the main sequence phase, the ratio between nitrogen and carbon abundances (N/C) remains unchanged for nonrotating models. However, N/C increases by factors of 10-20 in rotating models at the end of the MS. Cepheids coming from stars with Mini > 4-6 Msun are beyond the core helium burning phase and spend little time in the instability strip. Since they would evolve towards cooler effective temperatures, these Cepheids should show an increase of the pulsation period as a function of age.

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arXiv2018

Anisotropic turbulent transport in stably stratified rotating stellar radiation zones

Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones over the whole Hertzsprung-Russell diagram. Turbulent transport in differentially rotating stably stratified stellar radiation zones should be carefully modeled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. Only phenomenological prescriptions have been proposed for the transport in the horizontal direction, which however constitutes a cornerstone in current theoretical formalisms for stellar hydrodynamics in evolution codes. We derive a new theoretical prescription for the anisotropy of the turbulent transport in radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implement this framework in the stellar evolution code STAREVOL and quantify its impact on the rotational and structural evolution of low-mass stars from the pre-main-sequence to the red giant branch. The anisotropy of the turbulent transport scales as $N^4τ^2/\left(2Ω^2\right)$, $N$ and $Ω$ being the buoyancy and rotation frequencies respectively and $τ$ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. As a consequence, a complementary transport mechanism like internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along stellar evolution.

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arXiv2018

Star-planet interactions. V. Dynamical and equilibrium tides in convective zones

When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium tides, dynamical tides, drag (frictional and gravitational), and stellar mass loss. We used the Geneva stellar evolution code to compute the evolution of stars with initial masses of 1 and 1.5 solar mass with different rotation rates at solar metallicity. The star is evolved from the pre-main-sequence (PMS) up to the tip of the red giant branch. We used these models as input for computing the evolution of the planetary orbits. We explored the effects of changing the planet masses (of 1 Earth mass up to 20 Jupiter masses), the distance between the planet and the star (of 0.015 and more than 3 au), the mass, and the spin of the star. We present results when only the equilibrium tide was accounted for and when both equilibrium and dynamical tides were accounted for. The expression for the dynamical tide is a frequency-averaged dissipation of tidally excited inertial waves, obtained from a piecewise homogeneous two-layer stellar model. Gravity wave damping was neglected. Dynamical tides in convective zones have a significant effect on planetary orbits only during the PMS phase and only for fast-rotating stars. They have no significant effects during the PMS phase for initially slow-rotating stars and during the red giant branch phase, regardless of the initial rotation (abridged).

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arXiv2017

Star-planet interactions. IV. Possibility of detecting the orbit-shrinking of a planet around a red giant

The surface rotations of some red giants are so fast that they must have been spun up by tidal interaction with a close companion, either another star, a brown dwarf, or a planet. We focus here on the case of red giants that are spun up by tidal interaction with a planet. When the distance between the planet and the star decreases, the spin period of the star decreases, the orbital period of the planet decreases, and the reflex motion of the star increases. We study the change rate of these three quantities when the circular orbit of a planet of 15 M$_{J}$ that initially orbits a 2 M$_\odot$ star at 1 au shrinks under the action of tidal forces during the red giant phase. We use stellar evolution models coupled with computations of the orbital evolution of the planet, which allows us to follow the exchanges of angular momentum between the star and the orbit in a consistent way. We obtain that the reflex motion of the red giant star increases by more than 1 m s$^{-1}$ per year in the last $\sim$40 years before the planet engulfment. During this phase, the reflex motion of the star is between 660 and 710 m s$^{-1}$. The spin period of the star increases by more than about 10 minutes per year in the last 3000 y before engulfment. During this period, the spin period of the star is shorter than 0.7 year. During this same period, the variation in orbital period, which is shorter than 0.18 year, is on the same order of magnitude. Changes in reflex-motion and spin velocities are very small and thus most likely out of reach of being observed. The most promising way of detecting this effect is through observations of transiting planets, that is, through{\it } changes of the beginning or end of the transit. A space mission like PLATO might be of great interest for detecting planets that are on the verge of being engulfed by red giants.

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arXiv2017

Massive stars, successes and challenges

We give a brief overview of where we stand with respect to some old and new questions bearing on how massive stars evolve and end their lifetime. We focus on the following key points that are further discussed by other contributions during this conference: convection, mass losses, rotation, magnetic field and multiplicity. For purpose of clarity, each of these processes are discussed on its own but we have to keep in mind that they are all interacting between them offering a large variety of outputs, some of them still to be discovered.

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arXiv2017

Massive star formation by accretion II. Rotation: how to circumvent the angular momentum barrier?

Rotation plays a key role in the star-formation process, from pre-stellar cores to pre-main-sequence (PMS) objects. Understanding the formation of massive stars requires taking into account the accretion of angular momentum during their PMS phase. We study the PMS evolution of objects destined to become massive stars by accretion, focusing on the links between the physical conditions of the environment and the rotational properties of young stars. In particular, we look at the physical conditions that allow the production of massive stars by accretion. We present PMS models computed with a new version of the Geneva Stellar Evolution code self-consistently including accretion and rotation according to various accretion scenarios for mass and angular momentum. We describe the internal distribution of angular momentum in PMS stars accreting at high rates and we show how the various physical conditions impact their internal structures, evolutionary tracks, and rotation velocities during the PMS and the early main sequence. We find that the smooth angular momentum accretion considered in previous studies leads to an angular momentum barrier and does not allow the formation of massive stars by accretion. A braking mechanism is needed in order to circumvent this angular momentum barrier. This mechanism has to be efficient enough to remove more than 2/3 of the angular momentum from the inner accretion disc. Due to the weak efficiency of angular momentum transport by shear instability and meridional circulation during the accretion phase, the internal rotation profiles of accreting stars reflect essentially the angular momentum accretion history. As a consequence, careful choice of the angular momentum accretion history allows circumvention of any limitation in mass and velocity, and production of stars of any mass and velocity compatible with structure equations.

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arXiv2016

High surface magnetic field in red giants as a new signature of planet engulfment?

Context. Red-giant stars may engulf planets. This may increase the rotation rate of their convective envelope, which could lead to strong 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 stellar wind magnetic braking on the evolution of the surface velocity of the parent star. Methods. With rotating stellar models with and without planets and an empirical relation between the Rossby number and the surface magnetic field, we deduce the evolution of the surface magnetic field along the red-giant branch. The effects of wind magnetic braking is explored using a relation deduced from MHD simulations. Results. The stellar evolution model of a 1.7 M$_\odot$ without planet engulfment and that has a time-averaged rotation velocity during the Main-Sequence equal to 100 km s$^{-1}$, shows a surface magnetic field triggered by convection larger than 10 G only at the base of the red giant branch, that means for gravities log $g > 3$. When a planet engulfment occurs, such magnetic field can also appear at much lower gravities, i.e. at much higher luminosities along the red giant branch. Typically the engulfment of a 15 M$_J$ planet produces a dynamo triggered magnetic field larger than 10 G for gravities between 2.5 and 1.9. We show that for reasonable wind magnetic braking laws, the high surface velocity reached after a planet engulfment may be maintained sufficiently long for being observable. Conclusions. High surface magnetic fields for red giants in the upper part of the red giant branch is a strong indication of a planet engulfment or of an interaction with a companion. Our theory can be tested by observing fast rotating red giants and check whether they show magnetic fields.

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arXiv2016

Star-planet interactions: II. Is planet engulfment the origin of fast rotating red giants?

Context. Fast rotating red giants in the upper part of the red giant branch have surface velocities that cannot be explained by single star evolution. Aims. We check whether tides between a star and a planet followed by planet engulfment can indeed accelerate the surface rotation of red giants for a sufficient long time in order to produce these fast rotating red giants. Methods. Using rotating stellar models, accounting for the redistribution of the angular momentum inside the star by different transport mechanisms, for the exchanges of angular momentum between the planet orbit and the star before the engulfment and for the deposition of angular momentum inside the star at the engulfment, we study how the surface rotation velocity at the stellar surface evolves. Results. We show that the surface velocities reached at the end of the orbital decay due to tidal forces and planet engulfment can be similar to values observed for fast rotating red giants. This surface velocity then decreases when the star evolves along the red giant branch but at a sufficiently slow pace for allowing stars to be detected with such a high velocity. More quantitatively, star-planet interaction can produce a rapid acceleration of the surface of the star, above values equal to 8 km s$^{-1}$, for periods lasting up to more than 30% the red giant branch phase. The changes of the surface carbon isotopic ratios produced by the dilution of the planetary material into the convective envelope is quite modest. Much more important might be the increase of the lithium abundance due to this effect. However lithium may be affected by many different, still uncertain, processes. Conclusions. The acceleration of the stellar surface to rotation velocities above limits that depend on the surface gravity does appear at the moment as the clearest signature of a star-planet interaction.[abridged]

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