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Register a new userThe variation of the tidal quality factor of convective envelopes of rotating low-mass stars along their evolution
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S. Mathis
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More than 1500 exoplanets have been discovered around a large diversity of host stars (from M- to A-type stars). Tidal dissipation in their convective envelope is a key actor that shapes the orbital architecture of short-period systems and that still remains unknown. Using a simplified two-layer assumption and grids of stellar models, we compute analytically an equivalent modified tidal quality factor, which is proportional to the inverse of the frequency-averaged dissipation due to the viscous friction applied by turbulent convection on tidal waves. It leads the conversion of their kinetic energy into heat and tidal evolution of orbits and spin. During their Pre-Main-Sequence, all low-mass stars have a decrease of the equivalent modified tidal quality factor for a fixed angular velocity of their convective envelope. Next, it evolves on the Main Sequence to an asymptotic value that is minimum for $0.6M_{odot}$ K-type stars and that increases by several orders of magnitude with increasing stellar mass. Finally, the rotational evolution of low-mass stars strengthens tidal dissipation during the Pre-Main-Sequence.
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The dissipation of the kinetic energy of wave-like tidal flows within the convective envelope of low-mass stars is one of the key physical mechanisms that shapes the orbital and rotational dynamics of short-period exoplanetary systems. Although low-mass stars are magnetically active objects, the question of how the stars magnetic field impacts large-scale tidal flows and the excitation, propagation and dissipation of tidal waves still remains open. Our goal is to investigate the impact of stellar magnetism on the forcing of tidal waves, and their propagation and dissipation in the convective envelope of low-mass stars as they evolve. We have estimated the amplitude of the magnetic contribution to the forcing and dissipation of tidally induced magneto-inertial waves throughout the structural and rotational evolution of low-mass stars (from M to F-type). For this purpose, we have used detailed grids of rotating stellar models computed with the stellar evolution code STAREVOL. The amplitude of dynamo-generated magnetic fields is estimated via physical scaling laws at the base and the top of the convective envelope. We find that the large-scale magnetic field of the star has little influence on the excitation of tidal waves in the case of nearly-circular orbits and coplanar hot-Jupiter planetary systems, but that it has a major impact on the way waves are dissipated. Our results therefore indicate that a full magneto-hydrodynamical treatment of the propagation and dissipation of tidal waves is needed to properly assess the impact of star-planet tidal interactions throughout the evolutionary history of low-mass stars hosting short-period massive planets.
Tidal interactions in close star-planet or binary star systems may excite inertial waves (their restoring force is the Coriolis force) in the convective region of the stars. The dissipation of these waves plays a prominent role in the long-term orbital and rotational evolution of the bodies involved. If the primary star rotates as a solid body, inertial waves have a Doppler-shifted frequency restricted to the range $[-2Omega, 2Omega]$ ($Omega$ being the angular velocity of the star), and they can propagate in the entire convective region. However, turbulent convection can sustain differential rotation with an equatorial acceleration (as in the Sun) or deceleration that modifies the frequency range and propagation domain of inertial waves and allows corotation resonances for non-axisymmetric oscillations. In this work, we perform numerical simulations of tidally excited inertial waves in a differentially rotating convective envelope with a conical (or latitudinal) rotation profile. The tidal forcing that we adopt contains spherical harmonics that correspond to the case of a circular and coplanar orbit. We study the viscous dissipation of the waves as a function of tidal frequency for various stellar masses and differential rotation parameters, as well as its dependence on the turbulent viscosity coefficient. We compare our results with previous studies assuming solid-body rotation and point out the potential key role of corotation resonances in the dynamical evolution of close-in star-planet or binary systems.
Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. In low-mass stars, their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. Turbulent convection can sustain differential rotation in their envelope, with an equatorial acceleration (as in the Sun) or deceleration, which can modify the waves propagation properties. We explore in this first paper the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell. We assume that the angular velocity background flow depends on the latitudinal coordinate only, close to what is expected in the external convective envelope of low-mass stars. We use i) an analytical approach in the inviscid case to get the dispersion relation, from which we compute the characteristic trajectories along which energy propagates. This allows us to study the existence of attractor cycles and infer the different families of inertial modes; ii) high-resolution numerical calculations based on a spectral method for the viscous problem. We find that modes that propagate in the whole shell (D modes) behave the same way as with solid-body rotation. However, another family of inertial modes exists (DT modes), which can propagate only in a restricted part of the convective zone. Our study shows that they are less common than D modes and that the characteristic rays and shear layers often focus towards a wedge - or point-like attractor. More importantly, we find that for non-axisymmetric oscillation modes, shear layers may cross a corotation resonance with a local accumulation of kinetic energy. Their damping rate scales very differently from what we obtain for standard D modes and we show an example where it is independent of viscosity (Ekman number) in the astrophysical regime in which it is small.
Measurements of the physical properties of stars at the lower end of the main sequence are scarce. In this context we report masses, radii and surface gravities of ten very-low-mass stars in eclipsing binary systems, with orbital periods of the order of several days. The objects probe the stellar mass-radius relation in the fully convective regime, $M_star lesssim 0.35$ M$_odot$, down to the hydrogen burning mass-limit, $M_{mathrm{HB}} sim 0.07$ M$_odot$. The stars were detected by the WASP survey for transiting extra-solar planets, as low-mass, eclipsing companions orbiting more massive, F- and G-type host stars. We use eclipse observations of the host stars (TRAPPIST, Leonhard Euler, SPECULOOS telescopes), and radial velocities of the host stars (CORALIE spectrograph), to determine physical properties of the low-mass companions. Companion surface gravities are derived from the eclipse and orbital parameters of each system. Spectroscopic measurements of the host star effective temperature and metallicity are used to infer the host star mass and age from stellar evolution models. Masses and radii of the low-mass companions are then derived from the eclipse and orbital parameters of each system. The objects are compared to stellar evolution models for low-mass stars, to test for an effect of the stellar metallicity and orbital period on the radius of low-mass stars in close binary systems. Measurements are in good agreement with stellar models; an inflation of the radii of low-mass stars with respect to model predictions is limited to 1.6 $pm$ 1.2% in the fully convective regime. The sample of ten objects indicates a scaling of the radius of low-mass stars with the host star metallicity. No correlation between stellar radii and orbital periods of the binary systems is determined. A combined analysis with comparable objects from the literature is consistent with this result.
In our previous study of low mass stars using TESS, we found a handful which show a periodic modulation on a period <1 d but also displayed no flaring activity. Here we present the results of a systematic search for Ultra Fast Rotators (UFRs) in the southern ecliptic hemisphere which were observed in 2 min cadence with TESS. Using data from Gaia DR2, we obtain a sample of over 13,000 stars close to the lower main sequence. Of these, we identify 609 stars which lie on the lower main sequence and have a periodic modulation <1 d. The fraction of stars which show flares appears to drop significantly at periods <0.2 d. If the periods are a signature of the rotation rate, this would be a surprise, since faster rotators would be expected to have a stronger magnetic field and, therefore, produce more flares. We explore possible reasons for our finding: the flare inactive stars are members of binaries, in which case the stars rotation rate could have increased as the binary orbital separation reduced due to angular momentum loss over time, or that enhanced emission occurs at blue wavelengths beyond the pass band of TESS. Follow-up spectroscopy and flare monitoring at blue/ultraviolet wavelengths of these flare inactive stars are required to resolve this question.
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