# Publications by Caroline Terquem

## Non–adiabatic tidal oscillations induced by a planetary companion

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (0)

<jats:title>Abstract</jats:title> <jats:p>We calculate the dynamical tides raised by a close planetary companion on non–rotating stars of 1 M⊙ and 1.4 M⊙. Using the Henyey method, we solve the fully non–adiabatic equations throughout the star. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non–adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent with non–adiabaticity. Although this approximation generally applies in the low frequency limit, it also fails in the parts of the convection zone where the forcing frequency is small but larger than the Brunt-Väisälä frequency. We derive analytical estimates which give a good approximation to the numerical values of the magnitude of the ratio of the horizontal and radial displacements at the surface. The relative surface flux perturbation is also significant, on the order of 0.1% for a system modelled on 51 Pegasi b. Observations affected by the horizontal displacement may therefore be more achievable than previously thought, and brightness perturbations may be the result of flux perturbations rather than due to the radial displacement. We discuss the implication of this on the possibility of detecting such tidally excited oscillations, including the prospect of utilising the large horizontal motion for observations of systems such as 51 Pegasi.</jats:p>

## Theory of Turbulent Accretion Disks

ArXiv (0)

In low-mass disks, turbulent torques are probably the most important way of redistributing angular momentum. Here we present the theory of turbulent accretion disks. We show the molecular viscosity is far too small to account for the evolutionary timescale of disks, and we describe how turbulence may result in enhanced transport of (angular) momentum. We then turn to the magnetorotational instability, which thus far is the only mechanism that has been shown to initiate and sustain turbulence in disks. Finally, we present both the basis and the structure of alpha disk models.

## Tidally-induced warps in protostellar discs

ArXiv (0)

We review results on the dynamics of warped gaseous discs. We consider tidal perturbation of a Keplerian disc by a companion star orbiting in a plane inclined to the disc. The perturbation induces the precession of the disc, and thus of any jet it could drive. In some conditions the precession rate is uniform, and as a result the disc settles into a warp mode. The tidal torque also leads to the truncation of the disc, to the evolution of the inclination angle (not necessarily towards alignment of the disc and orbital planes) and to a transport of angular momentum in the disc. We note that the spectral energy distribution of such a warped disc is different from that of a flat disc. We conclude by listing observational effects of warps in protostellar discs.

## Discs and Planetary Formation

ArXiv (0)

The formation, structure and evolution of protoplanetary discs is considered. The formation of giant planets within the environment of these models is also discussed.

## Planet formation, orbital evolution and planet-star tidal interaction

ArXiv (0)

We consider several processes operating during the late stages of planet formation that can affect observed orbital elements. Disk-planet interactions, tidal interactions with the central star, long term orbital instability and the Kozai mechanism are discussed.

## Precessing warped discs in close binary systems

ArXiv (0)

We describe some recent nonlinear three dimensional hydrodynamic simulations of accretion discs in binary systems where the orbit is circular and not necessarily coplanar with the disc midplane. The calculations are relevant to a number of observed astrophysical phenomena, including the precession of jets associated with young stars, the high spectral index of some T Tauri stars, and the light curves of X-ray binaries such as Hercules X-1 which suggest the presence of precessing accretion discs.

## Tidally induced warps in T Tauri discs - II. A parametric study of spectral energy distributions

Monthly Notices of the Royal Astronomical Society **279** (1996) 415-428

We compute here the spectral energy distribution (SED) of warped T Tauri discs in a general way. In a previous paper we analytically calculated, in a linear approximation, the response of a circumstellar disc to tidal forces owing to a stellar companion in a non-coplanar young binary system. Here, we consider tidally induced warps of larger amplitude, and we use these previous results to parametrize the disc deformation. We then compute the energy emitted in a given direction by the system of the warped disc and central star, taking into account shadowing effects. We find that the parametrized warp model produces a broad variety of synthetic SEDs. Some of them are comparable to those of T Tauri stars with infrared excess (Class II sources), whereas others resemble Class I protostellar sources. By comparing models with actual observations of both a T Tauri star with high spectral index and a Class I source, we find that the derived warp and disc parameters are not unrealistic, and we conclude that tidal interactions in T Tauri binary systems with intermediate separations must play a role in shaping the SEDs of these stars.

## The tidally induced warping, precession and truncation of accretion discs in binary systems: Three-dimensional simulations

Monthly Notices of the Royal Astronomical Society **282** (1996) 597-613

We present the results of non-linear, hydrodynamic simulations, in three dimensions, of the tidal perturbation of accretion discs in binary systems where the orbit is circular and not necessarily coplanar with the disc mid-plane. The accretion discs are assumed to be geometrically thin, and of low mass relative to the stellar mass so that they are governed by thermal pressure and viscosity, but not self-gravity. The parameters that we consider in our models are the ratio of the orbital distance to the disc radius, D/R, the binary mass ratio, Ms/Mp, the initial inclination angle between the orbit and disc planes, δ, and the Mach number in the outer parts of the unperturbed disc, ℳ. Since we consider non-self-gravitating discs, these calculations are relevant to protostellar binaries with separations below a few hundred au. For binary mass ratios of around unity and D/R in the range 3 to 4, we find that the global evolution of the discs is governed primarily by the value of ℳ. For relatively low Mach numbers (i.e. ℳ = 10 to 20) we find that the discs develop a mildly warped structure, are tidally truncated, and undergo a near rigid body precession at a rate which is in close agreement with analytical arguments. For higher Mach numbers (ℳ ≈ 30), the evolution is towards a considerably more warped structure, but the disc none the less maintains itself as a long-lived, coherent entity. A further increase in Mach number to ℳ = 50 leads to a dramatic disruption of the disc as a result of differential precession, since the sound speed is too low to allow efficient communication between constituent parts of the disc. Additionally, it is found that the inclination angle between the disc and the orbital angular momentum vectors evolves on a longer time-scale, which is probably the viscous evolution time-scale of the disc. The calculations are relevant to a number of observed astrophysical phenomena, including the precession of jets associated with young stars, the high spectral index of some T Tauri stars, and the light curves of X-ray binaries such as Hercules X-1 which suggest the presence of precessing accretion discs.

## On the stability of an accretion disc containing a toroidal magnetic field

Monthly Notices of the Royal Astronomical Society **279** (1996) 767-784

We study the stability of an accretion disc with an embedded toroidal magnetic field to general perturbations. Disc models are considered in which the equilibrium variables depend on both the radial and vertical coordinates. We consider the full global problem in which the disc may be in the form of a narrow annulus, or occupy a significant radial extent. Perturbations with azimuthal mode number m in the range zero up to the ratio of the radius to disc scmithickness are considered. Discs containing a purely toroidal magnetic field are always found to be unstable. We find spectra of unstable modes using local techniques. In the absence of dissipation, these modes may occupy arbitrarily small scales in the radial and vertical directions. One class of modes is driven primarily by buoyancy, while the other is driven by shear independently of the equilibrium stratification. The first type of instability predominates if the field is large, while the second type predominates if the field is weak and the underlying medium is strongly stable to convection. We also investigate stability by solving the initial value problem for perturbations numerically. We find, for our disc models, that local instabilities predominate over any possible global instability. Their behaviour is in good accord with the local analysis. The associated growth rates become just less than the orbital frequency when the ratio of magnetic energy density to pressure reaches about 10 per cent. Instabilities of the kinds discussed here may provide a mechanism for limiting the growth of toroidal fields in dynamo models of accretion discs.

## Density waves and warps generated by tidal perturbation of a gaseous disk

WAVES IN ASTROPHYSICS **773** (1995) 261-276

## On the dynamics of tilted discs around young stars

Monthly Notices of the Royal Astronomical Society **274** (1995) 987-1001

## Tidally-Induced warps in T-Tauri Disks - I. First Order Perturbation Theory

Astronomy and Astrophysics **274** (1993) 291-303

## Tidally-induced angular momentum transport in disks

ArXiv (0)

We discuss the transport of angular momentum induced by tidal effects in a disk surrounding a star in a pre-main sequence binary system. We consider the effect of both density and bending waves. Although tidal effects are important for truncating protostellar disks and for determining their size, it is unlikely that tidally-induced angular momentum transport plays a dominant role in the evolution of protostellar disks. Where the disk is magnetized, transport of angular momentum is probably governed by MHD turbulence. In a non self-gravitating laminar disk, the amount of transport provided by tidal waves is probably too small to account for the lifetime of protostellar disks. In addition, tidal effects tend to be localized in the disk outer regions.

## Is planetary migration inevitable?

ArXiv (0)

According to current theories, tidal interactions between a disk and an embedded planet may lead to the rapid migration of the protoplanet on a timescale shorter than the disk lifetime or estimated planetary formation timescales. Therefore, planets can form only if there is a mechanism to hold at least some of the cores back on their way in. Once a giant planet has assembled, there also has to be a mechanism to prevent it from migrating down to the disk center. This paper reviews the different mechanisms that have been proposed to stop or slow down migration.

## Oscillations in solar-type stars tidally induced by orbiting planets

ArXiv (0)

We examine the effect of dynamical tides raised by a companion on a solar-type star. In these binaries, gravity or g mode oscillations are excited by the companion in the radiative region beneath the convective envelope of the star. They become evanescent in the convection zone. This is of particular interest in connection with the newly discovered planets, some of which are found to orbit around solar-type stars with a period comparable to that of the high order g modes of the star. One such example is 51 Pegasi. Here, we determine the magnitude of the perturbed velocity induced by the tides at the stellar surface. We show that, in the case of 51 Pegasi, this velocity is too small to be observed. This result is insensitive to the magnitude of the stellar turbulent viscosity assumed and is not affected by the possibility of resonance, which occurs when the frequency of the tidal disturbance is close to that of some normal mode of the star. We also discuss the orbital evolution and synchronization timescales associated with the tidal interaction.

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