Publications by Caroline Terquem

Tidally induced stellar oscillations: converting modelled oscillations excited by hot Jupiters into observables

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2021)

A Bunting, C TERQUEM

Non–adiabatic tidal oscillations induced by a planetary companion

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2019)

A Bunting, JCB Papaloizou, C Terquem

<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>

First-order mean motion resonances in two-planet systems: general analysis and observed systems

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2018)

CEJ TERQUEM, J Papaloizou

The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability

Monthly Notices of the Royal Astronomical Society Oxford University Press 476 (2017) 5032-5056

J Papaloizou, E Szuszkiewicz, C Terquem

We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on Gy time scales or longer, we require that the tidal parameter associated with the planets has to be such that Q΄ &gt; ∼102 − 3. At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, Q΄ associated with the planets has to be on the order (and not significantly exceeding) 102 − 3 for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.

CoRoT 223992193: Investigating the variability in a low-mass, pre-main sequence eclipsing binary with evidence of a circumbinary disk

Astronomy and Astrophysics EDP Sciences 599 (2017) A27

E Gillen, S Aigrain, C Terquem, J Bouvier, S Alencar, D Gandolfi, J Stauffer, A Cody, L Venuti, P Viana Almeida, G Micela, F Favata, H Deeg

CoRoT 223992193 is the only known low-mass, pre-main sequence eclipsing binary that shows evidence of a circumbinary disk. The system displays complex photometric and spectroscopic variability over a range of timescales and wavelengths. Using two optical CoRoT runs from 2008 and 2011/2012 (spanning 23 and 39 days), along with infrared Spitzer 3.6 and 4.5 µm observations (spanning 21 and 29 days, and simultaneous with the second CoRoT run), we model the out-of-eclipse light curves, finding that the large scale structure in both CoRoT light curves is consistent with the constructive and destructive interference of starspot signals at two slightly different periods. Using the v sin i of both stars, we interpret this as the two stars having slightly different rotation periods: the primary is consistent with synchronisation and the secondary rotates slightly supersynchronously. Comparison of the raw 2011/2012 light curve data to the residuals of our spot model in colour-magnitude space indicates additional contributions consistent with a combination of variable dust emission and obscuration. There appears to be a tentative correlation between this additional variability and the binary orbital phase, with the system displaying increases in its IR flux around primary and secondary eclipse. We also identify short-duration flux dips preceding secondary eclipse in all three CoRoT and Spitzer bands. We construct a model of the inner regions of the binary and propose that these dips could be caused by partial occultation of the central binary by the accretion stream onto the primary star. Analysis of 15 Hα profiles obtained with the FLAMES instrument on the Very Large Telescope reveal an emission profile associated with each star. The majority of this is consistent with chromospheric emission but additional higher velocity emission is also seen, which could be due to prominences. However, half of the secondary star’s emission profiles display full widths at 10% intensity that could also be interpreted as having an accretion-related origin. In addition, simultaneous u and r-band observations obtained with the MEGACam instrument on the Canada France Hawaii Telescope reveal a short-lived u-band excess consistent with either an accretion hot spot or stellar flare. The photometric and spectroscopic variations are very complex but are consistent with the picture of two active stars possibly undergoing non-steady, low-level accretion; the system’s very high inclination provides a new view of such variability

On the energy dissipation rate at the inner edge of circumbinary discs

Monthly Notices of the Royal Astronomical Society Oxford University Press 464 (2016) 2429-2440

C Terquem, JCB Papaloizou

We study, by means of numerical simulations and analysis, the details of the accretion process from a disc onto a binary system. We show that energy is dissipated at the edge of a circumbinary disc and this is associated with the tidal torque that maintains the cavity: angular momentum is transferred from the binary to the disc through the action of compressional shocks and viscous friction. These shocks can be viewed as being produced by fluid elements which drift into the cavity and, before being accreted, are accelerated onto trajectories that send them back to impact the disc. The rate of energy dissipation is approximately equal to the product of potential energy per unit mass at the disc’s inner edge and the accretion rate, estimated from the disc parameters just beyond the cavity edge, that would occur without the binary. For very thin discs, the actual accretion rate onto the binary may be significantly less. We calculate the energy emitted by a circumbinary disc taking into account energy dissipation at the inner edge and also irradiation arising there from reprocessing of light from the stars. We find that, for tight PMS binaries, the SED is dominated by emission from the inner edge at wavelengths between 1–4 and 10 µm. This may apply to systems like CoRoT 223992193 and V1481 Ori.

On the formation of planetary systems in photoevaporating transition discs

Monthly Notices of the Royal Astronomical Society Oxford University Press 464 (2016) 924-932

C Terquem

In protoplanetary discs, planetary cores must be at least 0.1 M⊕ at 1 au for migration to be significant; this mass rises to 1 M⊕ at 5 au. Planet formation models indicate that these cores form on million year time-scales. We report here a study of the evolution of 0.1 and 1 M⊕ cores, migrating from about 2 and 5 au, respectively, in million year old photoevaporating discs. In such a disc, a gap opens up at around 2 au after a few million years. The inner region subsequently accrete on to the star on a smaller time-scale. We find that, typically, the smallest cores form systems of non-resonant planets beyond 0.5 au with masses up to about 1.5 M⊕. In low-mass discs, the same cores may evolve in situ. More massive cores form systems of a few Earth-mass planets. They migrate within the inner edge of the disc gap only in the most massive discs. Delivery of material to the inner parts of the disc ceases with opening of the gap. Interestingly, when the heavy cores do not migrate significantly, the type of systems that are produced resembles our Solar system. This study suggests that low-mm flux transition discs may not form systems of planets on short orbits but may instead harbour Earth-mass planets in the habitable zone.

A circumbinary disc model for the variability of the eclipsing binary CoRoT 223992193


C Terquem, PM Sorensen-Clark, J Bouvier

On the formation of the Kepler-10 planetary system


C Terquem

Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance


J Teyssandier, C Terquem

CoRoT 223992193: A new, low-mass, pre-main sequence eclipsing binary with evidence of a circumbinary disk

Astronomy and Astrophysics EDP Sciences 562 (2014) 50-69

E Gillen, S Aigrain, A McQuillan, J Bouvier, S Hodgkin, SHP Alencar, C Terquem, J Southworth, NP Gibson, AM Cody, M Lendl, M Morales-Calderón, F Favata, J Stauffer, G Micela

We present the discovery of CoRoT 223992193, a double-lined, detached eclipsing binary, comprising two pre-main sequence M dwarfs, discovered by the CoRoT space mission during a 23-day observation of the 3 Myr old NGC 2264 star-forming region. Using multi-epoch optical and near-IR follow-up spectroscopy with FLAMES on the Very Large Telescope and ISIS on the William Herschel Telescope we obtain a full orbital solution and derive the fundamental parameters of both stars by modelling the light curve and radial velocity data. The orbit is circular and has a period of $3.8745745 \pm 0.0000014$ days. The masses and radii of the two stars are $0.67 \pm 0.01$ and $0.495 \pm 0.007$ $M_{\odot}$ and $1.30 \pm 0.04$ and $1.11 ~^{+0.04}_{-0.05}$ $R_{\odot}$, respectively. This system is a useful test of evolutionary models of young low-mass stars, as it lies in a region of parameter space where observational constraints are scarce; comparison with these models indicates an apparent age of $\sim$3.5-6 Myr. The systemic velocity is within $1\sigma$ of the cluster value which, along with the presence of lithium absorption, strongly indicates cluster membership. The CoRoT light curve also contains large-amplitude, rapidly evolving out-of-eclipse variations, which are difficult to explain using starspots alone. The system's spectral energy distribution reveals a mid-infrared excess, which we model as thermal emission from a small amount of dust located in the inner cavity of a circumbinary disk. In turn, this opens up the possibility that some of the out-of-eclipse variability could be due to occultations of the central stars by material located at the inner edge or in the central cavity of the circumbinary disk.

The effects of disc warping on the inclination of planetary orbits

MNRAS (2013)

C Terquem

Orbital evolution of a planet on an inclined orbit interacting with a disc

Monthly Notices of the Royal Astronomical Society 428 (2013) 658-669

J Teyssandier, C Terquem, JCB Papaloizou

Protoplanets with core masses below the critical mass fill in their Roche lobe

Monthly Notices of the Royal Astronomical Society 418 (2011) 1928-1934

C Terquem, T Heinemann

We study the evolution of a protoplanet of a few earth masses embedded in a protoplanetary disc. If we assume that the atmosphere of the protoplanet, i.e. the volume of gas in hydrostatic equilibrium bound to the core, has a surface radius smaller than the Roche lobe radius, we show that it expands as it accretes both planetesimals and gas at a fixed rate from the nebula until it fills in the Roche lobe. The evolution occurs on a time-scale shorter than the formation or migration time-scales. Therefore, we conclude that protoplanets of a few earth masses have an atmosphere that extends to the Roche lobe surface, where it joins on to the nebula. This is true even when the Bondi radius is smaller than the Roche lobe radius. This is in contrast to the commonly used models in which the static atmosphere extends up to the Bondi radius and is surrounded by a cold accretion flow. As a result, any calculation of the tidal torque exerted by the disc on to the protoplanet should exclude the material present in the Roche lobe, since it is bound to the protoplanet. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

Disk dynamics and planet migration

EAS Publications Series 41 (2010) 209-218

CEJMLJ Terquem

We review models of protoplanetary disks. In the earlier stages of evolution, disks are subject to gravitational instabilities that redistribute mass and angular momentum on short timescales. Later on, when the mass of the disk is below ten percent or so of that of the central star, accretion occurs through the magnetorotational instability. The parts of the disks that are not ionized enough to couple to the magnetic field may not accrete or accrete inefficiently. We also review theories of planet migration. Tidal interaction between a disk and an embedded planet leads to angular momentum exchange between the planetary orbital motion and the disk rotation. This results in low mass planets migrating with respect to the gas in the disk, while massive planets open up a gap in the vicinity of their orbit and migrate in as the disk is accreted. © EAS, EDP Sciences, 2010.

On the dynamics of multiple systems of hot super-Earths and Neptunes: Tidal circularization, resonance and the HD 40307 system

Monthly Notices of the Royal Astronomical Society 405 (2010) 573-592

JCB Papaloizou, C Terquem

In this paper, we consider the dynamics of a system of hot super-Earths or Neptunes such as HD 40307. We show that, as tidal interaction with the central star leads to small eccentricities, the planets in this system could be undergoing resonant coupling even though the period ratios depart significantly from very precise commensurability. In a three-planet system, this is indicated by the fact that resonant angles librate or are associated with long-term changes to the orbital elements. In HD 40307, we expect that three resonant angles could be involved in this way. We propose that the planets in this system were in a strict Laplace resonance while they migrated through the disc. After entering the disc inner cavity, tidal interaction would cause the period ratios to increase from two but with the inner pair deviating less than the outer pair, counter to what occurs in HD 40307. However, the relationship between these pairs that occur in HD 40307 might be produced if the resonance is impulsively modified by an event like a close encounter shortly after the planetary system decouples from the disc. We find this to be in principle possible for a small relative perturbation on the order of a few ×10-3, but then we find that the evolution to the present system in a reasonable time is possible only if the masses are significantly larger than the minimum masses and the tidal dissipation is very effective. On the other hand, we found that a system like HD 40307 with minimum masses and more realistic tidal dissipation could be produced if the eccentricity of the outermost planet was impulsively increased to ∼0.15. We remark that the form of resonantly coupled tidal evolution we consider here is quite general and could be of greater significance for systems with inner planets on significantly shorter orbital periods characteristic of, for example, CoRoT 7 b. © 2010 The Authors. Journal compilation © 2010 RAS.

Eccentricity pumping of a planet on an inclined orbit by a disc

Monthly Notices of the Royal Astronomical Society 404 (2010) 409-414

C Terquem, A Ajmia

In this paper, we show that the eccentricity of a planet on an inclined orbit with respect to a disc can be pumped up to high values by the gravitational potential of the disc, even when the orbit of the planet crosses the disc plane. This process is an extension of the Kozai effect. If the orbit of the planet is well inside the disc inner cavity, the process is formally identical to the classical Kozai effect. If the planet's orbit crosses the disc but most of the disc mass is beyond the orbit, the eccentricity of the planet grows when the initial angle between the orbit and the disc is larger than some critical value which may be significantly smaller than the classical value of 39{ring operator}. Both the eccentricity and the inclination angle then vary periodically with time. When the period of the oscillations of the eccentricity is smaller than the disc lifetime, the planet may be left on an eccentric orbit as the disc dissipates. © 2010 The Authors. Journal compilation. © 2010 RAS.

New composite models of partially ionized protoplanetary disks

Astrophysical Journal 689 (2008) 532-538

CEJML Terquem

Migration and the formation of systems of hot super-earths and neptunes

Astrophysical Journal 654 (2007) 1110-1120

C Terquem, JCB Papaloizou

Planet formation and migration

Reports on Progress in Physics 69 (2006) 119-180

JCB Papaloizou, C Terquem

We review the observations of extrasolar planets, ongoing developments in theories of planet formation, orbital migration and the evolution of multiplanet systems. © 2006 IOP Publishing Ltd.