arXiv subjects

J. C. B. Papaloizou

Publications and source records attributed to J. C. B. Papaloizou.

At least 55 records · Page 3Linked to original sources

arXiv2007

Orbital circularisation of white dwarfs and the formation of gravitational radiation sources in star clusters containing an intermediate mass black hole

(abbreviated) We consider how tight binaries consisting of a super-massive black hole of mass $M=10^{3}-10^{4}M_{\odot}$ and a white dwarf can be formed in a globular cluster. We point out that a major fraction of white dwarfs tidally captured by the black hole may be destroyed by tidal inflation during ongoing circularisation, and the formation of tight binaries is inhibited. However, some stars may survive being spun up to high rotation rates. Then the energy loss through gravitational wave emission induced by tidally excited pulsation modes and dissipation through non linear effects may compete with the increase of pulsation energy due to dynamic tides. The semi-major axes of these stars can be decreased below a 'critical' value where dynamic tides are not effective because pulsation modes retain phase coherence between successive pericentre passages. The rate of formation of such circularising stars is estimated assuming that they can be modelled as $n=1.5$ polytropes and that results of the tidal theory for slow rotators can be extrapolated to fast rotators. We estimate the total capture rate as $\sim \dot N\sim 2.5\cdot 10^{-8}M_{4}^{1.3}r_{0.1}^{-2.1}yr^{-1}$, where $M_{4}=M/10^4M_{\odot}$ and $r_{0.1}$ is the radius of influence of the black hole in units $0.1pc$. We find that the formation rate of tight pairs is approximately 10 times smaller than the total capture rate. It is used to estimate the probability of detection of gravitational waves coming from such tight binaries by LISA. We conclude that LISA may detect such binaries provided that the fraction of globular clusters with black holes in the mass range of interest is substantial and that the dispersion velocity of the cluster stars near the radius of influence of the black hole exceeds $\sim 20km/s$.

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arXiv2007

On the dynamics of a twisted disc immersed in a radiation field

We study the dynamics of a twisted tilted disc under the influence of an external radiation field. Assuming the effect of absorption and reemission/scattering is that a pressure is applied to the disc surface where the local optical depth is of order unity, we determine the response of the vertical structure and the influence it has on the possibility of instability to warping. We derive a pair of equations describing the evolution of a small tilt as a function of radius in the small amplitude regime that applies to both the diffusive and bending wave regimes. We also study the non linear vertical response of the disc numerically using an analogous one dimensional slab model. For global warps, we find that in order for the disc vertical structure to respond as a quasi uniform shift or tilt, as has been assumed in previous work, the product of the ratio of the external radiation momentum flux to the local disc mid plane pressure, where it is absorbed, with the disc aspect ratio should be significantly less than unity. Namely, this quantity should be of the order of or smaller than the ratio of the disc gas density corresponding to the layer intercepting radiation to the mid plane density, $λ\ll 1$. When this condition is not satisfied the disc surface tends to adjust so that the local normal becomes perpendicular to the radiation propagation direction. In this case dynamical quantities determined by the disc twist and warp tend to oscillate with a large characteristic period $T_{*}\sim λ^{-1}T_{K}$, where $T_{K}$ is some 'typical' orbital period of a gas element in the disc. The possibility of warping instability then becomes significantly reduced. In addition, when the vertical response is non uniform, the possible production of shocks may lead to an important dissipation mechanism.

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arXiv2006

One-armed oscillations in Be star discs

In this paper we study the effect of the quadrupole-term in the gravitational potential of a rotationally deformed central Be star on one armed density waves in the circumstellar disc. The aim is to explain the observed long-term violet over red (V/R) intensity variations of the double peaked Balmer emission-lines, not only in cool Be star systems, but also in the hot systems like gamma Cas. We have carried out semi-analytic and numerical studies of low-frequency one armed global oscillations in near Keplerian discs around Be stars. In these we have investigated surface density profiles for the circumstellar disc which have inner narrow low surface density or gap regions, just interior to global maxima close to the rapidly rotating star, as well as the mode inner boundary conditions. Our results indicate that it is not necessary to invoke extra forces such as caused by line absorption from the stellar flux in order to explain the long-term V/R variations in the discs around massive Be stars. When there exists a narrow gap between the star and its circumstellar disc, with the result that the radial velocity perturbation is non-zero at the inner disc boundary, we find oscillation (and V/R) periods in the observed range for plausible magnitudes for the rotational quadrupole term.

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arXiv2006

Disk-Planet Interactions During Planet Formation

The discovery of close orbiting extrasolar giant planets led to extensive studies of disk planet interactions and the forms of migration that can result as a means of accounting for their location. Early work established the type I and type II migration regimes for low mass embedded planets and high mass gap forming planets respectively. While providing an attractive means of accounting for close orbiting planets intially formed at several AU, inward migration times for objects in the earth mass range were found to be disturbingly short, making the survival of giant planet cores an issue. Recent progress in this area has come from the application of modern numerical techniques which make use of up to date supercomputer resources. These have enabled higher resolution studies of the regions close to the planet and the initiation of studies of planets interacting with disks undergoing MHD turbulence. This work has led to indications of how the inward migration of low to intermediate mass planets could be slowed down or reversed. In addition, the possibility of a new very fast type III migration regime, that can be directed inwards or outwards, that is relevant to partial gap forming planets in massive disks has been investigated.

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arXiv2005

Dynamic tides in rotating objects: orbital circularisation of extra solar planets for realistic planet models

(abbreviated) We consider the problem of the tidal capture or circularisation from large eccentricity of a uniformly rotating object. We extend the self-adjoint formalism introduced in Papaloizou \& Ivanov 2005 (PI) to derive general expressions for the energy and angular momentum transfered when the planet or a star passes through periastron in a parabolic or highly eccentric orbit around a central mass, without making a low frequency approximation as was done in PI. We show how these can be adapted to the low frequency limit in which only inertial modes contribute to the energy and angular momentum transfer. We calculate the inertial mode eigenspectrum for planet models of one and five Jupiter masses $M_J,$ without a solid core, with different radii corresponding to different ages. We consider the multi-passage problem when there is no dissipation finding that stochastic instability resulting in the stochastic gain of inertial mode energy over many periastron passages occurs under similar conditions to those already found for the $f$ modes. We apply our calculations to the problem of the tidal circularisation of the orbits of the extra solar planets in a state of pseudo synchronisation, and find that inertial mode excitation dominates the tidal interaction for $1 M_J$ planets that start with semi- major axes less than $10 AU$ and end up on circular orbits with final period in the $4-6$ day range. It is potentially able to account for initial circularisation up to a final $6$ day period within a few $Gyr$ But in the case of $5M_J$ oscillation modes excited in the star are more important.

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arXiv2005

Oscillations of rotating bodies: A self-adjoint formalism applied to dynamic tides and tidal capture

We consider the excitation of the inertial modes of a uniformly rotating fully convective body due to a close encounter with another object. This could lead to a tidal capture or orbital circularisation depending on whether the initial orbit is unbound or highly eccentric. We develop a general self-adjoint formalism for the response problem and thus solve it taking into account the inertial modes with $m=2$ for a full polytrope with $n=1.5.$ We are accordingly able to show in this case that the excitation of inertial modes dominates the response for large impact parameters and thus cannot be neglected in calculations of tidal energy and angular momentum exchange or orbital circularisation from large eccentricity.

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arXiv2005

On the migration-induced resonances in a system of two planets with masses in the Earth mass range

We investigate orbital resonances expected to arise when a system of two planets, with masses in the range 1-4 Earth masses, undergoes convergent migration while embedded in a section of gaseous disc where the flow is laminar. We consider surface densities corresponding to 0.5-4 times that expected for a minimum mass solar nebula at 5.2 AU. Using hydrodynamic simulations we find that when the configuration is such that convergent migration occurs the planets can become locked in a first order commensurability for which the period ratio is (p+1)/p with p being an integer and migrate together maintaining it for many orbits. Relatively rapid convergent migration as tends to occur for disparate masses, results in commensurabilities with p larger than 2. However, in these cases the dynamics is found to have a stochastic character. When the convergent migration is slower, such as occurs in the equal mass case, lower p commensurabilities such as 3:2 are attained which show much greater stability. In one already known example of a system with nearly equal masses in the several Earth mass range (planets around pulsar PSR B1257+12) the two largest planets are intriguingly close to a 3:2 commensurability. A very similar behaviour is obtained when the systems are modeled using an N body code with simple prescriptions for the disc planet interaction. Using that, we found that an 8:7 resonance established in a hydrodynamic simulation run for 10-100 thousand orbits could be maintained for more than million orbits. Resonant capture leads to a rise in eccentricities that can be predicted using a simple analytic model constructed in this paper. We find that the system with the 8:7 commensurability is fully consistent with this prediction.

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arXiv2004

Disk Planet Interactions and Early Evolution in Young Planetary Systems

We study and review disk protoplanet interactions using local shearing box simulations. These suffer the disadvantage of having potential artefacts arising from periodic boundary conditions but the advantage, when compared to global simulations, of being able to capture much of the dynamics close to the protoplanet at high resolution for low computational cost. Cases with and without self sustained MHD turbulence are considered. The conditions for gap formation and the transition from type I migration are investigated and found to depend on whether the single parameter M_p R^3/(M_* H^3), with M_p, M_*, R and H being the protoplanet mass, the central mass, the orbital radius and the disk semi-thickness respectively exceeds a number of order unity. We also investigate the coorbital torques experienced by a moving protoplanet in an inviscid disk. This is done by demonstrating the equivalence of the problem for a moving protoplanet to one where the protoplanet is in a fixed orbit which the disk material flows through radially as a result of the action of an appropriate external torque. For sustainable coorbital torques to be realized a quasi steady state must be realized in which the planet migrates through the disk without accreting significant mass. In that case although there is sensitivity to computational parameters, in agreement with earlier work by Masset & Papaloizou (2003) based on global simulations, the coorbital torques are proportional to the migration speed and result in a positive feedback on the migration, enhancing it and potentially leading to a runaway. This could lead to a fast migration for protoplanets in the Saturn mass range in massive disks and may be relevant to the mass period correlation for extrasolar planets which gives a preponderance of sub Jovian masses at short orbital period.

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arXiv2004

The Local Instability of Steady Astrophysical Flows with non Circular Streamlines with Application to Differentially Rotating Disks with Free Eccentricity

We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it finite eccentricity. We consider perturbations arbitrarily localized in the neighbourhood of unperturbed fluid streamlines.When conditions do not vary around them, perturbations take the form of oscillatory inertial or gravity modes. However, when conditions do vary so that a circulating fluid element is subject to periodic variations, parametric instability may occur. For nearly circular streamlines, the dense spectra associated with inertial or gravity modes ensure that resonance conditions can always be satisfied when twice the period of circulation round a streamline falls within. We apply our formalism to a differentially rotating disk for which the streamlines are Keplerian ellipses, with free eccentricity up to 0.7, which do not precess in an inertial frame. We show that for small $e,$ the instability involves parametric excitation of two modes with azimuthal mode number differing by unity in magnitude which have a period of twice the period of variation as viewed from a circulating unperturbed fluid element. Instability persists over a widening range of wave numbers with increasing growth rates for larger eccentricities. The nonlinear outcome is studied in a follow up paper which indicates development of small scale subsonic turbulence.

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arXiv2004

Resonantly-forced Eccentric Ringlets: Relationships between Surface Density, Resonance location, Eccentricity and Eccentricity-gradient

We use a simple model of the dynamics of a narrow-eccentric ring, to put some constraints on some of the observable properties of the real systems.In this work we concentrate on the case of the `Titan ringlet of Saturn'.Our approach is fluid-like, since our description is based on normal modes of oscillation rather than in individual particle orbits. Thus, the rigid precession of the ring is described as a global $m=1$ mode, which originates from a standing wave superposed on an axisymmetric background. An integral balance condition for the maintenance of the $m=1$ standing-wave can be set up, in which the differential precession induced by the oblateness of the central planet must cancel the contributions of self-gravity, the resonant satellite forcing and collisional effects. We expect that in nearly-circular narrow rings dominated by self-gravity, the eccentricity varies linearly across the ring. Thus, we take a first order expansion and we derive two integral relationships from the rigid-precession condition. These relate the surface density of the ring with the eccentricity at the center, the eccentricity gradient and the location of the secular resonance. These relationships are applied to the Titan ringlet of Saturn, which has a secular resonance with the satellite Titan in which the ring precession period is close to Titan's orbital period. In this case, we estimate the mean surface density and the location of the secular resonance.

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arXiv2004

Structuring eccentric-narrow planetary rings

(Abridged) A simple and general description of the dynamics of a narrow eccentric ring is presented.We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global $m=1$ mode originating from a standing wave superposed on an axisymmetric background.We adopt a continuum description using the language of fluid dynamics which gives equivalent results for the secular dynamics of thin rings as the the well known description using discrete elliptical streamlines formulated by Goldreich and Tremaine (1979). We use this to discuss the non linear mode interactions that appear through the excitation of higher $m$ modes due to the coupling of the $m=1$ mode with an external satellite potential, showing that they can lead to the excitation of the $m=1$ mode through a feedback process.Two conditions for the maintainance of a steady $m=1$ mode are obtained. One,being the condition for the normal mode pattern to precess uniformly requires a balance between the differential precession induced by the oblateness of the central planet,self-gravity and collisional effects and is the continuum form of that obtained from the $N$ streamline model of Goldreich and Tremaine (1979).The other condition is for the steady maintenance of the non-zero radial action of the ring on account of the normal mode.This requires a balance between input due to eccentric resonances due to external satellites and additional collisional damping associated with the presence of the $m=1$ mode We estimate that such a balance can occur in the $ε-$ring of Uranus,given its currently observed physical and orbital parameters.

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arXiv2003

On equilibrium tides in fully convective planets and stars

We consider the tidal interaction of a fully convective primary star and a point mass. Using a normal mode decomposition we calculate the evolution of the primary angular velocity and orbit for arbitrary eccentricity e. The dissipation acting on the tidal perturbation is associated with convective turbulence. A novel feature of the Paper is that, to take into account of the fact that there is a relaxation time t_{c}, being the turn-over time of convective eddies, associated with the process, this is allowed to act non locally in time, producing a dependence of the dissipation on tidal forcing frequency. Results are expressed in terms of the Fourier coefficients of the tidal potential. We find analytical approximations for these valid for $e>0.2$. When the tidal response is frequency independent, our results are equivalent to those obtained in the standard constant time lag approximation. When there is the frequency dependence of the dissipative response, the evolution can differ drastically. In that case the system can evolve through a sequence of spin-orbit corotation resonances with Omega_{r}/Omega_{orb}=n/2, where Omega_{r} and Omega_{orb} are the rotation and orbital frequencies and n is an integer. We study this case analytically and numerically.

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arXiv2003

Structuring the HD 141569 A circumstellar dust disk. Impact of eccentric bound stellar companions

Scattered light images of the optically thin dust disk around the 5 Myr old star HD141569 have revealed its complex asymmetric structure. We show in this paper that the surface density inferred from the observations presents similarities with that expected from a circumprimary disk within a highly eccentric binary system. We assume that either the two M stars in the close vicinity of HD141569 are bound companions or at least one of them is an isolated binary companion. We discuss the resulting interaction with an initially axisymmetric disk. This scenario accounts for the formation of a spiral structure, a wide gap in the disk and a broad faint extension outside the truncation radius of the disk after 10-15 orbital periods with no need for massive companion(s) in the midst of the disk resolved in scattered light. The simulations match the observations and the star age if the perturber is on an elliptic orbit with a periastron distance of 930 AU and an eccentricity from 0.7 to 0.9. We find that the numerical results can be reasonably well reproduced using an analytical approach proposed to explain the formation of a spiral structure by secular perturbation of a circumprimary disk by an external bound companion. We also interpret the redness of the disk in the visible reported by Clampin et al.(2003) and show that short-lived grains one order of magnitude smaller than the blow-out size limit are abundant in the disk. The most probable reason for this is that the disk sustains high collisional activity. Finally we conclude that additional processes are required to clear out the disk inside 150 AU and that interactions with planetary companions possibly coupled with the remnant gas disk are likely candidates.

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arXiv2003

On the tidal interaction of massive extra-solar planets on highly eccentric orbit

In this paper we develop a theory of disturbances induced by the stellar tidal field in a fully convective slowly rotating planet orbiting on a highly eccentric orbit around a central star. We show that there are two contributions to the mode energy and angular momentum gain due to impulsive tidal interaction: a) 'the quasi-static' contribution which requires dissipative processes operating in the planet; b) the dynamical contribution associated with excitation of modes of oscillation. These contributions are obtained self-consistently from a single set of the governing equations. We calculate a critical 'equilibrium' value of angular velocity of the planet Ω_{crit} determined by the condition that action of the dynamical tides does not alter the angular velocity at that rotation rate. We show that this can be much larger than the corresponding rate associated with quasi-static tides and that at this angular velocity, the rate of energy exchange is minimised. We also investigate the conditions for the stochastic increase in oscillation energy that may occur if many periastron passages are considered. We make some simple estimates of time scale of circularization of initially eccentric orbit due to tides, using a realistic model of the planet, for orbits withperiods after circularization typical of those observed for extra-solar planets P_{obs} > 3days. We find that dynamic tides could have produced a very large decrease of the semi-major axis of a planet with mass of the order of the Jupiter mass M_{J} and final periods P_{obs} < 4.5days on a time-scale < a few Gyrs. We also discuss several unresolved issues in the context of the scenario of the orbit circularization due to dynamic tides.

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arXiv2003

Runaway migration and the formation of hot Jupiters

[Abridged] We evaluate the coorbital corotation torque on a migrating protoplanet. The coorbital torque is assumed to come from orbit crossing fluid elements which exchange angular momentum with the planet when they execute a U-turn at the end of horseshoe streamlines. When the planet migrates inward, the fluid elements of the inner disk undergo one such exchange as they pass to the outer disk. The angular momentum they gain is removed from the planet, and this corresponds to a negative contribution to the corotation torque, which scales with the drift rate. In addition, the material trapped in the coorbital region drifts radially with the planet giving a positive contribution to the corotation torque, which also scales with the drift rate. These two contributions do not cancel out if the coorbital region is depleted, in which case there is a net corotation torque which scales with the drift rate and the mass deficit in the coorbital region, and which has same sign as the drift rate. This leads to a positive feedback on the migrating planet. In particular, if the coorbital mass deficit is larger than the planet mass, the migration rate undergoes a runaway which can vary the protoplanet semi-major axis by 50% over a few tens of orbits. This can happen only if the planet mass is sufficient to create a dip or gap in its surrounding region, and if the surrounding disk mass is larger than the planet mass. This typically corresponds to planet masses in the sub-Saturnian to Jovian mass range embedded in massive protoplanetary disks. Runaway migration is a good candidate to account for the orbital characteristics of close orbiting giant planets, most of which have sub-Jovian masses. Further, we show that in the runaway regime, migration can be directed outwards.

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arXiv2002

Global m=1 modes and migration of protoplanetary cores in eccentric protoplanetary discs

We calculate global $m=1$ modes with low pattern speed corresponding to introducing a finite eccentricity into a protoplanetary disc. We consider disc models which are either isolated or contain one or two protoplanets orbiting in an inner cavity. Global modes that are strongly coupled to inner protoplanets are found to have disc orbits which tend to have apsidal lines antialigned with respect to those of the inner protoplanets. Other modes corresponding to free disc modes may be global over a large range of length scales and accordingly be long lived. We consider the motion of a protoplanet in the earth mass range embedded in an eccentric disc and determine the equilibrium orbits which maintain fixed apsidal alignment with respect to the disc gas orbits. Equilibrium eccentricities are found to be comparable or possibly exceed the disc eccentricity. We then approximately calculate the tidal interaction with the disc in order to estimate the orbital migration rate. Results are found to deviate from the case of axisymmetric disc with near circular protoplanet orbit once eccentricities of protoplanet and disc orbits become comparable to the disc aspect ratio in magnitude. Aligned protoplanet orbits with very similar eccentricity to that of the gas disc are found to undergo litle eccentricity change while undergoing inward migration in general. However, for significantly larger orbital eccentricities, migration may be significantly reduced or even reverse from inwards to outwards. Thus the existence of global non circular motions in discs with radial excursions comparable to the semi-thickness may have important consequences for the migration and survival of protoplanetary cores in the earth mass range.

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arXiv2001

On disc driven inward migration of resonantly coupled planets with application to the system around GJ876

We consider two protoplanets gravitationally interacting with each other and a protoplanetary disc. The two planets orbit interior to a tidally maintained disc cavity while the disc interaction indices inward migration. When the migration is slow enough, the more rapidly migrating outer protoplanet approaches and becomes locked in a 2:1 commensurability with the inner one. This is maintained in subsequent evolution. We study this evolution using a simple anaytic model, full hydrodynamic 2D simulations of the disc planet system and longer time N body integrations incorporating simple prescriptions for the effect of the disc on the planet orbits. The eccentricity of the protoplanets are found to be determined by the migration rate induced in the outer planet orbit by the external disc. We apply our results to the recently discovered resonant planets around GJ876. Simulation shows that a disc with parameters expected for protoplanetary discs causes trapping in the 2:1 commensurability when the planets orbit in an inner cavity and that eccentricities in the observed range may be obtained.

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arXiv2001

Dynamical modeling of large scale asymmetries in the beta Pictoris dust disk

We report a new and complete model of the beta Pictoris disk, which succeeds in accounting for both the surface brightness distribution, warp characteristics, the outer ``butterfly'' asymmetry as observed by HST/STIS in scattered light, as well as the infrared emission. Our model includes the presence of a disk of planetesimals extending out to 120-150 AU, perturbed gravitationally by a giant planet on an inclined orbit, following the approach of Mouillet et al. (1997b). At any time, the planetesimal disk is assumed to be the source of a distribution of grains produced through collisional evolution, with the same initial orbital parameter distribution. The steady state spatial grain distribution is found incorporating the effects of radiation pressure which can cause the distribution of the smallest particles to become very distended. With realistic assumptions about the grains' chemical properties, the modeling confirms the previously evident need for an additional population of hot grains close to the star, to account for the 12 microns fluxes at short distances from the star. It also indicates that this population cannot explain the outer 12 microns flux distribution when the effects of gravity and radiation pressure determine the distribution. Very small grains, produced by collisions among aggregates, are tentatively proposed to account for this 12 microns outer emission.

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