Numerical simulations of the type III migration:I. Disc model and convergence tests

We investigate the fast (type III) migration regime of high-mass protoplanets orbiting in protoplanetary disks. This type of migration is dominated by corotational torques. We study the details of flow structure in the planet's vicinity, the dependence of migration rate on the adopted disc model, and the numerical convergence of models (independence of certain numerical parameters such as gravitational softening). We use two-dimensional hydrodynamical simulations with adaptive mesh refinement,based on the FLASH code with improved time-stepping scheme. We perform global disk simulations with sufficient resolution close to the planet, which is allowed to freely move throughout the grid. We employ a new type of equation of state in which the gas temperature depends on both the distance to the star and planet, and a simplified correction for self-gravity of the circumplanetary gas. We find that the migration rate in the type III migration regime depends strongly on the gas dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is sensitive to the aspect ratio of the circumplanetary disc. Furthermore, corrections due to the gas self-gravity are necessary to reduce numerical artifacts that act against rapid planet migration. Reliable numerical studies of Type III migration thus require consideration of both the thermal andthe self-gravity corrections, as well as a sufficient spatial resolution and the calculation of disk-planet attraction both inside and outside the Hill sphere. With this proviso, we find Type III migration to be a robust mode of migration, astrophysically promising because of a speed much faster than in the previously studied modes of migration.Comment: 17 pages, 15 figures, submitted to MNRAS. Comments welcom

The evolution of a supermassive binary caused by an accretion disc

The interaction of a massive binary and a non-self-gravitating circumbinary accretion disc is considered. The shape of the stationary twisted disc produced by the binary is calculated. It is shown that the inner part of the disc must lie in the binary orbital plane for any value of viscosity. When the inner disc midplane is aligned with the binary orbital plane on the scales of interest and it rotates in the same sense as the binary, the modification of the disc structure and the rate of decay of the binary orbit, assumed circular, due to tidal exchange of angular momentum with the disc, are calculated. It is shown that the modified disc structure is well described by a self-similar solution of the non-linear diffusion equation governing the evolution of the disc surface density. The calculated time scale for decay of the binary orbit is always smaller than the "accretion" time $t_{acc}=m/{\dot M}$ ($m$ is the mass of the secondary component, and $\dot M$ is the disc accretion rate), and is determined by ratio of secondary mass $m$, assumed to be much smaller than the primary mass, the disc mass inside the initial binary orbit, and the form of viscosity in the disc.Comment: to be published in MNRA

Collisional dust avalanches in debris discs

We quantitatively investigate how collisional avalanches may developin debris discs as the result of the initial break-up of a planetesimal or comet-like object, triggering a collisional chain reaction due to outward escaping small dust grains. We use a specifically developed numerical code that follows both the spatial distribution of the dust grains and the evolution of their size-frequency distribution due to collisions. We investigate how strongly avalanche propagation depends on different parameters (e.g., amount of dust released in the initial break-up, collisional properties of dust grains and their distribution in the disc). Our simulations show that avalanches evolve on timescales of ~1000 years, propagating outwards following a spiral-like pattern, and that their amplitude exponentially depends on the number density of dust grains in the system. We estimate a probability for witnessing an avalanche event as a function of disc densities, for a gas-free case around an A-type star, and find that features created by avalanche propagation can lead to observable asymmetries for dusty systems with a beta Pictoris-like dust content or higher. Characteristic observable features include: (i) a brightness asymmetry of the two sides for a disc viewed edge-on, and (ii) a one-armed open spiral or a lumpy structure in the case of face-on orientation. A possible system in which avalanche-induced structures might have been observed is the edge-on seen debris disc around HD32297, which displays a strong luminosity difference between its two sides.Comment: 18 pages, 19 figures; has been accepted for publication in Astronomy and Astrophysics, section 6. Interstellar and circumstellar matter. The official date of acceptance is 29/08/200

Survival of icy grains in debris discs. The role of photosputtering

We put theoretical constraints on the presence and survival of icy grains in debris discs. Particular attention is paid to UV sputtering of water ice, which has so far not been studied in detail in this context. We present a photosputtering model based on available experimental and theoretical studies. We quantitatively estimate the erosion rate of icy and ice-silicate grains, under the influence of both sublimation and photosputtering, as a function of grain size, composition and distance from the star. The effect of erosion on the grain's location is investigated through numerical simulations coupling the grain size to its dynamical evolution. Our model predicts that photodesorption efficiently destroy ice in optically thin discs, even far beyond the sublimation snow line. For the reference case of beta Pictoris, we find that only > 5mm grains can keep their icy component for the age of the system in the 50-150AU region. When taking into account the collisional reprocessing of grains, we show that the water ice survival on grains improves (grains down to ~ 20 um might be partially icy). However, estimates of the amount of gas photosputtering would produce on such a hypothetical population of big icy grains lead to values for the OI column density that strongly exceed observational constraints for beta Pic, thus ruling out the presence of a significant amount of icy grains in this system. Erosion rates and icy grains survival timescales are also given for a set of 11 other debris disc systems. We show that, with the possible exception of M stars, photosputtering cannot be neglected in calculations of icy grain lifetimes.Comment: 12 pages, 9 figures. accepted by A&

Eccentricity Evolution of Extrasolar Multiple Planetary Systems due to the Depletion of Nascent Protostellar Disks

Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But, prior to the disk depletion, self gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapse is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around Upsilon Andromedae and HD168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.Comment: 50 pages including 11 figures, submitted to Ap

The 1.2 Millimeter Image of the beta Pictoris Disk

We present millimeter imaging observations in the 1200 micron continuum of the disk around beta Pictoris. With the 25 arcsec beam, the beta Pic disk is unresolved perpendicularly to the disk plane (< 10 arcsec), but slightly resolved in the northeast-southwest direction (26 arcsec). Peak emission is observed at the stellar position. A secondary maximum is found 1000 AU along the disk plane in the southwest, which does not positionally coincide with a similar feature reported earlier at 850 micron. Arguments are presented which could be seen in support of the reality of these features. The observed submm/mm emission is consistent with thermal emission from dust grains, which are significantly larger than those generally found in the interstellar medium, including mm-size particles, and thus more reminiscent of the dust observed in protostellar disks. Modelling the observed scattered light in the visible and the emission in the submm/mm provides evidence for the particles dominating the scattering in the visible/NIR and those primarily responsible for the thermal emission at longer wavelengths belonging to different populations.Comment: 6 pages, 3 postscript figures, accepted for publication in Astronomy and Astrophysic

Narrow-Angle Astrometry with the Space Interferometry Mission: The Search for Extra-Solar Planets. II. Detection and Characterization of Planetary Systems

(Abridged) The probability of detecting additional companions is essentially unchanged with respect to the single-planet configurations, but after fitting and subtraction of orbits with astrometric signal-to-noise ratio $\alpha/\sigma_d\to 1$ the false detection rates can be enhanced by up to a factor 2; the periodogram approach results in robust multiple-planet detection for systems with periods shorter than the SIM mission length, even at low values of $\alpha/\sigma_d$, while the least squares technique combined with Fourier series expansions is arguably preferable in the long-period regime. The accuracy on multiple-planet orbit reconstruction and mass determination suffers a typical degradation of 30-40% with respect to single-planet solutions; mass and orbital inclination can be measured to better than 10% for periods as short as 0.1 yr, and for $\alpha/\sigma_d$ as low as $\sim 5$, while $\alpha/\sigma_d\simeq 100$ is required in order to measure with similar accuracy systems harboring objects with periods as long as three times the mission duration. For systems with all components producing $\alpha/\sigma_d\simeq 10$ or greater, quasi-coplanarity can be reliably established with uncertainties of a few degrees, for periods in the range $0.1\leq T\leq 15$ yr; in systems where at least one component has $\alpha/\sigma_d\to 1$, coplanarity measurements are compromised, with typical uncertainties on the mutual inclinations of order of $30^\circ-40^\circ$. Our findings are illustrative of the importance of the contribution SIM will make to the fields of formation and evolution of planetary systems.Comment: 61 pages, 14 figures, 5 tables, to appear in the September 2003 Issue of the Publications of the Astronomical Society of the Pacifi

Bimodal Brightness Oscillations in Models of Young Binary Systems

We consider a model for the cyclic activity of young binary stars that accrete matter from the remnants of a protostellar cloud. If the orbit of such a binary system is inclined at a small angle to the line of sight, then the streams of matter and the density waves excited in the circumbinary disk can screen the primary component of the binary from the observer. To study these phenomena by the SPH (smoothed particle hydrodynamics) method, we have computed grids of hydrodynamic models for binary systems based on which we have constructed the light curves as a function of the orbital phase.The main emphasis is on investigating the properties of the brightness oscillations. Therefore, the model parameters were varied within the following ranges: the component mass ratio q = M2 : M1 = 0.2 - 0.5 and the eccentricity e = 0 - 0.7. The parameter that defined the binary viscosity was also varied. We adopted optical grain characteristics typical of circumstellar dust. Our computations have shown that bimodal oscillations are excited in binaries with eccentric orbits, provided that the binary components do not differ too much in mass. In this case, the ratios of the periods and amplitudes of the bimodal oscillations and their shape depend strongly on the inclination of the binary plane and its orientation relative to the observer. Our analysis shows that the computed light curves can be used in interpreting the cyclic activity of UX Ori stars.Comment: 14 pages, 5 figures, 1 tabl

Hydrodynamic Processes in Young Binary Systems as a Source of Cyclic Variations of Circumstellar Extinction

Hydrodynamic models of a young binary system accreting matter from the remnants of a protostellar cloud have been calculated by the SPH method. It is shown that periodic variations in column density in projection onto the primary component take place at low inclinations of the binary plane to the line of sight. They can result in periodic extinction variations. Three periodic components can exist in general case. The first component has a period equal to the orbital one and is attributable to the streams of matter penetrating into the inner regions of the binary. The second component has a period that is a factor of 5-8 longer than the orbital one and is related to the density waves generated in a circumbinary (CB) disk. The third, longest period is attributable to the precession of the inner asymmetric region of CB disk. The relationship between the amplitudes of these cycles depends on the model parameters as well as on the inclination and orientation of the binary in space. We show that at a dust-to-gas ratio of 1:100 and and a mass extinction coefficient of 250 cm$^2$ g$^{-1}$, the amplitude of the brightness variations of the primary component in the V-band can reach $1^m$ at a mass accretion rate onto the binary components of $10^{-8} M_{\odot}$ yr$^{-1}$ and a $10^{\rm o}$ inclination of the binary plane to the line of sight. We discuss possible applications of the model to pre-main-sequence stars.Comment: 13 pages, 6 figures, published in Astronomy Letters (v.33, 2007