Spin-Orbit angle distribution and the origin of (mis)aligned hot Jupiters

For 61 transiting hot Jupiters, the projection of the angle between the orbital plane and the stellar equator (called the spin-orbit angle) has been measured. For about half of them, a significant misalignment is detected, and retrograde planets have been observed. This challenges scenarios of the formation of hot Jupiters. In order to better constrain formation models, we relate the distribution of the real spin-orbit angle $\Psi$ to the projected one $\beta$. Then, a comparison with the observations is relevant. We analyse the geometry of the problem to link analytically the projected angle $\beta$ to the real spin-orbit angle $\Psi$. The distribution of $\Psi$ expected in various models is taken from the literature, or derived with a simplified model and Monte-Carlo simulations in the case of the disk-torquing mechanism. An easy formula to compute the probability density function (PDF) of $\beta$ knowing the PDF of $\Psi$ is provided. All models tested here look compatible with the observed distribution beyond 40 degrees, which is so far poorly constrained by only 18 observations. But only the disk-torquing mechanism can account for the excess of aligned hot Jupiters, provided that the torquing is not always efficient. This is the case if the exciting binaries have semi-major axes as large as 10000 AU. Based on comparison with the set of observations available today, scattering models and the Kozai cycle with tidal friction models can not be solely responsible for the production of all hot Jupiters. Conversely, the presently observed distribution of the spin-orbit angles is compatible with most hot Jupiters having been transported by smooth migration inside a proto-planetary disk, itself possibly torqued by a companion.Comment: 8 pages, 8 figures. In press in Astronomy & Astrophysics. Changes with respect to the first arXiv version: section 2.4 (including fig. 4) has been modified after a mistake was found by Scott Tremaine ; thanks. This second, correct version is the one that will be eventually printed by A&

Migration of Earth-size planets in 3D radiative discs

In this paper, we address the migration of small mass planets in 3D radiative disks. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs parameters for which outward migration has been shown in the range of $[5, 35]$ Earth masses, we find that the transition to inward migration occurs for masses in the range $[3, 5]$ Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modeling of the energy equation.Comment: 17 pages, 20 figures, accepted. MNRAS, 201

The propeller and the frog

"Propellers" in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller, and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of the co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the "frog" resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Bl\'eriot in Saturn's A ring, our theory predicts a libration period of ~4 years, similar to the ~3.7 year period over which Bl\'eriot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.Comment: 11 pages, 2 figures. Accepted to ApJ Letter

Long range outward migration of giant planets, with application to Fomalhaut b

Recent observations of exoplanets by direct imaging, reveal that giant planets orbit at a few dozens to more than a hundred of AU from their central star. The question of the origin of these planets challenges the standard theories of planet formation. We propose a new way of obtaining such far planets, by outward migration of a pair of planets formed in the 10 AU region. Two giant planets in mean motion resonance in a common gap in the protoplanetary disk migrate outwards, if the inner one is significantly more massive than the outer one. Using hydrodynamical simulations, we show that their semi major axes can increase by almost one order of magnitude. In a flared disk, the pair of planets should reach an asymptotic radius. This mechanism could account for the presence of Fomalhaut b ; then, a second, more massive planet, should be orbiting Fomalhaut at about 75 AU.Comment: 6 pages, 4 figures, accepted for publication by ApJ Letter

Circum-planetary discs as bottlenecks for gas accretion onto giant planets

With hundreds of exoplanets detected, it is necessary to revisit giant planets accretion models to explain their mass distribution. In particular, formation of sub-jovian planets remains unclear, given the short timescale for the runaway accretion of massive atmospheres. However, gas needs to pass through a circum-planetary disc. If the latter has a low viscosity (as expected if planets form in "dead zones"), it might act as a bottleneck for gas accretion. We investigate what the minimum accretion rate is for a planet under the limit assumption that the circum-planetary disc is totally inviscid, and the transport of angular momentum occurs solely because of the gravitational perturbations from the star. To estimate the accretion rate, we present a steady-state model of an inviscid circum-planetary disc, with vertical gas inflow and external torque from the star. Hydrodynamical simulations of a circum-planetary disc were conducted in 2D, in a planetocentric frame, with the star as an external perturber in order to measure the torque exerted by the star on the disc. The disc shows a two-armed spiral wave caused by stellar tides, propagating all the way in from the outer edge of the disc towards the planet. The stellar torque is small and corresponds to a doubling time for a Jupiter mass planet of the order of 5 Myrs. Given the limit assumptions, this is clearly a lower bound of the real accretion rate. This result shows that gas accretion onto a giant planet can be regulated by circum-planetary discs. This suggests that the diversity of masses of extra-solar planets may be the result of different viscosities in these discs.Comment: Accepted for publication in Astronomy and Astrophysics. 7 pages, 2 figure

Highly inclined and eccentric massive planets I: Planet-disc interactions

In the Solar System, planets have a small inclination with respect to the equatorial plane of the Sun, but there is evidence that in extrasolar systems the inclination can be very high. This spin-orbit misalignment is unexpected, as planets form in a protoplanetary disc supposedly aligned with the stellar spin. Planet-planet interactions are supposed to lead to a mutual inclination, but the effects of the protoplanetary disc are still unknown. We investigate therefore planet-disc interactions for planets above 1M_Jup. We check the influence of the inclination i, eccentricity e, and mass M_p of the planet. We perform 3D numerical simulations of protoplanetary discs with embedded high-mass planets. We provide damping formulae for i and e as a function of i, e, and M_p that fit the numerical data. For highly inclined massive planets, the gap opening is reduced, and the damping of i occurs on time-scales of the order of 10^-4 deg/yr M_disc/(0.01 M_star) with the damping of e on a smaller time-scale. While the inclination of low planetary masses (<5M_Jup) is always damped, large planetary masses with large i can undergo a Kozai-cycle with the disc. These Kozai-cycles are damped in time. Eccentricity is generally damped, except for very massive planets (M_p = 5M_Jup) where eccentricity can increase for low inclinations. The dynamics tends to a final state: planets end up in midplane and can then, over time, increase their eccentricity as a result of interactions with the disc. The interactions with the disc lead to damping of i and e after a scattering event of high-mass planets. If i is sufficiently reduced, the eccentricity can be pumped up because of interactions with the disc. If the planet is scattered to high inclination, it can undergo a Kozai-cycle with the disc that makes it hard to predict the exact movement of the planet and its orbital parameters at the dispersal of the disc.Comment: accepted for publication in Astronomy and Astrophysic

Long-term & large-scale viscous evolution of dense planetary rings

We investigate the long-term and large-scale viscous evolution of dense planetary rings using a simple 1D numerical code. We use a physically realistic viscosity model derived from N-body simulations (Daisaka et al., 2001), and dependent on the disk's local properties (surface mass density, particle size, distance to the planet). Particularly, we include the effects of gravitational instabilities (wakes) that importantly enhance the disk's viscosity. We show that common estimates of the disk's spreading time-scales with constant viscosity significantly underestimate the rings' lifetime. With a realistic viscosity model, an initially narrow ring undergoes two successive evolutionary stages: (1) a transient rapid spreading when the disk is self-gravitating, with the formation of a density peak inward and an outer region marginally gravitationally stable, and with an emptying time-scale proportional to 1/M_0^2 (where M_0 is the disk's initial mass) (2) an asymptotic regime where the spreading rate continuously slows down as larger parts of the disk become not-self-gravitating due to the decrease of the surface density, until the disk becomes completely not-self-gravitating. At this point its evolution dramatically slows down, with an emptying time-scale proportional to 1/M_0, which significantly increases the disk's lifetime compared to the case with constant viscosity. We show also that the disk's width scales like t^{1/4} with the realistic viscosity model, while it scales like t^{1/2} in the case of constant viscosity, resulting in much larger evolutionary time-scales in our model. We find however that the present shape of Saturn's rings looks like a 100 million-years old disk in our simulations. Concerning Jupiter's, Uranus' and Neptune's rings that are faint today, it is not likely that they were much more massive in the past and lost most of their mass due to viscous spreading alone.Comment: 18 pages, 18 figures, 2 tables. Accepted for publication in Icaru

Efficient shoot regeneration from double cotyledonary node explants of green gram [Vigna radiata L. (Wilczek)]

Not AvailableAn efficient shoot regeneration protocol has been developed yielding up to 27 shoots using double cotyledonary node explants of cultivar ML 267 of green gram [Vigna radiata (L.) Wilczek]. The explants were derived from 3-d-old seedlings germinated on Murashige and Skoog (MS) and Gamborg’s medium (B5) containing (2.0 mg/L) 6-benzyl aminopurine (BAP). They were initially cultured onto MS B5 medium augmented with different concentrations of BAP and very low concentrations of different auxins (NAA, IAA & IBA) and cytokinin (Kn) for shoot bud induction. The explants showing multiple shoot bud initials were transferred to MS B5 media containing reduced concentrations of BAP for shoot proliferation. Among the different auxins and cytokinins tested, presence of BAP+NAA in shoot bud induction and low BAP in shoot proliferation medium gave the best regeneration response. Profuse rooting was achieved in 90% of explants on ½ MS B5 medium devoid of any hormones. Over 90% of the rooted plants grew well and were fertile after transfer to glass house and set seeds normally. Histological examination of 4-d-old explants confirmed direct organogenesis through axillary shoot regeneration. Protocol so developed is currently being utilized for genetic enhancement of green gram using Agrobacterium mediated transformation.Not Availabl