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Register a new userGap formation by inclined massive planets in locally isothermal three-dimensional discs
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Added by
F. J. Sanchez-Salcedo
Publication date
2017
fields
Physics
and research's language is
English
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We study gap formation in gaseous protoplanetary discs by a Jupiter mass planet. The planets orbit is circular and inclined relative to the midplane of the disc. We use the impulse approximation to estimate the gravitational tidal torque between the planet and the disc, and infer the gap profile. For low-mass discs, we provide a criterion for gap opening when the orbital inclination is $leq 30^{circ}$. Using the FARGO3D code, we simulate the disc response to an inclined massive planet. The dependence of the depth and width of the gap obtained in the simulations on the inclination of the planet is broadly consistent with the scaling laws derived in the impulse approximation. Although we mainly focus on planets kept on fixed orbits, the formalism permits to infer the temporal evolution of the gap profile in cases where the inclination of the planet changes with time. This study may be useful to understand the migration of massive planets on inclined orbit, because the strength of the interaction with the disc depends on whether a gap is opened or not.
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We study the interaction between massive planets and a gas disc with a mass in the range expected for protoplanetary discs. We use SPH simulations to study the orbital evolution of a massive planet as well as the dynamical response of the disc for planet masses between 1 and $6 rmn{M_J}$ and the full range of initial relative orbital inclinations. Gap formation can occur for planets in inclined orbits. For given planet mass, a threshold relative orbital inclination exists under which a gap forms. At high relative inclinations, the inclination decay rate increases for increasing planet mass and decreasing initial relative inclination. For an initial semi-major axis of 5 AU and relative inclination of $i_0=80^circ,$ the times required for the inclination to decay by $10^circ$ is $sim10^{6} rmn{yr}$ and $sim10^{5} rmn{yr}$ for $1 rmn{M_J}$ and $6 rmn{M_J}$. Planets on inclined orbits warp the disc by an extent that is negligible for $1 rmn{M_J}$ but increases with increasing mass becoming quite significant for a planet of mass $6 rmn{M_J}$. We also find a solid body precession of both the total disc angular momentum vector and the planet orbital momentum vector about the total angular momentum vector. Our results illustrate that the influence of an inclined massive planet on a protoplanetary disc can lead to significant changes of the disc structure and orientation which can in turn affect the orbital evolution of the planet significantly.
Over the last few years instruments such as VLT/SPHERE and Subaru/HiCIAO have been able to take detailed scattered light images of protoplanetary discs. Many of the features observed in these discs are generally suspected to be caused by an embedded planet, and understanding the cause of these features requires detailed theoretical models. In this work we investigate disc-planet interactions using the PLUTO code to run 2D and 3D hydrodynamic simulations of protoplanetary discs with embedded 30 M$_{oplus}$ and 300 M$_{oplus}$ planets on both an inclined ($i = 2.86^{circ}$) and non-inclined orbit, using an $alpha$-viscosity of $4 times 10^{-3}$. We produce synthetic scattered-light images of these discs at emph{H-band} wavelengths using the radiative transfer code RADMC3D. We find that while the surface density evolution in 2D and 3D simulations of inclined and non-inclined planets remain fairly similar, their observational appearance is remarkably different. Most of the features seen in the synthetic emph{H-band} images are connected to density variations of the disc at around 3.3 scale heights above and below the midplane, which emphasizes the need for 3D simulations. Planets on sustained orbital inclinations disrupt the discs upper-atmosphere and produce radically different observable features and intensity profiles, including shadowing effects and intensity variation in the order of 10-20 times the surrounding background. The vertical optical depth to the disc midplane for emph{H-band} wavelengths is $tau approx 20$ in the disc gap created by the high-mass planet. We conclude that direct imaging of planets embedded in the disc remains difficult to observe, even for massive planets in the gap.
We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the discs secular evolution induced by the planet. We find that, when the planet is massive enough and the induced gap is deep enough, the disc inside the planets orbit breaks from the outer disc. The inner and outer discs precess around the systems total angular momentum vector independently at different precession rates, which causes significant disc misalignment. We derive the analytical formulae, which are also verified numerically, for: 1) the relationship between the planet mass and the depth/width of the induced gap, 2) the migration and inclination damping rates for massive inclined planets, and 3) the condition under which the inner and outer discs can break and undergo differential precession. Then, we carry out Monte-Carlo radiative transfer calculations for the simulated broken discs. Both disc shadowing in near-IR images and gas kinematics probed by molecular lines (e.g. from ALMA) can reveal the misaligned inner disc. The relationship between the rotation rate of the disc shadow and the precession rate of the inner disc is also provided. Using our disc breaking condition, we conclude that the disc shadowing due to misaligned discs should be accompanied by deep gaseous gaps (e.g. in Pre/Transitional discs). This scenario naturally explains both the disc shadowing and deep gaps in several systems (e.g. HD 100453, DoAr 44, AA Tau, HD 143006) and these systems should be the prime targets for searching young massive planets ($>M_J$) in discs.
We describe a new mechanism that leads to the destabilisation of non-axisymmetric waves in astrophysical discs with an imposed radial temperature gradient. This might apply, for example, to the outer parts of protoplanetary discs. We use linear density wave theory to show that non-axisymmetric perturbations generally do not conserve their angular momentum in the presence of a forced temperature gradient. This implies an exchange of angular momentum between linear perturbations and the background disc. In particular, when the disturbance is a low-frequency trailing wave and the disc temperature decreases outwards, this interaction is unstable and leads to the growth of the wave. We demonstrate this phenomenon through numerical hydrodynamic simulations of locally isothermal discs in 2D using the FARGO code and in 3D with the ZEUS-MP and PLUTO codes. We consider radially structured discs with a self-gravitating region which remains stable in the absence of a temperature gradient. However, when a temperature gradient is imposed we observe exponential growth of a one-armed spiral mode (azimuthal wavenumber $m=1$) with co-rotation radius outside the bulk of the spiral arm, resulting in a nearly-stationary one-armed spiral pattern. The development of this one-armed spiral does not require the movement of the central star, as found in previous studies. Because destabilisation by a forced temperature gradient does not explicitly require disc self-gravity, we suggest this mechanism may also affect low-frequency one-armed oscillations in non-self-gravitating discs.
We study the three-dimensional evolution of a viscous protoplanetary disc which accretes gas material from a second protoplanetary disc during a close encounter in an embedded star cluster. The aim is to investigate the capability of the mass accretion scenario to generate strongly inclined gaseous discs which could later form misaligned planets. We use smoothed particle hydrodynamics to study mass transfer and disc inclination for passing stars and circumstellar discs with different masses. We explore different orbital configurations to find the parameter space which allows significant disc inclination generation. citet{Thi2011} suggested that significant disc inclination and disc or planetary system shrinkage can generally be produced by the accretion of external gas material with a different angular momentum. We found that this condition can be fullfilled for a large range of gas mass and angular momentum. For all encounters, mass accretion from the secondary disc increases with decreasing mass of the secondary proto-star. Thus, higher disc inclinations can be attained for lower secondary stellar masses. Variations of the secondary discs orientation relative to the orbital plane can alter the disc evolution significantly. The results taken together show that mass accretion can change the three-dimensional disc orientation significantly resulting in strongly inclined discs. In combination with the gravitational interaction between the two star-disc systems, this scenario is relevant for explaining the formation of highly inclined discs which could later form misaligned planets.
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