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Register a new userGrowing and moving low-mass planets in non-isothermal disks
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Added by
Sijme-Jan Paardekooper
Publication date
2007
fields
Physics
and research's language is
English
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We study the interaction of a low-mass planet with a protoplanetary disk with a realistic treatment of the energy balance by doing radiation-hydrodynamical simulations. We look at accretion and migration rates and compare them to isothermal studies. We used a three-dimensional version of the hydrodynamical method RODEO, together with radiative transport in the flux-limited diffusion approach. The accretion rate, as well as the torque on the planet, depend critically on the ability of the disk to cool efficiently. For densities appropriate to 5 AU in the solar nebula, the accretion rate drops by more than an order of magnitude compared to isothermal models, while at the same time the torque on the planet is positive, indicating outward migration. It is necessary to lower the density by a factor of 2 to recover inward migration and more than 2 orders of magnitude to recover the usual Type I migration. The torque appears to be proportional to the radial entropy gradient in the unperturbed disk. These findings are critical for the survival of protoplanets, and they should ultimately find their way into population synthesis models.
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Embedded planets disturb the density structure of the ambient disk and gravitational back-reaction will induce possibly a change in the planets orbital elements. The accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. In this paper we study the process of planet-disk interaction for small mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. We study the influence of the planet on the disk through two- and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. With respect to the wake structure and the torque density acting on the planet we demonstrate that the FARGO-algorithm yields correct results, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height of the disk. By comparing the torque densities of 2D and 3D simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.
As planets grow the exchange of angular momentum with the gaseous component of the protoplanetary disc produces a net torque resulting in a variation of the semi-major axis of the planet. For low-mass planets not able to open a gap in the gaseous disc this regime is known as type I migration. Pioneer works studied this mechanism in isothermal discs finding fast inward type I migration rates that were unable to reproduce the observed properties of extrasolar planets. In the last years, several improvements have been made in order to extend the study of type I migration rates to non-isothermal discs. Moreover, it was recently shown that if the planets luminosity due to solid accretion is taken into account, inward migration could be slowed down and even reversed. In this work, we study the planet formation process incorporating, and comparing, updated type I migration rates for non-isothermal discs and the role of planets luminosity over such rates. We find that the latter can have important effects on planetary evolution, producing a significant outward migration for the growing planets.
We investigate the unsaturated horseshoe drag exerted on a low-mass planet by an isothermal gaseous disk. In the globally isothermal case, we use a formal- ism, based on the use of a Bernoulli invariant, that takes into account pressure effects, and that extends the torque estimate to a region wider than the horse- shoe region. We find a result that is strictly identical to the standard horseshoe drag. This shows that the horseshoe drag accounts for the torque of the whole corotation region, and not only of the horseshoe region, thereby deserving to be called corotation torque. We find that evanescent waves launched downstream of the horseshoe U-turns by the perturbations of vortensity exert a feed-back on the upstream region, that render the horseshoe region asymmetric. This asymmetry scales with the vortensity gradient and with the disks aspect ratio. It does not depend on the planetary mass, and it does not have any impact on the horseshoe drag. Since the horseshoe drag has a steep dependence on the width of the horseshoe region, we provide an adequate definition of the width that needs to be used in horseshoe drag estimates. We then consider the case of locally isothermal disks, in which the tempera- ture is constant in time but depends on the distance to the star. The horseshoe drag appears to be different from the case of a globally isothermal disk. The difference, which is due to the driving of vortensity in the vicinity of the planet, is intimately linked to the topology of the flow. We provide a descriptive inter- pretation of these effects, as well as a crude estimate of the dependency of the excess on the temperature gradient.
We present optical and near-infrared adaptive optics (AO) imaging and spectroscopy of 13 ultracool (>M6) companions to late-type stars (K7-M4.5), most of which have recently been identified as candidate members of nearby young moving groups (YMGs; 8-120 Myr) in the literature. The inferred masses of the companions (~10-100 Mjup) are highly sensitive to the ages of the primary stars so we critically examine the kinematic and spectroscopic properties of each system to distinguish bona fide YMG members from old field interlopers. 2MASS J02155892-0929121 C is a new M7 substellar companion (40-60 Mjup) with clear spectroscopic signs of low gravity and hence youth. The primary, possibly a member of the ~40 Myr Tuc-Hor moving group, is visually resolved into three components, making it a young low-mass quadruple system in a compact (<100 AU) configuration. In addition, Li 1 $lambda$6708 absorption in the intermediate-gravity M7.5 companion 2MASS J15594729+4403595 B provides unambiguous evidence that it is young (<200 Myr) and resides below the hydrogen burning limit. Three new close-separation (<1) companions (2MASS J06475229-2523304 B, PYC J11519+0731 B, and GJ 4378 Ab) orbit stars previously reported as candidate YMG members, but instead are likely old (>1 Gyr) tidally-locked spectroscopic binaries without convincing kinematic associations with any known moving group. The high rate of false positives in the form of old active stars with YMG-like kinematics underscores the importance of radial velocity and parallax measurements to validate candidate young stars identified via proper motion and activity selection alone. Finally, we spectroscopically confirm the cool temperature and substellar nature of HD 23514 B, a recently discovered M8 benchmark brown dwarf orbiting the dustiest-known member of the Pleiades. [Abridged]
(abridged version) Identifying the processes that determine the initial mass function of stars (IMF) is a fundamental problem in star formation theory. One of the major uncertainties is the exact chemical state of the star forming gas and its influence on the dynamical evolution. Most simulations of star forming clusters use an isothermal equation of state (EOS). We address these issues and study the effect of a piecewise polytropic EOS on the formation of stellar clusters in turbulent, self-gravitating molecular clouds. We increase the polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we vary from from 4.3x10^4 cm^-3 to 4.3x10^7 cm^-3. The change of thermodynamic state at n_c selects a characteristic mass scale for fragmentation M_ch, which we relate to the peak of the observed IMF. We find a relation M_ch ~ n_c^-0.5, supporting the idea that the distribution of stellar masses largely depends on the thermodynamic state of the star-forming gas.
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