Canadian Institute for Theoretical Astrophysics

Toronto, Canada

Canadian Institute for Theoretical Astrophysics

Toronto, Canada

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News Article | May 16, 2017
Site: physicsworld.com

A system of seven rocky exoplanets – recently found to be orbiting the same star – avoid colliding with each because their orbits are highly synchronized, according to computer simulations done by astrophysicists in Canada. The TRAPPIST-1 system, which astronomers announced in February that they had discovered, is the largest known system of Earth-like exoplanets. Three of the planets appear to be in the habitable zone of the star, which means that they could harbour liquid water and possibly even life. Since its discovery, however, astronomers have puzzled over how TRAPPIST-1 remains stable. "If you simulate the system, the planets start crashing into one another in less than a million years," says Dan Tamayo, who works at the University of Toronto's Centre for Planetary Science. One possibility is that astronomers have been incredibly lucky to see the system before it falls apart – but Tamayo was convinced that there must be a reason why TRAPPIST-1 is stable. He therefore joined forces with Matt Russo, Andrew Santaguida and others at Toronto, who began by looking at the sequence of the ratios of the orbital periods of adjacent exoplanets in the system. Astronomers know that this sequence is a "resonant chain", which means that all of the orbits are synchronized with each other. The exoplanets therefore undergo a highly choreographed and repetitive dance as they travel around the star – and never collide with each other. "Most planetary systems are like bands of amateur musicians playing their parts at different speeds," says Russo. "TRAPPIST-1 is different. It's a super-group with all seven members synchronizing their parts in nearly perfect time." The problem, however, is that for such a resonant chain to remain stable for a very long time, the seven orbits must be perfectly aligned. And because astronomers cannot currently measure this alignment to high precision, computer simulations that incorporate this uncertainty suggested that TRAPPIST-1 is unstable. Tamayo and colleagues have taken a different approach by looking at how the system formed from a disc of gas and dust and evolved towards its current configuration. Using a supercomputing cluster at the Canadian Institute for Theoretical Astrophysics, the team did a number of simulations that traced the formation and evolution of TRAPPIST-1. In most cases, the system that formed was found to remain stable over a period of 50 million years, which is the longest period of time they were able to simulate. The team believes that the exoplanets settled naturally into the stable resonant condition during the formation process. "This means that early on, each planet's orbit was tuned to make it harmonious with its neighbours, in the same way that instruments are tuned by a band before it begins to play," says Russo. The simulations are described in The Astrophysical Journal Letters.


Hansen B.M.S.,University of California at Los Angeles | Murray N.,Canadian Institute for Theoretical Astrophysics
Astrophysical Journal | Year: 2012

We demonstrate that the observed distribution of "hot Neptune"/"super-Earth" systems is well reproduced by a model in which planet assembly occurs in situ, with no significant migration post-assembly. This is achieved only if the amount of mass in rocky material is 50-100 M ⊕ interior to 1AU. Such a reservoir of material implies that significant radial migration of solid material takes place, and that it occurs before the stage of final planet assembly. The model not only reproduces the general distribution of mass versus period but also the detailed statistics of multiple planet systems in the sample. We furthermore demonstrate that cores of this size are also likely to meet the criterion to gravitationally capture gas from the nebula, although accretion is rapidly limited by the opening of gaps in the gas disk. If the mass growth is limited by this tidal truncation, then the scenario sketched here naturally produces Neptune-mass objects with substantial components of both rock and gas, as is observed. The quantitative expectations of this scenario are that most planets in the "hot Neptune/super-Earth" class inhabit multiple-planet systems, with characteristic orbital spacings. The model also provides a natural division into gas-rich (hot Neptune) and gas-poor (super-Earth) classes at fixed period. The dividing mass ranges from 3 M ⊕ at 10day orbital periods to 10 M ⊕ at 100day orbital periods. For orbital periods <10days, the division is less clear because a gas atmosphere may be significantly eroded by stellar radiation. © 2012. The American Astronomical Society. All rights reserved..


Owen J.E.,Canadian Institute for Theoretical Astrophysics | Wu Y.,University of Toronto
Astrophysical Journal | Year: 2013

Inspired by the Kepler mission's planet discoveries, we consider the thermal contraction of planets close to their parent star, under the influence of evaporation. The mass-loss rates are based on hydrodynamic models of evaporation that include both X-ray and EUV irradiation. We find that only low mass planets with hydrogen envelopes are significantly affected by evaporation, with evaporation being able to remove massive hydrogen envelopes inward of ∼0.1 AU for Neptune-mass objects, while evaporation is negligible for Jupiter-mass objects. Moreover, most of the evaporation occurs in the first 100 Myr of stars' lives when they are more chromospherically active. We construct a theoretical population of planets with varying core masses, envelope masses, orbital separations, and stellar spectral types, and compare this population with the sizes and densities measured for low-mass planets, both in the Kepler mission and from radial velocity surveys. This exercise leads us to conclude that evaporation is the driving force of evolution for close-in Kepler planets. In fact, some 50% of the Kepler planet candidates may have been significantly eroded. Evaporation explains two striking correlations observed in these objects: a lack of large radius/low density planets close to the stars and a possible bimodal distribution in planet sizes with a deficit of planets around 2 R ⊕. Planets that have experienced high X-ray exposures are generally smaller than this size, and those with lower X-ray exposures are typically larger. A bimodal planet size distribution is naturally predicted by the evaporation model, where, depending on their X-ray exposure, close-in planets can either hold on to hydrogen envelopes ∼0.5%-1% in mass or be stripped entirely. To quantitatively reproduce the observed features, we argue that not only do low-mass Kepler planets need to be made of rocky cores surrounded with hydrogen envelopes, but few of them should have initial masses above 20 M ⊕ and the majority of them should have core masses of a few Earth masses. © 2013. The American Astronomical Society. All rights reserved..


Owen J.E.,Canadian Institute for Theoretical Astrophysics
Astrophysical Journal | Year: 2014

We investigate under what circumstances an embedded planet in a protoplanetary disk may sculpt the dust distribution such that it observationally presents as a "transition" disk. We concern ourselves with "transition" disks that have large holes (≳ 10 AU) and high accretion rates (10-9-10-8 M ⊙ yr -1), particularly, those disks which photoevaporative models struggle to explain. Adopting the observed accretion rates in "transition" disks, we find that the accretion luminosity from the forming planet is significant, and can dominate over the stellar luminosity at the gap edge. This planetary accretion luminosity can apply a significant radiation pressure to small (s ≲ 1 μm) dust particles provided they are suitably decoupled from the gas. Secular evolution calculations that account for the evolution of the gas and dust components in a disk with an embedded, accreting planet, show that only with the addition of the radiation pressure can we explain the full observed characteristics of a "transition" disk (NIR dip in the spectral energy distribution (SED), millimeter cavity, and high accretion rate). At suitably high planet masses (≳ 3-4 MJ ), radiation pressure from the accreting planet is able to hold back the small dust particles, producing a heavily dust-depleted inner disk that is optically thin to infrared radiation. The planet-disk system will present as a "transition" disk with a dip in the SED only when the planet mass and planetary accretion rate are high enough. At other times, it will present as a disk with a primordial SED, but with a cavity in the millimeter, as observed in a handful of protoplanetary disks. © 2014. The American Astronomical Society. All rights reserved.


Palenzuela C.,Canadian Institute for Theoretical Astrophysics
Monthly Notices of the Royal Astronomical Society | Year: 2013

This work presents an implementation of the resistive magnetohydrodynamic equations for a generic algebraic Ohm's law which includes the effects of finite resistivity within full General Relativity. The implementation naturally accounts for magnetic field induced anisotropies and, by adopting a phenomenological current, is able to accurately describe electromagnetic fields in the star and in its magnetosphere. We illustrate the application of this approach in interesting systems with astrophysical implications: the aligned rotator solution and the collapse of a magnetized rotating neutron star to a black hole. © 2013 The Author. Published by Oxford University Press on behalf of the Royal Astronomical Society.


Lin M.-K.,Canadian Institute for Theoretical Astrophysics
Astrophysical Journal | Year: 2012

Numerical calculations of the linear Rossby wave instability (RWI) in global three-dimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and two-dimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggests the RWI is predominantly a 2D instability and that 3D effects, such as vertical motion, can be interpreted as a perturbative consequence of the dominant 2D flow. The vertical flow around corotation, where vortex formation is expected, is examined. In locally isothermal disks, the expected vortex center remains in approximate vertical hydrostatic equilibrium. For polytropic disks, the vortex center has positive vertical velocity, whose magnitude increases with decreasing polytropic index n. © 2012. The American Astronomical Society. All rights reserved.


Lin M.K.,Canadian Institute for Theoretical Astrophysics
Monthly Notices of the Royal Astronomical Society | Year: 2013

The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite differences in the radial direction and spectral collocation in the vertical direction. RWI modes are calculated subject to different upper disc boundary conditions. These include free surface, solid boundaries and variable vertical domain size. Boundary conditions that oppose vertical motion increase the instability growth rate by a few per cent. The magnitude of vertical flow throughout the fluid column can be affected but the overall flow pattern is qualitatively unchanged. Numerical results support the notion that the RWI is intrinsically two dimensional. This implies that inconsistent upper disc boundary conditions, such as vanishing enthalpy perturbation, may inhibit the RWI in 3D.© 2012 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society.


Lin M.-K.,Canadian Institute for Theoretical Astrophysics
Astrophysical Journal | Year: 2013

Astrophysical disks with localized radial structure, such as protoplanetary disks containing dead zones or gaps due to disk-planet interaction, may be subject to the non-axisymmetric Rossby wave instability (RWI) that leads to vortex formation. The linear instability has recently been demonstrated in three-dimensional (3D) barotropic disks. It is the purpose of this study to generalize the 3D linear problem to include an energy equation, thereby accounting for baroclinity in three dimensions. Linear stability calculations are presented for radially structured, vertically stratified, geometrically thin disks with non-uniform entropy distribution in both directions. Polytropic equilibria are considered but adiabatic perturbations assumed. The unperturbed disk has a localized radial density bump, making it susceptible to the RWI. The linearized fluid equations are solved numerically as a partial differential equation eigenvalue problem. Emphasis on the ease of method implementation is given. It is found that when the polytropic index is fixed and adiabatic index increased, non-uniform entropy has negligible effect on the RWI growth rate, but pressure and density perturbation magnitudes near a pressure enhancement increase away from the midplane. The associated meridional flow is also qualitatively changed from homentropic calculations. Meridional vortical motion is identified in the nonhomentropic linear solution, as well as in a nonlinear global hydrodynamic simulation of the RWI in an initially isothermal disk evolved adiabatically. Numerical results suggest that buoyancy forces play an important role in the internal flow of Rossby vortices. © 2013. The American Astronomical Society. All rights reserved.


Lin M.-K.,Canadian Institute for Theoretical Astrophysics
Monthly Notices of the Royal Astronomical Society | Year: 2012

Numerical simulations of global three-dimensional (3D), self-gravitating discs with a gap opened by an embedded planet are presented. The simulations are customized to examine planetary gap stability. Previous results, obtained by Lin & Papaloizou from 2D disc models, are reproduced in 3D. These include (i) the development of vortices associated with local vortensity minima at gap edges and their merging on dynamical time-scales in weakly self-gravitating discs, (ii) the increased number of vortices as the strength of self-gravity is increased and their resisted merging, and (iii) suppression of the vortex instability and development of global spiral arms associated with local vortensity maxima in massive discs. The vertical structure of these disturbances is examined. In terms of the relative density perturbation, the vortex disturbance has weak vertical dependence when self-gravity is neglected. Vortices become more vertically stratified with increasing self-gravity. This effect is seen even when the unperturbed region around the planet's orbital radius has a Toomre stability parameter ∼10. The spiral modes display significant vertical structure at the gap edge, with the mid-plane density enhancement being several times larger than that near the upper disc boundary. However, for both instabilities the vertical Mach number is typically a fewper cent, and on average vertical motions near the gap edge do not dominate horizontal motions. © 2012 The Author Monthly Notices of the Royal Astronomical Society © 2012 RAS.


Chluba J.,Canadian Institute for Theoretical Astrophysics
Monthly Notices of the Royal Astronomical Society | Year: 2011

It is well known that our motion with respect to the cosmic microwave background (CMB) rest frame introduces a large dipolar CMB anisotropy, with an amplitude ∝β=v/c~ 10-3. In addition it should lead to a small breaking of statistical isotropy which becomes most notable at higher multipoles. In principle this could be used to determine our velocity with respect to the CMB rest frame using high angular resolution data from Planck, without directly relying on the amplitude and direction of the CMB dipole, allowing us to constrain cosmological models in which the cosmic dipole arises partly from large-scale isocurvature perturbations instead of being fully motion-induced. Here, we derive simple recursion relations that allow precise computation of the motion-induced coupling between different spherical harmonic coefficients. Although the lowest order approximations for the coupling kernel can be deficient by factors of 2-5 at multipoles l~ 1000-3000, using our results for the aberration kernel we explicitly confirm that for a statistical detection of the aberration effect only first-order terms in β matter. However, the expressions given here are not restricted to β~ 10-3, but can be used at much higher velocities. We demonstrate the robustness of these formulae, illustrating the dependence of the kernel on β, as well as the spherical harmonic indices l and m. © 2011 The Author Monthly Notices of the Royal Astronomical Society © 2011 RAS.

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