Orderly disorder: Simulations of planet-disk dynamics with AREPO

  • Title: Planet-disc interaction on a freely moving mesh.
  • Authors: D. J. Munoz, K. Kratter, V. Springel, L. Hernquist.
  • First Author’s Institution: Harvard Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138.
  • Paper status: Submitted to MNRAS.

Trace nature by (virtually) building it yourself!

Since the advent of computer simulations as a major tool in theoretical astronomy, the methods used have been perpetually refined. The use of ever increasing computer power helps us to achieve higher and higher resolution and perform simulations of increasingly realistic scenarios. Read this astrobite if you want to know more about supercomputers and computational challenges or read here about a recent, ambitious large scale simulation of cosmological structures. Computational models in general help astronomers to tackle problems which cannot be understood by observations alone. In astrophysics, only the combined effort of observational and theoretical methods can really bring us to a more thorough understanding of the Universe, since we cannot experimentally interact with our objects of investigation.

Fig. 1: Zoom-in onto the planet and its associated wake. The geometry and size of the fluid patches is adapted to the higher density in the region of the ‘planet’. This is a major advantage of the Voronoi tessellation. Source: Muñoz et al. (2014), http://arxiv.org/abs/1408.6550.

Fig. 1: Zoom-in onto the planet and its associated wake. The grey lines represent the boundaries in-between single cells, the color indicates column density. The geometry and size of the fluid patches is adapted to the higher density in the region of the ‘planet’. This is a major advantage of the Voronoi tessellation. Source: Munoz et al. (2014).

Predictive computer models of astrophysical phenomena are often based on the principles of fluid dynamics, which is the main driving mechanism of the dynamics of most astrophysical systems. Nearly all of the stuff we’re observing when looking through a telescope was initially formed from gas (i.e., a fluid). Therefore, to understand the underlying dynamics of the formation of astrophysical systems – from galactic structure to the build-up of terrestrial planets – fluid dynamics is a ubiquitous and mighty tool!

Evolution of technology as a boost for scientific advance

The authors of today’s paper use the code AREPO, one of a new and innovative breed of so-called ‘moving mesh’ codes, which was already featured in some great former astrobites with varying astronomical applications: AREPO vs. SPH, Pop III stars, galaxy evolution, structure & galaxy formation and Illustris & open science. The code’s main feature is its hybrid nature, computing the dynamics with grid patches that move with the flow (like SPH). The underlying equations are discretized (i.e., the continuous nature of the fluid flow is broken down into small tractable pieces) and solved on an unstructured grid. In this work AREPO is modified to deal with the dynamics of a young planetary object in a protoplanetary disk. This is the phase when the forming planet is still surrounded by a lot of gas and dust, but already accumulated enough matter to be clearly distinguishable from the surrounding material. To give you an idea of the code’s unique characteristics, Figure 1 shows the imprint of the unstructured mesh on the protoplanetary disk and the embedded planet, the red (and thus dense) region in the image. The geometry of all fluid parcels in the simulation adapts to the specific geometry of the problem (or body, notice that the planet also is entirely built-up of fluid cells) and shrinks the size of parcels if a region is  ‘interesting’. This enables a higher resolution with more precision in, e.g., the region around the planet. This kind of unstructured grid approach is called Voronoi tessellation.

The main goal of this paper is to benchmark the accuracy of AREPO, rather than develop new insights into the physics of planet formation itself. So, how do the authors go about doing this? To begin with they formulate a setup of a 2D protoplanetary disk and put a planet in it. They then evolve the complete system in time, quantify and analyse its behaviour and compare the results with simulations made with a code called FARGO (a well-established grid code for the use with such disks).

Number crunching for the sake of accuracy

The first thing they look at is the gap-opening criterion for different planet masses. This tells scientists the potential of a planet to open up a gap of negligible gas density in its surrounding disk, which, e.g., determines its migration behaviour. Throughout the paper they compare the evolution of a Neptune-sized and Jupiter-sized planet (to be more specific: the mass ratio of the planet to the central star in the simulation is comparable to that for Neptune/Jupiter and our Sun). You can see the effect of planet mass on the disk in Figure 2. The more massive planet alters the structure of  the disk much more than its lightweight counterpart!

Additional tests are done with vortensity (a measure of the potential swirlyness/vorticity, which is important for the initiation and cause of gap-opening) and torque and are partially compared to similar runs with the FARGO code. In most of the tests they find that the outcome from AREPO is comparable to that from FARGO. Minor differences can for example be seen in how well the code treats the pile-up of mass at the inner edges of the opened gap. Also, they argue that the dynamic tessellation introduces errors into the solution of the hydrodynamics equations due the shearing of cells at slightly different radii.

Fig. 2: Clearing of a gap in the gaseous disk by the planet. The planet on the left side is of Neptune mass, on the right hand side the planet’s mass is comparable to Jupiter. As you would guess, the lower-mass planet is having a hard time clearing all the gas from its orbit and thus eventually ends up (after 100 orbits) with a shallower and less pronounced gap. μ stands for planet/star ratio, ν for the amount of viscosity and NR for the number of initial fluid patches. Source: Muñoz et al. (2014), http://arxiv.org/abs/1408.6550.

Fig. 2: Clearing of a gap in the gaseous disk by the planet. The color scale is log density and cooler colors correspond to lower density. The planet on the left side is of Neptune mass, on the right hand side the planet’s mass is comparable to Jupiter. As you would guess, the lower-mass planet is having a hard time clearing all the gas from its orbit and thus eventually ends up (after 100 orbits) with a shallower and less pronounced gap. μ stands for planet/star ratio, ν for the amount of viscosity and NR for the number of initial fluid patches. Source: Munoz et al. (2014).

AREPO = panacea?

To shorten their findings, AREPO seems to behave quite well and be very suitable for further simulations of protoplanetary disks. They argue that the observed differences (which more or less always exist when you compare the results of numerical codes) are only of minor concern and thus more sophisticated studies of such problems are now possible. Finally, like in the other (above mentioned) applications of AREPO, astronomers now have access to an additional tool to model exciting and highly dynamic systems such as young (proto-)planetary systems, which extends the available range of problem approaches. In specific cases, when the scientists need to deal with effects demanding a high range of spatial scales (i.e., global effects which cover the entire disk and additionally small scale effects like local instabilities) the adaptive nature of the fluid parcels might be a huge advantage in comparison with other methods. Since this is much less computationally intensive than to refine the whole system it will enable the authors to study the details of the most important parts of such systems in much greater resolution than ever before. All in all we see another leap in technological advancement, which diversifies the range of theoretical instruments in the area of planet formation and will possibly help us to decipher the mysteries of planet forming environments!

About Tim Lichtenberg

I am a graduate student at ETH Zurich in planetary astrophysics. By combining astro- and geophysical numerical approaches I try to understand the influence of star-forming environments on the formation of terrestrial planets. Occasionally, when I am not at the bus swinging back and forth between the institutes, I enjoy doing sports or become involved in science outreach projects.

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