Computer simulation of the merger process of a Red Giant with a Brown Dwarf that lead to the white dwarf/brown dwarf binary system containing WD0137-349

Introduction
Purpose of our simulations
Simulations of the evolution and merger process leading to the binary system WD0137-349
The movies
The snapshot image
Credits

Introduction

In a paper published this week ()August 4, 2006) in Nature Maxted et al. report the orbital and stellar parameters of a binary system involving a white dwarf and a brown dwarf based on high-resolution spectroscopic observations. The observations where performed at the European Southern Observatory. Binary systems play an important role in population sysnthesis models. The particular results of Maxted et al. are due to their high accuracy extremely useful to constrain computer simulations of the merger processes that leads to systems like the one involving WD0137-349. Because of the importance of these observations we have immmediately started work on realistic computer simulations for the newly observed system.

Purpose of our simulations

The simulations have two goals. Obviously we want to reproduce the events that lead to the formation of the observed binary system, and obtain the observed final results. This tells us how these systems form. The most important quantitative result of the simulations is the efficiency with which the interaction of the in-spiraling companion (here the brown dwarf) can stir-up the stellar envelope material to the extent that this envelope material is in fact ejected. This ejection efficiency is the second objective of simulations presented here. Although we obtain an ejection efficiency with any simulations we usually cannot judge very well how accurate this determination is. The observational determination of Maxted et al. provide a unique opportunity to validate our complex, integrated computer simulation. If our simulation correctly leads to the observed properties of the system involving WD0137-349 we can extend our simulations to different but similar systems and determine the ejection efficiency with greater confidence. This will greatly improve the accuracy of population synthesis models, that aim, e.g., to determine the progenitor population of Supernova Type Ia, which are of great importance for the chemical evolution of the galaxy and the determination of the cosmological acceleration of the expansion of our Universe.

Simulations of the evolution and merger process leading to the binary system WD0137-349

The observations of Maxted etal determined the mass of the WD to be 0.39 solar masses. Using our stellar evolution simulation code we have followed the evolution of a star with initially one solar mass through the phase of central hydrogen burning. Once all hydrogen in the core is transformed into helium the star switches into the Red Giant configuration in which nuclear energy is generated in shell hydrogen burning. This burning adds helium to the already existing helium core. As the core of helium grows in mass the outer envelope is expanding to increasing dimensions. The helium core will in the end when all the envelope mass is lost emerge as the white dwarf.

The brown dwarf was initially in a wide orbit around the evolving Red Giant. However, as the Red Giant has grown in size its surface has eventually reached the orbit of the brown dwarf. We can determine the exact time of the start of the dynamical merger process because the stellar evolution calculation relates the growing core mass to the growing stellar radius. When the core has reached 0.39Msun the stellar radius is 90 solar radii. We have chosen the stellar structure model at this time as the initial model for the hydrodynamic merger simulation.

This three dimensional simulation was performed using the SNSPH code (Fryer et al. 2006). This parallel, smooth particle hydrodynamics code originally developed to model core-collapse supernovae has been adapted to model a range of astrophysics phenomena (see Fryer et al. 2006 for details).

The SPH simulation is performed in three dimensions. For our stable initial conditions, we adopt the radial pressure and density profile given by the spherically symmetric stellar structure model. Throughout the simulation we assume a simplified equation of state of an ideal gas to calculate the internal energy of the gas. Our simulation consists of 642000 SPH gas particles,where we keep the properties of the central particles representing the helium core and its surrounding gas within one solar radius fixed. The brown dwarf is treated purely as a point mass that starts out on a circular orbit around the surface of the red giant, with an orbital period of about 71days.

The movies

We have created a movie of our simulation, that is specifically intended to reproduce the merging event leading to the formation to the binary system of which WD0137-349 is a member. In order to visualize the merger processes we show the mass density projected to the orbital plane, where each SPH particle is properly projected according to its kernel onto a 512x512 pixel grid. The physical size of the frames is a 300x300 solar radii box centered at the position of the red giant core, the white dwarf to be. The color depicts density, scaled logarithmically between 10^-4 to 10^^-11Msun/Rsun^3. The in-spiraling brown dwarf is shown as a black dot. In the movie each frame corresponds to .25days in real evolution, showing a total of 177days or 2.5 original orbits in evolution. During this short time, the brown dwarf already spirals from the surface down to less than 5 solar radii.

In addition we created two other representations. One shows density - initial density with blue showing negative and red positive density deviations (both scaled logarithmically. Green is about the initial desnity. The last movie shows the time derivative of the density.

The movies can be played using mplayer (Mac OS or Linux), Xine (Linux) or Windows Media Player (Microsoft Windows).

The snapshot image

In addition to the movies there is an image with four panels available. Each panel shows a frame of the density movie at different times:

Upper left (Initial conditions): The brown dwarf is set just below the surface of the red giant on a circular orbit in positive y direction.
Upper right (after 40days). The brown dwarf has completed a little more than half an orbit and started to expell the outermost layers of the hydrogen envelope, but has not spiraled in significantly.
Lower left (after 80days): The brown dwarf has almost completed 1.5 orbits and starts to sink deeper into the red giant. A spiral density structure starts to form in its wake.
Lower right (after 120days): The brown dwarf has spiraled in closer to the center, while speeding up its rotation around the red giants core. One can easily see the spiral sound wave that transports the mass outwards, slowly succeeding in shedding the red giant's envelope.

Credits

The simulation team at LANL comprises Steven Diehl (diehl@lanl.gov), Chris Fryer (clfreyer@lanl.gov), Falk Herwig (fherwig@lanl.gov), and Gabriel Rockefeller. Diehl, Herwig (post-docs) and Rockefeller (graduate student) are working in the Theoretical Division, and Fryer is staff member in Computer and Computational Sciences Division.

The SPH simulations have been carrried out with the SNSPH code (Fryer, Rockefeller, Warren 2006, ApJ, 643, 292). The stellar evolution calculations providing the intial conditions for the hydrodynamic simulations have been carried out with the code EVOL (Herwig 2004, ApJ 605, 425).

This work was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396.

T-6, FHerwig@lanl.gov, tel: +1-505-667-0452, Last update :Thu Jul 27 22:15:50 MDT 2006