Radiative cooling in numerical astrophysics: the need for adaptive mesh refinement

Energy loss through optically thin radiative cooling plays an important part in the evolution of astrophysical gas dynamics and should therefore be considered a necessary element in any numerical simulation. Although the addition of this physical process to the equations of hydrodynamics is straightforward, it does create numerical challenges that have to be overcome in order to ensure the physical correctness of the simulation. First, the cooling has to be treated (semi-)implicitly, owing to the discrepancies between the cooling timescale and the typical timesteps of the simulation. Secondly, because of its dependence on a tabulated cooling curve, the introduction of radiative cooling creates the necessity for an interpolation scheme. In particular, we will argue that the addition of radiative cooling to a numerical simulation creates the need for extremely high resolution, which can only be fully met through the use of adaptive mesh refinement.Comment: 11 figures. Accepted for publication in Computers & Fluid

Multi-dimensional models of circumstellar shells around evolved massive stars

Massive stars shape their surrounding medium through the force of their stellar winds, which collide with the circumstellar medium. Because the characteristics of these stellar winds vary over the course of the evolution of the star, the circumstellar matter becomes a reflection of the stellar evolution and can be used to determine the characteristics of the progenitor star. In particular, whenever a fast wind phase follows a slow wind phase, the fast wind sweeps up its predecessor in a shell, which is observed as a circumstellar nebula. We make 2-D and 3-D numerical simulations of fast stellar winds sweeping up their slow predecessors to investigate whether numerical models of these shells have to be 3-D, or whether 2-D models are sufficient to reproduce the shells correctly. We focus on those situations where a fast Wolf-Rayet (WR) star wind sweeps up the slower wind emitted by its predecessor, being either a red supergiant or a luminous blue variable. As the fast WR wind expands, it creates a dense shell of swept up material that expands outward, driven by the high pressure of the shocked WR wind. These shells are subject to a fair variety of hydrodynamic-radiative instabilities. If the WR wind is expanding into the wind of a luminous blue variable phase, the instabilities will tend to form a fairly small-scale, regular filamentary lattice with thin filaments connecting knotty features. If the WR wind is sweeping up a red supergiant wind, the instabilities will form larger interconnected structures with less regularity. Our results show that 3-D models, when translated to observed morphologies, give realistic results that can be compared directly to observations. The 3-D structure of the nebula will help to distinguish different progenitor scenarios.Comment: Accepted for publication in A&A. All figures in low resolution. v2: language corrections and addition of DOI numbe

Luminous Blue Variables & Mass Loss near the Eddington Limit

During the course of their evolution, massive stars lose a substantial fraction of their initial mass, both through steady winds and through relatively brief eruptions during their Luminous Blue Variable (LBV) phase. This talk reviews the dynamical driving of this mass loss, contrasting the line-driving of steady winds to the potential role of continuum driving for eruptions during LBV episodes when the star exceeds the Eddington limit. A key theme is to emphasize the inherent limits that self-shadowing places on line-driven mass loss rates, whereas continuum driving can in principle drive mass up to the "photon-tiring" limit, for which the energy to lift the wind becomes equal to the stellar luminosity. We review how the "porosity" of a highly clumped atmosphere can regulate continuum-driven mass loss, but also discuss recent time-dependent simulations of how base mass flux that exceeds the tiring limit can lead to flow stagnation and a complex, time-dependent combination of inflow and outflow regions. A general result is thus that porosity-mediated continuum driving in super-Eddington phases can explain the large, near tiring-limit mass loss inferred for LBV giant eruptions.Comment: Conference proceedings, Massive Stars as Cosmic Engines, IAU Symp 250, ed. F. Bresolin, P. A. Crowther, & J. Puls (Cambridge Univ. Press

Can the magnetic field in the Orion arm inhibit the growth of instabilities in the bow shock of Betelgeuse?

Many evolved stars travel through space at supersonic velocities, which leads to the formation of bow shocks ahead of the star where the stellar wind collides with the interstellar medium (ISM). Herschel observations of the bow shock of $\alpha$-Orionis show that the shock is almost free of instabilities, despite being, at least in theory, subject to both Kelvin-Helmholtz and Rayleigh-Taylor instabilities. A possible explanation for the lack of instabilities lies in the presence of an interstellar magnetic field. We wish to investigate whether the magnetic field of the interstellar medium (ISM) in the Orion arm can inhibit the growth of instabilities in the bow shock of $\alpha$-Orionis. We used the code MPI-AMRVAC to make magneto-hydrodynamic simulations of a circumstellar bow shock, using the wind parameters derived for $\alpha$-Orionis and interstellar magnetic field strengths of $B\,=\,1.4,\, 3.0$, and $5.0\, \mu$G, which fall within the boundaries of the observed magnetic field strength in the Orion arm of the Milky Way. Our results show that even a relatively weak magnetic field in the interstellar medium can suppress the growth of Rayleigh-Taylor and Kelvin-Helmholtz instabilities, which occur along the contact discontinuity between the shocked wind and the shocked ISM. The presence of even a weak magnetic field in the ISM effectively inhibits the growth of instabilities in the bow shock. This may explain the absence of such instabilities in the Herschel observations of $\alpha$-Orionis.Comment: 5 pages, including 7 figures. The published version will include 4 animations. Accepted for publication in A&

Shape and evolution of wind-blown bubbles of massive stars: on the effect of the interstellar magnetic field

The winds of massive stars create large (>10 pc) bubbles around their progenitors. As these bubbles expand they encounter the interstellar coherent magnetic field which, depending on its strength, can influence the shape of the bubble. We wish to investigate if, and how much, the interstellar magnetic field can contribute to the shape of an expanding circumstellar bubble around a massive star. We use the MPI-AMRVAC code to make magneto-hydrodynamical simulations of bubbles, using a single star model, combined with several different field strengths: B = 5, 10, and 20 muG for the interstellar magnetic field. This covers the typical field strengths of the interstellar magnetic fields found in the galactic disk and bulge. Furthermore, we present two simulations that include both a 5 muG interstellar magnetic field and a 10,000 K interstellar medium and two different ISM densities to demonstrate how the magnetic field can combine with other external factors to influence the morphology of the circumstellar bubbles. Our results show that low magnetic fields, as found in the galactic disk, inhibit the growth of the circumstellar bubbles in the direction perpendicular to the field. As a result, the bubbles become ovoid, rather than spherical. Strong interstellar fields, such as observed for the galactic bulge, can completely stop the expansion of the bubble in the direction perpendicular to the field, leading to the formation of a tube-like bubble. When combined with a warm, high-density ISM the bubble is greatly reduced in size, causing a dramatic change in the evolution of temporary features inside the bubble. The magnetic field of the interstellar medium can affect the shape of circumstellar bubbles. This effect may have consequences for the shape and evolution of circumstellar nebulae and supernova remnants, which are formed within the main wind-blown bubble.Comment: Proposed for acceptance for publication in Astronomy & Astrophysics. The published version will contain animations of each simulatio

Constraints on gamma-ray burst and supernova progenitors through circumstellar absorption lines

Long gamma-ray bursts are thought to be caused by a subset of exploding Wolf-Rayet stars. We argue that the circumstellar absorption lines in early supernova and in gamma-ray burst afterglow spectra may allow us to determine the main properties of the Wolf-Rayet star progenitors which can produce those two events. To demonstrate this, we first simulate the hydrodynamic evolution of the circumstellar medium around a 40 Msun star up to the time of the supernova explosion. Knowledge of density, temperature and radial velocity of the circumstellar matter as function of space and time allows us to compute the column density in the line of sight to the centre of the nebula, as a function of radial velocity, angle, and time. Our column density profiles indicate the possible number, strengths, widths and velocities of absorption line components in supernova and gamma-ray burst afterglow spectra. Our example calculation shows four distinct line features during the Wolf-Rayet stage, at about 0, 50, 150-700 and 2200 km/s, with only those of the lowest and highest velocity present at all times. The 150-700 km/s feature decays rapidly as function of time after the onset of the Wolf-Rayet stage. It consists of a variable number of components, and, especially in its evolved stage, is depending strongly on the particular line of sight. A comparison with absorption lines detected in the afterglow of GRB 021004 suggests that the high velocity absorption component in GRB 021004 may be attributed to the free streaming Wolf-Rayet wind, which is consistent with the steep density drop indicated by the afterglow light curve. The presence of the intermediate velocity components implies that the duration of the Wolf-Rayet phase of the progenitor of GRB 021004 was much smaller than the average Wolf-Rayet life time.Comment: 13 pages, 13 figures, accepted by Astronomy & Astrophysics The newest version contains the changes requested by the A&A style edito

Computing the dust distribution in the bowshock of a fast moving, evolved star

We study the hydrodynamical behavior occurring in the turbulent interaction zone of a fast moving red supergiant star, where the circumstellar and interstellar material collide. In this wind-interstellar medium collision, the familiar bow shock, contact discontinuity, and wind termination shock morphology forms, with localized instability development. Our model includes a detailed treatment of dust grains in the stellar wind, and takes into account the drag forces between dust and gas. The dust is treated as pressureless gas components binned per grainsize, for which we use ten representative grainsize bins. Our simulations allow to deduce how dust grains of varying sizes become distributed throughout the circumstellar medium. We show that smaller dust grains (radius <0.045 micro-meters) tend to be strongly bound to the gas and therefore follow the gas density distribution closely, with intricate finestructure due to essentially hydrodynamical instabilities at the wind-related contact discontinuity. Larger grains which are more resistant to drag forces are shown to have their own unique dust distribution, with progressive deviations from the gas morphology. Specifically, small dust grains stay entirely within the zone bound by shocked wind material. The large grains are capable of leaving the shocked wind layer, and can penetrate into the shocked or even unshocked interstellar medium. Depending on how the number of dust grains varies with grainsize, this should leave a clear imprint in infrared observations of bowshocks of red supergiants and other evolved stars.Comment: Accepted for publication in ApJL, 4 figure

Using numerical models of bow shocks to investigate the circumstellar medium of massive stars

Many massive stars travel through the interstellar medium at supersonic speeds. As a result they form bow shocks at the interface between the stellar wind. We use numerical hydrodynamics to reproduce such bow shocks numerically, creating models that can be compared to observations. In this paper we discuss the influence of two physical phenomena, interstellar magnetic fields and the presence of interstellar dust grains on the observable shape of the bow shocks of massive stars. We find that the interstellar magnetic field, though too weak to restrict the general shape of the bow shock, reduces the size of the instabilities that would otherwise be observed in the bow shock of a red supergiant. The interstellar dust grains, due to their inertia can penetrate deep into the bow shock structure of a main sequence O-supergiant, crossing over from the ISM into the stellar wind. Therefore, the dust distribution may not always reflect the morphology of the gas. This is an important consideration for infrared observations, which are dominated by dust emission. Our models clearly show, that the bow shocks of massive stars are useful diagnostic tools that can used to investigate the properties of both the stellar wind as well as the interstellar medium.Comment: 7 pages, 4 figures, to be published in the Journal of Physics: Conference Series (JPCS) as part of the proceedings of the 13th Annual International Astrophysics Conferenc

3-D simulations of shells around massive stars

As massive stars evolve, their winds change. This causes a series of hydrodynamical interactions in the surrounding medium. Whenever a fast wind follows a slow wind phase, the fast wind sweeps up the slow wind in a shell, which can be observed as a circumstellar nebula. One of the most striking examples of such an interaction is when a massive star changes from a red supergiant into a Wolf-Rayet star. Nebulae resulting from such a transition have been observed around many Wolf-Rayet stars and show detailed, complicated structures owing to local instabilities in the swept-up shells. Shells also form in the case of massive binary stars, where the winds of two stars collide with one another. Along the collision front gas piles up, forming a shell that rotates along with the orbital motion of the binary stars. In this case the shell follows the surface along which the ram pressure of the two colliding winds is in balance. Using the MPI-AMRVAC hydrodynamics code we have made multi-dimensional simulations of these interactions in order to model the formation and evolution of these circumstellar nebulae and explore whether full 3D simulations are necessary to obtain accurate models of such nebulae.Comment: 5 Pages, 4 figures, Proceedings of the 39th Liege Astrophysical Colloquium, held in Liege 12-16 July 201

Pinwheels in the sky, with dust: 3D modeling of the Wolf-Rayet 98a environment

The Wolf-Rayet 98a (WR 98a) system is a prime target for interferometric surveys, since its identification as a "rotating pinwheel nebulae", where infrared images display a spiral dust lane revolving with a 1.4 year periodicity. WR 98a hosts a WC9+OB star, and the presence of dust is puzzling given the extreme luminosities of Wolf-Rayet stars. We present 3D hydrodynamic models for WR 98a, where dust creation and redistribution are self-consistently incorporated. Our grid-adaptive simulations resolve details in the wind collision region at scales below one percent of the orbital separation (~4 AU), while simulating up to 1300 AU. We cover several orbital periods under conditions where the gas component alone behaves adiabatic, or is subject to effective radiative cooling. In the adiabatic case, mixing between stellar winds is effective in a well-defined spiral pattern, where optimal conditions for dust creation are met. When radiative cooling is incorporated, the interaction gets dominated by thermal instabilities along the wind collision region, and dust concentrates in clumps and filaments in a volume-filling fashion, so WR 98a must obey close to adiabatic evolutions to demonstrate the rotating pinwheel structure. We mimic Keck, ALMA or future E-ELT observations and confront photometric long-term monitoring. We predict an asymmetry in the dust distribution between leading and trailing edge of the spiral, show that ALMA and E-ELT would be able to detect fine-structure in the spiral indicative of Kelvin-Helmholtz development, and confirm the variation in photometry due to the orientation. Historic Keck images are reproduced, but their resolution is insufficient to detect the details we predict.Comment: Accepted for publication in mnra