arXiv subjects

Allard Jan van Marle

Publications and source records attributed to Allard Jan van Marle.

At least 19 recordsLinked to original sources

arXiv2025

Combining PIC and MHD to model particle acceleration in astrophysical shocks

When supersonic plasma flows collide, many physical processes contribute to the morphology of the resulting shock. One of these processes is the acceleration of non-thermal ions, which will, eventually, reach relativistic speeds and become cosmic rays. This process is difficult to simulate in a computer model because it requires both macro-physics (the overall shape of the shock) and micro-physics (the interaction between individual particles and the magnetic field). The combined PIC-MHD method is one of several options to get around this problem. It is based on the assumption that a plasma can be described as a combination of a thermal gas, which can be accurately described as a fluid using grid-based magnetohydrodynamics (MHD) and a small non-thermal component which has to be described as individual particles using particle-in-cell (PIC). By combining aspects of both methods, we reduce the computational costs while maintaining the ability to trace the acceleration of individual particles. We apply this method to a variety of astrophysical shock configurations to investigate if, and how, they can contribute to the cosmic ray spectrum.

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arXiv2024

Diffusive shock acceleration in relativistic, oblique shocks

Cosmic rays are charged particles that are accelerated to relativistic speeds by astrophysical shocks. Numerical models have been successful in confirming the acceleration process for (quasi-)parallel shocks, which have the magnetic field aligned with the direction of the shock motion. However, the process is less clear when it comes to (quasi-)perpendicular shocks, where the field makes a large angle with the shock-normal. For such shocks, the angle between the magnetic field and flow ensures that only highly energetic particles can travel upstream at all, reducing the upstream current. This process is further inhibited for relativistic shocks, since the shock can become superluminal when the required particle velocity exceeds the speed of light, effectively inhibiting any upstream particle flow. In order to determine whether such shocks can accelerate particles, we use the particle-in-cell (PIC) method to determine what fraction of particles gets reflected initially at the shock. We then use this as input for a new simulation that combines the PIC method with grid-based magnetohydrodynamics to follow the acceleration (if any) of the particles over a larger time-period in a two-dimensional grid. We find that quasi-perpendicular, relativistic shocks are capable of accelerating particles through the DSA process, provided that the shock has a sufficiently high Alfvenic Mach number.

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arXiv2024

Kinetic simulations of electron-positron induced streaming instability in the context of gamma-ray halos around pulsars

The possibility of slow diffusion regions as the origin for extended TeV emission halos around some pulsars (such as PSR J0633+1746 and PSR B0656+14) challenges the standard scaling of the electron diffusion coefficient in the interstellar medium. Self-generated turbulence by electron-positron pairs streaming out of the pulsar wind nebula was proposed as a possible mechanism to produce the enhanced turbulence required to explain the morphology and brightness of these TeV halos. We perform fully kinetic 1D3V particle-in-cell simulations of this instability, considering the case where streaming electrons and positrons have the same density. This implies purely resonant instability as the beam does not carry any current. We compare the linear phase of the instability with analytical theory and find very reasonable agreement. The non-linear phase of the instability is also studied, which reveals that the intensity of saturated waves is consistent with a momentum exchange criterion between a decelerating beam and growing magnetic waves. With the adopted parameters, the instability-driven wavemodes cover both the Alfvénic (fluid) and kinetic scales. The spectrum of the produced waves is non-symmetric, with left-handed circular polarisation waves being strongly damped when entering the ion-cyclotron branch, while right-handed waves are suppressed at smaller wavelength when entering the Whistler branch. The low-wavenumber part of the spectrum remains symmetric when in the Alfvénic branch. As a result, positrons behave dynamically differently compared to electrons. We also observed a second harmonic plasma emission in the wave spectrum. An MHD-PIC approach is warranted to probe hotter beams and investigate the Alfvén branch physics. This work confirms that the self-confinement scenario develops essentially according to analytical expectations [...](abridged)

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arXiv2023

Using PIC and PIC-MHD to investigate cosmic ray acceleration in mildly relativistic shocks

Astrophysical shocks create cosmic rays by accelerating charged particles to relativistic speeds. However, the relative contribution of various types of shocks to the cosmic ray spectrum is still the subject of ongoing debate. Numerical studies have shown that in the non-relativistic regime, oblique shocks are capable of accelerating cosmic rays, depending on the Alfvénic Mach number of the shock. We now seek to extend this study into the mildly relativistic regime. In this case, dependence of the ion reflection rate on the shock obliquity is different compared to the nonrelativistic regime. Faster relativistic shocks are perpendicular for the majority of shock obliquity angles therefore their ability to initialize efficient DSA is limited. We define the ion injection rate using fully kinetic PIC simulation where we follow the formation of the shock and determine the fraction of ions that gets involved into formation of the shock precursor in the mildly relativistic regime covering a Lorentz factor range from 1 to 3. Then, with this result, we use a combined PIC-MHD method to model the large-scale evolution of the shock with the ion injection recipe dependent on the local shock obliquity. This methodology accounts for the influence of the self-generated or pre-existing upstream turbulence on the shock obliquity which allows study substantially larger and longer simulations compared to classical hybrid techniques.

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arXiv2022

Diffusive shock acceleration at oblique high Mach number shocks

The current paradigm of cosmic ray (CR) origin states that the most part of galactic CRs is produced by supernova remnants. The interaction of supernova ejecta with the interstellar medium after supernova's explosions results in shocks responsible for CR acceleration via diffusive shock acceleration (DSA). We use particle-in-cell (PIC) simulations and a combined PIC-magnetohydrodynamic (PIC-MHD) technique to investigate whether DSA can occur in oblique high Mach number shocks. Using the PIC method, we follow the formation of the shock and determine the fraction of the particles that gets involved in DSA. Then, with this result, we use PIC-MHD simulations to model the large-scale structure of the plasma and the magnetic field surrounding the shock and find out whether or not the reflected particles can generate the upstream turbulence and trigger DSA. We find that the feasibility of this process in oblique shocks depends strongly on the Alfvenic Mach number, and the DSA process is more likely triggered at high Mach number shocks.

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arXiv2021

Direct Numerical Simulations of Cosmic-ray Acceleration at Dense Circumstellar Medium: Magnetic Field Amplification by Bell Instability and Maximum Energy

Galactic cosmic rays are believed to be accelerated at supernova remnants. However, whether supernova remnants can be Pevatrons is still very unclear. In this work we argue that PeV cosmic rays can be accelerated during the early phase of a supernova blast wave expansion in dense red supergiant winds. We solve in spherical geometry a system combining a diffusive-convection equation which treats cosmic-ray dynamics coupled to magnetohydrodynamics to follow gas dynamics. The fast shock expanding in a dense ionized wind is able to trigger the fast non-resonant streaming instability over day timescales, and energizes cosmic-rays even under the effect of p-p losses. We find that such environments make the blast wave a Pevatron, although the maximum energy depends on various parameters such as the injection rate and mass-loss rate of the winds. Multi-PeV energies can be reached if the progenitor mass loss rates are of the order of $10^{-3}$ Msun yr$^{-1}$. It has been recently invoked that, prior to the explosion, hydrogen rich massive stars can produce enhanced mass loss rates. These enhanced rates would then favor the production of a Pevatron phase in early times after the shock breakout.

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arXiv2020

On the influence of supra-thermal particle acceleration on the morphology of low-Mach, high-$β$ shocks

When two galaxy clusters encounter each other, the interaction results in a collisionless shock that is characterized by a low (1-4) sonic Mach number, and a high Alfv{é}nic Mach number. Our goal is to determine if, and to what extent, such shocks can accelerate particles to sufficient velocities that they can contribute to the cosmic ray spectrum. We combine two different computational methods, magnetohydrodynamics (MHD) and particle-in-cell (PIC) into a single code that allows us to take advantage of the high computational efficiency of MHD while maintaining the ability to model the behaviour of individual non-thermal particles. Using this method, we perform a series of simulations covering the expected parameter space of galaxy cluster collision shocks. Our results show that for shocks with a sonic Mach number below 2.25 no diffusive shock acceleration can take place because of a lack of instabilities in the magnetic field, whereas for shocks with a sonic Mach number $\geq\,3$ the acceleration is efficient and can accelerate particles to relativistic speeds. In the regime between these two extremes, diffusive shock acceleration can occur but is relatively inefficient because of the time- and space-dependent nature of the instabilities. For those shocks that show efficient acceleration, the instabilities in the upstream gas increase to the point where they change the nature of the shock, which, in turn, will influence the particle injection process.

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arXiv2019

Three-dimensional simulations of non-resonant streaming instability and particle acceleration near non-relativistic astrophysical shocks

We use particle-in-magnetohydrodynamics-cells to model particle acceleration and magnetic field amplification in a high Mach, parallel shock in three dimensions and compare the result to 2-D models. This allows us to determine whether 2-D simulations can be relied upon to yield accurate results in terms of particle acceleration, magnetic field amplification and the growth rate of instabilities. Our simulations show that the behaviour of the gas and the evolution of the instabilities are qualitatively similar for both the 2-D and 3-D models, with only minor quantitative differences that relate primarily to the growth speed of the instabilities. The main difference between 2-D and 3-D models can be found in the spectral energy distributions (SEDs) of the non-thermal particles. The 2-D simulations prove to be more efficient, accelerating a larger fraction of the particles and achieving higher velocities. We conclude that, while 2-D models are sufficient to investigate the instabilities in the gas, their results have to be treated with some caution when predicting the expected SED of a given shock.

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arXiv2018

Developing a self-consistent AGB wind model: I. Chemical, thermal, and dynamical coupling

The material lost through stellar winds of Asymptotic Giant Branch (AGB) stars is one of the main contributors to the chemical enrichment of galaxies. The general hypothesis of the mass loss mechanism of AGB winds is a combination of stellar pulsations and radiative pressure on dust grains, yet current models still suffer from limitations. Among others, they assume chemical equilibrium of the gas, which may not be justified due to rapid local dynamical changes in the wind. This is important as it is the chemical composition that regulates the thermal structure of the wind, the creation of dust grains in the wind, and ultimately the mass loss by the wind. Using a self-consistent hydrochemical model, we investigated how non-equilibrium chemistry affects the dynamics of the wind. This paper compares a hydrodynamical and a hydrochemical dust-free wind, with focus on the chemical heating and cooling processes. No sustainable wind arises in a purely hydrodynamical model with physically reasonable pulsations. Moreover, temperatures are too high for dust formation to happen, rendering radiative pressure on grains impossible. A hydrochemical wind is even harder to initiate due to efficient chemical cooling. However, temperatures are sufficiently low in dense regions for dust formation to take place. These regions occur close to the star, which is needed for radiation pressure on dust to sufficiently aid in creating a wind. Extending this model self-consistently with dust formation and evolution, and including radiation pressure, will help to understand the mass loss by AGB winds.

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arXiv2018

Proton Acceleration in Weak Quasi-parallel Intracluster Shocks: Injection and Early Acceleration

Collisionless shocks with low sonic Mach numbers, $M_{\rm s} \lesssim 4$, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the ICM has yet to be established. Performing particle-in-cell simulations, we study the injection of protons into DSA and the early development of a nonthermal particle population in weak shocks in high $β$ ($\approx 100$) plasmas. Reflection of incident protons, self-excitation of plasma waves via CR-driven instabilities, and multiple cycles of shock drift acceleration are essential to the early acceleration of CR protons in supercritical quasi-parallel shocks. We find that only in ICM shocks with $M_{\rm s} \gtrsim M_{\rm s}^*\approx 2.25$, a sufficient fraction of incoming protons are reflected by the overshoot in the shock electric potential and magnetic mirror at locally perpendicular magnetic fields, leading to efficient excitation of magnetic waves via CR streaming instabilities and the injection into the DSA process. Since a significant fraction of ICM shocks have $M_{\rm s} < M_{\rm s}^*$, CR proton acceleration in the ICM might be less efficient than previously expected. This may explain why the diffuse gamma-ray emission from galaxy clusters due to proton-proton collisions has not been detected so far.

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arXiv2017

On magnetic field amplification and particle acceleration near non-relativistic astrophysical shocks: Particles in MHD Cells simulations

We present simulations of magnetized astrophysical shocks taking into account the interplay between the thermal plasma of the shock and supra-thermal particles. Such interaction is depicted by combining a grid-based magneto-hydrodynamics description of the thermal fluid with particle in cell techniques devoted to the dynamics of supra-thermal particles. This approach, which incorporates the use of adaptive mesh refinement features, is potentially a key to simulate astrophysical systems on spatial scales that are beyond the reach of pure particle-in-cell simulations. We consider in this study non-relativistic shocks with various Alfvenic Mach numbers and magnetic field obliquity. We recover all the features of both magnetic field amplification and particle acceleration from previous studies when the magnetic field is parallel to the normal to the shock. In contrast with previous particle-in-cell-hybrid simulations, we find that particle acceleration and magnetic field amplification also occur when the magnetic field is oblique to the normal to the shock but on larger timescales than in the parallel case. We show that in our simulations, the supra-thermal particles are experiencing acceleration thanks to a pre-heating process of the particle similar to a shock drift acceleration leading to the corrugation of the shock front. Such oscillations of the shock front and the magnetic field locally help the particles to enter the upstream region and to initiate a non-resonant streaming instability and finally to induce diffuse particle acceleration.

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arXiv2016

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.

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arXiv2015

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.

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arXiv2015

Simplified models of stellar wind anatomy for interpreting high-resolution data: Analytical approach to embedded spiral geometries

Recent high-resolution observations have shown stellar winds to harbour complexities which strongly deviate from spherical symmetry, generally assumed as standard wind model. One such morphology is the archimedean spiral, generally believed to be formed by binary interactions, which has been directly observed in multiple sources. We seek to investigate the manifestation in the observables of spiral structures embedded in the spherical outflows of cool stars. We aim to provide an intuitive bedrock with which upcoming ALMA data can be compared and interpreted. By means of an extended parameter study, we model rotational CO emission from the stellar outflow of asymptotic giant branch stars. To this end, we develop a simplified analytical parametrised description of a 3D spiral structure. This model is embedded into a spherical wind, and fed into the 3D radiative transfer code LIME, which produces 3D intensity maps throughout velocity space. Subsequently, we investigate the spectral signature of rotational transitions of CO of the models, as well as the spatial aspect of this emission by means of wide-slit PV diagrams. Additionally, the potential for misinterpretation of the 3D data in a 1D context is quantified. Finally, we simulate ALMA observations to explore the impact of interefrometric noise and artifacts on the emission signatures. The spectral signatures of the CO rotational transition v=0 J=3-2 are very efficient at concealing the dual nature of the outflow. Only a select few parameter combinations allow for the spectral lines to disclose the presence of the spiral structure. The inability to disentangle the spiral from the spherical signal can result in an incorrect interpretation in a 1D context. Consequently, erroneous mass loss rates would be calculated...

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arXiv2014

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.

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arXiv2013

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 $α$-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 $α$-Orionis. We used the code MPI-AMRVAC to make magneto-hydrodynamic simulations of a circumstellar bow shock, using the wind parameters derived for $α$-Orionis and interstellar magnetic field strengths of $B\,=\,1.4,\, 3.0$, and $5.0\, μ$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 $α$-Orionis.

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arXiv2012

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.

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arXiv2012

A hydrodynamical model of the circumstellar bubble created by two massive stars

Numerical models of the wind-blown bubble of massive stars usually only account for the wind of a single star. However, since massive stars are usually formed in clusters, it would be more realistic to follow the evolution of a bubble created by several stars. We develope a two-dimensional (2D) model of the circumstellar bubble created by two massive stars, a 40 solar mass star and a 25 solar mass star, and follow its evolution. The stars are separated by approximately 16 pc and surrounded by a cold medium with a density of 20 particles per cubic cm. We use the MPI-AMRVAC hydrodynamics code to solve the conservation equations of hydrodynamics on a 2D cylindrical grid using time-dependent models for the wind parameters of the two stars. At the end of the stellar evolution (4.5 and 7.0 million years for the 40 and 25 solar mass stars, respectively), we simulate the supernova explosion of each star. Each star initially creates its own bubble. However, as the bubbles expand they merge, creating a combined, aspherical bubble. The combined bubble evolves over time, influenced by the stellar winds and supernova explosions. The evolution of a wind-blown bubble created by two stars deviates from that of the bubbles around single stars. In particular, once one of the stars has exploded, the bubble is too large for the wind of the remaining star to maintain and the outer shell starts to disintegrate. The lack of thermal pressure inside the bubble also changes the behavior of circumstellar features close to the remaining star. The supernovae are contained inside the bubble, which reflects part of the energy back into the circumstellar medium.

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