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Register a new userStandoff Distance of Bow Shocks in Galaxy Clusters as Proxy for Mach Number
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X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre- (post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre- and post-merger stages.
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An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters such as CIZA J2242.8+5301 which has well defined radio relics.
Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of runaway merger shocks, which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster center. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius) affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper. We show examples of such MA-shocks in 1D and 3D simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a flower-like morphology. In 3D, MA-shocks occupy space between the dense accreting filaments. (2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius.
We discuss a new technique to constrain models for the origin of radio relics in galaxy clusters using the correlation between the shock Mach number and the radio power of relics. This analysis is carried out using a sample of relics with information on both the Mach numbers derived from X-ray observation, $mathcal{M}_X$, and using spectral information from radio observations of the peak and the average values of the spectral index along the relic, $mathcal{M}_R$. We find that there is a lack of correlation between $mathcal{M}_X$ and $mathcal{M}_R$; this result is an indication that the spectral index of the relic is likely not due to the acceleration of particles operated by the shock but it is related to the properties of a fossil electrons population. We also find that the available data on the correlation between the radio power $P_{1.4}$ and Mach numbers ($mathcal{M}_R$ and $mathcal{M}_X$) in relics indicate that neither the DSA nor the adiabatic compression can simply reproduce the observed $P_{1.4}-mathcal{M}$ correlations. Furthermore, we find that the radio power is not correlated with $mathcal{M}_X$, whereas it is not possible to exclude a correlation with $mathcal{M}_R$. This also indicates that the relic power is mainly determined by the properties of a fossil electron population rather than by the properties of the shock. Our results require either to consider models of shock (re)acceleration that go beyond the proposed scenarios of DSA and adiabatic compression at shocks, or to reconsider the origin of radio relics in terms of other physical scenarios.
Expanding nebulae are produced by mass loss from stars, especially during late stages of evolution. Multi-dimensional simulation of these nebulae requires high resolution near the star and permits resolution that decreases with distance from the star, ideally with adaptive timesteps. We report the implementation and testing of static mesh-refinement in the radiation-magnetohydrodynamics code PION, and document its performance for 2D and 3D calculations. The bow shock produced by a hot, magnetized, slowly rotating star as it moves through the magnetized ISM is simulated in 3D, highlighting differences compared with 2D calculations. Latitude-dependent, time-varying magnetized winds are modelled and compared with simulations of ring nebulae around blue supergiants from the literature. A 3D simulation of the expansion of a fast wind from a Wolf-Rayet star into the slow wind from a previous red supergiant phase of evolution is presented, with results compared with results in the literature and analytic theory. Finally the wind-wind collision from a binary star system is modelled with 3D MHD, and the results compared with previous 2D hydrodynamic calculations. A python library is provided for reading and plotting simulation snapshots, and the generation of synthetic infrared emission maps using torus is also demonstrated. It is shown that state-of-the-art 3D MHD simulations of wind-driven nebulae can be performed using PION with reasonable computational resources. The source code and user documentation is made available for the community under a BSD3 licence.
Stellar bow shocks are observed in a variety of interstellar environments and are shaped by the conditions of gas in the interstellar medium (ISM). In situ measurements of turbulent density fluctuations near stellar bow shocks are only achievable with a few observational probes, including H$alpha$ emitting bow shocks and the Voyager Interstellar Mission (VIM). In this paper, we examine density variations around the Guitar Nebula, an H$alpha$ bow shock associated with PSR B2224$+$65, in tandem with density variations probed by VIM near the boundary of the solar wind and ISM. High-resolution Hubble Space Telescope observations of the Guitar Nebula taken between 1994 and 2006 trace density variations over scales from 100s to 1000s of au, while VIM density measurements made with the Voyager 1 Plasma Wave System constrain variations from 1000s of meters to 10s of au. The power spectrum of density fluctuations constrains the amplitude of the turbulence wavenumber spectrum near the Guitar Nebula to ${rm log}_{10}C_{rm n}^2 = -0.8pm0.2$ m$^{-20/3}$ and for the very local ISM probed by Voyager ${rm log}_{10}C_{rm n}^2 = -1.57pm0.02$ m$^{-20/3}$. Spectral amplitudes obtained from multi-epoch observations of four other H$alpha$ bow shocks also show significant enhancements in $C_{rm n}^2$ from values that are considered typical for the diffuse, warm ionized medium, suggesting that density fluctuations near these bow shocks may be amplified by shock interactions with the surrounding medium, or by selection effects that favor H$alpha$ emission from bow shocks embedded in denser media.
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