Cosmological Shock Waves Research Articles

Exploring the role of cosmological shock waves in the Dianoga simulations of galaxy clusters

ABSTRACT Cosmological shock waves are ubiquitous to cosmic structure formation and evolution. As a consequence, they play a major role in the energy distribution and thermalization of the intergalactic medium (IGM). We analyze the Mach number distribution in the Dianoga simulations of galaxy clusters performed with the SPH code gadget-3. The simulations include the effects of radiative cooling, star formation, metal enrichment, supernova, and active galactic nuclei feedback. A grid-based shock-finding algorithm is applied in post-processing to the outputs of the simulations. This procedure allows us to explore in detail the distribution of shocked cells and their strengths as a function of cluster mass, redshift, and baryonic physics. We also pay special attention to the connection between shock waves and the cool-core/non-cool-core (CC/NCC) state and the global dynamical status of the simulated clusters. In terms of general shock statistics, we obtain a broad agreement with previous works, with weak (low-Mach number) shocks filling most of the volume and processing most of the total thermal energy flux. As a function of cluster mass, we find that massive clusters seem more efficient in thermalizing the IGM and tend to show larger external accretion shocks than less massive systems. We do not find any relevant difference between CC and NCC clusters. However, we find a mild dependence of the radial distribution of the shock Mach number on the cluster dynamical state, with disturbed systems showing stronger shocks than regular ones throughout the cluster volume.

Collisionless shock heating of heavy ions in SN 1987A

Astrophysical shocks at all scales, from those in the heliosphere up to the cosmological shock waves, are typically "collisionless", because the thickness of their jump region is much shorter than the collisional mean free path. Across these jumps, electrons, protons, and ions are expected to be heated at different temperatures. Supernova remnants (SNRs) are ideal targets to study collisionless processes because of their bright post-shock emission and fast shocks. Although optical observations of Balmer-dominated shocks in young SNRs showed that the post-shock proton temperature is higher than the electron temperature, the actual dependence of the post-shock temperature on the particle mass is still widely debated. We tackle this longstanding issue through the analysis of deep multi-epoch and high-resolution observations of the youngest nearby supernova remnant, SN 1987A, made with the Chandra X-ray telescope. We introduce a novel data analysis method by studying the observed spectra in close comparison with a dedicated full 3-D hydrodynamic simulation. The simulation is able to reproduce self-consistently the whole broadening of the spectral lines of many ions altogether. We can therefore measure the post shock temperature of protons and selected ions through comparison of the model with observations. We have obtained information about the heating processes in collisional shocks by finding that the ion to proton temperature ratio is always significantly higher than one and increases linearly with the ion mass for a wide range of masses and shock parameters.

On the interplay between cosmological shock waves and their environment

Cosmological shock waves are tracers of the thermal history of the structures in the Universe. They play a crucial role in redistributing the energy within the cosmic structures and are also amongst the main ingredients of galaxy and galaxy cluster formation. Understanding this important function requires a proper description of the interplay between shocks and the different environments where they can be found. In this paper, an Adaptive Mesh Refinement (AMR) Eulerian cosmological simulation is analysed by means of a shock-finding algorithm that allows to generate shock wave maps. Based on the population of dark matter halos and on the distribution of density contrast in the simulation, we classify the shocks in five different environments. These range from galaxy clusters to voids. The shock distribution function and the shocks power spectrum are studied for these environments dynamics. We find that shock waves on different environments undergo different formation and evolution processes, showing as well different characteristics. We identify three different phases of formation, evolution and dissipation of these shock waves, and an intricate migration between distinct environments and scales. Shock waves initially form at external, low density regions and are merged and amplified through the collapse of structures. Shock waves and cosmic structures follow a parallel evolution. Later on, shocks start to detach from them and dissipate. We also find that most of the power that shock waves dissipate is found at scales of k sim0.5~mbox{Mpc}^{-1}, with a secondary peak at k sim8~mbox{Mpc}^{-1}. The evolution of the shocks power spectrum confirms that shock waves evolution is coupled and conditioned by their environment.

Shock finding on a moving mesh – I. Shock statistics in non-radiative cosmological simulations

Cosmological shock waves play an important role in hierarchical structure formation by dissipating and thermalizing kinetic energy of gas flows, thereby heating the universe. Furthermore, identifying shocks in hydrodynamical simulations and measuring their Mach number accurately is critical for calculating the production of non-thermal particle components through diffusive shock acceleration. However, shocks are often significantly broadened in numerical simulations, making it challenging to implement an accurate shock finder. We here introduce a refined methodology for detecting shocks in the moving-mesh code AREPO, and show that results for shock statistics can be sensitive to implementation details. We put special emphasis on filtering against spurious shock detections due to tangential discontinuities and contacts. Both of them are omnipresent in cosmological simulations, for example in the form of shear-induced Kelvin-Helmholtz instabilities and cold fronts. As an initial application of our new implementation, we analyse shock statistics in non-radiative cosmological simulations of dark matter and baryons. We find that the bulk of energy dissipation at redshift zero occurs in shocks with Mach numbers around ${\cal M}\approx2.7$. Furthermore, almost $40\%$ of the thermalization is contributed by shocks in the warm hot intergalactic medium (WHIM), whereas $\approx60\%$ occurs in clusters, groups and smaller halos. Compared to previous studies, these findings revise the characterization of the most important shocks towards higher Mach numbers and lower density structures. Our results also suggest that regions with densities above and below $\delta_b=100$ should be roughly equally important for the energetics of cosmic ray acceleration through large-scale structure shocks.

COSMOLOGICAL SHOCK WAVES IN THE LARGE SCALE STRUCTURE OF THE UNIVERSE

Based on the cosmological hydrodynamic simulation, we study the properties of shock waves formed during the formation of the large scale structure (LSS) of the universe, and investigate their contribution to the cosmic ray (CR) fraction in the intergalactic medium (IGM). It is found that while strong accretion shocks prevail at high redshift, weak internal shocks become dominant in the intracluster medium (ICM) as galaxy clusters form and virialize at low redshift, z < 1. The accumulated CR proton energy is likely to be less than 10 % of the thermal energy in the ICM, since weak shocks of M ≲ 3 are most abundant. This is consistent with the upper limit constrained by radio and gamma-ray observations of galaxy clusters. In the warm-hot medium (WHIM) inside filaments, CRs and gas could be almost in energy equipartition, since relatively stronger shocks of 5 ≲ M ≲ 10 are dominant there. We suggest that the non-thermal emissions from the CR electrons and protons accelerated by cosmological shock waves could provide a new way to detect the WHIM of the universe.

Cosmological shock waves: clues to the formation history of haloes

Shock waves developed during the formation and evolution of cosmic structures encode crucial information on the hierarchical formation of the Universe. We analyze an Eulerian AMR hydro + N-body simulation in a $\Lambda$CDM cosmology focused on the study of cosmological shock waves. The combination of a shock-capturing algorithm together with the use of a halo finder allows us to study the morphological structures of the shock patterns, the statistical properties of shocked cells, and the correlations between the cosmological shock waves appearing at different scales and the properties of the haloes harbouring them. The shocks in the simulation can be split into two broad classes: internal weak shocks related with evolutionary events within haloes, and external strong shocks associated with large-scale events. The shock distribution function contains information on the abundances and strength of the different shocks, and it can be fitted by a double power law with a break in the slope around a Mach number of 20. We introduce a generalised scaling relation that correlates the average Mach numbers within the virial radius of haloes and their virial masses. In this plane, haloes occupy different areas according to their early evolutionary histories: those with a quiet evolution have an almost constant Mach number independently of their masses, whereas haloes undergoing significant merger events very early in their evolution show a linear dependence with their masses. At high redshift, the halo distribution in this scaling relation forms a L-like pattern that changes due to the evolution of the haloes. The analysis of the propagation speed and size of the shock waves around haloes could give some hints on the formation time and main features of the haloes. (Abridged)

Cosmic Rays Accelerated at Cosmological Shock Waves

Based on hydrodynamic numerical simulations and diffusive shock acceleration model, we calculated the ratio of cosmic ray (CR) to thermal energy. We found that the CR fraction can be less than ~0.1 in the intracluster medium, while it would be of order unity in the warm-hot intergalactic medium.

Shock waves in the large-scale structure of the Universe

Cosmological shock waves are induced during hierarchical formation of large-scale structure in the universe. Like most astrophysical shocks, they are collisionless, since they form in the tenuous intergalactic medium through electromagnetic viscosities. The gravitational energy released during structure formation is transferred by these shocks to the intergalactic gas as heat, cosmic-rays, turbulence, and magnetic fields. Here we briefly described the properties and consequences of the shock waves in the context of the large-scale structure of the universe.

Cosmological Shock Waves in the Large‐Scale Structure of the Universe: Nongravitational Effects

Cosmological shock waves result from supersonic flow motions induced by hierarchical clustering of nonlinear structures in the universe. These shocks govern the nature of cosmic plasma through thermalization of gas and acceleration of nonthermal, cosmic-ray (CR) particles. We study the statistics and energetics of shocks formed in cosmological simulations of a concordance ΛCDM universe, with a special emphasis on the effects of nongravitational processes such as radiative cooling, photoionization/heating, and galactic superwind feedbacks. Adopting an improved model for gas thermalization and CR acceleration efficiencies based on nonlinear diffusive shock acceleration calculations, we then estimate the gas thermal energy and the CR energy dissipated at shocks through the history of the universe. Since shocks can serve as sites for generation of vorticity, we also examine the vorticity that should have been generated mostly at curved shocks in cosmological simulations. We find that the dynamics and energetics of shocks are governed primarily by the gravity of matter, so other nongravitational processes do not significantly affect the global energy dissipation and vorticity generation at cosmological shocks. Our results reinforce scenarios in which the intracluster medium and warm-hot intergalactic medium contain energetically significant populations of nonthermal particles and turbulent flow motions.

Shock‐heated Gas in the Large‐Scale Structure of the Universe

Cosmological shock waves play a major role in heating baryonic gas in the large scale structure of the universe. In this contribution we study the shock-heated gas in connection with shocks themselves. The distributions of shock speed and temperature of shock-hated gas both should reflect the depth of gravitational potential of associated nonlinear structures, so their morphology. From their distributions we find, in addition to hot gas in and around clusters/groups and warm-hot intergalactic medium (WHIM) with T=10^5-10^7 K mostly in filaments, there is a significant amount of low temperature WHIM with T < 10^5 K distributed mostly as sheet-like structures. Not only the WHIM with T=10^5-10^7 K but also the WHIM with T < 10^5 K make up a significant fraction of gas mass, implying the low temperature WHIM could be important in resolving the missing baryon problem. The shock-heated gas in filaments and sheets are manifested best through emissions and absorptions in soft X-ray and far UV. We confirm that the WHIM with T=10^5-10^7 K makes significant contributions to the soft X-ray background, absorptions of highly ionized species such as OVII and OVIII in AGN spectra, and line emissions from OVII and OVIII ions, as pointed by previous studies. However, the WHIM with T < 10^5 K is the major contributor to absorptions of lower ionized species such as OV and OVI, because these photo-ionized ions are most abundant in sheets of low density and temperature. (abridged)

COSMIC RAYS ACCELERATED AT SHOCK WAVES IN LARGE SCALE STRUCTURE

Shock waves form in the intergalactic space as an ubiquitous consequence of cosmic structure formation. Using N-body/hydrodynamic simulation data of a ACDM universe, we examined the properties of cosmological shock waves including their morphological distribution. Adopting a diffusive shock acceleration model, we then calculated the amount of cosmic ray energy as well as that of gas thermal energy dissipated at the shocks. Finally, the dynamical consequence of those cosmic rays on cluster properties is discussed.

Cosmological Shock Waves and Their Role in the Large‐Scale Structure of the Universe

We study the properties of cosmological shock waves identified in high-resolution, N-body/hydrodynamic simulations of a $\Lambda$CDM universe and their role on thermalization of gas and acceleration of nonthermal, cosmic ray (CR) particles. External shocks form around sheets, filaments and knots of mass distribution when the gas in void regions accretes onto them. Within those nonlinear structures, internal shocks are produced by infall of previously shocked gas to filaments and knots, and during subclump mergers, as well as by chaotic flow motions. Due to the low temperature of the accreting gas, the Mach number of external shocks is high, extending up to $M\sim 100$ or higher. In contrast, internal shocks have mostly low Mach numbers. For all shocks of $M\ge1.5$ the mean distance between shock surfaces over the entire computed volume is $\sim4 h^{-1}$ Mpc at present, or $\sim 1 h^{-1}$ Mpc for internal shocks within nonlinear structures. Identified external shocks are more extensive, with their surface area $\sim2$ times larger than that of identified internal shocks at present. However, especially because of higher preshock densities, but also due to higher shock speeds, internal shocks dissipate more energy. Hence, the internal shocks are mainly responsible for gas thermalization as well as CR acceleration. In fact, internal shocks with $2 \la M \la 4$ contribute $\sim 1/2$ of the total dissipation. Using a nonlinear diffusive shock acceleration model for CR protons, we estimate the ratio of CR energy to gas thermal energy dissipated at cosmological shock waves to be $\sim1/2$ through the history of the universe. Our result supports scenarios in which the intracluster medium contains energetically significant populations of CRs.

Are Simple Real Pole Solutions Physical?

We consider exact solutions generated by the inverse scattering technique, also known as the soliton transformation. In particular, we study the class of simple real pole solutions. For quite some time, those solutions have been considered interesting as models of cosmological shock waves. A coordinate singularity on the wave fronts was removed by a transformation which induces a null fluid with negative energy density on the wave front. This null fluid is usually seen as another coordinate artifact, since there seems to be a general belief that this kind of solution can be seen as the real pole limit of the smooth solution generated with a pair of complex conjugate poles in the transformation. We perform this limit explicitly, and find that the belief is unfounded: two coalescing complex conjugate poles cannot yield a solution with one real pole. Instead, the two complex conjugate poles go to a different limit, what we call a “pole on a pole”. The limiting procedure is not unique; it is sensitive to how quickly some parameters approach zero. We also show that there exists no improved coordinate transformation which would remove the negative energy density. We conclude that negative energy is an intrinsic part of this class of solutions.

Collision of cosmological shock waves produced by explosions and formation of large-scale structures

The formation of large-scale structures is investigated through a two-dimensional numerical hydrodynamical modeling of the collisional process initiated by two cosmological shock waves. The structures generated by the collisions can be classified into four categories: (1) complete merging, (2) merging with a dense ring at the intersection of two shock waves, (3) nonmerging-with-ring, and (4) nonmerging, separated by dense wall. The parameter-dependence of the structures formed was obtained in view of the explosion redshift, the comoving distance between the two explosions, and the explosion energy for the case in which the two explosions are identical. Attention is given to conditions for merging and ring formation; rings are found to result from the cancellation of momenta in the direction perpendicular to the interaction plane at the collision. 48 refs.

Cosmological shock waves in general relativity

The problem of finding spherically symmetric self-similar solutions of Einstein's field equations with a barotropic perfect fluid, which can be joined through a shock wave to some cosmological models, is considered. It is found that such solutions comprise an expanding shell of matter surrounding a horizon with an interior singularity.