Galactic Wind Termination Shock Research Articles

Numerical modeling of time dependent Diffusive Shock Acceleration

Motivated by cosmic ray (CR) re-acceleration at a potential Galactic Wind Termination Shock (GWTS), we present a numerical model for time-dependent Diffusive Shock Acceleration (DSA). We use the stochastic differential equation solver (DiffusionSDE) of the cosmic ray propagation framework CRPropa3.2 with two modifications: An importance sampling module is introduced to improve statistics at high energies in order to keep the simulation time short. An adaptive time step is implemented in the DiffusionSDE module. This ensures to efficiently meet constraints on the time and diffusion step, which is crucial to obtain the correct shock spectra. The time evolution of the spectrum at a one-dimensional planar shock is verified against the solution obtained by the grid-based solver VLUGR3 for both energy-independent and energy-dependent diffusion. We show that the injection of pre-accelerated particles can lead to a broken power law spectrum in momentum if the incoming spectrum of CRs is harder than the re-accelerated spectrum. If the injected spectrum is steeper, the shock spectrum dominates at all energies. We finally apply the developed model to the GWTS by considering a spherically symmetric shock, a spiral Galactic magnetic field, and anisotropic diffusion. The time-dependent spectrum at the shock is modeled as a basis for further studies.

Reacceleration of Galactic Cosmic Rays beyond the Knee at the Termination Shock of a Cosmic-Ray-driven Galactic Wind

The origin of cosmic rays (CRs) above the knee in the spectrum is an unsolved problem. We present a wind model in which interstellar gas flows along a nonrotating, expanding flux tube with a changing speed and cross-sectional area. CRs from Galactic sources, such as supernova remnants, which are coupled to the plasma via Alfvén waves, provide the main pressure source for driving this outflow. These CRs are then subject to diffusive shock reacceleration at the Galactic wind termination shock, which is located at a distance ∼200 kpc. Some of the highest-energy reaccelerated particles propagate upstream against the wind and can contribute to the petaelectronvolt to exaelectronvolt range of the spectrum. We analyze the conditions under which efficient reacceleration can occur and find that rigidities ∼10–40 PV can be obtained and that the termination shock may account for between 10% and 50% of the proton spectrum measured in IceCube/IceTop experiment. In our model, the termination shock is unable to fully explain the CR spectrum in the petaelectronvolt to exaelectronvolt range. The highest-energy particles that escape downstream from our termination shock, and similar shocks surrounding most galaxies, can be further accelerated by intergalactic shock fronts.

Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples

ABSTRACT Weakly collisional, magnetized plasmas characterized by anisotropic viscosity and conduction are ubiquitous in galaxies, haloes, and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with CRs using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy (Δp) of the thermal plasma. We find that this Δp dependence introduces a phase shift between the CR-pressure and gas-density fluctuations. This drives a fast-growing acoustic instability: CRs offset the damping of acoustic waves by anisotropic viscosity and give rise to wave growth when the ratio of CR pressure to gas pressure is ≳αβ−1/2, where β is the ratio of thermal to magnetic pressure, and α, typically ≲1, depends on other dimensionless parameters. In high-β environments like the ICM, this condition is satisfied for small CR pressures. We speculate that the instability studied here may contribute to the scattering of high-energy CRs and to the excitation of sound waves in galaxy-halo, group and cluster plasmas, including the long-wavelength X-ray fluctuations in Chandra observations of the Perseus cluster. It may also be important in the vicinity of shocks in dilute plasmas (e.g. cluster virial shocks or galactic wind termination shocks), where the CR pressure is locally enhanced.

The Propagation of Cosmic Rays from the Galactic Wind Termination Shock: Back to the Galaxy?

Abstract Although several theories exist for the origin of cosmic rays (CRs) in the region between the spectral “knee” and “ankle,” this problem is still unsolved. A variety of observations suggest that the transition from Galactic to extragalactic sources occurs in this energy range. In this work, we examine whether a Galactic wind that eventually forms a termination shock far outside the Galactic plane can contribute as a possible source to the observed flux in the region of interest. Previous work by Bustard et al. estimated that particles can be accelerated to energies above the “knee” up to R max = 1016 eV for parameters drawn from a model of a Milky Way wind. A remaining question is whether the accelerated CRs can propagate back into the Galaxy. To answer this crucial question, we simulate the propagation of the CRs using the low-energy extension of the CRPropa framework, based on the solution of the transport equation via stochastic differential equations. The setup includes all relevant processes, including three-dimensional anisotropic spatial diffusion, advection, and corresponding adiabatic cooling. We find that, assuming realistic parameters for the shock evolution, a possible Galactic termination shock can contribute significantly to the energy budget in the “knee” region and above. We estimate the resulting produced neutrino fluxes and find them to be below measurements from IceCube and limits by KM3NeT.

Cosmic Ray Acceleration by a Versatile Family of Galactic Wind Termination Shocks

Abstract There are two distinct breaks in the cosmic ray (CR) spectrum: the so-called “knee” around 3 × 1015 eV and the so-called “ankle” around 1018 eV. Diffusive shock acceleration (DSA) at supernova remnant (SNR) shock fronts is thought to accelerate galactic CRs to energies below the knee, while an extragalactic origin is presumed for CRs with energies beyond the ankle. CRs with energies between 3 × 1015 and 1018 eV, which we dub the “shin,” have an unknown origin. It has been proposed that DSA at galactic wind termination shocks, rather than at SNR shocks, may accelerate CRs to these energies. This paper uses the galactic wind model of Bustard et al. to analyze whether galactic wind termination shocks may accelerate CRs to shin energies within a reasonable acceleration time and whether such CRs can subsequently diffuse back to the Galaxy. We argue for acceleration times on the order of 100 Myr rather than a few billion years, as assumed in some previous works, and we discuss prospects for magnetic field amplification at the shock front. Ultimately, we generously assume that the magnetic field is amplified to equipartition. This formalism allows us to obtain analytic formulae, applicable to any wind model, for CR acceleration. Even with generous assumptions, we find that very high wind velocities are required to set up the necessary conditions for acceleration beyond 1017 eV. We also estimate the luminosities of CRs accelerated by outflow termination shocks, including estimates for the Milky Way wind.

Cosmic-ray energy spectrum and composition up to the ankle: the case for a second Galactic component

We have carried out a detailed study to understand the observed energy spectrum and composition of cosmic rays with energies up to ~10^18 eV. Our study shows that a single Galactic component with subsequent energy cut-offs in the individual spectra of different elements, optimised to explain the observed spectra below ~10^14 eV and the knee in the all-particle spectrum, cannot explain the observed all-particle spectrum above ~2x10^16 eV. We discuss two approaches for a second component of Galactic cosmic rays -- re-acceleration at a Galactic wind termination shock, and supernova explosions of Wolf-Rayet stars, and show that the latter scenario can explain almost all observed features in the all-particle spectrum and the composition up to ~10^18 eV, when combined with a canonical extra-galactic spectrum expected from strong radio galaxies or a source population with similar cosmological evolution. In this two-component Galactic model, the knee at ~ 3x10^15 eV and the second knee at ~10^17 eV in the all-particle spectrum are due to the cut-offs in the first and second components, respectively. We also discuss several variations of the extra-galactic component, from a minimal contribution to scenarios with a significant component below the ankle (at ~4x10^18 eV), and find that extra-galactic contributions in excess of regular source evolution are neither indicated nor in conflict with the existing data. Our main result is that the second Galactic component predicts a composition of Galactic cosmic rays at and above the second knee that largely consists of helium or a mixture of helium and CNO nuclei, with a weak or essentially vanishing iron fraction, in contrast to most common assumptions. This prediction is in agreement with new measurements from LOFAR and the Pierre Auger Observatory which indicate a strong light component and a rather low iron fraction between ~10^17 and 10^18 eV.

The ultimate fate of cosmic rays from galaxies and their role in the intergalactic medium

Abstract The majority of cosmic rays (CRs) generated by star-forming galaxies escape them and enter the intergalactic medium (IGM). Galactic wind termination shocks might also accelerate CRs. I show that the mean pressure of these CRs can reach to within an order of magnitude of the mean Lyman α forest thermal pressure. At z ≳ 1, their pressure may have even been dominant. I also demonstrate that, whichever IGM phase the CRs reside in, they contribute significantly to its pressure if its temperature is ∼104 K, as long as pionic and Coulomb losses are negligible. Where CRs end up depends on the structure and strength of intergalactic magnetic fields. I argue that CRs end up at least 30 kpc from their progenitor galaxies. CRs may self-confine in the IGM to the sound speed, generating ≳ 10− 13 G magnetic fields. These considerations imply the existence and importance of a non-thermal IGM.

The Fermi bubbles as starburst wind termination shocks

Abstract The enhanced star formation in the inner 100 pc of the Galaxy launches a superwind at ∼1600 km s-1 for M82-like parameters. The ram pressure of the wind is very low compared to more powerful starburst winds. I show that halo gas stops the wind a few kpc from the Galactic Centre. I suggest that the termination shock accelerates cosmic rays, and that the resulting inverse Compton γ-rays are visible as the Fermi bubbles. The bubbles are then wind bubbles, which the starburst can inflate within 10 Myr. They can remain in steady state as long as the starburst lasts. The shock may accelerate PeV electrons and EeV protons. The bubbles may be analogues of galactic wind termination shocks in the intergalactic medium. I discuss the advantages and problems of this model. I note that any jets from Sgr A* must burrow through the starburst wind bubble before reaching the halo gas, which could affect the early evolution of such jets.

Cosmic ray reacceleration on the galactic wind termination shock

Reacceleration of cosmic rays produced by galactic sources on the galactic wind termination shock is considered. The problem of the cosmic ray spectrum continuity is investigated. Numeric results are presented and discussed. We found that a smooth spectral transition from the galactic cosmic rays to the cosmic rays reaccelerated at the galactic wind termination shock is difficult to produce, if the maximum energy of accelerated particles is the same throughout the surface of the termination shock. The possible solution of this problem is the non-spherical termination shock with different maximum energies at different places of the shock.

Cosmic ray acceleration by spiral shocks in the galactic wind

Cosmic ray acceleration by shocks related with Slipping Interaction Regions (SIRs) in the Galactic Wind is considered. SIRs are similar to Solar Wind Corotating Interaction Regions. The spiral structure of our Galaxy results in a strong nonuniformity of the Galactic Wind flow and in SIR formation at distances of 50 to 100 kpc. SIRs are not corotating with the gas and magnetic field because the angular velocity of the spiral pattern differs from that of the Galactic rotation. It is shown that the collective reacceleration of the cosmic ray particles with charge $Z\rm e$ in the resulting shock ensemble can explain the observable cosmic ray spectrum beyond the “knee” up to energies of the order of $10^{17}\,Z$ eV. For the reaccelerated particles the Galactic Wind termination shock acts as a reflecting boundary.

Galactic Winds: The Role of Cosmic Rays

The symbiotic nature of the relationship between galactic winds and cosmic rays (CR's) is attracting increasing interest since, on the one hand, galactic wind termination shocks have been invoked to explain the origin of the highest energy CR's (Jokipii and Morfill, 1985) while, on the other hand, it is thought that CR's may be the principal agent responsible for driving winds (Ipavich, 1975). A simple, spherically-symmetric galactic wind model which includes the dynamical effect of spatially diffusing CR's with an outward pressure gradient is presented. A hydrodynamic form of the cosmic ray transport equation is used, and the spatial diffusion coefficient κ is modelled as κ ∞ ρα (ρ the gas density) for some parameter α. The choice of α < 0 yields flow solutions which are subsonic at the source and supersonic at infinity. Such a choice of α corresponds to assuming that the level of Alfvén wave turbulence decreases with increasing distance from the galaxy. Near the galaxy κ is small and the cosmic rays are strongly coupled to the thermal gas, thus supplying additional momentum in the subsonic wind regime. Further from the galaxy, as κ increases, the cosmic rays decouple from the thermal gas and no longer contribute to the dynamics of the flow. Hence far from the galaxy, the Euler equations should be a suitable model. Furthermore, unlike classical wind models, a multiplicity of saddle points, and therefore flow solutions, exists. Finally, we show that α < 0 is most likely to lead to stable, steady-state flows.

On the origin of high-energy cosmic rays

It is suggested that cosmic rays, up to the highest energies observed, originate in the Galaxy and are accelerated in astrophysical shock waves. If there is a galactic wind, in analogy with the solar wind, a hierarchy of shocks ranging from supernova shocks to the galactic wind termination shock is expected. This leads to a consistent model in which most cosmic rays, up to perhaps 10 to the 14th eV energy, are accelerated by supernova shocks, but that particles with energies of 10 to the 15th eV and higher are accelerated at the termination shock of the galactic wind. Intermediate energies may be accerelated by intermediate-scale shocks, and there may be larger scale shocks associated with the Local Group of galaxies.