Institut für Physik und Astronomie
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Institute
Relativistic pair beams produced in the cosmic voids by TeV gamma rays from blazars are expected to produce a detectable GeV-scale cascade emission missing in the observations. The suppression of this secondary cascade implies either the deflection of the pair beam by intergalactic magnetic fields (IGMFs) or an energy loss of the beam due to the electrostatic beam-plasma instability. IGMF of femto-Gauss strength is sufficient to significantly deflect the pair beams reducing the flux of secondary cascade below the observational limits. A similar flux reduction may result in the absence of the IGMF from the beam energy loss by the instability before the inverse Compton cooling. This dissertation consists of two studies about the instability role in the evolution of blazar-induced beams.
Firstly, we investigated the effect of sub-fG level IGMF on the beam energy loss by the instability. Considering IGMF with correlation lengths smaller than a few kpc, we found that such fields increase the transverse momentum of the pair beam particles, dramatically reducing the linear growth rate of the electrostatic instability and hence the energy-loss rate of the pair beam. Our results show that the IGMF eliminates beam plasma instability as an effective energy-loss agent at a field strength three orders of magnitude below that needed to suppress the secondary cascade emission by magnetic deflection. For intermediate-strength IGMF, we do not know a viable process to explain the observed absence of GeV-scale cascade emission and hence can be excluded.
Secondly, we probed how the beam-plasma instability feeds back on the beam, using a realistic two-dimensional beam distribution. We found that the instability broadens the beam opening angles significantly without any significant energy loss, thus confirming a recent feedback study on a simplified one-dimensional beam distribution. However, narrowing diffusion feedback of the beam particles with Lorentz factors less than 1e6 might become relevant even though initially it is negligible. Finally, when considering the continuous creation of TeV pairs, we found that the beam distribution and the wave spectrum reach a new quasi-steady state, in which the scattering of beam particles persists and the beam opening angle may increase by a factor of hundreds. This new intrinsic scattering of the cascade can result in time delays of around ten years, thus potentially mimicking the IGMF deflection. Understanding the implications on the GeV cascade emission requires accounting for inverse Compton cooling and simulating the beam-plasma system at different points in the IGM.
We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. The helicity shed is found to vary over a broad range from a minor to a major part of the initial helicity, with self helicity being largely or completely shed and mutual helicity, which makes up the larger part of the initial helicity, being shed only partly. Torus-unstable configurations with subcritical twist and without a guide field shed up to about two-thirds of the initial helicity, while a highly twisted, kink-unstable configuration sheds only about one-quarter. The parametric study also yields stable force-free flux rope equilibria up to a total flux-normalized helicity of 0.25, with a ratio of self- to total helicity of 0.32 and a ratio of flux rope to external poloidal flux of 0.94. These results numerically demonstrate the conjecture of helicity shedding by coronal mass ejections and provide a first account of its parametric dependence. Both self- and mutual helicity are shed significantly; this reduces the total initial helicity by a fraction of ∼0.4--0.65 for typical source region parameters.
Context
Line-driven wind instability is expected to cause small-scale wind inhomogeneities, X-ray emission, and wind line profile variability. The instability can already develop around the sonic point if it is initiated close to the photosphere due to stochastic turbulent motions. In such cases, it may leave its imprint on the light curve as a result of wind blanketing.
Aims
We study the photometric signatures of the line-driven wind instability.
Methods
We used line-driven wind instability simulations to determine the wind variability close to the star. We applied two types of boundary perturbations: a sinusoidal one that enables us to study in detail the development of the instability and a stochastic one given by a Langevin process that provides a more realistic boundary perturbation. We estimated the photometric variability from the resulting mass-flux variations. The variability was simulated assuming that the wind consists of a large number of independent conical wind sectors. We compared the simulated light curves with TESS light curves of OB stars that show stochastic variability.
Results
We find two typical signatures of line-driven wind instability in photometric data: a knee in the power spectrum of magnitude fluctuations, which appears due to engulfment of small-scale structure by larger structures, and a negative skewness of the distribution of fluctuations, which is the result of spatial dominance of rarefied regions. These features endure even when combining the light curves from independent wind sectors.
Conclusions
The stochastic photometric variability of OB stars bears certain signatures of the line-driven wind instability. The distribution function of observed photometric data shows negative skewness and the power spectra of a fraction of light curves exhibit a knee. This can be explained as a result of the line-driven wind instability triggered by stochastic base perturbations.
A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit type. The flows are unstable against non-axisymmetric perturbations which form electromotive forces defining a effect and eddy diffusivity. If both degenerated modes with m = +/- 1 are excited with the same power then the global a effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite alpha effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an alpha(2) dynamo. Moreover, an alpha Omega dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm similar or equal to 2000 to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, eta(T) similar or equal to eta. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.
Many solar wind observations at 1 au indicate that the proton (as well as electron) temperature anisotropy is limited. The data distribution in the (A(a), beta(a),(parallel to))-plane have a rhombic-shaped form around beta(a),(parallel to) similar to 1. The boundaries of the temperature anisotropy at beta(a),(parallel to) > 1 can be well explained by the threshold conditions of the mirror (whistler) and oblique proton (electron) firehose instabilities in a bi-Maxwellian plasma, whereas the physical mechanism of the similar restriction at beta(a),(parallel to) < 1 is still under debate. One possible option is Coulomb collisions, which we revisit in the current work. We derive the relaxation rate nu(A)(aa) of the temperature anisotropy in a bi-Maxwellian plasma that we then study analytically and by observed proton data from WIND. We found that nu(A)(pp) increases toward small beta(p),(parallel to) < 1. We matched the data distribution in the (A(p), beta(p),(parallel to))-plane with the constant contour nu(A)(pp) = 2.8 . 10(-6) s(-1), corresponding to the minimum value for collisions to play a role. This contour fits rather well the left boundary of the rhombic-shaped data distribution in the (A(p), beta(p),(parallel to))-plane. Thus, Coulomb collisions are an interesting candidate for explaining the limitations of the temperature anisotropy in the solar wind with small beta(a),(parallel to) < 1 at 1 au.
Electron injection at high Mach number nonrelativistic perpendicular shocks is studied here for parameters that are applicable to young SNR shocks. Using high-resolution large-scale two-dimensional fully kinetic particle-in-cell simulations and tracing individual particles, we in detail analyze the shock-surfing acceleration (SSA) of electrons at the leading edge of the shock foot. The central question is to what degree the process can be captured in 2D3V simulations. We find that the energy gain in SSA always arises from the electrostatic field of a Buneman wave. Electron energization is more efficient in the out-of-plane orientation of the large-scale magnetic field because both the phase speed and the amplitude of the waves are higher than for the in-plane scenario. Also, a larger number of electrons is trapped by the waves compared to the in-plane configuration. We conclude that significant modifications of the simulation parameters are needed to reach the same level of SSA efficiency as in simulations with out-of-plane magnetic field or 3D simulations.
We revisit the effect of nonlinear Landau (NL) damping on the electrostatic instability of blazar-induced pair beams, using a realistic pair-beam distribution. We employ a simplified 2D model in k-space to study the evolution of the electric-field spectrum and to calculate the relaxation time of the beam. We demonstrate that the 2D model is an adequate representation of the 3D physics. We find that nonlinear Landau damping, once it operates efficiently, transports essentially the entire wave energy to small wave numbers where wave driving is weak or absent. The relaxation time also strongly depends on the intergalactic medium temperature, T-IGM, and for T-IGM << 10 eV, and in the absence of any other damping mechanism, the relaxation time of the pair beam is longer than the inverse Compton (IC) scattering time. The weak late-time beam energy losses arise from the accumulation of wave energy at small k, that nonlinearly drains the wave energy at the resonant k of the pair-beam instability. Any other dissipation process operating at small k would reduce that wave-energy drain and hence lead to stronger pair-beam energy losses. As an example, collisions reduce the relaxation time by an order of magnitude, although their rate is very small. Other nonlinear processes, such as the modulation instability, could provide additional damping of the nonresonant waves and dramatically reduce the relaxation time of the pair beam. An accurate description of the spectral evolution of the electrostatic waves is crucial for calculating the relaxation time of the pair beam.
Due to the relatively low rate of particle-particle collisions in the solar wind, kinetic instabilities (e.g., the mirror and firehose) play an important role in regulating large deviations from temperature isotropy. These instabilities operate in the high beta(parallel to) > 1 plasmas, and cannot explain the other limits of the temperature anisotropy reported by observations in the low beta beta(parallel to) < 1 regimes. However, the instability conditions are drastically modified in the presence of streaming (or counterstreaming) components, which are ubiquitous in space plasmas. These effects have been analyzed for the solar wind conditions in a large interval of heliospheric distances, 0.3-2.5 AU. It was found that proton counter-streams are much more crucial for plasma stability than electron ones. Moreover, new instability thresholds can potentially explain all observed bounds on the temperature anisotropy, and also the level of differential streaming in the solar wind.
This work revisits the electrostatic instability for blazar-induced pair beams propagating through the intergalactic medium (IGM) using linear analysis and PIC simulations. We study the impact of the realistic distribution function of pairs resulting from the interaction of high-energy gamma-rays with the extragalactic background light. We present analytical and numerical calculations of the linear growth rate of the instability for the arbitrary orientation of wave vectors. Our results explicitly demonstrate that the finite angular spread of the beam dramatically affects the growth rate of the waves, leading to the fastest growth for wave vectors quasi-parallel to the beam direction and a growth rate at oblique directions that is only a factor of 2-4 smaller compared to the maximum. To study the nonlinear beam relaxation, we performed PIC simulations that take into account a realistic wide-energy distribution of beam particles. The parameters of the simulated beam-plasma system provide an adequate physical picture that can be extrapolated to realistic blazar-induced pairs. In our simulations, the beam looses only 1% of its energy, and we analytically estimate that the beam would lose its total energy over about 100 simulation times. An analytical scaling is then used to extrapolate the parameters of realistic blazar-induced pair beams. We find that they can dissipate their energy slightly faster by the electrostatic instability than through inverse-Compton scattering. The uncertainties arising from, e.g., details of the primary gamma-ray spectrum are too large to make firm statements for individual blazars, and an analysis based on their specific properties is required.
An interesting feature of solar wind fluctuations is the occasional presence of a well-pronounced peak near the spectral knee. These peaks are well investigated in the context of magnetic field fluctuations in the magnetosheath and they are typically related to kinetic plasma instabilities. Recently, similar peaks were observed in the spectrum of ion flux fluctuations of the solar wind and magnetosheath. In this paper, we propose a simple analytical model to describe such peaks in the ion flux spectrum based on the linear theory of plasma fluctuations. We compare our predictions with a sample observation in the solar wind. For the given observation, the peak requires similar to 10 minutes to grow up to the observed level that agrees with the quasi-linear relaxation time. Moreover, our model well reproduces the form of the measured peak in the ion flux spectrum. The observed lifetime of the peak is about 50 minutes, which is relatively close to the nonlinear Landau damping time of 30-40 minutes. Overall, our model proposes a plausible scenario explaining the observation.