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We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh AREPO code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretized using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of AREPO. The interaction of CRs and gyroresonant Alfven waves is described by short time-scale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magnetohydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetized discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magnetohydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.
Photospheric radiation can drive winds from hot, massive stars by direct momentum transfer through scattering in bound-bound transitions of atmospheric ions. The line radiation force should cause a new radiative wave mode. The dispersion relation from perturbations of the line force was analysed so far either in Sobolev approximation or for pure line absorption. The former does not include the line-driven instability, and the latter cannot account for upstream propagating, radiative waves. We consider a non-Sobolev line force that includes scattering in a simplified way, accounting however for the important line-drag effect. We derive a new dispersion relation for radiative waves, and analyse wave propagation using Fourier methods, and by numerical solution of an integro-differential equation. The existence of an upstream propagating, dispersive radiative wave mode is demonstrated.
Cosmic-ray hydrodynamics
(2019)
Star formation in galaxies appears to be self-regulated by energetic feedback processes. Among the most promising agents of feedback are cosmic rays (CRs), the relativistic ion population of interstellar and intergalactic plasmas. In these environments, energetic CRs are virtually collisionless and interact via collective phenomena mediated by kinetic-scale plasma waves and large-scale magnetic fields. The enormous separation of kinetic and global astrophysical scales requires a hydrodynamic description. Here, we develop a new macroscopic theory for CR transport in the self-confinement picture, which includes CR diffusion and streaming. The interaction between CRs and electromagnetic fields of Alfvenic turbulence provides the main source of CR scattering, and causes CRs to stream along the magnetic field with the Alfven velocity if resonant waves are sufficiently energetic. However, numerical simulations struggle to capture this effect with current transport formalisms and adopt regularization schemes to ensure numerical stability. We extent the theory by deriving an equation for the CRmomentum density along the mean magnetic field and include a transport equation for the Alfven-wave energy. We account for energy exchange of CRs and Alfven waves via the gyroresonant instability and include other wave damping mechanisms. Using numerical simulations, we demonstrate that our new theory enables stable, self-regulated CR transport. The theory is coupled to magnetohydrodynamics, conserves the total energy and momentum, and correctly recovers previous macroscopic CR transport formalisms in the steady-state flux limit. Because it is free of tunable parameters, it holds the promise to provide predictable simulations of CR feedback in galaxy formation.
One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Blériot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Blériot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν0 = 340 cm2 s−1, a dispersion velocity in the range of 0.3 cm s−1 < c0 < 1.5 cm s−1, and a fairly high bulk viscosity 7 < ξ0/ν0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.
The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn's rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn's moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn's dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.
Heat conduction has been found a plausible solution to explain discrepancies between expected and measured temperatures in hot bubbles of planetary nebulae (PNe). While the heat conduction process depends on the chemical composition, to date it has been exclusively studied for pure hydrogen plasmas in PNe. A smaller population of PNe show hydrogen-deficient and helium-and carbon-enriched surfaces surrounded by bubbles of the same composition; considerable differences are expected in physical properties of these objects in comparison to the pure hydrogen case. The aim of this study is to explore how a chemistry-dependent formulation of the heat conduction affects physical properties and how it affects the X-ray emission from PN bubbles of hydrogen-deficient stars. We extend the description of heat conduction in our radiation hydrodynamics code to work with any chemical composition. We then compare the bubble-formation process with a representative PN model using both the new and the old descriptions. We also compare differences in the resulting X-ray temperature and luminosity observables of the two descriptions. The improved equations show that the heat conduction in our representative model of a hydrogen-deficient PN is nearly as efficient with the chemistry-dependent description; a lower value on the diffusion coefficient is compensated by a slightly steeper temperature gradient. The bubble becomes somewhat hotter with the improved equations, but differences are otherwise minute. The observable properties of the bubble in terms of the X-ray temperature and luminosity are seemingly unaffected.
X-ray observations of the double-binary OB-star system QZ Car (HD 93206) obtained with the Chandra X-ray Observatory over a period of roughly 2 years are presented. The respective orbits of systems A (O9.7 I+b2 v, P-A = 21 days) and B (O8 III+o9 v, P-B = 6 days) are reasonably well sampled by the observations, allowing the origin of the X-ray emission to be examined in detail. The X-ray spectra can be well fitted by an attenuated three-temperature thermal plasma model, characterized by cool, moderate, and hot plasma components at kT similar or equal to 0.2, 0.7, and 2 keV, respectively, and a circumstellar absorption of similar or equal to 0.2 x 10(22) cm(-2). Although the hot plasma component could be indicating the presence of wind-wind collision shocks in the system, the model fluxes calculated from spectral fits, with an average value of similar or equal to 7x10(-13) erg s(-1) cm(-2), do not show a clear correlation with the orbits of the two constituent binaries. A semi-analytical model of QZ Car reveals that a stable momentum balance may not be established in either system A or B. Yet, despite this, system B is expected to produce an observed X-ray flux well in excess of the observations. If one considers the wind of the O8 III star to be disrupted by mass transfer, the model and observations are in far better agreement, which lends support to the previous suggestion of mass transfer in the O8 III+o9 v binary. We conclude that the X-ray emission from QZ Car can be reasonably well accounted for by a combination of contributions mainly from the single stars and the mutual wind-wind collision between systems A and B.
Two-dimensional modeling of density and thermal structure of dense circumstellar outflowing disks
(2018)
Context. Evolution of massive stars is affected by a significant loss of mass either via (nearly) spherically symmetric stellar winds or by aspherical mass-loss mechanisms, namely the outflowing equatorial disks. However, the scenario that leads to the formation of a disk or rings of gas and dust around massive stars is still under debate. It is also unclear how various forming physical mechanisms of the circumstellar environment affect its shape and density, as well as its kinematic and thermal structure. Results. Our models show the geometric distribution and contribution of viscous heating that begins to dominate in the central part of the disk for mass-loss rates higher than (M) over dot greater than or similar to 10(-10) M-circle dot yr(-1). In the models of dense viscous disks with (M) over dot > 10(-8) M-circle dot yr(-1), the viscosity increases the central temperature up to several tens of thousands of Kelvins, however the temperature rapidly drops with radius and with distance from the disk midplane. The high mass-loss rates and high viscosity lead to instabilities with significant waves or bumps in density and temperature in the very inner disk region. Conclusions. The two-dimensional radial-vertical models of dense outflowing disks including the full Navier-Stokes viscosity terms show very high temperatures that are however limited to only the central disk cores inside the optically thick area, while near the edge of the optically thick region the temperature may be low enough for the existence of neutral hydrogen, for example.
Context. During their evolution massive stars can reach the phase of critical rotation when a further increase in rotational speed is no longer possible. Direct centrifugal ejection from a critically or near-critically rotating surface forms a gaseous equatorial decretion disk. Anomalous viscosity provides the efficient mechanism for transporting the angular momentum outwards. The outer part of the disk can extend up to a very large distance from the parent star.
Aims. We study the evolution of density, radial and azimuthal velocity, and angular momentum loss rate of equatorial decretion disks out to very distant regions. We investigate how the physical characteristics of the disk depend on the distribution of temperature and viscosity.
Methods. We calculated stationary models using the Newton-Raphson method. For time-dependent hydrodynamic modeling we developed the numerical code based on an explicit finite difference scheme on an Eulerian grid including full Navier-Stokes shear viscosity.
Results. The sonic point distance and the maximum angular momentum loss rate strongly depend on the temperature profile and are almost independent of viscosity. The rotational velocity at large radii rapidly drops accordingly to temperature and viscosity distribution. The total amount of disk mass and the disk angular momentum increase with decreasing temperature and viscosity.
Conclusions. The time-dependent one-dimensional models basically confirm the results obtained in the stationary models as well as the assumptions of the analytical approximations. Including full Navier-Stokes viscosity we systematically avoid the rotational velocity sign change at large radii. The unphysical drop of the rotational velocity and angular momentum loss at large radii (present in some models) can be avoided in the models with decreasing temperature and viscosity.
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 small fraction of the radiative flux emitted by hot stars is absorbed by their winds and redistributed towards longer wavelengths. This effect, which leads also to the heating of the stellar photosphere, is termed wind blanketing. For stars with variable winds, the effect of wind blanketing may lead to the photometric variability. We have studied the consequences of line driven wind instability and wind blanketing for the light variability of O stars. We combined the results of wind hydrodynamic simulations and of global wind models to predict the light variability of hot stars due to the wind blanketing and instability. The wind instability causes stochastic light variability with amplitude of the order of tens of millimagnitudes and a typical timescale of the order of hours for spatially coherent wind structure. The amplitude is of the order of millimagnitudes when assuming that the wind consists of large number of independent concentric cones. The variability with such amplitude is observable using present space borne photometers. We show that the simulated light curve is similar to the light curves of O stars obtained using BRITE and CoRoT satellites.
One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. model using a granular flow model to define the shear and bulk viscosities, ν and ζ, and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings. Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps
Since the detection of nonthermal radio emission from the bow shock of the massive runaway star BD +43 degrees 3654, simple models have predicted high-energy emission, at X-rays and gamma-rays, from these Galactic sources. Observational searches for this emission so far give no conclusive evidence but a few candidates at gamma-rays. In this work we aim at developing a more sophisticated model for the nonthermal emission from massive runaway star bow shocks. The main goal is to establish whether these systems are efficient nonthermal emitters, even if they are not strong enough yet to be detected. For modeling the collision between the stellar wind and the interstellar medium we use 2D hydrodynamic simulations. We then adopt the flow profile of the wind and the ambient medium obtained with the simulation as the plasma state for solving the transport of energetic particles injected in the system, as well as the nonthermal emission they produce. For this purpose we solve a 3D (two spatial vertical bar energy) advection-diffusion equation in the test-particle approximation. We find that a massive runaway star with a powerful wind converts 0.16%-0.4% of the power injected in electrons into nonthermal emission, mostly produced by inverse Compton scattering of dust-emitted photons by relativistic electrons, and second by synchrotron radiation. This represents a fraction of similar to 10(-5) to 10(-4) of the wind kinetic power. Given the better sensibility of current instruments at radio wavelengths, these systems are more prone to be detected at radio through the synchrotron emission they produce rather than at gamma energies.