Numerical simulations of stellar winds: polytropic models

We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spherically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arrive at axisymmetric, polytropic, magnetized, rotating models. These represent 2D generalisations of the analytical 1D Weber-Davis wind solution, which we obtain in the process. Axisymmetric wind solutions containing both a `wind' and a `dead' zone are presented. Since we are solving for steady-state solutions, we efficiently exploit fully implicit time stepping. The method allows us to model thermally and/or magneto-centrifugally driven stellar outflows. We particularly emphasize the boundary conditions imposed at the stellar surface. For these axisymmetric, steady-state solutions, we can use the knowledge of the flux functions to verify the physical correctness of the numerical solutions.Comment: 11 pages, 6 figures, accepted for Astron. Astrophys. 342, to appear 199

Unstable magnetohydrodynamical continuous spectrum of accretion disks. A new route to magnetohydrodynamical turbulence in accretion disks

We present a detailed study of localised magnetohydrodynamical (MHD) instabilities occuring in two--dimensional magnetized accretion disks. We model axisymmetric MHD disk tori, and solve the equations governing a two--dimensional magnetized accretion disk equilibrium and linear wave modes about this equilibrium. We show the existence of novel MHD instabilities in these two--dimensional equilibria which do not occur in an accretion disk in the cylindrical limit. The disk equilibria are numerically computed by the FINESSE code. The stability of accretion disks is investigated analytically as well as numerically. We use the PHOENIX code to compute all the waves and instabilities accessible to the computed disk equilibrium. We concentrate on strongly magnetized disks and sub--Keplerian rotation in a large part of the disk. These disk equilibria show that the thermal pressure of the disk can only decrease outwards if there is a strong gravitational potential. Our theoretical stability analysis shows that convective continuum instabilities can only appear if the density contours coincide with the poloidal magnetic flux contours. Our numerical results confirm and complement this theoretical analysis. Furthermore, these results show that the influence of gravity can either be stabilizing or destabilizing on this new kind of MHD instability. In the likely case of a non--constant density, the height of the disk should exceed a threshold before this type of instability can play a role. This localised MHD instability provides an ideal, linear route to MHD turbulence in strongly magnetized accretion disk tori.Comment: 20 pages, 10 figures, accepted for publication in Astronomy & Astrophysic

Toward detailed prominence seismology - II. Charting the continuous magnetohydrodynamic spectrum

Starting from accurate MHD flux rope equilibria containing prominence condensations, we initiate a systematic survey of their linear eigenoscillations. To quantify the full spectrum of linear MHD eigenmodes, we require knowledge of all flux-surface localized modes, charting out the continuous parts of the MHD spectrum. We combine analytical and numerical findings for the continuous spectrum for realistic prominence configurations. The equations governing all eigenmodes for translationally symmetric, gravitating equilibria containing an axial shear flow, are analyzed, along with their flux-surface localized limit. The analysis is valid for general 2.5D equilibria, where either density, entropy, or temperature vary from one flux surface to another. We analyze the mode couplings caused by the poloidal variation in the flux rope equilibria, by performing a small gravity parameter expansion. We contrast the analytical results with continuous spectra obtained numerically. For equilibria where the density is a flux function, we show that continuum modes can be overstable, and we present the stability criterion for these convective continuum instabilities. Furthermore, for all equilibria, a four-mode coupling scheme between an Alfvenic mode of poloidal mode number m and three neighboring (m-1, m, m+1) slow modes is identified, occurring in the vicinity of rational flux surfaces. For realistically prominence equilibria, this coupling is shown to play an important role, from weak to stronger gravity parameter g values. The analytic predictions for small g are compared with numerical spectra, and progressive deviations for larger g are identified. The unstable continuum modes could be relevant for short-lived prominence configurations. The gaps created by poloidal mode coupling in the continuous spectrum need further analysis, as they form preferred frequency ranges for global eigenoscillations.Comment: Accepted by Astronmy & Astrophysics, 21 pages, 15 figure

Toward detailed prominence seismology - I. Computing accurate 2.5D magnetohydrodynamic equilibria

Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydro- dynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations. Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion). Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case. Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi- layered prominences. Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper.Comment: Accepted by Astronomy & Astrophysics, 15 pages, 15 figure

Waves and Instabilities in Accretion Disks: MHD Spectroscopic Analysis

A complete analytical and numerical treatment of all magnetohydrodynamic waves and instabilities for radially stratified, magnetized accretion disks is presented. The instabilities are a possible source of anomalous transport. While recovering results on known hydrodynamicand both weak- and strong-field magnetohydrodynamic perturbations, the full magnetohydrodynamic spectra for a realistic accretion disk model demonstrates a much richer variety of instabilities accessible to the plasma than previously realized. We show that both weakly and strongly magnetized accretion disks are prone to strong non-axisymmetric instabilities.The ability to characterize all waves arising in accretion disks holds great promise for magnetohydrodynamic spectroscopic analysis.Comment: FOM-Institute for plasma physics "Rijnhuizen", Nieuwegein, the Netherlands 12 pages, 3 figures, Accepted for publication in ApJ

Comment on 'Alfven Instability in a Compressible Flow' [Phys. Rev. Lett. 101, 245001 (2008)]

In a recent paper [Y. Taroyan, Phys. Rev. Lett 101, 245001 (2008) it is claimed that a new MHD instability of the Alfven wave has been found: incompressible Alfven modes propagating in a compressible spatially varying flow were apparently exponentially amplified. We show that the results of the work follow from an impossible equilibrium and therefore should be disregarded

Waves in a warm pair plasma: a relativistically complete two-fluid analysis

We present an ideal two-fluid wave mode analysis for a pair plasma, extending an earlier study for cold conditions to the warm pair plasma case. Starting from the completely symmetrized means for writing the governing linearized equations in the pair fluid rest frame, we discuss the governing dispersion relation containing all six pairs of forward and backward propagating modes, which are conveniently labelled as S, A, F, M, O and X. These relate to the slow (S), Alfven (A) and fast (F) magnetohydrodynamic waves, include a modified (M) electrostatic mode, as well as the electromagnetic O and X branches. In the dispersion relation, only two parameters appear, which define the pair plasma magnetization E2 E[0, infinity] and the squared pair plasma sound speed v2, measured in units of the light speed c. The description is valid also in the highly relativistic regime, where either a high magnetization and/or a relativistic temperature (hence sound speed) is reached. We recover the exact relativistic single-fluid magnetohydrodynamic expressions for the S, A and F families in the low wavenumber–frequency regime, which can be obtained for any choice of the equation of state. We argue that, as in a cold pair plasma, purely parallel or purely perpendicular propagation with respect to the magnetic field vector B is special, and near-parallel or near-perpendicular orientations demonstrate avoided crossings of branches at computable wavenumbers and frequencies. The complete six-mode phase and group diagram views are provided as well, visually demonstrating the intricate anisotropies in all wave modes, as well as their transformations. Analytic expressions for all six wave group speeds at both small and large wavenumbers complement the analysis.</p

The Spectral Web of stationary plasma equilibria. II. Internal modes

The new method of the Spectral Web to calculate the spectrum of waves and instabilities of plasma equilibria with sizeable flows, developed in the preceding Paper I [Goedbloed, Phys. Plasmas 25, 032109 (2018)], is applied to a collection of classical magnetohydrodynamic instabilities operating in cylindrical plasmas with shear flow or rotation. After a review of the basic concepts of the complementary energy giving the solution path and the conjugate path, which together constitute the Spectral Web, the cylindrical model is presented and the spectral equations are derived. The first example concerns the internal kink instabilities of a cylindrical force-free magnetic field of constant α subjected to a parabolic shear flow profile. The old stability diagram and the associated growth rate calculations for static equilibria are replaced by a new intricate stability diagram and associated complex growth rates for the stationary model. The power of the Spectral Web method is demonstrated by showing that the two associated paths in the complex ω-plane nearly automatically guide to the new class of global Alfvén instabilities of the force-free configuration that would have been very hard to predict by other methods. The second example concerns the Rayleigh–Taylor instability of a rotating theta-pinch. The old literature is revisited and shown to suffer from inconsistencies that are remedied. The most global n = 1 instability and a cluster sequence of more local but much more unstable n=2,3,…∞ modes are located on separate solution paths in the hydrodynamic (HD) version of the instability, whereas they merge in the MHD version. The Spectral Web offers visual demonstration of the central position the HD flow continuum and of the MHD Alfvén and slow magneto-sonic continua in the respective spectra by connecting the discrete modes in the complex plane by physically meaningful curves towards the continua. The third example concerns the magneto-rotational instability (MRI) thought to be operating in accretion disks about black holes. The sequence n=1,2,… of unstable MRIs is located on one continuous solution path, but also on infinitely many separate loops (“pancakes”) of the conjugate path with just one MRI on each of them. For narrow accretion disks, those sequences are connected with the slow magneto-sonic continuum, which is far away though from the marginal stability transition. In this case, the Spectral Web method is the first to effectively incorporate the MRIs into the general MHD spectral theory of equilibria with background flows. Together, the three examples provide compelling evidence of the computational power of the Spectral Web Method.</p

Stationary field-aligned MHD flows at astropauses and in astrotails. Principles of a counterflow configuration between a stellar wind and its interstellar medium wind

A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points of the magnetic field within these flows. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfven Mach number for the corresponding stationary equilibria is finite. The topological structure determines the geometrical structure of the interstellar gas - stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail region beyond the reverse shock. The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfven Mach numbers in the case of subalfvenic flows.Comment: 19 pages, 17 figures, accepted for publication in A&

MS 671 Anthropology

COURSE DESCRIPTION This course is “An introduction to cultural anthropology, with application to Christian evangelization and mission.” From before the beginning (Genesis 1), our Triune God has been in mission, reaching out in self-giving, other-embracing love (John 1 & I John 1). We now call this the missio Dei, “the mission of God” to remind us that it is not our mission, nor does mission belong to the church. How God does mission is best understood in the sending of Jesus the Christ (Ephesians 2:11-15). As the Father has sent Jesus, so Jesus sends us (John 20:21). It is in the life of Jesus here on earth that we most clearly see our example for mission: Jesus emptied himself, came down to the people, developed relationships and learned the local language and culture for 30 years; and then he began to preach about the Kingdom of God (Matthew 4:17; Luke 4:43) and perform acts of mercy and justice (Luke 4:18-21) that the people saw as signs and wonders of the presence of God among them (Luke 4:22,32,36). The acts of Jesus Christ through the Holy Spirit (the proper title of Acts) continued in the apostles, deacons and those who were called later, like Paul. The apostles began in mission with the Jews (Acts 2-7). The deacons reached out a little further to the half- Jews (Acts 8) and then to the proselytes (Acts 8). Finally, Peter reluctantly reached out to those who were not Jewish, half-Jewish or even wanna-be Jews but were full fledged Gentiles (Acts 10). Still, it was the multi-cultural church at Antioch (not the monocultural church at Jerusalem) that commissioned and sent out the first missionaries: Paul and Barnabas (Acts 13). What they did changed not just the composition of the church but the life of the church. Jesus the Messiah (Christos) became Jesus the Lord (Kyrios) (Acts 28), because that is what the Greeks and Romans were looking for. New understandings of Jesus brought fuller meaning to the cosmic event of the death and resurrection of Jesus. Jesus was interpreted anew as the Logos (John 1), the Pleroma (Colossians 1:19, 2:9-10), the Mystery and Wisdom of God (Ephesians). Every generation deserves a fresh reading of the gospel. Who will speak now to the migrant generation of this globalized world? A critical view of anthropology as it relates to theology will lead us to our main concern, and that is missiology. There will be a conscious effort in our course to maintain a trialogue between anthropology, theology and missiology. Our goal is to gain insights about missiological issues and concerns.https://place.asburyseminary.edu/syllabi/3533/thumbnail.jp