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Astrophysical accretion discs that carry a significant mass compared with their central object are subject to the effect of self-gravity. In the context of circumstellar discs, this can, for instance, cause fragmentation of the disc gas, and -- under suitable conditions -- lead to the direct formation of gas-giant planets. If one wants to study these phenomena, the disc's gravitational potential needs to be obtained by solving the Poisson equation. This requires to specify suitable boundary conditions. In the case of a spherical-polar computational mesh, a standard multipole expansion for obtaining boundary values is not practicable. We hence compare two alternative methods for overcoming this limitation. The first method is based on a known Green's function expansion (termed "CCGF") of the potential, while the second (termed "James' method") uses a surface screening mass approach with a suitable discrete Green's function. We demonstrate second-order convergence for both methods and test the weak scaling behaviour when using thousands of computational cores. Overall, James' method is found superior owing to its favourable algorithmic complexity of $\sim \mathcal{O}(n^3)$ compared with the $\sim\mathcal{O}(n^4)$ scaling of the CCGF method., Comment: 12 pages, 8 figures, submitted to AN

Understanding the complex evolution of protoplanetary disks (PPDs) and their dispersal via energetic stellar radiation are prominent challenges in astrophysics. It has recently been established that specifically the X-ray luminosity from the central protostar can significantly heat the surface of the disk, causing powerful photoevaporative winds that eject a considerable fraction of the disc's mass. Recent work in the field has moreover shown the importance of global PPD simulations that simultaneously take into account non-ideal magnetohydrodynamic (MHD) effects and detailed thermochemistry. Our motivation with the current paper lies in combining these two aspects and figure out how they interact. Focus is put on the Hall Effect (HE) and the impact it has on the overall field topology and mass loss/accretion rates. Utilizing a novel X-ray temperature parametrisation, we perform 2D-axisymmetric MHD simulations with the NIRVANA fluid code, covering all non-ideal effects. We find that, in the aligned orientation, the HE causes prominent inward displacement of the poloidal field lines that can increase the accretion rate through a laminar Maxwell stress. We find that outflows are mainly driven by photoevaporation -- unless the magnetic field strength is considerable (i.e., $\beta_p\leq 10^{3}$) or the X-ray luminosity low enough (i.e., $\log{L_X}\leq 29.3$). Inferred mass loss rate are in the range of the expected values $10^{-8}$ to $10^{-7}M_{\odot}yr^{-1}$. For comparison, we have also performed pure hydrodynamic (HD) runs and compared them with the equivalent MHD runs. Here we have found that the magnetic field does indeed contribute to the mass loss rate, albeit only discernibly so for low enough $L_X$ (i.e., $\log{L_X}\leq 30.8$). For values higher than that, the wind mass loss predicted from the MHD set converges to the ones predicted from pure HD., Comment: 12 pages, 11 figures, to be submitted to MNRAS

A mean-field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, $\mathbf{g}$. It is shown that for such homogeneous fluids a strong turbulence-induced field advection anti-parallel to $\mathbf{g}$ arises almost independently of rotation. For rotating fluids, an extra $\alpha$ effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the NIRVANA code demonstrate that the radial advection velocity, $\gamma$, always dominates the $\alpha$ term. We show finally with simplified models that $\alpha^2$ dynamos are strongly influenced by the radial pumping: for $\gamma<\alpha$ the solutions become oscillatory, while for $\gamma>\alpha$ they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid-body rotation on the basis of finite conductivity-velocity correlations are unlikely to work, at least for $\alpha^2\Omega$ dynamos without strong shear., Comment: 10 pages, 8 figures, to be published in AN

The assembly and architecture of planetary systems strongly depend on the physical processes governing the evolution and dispersal of protoplanetary disks. Since Protostars and Planets VI, new observations and theoretical insights favor disk winds as being one of those key processes. This chapter provides a comprehensive review of recent observations probing outflowing gas launched over a range of disk radii for a wide range of evolutionary stages, enabling an empirical understanding of how winds evolve. In parallel, we review theoretical advancements in both magnetohydrodynamic and photoevaporative disk wind models and identify predictions that can be confronted with observations. By linking theory and observations we critically assess the role of disk winds in the evolution and dispersal of protoplanetary disks. Finally, we explore the impact of disk winds on planet formation and evolution and highlight theoretical work, observations, and critical tests for future progress., Comment: Review chapter to appear in Protostars and Planets VII, Editors: Shu-ichiro Inutsuka, Yuri Aikawa, Takayuki Muto, Kengo Tomida, and Motohide Tamura

Accretion disc turbulence along with its effect on large-scale magnetic fields plays an important role in understanding disc evolution in general, and the launching of astrophysical jets in particular. Motivated by enabling a comprehensive sub-grid description for global long-term simulations of accretions discs, we aim to further characterize the transport coefficients emerging in local simulations of magnetorotational disc turbulence. For the current investigation, we leverage a time-dependent version of the test-field method, which is sensitive to the turbulent electromotive force (EMF) generated as a response to a set of pulsating background fields. We obtain Fourier spectra of the transport coefficients as a function of oscillation frequency. These are well approximated by a simple response function, describing a finite-time build-up of the EMF as a result of a time-variable mean magnetic field. For intermediate timescales (i.e., slightly above the orbital frequency), we observe a significant phase lag of the EMF compared to the causing field. Augmented with our previous result on a non-local closure relation in space, and incorporated into a suitable mean-field description that we briefly sketch out here, the new framework will allow to drop the restrictive assumption of scale separation., Comment: 8 pages, 4 figures, 1 table, accepted for publication in the ApJ

Large-scale coherent magnetic fields observed in the nearby galaxies are thought to originate by a mean-field dynamo. This is governed via the turbulent electromotive force (EMF, $\overline{\mathcal{E}} $) generated by the helical turbulence driven by supernova (SN) explosions in the differentially rotating interstellar medium (ISM). In this paper we aim to investigate the possibility of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component injected through the SN explosions. We do this by analysing the magnetohydrodynamic simulations of local shearing box of ISM, in which the turbulence is driven via random SN explosions and the energy of the explosion is distributed in the CR and/or thermal energy components. We use the magnetic field aligned diffusion prescription for the propagation of CR. We compare the evolution of magnetic fields in the models with the CR component to our previous models that did not involve the CR. We demonstrate that the inclusion of CR component enhances the growth of dynamo slightly. We further compute the underlying dynamo coefficients using the test-fields method, and argue that the entire evolution of the large scale mean magnetic field can be reproduced with an $\alpha-\Omega$ dynamo model. We also show that the inclusion of CR component leads to an unbalanced turbulent pumping between magnetic field components and additional dynamo action by the R\"adler effect., Comment: 9 pages, 5 figures, 1 tables

Outflows driven by large-scale magnetic fields likely play an important role in the evolution and dispersal of protoplanetary disks, and in setting the conditions for planet formation. We extend our 2-D axisymmetric non-ideal MHD model of these outflows by incorporating radiative transfer and simplified thermochemistry, with the twin aims of exploring how heating influences wind launching, and illustrating how such models can be tested through observations of diagnostic spectral lines. Our model disks launch magnetocentrifugal outflows primarily through magnetic tension forces, so the mass-loss rate increases only moderately when thermochemical effects are switched on. For typical field strengths, thermochemical and irradiation heating are more important than magnetic dissipation. We furthermore find that the entrained vertical magnetic flux diffuses out of the disk on secular timescales as a result of non-ideal MHD. Through post-processing line radiative transfer, we demonstrate that spectral line intensities and moment-1 maps of atomic oxygen, the HCN molecule, and other species show potentially observable differences between a model with a magnetically driven outflow and one with a weaker, photoevaporative outflow. In particular, the line shapes and velocity asymmetries in the moment-1 maps could enable the identification of outflows emanating from the disk surface., Comment: 35 pages, 20 figures, accepted for publication in ApJ

The interstellar medium of the Milky Way and nearby disk galaxies harbours large-scale coherent magnetic fields of Microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalise our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent multi-phase interstellar medium. By introducing spatially (temporally) modulated mean fields, we extend the previously used test-field method to the spectral realm -- providing the Fourier representation of the convolution kernels. The resulting spectra of the dynamo mean-field coefficients that we obtain broadly match expectations and allow to rigorously constrain the degree of scale separation in the Galactic dynamo. A surprising result is found for the diamagnetic pumping term, which increases in amplitude when going to smaller scales. Our results amount to the most comprehensive description of dynamo mean-field effects in the Galactic context to date. Surveying the relevant parameter space and quenching behaviour, this will ultimately enable the development of assumption-free sub-grid prescriptions for otherwise unresolved global galaxy simulations., Comment: 9 pages, 11 figures, accepted for publication in MNRAS

We present simulations of low-mass planet--disc interactions in inviscid three-dimensional discs. We show that a wind-driven laminar accretion flow through the surface layers of the disc does not significantly modify the migration torque experienced by embedded planets. More importantly, we find that 3D effects lead to a dramatic change in the behaviour of the dynamical corotation torque compared to earlier 2D theory and simulations. Although it was previously shown that the dynamical corotation torque could act to slow and essentially stall the inward migration of a low-mass planet, our results in 3D show that the dynamical corotation torque has the complete opposite effect and speeds up inward migration. Our numerical experiments implicate buoyancy resonances as the cause. These have two effects: (i) they exert a direct torque on the planet, whose magnitude relative to the Lindblad torque is measured in our simulations to be small; (ii) they torque the gas librating on horseshoe orbits in the corotation region and drive evolution of its vortensity, leading to the negative dynamical corotation torque. This indicates that at low turbulent viscosity, the detailed vertical thermal structure of the protoplanetary disc plays an important role in determining the migration behaviour of embedded planets. If this result holds up under a more refined treatment of disc thermal evolution, then it has important implications for understanding the formation and early evolution of planetary systems., Comment: 19 pages, 19 figures, MNRAS, updated to match published version

Coherent magnetic fields in disc galaxies are thought to be generated by a large-scale (or mean-field) dynamo operating in their interstellar medium. A key driver of mean magnetic field growth is the turbulent electromotive force (EMF), which represents the influence of correlated small-scale (or fluctuating) velocity and magnetic fields on the mean field. The EMF is usually expressed as a linear expansion in the mean magnetic field and its derivatives, with the dynamo tensors as expansion coefficients. Here, we adopt the singular value decomposition (SVD) method to directly measure these turbulent transport coefficients in a simulation of the turbulent interstellar medium that realizes a large-scale dynamo. Specifically, the SVD is used to least-square fit the time series data of the EMF with that of the mean field and its derivatives, to determine these coefficients. We demonstrate that the spatial profiles of the EMF reconstructed from the SVD coefficients match well with that taken directly from the simulation. Also, as a direct test, we use the coefficients to simulate a 1-D mean-field dynamo model and find an overall similarity in the evolution of the mean magnetic field between the dynamo model and the direct simulation. We also compare the results with those which arise using simple regression and the ones obtained previously using the test-field (TF) method, to find reasonable qualitative agreement. Overall, the SVD method provides an effective post-processing tool to determine turbulent transport coefficients from simulations., Comment: 14 pages, 14 figures

The migration of planetary cores embedded in a protoplanetary disk is an important mechanism within planet-formation theory, relevant for the architecture of planetary systems. Consequently, planet migration is actively discussed, yet often results of independent theoretical or numerical studies are unconstrained due to the lack of observational diagnostics designed in light of planet migration. In this work we follow the idea of inferring the migration behavior of embedded planets by means of the characteristic radial structures that they imprint in the disk's dust density distribution. We run hydrodynamical multifluid simulations of gas and several dust species in a locally isothermal $\alpha$-disk in the low-viscosity regime ($\alpha=10^{-5}$) and investigate the obtained dust structures. In this framework, a planet of roughly Neptune mass can create three (or more) rings in which dust accumulates. We find that the relative spacing of these rings depends on the planet's migration speed and direction. By performing subsequent radiative transfer calculations and image synthesis we show that - always under the condition of a near-inviscid disk - different migration scenarios are, in principle, distinguishable by long-baseline, state-of-the-art ALMA observations., Comment: 19 pages, 13 figures, accepted for publication in Astrophysical Journal

The streaming instability is thought to play a central role in the early stages of planet formation by enabling the efficient bypass of a number of barriers hindering the formation of planetesimals. We present the first study exploring the efficiency of the linear streaming instability when a particle-size distribution is considered. We find that, for a given dust-to-gas mass ratio, the multi-species streaming instability grows on timescales much longer than those expected when only one dust species is involved. In particular, distributions that contain close-to-order-unity dust-to-gas mass ratios lead to unstable modes that can grow on timescales comparable, or larger, with those of secular instabilities. We anticipate that processes leading to particle segregation and/or concentration can create favourable conditions for the instability to grow fast. Our findings may have important implications for a large number of processes in protoplanetary disks that rely on the streaming instability as usually envisioned for a unique dust species. Our results suggest that the growth rates of other resonant-drag-instabilities may also decrease considerably when multiple species are considered., Comment: 8 pages, 6 figures; accepted for publication in The Astrophysical Journal Letters

Jupiter and Saturn formed early, before the gas disk dispersed. The presence of gap-opening planets affects the dynamics of the gas and embedded solids and halts the inward drift of grains above a certain size. A drift barrier can explain the absence of calcium aluminium rich inclusions (CAIs) in chondrites originating from parent bodies that accreted in the inner solar system. Employing an interdisciplinary approach, we use a $\mu$-X-Ray-fluorescence scanner to search for large CAIs and a scanning electron microscope to search for small CAIs in the ordinary chondrite NWA 5697. We carry out long-term, two-dimensional simulations including gas, dust, and planets to characterize the transport of grains within the viscous $\alpha$-disk framework exploring the scenarios of a stand-alone Jupiter, Jupiter and Saturn \textit{in situ}, or Jupiter and Saturn in a 3:2 resonance. In each case, we find a critical grain size above which drift is halted as a function of the physical conditions in the disk. From the laboratory search we find four CAIs with a largest size of $\approx$200$\,\mu$m. \Combining models and data, we provide an estimate for the upper limit of the $\alpha$-viscosity and the surface density at the location of Jupiter, using reasonable assumptions about the stellar accretion rate during inward transport of CAIs, and assuming angular momentum transport to happen exclusively through viscous effects. Moreover, we find that the compound gap structure in the presence of Saturn in a 3:2 resonance favors inward transport of grains larger than CAIs currently detected in ordinary chondrites., Comment: 16 pages, 10 figures, updated to match published version in Astrophysical Journal

Modern astronomy has finally been able to observe protoplanetary disks in reasonable resolution and detail, unveiling the processes happening during planet formation. These observed processes are understood under the framework of disk-planet interaction, a process studied analytically and modeled numerically for over 40 years. Long a theoreticians' game, the wealth of observational data has been allowing for increasingly stringent tests of the theoretical models. Modeling efforts are crucial to support the interpretation of direct imaging analyses, not just for potential detections but also to put meaningful upper limits on mass accretion rates and other physical quantities in current and future large-scale surveys. This white paper addresses the questions of what efforts on the computational side are required in the next decade to advance our theoretical understanding, explain the observational data, and guide new observations. We identified the nature of accretion, ab initio planet formation, early evolution, and circumplanetary disks as major fields of interest in computational planet formation. We recommend that modelers relax the approximations of alpha-viscosity and isothermal equations of state, on the grounds that these models use flawed assumptions, even if they give good visual qualitative agreement with observations. We similarly recommend that population synthesis move away from 1D hydrodynamics. The computational resources to reach these goals should be developed during the next decade, through improvements in algorithms and the hardware for hybrid CPU/GPU clusters. Coupled with high angular resolution and great line sensitivity in ground based interferometers, ELTs and JWST, these advances in computational efforts should allow for large strides in the field in the next decade., Comment: White paper submitted to the Astro2020 decadal survey

Imaging of the dust continuum emitted from disks around nearby protostars reveals diverse substructure. In recent years, theoretical efforts have been intensified to investigate how far the intrinsic dynamics of protoplanetary disks (PPDs) can lead to such features. Turbulence in the realm of non-ideal magnetohydrodynamics (MHD) is one candidate for explaining the generation of zonal flows which can lead to local dust enhancements. Adopting a radially varying cylindrical disk model, and considering combinations of vertical and azimuthal initial net flux, we perform 3D non-ideal MHD simulations aimed at studying self-organization induced by the Hall effect in turbulent PPDs. To this end, new modules have been incorporated into the NIRVANA-III and FARGO3D MHD codes. We moreover include dust grains, treated in the fluid approximation, in order to study their evolution subject to the emerging zonal flows. In the regime of a dominant Hall effect, we robustly obtain large-scale organized concentrations in the vertical magnetic field that remain stable for hundreds of orbits. For disks with vertical initial net flux alone, we confirm the presence of zonal flows and vortices that introduce regions of super-Keplerian gas flow. Including a moderately strong net-azimuthal magnetic flux can significantly alter the dynamics, partially preventing the self-organization of zonal flows. For plasma beta-parameters smaller than 50, large-scale, near-axisymmetric structures develop in the vertical magnetic flux. In all cases, we demonstrate that the emerging features are capable of accumulating dust grains for a range of Stokes numbers., Comment: 20 pages, 14 figures. Accepted for publication in The Astrophysical Journal

Recent developments in non-ideal magnetohydrodynamic simulations of protoplanetary disks suggest that instead of being traditional turbulent (viscous) accretion disks, they have a largely laminar flow with accretion driven by large-scale wind torques. These disks are possibly threaded by Hall-effect generated large-scale horizontal magnetic fields. We have examined the dynamics of the corotation region of a low mass planet embedded in such a disk and the evolution of the associated migration torque. These disks lack strong turbulence and associated turbulent diffusion, and the presence of a magnetic field and radial gas flow presents a situation outside the applicability of previous corotation torque theory. We summarize the analytical analysis of the corotation torque, give details on the numerical methods used, and in particular the relative merits of different numerical schemes for the inviscid problem., Comment: 7 pages, 4 figures, Proceedings of the 12th International Conference on Numerical Modeling of Space Plasma Flows: ASTRONUM-2017

Aerodynamic theory predicts that dust grains in protoplanetary disks will drift radially inward on comparatively short timescales. In this context, it has long been known that the presence of a gap opened by a planet can alter the dust dynamics significantly. In this paper, we carry out a systematic study employing long-term numerical simulations aimed at characterizing the critical particle-size for retention outside a gap as a function of particle size and for various key parameters defining the protoplanetary disk model. To this end, we perform multifluid hydrodynamical simulations in two dimensions, including different dust species, which we treat as pressureless fluids. We initialize the dust outside of the planet's orbit and study under which conditions dust grains are able to cross the gap carved by the planet. In agreement with previous work, we find that the permeability of the gap depends both on dust dynamical properties and the gas disk structure: while small dust follows the viscously accreting gas through the gap, dust grains approaching a critical size are progressively filtered out. Moreover, we introduce and compute a depletion factor that enables us to quantify the way in which higher viscosity, smaller planet mass, or a more massive disk can shift this critical size to larger values. Our results indicate that gap-opening planets may act to deplete the inner reaches of protoplanetary disks of large dust grains -- potentially limiting the accretion of solids onto forming terrestrial planets., Comment: 18 pages, 14 figures, accepted for publication in ApJ

Motivated by models suggesting that the inner planet forming regions of protoplanetary discs are predominantly lacking in viscosity-inducing turbulence, and are possibly threaded by Hall-effect generated large-scale horizontal magnetic fields, we examine the dynamics of the corotation region of a low-mass planet in such an environment. The corotation torque in an inviscid, isothermal, dead zone ought to saturate, with the libration region becoming both symmetrical and of a uniform vortensity, leading to fast inward migration driven by the Lindblad torques alone. However, in such a low viscosity situation, the material on librating streamlines essentially preserves its vortensity. If there is relative radial motion between the disc gas and the planet, the librating streamlines will no longer be symmetrical. Hence, if the gas is torqued by a large scale magnetic field so that it undergoes a net inflow or outflow past the planet, driving evolution of the vortensity and inducing asymmetry of the corotation region, the corotation torque can grow, leading to a positive torque. In this paper we treat this effect by applying a symmetry argument to the previously studied case of a migrating planet in an inviscid disc. Our results show that the corotation torque due to a laminar Hall-induced magnetic field in a dead zone behaves quite differently from that studied previously for a viscous disc. Furthermore, the magnetic field induced corotation torque and the dynamical corotation torque in a low viscosity disc can be regarded as one unified effect., Comment: 12 pages, 9 figures, MNRAS in press, update to match journal corrected proofs

We review the general theoretical concepts and observational constraints on the distribution and evolution of water vapor and ice in protoplanetary disks, with a focus on the Solar System. Water is expected to freeze out at distances greater than 1-3 AU from solar-type central stars; more precise estimates are difficult to obtain due to uncertainties in the complex processes involved in disk evolution, including dust growth, settling, and radial drift, and the level of turbulence and viscous dissipation within disks. Interferometric observations are now providing constraints on the positions of CO snow lines, but extrapolation to the unresolved regions where water ice sublimates will require much better theoretical understanding of mass and angular momentum transport in disks as well as more refined comparison of observations with sophisticated disk models., Comment: 26 pages, 8 figures: in the proceedings of the ISSI workshop on "The delivery of water to proto-planets, planets and satellites", to appear in Space Science Reviews

We investigate the formation of hot and massive circumplanetary disks (CPDs) and the orbital evolution of satellites formed in these disks. Because of the comparatively small size-scale of the sub-disk, quick magnetic diffusion prevents the magnetorotational instability (MRI) from being well-developed at ionization levels that would allow MRI in the parent protoplanetary disk. In the absence of significant angular momentum transport, continuous mass supply from the parental protoplanetary disk leads to the formation of a massive CPD. We have developed an evolutionary model for this scenario and have estimated the orbital evolution of satellites within the disk. We find, in a certain temperature range, that inward migration of a satellite can be stopped by a change in the structure due to the opacity transitions. Moreover, by capturing second and third migrating satellites in mean motion resonances, a compact system in Laplace resonance can be formed in our disk models., Comment: 10 pages, 9 figures

Protoplanetary disks (PPDs) accrete onto their central T Tauri star via magnetic stresses. When the effect of ambipolar diffusion (AD) is included, and in the presence of a vertical magnetic field, the disk remains laminar between 1-5 au, and a magnetocentrifugal disk wind forms that provides an important mechanism for removing angular momentum. We present global MHD simulations of PPDs that include Ohmic resistivity and AD, where the time-dependent gas-phase electron and ion fractions are computed under FUV and X-ray ionization with a simplified recombination chemistry. To investigate whether the mass loading of the wind is potentially affected by the limited vertical extent of our existing simulations, we attempt to develop a model of a realistic disk atmosphere. To this end, by accounting for stellar irradiation and diffuse reprocessing of radiation, we aim at improving our models towards more realistic thermodynamic properties., Comment: 8 pages, 3 figures, ASTRONUM-2016 proceedings

Recent high angular resolution ($\sim$0.2") ALMA observations of the 1.1 mm continuum and of HCO+ J=3-2 and HCN J=3-2 gas towards the binary protostar IRS 43 reveal multiple Keplerian disks which are significantly misaligned ($\gt$ 60$^\circ$), both in inclination and position angle and also with respect to the binary orbital plane. Each stellar component has an associated circumstellar disk while the binary is surrounded by a circumbinary disk. Together with archival VLA measurements of the stellar positions over 25 years, and assuming a circular orbit, we use our continuum measurements to determine the binary separation, a = 74 $\pm$ 4 AU, and its inclination, i $\lt$ 30$^\circ$. The misalignment in this system suggests that turbulence has likely played a major role in the formation of IRS 43., Comment: 7 pages, 4 figures

The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale dependence of these closure coefficients, with the latter describing non-local contributions to the turbulent electromotive force. Based on this, we infer a scale-separation ratio of about ten for the large-scale dynamo. We finally determine scaling properties of the mean-field dynamo coefficients. The relevant component of the dynamo {\alpha} effect is found to scale linearly with the shear rate, as is the corresponding turbulent diffusion, {\eta}. Together, these scalings allow us to predict, in a quantitative manner, the cycle period of the well-known butterfly diagram. This lends new support to the importance of the {\alpha}{\Omega} mechanism in determining the evolution of large-scale magnetic fields in turbulent accretion disks., Comment: 15 pages, 13 figures, accepted for publication in ApJ

Protoplanetary disks are believed to accrete onto their central T Tauri star because of magnetic stresses. Recently published shearing box simulations indicate that Ohmic resistivity, ambipolar diffusion and the Hall effect all play important roles in disk evolution. In the presence of a vertical magnetic field, the disk remains laminar between 1-5au, and a magnetocentrifugal disk wind forms that provides an important mechanism for removing angular momentum. Questions remain, however, about the establishment of a true physical wind solution in the shearing box simulations because of the symmetries inherent in the local approximation. We present global MHD simulations of protoplanetary disks that include Ohmic resistivity and ambipolar diffusion, where the time-dependent gas-phase electron and ion fractions are computed under FUV and X-ray ionization with a simplified recombination chemistry. Our results show that the disk remains laminar, and that a physical wind solution arises naturally in global disk models. The wind is sufficiently efficient to explain the observed accretion rates. Furthermore, the ionization fraction at intermediate disk heights is large enough for magneto-rotational channel modes to grow and subsequently develop into belts of horizontal field. Depending on the ionization fraction, these can remain quasi-global, or break-up into discrete islands of coherent field polarity. The disk models we present here show a dramatic departure from our earlier models including Ohmic resistivity only. It will be important to examine how the Hall effect modifies the evolution, and to explore the influence this has on the observational appearance of such systems, and on planet formation and migration., Comment: 18 pages, 12 figures, accepted for publication in ApJ

We aim to estimate the contribution of the radial component of the Lorentz force to the gas rotation in several types of galaxies. Using typical parameters for the exponential scale of synchrotron emission and the scale length of HI gas, under the assumption of equipartition between the energies of cosmic rays and total magnetic fields, we derive the Lorentz force and compare it to the gravitational force in the radial component of the momentum equation. We distinguish the different contributions between the large-scale and the small-scale turbulent fields by Reynolds averaging. We compare these findings with a dynamical dynamo model. We find a possible reduction of circular gas velocity in the very outer parts and an increase inside a radius of four times the synchrotron scale length. Sufficiently localized radial reversals of the magnetic field may cause characteristic modulations in the gas rotation curve with typical amplitudes of 10-20 km/s. It is unlikely that the magnetic field contributes to the flat rotation in the outer parts of galaxies. If anything, it will \emph{impede} the gravitationally supported rotation, demanding for an even higher halo mass to explain the observed rotation profile. We speculate that this may have consequences for ram pressure stripping and the truncation of the stellar disc.

(Abridged) Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field is now modelled with an unprecedented level of detail and complexity. We aim to complement this heuristic approach with a physically motivated, quantitative Galactic dynamo model -- a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we perform three-dimensional global simulations of the Galactic disc. Closure coefficients embodying the mean-field dynamo are calibrated against resolved box simulations of supernova-driven interstellar turbulence. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode, with even parity, and a subdominant A0 mode, with odd parity. Notably, such a superposition of modes creates a strong localised vertical field on one side of the Galactic disc. We moreover find significant radial pitch angles, which decay with radius -- explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the less-stirred outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for the case of a mean-field dynamo alone) to about 10 kpc in the hybrid models. There remain aspects (e.g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, the work presented demonstrates that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts., Comment: 12 pages, 12 figures, 2 tables, accepted for publication in A&A

We present global hydrodynamic and magnetohydrodynamic (MHD) simulations with mesh refinement of accreting planets embedded in protoplanetary disks (PPDs). The magnetized disk includes Ohmic resistivity that depends on the overlying mass column, leading to turbulent surface layers and a dead zone near the midplane. The main results are: (i) The accretion flow in the Hill sphere is intrinsically 3D for hydrodynamic and MHD models. Net inflow toward the planet is dominated by high latitude flows. A circumplanetary disk (CPD) forms. Its midplane flows outward in a pattern whose details differ between models. (ii) Gap opening magnetically couples and ignites the dead zone near the planet, leading to stochastic accretion, a quasi-turbulent flow in the Hill sphere and a CPD whose structure displays high levels of variability. (iii) Advection of magnetized gas onto the rotating CPD generates helical fields that launch magnetocentrifugally driven outflows. During one specific epoch a highly collimated, one-sided jet is observed. (iv) The CPD's surface density $\sim30{\rm\,g\,cm^{-2}}$, small enough for significant ionization and turbulence to develop. (v) The accretion rate onto the planet in the MHD simulation reaches a steady value $8 \times 10^{-3} {\rm M_\oplus yr^{-1}}$, and is similar in the viscous hydrodynamic runs. Our results suggest that gas accretion onto a forming giant planet within a magnetized PPD with dead zone allows rapid growth from Saturnian to Jovian masses. As well as being relevant for giant planet formation, these results have important implications for the formation of regular satellites around gas giant planets., Comment: 22 pages, 20 figures, second minor revision, accepted for publication in ApJ

We investigate the saturation level of hydromagnetic turbulence driven by the magnetorotational instability in the case of vanishing net flux. Motivated by a recent paper of Bodo, Cattaneo, Mignone, & Rossi, we here focus on the case of a non-isothermal equation of state with constant thermal diffusivity. The central aim of the paper is to complement the previous result with closure parameters for mean-field dynamo models, and to test the hypothesis that the dynamo is affected by the mode of heat transport. We perform computer simulations of local shearing-box models of stratified accretion disks with approximate treatment of radiative heat transport, which is modeled via thermal conduction. We study the effect of varying the (constant) thermal diffusivity, and apply different vertical boundary conditions. In the case of impenetrable vertical boundaries, we confirm the transition from mainly conductive to mainly convective vertical heat transport below a critical thermal diffusivity. This transition is however much less dramatic when more natural outflow boundary conditions are applied. Similarly, the enhancement of magnetic activity in this case is less pronounced. Nevertheless, heating via turbulent dissipation determines the thermodynamic structure of accretion disks, and clearly affects the properties of the related dynamo. This effect may however have been overestimated in previous work, and a careful study of the role played by boundaries will be required., Comment: 7 pages, 9 figures, accepted for publication in ApJ

The emergence of large-scale magnetic fields observed in the diffuse interstellar medium is explained by a turbulent dynamo. The underlying transport coefficients have previously been extracted from numerical simulations. So far, this was restricted to the kinematic regime, but we aim to extend our analysis into the realm of dynamically important fields. This marks an important step on which derived mean-field models rely to explain observed equipartition strength fields. As in previous work, we diagnose turbulent transport coefficients by means of the test-field method. We derive quenching functions for the dynamo {\alpha} effect, diamagnetic pumping, and turbulent diffusivity, which are compared with theoretical expectations. At late times, we observe the suppression of the vertical wind. Because this potentially affects the removal of small-scale magnetic helicity, new concerns arise about circumventing constraints imposed by the conservation of magnetic helicity at high magnetic Reynolds numbers. While present results cannot safely rule out this possibility, the issue only becomes important at late stages and is absent when the dynamo is quenched by the wind itself., Comment: 5 pages, 6 figures, to be published in MNRAS

(Abridged) We analyse the stability and evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are power-law functions of cylindrical radius. We employ two different hydrodynamic codes to perform 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the viscosity. We present a stability analysis of the problem that we use to interpret the simulation results. We find that disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k_R/k_Z| >> 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or `vertical shear' linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability operates when the dimensionless disc kinematic viscosity nu < 10^{-6} (Reynolds numbers Re>H c_s/nu > 2500). In 3D the instability generates a quasi-turbulent flow, and the Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches alpha ~ 6 x 10^{-4} by the end of the simulation. The vertical shear instability in disc models which include realistic thermal physics has yet to be examined. Should it occur, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance., Comment: 19 pages, 15 figures, submitted to MNRAS for publication. A version with full resolution figures is available at http://www.maths.qmul.ac.uk/~rpn/Corrugation/NGU.pdf

Magnetic field amplification by a fast dynamo is seen in local box simulations of SN-driven ISM turbulence, where the self-consistent emergence of large-scale fields agrees very well with its mean-field description. We accordingly derive scaling laws of the turbulent transport coef- ficients in dependence of the SN rate, density and rotation. These provide the input for global simulations of regular magnetic fields in galaxies within a mean-field MHD framework. Using a Kennicutt-Schmidt relation between the star formation (SF) rate and midplane density, we can reduce the number of free parameters in our global models. We consequently present dynamo models for different rotation curves and radial density distributions.

(Abridged) Planetesimals embedded in a protoplanetary disc are stirred by gravitational torques exerted by density fluctuations in the surrounding turbulence. In particular, planetesimals in a disc supporting fully developed magneto-rotational turbulence are readily excited to velocity dispersions above the threshold for catastrophic disruption, halting planet formation. We aim to examine the stirring of planetesimals lying instead in a magnetically-decoupled midplane dead zone, stirred only by spiral density waves propagating out of the disc's magnetically-coupled turbulent surface layers. We extend previous studies to include a wider range of disc models, and explore the effects of varying the disc column density and external magnetic field strength. [...] The strength of the stirring is found to be independent of the gas surface density, which is contrary to the increase with disc mass expected from a simple linear wave picture. The discrepancy arises from the shearing out of density waves as they propagate into the dead zone, resulting in density structures near the midplane that exert weaker stochastic torques on average. We provide a simple analytic fit to our numerically obtained torque amplitudes that accounts for this effect. The stirring on the other hand depends sensitively on the net vertical magnetic flux, up to a saturation level above which magnetic forces dominate in the turbulent layers. For the majority of our models, the equilibrium planetesimal velocity dispersions lie between the thresholds for disrupting strong and weak aggregates, suggesting that collision outcomes will depend on material properties. However, discs with relatively weak magnetic fields yield reduced stirring, and their dead zones provide safe-havens even for the weakest planetesimals against collisional destruction., Comment: 20 pages, 18 figures, 3 tables, to be published in MNRAS

(abridged) Accretion in protoplanetary discs is thought to be driven by [...] turbulence via the magnetorotational instability (MRI). Recent work has shown that a planetesimal swarm embedded in a fully turbulent disc is subject to strong excitation of the velocity dispersion, leading to collisional destruction of bodies with radii R_p < 100 km. Significant diffusion of planetesimal semimajor axes also arises, leading to large-scale spreading of the planetesimal population throughout the inner regions of the protoplanetary disc, in apparent contradiction of constraints provided by the distribution of asteroids within the asteroid belt. In this paper, we examine the dynamics of planetesimals embedded in vertically stratified turbulent discs, with and without dead zones. Our main aims are to examine the turbulent excitation of the velocity dispersion, and the radial diffusion, of planetesimals in these discs. We employ three dimensional MHD simulations [...], along with an equilibrium chemistry model [...] We find that planetesimals in fully turbulent discs develop large random velocities that will lead to collisional destruction/erosion for bodies with sizes below 100 km, and undergo radial diffusion on a scale \sim 2.5 au over a 5 Myr disc life time. But planetesimals in a dead zone experience a much reduced excitation of their random velocities, and equilibrium velocity dispersions lie between the disruption thresholds for weak and strong aggregates for sizes R_p < 100 km. We also find that radial diffusion occurs over a much reduced length scale \sim 0.25 au over the disc life time, this being consistent with solar system constraints. We conclude that planetesimal growth via mutual collisions between smaller bodies cannot occur in a fully turbulent disc. By contrast, a dead zone may provide a safe haven in which km-sized planetesimals can avoid mutual destruction through collisions., Comment: 18 pages, 13 figures, 3 tables, MNRAS in press, minor corrections to match the published version

The fractal shape and multi-component nature of the interstellar medium together with its vast range of dynamical scales provides one of the great challenges in theoretical and numerical astrophysics. Here we will review recent progress in the direct modelling of interstellar hydromagnetic turbulence, focusing on the role of energy injection by supernova explosions. The implications for dynamo theory will be discussed in the context of the mean-field approach. Results obtained with the test field-method are confronted with analytical predictions and estimates from quasilinear theory. The simulation results enforce the classical understanding of a turbulent Galactic dynamo and, more importantly, yield new quantitative insights. The derived scaling relations enable confident global mean-field modelling., Comment: 7 pages, 2 figures, conference proceedings of the IAU Symposium 274, Advances in Plasma Astrophysics

(abridged) Angular momentum transport and accretion in protoplanetary discs are generally believed to be driven by MHD turbulence via the magneto-rotational instability (MRI). The dynamics of solid bodies embedded in such discs (dust grains, boulders, planetesimals and planets) may be strongly affected by the turbulence, such that the formation pathways for planetary systems are determined in part by the strength and spatial distribution of the turbulent flow. We examine the dynamics of planetesimals, with radii between 1m \^a 10 km, embedded in turbulent protoplanetary discs, using three dimensional MHD simulations. The planetesimals experience gas drag and stochastic gravitational forces due to the turbulent disc. We use, and compare the results from, local shearing box simulations and global models in this study. The main aims of this work are to examine: the growth, and possible saturation, of the velocity dispersion of embedded planetesimals as a function of their size and disc parameters; the rate of radial migration and diffusion of planetesimals; the conditions under which the results from shearing box and global simulations agree. We find good agreement between local and global simulations when shearing boxes of dimension 4H x 16H x 2H are used (H being the local scale height). The magnitude of the density fluctuations obtained is sensitive to the box size, due to the excitation and propagation of spiral density waves. This affects the stochastic forcing experienced by planetesimals. [...] Our models show that fully developed MHD turbulence in protoplanetary discs would have a destructive effect on embedded planetesimals. Relatively low levels of turbulence are required for traditional models of planetesimal accretion to operate, this being consistent with the existence of a dead zone in protoplanetary discs., Comment: 23 pages, 28 figures, 3 tables, accepted for publication in MNRAS

Simulations of the magnetorotational instability (MRI) in 'unstratified' shearing boxes exhibit powerful coherent flows, whereby the fluid vertically splits into countermoving planar jets or `channels'. Channel flows correspond to certain axisymmetric linear MRI modes, and their preponderance follows from the remarkable fact that they are approximate nonlinear solutions of the MHD equations in the limit of weak magnetic fields. We show in this paper, analytically and with one-dimensional numerical simulations, that this property is also shared by certain axisymmetric MRI modes in vertically-stratified shearing boxes. These channel flows rapidly capture significant amounts of magnetic and kinetic energy, and thus are vulnerable to secondary shear instabilities. We examine these parasites in the vertically stratified context, and estimate the maximum amplitudes that channels attain before they are destroyed. These estimates suggest that a dominant channel flow will usually drive the disk's magnetic field to thermal strengths. The prominence of these flows and their destruction place enormous demands on simulations, but channels in their initial stages also offer a useful check on numerical codes. These benchmarks are especially valuable given the increasing interest in the saturation of the stratified MRI. Lastly we speculate on the potential connection between 'run-away' channel flows and outburst behaviour in protostellar and dwarf nova disks., Comment: 17 pages, 12 figures. MNRAS, accepted.

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100Myr. The self-consistent numerical verification of such a "fast dynamo" is highly beneficial in explaining the observed strong magnetic fields in young galaxies. We, furthermore, highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field. This finding impressively confirms the classical picture of a dynamo based on cyclonic turbulence., Comment: 99 pages, 46 figures (in part strongly degraded), 8 tables, PhD thesis, University of Potsdam (2009). Resolve URN "urn:nbn:de:kobv:517-opus-29094" (e.g. via http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29094) for a version with high-resolution figures

Local shearing box simulations of stratified magneto rotational turbulence invariably exhibit cyclic field patterns which propagate away from the disc midplane. A common explanation for this is magnetic buoyancy. The recent analysis by Shi et al. however shows that the flow is buoyantly stable below one disc scale height H, necessitating an alternative explanation in this region. We here conduct and analyse direct numerical simulations to explain the observed behaviour by means of a mean-field description. Apart from the mean radial and azimuthal field, we monitor the small-scale current helicity, which we propose as a key indicator for saturation. Reconstructing the horizontally averaged field, we demonstrate that the problem can be reduced to a one-dimensional induction equation. By means of the so-called test field method, we then determine the underlying closure parameters. Our analysis shows that, apart from a possible direct MRI dynamo, two distinct indirect dynamo mechanisms operate in the disc. This resolves the issue of the "wrong" sign of the MRI dynamo effect. Finally, we use the obtained closure parameters to run a dynamically quenched dynamo model. This model approximately recovers the observed field patterns in the mean fields. Moreover, the model reproduces the prevailing parity and the distinct phase pattern in the small-scale current helicity. The latter property might open a potential route to understand the saturation of MRI induced turbulence., Comment: 8 pages, 6 figures, accepted for publication in MNRAS

Adequate modelling of the multiphase interstellar medium requires optically thin radiative cooling, comprising an inherent thermal instability. The size of the occurring condensation and evaporation interfaces is determined by the so-called Field-length, which gives the dimension at which the instability is significantly damped by thermal conduction. Our aim is to study the relevance of conduction scale effects in the numerical modelling of a bistable medium and check the applicability of conventional and alternative adaptive mesh techniques. The low physical value of the thermal conduction within the ISM defines a multiscale problem, hence promoting the use of adaptive meshes. We here introduce a new refinement strategy that applies the Field condition by Koyama & Inutsuka as a refinement criterion. The described method is very similar to the Jeans criterion for gravitational instability by Truelove and efficiently allows to trace the unstable gas situated at the thermal interfaces. We present test computations that demonstrate the greater accuracy of the newly proposed refinement criterion in comparison to refinement based on the local density gradient. Apart from its usefulness as a refinement trigger, we do not find evidence in favour of the Field criterion as a prerequisite for numerical stability., Comment: 5 pages, 5 figures, accepted for publication in A&A

Recent simulations of supernova-driven turbulence within the ISM support the existence of a large-scale dynamo. With a growth time of about two hundred million years, the dynamo is quite fast -- in contradiction to many assertions in the literature. We here present details on the scaling of the dynamo effect within the simulations and discuss global mean-field models based on the adopted turbulence coefficients. The results are compared to global simulations of the magneto-rotational instability., Comment: 10 pages, 5 figures, IAU Symp. 259 proceedings (in press)

Supernovae are the dominant energy source for driving turbulence within the interstellar plasma. Until recently, their effects on magnetic field amplification in disk galaxies remained a matter of speculation. By means of self-consistent simulations of supernova-driven turbulence, we find an exponential amplification of the mean magnetic field on timescales of a few hundred million years. The robustness of the observed fast dynamo is checked at different magnetic Reynolds numbers, and we find sustained dynamo action at moderate Rm. This indicates that the mechanism might indeed be of relevance for the real ISM. Sensing the flow via passive tracer fields, we infer that SNe produce a turbulent alpha effect which is consistent with the predictions of quasilinear theory. To lay a foundation for global mean-field models, we aim to explore the scaling of the dynamo tensors with respect to the key parameters of our simulations. Here we give a first account on the variation with the supernova rate., Comment: 6 pages, 5 figures, IAU Symp. 259 proceedings (in press)

Within the interstellar medium, supernovae are thought to be the prevailing agents in driving turbulence. Until recently, their effects on magnetic field amplification in disk galaxies remained uncertain. Analytical models based on the uncorrelated-ensemble approach predicted that any created field would be expelled from the disk before it could be amplified significantly. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for galactic differential rotation and vertical stratification, we find an exponential amplification of the mean field on timescales of several hundred million years. We especially highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field., Comment: 4 pages, 3 figures, proceedings of the JENAM 2008, Symp. 7

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Previous analytical models, based on the evolution of isolated, non-interacting supernova remnants, predicted a dominant vertical pumping that would render dynamo action improbable. In the present work, we address the issue of vertical transport, which is thought to be the key process that inhibits dynamo action in the galactic context. We aim to demonstrate that supernova driving is a powerful mechanism to amplify galactic magnetic fields. We conduct direct numerical simulations in the framework of resistive magnetohydrodynamics. Our local box model of the interstellar medium comprises optically-thin radiative cooling, an external gravitational potential, and background shear. Dynamo coefficients for mean-field models are measured by means of passive test fields. Our simulations show that supernova-driven turbulence in conjunction with shear leads to an exponential amplification of the mean magnetic field. We found turbulent pumping to be directed inward and approximately balanced by a galactic wind., Comment: minor changes, 4 pages, 4 figures, accepted for publication in A&A L

Observations in polarized emission reveal the existence of large-scale coherent magnetic fields in a wide range of spiral galaxies. Radio-polarization data show that these fields are strongly inclined towards the radial direction, with pitch angles up to $35\degr$ and thus cannot be explained by differential rotation alone. Global dynamo models describe the generation of the radial magnetic field from the underlying turbulence via the so called $\alpha$-effect. However, these global models still rely on crude assumptions about the small-scale turbulence. To overcome these restrictions we perform fully dynamical MHD simulations of interstellar turbulence driven by supernova explosions. From our simulations we extract profiles of the contributing diagonal elements of the dynamo $\alpha$-tensor as functions of galactic height. We also measure the coefficients describing vertical pumping and find that the ratio $\hat{\gamma}$ between these two effects has been overestimated in earlier analytical work, where dynamo action seemed impossible. In contradiction to these models based on isolated remnants we always find the pumping to be directed inward. In addition we observe that $\hat{\gamma}$ depends on whether clustering in terms of super-bubbles is taken into account. Finally, we apply a test field method to derive a quantitative measure of the turbulent magnetic diffusivity which we determine to be ~ 2 kpc kms., Comment: 6 pages, 3 figures, to be published in AN

We describe the implementation of the shearingbox approach into the Godunov-type central-upwind/constraint-transport magnetohydrodynamics code NIRVANA. This will allow for applications which require sheared-periodic boundary conditions as typically used in local Cartesian simulations of differentially rotating systems. We present the algorithm in detail and discuss necessary modifications in the numerical fluxes in order to preserve conserved quantities and to fulfill other analytical constraints as good as seem feasible within the numerical scheme. We check the source terms which come with the shearingbox formulation by investigating the conservation of the epicyclic mode energy. We also perform more realistic simulations of the magneto-rotational instability with initial zero-net-flux vertical magnetic field and compare the obtained stresses and energetics with previous non-conservative results exploring the same parameter regime., Comment: 17 pages, 4 figures, to be published in CPC