# Posts Tagged angular momentum transport

## Recent Postings from angular momentum transport

### Seismic evidence for a weak radial differential rotation in intermediate-mass core helium burning stars

The detection of mixed modes that are split by rotation in Kepler red giants has made it possible to probe the internal rotation profiles of these stars, which brings new constraints on the transport of angular momentum in stars. Mosser et al. (2012) have measured the rotation rates in the central regions of intermediate-mass core helium burning stars (secondary clump stars). Our aim was to exploit& the rotational splittings of mixed modes to estimate the amount of radial differential rotation in the interior of secondary clump stars using Kepler data, in order to place constraints on angular momentum transport in intermediate-mass stars. We selected a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we showed that the splittings of both gravity-dominated modes (trapped in central regions) and p-dominated modes (trapped in the envelope) can be measured. We then used these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory (Goupil et al. 2013). We obtained evidence for a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating $1.8\pm0.3$ to $3.2\pm1.0$ times faster than the envelope. The last target was found to be consistent with a solid-body rotation. This demonstrates that an efficient redistribution of angular momentum occurs after the end of the main sequence in the interior of intermediate-mass stars, either during the short-lived subgiant phase, or once He-burning has started in the core. In either case, this should bring constraints on the angular momentum transport mechanisms that are at work.

### A Dynamical Model for the Formation of Gas Rings and Episodic Starbursts Near Galactic Centres

We develop a simple dynamical model for the evolution of gas in the centres of barred spiral galaxies, using the Milky Way’s Central Molecular Zone (CMZ, i.e., the central few hundred pc) as a case study. We show that, in the presence of a galactic bar, gas in a disc in the central regions of a galaxy will be driven inwards by angular momentum transport induced by acoustic instabilities within the bar’s inner Lindblad resonance. This transport process drives turbulence within the gas that temporarily keeps it strongly gravitationally stable and prevents the onset of rapid star formation. However, at some point the rotation curve must transition from approximately flat to approximately solid body, and the resulting reduction in shear reduces the transport rates and causes gas to build up, eventually producing a gravitationally-unstable region that is subject to rapid and violent star formation. For the observed rotation curve of the Milky Way, the accumulation happens $\sim 100$ pc from the centre of the Galaxy, in good agreement with the observed location of gas clouds and young star clusters in the CMZ. The characteristic timescale for gas accumulation and star formation is of order $10-20$ Myr. We argue that similar phenomena should be ubiquitous in other barred spiral galaxies.

### A Dynamical Model for the Formation of Gas Rings and Episodic Starbursts Near Galactic Centres [Replacement]

We develop a simple dynamical model for the evolution of gas in the centres of barred spiral galaxies, using the Milky Way’s Central Molecular Zone (CMZ, i.e., the central few hundred pc) as a case study. We show that, in the presence of a galactic bar, gas in a disc in the central regions of a galaxy will be driven inwards by angular momentum transport induced by acoustic instabilities within the bar’s inner Lindblad resonance. This transport process drives turbulence within the gas that temporarily keeps it strongly gravitationally stable and prevents the onset of rapid star formation. However, at some point the rotation curve must transition from approximately flat to approximately solid body, and the resulting reduction in shear reduces the transport rates and causes gas to build up, eventually producing a gravitationally-unstable region that is subject to rapid and violent star formation. For the observed rotation curve of the Milky Way, the accumulation happens $\sim 100$ pc from the centre of the Galaxy, in good agreement with the observed location of gas clouds and young star clusters in the CMZ. The characteristic timescale for gas accumulation and star formation is of order $10-20$ Myr. We argue that similar phenomena should be ubiquitous in other barred spiral galaxies.

### Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit

Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Unstratified shearing boxes simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. The latter constitutes the largest resolution ever attained for a simulation of MRI turbulence. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that {\beta}, the ratio between the thermal and magnetic pressure, equals 1000, we find {\alpha}~0.032 when Pm approaches zero. In the case of a mean toroidal field for which {\beta}=100, we find {\alpha}~0.018 in the same limit. Both implicit LES and Chollet-Lesieur closure model reproduces these results for the {\alpha} parameter and the power spectra. A reduction in computational cost of a factor at least 16 (and up to 256) is achieved when using such methods. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient mean of investigation of this regime but should be used with care, particularly in the case of a vertical field. Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.

### Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks

It is difficult to understand how cold circumstellar disks accrete onto their central stars. A hydrodynamic mechanism, the vertical shear instability (VSI), offers a means to drive angular momentum transport in cold accretion disks such as protoplanetary disks (PPDs). The VSI is driven by a weak vertical gradient in the disk’s orbital motion. In order to grow, the VSI must overcome vertical buoyancy, a strongly stabilizing influence in cold disks, where heating is dominated by external irradiation. Rapid cooling, via radiative losses, reduces the effective buoyancy and allows the VSI to operate. In this paper, we quantify the cooling timescale, $t_c$, needed for growth of the VSI. We perform a linear analysis of the VSI with cooling in vertically global and radially local disk models. For irradiated disks, we find that the VSI is most vigorous for rapid cooling with $t_c < \Omega_\mathrm{K}^{-1} h |q| / (\gamma -1)$ in terms of the Keplerian orbital frequency, $\Omega_\mathrm{K}$, the disk’s aspect ratio, $h \ll 1$, the radial power-law temperature gradient, $q$, and the adiabatic index, $\gamma$. For longer cooling times, the VSI is much less effective because growth slows and shifts to smaller length scales, which are more prone to viscous or turbulent decay. We apply our results to PPD models where $t_c$ is determined by the opacity of dust grains. We find that the VSI is most effective at intermediate radii, from $\sim 5$AU to $\sim 50$AU with a characteristic growth time of $\sim 30$ local orbital periods. Growth is suppressed by long cooling times both in the opaque inner disk and the optically thin outer disk. A reduction in the dust opacity by a factor of 10 increases cooling times enough to quench the VSI at all disk radii. Thus the formation of solid protoplanets, a sink for dust grains, can impede the VSI.

### Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks [Replacement]

The vertical shear instability (VSI) offers a potential hydrodynamic mechanism for angular momentum transport in protoplanetary disks (PPDs). The VSI is driven by a weak vertical gradient in the disk’s orbital motion, but must overcome vertical buoyancy, a strongly stabilizing influence in cold disks, where heating is dominated by external irradiation. Rapid radiative cooling reduces the effective buoyancy and allows the VSI to operate. We quantify the cooling timescale $t_c$ needed for efficient VSI growth, through a linear analysis of the VSI with cooling in vertically global, radially local disk models. We find the VSI is most vigorous for rapid cooling with $t_c<\Omega_\mathrm{K}^{-1}h|q|/(\gamma -1)$ in terms of the Keplerian orbital frequency, $\Omega_\mathrm{K}$; the disk’s aspect-ratio, $h\ll1$; the radial power-law temperature gradient, $q$; and the adiabatic index, $\gamma$. For longer $t_c$, the VSI is much less effective because growth slows and shifts to smaller length scales, which are more prone to viscous or turbulent decay. We apply our results to PPD models where $t_c$ is determined by the opacity of dust grains. We find that the VSI is most effective at intermediate radii, from $\sim5$AU to $\sim50$AU with a characteristic growth time of $\sim30$ local orbital periods. Growth is suppressed by long cooling times both in the opaque inner disk and the optically thin outer disk. Reducing the dust opacity by a factor of 10 increases cooling times enough to quench the VSI at all disk radii. Thus the formation of solid protoplanets, a sink for dust grains, can impede the VSI.

### Wave mediated angular momentum transport in astrophysical boundary layers

Context. Disk accretion onto weakly magnetized stars leads to the formation of a boundary layer (BL) where the gas loses its excess kinetic energy and settles onto the star. There are still many open questions concerning the BL, for instance the transport of angular momentum (AM) or the vertical structure. Aims. It is the aim of this work to investigate the AM transport in the BL where the magneto-rotational instability (MRI) is not operating owing to the increasing angular velocity $\Omega(r)$ with radius. We will therefore search for an appropriate mechanism and examine its efficiency and implications. Methods. We perform 2D numerical hydrodynamical simulations in a cylindrical coordinate system $(r, \varphi)$ for a thin, vertically inte- grated accretion disk around a young star. We employ a realistic equation of state and include both cooling from the disk surfaces and radiation transport in radial and azimuthal direction. The viscosity in the disk is treated by the {\alpha}-model; in the BL there is no viscosity term included. Results. We find that our setup is unstable to the sonic instability which sets in shortly after the simulations have been started. Acoustic waves are generated and traverse the domain, developing weak shocks in the vicinity of the BL. Furthermore, the system undergoes recurrent outbursts where the activity in the disk increases strongly. The instability and the waves do not die out for over 2000 orbits. Conclusions. There is indeed a purely hydrodynamical mechanism that enables AM transport in the BL. It is efficient and wave mediated; however, this renders it a non-local transport method, which means that models of a effective local viscosity like the {\alpha}-viscosity are probably not applicable in the BL. A variety of further implications of the non-local AM transport are discussed.

### Accretion disc viscosity: a limit on the anisotropy

Observations of warped discs can give insight into the nature of angular momentum transport in accretion discs. Only a few objects are known to show strong periodicity on long timescales, but when such periodicity is present it is often attributed to precession of the accretion disc. The X-ray binary Hercules X-1/HZ Herculis (Her X-1) is one of the best examples of such periodicity and has been linked to disc precession since it was first observed. By using the current best-fitting models to Her X-1, which invoke precession driven by radiation warping, I place a constraint on the effective viscosities that act in a warped disc. These effective viscosities almost certainly arise due to turbulence induced by the magneto-rotational instability. The constraints derived here are in agreement with analytical and numerical investigations into the nature of magneto-hydrodynamic disc turbulence, but at odds with some recent global simulations.

### The spin rate of pre-collapse stellar cores: wave driven angular momentum transport in massive stars

The core rotation rates of massive stars have a substantial impact on the nature of core collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical ($10 \, M_\odot \lesssim M \lesssim 20 \, M_\odot$) supernova progenitors, IGW may substantially spin down the core, leading to iron core rotation periods $P_{\rm min,Fe} \gtrsim 50 \, {\rm s}$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm min,NS} \gtrsim 3 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially longer rotation periods. However, the stochastic influx of AM delivered by IGW during shell burning phases inevitably spin up a slowly rotating stellar core, leading to a maximum possible core rotation period. We estimate maximum iron core rotation periods of $P_{\rm max,Fe} \lesssim 10^4 \, {\rm s}$ in typical core collapse supernova progenitors, and a corresponding spin period of $P_{\rm max, NS} \lesssim 400 \, {\rm ms}$ for newborn neutron stars. This is comparable to the typical birth spin periods of most radio pulsars. Stochastic spin-up via IGW during shell O/Si burning may thus determine the initial rotation rate of most neutron stars. For a given progenitor, this theory predicts a Maxwellian distribution in pre-collapse core rotation frequency that is uncorrelated with the spin of the overlying envelope.

### The spin rate of pre-collapse stellar cores: wave-driven angular momentum transport in massive stars [Replacement]

The core rotation rates of massive stars have a substantial impact on the nature of core-collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical ($10 \, M_\odot \lesssim M \lesssim 20 \, M_\odot$) supernova progenitors, IGW may substantially spin down the core, leading to iron core rotation periods $P_{\rm min,Fe} \gtrsim 30 \, {\rm s}$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm min,NS} \gtrsim 3 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially longer rotation periods. However, the stochastic influx of AM delivered by IGW during shell burning phases inevitably spin up a slowly rotating stellar core, leading to a maximum possible core rotation period. We estimate maximum iron core rotation periods of $P_{\rm max,Fe} \lesssim 5 \times 10^3 \, {\rm s}$ in typical core-collapse supernova progenitors, and a corresponding spin period of $P_{\rm max, NS} \lesssim 500 \, {\rm ms}$ for newborn neutron stars. This is comparable to the typical birth spin periods of most radio pulsars. Stochastic spin-up via IGW during shell O/Si burning may thus determine the initial rotation rate of most neutron stars. For a given progenitor, this theory predicts a Maxwellian distribution in pre-collapse core rotation frequency that is uncorrelated with the spin of the overlying envelope.

### Angular Momentum Transport and Particle Acceleration during Magnetorotational Instability in a Kinetic Accretion Disk

Angular momentum transport and particle acceleration during the magnetorotational instability (MRI) in a collisionless accretion disk are investigated using three-dimensional particle-in-cell (PIC) simulation. We show that the kinetic MRI can provide not only high energy particle acceleration but also enhancement of angular momentum transport. We find that the plasma pressure anisotropy inside the channel flow with $p_{\|} > p_{\perp}$ induced by active magnetic reconnection suppresses the onset of subsequent reconnection, which in turn leads to high magnetic field saturation and enhancement of Maxwell stress tensor of angular momentum transport. Meanwhile, during the quiescent stage of reconnection the plasma isotropization progresses in the channel flow, and the anisotropic plasma with $p_{\perp} > p_{\|}$ due to the dynamo action of MRI outside the channel flow contributes to rapid reconnection and strong particle acceleration. This efficient particle acceleration and enhanced angular momentum transport in a collisionless accretion disk may explain the origin of high energy particles observed around massive black holes.

### Radiation Magnetohydrodynamic Simulations of Protostellar Collapse: Non-Ideal Magnetohydrodynamic Effects and Early Formation of Circumstellar Disks

The transport of angular momentum by magnetic fields is a crucial physical process in formation and evolution of stars and disks. Because the ionization degree in star forming clouds is extremely low, non-ideal magnetohydrodynamic (MHD) effects such as ambipolar diffusion and Ohmic dissipation work strongly during protostellar collapse. These effects have significant impacts in the early phase of star formation as they redistribute magnetic flux and suppress angular momentum transport by magnetic fields. We perform three-dimensional nested-grid radiation magnetohydrodynamic (RMHD) simulations including Ohmic dissipation and ambipolar diffusion. Without these effects, magnetic fields transport angular momentum so efficiently that no rotationally supported disk is formed even after the second collapse. Ohmic dissipation works only in a relatively high density region within the first core and suppresses angular momentum transport, enabling formation of a very small rotationally supported disk after the second collapse. With both Ohmic dissipation and ambipolar diffusion, these effects work effectively in almost the entire region within the first core and significant magnetic flux loss occurs. As a result, a rotationally supported disk is formed even before a protostellar core forms. The size of the disk is still small, about 5 AU at the end of the first core phase, but this disk will grow later as gas accretion continues. Thus the non-ideal MHD effects can resolve the so-called magnetic braking catastrophe while maintaining the disk size small in the early phase, which is implied from recent interferometric observations.

### Type I Planet Migration in a Magnetized Disk. II. Effect of Vertical Angular Momentum Transport

We study the effects of a large-scale, ordered magnetic field in protoplanetary disks on Type I planet migration using a linear perturbation analysis in the ideal-MHD limit. We focus on wind-driving disks, in which a magnetic torque $\propto B_{0z} \partial B_{0\varphi}/\partial z$ (where $B_{0z}$ and $B_{0\varphi}$ are the equilibrium vertical and azimuthal field components) induces vertical angular momentum transport. We derive the governing differential equation for the disk response and identify its resonances and turning points. For a disk containing a slightly subthermal, pure-$B_{0z}$ field, the total 3D torque is close to its value in the 2D limit but remains lower than the hydrodynamic torque. In contrast with the 2D pure-$B_{0\varphi}$ field model considered by Terquem (2003), inward migration is not reduced in this case when the field amplitude decreases with radius. The presence of a subdominant $B_{0\varphi}$ component whose amplitude increases from zero at $z=0$ has little effect on the torque when acting alone, but in conjunction with a $B_{0z}$ component it gives rise to a strong torque that speeds up the inward migration by a factor $\gtrsim 200$. This factor could, however, be reduced in a real disk by dissipation and magnetic diffusivity effects. Unlike all previously studied disk migration models, in the $B_{0z}+\partial B_{0\varphi}/\partial z$ case the dominant contributions to the torque add with the same sign from the two sides of the planet. We attribute this behavior to a new mode of interaction wherein a planet moves inward by plugging into the disk’s underlying angular momentum transport mechanism.

### Effects of Turbulent Viscosity on A Rotating Gas Ring Around A Black Hole: The Density Profile of Numerical Simulation

In this paper, we present the time evolution of a rotationally axisymmetric gas ring around a non rotating black hole using two dimensional grid-based hydrodynamic simulation. We show the way in which angular momentum transport is included in simulations of non-self-gravitating accretion of matter towards a black hole. We use the Shakura-Sunyaev {\alpha} viscosity prescription to estimate the turbulent viscosity. We investigate how a gas ring which is initially assumed to rotate with Keplerian angular velocity is accreted on to a back hole and hence forms accretion disc in the presence of turbulent viscosity. Furthermore, we also show that increase of the {\alpha} coefficient increases the rate of advection of matter towards the black hole. The density profile we obtain is in good quantitative agreement with that obtained from the analytical results. The dynamics of resulting angular momentum depends strongly on {\alpha}.

### Motivation and challenge to capture both large scale and local transport in next generation accretion theory [Replacement]

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate insight gained from simulations back into improving practical models for comparison with observations. Here we emphasize the need to incorporate the role of non-local transport more precisely. To show where large scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura-Sunyaev (1973,SS73) is necessarily a mean field theory, and one which does not include large scale transport. Observations of coronae and jets combined with the interpretation of results even from shearing box simulations of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large scale contributions and the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRi as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona, and outflow contributions. Finally, we note that any mean field theory has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

### Motivation and challenge to capture both large scale and local transport in next generation accretion theory [Replacement]

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate insight gained from simulations back into improving practical models for comparison with observations. Here we emphasize the need to incorporate the role of non-local transport more precisely. To show where large scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura-Sunyaev (1973,SS73) is necessarily a mean field theory, and one which does not include large scale transport. Observations of coronae and jets combined with the interpretation of results even from shearing box simulations of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large scale contributions and the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI such that it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona, and outflow contributions. Finally, we note that any mean field theory has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

### Some challenges and directions for next generation accretion disc theory

Accretion disc theory is far less developed than that of stellar evolution, although a similarly mature phenomenological picture is ultimately desired. While conceptual progress from the interplay of theory and numerical simulations has amplified awareness of the role of magnetic fields in angular momentum transport, there remains a significant gap between the output of magneto-rotational instability (MRI) simulations and the synthesis of lessons learned into improved practical models. If discs are turbulent, then axisymmetric models must be recognized to be sensible only as mean field theories. Such is the case for the wonderfully practical and widely used framework of Shakura-Sunyaev (SS73). This model is most justifiable when the radial angular momentum transport dominates in discs and the transport is assumed to take the form of a local viscosity. However, the importance of large scale fields in coronae and jets and numerical evidence from MRI simulations points to a significant fraction of transport being non-local. We first review how the SS73 viscous closure emerges from a mean field theory and then discuss the reasons the theory must be augmented to include large scale transport. We discuss a number of open opportunities for theory and interpretation of numerical simulations, with the ultimate challenge being a mean field accretion theory that also couples to large scale dynamo theory and self-consistently produces coronae and jets. While there has elsewhere been well-deserved focus toward small scale collisionless plasma processes in the context of transport in low density accretion discs, here we emphasize the importance of large scales as a fundamental frontier. Computational limitations have focused attention toward smaller scales when it comes to transport but hopefully the next generation of global simulations can help inform mean field models.

### Zombie Vortex Instability I: A Purely Hydrodynamic Instability to Resurrect the Dead Zones of Protoplanetary Disks [Replacement]

There is considerable interest in hydrodynamic instabilities in dead zones of protoplanetary disks as a mechanism for driving angular momentum transport and as a source of particle-trapping vortices to mix chondrules and incubate planetesimal formation. We present simulations with a pseudo-spectral anelastic code and with the compressible code Athena, showing that stably stratified flows in a shearing, rotating box are violently unstable and produce space-filling, sustained turbulence dominated by large vortices with Rossby numbers of order 0.2-0.3. This Zombie Vortex Instability (ZVI) is observed in both codes and is triggered by Kolmogorov turbulence with Mach numbers less than 0.01. It is a common view that if a given constant density flow is stable, then stable vertical stratification should make the flow even more stable. Yet, we show that sufficient vertical stratification can be unstable to ZVI. ZVI is robust and requires no special tuning of boundary conditions, or initial radial entropy or vortensity gradients (though we have studied ZVI only in the limit of infinite cooling time). The resolution of this paradox is that stable stratification allows for a new avenue to instability: baroclinic critical layers. ZVI has not been seen in previous studies of flows in rotating, shearing boxes because those calculations frequently lacked vertical density stratification and/or sufficient numerical resolution. Although we do not expect appreciable angular momentum transport from ZVI in the small domains in this study, we hypothesize that ZVI in larger domains with compressible equations may lead to angular transport via spiral density waves.

### Zombie Vortex Instability I: The "Dead" Zones of Protoplanetary Disks are Not Dead

There has been considerable interest in purely hydrodynamic instabilities in the dead zones of protoplanetary disks (PPDs) as a mechanism for driving angular momentum transport and as a source of vortices to incubate planetesimal formation. We present a series of numerical simulations with both a pseudo-spectral anelastic code and the fully compressible Godunov finite-volume code Athena, showing that stably stratified flows in a shearing, rotating box are violently unstable and produce space-filling, sustained turbulence dominated by large vortices with Rossby numbers of order 0.2-0.3. This Zombie Vortex Instability (ZVI) is observed in both codes and is triggered by initial Kolmogorov turbulence with Mach numbers less than 0.01. ZVI is robust and requires no special tuning of cooling times, boundary conditions, or initial radial entropy or vortensity gradients. ZVI has not been seen in previous studies of flows in a rotating, shearing box because those calculations frequently lacked vertical density stratification and/or sufficient numerical resolution. Although we do not observe appreciable angular momentum transport from ZVI in small domains, we hypothesize that ZVI in larger domains with the fully compressible equations may lead to significant angular transport via spiral density waves launched by vortices. In a companion paper, we derive the instability criterion for ZVI; although ZVI is a subcritical instability, rather than a linear one, we show that initial Kolmogorov noise with Mach number no greater than 10^{-6} will trigger ZVI.

### Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.

### Vertical shear instability in accretion disc models with radiation transport

The origin of turbulence in accretion discs is still not fully understood. While the magneto-rotational instability is considered to operate in sufficiently ionized discs, its role in the poorly ionized protoplanetary disc is questionable. Recently, the vertical shear instability (VSI) has been suggested as a possible alternative. Our goal is to study the characteristics of this instability and the efficiency of angular momentum transport, in extended discs, under the influence of radiative transport and irradiation from the central star. We use multi-dimensional hydrodynamic simulations to model a larger section of an accretion disc. First we study inviscid and weakly viscous discs using a fixed radial temperature profile in two and three spatial dimensions. The simulations are then extended to include radiative transport and irradiation from the central star. In agreement with previous studies we find for the isothermal disc a sustained unstable state with a weak positive angular momentum transport of the order of $\alpha \approx 10^{-4}$. Under the inclusion of radiative transport the disc cools off and the turbulence terminates. For discs irradiated from the central star we find again a persistent instability with a similar $\alpha$ value as for the isothermal case. We find that the VSI can indeed generate sustained turbulence in discs albeit at a relatively low level with $\alpha$ about few times $10^{-4}$

### Angular Momentum Transport via Internal Gravity Waves in Evolving Stars

Recent asteroseismic advances have allowed for direct measurements of the internal rotation rates of many sub-giant and red giant stars. Unlike the nearly rigidly rotating Sun, these evolved stars contain radiative cores that spin faster than their overlying convective envelopes, but slower than they would in the absence of internal angular momentum transport. We investigate the role of internal gravity waves in angular momentum transport in evolving low mass stars. In agreement with previous results, we find that convectively excited gravity waves can prevent the development of strong differential rotation in the radiative cores of Sun-like stars. As stars evolve into sub-giants, however, low frequency gravity waves become strongly attenuated and cannot propagate below the hydrogen burning shell, allowing the spin of the core to decouple from the convective envelope. This decoupling occurs at the base of the sub-giant branch when stars have surface temperatures of roughly 5500 K. However, gravity waves can still spin down the upper radiative region, implying that the observed differential rotation is likely confined to the deep core near the hydrogen burning shell. The torque on the upper radiative region may also prevent the core from accreting high-angular momentum material and slow the rate of core spin-up. The observed spin-down of cores on the red giant branch cannot be totally attributed to gravity waves, but the waves may enhance shear within the radiative region and thus increase the efficacy of viscous/magnetic torques.

### Statistical simulation of the magnetorotational dynamo [Replacement]

Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasi-linear statistical simulation methods. It is found that homogenous turbulence is unstable to a large scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasi-linear model is qualitatively similar to that of nonlinear MRI turbulence. This indicates that recent convergence problems may be related to large scale dynamo and suggests how dramatically simplified models may be used to gain insight into the astrophysically relevant regimes of very low or high Pm.

### Angular momentum transport and evolution of lopsided galaxies

The surface brightness distribution in the majority of stellar galactic discs falls off exponentially. Often what lies beyond such a stellar disc is the neutral hydrogen gas whose distribution also follows a nearly exponential profile at least for a number of nearby disc galaxies. Both the stars and gas are commonly known to host lopsided asymmetry especially in the outer parts of a galaxy. The role of such asymmetry in the dynamical evolution of a galaxy has not been explored so far. Following Lindblad’s original idea of kinematic density waves, we show that the outer part of an exponential disc is ideally suitable for hosting lopsided asymmetry. Further, we compute the transport of angular momentum in the combined stars and gas disc embedded in a dark matter halo. We show that in a pure star and gas disc, there is a transition point where the free precession frequency of a lopsided mode, $\Omega -\kappa$, changes from retrograde to prograde and this in turn reverses the direction of angular momentum flow in the disc leading to an unphysical behaviour. We show that this problem is overcome in the presence of a dark matter halo, which sets the angular momentum flow outwards as required for disc evolution, provided the lopsidedness is leading in nature. This, plus the well-known angular momentum transport in the inner parts due to spiral arms, can facilitate an inflow of gas from outside perhaps through the cosmic filaments.

### Asymmetric evolution of magnetic reconnection in collisionless accretion disk

An evolution of a magnetic reconnection in a collisionless accretion disk is investigated using a 2.5 dimensional hybrid code simulation. In astrophysical disks, magnetorotational instability (MRI) is considered to play an important role by generating turbulence in the disk and contributes to an effective angular momentum transport through a turbulent viscosity. Magnetic reconnection, on the other hand, also plays an important role on the evolution of the disk through a dissipation of a magnetic field enhanced by a dynamo effect of MRI. In this study, we developed a hybrid code to calculate an evolution of a differentially rotating system. With this code, we first confirmed a linear growth of MRI. We also investigated a behavior of a particular structure of a current sheet, which would exist in the turbulence in the disk. From the calculation of the magnetic reconnection, we found an asymmetric structure in the out-of-plane magnetic field during the evolution of reconnection, which can be understood by a coupling of the Hall effect and the differential rotation. We also found a migration of X-point whose direction is determined only by an initial sign of J_0 \times \Omega_0, where J_0 is the initial current density in the neutral sheet and \Omega_0 is the rotational vector of the background Keplerian rotation. Associated with the migration of X-point, we also found a significant enhancement of the perpendicular magnetic field compared to an ordinary MRI. MRI-Magnetic reconnection coupling and the resulting magnetic field enhancement can be an effective process to sustain a strong turbulence in the accretion disk and to a transport of angular momentum.

### Differential rotation in main-sequence solar-like stars: Qualitative inference from asteroseismic data [Replacement]

Understanding differential rotation of Sun-like stars is of great importance for insight into the angular momentum transport in these stars. One means of gaining such information is that of asteroseismology. By a forward modeling approach we analyze in a qualitative manner the impact of different differential rotation profiles on the splittings of p-mode oscillation frequencies. The optimum modes for inference on differential rotation are identified along with the best value of the stellar inclination angle. We find that in general it is not likely that asteroseismology can be used to make an unambiguous distinction between a rotation profile such as, e.g., a conical Sun-like profile and a cylindrical profile. In addition, it seems unlikely that asteroseismology of Sun-like stars will result in inferences on the radial profile of the differential rotation, such as can be done for, e.g., red giants. At best one could possibly obtain the sign of the radial differential rotation gradient. Measurements of the extent of the latitudinal differential from frequency splitting are, however, more promising. One very interesting aspect that could likely be tested from frequency splittings is whether the differential rotation is solar-like or anti-solar-like in nature, in the sense that a solar-like profile has an equator rotating faster than the poles.

### Differential rotation in main-sequence solar-like stars: Qualitative inference from asteroseismic data [Replacement]

Understanding differential rotation of Sun-like stars is of great importance for insight into the angular momentum transport in these stars. One means of gaining such information is that of asteroseismology. By a forward modeling approach we analyze in a qualitative manner the impact of different differential rotation profiles on the splittings of p-mode oscillation frequencies. The optimum modes for inference on differential rotation are identified along with the best value of the stellar inclination angle. We find that in general it is not likely that asteroseismology can be used to make an unambiguous distinction between a rotation profile such as, e.g., a conical Sun-like profile and a cylindrical profile. In addition, it seems unlikely that asteroseismology of Sun-like stars will result in inferences on the radial profile of the differential rotation, such as can be done for, e.g., red giants. At best one could possibly obtain the sign of the radial differential rotation gradient. Measurements of the extent of the latitudinal differential from frequency splitting are, however, more promising. One very interesting aspect that could likely be tested from frequency splittings is whether the differential rotation is solar-like or anti-solar-like in nature, in the sense that a solar-like profile has an equator rotating faster than the poles.

### Differential rotation in main-sequence solar-like stars --- Qualitative inference from asteroseismic data ---

Understanding differential rotation of sun-like stars is of great importance for insight into the angular momentum transport in these stars. One means of gaining such information is that of asteroseismology. By a forward modeling approach we analyze in a qualitative manner the impact of different differential rotation profiles on the splittings of p-mode oscillation frequencies. The optimum modes for inference on differential rotation are identified along with the best value of the stellar inclination angle. We find that in general it is not likely that asteroseismology can be used to make an unambiguous distinction between a rotation profile such as, e.g., a conical sun-like profile and a cylindrical profile. In addition, it seems unlikely that asteroseismolgy of sun-like stars will result in inferences on the radial profile of the differential rotation, such as can be done for e.g. red giants. At best one could possibly obtain the sign of the radial differential rotation gradient. Measurements of the extent of the latitudinal differential from frequency splitting are, however, more promising. One very interesting aspect that could likely be tested from frequency splittings is whether the differential rotation is solar-like or anti-solar-like in nature, in the sense that a solar-like profile has an equator rotating faster than the poles.

### Snow-lines as probes of turbulent diffusion in protoplanetary discs

Sharp chemical discontinuities can occur in protoplanetary discs, particularly at snow-lines’ where a gas-phase species freezes out to form ice grains. Such sharp discontinuities will diffuse out due to the turbulence suspected to drive angular momentum transport in accretion discs. We demonstrate that the concentration gradient – in the vicinity of the snow-line – of a species present outside a snow-line but destroyed inside is strongly sensitive to the level of turbulent diffusion (provided the chemical and transport time-scales are decoupled) and provides a direct measurement of the radial Schmidt number’ (the ratio of the angular momentum transport to radial turbulent diffusion). Taking as an example the tracer species N$_2$H$^+$, which is expected to be destroyed inside the CO snow-line (as recently observed in TW Hya) we show that ALMA observations possess significant angular resolution to constrain the Schmidt number. Since different turbulent driving mechanisms predict different Schmidt numbers, a direct measurement of the Schmidt number in accretion discs would allow inferences about the nature of the turbulence to be made.

### VADER: A Flexible, Robust, Open-Source Code for Simulating Viscous Thin Accretion Disks [Replacement]

The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While models based on this simplified geometry provide only approximations to the true processes of instability-driven mass and angular momentum transport, their simplicity makes them invaluable tools for both semi-analytic modeling and simulations of long-term evolution where two- or three-dimensional calculations are too computationally costly. Despite the utility of these models, the only publicly-available frameworks for simulating them are rather specialized and non-general. Here we describe a highly flexible, general numerical method for simulating viscous thin disks with arbitrary rotation curves, viscosities, boundary conditions, grid spacings, equations of state, and rates of gain or loss of mass (e.g., through winds) and energy (e.g., through radiation). Our method is based on a conservative, finite-volume, second-order accurate discretization of the equations, which we solve using an unconditionally-stable implicit scheme. We implement Anderson acceleration to speed convergence of the scheme, and show that this leads to factor of $\sim 5$ speed gains over non-accelerated methods in realistic problems, though the amount of speedup is highly problem-dependent. We have implemented our method in the new code Viscous Accretion Disk Evolution Resource (VADER), which is freely available for download from https://bitbucket.org/krumholz/vader/ under the terms of the GNU General Public License.

### VADER: A Flexible, Robust, Open-Source Code for Simulating Viscous Thin Accretion Disks

The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While such models provide only approximations to the true processes of instability-driven mass and angular momentum transport, their simplicity makes them invaluable tools for both semi-analytic modeling and simulations of long-term evolution where two- or three-dimensional calculations are too computationally costly. Despite the utility of these models, there is no publicly-available framework for simulating them. Here we describe a highly flexible, general numerical method for simulating viscous thin disks with arbitrary rotation curves, viscosities, boundary conditions, grid spacings, equations of state, and rates of gain or loss of mass (e.g., through winds) and energy (e.g., through radiation). Our method is based on a conservative, finite-volume, second-order accurate discretization of the equations, which we solve using an unconditionally-stable implicit scheme. We implement Anderson acceleration to speed convergence of the scheme, and show that this leads to factor of ~5 speed gains over non-accelerated methods in realistic problems. We have implemented our method in the new code Viscous Accretion Disk Evolution Resource (VADER), which is freely available for download from https://bitbucket.org/krumholz/vader/ under the terms of the GNU General Public License.

### Dynamical Tides in Compact White Dwarf Binaries: Influence of Rotation

Tidal interactions play an important role in the evolution and ultimate fate of compact white dwarf (WD) binaries. Not only do tides affect the pre-merger state (such as temperature and rotation rate) of the WDs, but they may also determine which systems merge and which undergo stable mass transfer. In this paper, we attempt to quantify the effects of rotation on tidal angular momentum transport in binary stars, with specific calculations applied to WD stellar models. We incorporate the effect of rotation using the traditional approximation, in which the dynamically excited gravity waves within the WDs are transformed into gravito-inertial Hough waves. The Coriolis force has only a minor effect on prograde gravity waves, and previous results predicting the tidal spin-up and heating of inspiraling WDs are not significantly modified. However, rotation strongly alters retrograde gravity waves and inertial waves, with important consequences for the tidal spin-down of accreting WDs. We identify new dynamical tidal forcing terms that arise from a proper separation of the equilibrium and dynamical tide components; these new forcing terms are very important for systems near synchronous rotation. Additionally, we discuss the impact of Stokes drift currents on the wave angular momentum flux. Finally, we speculate on how tidal interactions will affect super-synchronously rotating WDs in accreting systems.

### The Driving of Decretion by Maxwell Stress in Disks

Radial magnetic fields that resist orbital shear can explain the outwards angular momentum transport required for accretion in non-self-gravitating disks. This generates azimuthal magnetic fields and thus Maxwell stresses that transfer angular momentum radially. Variations on this idea include both the magnetorotational instability and disk winds. We demonstrate here that these transport mechanisms generate dynamically significant radial Poynting flux, so they are inherently not local. Simulations treating this problem typically use either the shear-periodic, shearing sheet approximation, or disk annuli with artificial radial boundary conditions. Spurious energy flows through these boundaries generally control the magnitude and even the sign of angular momentum transport. We then demonstrate that, when dominated by radial stresses, shearing sheets must decrete, as must self-similar regions of disks with power-law variations in physical quantities. Only the innermost edge of the disk, where magnetic energy increases with radius, can actually accrete. The transition radius between accretion and decretion varies vertically, resulting in a decreting midplane layer and accreting surface layers, similar to a viscous meridional circulation, except that here the power provided to the midplane outflow is transported radially, rather than vertically. Energy from the thin region deep in the potential well can drive decretion throughout the remainder of the disk. The short orbital time at the outer edge of this accretion region determines the viscous timescale, suggesting that disks are inherently unsteady. Among other implications, the decretion that we find may transport high-temperature minerals outwards in disks, explaining their presence in comet dust.

### Angular momentum transport within evolved low-mass stars

Asteroseismology of 1.0-2.0 Msun red giants by the Kepler satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the Helium burning clump. The inferred rotation rates are 10-30 days for the ~0.2Msun He degenerate cores on the RGB and 30-100 days for the He burning core in a clump star. Using the MESA code we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, to explicitly highlight this shortfall when applied to a specific Kepler asteroseismic target, KIC8366239. The MESA inlist adopted to calculate the models in this paper can be found at \url{https://authorea.com/1608/} (bottom of the document).

### Angular momentum transport by stochastically excited oscillations in rapidly rotating massive stars

We estimate the amount of angular momentum transferred by the low-frequency oscillations detected in the rapidly rotating hot Be star HD 51452. Here, we assume that the oscillations detected are stochastically excited by convective motions in the convective core of the star, that is, we treat the oscillations as forced oscillations excited by the periodic convective motions of the core fluids having the frequencies observationally determined. With the observational amplitudes of the photometric variations, we determine the oscillation amplitudes, which makes it possible to estimate the net amount of angular momentum transferred by the oscillations using the wave-meanflow interaction theory. Since we do not have any information concerning the azimuthal wavenumber $m$ and spherical harmonic degree $l$ for each of the oscillations, we assume that all the frequencies detected are prograde or retrograde in the observer’s frame and they are all associated with a single value of $m$ both for even modes ($l=|m|$) and for odd modes ($l=|m|+1$). We estimate the amount of angular momentum transferred by the oscillations for $|m|=1$ and 2, which are typical $|m|$ values for Be stars, and find that the amount is large enough for a decretion disc to form around the star. Therefore, transport of angular momentum by waves stochastically excited in the core of Be stars might be responsible for the Be phenomenon.

### The angular momentum transport by unstable toroidal magnetic fields

We demonstrate with a nonlinear MHD code that angular momentum can be transported due to the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. The fields are assumed strong enough and the density stratification weak enough that the influence of the ‘negative’ buoyancy in the radiative zones can be neglected. Only permanent current-free fields and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity are considered. We find that the dimensionless ratio of the turbulent over molecular viscosity, \nu_T/\nu, linearly grows with growing magnetic Reynolds number of the rotating fluid multiplied by the square root of the magnetic Prandtl number – which is of order unity for the considered red subgiant KIC 7341231, in contrast to the smaller values of the solar radiative interior. The outward angular momentum transport is thus stronger for hot and fast rotators than for solar-type stars. For the considered interval of magnetic Reynolds numbers – which is restricted by numerical constraints of the nonlinear MHD code – there is a remarkable influence of the magnetic Prandtl number on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm > 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e. the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core, as the viscosity is reduced when the rotation law becomes flat.

### The angular momentum transport by unstable toroidal magnetic fields [Replacement]

We demonstrate with a nonlinear MHD code that angular momentum can be transported due to the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. Only stationary current-free fields and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity are considered. We find that the dimensionless ratio of the effective over molecular viscosity, $\nu_T/\nu$;, linearly grows with the Reynolds number of the rotating fluid multiplied with the square-root of the magnetic Prandtl number – which is of order unity for the considered red sub-giant KIC 7341231. For the considered interval of magnetic Reynolds numbers – which is restricted by numerical constraints of the nonlinear MHD code – there is a remarkable influence of the magnetic Prandtl number on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm $\gtrsim$ 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e. the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core.

### Magnetic diffusivity and angular momentum transport in magnetized and differentially rotating stellar radiation zones

With a linear theory the instability of a toroidal background field system with dipolar parity for inner stellar radiative zones under the presence of density stratification, differential rotation and for realistically small Prandtl numbers is analyzed. The physical parameters are the normalized latitudinal shear $a$ and the normalized field amplitude $b \simeq \Omega_A/\Omega$. Only the solutions for the wavelengths with the maximal growth rates are considered. If these scales are combined to the radial values of velocity one finds that for $b \gsim 0.1$ the (very small) radial velocity does only slightly depend on $a$ and $b$ so that it can be used as the free parameter of the eigenvalue system. The resulting instability-generated tensors of magnetic diffusivity and eddy viscosity are highly anisotropic. The eddy diffusivity in latitudinal direction exceeds the eddy diffusivity in radial direction by orders of magnitude. Its latitudinal profile shows a strong concentration to the poles and (for rigid rotation) a numerical value of $10^{12}$ cm$^2$/s. On the other hand, the instability pattern transports angular momentum equatorward even for rigid rotation producing a slightly faster rotation of the equator of the radiative zone. The resulting effective magnetic Prandtl number reaches values of $O(10^3)$ so that differential rotation decays much faster than the toroidal background field which is {\em the} necessary condition to explain the observed slow rotation of the early red-giant and subgiant cores by means of magnetic instabilities.

### Global simulations of magnetorotational turbulence III: influence of field configuration and mass injection

The stresses produced by magnetorotational turbulence can provide effective angular momentum transport in accretion disks. However, questions remain about the ability of simulated disks to reproduce observationally inferred stress-to-gas-pressure ratios. In this paper we present a set of high resolution global magnetohydrodynamic disk simulations which are initialised with different field configurations: purely toroidal, vertical field lines, and nested poloidal loops. A mass source term is included which allows the total disk mass to equilibrate in simulations with long run times, and also enables the impact of rapid mass injection to be explored. Notably different levels of angular momentum transport are observed during the early-time transient disk evolution. However, given sufficient time to relax, the different models evolve to a statistically similar quasi-steady state with a stress-to-gas-pressure ratio, $\alpha \sim 0.032-0.036$. The indication from our results is that {\it steady, isolated} disks may be unable to maintain a large-scale magnetic field or produce values for the stress-to-gas-pressure ratio implied by some observations. Supplementary simulations exploring the influence of trapping magnetic field, injecting vertical field, and rapidly injecting additional mass into the disk show that large stresses ($\alpha \sim 0.1-0.25$) can be induced by these mechanisms. The simulations highlight the common late-time evolution and characteristics of turbulent disks for which the magnetic field is allowed to evolve freely. If the boundaries of the disk, the rate of injection of magnetic field, or the rate of mass replenishment are modified to mimic astrophysical disks, markedly different disk evolution occurs.

### On characterizing nonlocality and anisotropy for the magnetorotational instability [Replacement]

The extent to which angular momentum transport in accretion discs is primarily local or non-local and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyze simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona where the disc is the MRI unstable region and corona is the magnetically dominated region. We calculate the fractional power in different quantities, including magnetic energy and Maxwell stresses and find that they are dominated by contributions from the lowest wave numbers. This is even more dramatic for the corona than the disc, suggesting that transport in the corona region is dominated by larger structures than the disc. By calculating averaged power spectra in one direction of $k$ space at a time, we also show that the MRI turbulence is strongly anisotropic on large scales when analyzed by this method, but isotropic on small scales. Although the shearing box itself is meant to represent a local section of an accretion disc, the fact that the stress and energy are dominated by the largest scales highlights that the locality is not captured within the box. This helps to quantify the intuitive importance of global simulations for addressing the question of locality of transport, for which similar analyses can be performed.

### On characterizing nonlocality and anisotropy in magnetorotational instability

The extent to which angular momentum transport in accretion discs is primarily local or non-local and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyze simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona where the disc is the MRI unstable region and corona is the magnetically dominated region. We calculate the fractional power in different quantities, including magnetic energy and Maxwell stresses and find that they are dominated by contributions from the lowest wave numbers. This is even more dramatic for the corona than the disc, suggesting that transport in the corona region is dominated by larger structures than the disc. By calculating averaged power spectra in one direction of $k$ space at a time, we also show that the MRI turbulence is strongly anisotropic on large scales when analyzed by this method, but isotropic on small scales. Although the shearing box itself is meant to represent a local section of an accretion disc, the fact that the stress and energy are dominated by the largest scales highlights that the locality is not captured within the box. This helps to quantify the intuitive importance of global simulations for addressing the question of locality of transport, for which similar analyses can be performed.

### Theoretical seismology in 3D : nonlinear simulations of internal gravity waves in solar-like stars

Internal gravity waves (hereafter IGWs) are studied for their impact on the angular momentum transport in stellar radiation zones and the information they provide about the structure and dynamics of deep stellar interiors. We here present the first 3D nonlinear numerical simulations of IGWs excitation and propagation in a solar-like star. The aim is to study the behavior of waves in a realistic 3D nonlinear time dependent model of the Sun and to characterize their properties. We compare our results with theoretical and 1D predictions. It allows us to point out the complementarity between theory and simulation and to highlight the convenience but also the limits of the asymptotic and linear theories. We show that a rich spectrum of IGWs is excited by the convection, representing about 0.4\% of the total solar luminosity. We study the spatial and temporal properties of this spectrum, the effect of thermal damping and nonlinear interactions between waves. We give quantitative results about the modes frequencies, evolution with time and rotational splitting and we discuss the amplitude of IGWs considering different regimes of parameters. This work points out the importance of high performance simulation for its complementarity with observation and theory. It opens a large field of investigation concerning IGWs propagating nonlinearly in 3D spherical structures. The extension of this work to other types of stars, with different masses, structures and rotation rates will lead to a deeper and more accurate comprehension of IGWs in stars.

### Theoretical seismology in 3D : nonlinear simulations of internal gravity waves in solar-like stars [Replacement]

Internal gravity waves (hereafter IGWs) are studied for their impact on the angular momentum transport in stellar radiation zones and the information they provide about the structure and dynamics of deep stellar interiors. We here present the first 3D nonlinear numerical simulations of IGWs excitation and propagation in a solar-like star. The aim is to study the behavior of waves in a realistic 3D nonlinear time dependent model of the Sun and to characterize their properties. We compare our results with theoretical and 1D predictions. It allows us to point out the complementarity between theory and simulation and to highlight the convenience but also the limits of the asymptotic and linear theories. We show that a rich spectrum of IGWs is excited by the convection, representing about 0.4% of the total solar luminosity. We study the spatial and temporal properties of this spectrum, the effect of thermal damping and nonlinear interactions between waves. We give quantitative results about the modes frequencies, evolution with time and rotational splitting and we discuss the amplitude of IGWs considering different regimes of parameters. This work points out the importance of high performance simulation for its complementarity with observation and theory. It opens a large field of investigation concerning IGWs propagating nonlinearly in 3D spherical structures. The extension of this work to other types of stars, with different masses, structures and rotation rates will lead to a deeper and more accurate comprehension of IGWs in stars.

### On the Viability of the Magnetorotational Instability in Circumplanetary Disks

We examine whether the magnetorotational instability (MRI) can serve as a mechanism of angular momentum transport in circumplanetary disks. For the MRI to operate the ionization degree must be sufficiently high and the magnetic pressure must be sufficiently lower than the gas pressure. We calculate the spatial distribution of the ionization degree and search for the MRI-active region where the two criteria are met. We find that there can be thin active layers at the disk surface depending on the model parameters, however, we find hardly any region which can sustain well-developed MRI turbulence; when the magnetic field is enhanced by MRI turbulence at the disk surface layer, a magnetically dominated atmosphere encroaches on a lower altitude and a region of well-developed MRI turbulence becomes smaller. We conclude that if there are no angular momentum transfer mechanisms other than MRI in gravitationally stable circumplanetary disks, gas is likely to pile up until disks become gravitationally unstable, and massive disks may survive for a long time.

### On the Viability of the Magnetorotational Instability in Circumplanetary Disks [Replacement]

We examine whether the magnetorotational instability (MRI) can serve as a mechanism of angular momentum transport in circumplanetary disks. For the MRI to operate the ionization degree must be sufficiently high and the magnetic pressure must be sufficiently lower than the gas pressure. We calculate the spatial distribution of the ionization degree and search for the MRI-active region where the two criteria are met. We find that there can be thin active layers at the disk surface depending on the model parameters, however, we find hardly any region which can sustain well-developed MRI turbulence; when the magnetic field is enhanced by MRI turbulence at the disk surface layer, a magnetically dominated atmosphere encroaches on a lower altitude and a region of well-developed MRI turbulence becomes smaller. We conclude that if there are no angular momentum transfer mechanisms other than MRI in gravitationally stable circumplanetary disks, gas is likely to pile up until disks become gravitationally unstable, and massive disks may survive for a long time.

### The fate of fallback matter around newly born compact objects

The presence of fallback disks around young neutron stars has been invoked over the years to explain a large variety of phenomena. Here we perform a numerical investigation of the formation of such disks during a supernova explosion, considering both neutron star (NS) and black hole (BH) remnants. Using the public code MESA, we compute the angular momentum distribution of the pre-supernova material, for stars with initial masses M in the range 13 – 40 Msun, initial surface rotational velocities vsurf between 25% and 75% of the critical velocity, and for metallicities Z of 1%, 10% and 100% of the solar value. These pre SN models are exploded with energies E varying between 10^{50} – 3×10^{52} ergs, and the amount of fallback material is computed. We find that, if magnetic torques play an important role in angular momentum transport, then fallback disks around NSs, even for low-metallicity main sequence stars, are not an outcome of SN explosions. Formation of such disks around young NSs can only happen under the condition of negligible magnetic torques and a fine-tuned explosion energy. For those stars which leave behind BH remnants, disk formation is ubiquitous if magnetic fields do not play a strong role; however, unlike the NS case, even with strong magnetic coupling in the interior, a disk can form in a large region of the {Z,M,vsurf,E} parameter space. Together with the compact, hyperaccreting fallback disks widely discussed in the literature, we identify regions in the above parameter space which lead to extended, long-lived disks around BHs. We find that the physical conditions in these disks may be conducive to planet formation, hence leading to the possible existence of planets orbiting black holes.

### Angular momentum evolution of young low-mass stars and brown dwarfs: observations and theory

This chapter aims at providing the most complete review of both the emerging concepts and the latest observational results regarding the angular momentum evolution of young low-mass stars and brown dwarfs. In the time since Protostars & Planets V, there have been major developments in the availability of rotation period measurements at multiple ages and in different star-forming environments that are essential for testing theory. In parallel, substantial theoretical developments have been carried out in the last few years, including the physics of the star-disk interaction, numerical simulations of stellar winds, and the investigation of angular momentum transport processes in stellar interiors. This chapter reviews both the recent observational and theoretical advances that prompted the development of renewed angular momentum evolution models for cool stars and brown dwarfs. While the main observational trends of the rotational history of low mass objects seem to be accounted for by these new models, a number of critical open issues remain that are outlined in this review.

### Star formation and accretion in the circumnuclear disks of active galaxies

We explore the evolution of supermassive black holes (SMBH) centered in a circumnuclear disk (CND) as a function of the mass supply from the host galaxy and considering different star formation laws, which may give rise to a self-regulation via the injection of supernova-driven turbulence. A system of equations describing star formation, black hole accretion and angular momentum transport was solved for an axisymmetric disk in which the gravitational potential includes contributions from the black hole, the disk and the hosting galaxy. Our model extends the framework provided by Kawakatu et al. (2008) by separately considering the inner and outer part of the disk, and by introducing a potentially non-linear dependence of the star formation rate on the gas surface density and the turbulent velocity. The star formation recipes are calibrated using observational data for NGC 1097, while the accretion model is based on turbulent viscosity as a source of angular momentum transport in a thin viscous accretion disk. We find that current data provide no strong constraint on the star formation recipe, and can in particular not distinguish between models entirely regulated by the surface density, and models including a dependence on the turbulent velocity. The evolution of the black hole mass, on the other hand, strongly depends on the applied star formation law, as well as the mass supply from the host galaxy. We suggest to explore the star formation process in local AGN with high-resolution ALMA observations to break the degeneracy between different star formation models.

### MHD Simulation of a Disk Subjected to Lense-Thirring Precession

When matter orbits around a central mass obliquely with respect to the mass’s spin axis, the Lense-Thirring effect causes it to precess at a rate declining sharply with radius. Ever since the work of Bardeen & Petterson (1975), it has been expected that when a fluid fills an orbiting disk, the orbital angular momentum at small radii should then align with the mass’s spin. Nearly all previous work has studied this alignment under the assumption that a phenomenological "viscosity" isotropically degrades fluid shears in accretion disks, even though it is now understood that internal stress in flat disks is due to anisotropic MHD turbulence. In this paper we report a pair of matched simulations, one in MHD and one in pure (non-viscous) HD in order to clarify the specific mechanisms of alignment. As in the previous work, we find that disk warps induce radial flows that mix angular momentum of different orientation; however, we also show that the speeds of these flows are generically transonic and are only very weakly influenced by internal stresses other than pressure. In particular, MHD turbulence does not act in a manner consistent with an isotropic viscosity. When MHD effects are present, the disk aligns, first at small radii and then at large; alignment is only partial in the HD case. We identify the specific angular momentum transport mechanisms causing alignment and show how MHD effects permit them to operate more efficiently. Lastly, we relate the speed at which an alignment front propagates outward (in the MHD case) to the rate at which Lense-Thirring torques deliver angular momentum at smaller radii.

### Multidimensional Simulations of Rotating Pair Instability Supernovae

We study the effects of rotation on the dynamics, energetics and Ni-56 production of Pair Instability Supernova explosions by performing rotating two-dimensional ("2.5-D") hydrodynamics simulations. We calculate the evolution of eight low metallicity (Z = 10^-3, 10^-4 Zsun) massive (135-245 Msun) PISN progenitors with initial surface rotational velocities 50% that of the critical Keplerian value using the stellar evolution code MESA. We allow for both the inclusion and the omission of the effects of magnetic fields in the angular momentum transport and in chemical mixing, resulting in slowly-rotating and rapidly-rotating final carbon-oxygen cores, respectively. Increased rotation for carbon-oxygen cores of the same mass and chemical stratification leads to less energetic PISN explosions that produce smaller amounts of Ni-56 due to the effect of the angular momentum barrier that develops and slows the dynamical collapse. We find a non-monotonic dependence of Ni-56 production on rotational velocity in situations when smoother composition gradients form at the outer edge of the rotating cores. In these cases, the PISN energetics are determined by the competition of two factors: the extent of chemical mixing in the outer layers of the core due to the effects of rotation in the progenitor evolution and the development of angular momentum support against collapse. Our 2.5-D PISN simulations with rotation are the first presented in the literature. They reveal hydrodynamic instabilities in several regions of the exploding star and increased explosion asymmetries with higher core rotational velocity.

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