# Posts Tagged angular momentum transport

## Recent Postings from angular momentum transport

### On the survival of zombie vortices in protoplanetary discs

Recently it has been proposed that the zombie vortex instability (ZVI) could precipitate hydrodynamical activity and angular momentum transport in unmagnetised regions of protoplanetary discs, also known as "dead zones". In this letter we scrutinise, with high resolution 3D spectral simulations, the onset and survival of this instability in the presence of viscous and thermal physics. First, we find that the ZVI is strongly dependent on the nature of the viscous operator. Although the ZVI is easily obtained with hyper-diffusion, it is difficult to sustain with physical (second order) diffusion operators up to Reynolds numbers as high as 10^7. This sensitivity is probably due to the ZVI's reliance on critical layers, whose characteristic lengthscale, structure, and dynamics are controlled by viscous diffusion. Second, we observe that the ZVI is sensitive to radiative processes, and indeed only operates when the Peclet number is greater than a critical value ~10^4, or when the cooling time is longer than ~10 Omega^{-1}. As a consequence, the ZVI struggles to appear at R>0.3 AU in standard 0.01 M_sun T Tauri disc models, though younger more massive disks provide a more hospitable environment. Together these results question the prevalence of the ZVI in protoplanetary discs.

### Lithium depletion is a strong test of core-envelope recoupling

Rotational mixing is a prime candidate for explaining the gradual depletion of lithium from the photospheres of cool stars during the main sequence. However, previous mixing calculations have relied primarily on treatments of angular momentum transport in stellar interiors incompatible with solar and stellar data, in the sense that they overestimate internal differential rotation. Instead, recent studies suggest that stars are strongly differentially rotating at young ages, but approach solid body rotation during their lifetimes. We modify our rotating stellar evolution code to include an additional source of angular momentum transport, a necessary ingredient for explaining the open cluster rotation pattern, and examine the consequences for mixing. We confirm that core-envelope recoupling with a $\sim$20 Myr timescale is required to explain the evolution of the mean solar-mass rotation pattern along the main sequence, and demonstrate that it also provides a more accurate description of the Li depletion pattern seen in open clusters. Recoupling produces a characteristic pattern of efficient mixing at early ages and little mixing at late ages, thus predicting a flattening of Li depletion at a few Gyr, in agreement with the observed late-time evolution. Using Li abundances, we argue that the timescale for core-envelope recoupling during the main sequence decreases sharply with increasing mass. We discuss implications of this finding for stellar physics, including the viability of gravity waves and magnetic fields as agents of angular momentum transport. We also raise the possibility of intrinsic differences in initial conditions in star clusters, using M67 as an example.

### Gravitoturbulence in magnetised protostellar discs

Gravitational instability (GI) features in several aspects of protostellar disk evolution, most notably in angular momentum transport, fragmentation, and the outbursts exemplified by FU Ori and EX Lupi systems. The outer regions of protostellar discs may also be coupled to magnetic fields, which could then modify the development of GI. To understand the basic elements of their interaction, we perform local 2D ideal and resistive MHD simulations with an imposed toroidal field. In the regime of moderate plasma beta, we find that the system supports a hot gravito-turbulent state, characterised by considerable magnetic energy and stress and a surprisingly large Toomre parameter $Q~10$. This result has potential implications for disk structure, vertical thickness, ionisation, etc. Our simulations also reveal the existence of long-lived and dense magnetic islands' or plasmoids. Lastly, we find that the presence of a magnetic field has little impact on the fragmentation criterion of the disk. Though our focus is on protostellar disks, some of our results may be relevant for the outer radii of AGN.

### Precision Stellar Astrophysics in the Kepler Era

The study of fundamental properties (such as temperatures, radii, masses, and ages) and interior processes (such as convection and angular momentum transport) of stars has implications on various topics in astrophysics, ranging from the evolution of galaxies to understanding exoplanets. In this contribution I will review the basic principles of two key observational methods for constraining fundamental and interior properties of single field stars: the study stellar oscillations (asteroseismology) and optical long-baseline interferometry. I will highlight recent breakthrough discoveries in asteroseismology such as the measurement of core rotation rates in red giants and the characterization of exoplanet systems. I will furthermore comment on the reliability of interferometry as a tool to calibrate indirect methods to estimate fundamental properties, and present a new angular diameter measurement for the exoplanet host star HD219134 which demonstrates that diameters for stars which are relatively well resolved (~> 1 mas for the K band) are consistent across different instruments. Finally I will discuss the synergy between asteroseismology and interferometry to test asteroseismic scaling relations, and give a brief outlook on the expected impact of space-based missions such as K2, TESS and Gaia.

### Evidence for Cluster to Cluster Variations in Low-Mass Stellar Rotational Evolution

A concordance model for angular momentum evolution has been developed by multiple investigators. This approach postulates that star forming regions and clusters are an evolutionary sequence which can be modeled with assumptions about the coupling between protostars and accretion disks, angular momentum loss from magnetized winds that saturates in a mass-dependent fashion at high rotation rates, and core-envelope decoupling for solar analogs. We test this approach by combining established data with the large h Per dataset from the MONITOR project and new low-mass Pleiades data. We confirm prior results that young low-mass stars can be used to test star-disk coupling and angular momentum loss independent of the treatment of internal angular momentum transport. For slow rotators, we confirm the need for star-disk interactions to evolve the ONC to older systems, using h Per (age 13~Myr) as our natural post-disk case. Further interactions are not required to evolve slow rotators from h Per to older systems, implying no justification for extremely long-lived disks as an alternative to core-envelope decoupling. However, our wind models cannot evolve rapid rotators from h Per to older systems consistently; this appears to be a general problem for any wind model that becomes ineffective in low-mass young stars. We outline two possible solutions: either there is cosmic variance in the distribution of stellar rotation rates in different clusters or there are substantially enhanced torques in low-mass rapid rotators. We favor the former explanation and discuss observational tests that could be used to distinguish them. If the distribution of initial conditions depends on environment, models which test parameters by assuming a universal underlying distribution of initial conditions will need to be re-evaluated.

### Global MHD Simulations of Accretion Disks in Cataclysmic Variables (CVs): I. The Importance of Spiral Shocks

We present results from the first global 3D MHD simulations of accretion disks in Cataclysmic Variable (CV) systems in order to investigate the relative importance of angular momentum transport via turbulence driven by the magnetorotational instability (MRI) compared to that driven by spiral shock waves. Remarkably, we find that even with vigorous MRI turbulence, spiral shocks are an important component to the overall angular momentum budget, at least when temperatures in the disk are high (so that Mach numbers are low). In order to understand the excitation, propagation, and damping of spiral density waves in our simulations more carefully, we perform a series of 2D global hydrodynamical simulations with various equation of states and both with and without mass inflow via the Lagrangian point (L1). Compared with previous similar studies, we find the following new results. 1) Linear wave dispersion relation fits the pitch angles of spiral density waves very well. 2) We demonstrate explicitly that mass accretion is driven by the deposition of negative angular momentum carried by the waves when they dissipate in shocks. 3) Using Reynolds stress scaled by gas pressure to represent the effective angular momentum transport rate alpha_{eff} is not accurate when mass accretion is driven by non-axisymmetric shocks. 4) Using the mass accretion rate measured in our simulations to directly measure alpha defined in standard thin-disk theory, we find 0.02 < alpha_{eff} < 0.05 for CV disks, consistent with observed values in quiescent states of dwarf novae (DNe). In this regime the disk may be too cool and neutral for the MRI to operate and spiral shocks are a possible accretion mechanism. However, we caution that our simulations use unrealistically low Mach numbers in this regime, and therefore future models with more realistic thermodynamics and non-ideal MHD are warranted.

### Gravitational Instabilities in Circumstellar Disks

[Abridged] Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability, and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small scale turbulence-like density fluctuations, and fragmentation of the disk itself. We present the analytic theory that describes the linear growth phase of the instability, supplemented with a survey of numerical simulations that aim to capture the non-linear evolution. We emphasize the role of thermodynamics and large scale infall in controlling the outcome of the instability. Despite apparent controversies in the literature, we show a remarkable level of agreement between analytic predictions and numerical results. We highlight open questions related to (1) the development of a turbulent cascade in thin disks, and (2) the role of mode-mode coupling in setting the maximum angular momentum transport rate in thick disks.

### Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and red giant stars. Under the assumption of local angular momentum conservation, the core contraction and envelope expansion occurring at the end of the main sequence would result in a much larger internal differential rotation than observed. This suggests that angular momentum redistribution must be taking place in the interior of these stars. Aims. We investigate the physical nature of the angular momentum redistribution mechanisms operating in stellar interiors by constraining the efficiency of post-main sequence rotational coupling. Methods. We model the rotational evolution of a 1.25 Msun star using the Yale Rotational stellar Evolution Code. Our models take into account the magnetic wind braking occurring at the surface of the star and the angular momentum transport in the interior, with an efficiency dependent on the degree of internal differential rotation. Results. We find that models including a dependence of the angular momentum transport efficiency on the radial rotational shear reproduce very well the observations. The best fit of the data is obtained with an angular momentum transport coefficient scaling with the ratio of the rotation rate of the radiative interior over that of the convective envelope of the star as a power law of exponent ~3. This scaling is consistent with the predictions of recent numerical simulations of the Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular momentum transport process whose efficiency varies during the stellar evolution through a dependence on the level of internal differential rotation is required to explain the observed post-main sequence rotational evolution of low-mass stars.

### Spiral-driven accretion in protoplanetary discs - II Self-similar solutions

Accretion discs are ubiquitous in the universe and it is a crucial issue to understand how angular momentum and mass are being radially transported in these objects. Here, we study the role played by non-linear spiral patterns within hydrodynamical and non self-gravitating accretion disc assuming that external disturbances such as infall onto the disc may trigger them. To do so, we computed self-similar solutions that describe discs in which a spiral wave propagates. Such solutions present both shocks and critical sonic points that we carefully analyze. For all allowed temperatures and for several spiral shocks, we calculated the wave structure. In particular we inferred the angle of the spiral patern, the stress it exerts on the disc as well as the associated flux of mass and angular momentum as a function of temperature. We quantified the rate of angular momentum transport by means of the dimensionless $\alpha$ parameter. For the thickest disc we considered (corresponding to $h/r$ values of about 1/3), we found values of $\alpha$ as high as $0.1$, and scaling with the temperature $T$ such that $\alpha \propto T^{3/2} \propto (h/r)^3$. The spiral angle scales with the temperature as $\arctan(r/h)$. The existence of these solutions suggests that perturbations occurring at disc outer boundaries, such as for example perturbations due to infall motions, can propagate deep inside the disc and therefore should not be ignored, even when considering small radii.

### Rossby Wave Instability and Long-Term Evolution of Dead Zones in Protoplanetary Discs

The physical mechanism of angular momentum transport in poorly ionized regions of protoplanetary discs, the dead zones (DZs), is not understood. The presence of a DZ naturally leads to conditions susceptible to the Rossby wave instability (RWI), which produces vortices and spiral density waves that may revive the DZ and be responsible for observed large-scale disc structures. We present a series of two-dimensional hydrodynamic simulations to investigate the role of the RWI in DZs, including its impact on the long-term evolution of the disc and its morphology. The nonlinear RWI can generate Reynolds stresses (effective $\alpha$ parameter) as large as $0.01 - 0.05$ in the DZ, helping to sustain quasi-steady accretion throughout the disc. It also produces novel disc morphologies, including azimuthal asymmetries with $m = 1, 2$, and atypical vortex shapes. The angular momentum transport strength and morphology are most sensitive to two parameters: the radial extent of the DZ and the disc viscosity. The largest Reynolds stresses are produced when the radial extent of the DZ is less than its distance to the central star. Such narrow DZs lead to a single vortex or two coherent antipodal vortices in the quasi-steady state. The edges of wider DZs evolve separately, resulting in two independent vortices and reduced angular momentum transport efficiency. In either case, we find that, because of the Reynolds stresses generated by the nonlinear RWI, gravitational instability is unlikely to play a role in angular momentum transport across the DZ, unless the accretion rate is sufficiently high.

### Parsec-scale accretion and winds irradiated by a quasar

We present numerical simulations of properties of a parsec-scale torus exposed to illumination by the central black hole in an active galaxy (AGN). Our physical model allows to investigate the balance between the formation of winds and accretion simultaneously. Radiation-driven winds are allowed by taking into account radiation pressure due to UV and IR radiation along with X-ray heating and dust sublimation. Accretion is allowed through angular momentum transport and the solution of the equations of radiation hydrodynamics. Our methods adopt flux-limited diffusion radiation-hydrodynamics for the dusty, infrared pressure driven part of the flow, along with X-ray heating and cooling. Angular momentum transport in the accreting part of the flow is modeled using effective viscosity. Our results demonstrate that radiation pressure on dust can play an important role in shaping AGN obscuration. For example, when the luminosity illuminating the torus exceeds $L>0.01\,L_{\rm Edd}$, where $L_{\rm Edd}$ is the Eddington luminosity, we find no episodes of sustained disk accretion because radiation pressure does not allow a disk to form. Despite the absence of the disk accretion, the flow of gas to smaller radii still proceeds at a rate $10^{-4}-10^{-1}\,M_\odot\,{\rm yr}^{-1}$ through the capturing of the gas from the hot evaporative flow, thus providing a mechanism to deliver gas from a radiation-pressure dominated torus to the inner accretion disk. As $L/L_{\rm edd}$ increases, larger radiation input leads to larger torus aspect ratios and increased obscuration of the central black hole. We also find the important role of the X-ray heated gas in shaping of the obscuring torus.

### Parsec-scale accretion and winds irradiated by a quasar [Replacement]

We present numerical simulations of properties of a parsec-scale torus exposed to illumination by the central black hole in an active galaxy (AGN). Our physical model allows to investigate the balance between the formation of winds and accretion simultaneously. Radiation-driven winds are allowed by taking into account radiation pressure due to UV and IR radiation along with X-ray heating and dust sublimation. Accretion is allowed through angular momentum transport and the solution of the equations of radiation hydrodynamics. Our methods adopt flux-limited diffusion radiation-hydrodynamics for the dusty, infrared pressure driven part of the flow, along with X-ray heating and cooling. Angular momentum transport in the accreting part of the flow is modeled using effective viscosity. Our results demonstrate that radiation pressure on dust can play an important role in shaping AGN obscuration. For example, when the luminosity illuminating the torus exceeds $L>0.01\,L_{\rm Edd}$, where $L_{\rm Edd}$ is the Eddington luminosity, we find no episodes of sustained disk accretion because radiation pressure does not allow a disk to form. Despite the absence of the disk accretion, the flow of gas to smaller radii still proceeds at a rate $10^{-4}-10^{-1}\,M_\odot\,{\rm yr}^{-1}$ through the capturing of the gas from the hot evaporative flow, thus providing a mechanism to deliver gas from a radiation-pressure dominated torus to the inner accretion disk. As $L/L_{\rm edd}$ increases, larger radiation input leads to larger torus aspect ratios and increased obscuration of the central black hole. We also find the important role of the X-ray heated gas in shaping of the obscuring torus.

### Spreading layers in accreting objects: role of acoustic waves for angular momentum transport, mixing and thermodynamics

Disk accretion at high rate onto a white dwarf or a neutron star has been suggested to result in the formation of a spreading layer (SL) - a belt-like structure on the object's surface, in which the accreted matter steadily spreads in the poleward (meridional) direction while spinning down. To assess its basic characteristics we perform two-dimensional hydrodynamic simulations of supersonic SLs in the relevant morphology with a simple prescription for cooling. We demonstrate that supersonic shear naturally present at the base of the SL inevitably drives sonic instability that gives rise to large scale acoustic modes governing the evolution of the SL. These modes dominate the transport of momentum and energy, which is intrinsically global and cannot be characterized via some form of local effective viscosity (e.g. $\alpha$-viscosity). The global nature of the wave-driven transport should have important implications for triggering Type I X-ray bursts in low mass X-ray binaries. The nonlinear evolution of waves into a system of shocks drives effective re-arrangement (sensitively depending on thermodynamical properties of the flow) and deceleration of the SL, which ultimately becomes transonic and susceptible to regular Kelvin-Helmholtz instability. We interpret this evolution in terms of the global structure of the SL and suggest that mixing of the SL material with the underlying stellar fluid should become effective only at intermediate latitudes on the accreting object's surface, where the flow has decelerated appreciably. In the near-equatorial regions the transport is dominated by acoustic waves and mixing is less efficient. We speculate that this latitudinal non-uniformity of mixing in accreting white dwarfs may be linked to the observed bipolar morphology of classical novae ejecta.

### Magneto-thermal Disk Wind from Protoplanetary Disks

Global evolution and dispersal of protoplanetary disks (PPDs) is governed by disk angular momentum transport and mass-loss processes. Recent numerical studies suggest that angular momentum transport in the inner region of PPDs is largely driven by magnetized disk wind, yet the wind mass-loss rate remains unconstrained. On the other hand, disk mass loss has conventionally been attributed to photoevaporation, where external heating on the disk surface drives a thermal wind. We unify the two scenarios by developing a 1D model of magnetized disk winds with a simple treatment of thermodynamics as a proxy for external heating. The wind properties largely depend on 1) the magnetic field strength at the wind base, characterized by the poloidal Alfv\'en speed $v_{Ap}$, 2) the sound speed $c_s$ near the wind base, and 3) how rapidly poloidal field lines diverge (achieve $R^{-2}$ scaling). When $v_{Ap}\gg c_s$, corotation is enforced near the wind base, resulting in centrifugal acceleration. Otherwise, the wind is accelerated mainly by the pressure of the toroidal magnetic field. In both cases, the dominant role played by magnetic forces likely yields wind outflow rates that well exceed purely hydrodynamical mechanisms. For typical PPD accretion-rate and wind-launching conditions, we expect $v_{Ap}$ to be comparable to $c_s$ at the wind base. The resulting wind is heavily loaded, with total wind mass loss rate likely reaching a considerable fraction of wind-driven accretion rate. Implications for modeling global disk evolution and planet formation are also discussed.

### On the Differential Rotation of Massive Main Sequence Stars

To date, asteroseismology has provided core to surface differential rotation measurements in eight main-sequence stars. These stars, ranging in mass from $\sim$1.5-9$M_\odot$, show rotation profiles ranging from uniform to counter-rotation. Although they have a variety of masses, these stars all have convective cores and overlying radiative regions, conducive to angular momentum transport by internal gravity waves (IGW). Using two-dimensional (2D) numerical simulations we show that angular momentum transport by IGW can explain all of these rotation profiles. We further predict that should high mass, faster rotating stars be observed, the core to envelope differential rotation will be positive, but less than one.

### 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 [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.

### 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.

### 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.

### 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).