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Register a new userMeridional circulation and reverse advection in hot thin accretion discs
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Pavel Abolmasov
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In standard accretion discs, outward angular momentum transfer by viscous forces is compensated by the inward motion of the accreting matter. However, the vertical structure of real accretion discs leads to meridional circulation with comparable amplitudes of poloidal velocities. Using thin-disc approximation, we consider different regimes of disc accretion with different vertical viscosity scalings. We show that, while gas-pressure-dominated discs can easily have a midplane outflow, standard thin radiation-pressure-dominated disc is normally moving inwards at all the heights. However, quasi-spherical scaling for pressure ($ppropto varpi^{-5/2}$) leads to a midplane outflow for a very broad range of parameters. It particular, this may lead to a reversed, outward heat advection in geometrically thick discs when the temperature decreases rapidly enough with height. While the overall direction of heat advection depends on the unknown details of vertical structure and viscosity mechanisms, existence of the midplane counterflow in quasi-spherical flows is a robust result weakly dependent on the parameters and the assumptions of the model. Future models of thick radiatively inefficient flows should take meridional circulation into account.
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Radial transport of particles, elements and fluid driven by internal stresses in three-dimensional (3D) astrophysical accretion disks is an important phenomenon, potentially relevant for the outward dust transport in protoplanetary disks, origin of the refractory particles in comets, isotopic equilibration in the Earth-Moon system, etc. To gain better insight into these processes, we explore the dependence of meridional circulation in 3D disks with shear viscosity on their thermal stratification, and demonstrate strong effect of the latter on the radial flow. Previous locally isothermal studies have normally found a pattern of the radial outflow near the midplane, switching to inflow higher up. Here we show, both analytically and numerically, that a flow, which is inward at all altitudes, is possible in disks with entropy and temperature steeply increasing with height. Such thermodynamic conditions may be typical in the optically thin, viscously heated accretion disks. Disks in which these conditions do not hold should feature radial outflow near the midplane, as long as their internal stress is provided by the shear viscosity. Our results can also be used for designing hydrodynamical disk simulations with a prescribed pattern of the meridional circulation.
Context. Quasi-periodic variability has been observed in a number of X-ray binaries harboring black hole candidates. In general relativity, black holes are uniquely described by the Kerr metric and, according to the cosmic censorship conjecture, curvature singularities always have to be clothed by an event horizon. Aims. In this paper, we study the effect of an external magnetic field on the observed light curves of orbiting hot spots in thin accretion discs around Kerr black holes and naked singularities. Methods. We employ a ray-tracing algorithm to calculate the light curves and power spectra of such hot spots as seen by a distant observer for uniform and dipolar magnetic field configurations assuming a weak coupling between the magnetic field and the disc matter. Results. We show that the presence of an external dipolar magnetic field leads to potentially observable modifications of these signals for both Kerr black holes and naked singularities, while an external uniform magnetic field has practically no effect. In particular, we demonstrate that the emission from a hot spot orbiting near the innermost stable circular orbit of a naked singularity in a dipolar magnetic field can be significantly harder than the emission of the same hot spot in the absence of such a magnetic field. Conclusions. The comparison of our model with observational data may allow us study the geometry of magnetic fields around compact objects and to test the cosmic censorship conjecture in conjunction with other observables such as thermal continuum spectra and iron line profiles.
Surface observations indicate that the speed of the solar meridional circulation in the photosphere varies in anti-phase with the solar cycle. The current explanation for the source of this variation is that inflows into active regions alter the global surface pattern of the meridional circulation. When these localized inflows are integrated over a full hemisphere, they contribute to the slow down of the axisymmetric poleward horizontal component. The behavior of this large scale flow deep inside the convection zone remains largely unknown. Present helioseismic techniques are not sensitive enough to capture the dynamics of this weak large scale flow. Moreover, the large time of integration needed to map the meridional circulation inside the convection zone, also masks some of the possible dynamics on shorter timescales. In this work we examine the dynamics of the meridional circulation that emerges from a 3D MHD global simulation of the solar convection zone. Our aim is to assess and quantify the behavior of meridional circulation deep inside the convection zone, where the cyclic large-scale magnetic field can reach considerable strength. Our analyses indicate that the meridional circulation morphology and amplitude are both highly influenced by the magnetic field, via the impact of magnetic torques on the global angular momentum distribution. A dynamic feature induced by these magnetic torques is the development of a prominent upward flow at mid latitudes in the lower convection zone that occurs near the equatorward edge of the toroidal bands and that peaks during cycle maximum. Globally, the dynamo-generated large-scale magnetic field drives variations in the meridional flow, in stark contrast to the conventional kinematic flux transport view of the magnetic field being advected passively by the flow.
A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded conflicting inferences. Here, following a summary of existing results we show how a large center-to-limb systematics (CLS) in the measured travel times of acoustic waves affect the inferences through an analysis of frequency dependence of CLS, using data from the Helioseismic and Doppler Imager (HMI) onboard Solar Dynamics Observatory (SDO). Our results point to the residual systematics in travel times as a major cause of differing inferences on the deep structure of MC.
Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as a double-cell meridional circulation profile. The velocities are generated using a mean-field hydrodynamic and dynamo model -- moving through the regimes with minimal parameter changes; counter-rotation near the base of the tachocline is induced by sign inversion of the non-diffusive action of turbulent Reynolds stresses ($Lambda$-effect) due to the radial inhomogeneity of the Coriolis number. By mimicking the stochastic excitation of resonant modes in the convective interior, we simulate realization noise present in solar observations. Using deep-focusing to analyze differences in travel-time signatures between the three regimes, as well as comparing to solar observations, we show that current helioseismology techniques may offer important insights about the location of the return flow, however, that it may not be possible to definitively distinguish between profiles of single-cell or double-cell meridional circulation.
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