Viscous Disk Research Articles

Spiral structures in gravito-turbulent gaseous disks

Context.Gravitational instabilities can drive small-scale turbulence and large-scale spiral arms in massive gaseous disks under conditions of slow radiative cooling. These motions affect the observed disk morphology, its mass accretion rate and variability, and could control the process of planet formation via dust grain concentration, processing, and collisional fragmentation.Aims.We study gravito-turbulence and its associated spiral structure in thin gaseous disks subject to a prescribed cooling law. We characterize the morphology, coherence, and propagation of the spirals and examine when the flow deviates from viscous disk models.Methods.We used the finite-volume code PLUTOto integrate the equations of self-gravitating hydrodynamics in three-dimensional spherical geometry. The gas was cooled over longer-than-orbital timescales to trigger the gravitational instability and sustain turbulence. We ran models for various disk masses and cooling rates.Results.In all cases considered, the turbulent gravitational stress transports angular momentum outward at a rate compatible with viscous disk theory. The dissipation of orbital energy happens via shocks in spiral density wakes, heating the disk back to a marginally stable thermal equilibrium. These wakes drive vertical motions and contribute to mix material from the disk with its corona. They are formed and destroyed intermittently, and they nearly corotate with the gas at every radius. As a consequence, large-scale spiral arms exhibit no long-term global coherence, and energy thermalization is an essentially local process.Conclusions.In the absence of radial substructures or tidal forcing, and provided a local cooling law, gravito-turbulence reduces to a local phenomenon in thin gaseous disks.

An ALMA Survey of Protoplanetary Disks in Lynds 1641

Abstract We present ALMA observations of 101 protoplanetary disks within the star-forming region Lynds 1641 in the Orion Molecular Cloud A. Our observations include 1.33 mm continuum emission and spectral windows covering the J = 2–1 transition of 12CO, 13CO, and C18O. We detect 89 protoplanetary disks in the dust continuum at the 4σ level (∼88% detection rate) and 31 in 12CO, 13 in 13CO, and 4 in C18O. Our sample contains 23 transitional disks, 20 of which are detected in the continuum. We target infrared-bright Class II objects, which biases our sample toward massive disks. We determine dust masses or upper limits for all sources in our sample and compare our sample to protostars in this region. We find a decrease in dust mass with evolutionary state. We also compare this sample to other regions surveyed in the (sub)millimeter and find that Lynds 1641 has a relatively massive dust disk population compared to regions of similar and older ages, with a median dust mass of M ⊕ and 27% with dust masses equal to or greater than the minimum solar nebula dust mass value of ∼30 M ⊕. We analyze the disk mass–accretion rate relationship in this sample and find that the viscous disk lifetimes are similar to the age of the region, though with a large spread. One object, [MGM2012] 512, shows a large-scale (>5000 au) structure in both the dust continuum and the three gas lines. We discuss potential origins for this emission, including an accretion streamer with large dust grains.

Maximum temperatures in evolving protoplanetary discs and composition of planetary building blocks

ABSTRACT The maximum temperature and radial temperature profile in a protoplanetary disc are important for the condensation of different elements in the disc. We simulate the evolution of a set of protoplanetary discs from the collapse of their progenitor molecular cloud cores as well as the dust decoupling within the discs as they evolve. We show how the initial properties of the cloud cores affect the thermal history of the protoplanetary discs using a simple viscous disc model. Our results show that the maximum mid-plane temperature in the disc occurs within 0.5 au. It increases with the initial cloud temperature and decreases with its angular velocity and the viscosity of the disc. From the observed properties of the molecular cloud cores, we find the median value of the maximum temperature is around 1250 K, with roughly 90 per cent of them being less than 1500 K – a value that is lower than the 50 per cent condensation temperatures of most refractory elements. Therefore, only cloud cores with high initial temperatures or low-angular velocities and/or low viscosities within the planet-forming discs will result in refractory-rich planetesimals. To reproduce the volatile depletion pattern of CM, CO, and CV chondrites and the terrestrial planets in Solar system, one must either have rare properties of the initial molecular cloud cores like high core temperature, or other sources of energy to heat the disc to sufficiently high temperatures. Alternatively, the volatile depletion observed in these chondrites may be inherited from the progenitor molecular cloud.

A Multi–Observing Technique Study of the Dynamical Evolution of the Viscous Disk around the Be Star ω CMa

Abstract The observed emission lines of Be stars originate from a circumstellar Keplerian disk, which is generally well explained by the viscous decretion disk model. In an earlier work we performed modeling of the full light curve of the bright Be star ω CMa with the 1D time-dependent hydrodynamic code SINGLEBE and the Monte Carlo radiative transfer code HDUST. We used a V-band light curve that probes the inner disk through four disk formation and dissipation cycles. This new study compares predictions of the same set of model parameters with time-resolved photometry from the near-UV through the mid-IR, comprehensive series of optical spectra, and optical broadband polarimetry, which overall represent a larger volume of the disk. Qualitatively, the models reproduce the trends in the observed data due to the growth and decay of the disk. However, quantitative differences exist, e.g., an overprediction of flux increasing with wavelength, too slow decreases in Balmer emission line strength during disk dissipation, and a discrepancy between the range of polarimetric data and the model. We find that a larger value of the viscosity parameter alone or a disk truncated by a companion star reduces these discrepancies by increasing the dissipation rate in the outer regions of the disk.

Magnetic Braking of Accreting T Tauri Stars: Effects of Mass Accretion Rate, Rotation, and Dipolar Field Strength

The rotational evolution of accreting pre-main-sequence stars is influenced by its magnetic interaction with its surrounding circumstellar disk. Using the PLUTO code, we perform 2.5D magnetohydrodynamic, axisymmetric, time-dependent simulations of star-disk interaction---with an initial dipolar magnetic field structure, and a viscous and resistive accretion disk---in order to model the three mechanisms that contribute to the net stellar torque: accretion flow, stellar wind, and magnetospheric ejections (periodic inflation and reconnection events). We investigate how changes in the stellar magnetic field strength, rotation rate, and mass accretion rate (changing the initial disk density) affect the net stellar torque. All simulations are in a net spin-up regime. We fit semi-analytic functions for the three stellar torque contributions, allowing for the prediction of the net stellar torque for our parameter regime, and the possibility of investigating spin-evolution using 1D stellar evolution codes. The presence of an accretion disk appears to increase the efficiency of stellar torques compared to isolated stars, for cases with outflow rates much smaller than accretion rates, because the star-disk interaction opens more of the stellar magnetic flux compared to that from isolated stars. In our parameter regime, a stellar wind with a mass loss rate of $\approx 1 \%$ of the mass accretion rate is capable of extracting $\lesssim 50 \%$ of the accreting angular momentum. These simulations suggest that achieving spin-equilibrium in a representative T Tauri case within our parameter regime, e.g., BP Tau, would require a wind mass loss rate of $\approx 25\%$ of the mass accretion rate.

Stationary models of magnetized viscous tori around a Schwarzschild black hole

We present stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole. We assume that the tori are not self-gravitating, are endowed with a toroidal magnetic field, and obey a constant angular momentum law. Our study focuses on the role of the black hole curvature in the shear viscosity tensor and in their potential combined effect on the stationary solutions. Those are built in the framework of a causality-preserving, second-order gradient expansion scheme of relativistic hydrodynamics in the Eckart frame description which gives rise to hyperbolic equations of motion. The stationary models are constructed by numerically solving the general relativistic momentum conservation equation using the method of characteristics. We place constraints in the range of validity of the second-order transport coefficients of the theory. Our results reveal that the effects of the shear viscosity and curvature are particularly noticeable only close to the cusp of the disks. The surfaces of constant pressure are affected by viscosity and curvature and the self-intersecting isocontour - the cusp - moves to smaller radii (i.e. towards the black hole horizon) as the effects become more significant. For highly magnetized disks the shift in the cusp location is smaller. Our findings might have implications on the dynamical stability of constant angular momentum tori which, in the inviscid case, are affected by the runaway instability.

Accretion of Gas Giants Constrained by the Tidal Barrier

Abstract After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under the effect of viscous dissipation, and to meander in and out of the planets’ Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host star’s tidal perturbation induces a barrier across the converging streamlines’ interface. Viscous transfer of angular momentum across this tidal barrier determines the rate of mass diffusion from the horseshoe streamlines onto the circumplanetary disks, and eventually the accretion rate onto the protoplanets. We carry out a series of numerical simulations to test the influence of this tidal barrier on superthermal planets. In weakly viscous disks, the protoplanets’ accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion timescale, their masses reach asymptotic values comparable to that of Jupiter. In relatively thick and strongly viscous disks, protoplanets’ asymptotic masses exceed several times that of Jupiter. Two-dimensional numerical simulations show that such massive protoplanets strongly excite the eccentricity of nearby horseshoe streamlines, destabilize orderly flow, substantially enhance the diffusion rate across the tidal barrier, and elevate their growth rate until their natal disk is severely depleted. In contrast, eccentric streamlines remain stable in three-dimensional simulations. Based on the upper falloff in the observed mass distribution of known exoplanets, we suggest that their natal disks had relatively low viscosity (α ∼ 10−3) and modest thickness (H/R ∼ 0.03–0.05).

Linking planetary embryo formation to planetesimal formation

Context. The growth-timescales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk. Aims. We quantify the timescales and spatial distribution of planetary embryos through collisional growth and fragmentation of dynamically forming 100 km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone. Methods. We connected a one-dimensional model for viscous gas evolution, dust and pebble dynamics, and pebble flux-regulated planetesimal formation to the N-body code LIPAD. Our framework enabled us to study the formation, growth, fragmentation, and evolution of planetesimals with an initial size of 100 km in diameter for the first million years of a viscous disk. Results. Our study shows the effect of the planetesimal surface density evolution on the preferential location and timescales of planetary embryo formation. Only the innermost embryos (<2 au) in our study form well within the lifetime of an active pebble flux for any disk studied. Higher planetesimal disk masses and steeper planetesimal surface density profiles result in more massive embryos within a larger area, rather than in a higher number of embryos. A one-dimensional analytically derived model for embryo formation based on the local planetesimal surface density evolution is presented. This model can reproduce the spatial distribution, formation rate, and total number of planetary embryos at a fraction of the computational cost of the N-body simulations. Conclusions. The formation of planetary embryos in the terrestrial planet zone occurs simultaneously with the formation of planetesimals. The local planetesimal surface density evolution and the orbital spacing of planetary embryos in the oligarchic regime are good constraints for modeling planetary embryo formation analytically. Our embryo formation model is a valuable asset in future studies of planet formation.

Magnetic Braking of Accreting T Tauri Stars: Effects of Mass Accretion Rate, Rotation, and Dipolar Field Strength

Abstract The rotational evolution of an accreting pre-main-sequence star is influenced by its magnetic interaction with its surrounding circumstellar disk. Using the PLUTO code, we perform 2.5D magnetohydrodynamic, axisymmetric, time-dependent simulations of star–disk interaction—with an initial dipolar magnetic field structure, and a viscous and resistive accretion disk—in order to model the three mechanisms that contribute to the net stellar torque: accretion flow, stellar wind, and magnetospheric ejections (periodic inflation and reconnection events). We investigate how changes in the stellar magnetic field strength, rotation rate, and mass accretion rate (changing the initial disk density) affect the net stellar torque. All simulations are in a net spin-up regime. We fit semi-analytic functions for the three stellar torque contributions, allowing for the prediction of the net stellar torque for our parameter regime, as well as the possibility of investigating spin evolution using 1D stellar evolution codes. The presence of an accretion disk appears to increase the efficiency of stellar torques compared to isolated stars, for cases with outflow rates much smaller than accretion rates, because the star–disk interaction opens more of the stellar magnetic flux compared to that from isolated stars. In our parameter regime, a stellar wind with a mass-loss rate of ≈1% of the mass accretion rate is capable of extracting ≲50% of the accreting angular momentum. These simulations suggest that achieving spin equilibrium in a representative T Tauri case within our parameter regime, e.g., BP Tau, would require a wind mass-loss rate of ≈25% of the mass accretion rate.

Analytical model for the local vertical structure of thin accretion discs

ABSTRACT We derive several analytical relations and approximate solutions for the local vertical structure of viscous thin accretion discs. Under the alpha prescription, when the viscous heating is proportional to the gas pressure p, we derive the analytical relation between the radiative flux F and the radiation pressure P: (F/F0)2 = [1 − (P/Pc)5/4]/[1 − (P0/Pc)5/4], where the subscript 0 means the value at the surface and the subscript c is the value at the disc centre. Both F and P are approximately integrated to yield the well-known uniform heating model. In this case, furthermore, the height z and density ρ are approximately fitted as a function of the optical depth τ. When the viscous heating is proportional to the radiation pressure P and the disc is almost isothermal, the flux F is proportional to z as F = (3/2)αΩPz, where α and Ω are the alpha parameter and angular speed, respectively. In this case, moreover, the height and density are analytically solved and expressed as $z=(\sqrt{2}c_{\rm T}/\Omega) {\rm erf}^{-1}(1-\tau /\tau _{\rm c})$ and ρ = ρcexp { − [erf−1(1 − τ/τc)]2}, cT being the isothermal sound speed, and erf−1 the inverse of the error function.

Magnetic field transport in compact binaries

Context. Dwarf novæ (DNe) and low mass X-ray binaries (LMXBs) show eruptions that are thought to be due to a thermal-viscous instability in their accretion disk. These eruptions provide constraints on angular momentum transport mechanisms. Aims. We explore the idea that angular momentum transport could be controlled by the dynamical evolution of the large-scale magnetic field. We study the impact of different prescriptions for the magnetic field evolution on the dynamics of the disk. This is a first step in confronting the theory of magnetic field transport with observations. Methods. We developed a version of the disk instability model that evolves the density, the temperature, and the large-scale vertical magnetic flux simultaneously. We took into account the accretion driven by turbulence or by a magnetized outflow with prescriptions taken, respectively, from shearing box simulations or self-similar solutions of magnetized outflows. To evolve the magnetic flux, we used a toy model with physically motivated prescriptions that depend mainly on the local magnetization β, where β is the ratio of thermal pressure to magnetic pressure. Results. We find that allowing magnetic flux to be advected inwards provides the best agreement with DNe light curves. This leads to a hybrid configuration with an inner magnetized disk, driven by angular momentum losses to an MHD outflow, sharply transiting to an outer weakly-magnetized turbulent disk where the eruptions are triggered. The dynamical impact is equivalent to truncating a viscous disk so that it does not extend down to the compact object, with the truncation radius dependent on the magnetic flux and evolving as Ṁ−2/3. Conclusions. Models of DNe and LMXB light curves typically require the outer, viscous disk to be truncated in order to match the observations. There is no generic explanation for this truncation. We propose that it is a natural outcome of the presence of large-scale magnetic fields in both DNe and LMXBs, with the magnetic flux accumulating towards the center to produce a magnetized disk with a fast accretion timescale.

Observed sizes of planet-forming disks trace viscous spreading

Context. The evolution of protoplanetary disks is dominated by the conservation of angular momentum, where the accretion of material onto the central star is fed by the viscous expansion of the outer disk or by disk winds extracting angular momentum without changing the disk size. Studying the time evolution of disk sizes therefore allows us to distinguish between viscous stresses or disk winds as the main mechanism of disk evolution. Observationally, estimates of the size of the gaseous disk are based on the extent of CO submillimeter rotational emission, which is also affected by the changing physical and chemical conditions in the disk during the evolution. Aims. We study how the gas outer radius measured from the extent of the CO emission changes with time in a viscously expanding disk. We also investigate to what degree this observable gas outer radius is a suitable tracer of viscous spreading and whether current observations are consistent with viscous evolution. Methods. For a set of observationally informed initial conditions we calculated the viscously evolved density structure at several disk ages and used the thermochemical code DALI to compute synthetic emission maps, from which we measured gas outer radii in a similar fashion as observations. Results. The gas outer radii (RCO, 90%) measured from our models match the expectations of a viscously spreading disk: RCO, 90% increases with time and, for a given time, RCO, 90% is larger for a disk with a higher viscosity αvisc. However, in the extreme case in which the disk mass is low (Mdisk ≤ 10−4 M⊙) and αvisc is high (≥10−2), RCO, 90% instead decreases with time as a result of CO photodissociation in the outer disk. For most disk ages, RCO, 90% is up to ~12× larger than the characteristic size Rc of the disk, and RCO, 90%/Rc is largest for the most massive disk. As a result of this difference, a simple conversion of RCO, 90% to αvisc overestimates the true αvisc of the disk by up to an order of magnitude. Based on our models, we find that most observed gas outer radii in Lupus can be explained using viscously evolving disks that start out small (Rc(t = 0) ≃ 10 AU) and have a low viscosity (αvisc = 10−4−10−3). Conclusions. Current observations are consistent with viscous evolution, but expanding the sample of observed gas disk sizes to star-forming regions, both younger and older, would better constrain the importance of viscous spreading during disk evolution.

Large exit flanges in diffuser-augmented turbines lead to sub-optimal performance

The use of a diffuser enhances turbine performance by augmenting the mass flow rate through the rotor. The use of large annular flanges at the exit of the diffuser has been studied extensively, but the present study shows that large exit flanges lead to sub-optimal performance when considering the power coefficient as defined by the maximum frontal area of the combined diffuser-rotor system (CPtot). Viscous actuator disk simulations are employed to investigate the effect of variable diffuser geometry on performance, and the investigation is divided into two sub-studies. In the first, it is shown that the mass flow rate exhibits a consistent linear relationship to the sectional diffuser lift coefficient, across geometries and rotor thrust coefficients. Since large flanges tend to enhance diffuser thrust more so than sectional lift, their utility is called into question. In the second sub-study, flange height is varied for an otherwise fixed geometry, and it is shown that a flange height of h/Di ​= ​0.04 yields the best performance of CPtot ​= ​0.576. This flange height is much smaller than the flanges typically considered in the literature; it is effectively a Gurney flap, a small trailing edge device known to enhance lift on airfoils.

Protoplanetary disks meet artificial neural networks: revisiting the viscous disk model and updated disk masses

Protoplanetary disks meet artificial neural networks: revisiting the viscous disk model and updated disk masses

How consumption and repulsion set planetary gap depths and the final masses of gas giants

ABSTRACT Planets open gaps in discs. Gap opening is typically modelled by considering the planetary Lindblad torque which repels disc gas away from the planet’s orbit. But gaps also clear because the planet consumes local material. We present a simple, easy-to-use, analytic framework for calculating how gaps deplete and how the disc’s structure as a whole changes by the combined action of Lindblad repulsion and planetary consumption. The final mass to which a gap-embedded gas giant grows is derived in tandem. The analytics are tested against 1D numerical experiments and calibrated using published multidimensional simulations. In viscous alpha discs, the planet, while clearing a gap, initially accretes practically all of the gas that tries to diffuse past, rapidly achieving super-Jupiter if not brown dwarf status. By contrast, in inviscid discs – that may still accrete on to their central stars by, say, magnetized winds – planets open deep, repulsion-dominated gaps. Then only a small fraction of the disc accretion flow is diverted on to the planet, which grows to a fraction of a Jupiter mass. Transitional disc cavities might be cleared by families of such low-mass objects opening inviscid, repulsion-dominated, overlapping gaps which allow most of the outer disc gas to flow unimpeded on to host stars.

Effectiveness of Hall current and thermophysical properties in compressible flow of viscous fluid thorough spinning oscillatory disk

This study investigates the features of Hall current and thermophysical properties (viscosity, density and thermal conductivity) on unsteady, compressible, laminar flow of viscous fluid. Swirl flow is perceived by oscillatory movement of revolving disk. The well suited variables are adapted in order to achieve the non-similar system of expressions. The non-similar solutions are worked out numerically through scheme of finite differences and then utilizing Successive over Relaxation (SOR) technique. Physical parameters are discussed through one, two and three dimensional graphical forms. Tabular description of the resulting quantities is also formulated. The oscillatory thermal traces enhanced corresponding to increased magnetic parameter. An enhancement in Prandtl number contributes to lower down the thermal field but improves the rate of heat transportation.

Testing viscous disc theory using the balance between stellar accretion and external photoevaporation of protoplanetary discs

ABSTRACT The nature and rate of (viscous) angular momentum transport in protoplanetary discs (PPDs) have important consequences for the formation process of planetary systems. While accretion rates on to the central star yield constraints on such transport in the inner regions of a PPD, empirical constraints on viscous spreading in the outer regions remain challenging to obtain. Here, we demonstrate a novel method to probe the angular momentum transport at the outer edge of the disc. This method applies to PPDs that have lost a significant fraction of their mass due to thermal winds driven by UV irradiation from a neighbouring OB star. We demonstrate that this external photoevaporation can explain the observed depletion of discs in the 3–5 Myr old σ Orionis region, and use our model to make predictions motivating future empirical investigations of disc winds. For populations of intermediate-age PPDs, in viscous models we show that the mass flux outwards due to angular momentum redistribution is balanced by the mass-loss in the photoevaporative wind. A comparison between wind mass-loss and stellar accretion rates therefore offers an independent constraint on viscous models in the outer regions of PPDs.

Long-Term Evolution of Convectively Unstable Disk

AbstractWe continue studying convection as a possible factor of episodic accretion in protoplanetary disks. Within the model of a viscous disk, the accretion history is analyzed at different rates and regions of matter inflow from the envelope onto the disk. It is shown that the burst-like regime occurs in a wide range of parameters. The long-term evolution of the disk is modeled, including the decreasing-with-time matter inflow from the envelope. It is demonstrated that the disk becomes convectively unstable and maintains burst-like accretion onto the star for several million years. The general conclusion of the study is that convection can serve as one of the mechanisms of episodic accretion in protostellar disks, but this conclusion needs to be verified using more consistent hydrodynamic models.

Gravitoviscous protoplanetary disks with a dust component

Aims. We study the dynamics and growth of dust particles in circumstellar disks of different masses that are prone to gravitational instability during the critical first Myr of their evolution. Methods. We solved the hydrodynamics equations for a self-gravitating and viscous circumstellar disk in a thin-disk limit using the FEOSAD numerical hydrodynamics code. The dust component is made up of two different components: micron-sized dust and grown dust of evolving size. For the dust component, we considered the dust coagulation, fragmentation, momentum exchange with the gas, and dust self-gravity. Results. We found that the micron-sized dust particles grow rapidly in the circumstellar disk, reaching a few cm in size in the inner 100 au of the disk during less than 100 kyr after the disk formation, provided that fragmentation velocity is 30 ms−1. Due to the accretion of micron dust particles from the surrounding envelope, which serves as a micron dust reservoir, the approximately cm-sized dust particles continue to be present in the disk for more than 900 kyr after the disk formation and maintain a dust-to-gas ratio close to 0.01. We show that a strong correlation exists between the gas and pebble fluxes in the disk. We find that radial surface density distribution of pebbles in the disk shows power-law distribution with an index similar to that of the Minimum-mass solar nebula regardless the disk mass. We also show that the gas surface density in our models agrees well with measurements of dust in protoplanetary disks of AS 209, HD 163296, and DoAr 25 systems. Conclusions. Pebbles are formed during the very early stages of protoplanetary disk evolution. They play a crucial role in the planet formation process. Our disc simulations reveal the early onset (<105 yr) of an inwards-drifting flux of pebble-sized particles that makes up approximately between one hundredth and one tenth of the gas mass flux, which appears consistent with mm-observations of discs. Such a pebble flux would allow for the formation of planetesimals by streaming instability and the early growth of embryos by pebble accretion. We conclude that unlike the more common studies of isolated steady-state protoplanetary disks, more sophisticated global numerical simulations of circumstellar disk formation and evolution, including the pebble formation from the micron dust particles, are needed for performing realistic planet formation studies.

Visible and near-infrared spectro-interferometric analysis of the edge-on Be star o Aquarii

Aims. We present a detailed visible and near-infrared spectro-interferometric analysis of the Be-shell star o Aquarii from quasi-contemporaneous CHARA/VEGA and VLTI/AMBER observations. Methods. We analyzed spectro-interferometric data in the Hα (VEGA) and Brγ (AMBER) lines using models of increasing complexity: simple geometric models, kinematic models, and radiative transfer models computed with the 3D non-LTE code HDUST. Results. We measured the stellar radius of o Aquarii in the visible with a precision of 8%: 4.0 ± 0.3 R⊙. We constrained the circumstellar disk geometry and kinematics using a kinematic model and a MCMC fitting procedure. The emitting disk sizes in the Hα and Brγ lines were found to be similar, at ~10–12 stellar diameters, which is uncommon since most results for Be stars indicate a larger extension in Hα than in Brγ. We found that the inclination angle i derived from Hα is significantly lower (~15°) than the one derived from Brγ: i ~ 61.2° and 75.9°, respectively. While the two lines originate from a similar region of the disk, the disk kinematics were found to be near to the Keplerian rotation (i.e., β = −0.5) in Brγ (β ~ −0.43), but not in Hα (β ~ −0.30). After analyzing all our data using a grid of HDUST models (BeAtlas), we found a common physical description for the circumstellar disk in both lines: a base disk surface density Σ0 = 0.12 g cm−2 and a radial density law exponent m = 3.0. The same kind of discrepancy, as with the kinematic model, is found in the determination of i using the BeAtlas grid. The stellar rotational rate was found to be very close (~96%) to the critical value. Despite being derived purely from the fit to interferometric data, our best-fit HDUST model provides a very reasonable match to non-interferometric observables of o Aquarii: the observed spectral energy distribution, Hα and Brγ line profiles, and polarimetric quantities. Finally, our analysis of multi-epoch Hα profiles and imaging polarimetry indicates that the disk structure has been (globally) stable for at least 20 yr. Conclusions. Looking at the visible continuum and Brγ emission line only, o Aquarii fits in the global scheme of Be stars and their circumstellar disk: a (nearly) Keplerian rotating disk well described by the viscous decretion disk (VDD) model. However, the data in the Hα line shows a substantially different picture that cannot fully be understood using the current generation of physical models of Be star disks. The Be star o Aquarii presents a stable disk (close to the steady-state), but, as in previous analyses, the measured m is lower than the standard value in the VDD model for the steady-state regime (m = 3.5). This suggests that some assumptions of this model should be reconsidered. Also, such long-term disk stability could be understood in terms of the high rotational rate that we measured for this star, the rate being a main source for the mass injection in the disk. Our results on the stellar rotation and disk stability are consistent with results in the literature showing that late-type Be stars are more likely to be fast rotators and have stable disks.