Viscous Disk Research Articles

Generation of highly inclined protoplanetary discs through single stellar flybys

We study the three-dimensional evolution of a viscous protoplanetary disc which is perturbed by a passing star on a parabolic orbit. The aim is to test whether a single stellar flyby is capable to excite significant disc inclinations which would favour the formation of so-called misaligned planets. We use smoothed particle hydrodynamics to study inclination, disc mass and angular momentum changes of the disc for passing stars with different masses. We explore different orbital configurations for the perturber's orbit to find the parameter spaces which allow significant disc inclination generation. Prograde inclined parabolic orbits are most destructive leading to significant disc mass and angular momentum loss. In the remaining disc, the final disc inclination is only below $20^\circ$. This is due to the removal of disc particles which have experienced the strongest perturbing effects. Retrograde inclined parabolic orbits are less destructive and can generate disc inclinations up to $60^\circ$. The final disc orientation is determined by the precession of the disc angular momentum vector about the perturber's orbital angular momentum vector and by disc orbital inclination changes. We propose a sequence of stellar flybys for the generation of misalignment angles above $60^\circ$. The results taken together show that stellar flybys are promising and realistic for the explanation of misaligned Hot Jupiters with misalignment angles up to 60\degr.

Multitechnique testing of the viscous decretion disk model

The viscous decretion disk (VDD) model is able to explain most of the currently observable properties of the circumstellar disks of Be stars. However, more stringent tests, focusing on reproducing multitechnique observations of individual targets via physical modeling, are needed to study the predictions of the VDD model under specific circumstances. In the case of nearby, bright Be star $\beta$ CMi, these circumstances are a very stable low-density disk and a late-type (B8Ve) central star. The aim is to test the VDD model thoroughly, exploiting the full diagnostic potential of individual types of observations, in particular, to constrain the poorly known structure of the outer disk if possible, and to test truncation effects caused by a possible binary companion using radio observations. We use the Monte Carlo radiative transfer code HDUST to produce model observables, which we compare with a very large set of multitechnique and multiwavelength observations that include ultraviolet and optical spectra, photometry covering the interval between optical and radio wavelengths, optical polarimetry, and optical and near-IR (spectro)interferometry. Due to the absence of large scale variability, data from different epochs can be combined into a single dataset. A parametric VDD model with radial density exponent of $n$ = 3.5, which is the canonical value for isothermal flaring disks, is found to explain observables typically formed in the inner disk, while observables originating in the more extended parts favor a shallower, $n$ = 3.0, density falloff. Modeling of radio observations allowed for the first determination of the physical extent of a Be disk (35$^{+10}_{-5}$ stellar radii), which might be caused by a binary companion. Finally, polarization data allowed for an indirect measurement of the rotation rate of the star, which was found to be $W \gtrsim 0.98$, i.e., very close to critical.

Suppression of type I migration by disk winds

Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw < 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths.

THE KOZAI–LIDOV MECHANISM IN HYDRODYNAMICAL DISKS. III. EFFECTS OF DISK MASS AND SELF-GRAVITY

Previously we showed that a substantially misaligned viscous accretion disk with pressure that orbits around one component of a binary system can undergo global damped Kozai-Lidov (KL) oscillations. These oscillations produce periodic exchanges of the disk eccentricity with inclination. The disk KL mechanism is quite robust and operates over a wide range of binary and disk parameters. However, the effects of self-gravity, which are expected to suppress the KL oscillations for sufficiently massive disks, were ignored. Here, we analyze the effects of disk self-gravity by means of hydrodynamic simulations and compare the results with the expectations of analytic theory. The disk mass required for suppression in the simulations is a few percent of the mass of the central star and this roughly agrees with an analytical estimate. The conditions for suppression of the KL oscillations in the simulations are close to requiring that the disk be gravitationally unstable. We discuss some implications of our results for the dynamics of protoplanetary disks and the related planet formation.

The pseudo-photosphere model for the continuum emission of gaseous discs

We investigate the continuum emission of viscous decretion discs around Be stars in this paper. The results obtained from non-LTE (local thermodynamic equilibrium) radiative transfer models show two regimes in the disc surface brightness profile: an inner optically thick region, which behaves as a pseudo-photosphere with a wavelength-dependent size, and an optically thin tenuous outer part, which contributes with about a third of the total flux. The isophotal shape of the surface brightness is well described by elliptical contours with an axial ratio $b/a=\cos i$ for inclinations $i<75^{\circ}$. Based on these properties, a semi-analytical model was developed to describe the continuum emission of gaseous discs. It provides fluxes and spectral slopes at the infrared within an accuracy of $10\%$ and $5\%$, respectively, when compared to the numerical results. The model indicates that the infrared spectral slope is mainly determined by both the density radial slope and the disc flaring exponent, being practically independent of disc inclination and base density. As a first application, the density structure of 15 Be stars was investigated, based on the infrared flux excess, and the results compared to previous determinations in the literature. Our results indicate that the decretion rates are in the range of $10^{-12}$ to $10^{-9}\,{\rm M_{\odot}\,yr^{-1}}$, which is at least two orders of magnitude smaller than the previous outflowing disc model predictions.

OPTICAL AND NEAR-INFRARED SPECTROSCOPY OF THE BLACK HOLE SWIFT J1753.5–0127

We report on a multiwavelength observational campaign of the black hole X-ray binary Swift J1753.5-0127 that consists of an ESO/X-shooter spectrum supported by contemporaneous Swift/XRT+UVOT and ATCA data. ISM absorption lines in the X-shooter spectrum allows us to determine E(B-V)=0.45+/-0.02 along the line-of-sight to the source. We also report detection of emission signatures of He II at 4686 angstrom, H alpha, and, for the first time, H I at 10906 angstrom and Paschen Beta. The double-peaked morphology of these four lines is typical of the chromosphere of a rotating accretion disk. Nonetheless, the paucity of disk features points towards a low level of irradiation in the system. This is confirmed through spectral energy distribution modeling and we find that the UVOT+X-shooter continuum mostly stems from the thermal emission of a viscous disk. We speculate that the absence of reprocessing is due to the compactness of an illumination-induced envelope that fails to reflect enough incoming hard X-ray photons back to the outer regions. The disk also marginally contributes to the Compton-dominated X-ray emission and is strongly truncated, with an inner radius about a thousand times larger than the black hole's gravitational radius. A near-infrared excess is present, and we associate it with synchrotron radiation from a compact jet. However, the measured X-ray flux is significantly higher than what can be explained by the optically thin synchrotron jet component. We discuss these findings in the framework of the radio quiet versus X-ray bright hypothesis, favoring the presence of a residual disk, predicted by evaporation models, that contributes to the X-ray emission without enhancing the radio flux.

On the migration of two planets in a disc and the formation of mean motion resonances

We study the dynamics of a system of two super-Earths embedded in a protoplanetary disc. We build a simple model of an irradiated viscous disc and use analytical prescriptions for the planet-disc interactions which lead to migration. We show that depending on the disc parameters, planets' masses and their positions in the disc, the migration of each planet can be inward or outward and the migration of a two-planet system can be convergent (which may lead to formation of a first order mean motion resonance, MMR) or divergent (a system moves away from MMR). We performed $3500$ simulations of the migration of two-planet systems with various masses and initial orbits. Almost all of them end up as resonant configurations, although the period ratios may be very distant from the nominal values of a given MMR. We found that almost all the systems resulting from the migration are periodic configurations.

Chondrule transport in protoplanetary discs

Chondrule formation remains one of the most elusive early Solar system events. Here, we take the novel approach of employing numerical simulations to investigate chondrule origin beyond purely cosmochemical methods. We model the transport of generically produced chondrules and dust in a 1D viscous protoplanetary disc model in order to constrain the chondrule formation events. For a single formation event we are able to match analytical predictions of the memory they retain of each other (complementarity), finding that a large mass accretion rate (10−7 M yr−1) allows for delays on the order of the disc’s viscous time-scale between chondrule formation and chondrite accretion. Further, we find older discs to be severely diminished of chondrules, with accretion rates 10−9 M yr−1 for nominal parameters. We then characterize the distribution of chondrule origins in both space and time, as functions of disc parameters and chondrule formation rates, in runs with continuous chondrule formation and both static and evolving discs. Our data suggest that these can account for the observed diversity between distinct chondrite classes, if some diversity in accretion time is allowed for

PROTOPLANETARY DISKS INCLUDING RADIATIVE FEEDBACK FROM ACCRETING PLANETS

While recent observational progress is converging on the detection of compact regions of thermal emission due to embedded protoplanets, further theoretical predictions are needed to understand the response of a protoplanetary disk to the planet formation radiative feedback. This is particularly important to make predictions for the observability of circumplanetary regions. In this work we use 2D hydrodynamical simulations to examine the evolution of a viscous protoplanetary disk in which a luminous Jupiter-mass planet is embedded. We use an energy equation which includes the radiative heating of the planet as an additional mechanism for planet formation feedback. Several models are computed for planet luminosities ranging from $10^{-5}$ to $10^{-3}$ Solar luminosities. We find that the planet radiative feedback enhances the disk's accretion rate at the planet's orbital radius, producing a hotter and more luminous environement around the planet, independently of the prescription used to model the disk's turbulent viscosity. We also estimate the thermal signature of the planet feedback for our range of planet luminosities, finding that the emitted spectrum of a purely active disk, without passive heating, is appreciably modified in the infrared. We simulate the protoplanetary disk around HD 100546 where a planet companion is located at about 68 au from the star. Assuming the planet mass is 5 Jupiter masses and its luminosity is $\sim 2.5 \times 10^{-4} \, L_\odot$, we find that the radiative feedback of the planet increases the luminosity of its $\sim 5$ au circumplanetary disk from $10^{-5} \, \rm L_\odot$ (without feedback) to $10^{-3} \, \rm L_\odot$, corresponding to an emission of $\sim 1 \, \rm mJy$ in $L^\prime$ band after radiative transfer calculations, a value that is in good agreement with HD 100546b observations.

The link between disc dispersal by photoevaporation and the semimajor axis distribution of exoplanets

We investigate the influence of photoevaporation of protoplanetary discs on the final distribution of exoplanets semimajor axis distances. We model giant planet migration in viscous discs affected by photoevaporation driven by either pure EUV or soft X-ray radiation (XEUV). We show that the final exoplanet distributions are strongly dependant on the choice of the photoevaporation model. In particular, we find that XEUV is more efficient than pure EUV radiation at parking planets at approximately 1-2 au distance from their central star, hence roughly reproducing the observed peak in the exoplanets semimajor axis distributions. We note however that a more quantitative comparison with the observations is hindered by the oversimplified treatment of planetary accretion, which severely affects migration rates. For this reason, caution should be used when using these models to constrain details of disc clearing and/or migration from the observations. Nevertheless our results indicate that disc dispersal by photoevaporation may be the main driver of the features in the exoplanets semimajor axis distribution observed by recent surveys.

Self-similar evolution of self-gravitating viscous accretion discs

A new one-dimensional, dynamical model is proposed for geometrically thin, self-gravitating viscous accretion discs. The vertically integrated equations are simplified using the slow accretion limit and the monopole approximation with a time-dependent central point mass to account for self-gravity and accretion. It is shown that the system of partial differential equations can be reduced to a single non-linear advection diffusion equation which describes the time evolution of angular velocity. In order to solve the equation three different turbulent viscosity prescriptions are considered. It is shown that for these parametrizations the differential equation allows for similarity transformations depending only on a single non-dimensional parameter. A detailed analysis of the similarity solutions reveals that this parameter is the initial power law exponent of the angular velocity distribution at large radii. The radial dependence of the self-similar solutions is in most cases given by broken power laws. At small radii the rotation law always becomes Keplerian with respect to the current central point mass. In the outer regions the power law exponent of the rotation law deviates from the Keplerian value and approaches asymptotically the value determined by the initial condition. It is shown that accretion discs with flatter rotation laws at large radii yield higher accretion rates. The methods are applied to self-gravitating accretion discs in active galactic nuclei. Fully self-gravitating discs are found to evolve faster than nearly Keplerian discs. The implications on supermassive black hole formation and Quasar evolution are discussed.

Thickness of Saturn’s B ring as derived from seasonal temperature variations measured by Cassini CIRS

Structural and thermal properties of Saturn’s B ring and its particles are derived from orbital and seasonal temperatures variations observed by the Cassini CIRS spectrometer between 2004 and 2009 equinox. Our multiscale thermal model (Ferrari, C., Reffet, E. [2013]. Icarus 223, 28–39), which assumes negligible heat transfer by vertical motion of particles in dense rings, is adjusted to the data. Most observations were focused on the center of the B ring, at 105,000km from Saturn. A very good fit is obtained for conductive particles embedded in a moderately conductive ring medium. Assuming a bulk composition of water ice, the thermal inertia of particles is found to be Γ1=160–200J/m2/K/s1/2 and to vary with seasons as part of the heat transfer is radiative, then temperature-dependent. For the same reason, the thermal inertia of the ring, Γ0, varies with seasons, between 30 and 35J/m2/K/s1/2. It is very comparable to the thermal inertia of icy satellite surfaces. The porosity of particles p1 found to fit this thermal inertia is very high (0.93) and may emphasize an inappropriate modeling of particles by an effective porous medium. The ring filling factor is fairly high, D=0.34±0.01, but stays typical of a compact medium and compatible with the output of numerical simulations of dense ring dynamics. The thickness of the B ring at 105,000km from Saturn is estimated at HS=2.2±0.2m. The observed correlation of its optical depth with the thermal gradient between lit and unlit sides is easily reproduced by the model if the radial variations in optical depth are due to varying thickness HS(a) with constant filling factor. This thickness varies between 1 and 3m across theB2,B3 and B4 regions. It is thinner than the neighboring C ring and Cassini Division. This can be understood as a consequence of self-gravity. The ring surface mass density Σ=(1-p1)ρ0DHS(a) derived from these structural parameters is too low for a self-gravitating ring, due to the high porosity found. But its radial variations, if deduced from coupling HS(a) with known aspect-ratios H/λ of self-gravity wakes, range between 300 in the inner B ring and most certainly exceed 1000kg/m2 in the B3 ring, values compatible with a self-gravitating ring. The inferred minimum total mass of Saturn's rings is MR=1.4±0.2·1019kg, close to the mass expected for a viscous disk evolving over the age of the Solar System and compatible with current higher estimates.

Misaligned gas discs around eccentric black hole binaries and implications for the final-parsec problem

We investigate the evolution of low mass (Md /Mb = 0.005) misaligned gaseous discs around eccentric supermassive black hole (SMBH) binaries. These are expected to form from randomly oriented accretion events onto a SMBH binary formed in a galaxy merger. When expanding the interaction terms between the binary and a circular ring to quadrupole order and averaging over the binary orbit, we expect four non-precessing disc orientations: aligned or counter-aligned with the binary, or polar orbits around the binary eccentricity vector with either sense of rotation. All other orientations precess around either of these, with the polar precession dominating for high eccentricity. These expectations are borne out by smoothed particle hydrodynamics simulations of initially misaligned viscous circumbinary discs, resulting in the formation of polar rings around highly eccentric binaries in contrast to the co-planar discs around circular binaries. Moreover, we observe disc tearing and violent interactions between differentially precessing rings in the disc significantly disrupting the disc structure and causing gas to fall onto the binary with little angular momentum. While accretion from a polar disc may not promote SMBH binary coalescence (solving the `final-parsec problem'), ejection of this infalling low-angular momentum material via gravitational slingshot is a possible mechanism to reduce the binary separation. Moreover, this process acts on dynamical rather than viscous time scales, and so is much faster.

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 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 ∼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.

Formation of a disc gap induced by a planet: effect of the deviation from Keplerian disc rotation

The gap formation induced by a giant planet is important in the evolution of the planet and the protoplanetary disc. We examine the gap formation by a planet with a new formulation of one-dimensional viscous discs which takes into account the deviation from Keplerian disc rotation due to the steep gradient of the surface density. This formulation enables us to naturally include the Rayleigh stable condition for the disc rotation. It is found that the derivation from Keplerian disc rotation promotes the radial angular momentum transfer and makes the gap shallower than in the Keplerian case. For deep gaps, this shallowing effect becomes significant due to the Rayleigh condition. In our model, we also take into account the propagation of the density waves excited by the planet, which widens the range of the angular momentum deposition to the disc. The effect of the wave propagation makes the gap wider and shallower than the case with instantaneous wave damping. With these shallowing effects, our one-dimensional gap model is consistent with the recent hydrodynamic simulations.

1D accretion discs around eccentric planets: observable near-infrared variability

Abstract I present the results of 1D models of circumplanetary discs around planets on eccentric orbits. I use a classical viscous heating model to calculate emission fluxes at the wavelengths targeted by the NIRCam instrument on JWST, and compare the variability of this signal with the published NIRCam sensitivity specifications. This variability is theoretically detectable by JWST for a sufficiently viscous disc (α ∼ 10−2) around a sufficiently eccentric planet (e ∼ 0.1–0.2) and if the circumplanetary disc accretes material from its parent disc at a rate $\skew4\dot{M} \gtrsim 10^{-7}\,\mathrm{M}_{\odot }$ yr−1. I discuss the limitations of the models used, and the implications of the result for probing the effectiveness of disc interactions for growing a planet's orbital eccentricity.

STATISTICAL ANALYSIS OF INTERFEROMETRIC MEASUREMENTS OF AXIS RATIOS FOR CLASSICAL Be STARS

This work presents a novel method to estimate the effective opening angle of CBe star disks from projected axis ratio measurements, obtained by interferometry using Bayesian statistics. A Monte Carlo scheme was used to generate a large set of theoretical axis ratios from disk models using different distributions of disk densities and opening angles. These theoretical samples were then compared to observational samples, using a two-sample Kolmogorov-Smirnov test, to determine which theoretical distribution best reproduces the observations. The results suggest that the observed ratio distributions in the K-, H-, and N-band can best be explained by the presence of thin disks, with opening half-angles of the order of 0.15$^{\circ}$ to 4.0$^{\circ}$. Results for measurements over the H$\alpha$ line point toward slightly thicker disks, 3.7$^{\circ}$ to 14$^{\circ}$, which is consistent with a flaring disk predicted by the viscous disk model.

RADIAL TRANSPORT OF LARGE-SCALE MAGNETIC FIELDS IN ACCRETION DISKS. II. RELAXATION TO STEADY STATES

We study the time evolution of a large-scale magnetic flux threading an accretion disk. Induction equation of the mean poloidal field is solved under the standard viscous disk model. Magnetic flux evolution is controlled by the two timescales: One is the timescale of the inward advection of the magnetic flux, tau_{adv}. This is induced by the dragging of the flux by the accreting gas. The other is the outward diffusion timescale of the magnetic flux tau_{dif}. We consider diffusion due to the Ohmic resistivity. These timescales can be significantly different from the disk viscous timescale tau_{disk}. The behaviors of the magnetic flux evolution is quite different depending on the magnitude relationship of the timescales tau_{adv}, \tau_{dif}, and tau_{disk}. The most interesting phenomena occurs when tau_{adv} << tau_{dif}, tau_{disk}. In such a case, the magnetic flux distribution approaches a quasi-steady profile much faster than the viscous evolution of the gas disk, and also the magnetic flux has been tightly bundled to the inner part of the disk. In the inner part, although the poloidal magnetic field becomes much stronger than the interstellar magnetic field, the field strength is limited to the maximum value that is analytically given by our previous work (Okuzumi et al. 2014, ApJ, 785, 127). We also find a condition for that the initial large magnetic flux, which is a fossil of the magnetic field dragging during the early phase of star formation, survives for a duration in which significant gas disk evolution proceeds.

HerschelOBSERVATIONS OF DUST AROUND THE HIGH-MASS X-RAY BINARY GX 301-2

We aim at characterising the structure of the gas and dust around the high mass X-ray binary GX 301-2, a highly obscured X-ray binary hosting a hypergiant star and a neutron star, in order to better constrain its evolution. We used Herschel PACS to observe GX 301-2 in the far infrared and completed the spectral energy distribution of the source using published data or catalogs, from the optical to the radio range (0.4 to 4x10^4 micrometer). GX 301-2 is detected for the first time at 70 and 100 micrometer. We fitted different models of circumstellar environments to the data. All tested models are statistically acceptable, and consistent with a hypergiant star at ~3 kpc. We found that the addition of a free-free emission component from the strong stellar wind is required and could dominate the far infrared flux. Through comparisons with similar systems and discussion on the estimated model parameters, we favour a disk-like circumstellar environment of ~8 AU that would enshroud the binary system. The temperature goes down to ~200 K at the edge of the disk, allowing for dust formation. This disk is probably a rimmed viscous disk with an inner rim at the temperature of the dust sublimation temperature (~1500 K). The similarities between the hypergiant GX 301-2, B[e] supergiants and the highly obscured X-ray binaries (in particular IGR J16318-4848) are strengthened. GX 301-2 might represent a transition stage in the evolution of massive stars in binary systems, connecting supergiant B[e] systems to luminous blue variables.

Drag and torque coefficients for plate and disk induced stokes flows with slip

A key purpose of this paper is to demonstrate that the introduction of slip changes the structure of viscous flow past plates and disks by precluding edge singularities in the stresses. It is well-known that the inviscid limit flow is not recovered by letting the viscosity tend to zero. Here it is demonstrated that, similarly, the no-slip limit flow is not recovered by letting the slip coefficient tend to zero. For each of the three cases involving a translating plate and a rotating or translating disk, the determination of the tangential stress is reduced to a linear system of equations with simple coefficients. Values of the drag or torque and edge stresses are displayed.