Viscous Evolution Research Articles

“Near Ground” Vertical Vorticity in Supercell Thunderstorm Models

Abstract Numerical models of supercell thunderstorms produce near-ground rotation about a vertical axis (i.e., vertical vorticity) after the development of rain-cooled outflows and downdrafts. The physical processes involved in the production of near-ground vertical vorticity in simulated supercells have been a subject of discussion in the literature for over 30 years. One cause for this lengthy discussion is the difficulty in applying the principles of inviscid vorticity dynamics in a continuous fluid to the viscous evolution of discrete Eulerian simulations. The present paper reports on a Lagrangian analysis of near-ground vorticity from an idealized-supercell simulation with enhanced vertical resolution near the lower surface. The parcel that enters the low-level maximum of vertical vorticity has a history of descent during which its horizontal vorticity is considerably enhanced. In its final approach to this region, the parcel’s enhanced horizontal vorticity is tilted to produce vertical vorticity, which is then amplified through vertical stretching as the parcel rises. A simplified theoretical model is developed that exhibits these same features. The principal conclusion is that vertical vorticity at the parcel’s nadir (its lowest point), although helpful, does not need to be positive for rapid near-surface amplification of vertical vorticity.

Determination of the turbulent parameter in accretion discs: effects of self-irradiation in 4U 1543−47 during the 2002 outburst

We investigate the viscous evolution of the accretion disk in 4U 1543-47, a black hole binary system, during the first 30 days after the peak of the 2002 burst by comparing the observed and theoretical accretion rate evolution $\dot M(t)$. The observed $\dot M(t)$ is obtained from spectral modelling of the archival RXTE/PCA data. Different scenarios of disk decay evolution are possible depending on a degree of self-irradiation of the disk by the emission from its centre. If the self-irradiation, which is parametrized by factor $C_\mathrm{irr}$, had been as high as $\sim 5\times10^{-3}$, then the disk would have been completely ionized up to the tidal radius and the short time of the decay would have required the turbulent parameter $\alpha\sim 3$. We find that the shape of the $\dot M(t)$ curve is much better explained in a model with a shrinking high-viscosity zone. If $C_\mathrm{irr}\approx(2-3)\times 10^{-4}$, the resulting $\alpha$ lie in the interval $0.5-1.5$ for the black hole masses in the range $6-10~\mathrm{M}_\odot$, while the radius of the ionized disk is variable and controlled by irradiation. For very weak irradiation, $C_\mathrm{irr} < 1.5 \times10^{-4}$, the burst decline develops as in normal outbursts of dwarf novae with $\alpha \sim 0.08-0.32$. The optical data indicate that $C_\mathrm{irr}$ in 4U 1543-47 (2002) was not greater than approximately $(3-6)\times10^{-4}$. Generally, modelling of an X-ray nova burst allows one to estimate $\alpha$ that depends on the black hole parameters. We present the public 1-D code Freddi to model the viscous evolution of an accretion disk. Analytic approximations are derived to estimate $\alpha$ in X-ray novae using $\dot M(t)$.

Quasiparticle second-order viscous hydrodynamics from kinetic theory

We present the derivation of second-order relativistic viscous hydrodynamics from an effective Boltzmann equation for a system consisting of quasiparticles of a single species. We consider temperature-dependent masses of the quasiparticles and devise a thermodynamically-consistent framework to formulate second-order evolution equations for shear and bulk viscous pressure corrections. The main advantage of this formulation is that one can consistently implement realistic equation of state of the medium within the framework of kinetic theory. Specializing to the case of one-dimensional purely-longitudinal boost-invariant expansion, we study the effect of this new formulation on viscous hydrodynamic evolution of strongly-interacting matter formed in relativistic heavy-ion collisions.

Evolution of a protolunar disk in vapor/melt equilibrium

AbstractA model of the viscous evolution of a two‐phase, vapor/melt protolunar disk is described. Droplets condense from the vapor and “rain out,” forming a stratified structure with a midplane magma layer surrounded by a vapor reservoir. The magma layer is gravitationally unstable, but material interior to the Roche distance cannot fragment, and instead develops an effective viscosity. However, magma flowing across the Roche limit can fragment and accrete into moonlets, while magma spreading inward is accreted by Earth. As mass leaves the melt layer, it is replenished by vapor condensation, leading to a quasi steady state (QSS). The layer's mass is maintained at ~13% of a lunar mass and replaced every ~ 3.2 years. The vapor atmosphere steadily decreases, and once exhausted, the disk would cool below condensation temperature and spread as a time‐dependent disk until it too is exhausted. The timescale of the QSS is regulated by the disk's ability to radiate all the released latent heat plus viscous dissipation energy to space at the photospheric temperature, i.e., ~2000 K for silicon phase equilibrium. For the protolunar disk, latent heat dominates viscous heating, and the QSS for a ~2 lunar mass disk lasts for ~ 50 years. For comparison, a hypothetical water/steam disk orbiting an ice giant planet in which viscous heating dominates is also modeled. The photospheric temperature is closer to ~373 K, and the replacement time of the water layer is ~136 years. Finally, disks confined by external torques at either the planet‐disk boundary or at its outer edge are also briefly examined.

Longitudinal correlations in the initial stages of ultra-relativistic nuclear collisions

In this talk we review some of our results for the longitudinal correlations in connection with recent experimental data, in particular for the {\em torque} effect and for the two-particle correlations in pseudorapidity, $C(\eta_1,\eta_2)$. The model framework involves event-by-event fluctuations of the initial conditions, followed with 3D viscous hydrodynamic evolution and statistical hadronization.

Merger of a white dwarf–neutron star binary to 1029carat diamonds: origin of the pulsar planets

We show that the merger and tidal disruption of a C/O white dwarf (WD) by a neutron star (NS) binary companion provides a natural formation scenario for the PSR B1257+12 planetary system. Starting with initial conditions for the debris disk produced of the disrupted WD, we model its long term viscous evolution, including for the first time the effects of mass and angular momentum loss during the early radiatively inefficient accretion flow (RIAF) phase and accounting for the unusual C/O composition on the disk opacity. For plausible values of the disk viscosity $\alpha \sim 10^{-3}-10^{-2}$ and the RIAF mass loss efficiency, we find that the disk mass remaining near the planet formation radius at the time of solid condensation is sufficient to explain the pulsar planets. Rapid rocky planet formation via gravitational instability of the solid carbon-dominated disk is facilitated by the suppression of vertical shear instabilities due to the high solid-to-gas ratio. Additional evidence supporting a WD-NS merger scenario includes (1) the low observed occurrence rate of pulsar planets ($\lesssim 1\%$ of NS birth), comparable to the expected WD-NS merger rate; (2) accretion by the NS during the RIAF phase is sufficient to spin PSR B1257+12 up to its observed 6 ms period; (3) similar models of `low angular momentum' disks, such as those produced from supernova fallback, find insufficient mass reaching the planet formation radius. The unusually high space velocity of PSR B1257+12 of $\gtrsim 326\,{\rm km\,s}^{-1}$ suggests a possible connection to the Calcium-rich transients, dim supernovae which occur in the outskirts of their host galaxies and were proposed to result from mergers of WD-NS binaries receiving SN kicks. The C/O disk composition implied by our model likely results in carbon-rich planets with diamond interiors.

Close-in planetesimal formation by pile-up of drifting pebbles

The consistency of planet formation models suffers from the disconnection between the regime of small and large bodies. This is primarily caused by so-called growth barriers: the direct growth of larger bodies is halted at centimetre-sized objects and particular conditions are required for the formation of larger, gravitationally bound planetesimals. We aim to connect models of dust evolution and planetesimal formation to identify regions of protoplanetary discs that are favourable for the formation of kilometre-sized bodies and the first planetary embryos. We combine semi-analytical models of viscous protoplanetary disc evolution, dust growth and drift including backreaction of the dust particles on the gas, and planetesimal formation via the streaming instability into one numerical code. We investigate how planetesimal formation is affected by the mass of the protoplanetary disc, its initial dust content, and the stickiness of dust aggregates. We find that the dust growth and drift leads to a global redistribution of solids. The pile-up of pebbles in the inner disc provides local conditions where the streaming instability is effective. Planetesimals form in an annulus with its inner edge lying between 0.3 AU and 1 AU and its width ranging from 0.3 AU to 3 AU. The resulting surface density of planetesimals follows a radial profile that is much steeper than the initial disc profile. These results support formation of terrestrial planets in the solar system from a narrow annulus of planetesimals, which reproduces their peculiar mass ratios.

IN SITU AND EX SITU FORMATION MODELS OF KEPLER 11 PLANETS

ABSTRACT We present formation simulations of the six Kepler 11 planets. Models assume either in situ or ex situ assembly, the latter with migration, and are evolved to the estimated age of the system, . Models combine detailed calculations of both the gaseous envelope and the condensed core structures, including accretion of gas and solids, of the disk’s viscous and thermal evolution, including photo-evaporation and disk-planet interactions, and of the planet’s evaporative mass loss after disk dispersal. Planet–planet interactions are neglected. Both sets of simulations successfully reproduce measured radii, masses, and orbital distances of the planets, except for the radius of Kepler 11b, which loses its entire gaseous envelope shortly after formation. Gaseous (H+He) envelopes account for % of the planet masses, and between and % of the planet radii. In situ models predict a very massive inner disk, whose solid surface density ( ) varies from over 104 to at stellocentric distances . Initial gas densities would be in excess of if solids formed locally. Given the high disk temperatures ( ), planetary interiors can only be composed of metals and highly refractory materials. Sequestration of hydrogen by the core and subsequent outgassing is required to account for the observed radius of Kepler 11b. Ex situ models predict a relatively low-mass disk, whose initial varies from to at and whose initial gas density ranges from to . All planetary interiors are expected to be rich in H2O, as core assembly mostly occurs exterior to the ice condensation front. Kepler 11b is expected to have a steam atmosphere, and H2O is likely mixed with H+He in the envelopes of the other planets. Results indicate that Kepler 11g may not be more massive than Kepler 11e.

Relatingq̂, η/s, andΔEin an expanding quark-gluon plasma

We use linear viscous hydrodynamics to describe the energy and momentum deposited by a fast moving parton in a quark gluon plasma. This energy-momentum is in turn used to compute the probability density for the production of soft partons by means of the Cooper-Frye formula. We use this probability density to render manifest a relation between the average transverse momentum given to the fast moving parton from the medium $\hat{q}$, the entropy density to shear viscosity ratio $\eta/s$ and the energy lost by the fast moving parton $\Delta E$ in an expanding medium under similar conditions to those generated in nucleus-nucleus collisions at the LHC. We find that $\hat{q}$ increases linearly with $\Delta E$ for both trigger and away side partons that have been produced throughout the medium. On the other hand, $\eta/s$ is more stable with $\Delta E$. We also study how these transport coefficients vary with the geometrical location of the hard scattering that produces the fast moving partons. The behavior of $\hat{q}$, with $\Delta E$ is understood as arising from the length of medium the parton traverses from the point where it is produced. However, since $\eta/s$ is proportional to the ratio of the length of medium traversed by the fast parton and the average number of scatterings it experiences, it has a milder dependence on the energy it loses. This study represents a tool to obtain a direct connection between transport coefficients and the description of in-medium energy loss within a linear viscous hydrodynamical evolution of the bulk.

Effect of radial flow on two particle correlations with identified triggers at intermediate p T in p–Pb collisions atsNN=5.02 TeV

Results from the two-particle correlation between identified triggers (pions ($\pi^{\pm}$) , protons (p/$\bar{p}$))) and un-identified charged particles at intermediate transverse momentum ($p_{T}$) in p-Pb collisions at $\sqrt{s_{NN}} = $ 5.02 TeV have been presented. The events generated from a hybrid Monte-Carlo event generator, EPOS 3.107 that implements a flux-tube initial conditions followed by event by event 3+1D viscous hydrodynamical evolution, have been analysed to calculate two-dimensional correlation functions in $\Delta\eta$-$\Delta\phi$. The strength of angular correlations at small relative angles (jet-like correlations), quantified in terms of near-side jet-like per-trigger yield has been calculated as a function of the event multiplicity. The yield associated with pion triggers exhibit negligible multiplicity dependence, while the proton-triggered yield shows a gradual suppression from low to high multiplicity events. In small collision systems like p-Pb where jet modification is expected to be less dominant, the observed suppression may be associated with the hydrodynamical evolution of the bulk system that generates an outward radial flow. Analogous measurements in Au-Au collisions at RHIC energy have shown a hint of dilution in proton-triggered correlation at its highest multiplicity suggesting that the soft physics processes in p-Pb and heavy ion collisions may have qualitative similarity.

LONG-TERM AND LARGE-SCALE HYDRODYNAMICAL SIMULATIONS OF MIGRATING PLANETS

ABSTRACT We present a new method that allows for long-term and large-scale hydrodynamical simulations of migrating planets over a grid-based Eulerian code. This technique, which consists of a remapping of the disk by tracking the planetary migration, enables runs of migrating planets over a time comparable to the age of protoplanetary disks. This method also has the potential to address efficiency problems related to the migration of multi-planet systems in gaseous disks and to improve the current results of the migration of massive planets by including global viscous evolution as well as detailed studies of the co-orbital region during migration. We perform different tests using the public code FARGO3D to validate this method and compare its results with those obtained using a classical fixed grid.

FINAL MASSES OF GIANT PLANETS. II. JUPITER FORMATION IN A GAS-DEPLETED DISK

ABSTRACT First, we study the final masses of giant planets growing in protoplanetary disks through capture of disk gas, by employing empirical formulae for the gas capture rate and a shallow disk gap model, which are both based on hydrodynamic simulations. We find that, for planets less massive than 10 Jupiter masses, their growth rates are mainly controlled by the gas supply through the global disk accretion, and the gap opening does not limit the accretion. The insufficient gas supply compared with the rapid gas capture causes a depletion of the gas surface density even at the outside the gap, which can create an inner hole in the disk. Second, our findings are applied to the formation of our solar system. For the formation of Jupiter, a very low-mass gas disk of several Jupiter masses is required at the beginning of its gas capture because of the continual capture. Such a low-mass gas disk with sufficient solid material can be formed through viscous evolution from a compact disk of initial size ∼10 au. By viscous evolution with a moderate viscosity of α ∼ 10−3, most of the disk gas accretes onto the Sun and a widely spread low-mass gas disk remains when the solid core of Jupiter starts gas capture at t ∼ 107 yr. A very low-mass gas disk also provides a plausible path where type I and II planetary migrations are both suppressed significantly. In particular, the type II migration of Jupiter-size planets becomes inefficient because of the additional gas depletion due to the rapid gas capture by such planets.

Trapping planets in an evolving protoplanetary disk: preferred time, locations, and planet mass

Planet traps are necessary to prevent forming planets from falling onto their host star by type I migration. Surface mass density and temperature gradient irregularities favor the apparition of traps and deserts. Such features are found at the dust sublimation lines and heat transition barriers. We study how planets may remain trapped or escape as they grow and as the disk evolves. We model the temporal viscous evolution of a protoplanetary disk by coupling its dynamics, thermodynamics, geometry and composition. The resulting mid-plane density and temperature profiles allow the modeling of the interactions of such an evolving disk with potential planets, even before the steady state is reached. We follow the viscous evolution of a MMSN and compute the Lindblad and corotation torques that such a disk would exert on potential planets of various masses located within the planetary formation region. We determine the position of planet traps and deserts in relationship with the sublimation lines, shadowed regions and heat transition barriers. Planets that are a few tens of Earth masses can be trapped at the sublimation lines until they reach a certain mass while planets more massive than 100ME can only be trapped permanently at the heat transition barriers. Coupling a bimodal planetary migration model with a self-consistent evolved disk, we were able to distinguish several potential planet populations after 5 million years of evolution: two populations of giant planets that could stay trapped around 5.5 and 9 au and possibly open gaps, some super-Earths trapped around 5 and 7.5 au and a population of close-in super-Earths trapped inside 1 au. The traps corresponding to the last group could help validating the in-situ formation scenarios of the observed close-in super-Earths.

GodunovSPH with shear viscosity: implementation and tests

The acceleration and energy dissipation terms due to the shear viscosity have been implemented and tested in GodunovSPH. The double summation method has been employed to avoid the well known numerical noise of the second derivative in particle based codes. The plane Couette flow with various initial and boundary conditions have been used as tests, and the numerical and analytical results show a good agreement. Not only the viscosity--only calculation, but the full hydrodynamics simulations have been performed, and they show expected results as well. The very low kinematic viscosity simulations show a turbulent pattern when the Reynolds number exceeds $\sim$$10^2$. The critical value of the Reynolds number at the transition point of the laminar and turbulent flows coincides with the previous works approximately. A smoothed dynamic viscosity has been suggested to describe the individual kinematic viscosity of particles. The infinitely extended Couette flow which has two layers of different viscosities has been simulated to check the smoothed dynamic viscosity, and the result agrees well with the analytic solution. In order to compare the standard SPH and GodunovSPH, the two layers test has been performed again with a density contrast. GodunovSPH shows less dispersion than the standard SPH, but there is no significant difference in the results. The results of the viscous ring evolution has also been presented as well, and the numerical results agrees with the analytic solution.

On the formation of compact planetary systems via concurrent core accretion and migration

We present the results of planet formation N-body simulations based on a comprehensive physical model that includes planetary mass growth through mutual embryo collisions and planetesimal/boulder accretion, viscous disc evolution, planetary migration and gas accretion onto planetary cores. The main aim of this study is to determine which set of model parameters leads to the formation of planetary systems that are similar to the compact low mass multi-planet systems that have been discovered by radial velocity surveys and the Kepler mission. We vary the initial disc mass, solids-to-gas ratio and the sizes of the boulders/planetesimals, and for a restricted volume of the parameter space we find that compact systems containing terrestrial planets, super-Earths and Neptune-like bodies arise as natural outcomes of the simulations. Disc models with low values of the solids-to-gas ratio can only form short-period super-Earths and Neptunes when small planetesimals/boulders provide the main source of accretion, since the mobility of these bodies is required to overcome the local isolation masses for growing embryos. The existence of short-period super-Earths around low metallicity stars provides strong evidence that small, mobile bodies (planetesimals, boulders or pebbles) played a central role in the formation of the observed planets.

TATOOINE NURSERIES: STRUCTURE AND EVOLUTION OF CIRCUMBINARY PROTOPLANETARY DISKS

ABSTRACT Recent discoveries of circumbinary planets by the Kepler mission provide motivation for understanding their birthplaces—protoplanetary disks around stellar binaries with separations &lsim; 1 AU ?> . We explore properties and evolution of such circumbinary disks focusing on modification of their structure caused by tidal coupling to the binary. We develop a set of analytical scaling relations describing viscous evolution of the disk properties, which are verified and calibrated using 1D numerical calculations with realistic inputs. Injection of angular momentum by the central binary suppresses mass accretion onto the binary and causes radial distribution of the viscous angular momentum flux F J ?> to be different from that in a standard accretion disk around a single star with no torque at the center. Disks with no mass accretion at the center develop an F J ?> profile that is flat in radius. Radial profiles of temperature and surface density are also quite different from those in disks around single stars. Damping of the density waves driven by the binary and viscous dissipation dominates heating of the inner disk (within 1–2 AU), pushing the ice line beyond 3–5 AU, depending on disk mass and age. Irradiation by the binary governs disk thermodynamics beyond ∼10 AU. However, self-shadowing by the hot inner disk may render central illumination irrelevant out to ∼20 AU. Spectral energy distribution of a circumbinary disk exhibits a distinctive bump around 10 μm, which may facilitate identification of such disks around unresolved binaries. Efficient tidal coupling to the disk drives orbital inspiral of the binary and may cause low-mass and relatively compact binaries to merge into a single star within the disk lifetime. We generally find that circumbinary disks present favorable sites for planet formation (despite their wider zone of volatile depletion), in agreement with the statistics of Kepler circumbinary planets.

VISCOUS INSTABILITY TRIGGERED BY LAYERED ACCRETION IN PROTOPLANETARY DISKS

Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate ($\dot{M}$), while the disk midplane where MRIs are generally quenched ends up with a low value of $\dot{M}$. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of $\alpha$ in 1D disk models. To this end, we obtain a new expression of $\alpha$ by utilizing an empirical formula that is derived from recent MHD simulations of stratified disks with Ohmic diffusion. It is interesting that this new formulation can be regarded as a general extension of the classical $\alpha$. Armed with the new $\alpha$, we perform a linear stability analysis of protoplanetary disks that undergo layered accretion, and find that a viscous instability can occur around the outer edge of dead zones. Disks become stable in using the classical $\alpha$. We identify that the difference arises from $\Sigma-$dependence of $\dot{M}$; whereas $\Sigma$ is uniquely determined for a given value of $\dot{M}$ in the classical approach, the new approach leads to $\dot{M}$ that is a multi-valued function of $\Sigma$. We confirm our finding both by exploring a parameter space as well as by performing the 1D, viscous evolution of disks. We finally discuss other non-ideal MHD effects that are not included in our analysis, but may affect our results.

Protoplanetary Disk Evolution: Singles vs. Binaries

AbstractBased on a large number of observations carried out in the last decade it appears that the fraction of stars with protoplanetary disks declines steadily between ~1 Myr and ~10 Myr. We do, however, know that the multiplicity fraction of star-forming regions can be as high as &gt;50% and that multiples have reduced disk lifetimes on average. As a consequence, the observed roughly exponential disk decay can be fully attributed neither to single nor binary stars and its functional form may need revision. Observational evidence for a non-exponential decay has been provided by Kraus et al. (2012), who statistically correct previous disk frequency measurements for the presence of binaries and find agreement with models that feature a constantly high disk fraction up to ~3 Myr, followed by a rapid (≲2 Myr) decline.We present results from our high angular resolution observational program to study the fraction of protoplanetary disks of single and binary stars separately. We find that disk evolution timescales of stars bound in close binaries (&lt;100 AU) are significantly reduced compared to wider binaries. The frequencies of accretors among single stars and wide binaries appear indistinguishable, and are found to be lower than predicted from planet forming disk models governed by viscous evolution and photoevaporation.

Consistency of Perfect Fluidity and Jet Quenching in Semi-Quark-Gluon Monopole Plasmas**Supported by the USA DOE Nuclear Science under Grant No DE-FG02-93ER40764, the National Science Foundation under Grant No PHY-1352368, and the RIKEN BNL Research Center.

We utilize a new framework, CUJET3.0, to deduce the energy and temperature dependence of the jet transport parameter, q̂(E > 10 GeV, T), from a combined analysis of available data on nuclear modification factor and azimuthal asymmetries from high energy nuclear collisions at RHIC/BNL and LHC/CERN. Extending a previous perturbative-QCD based jet energy loss model (known as CUJET2.0) with (2+1)D viscous hydrodynamic bulk evolution, this new framework includes three novel features of nonperturbative physics origin: (i) the Polyakov loop suppression of color-electric scattering (aka ‘semi-QGP’ of Pisarski et al.), (ii) the enhancement of jet scattering due to emergent magnetic monopoles near Tc (aka ‘magnetic scenario’ of Liao and Shuryak), and (iii) thermodynamic properties constrained by lattice QCD data. CUJET3.0 reduces to v2.0 at high temperatures T >400 MeV, while greatly enhances q̂ near the QCD deconfinement transition temperature range. This enhancement accounts well for the observed elliptic harmonics of jets with pT > 10 GeV. Extrapolating our data-constrained q̂ down to thermal energy scales, E∼2 GeV, we find for the first time a remarkable consistency between high energy jet quenching and bulk perfect fluidity with η/s ∼ T3/q̂ ∼ 0.1 near Tc.

Faraday pilot-wave dynamics: modelling and computation

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet’s bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect and walker–walker interactions.