Vertical structure of Jupiter's troposphere from nonlinear simulations of long-lived vortices

Numerical simulations of jovian vortices at tropical and temperate latitudes, under different atmospheric conditions, have been performed using the EPIC code [Dowling, T.E., Fisher, A.S., Gierasch, P.J., Harrington, J., LeBeau, R.P., Santori, C.M., 1998. Icarus 132, 221-238] to simulate the high-resolution observations of motions and of the lifetimes presented in a previous work [Legarreta, J., Sánchez-Lavega, A., 2005. Icarus 174, 178-191] and infer the vertical structure of Jupiter's troposphere. We first find that in order to reproduce the longevity and drift rate of the vortices, the Brunt-Väisälä frequency of the atmosphere in the upper troposphere (pressures P∼1 to 7 bar) should have a lower limit value of 5×¹⁰⁻³ s⁻¹, increasing upward up to 1.25×¹⁰⁻² s⁻¹ at pressures P∼0.5 bar (latitudes between 15° and 45° in both hemispheres). Second, the vortices drift also depend on the vertical structure of the zonal wind speed in the same range of altitudes. Simulations of the slowly drifting Southern hemisphere vortices (GRS, White Ovals and anticyclones at 40° S) require a vertically-constant zonal-wind with depth, but Northern hemisphere vortices (cyclonic “barges” and anticyclones at 19, 41 and 45° N) require decreasing winds at a rate of ∼5 m s⁻¹ per scale height. However vortices drifting at a high speed, close to or in the peak of East or West jets and in both hemispheres, require the wind speed slightly increasing with depth, as is the case for the anticyclones at 20° S and at 34° N. We deduce that the maximum absolute vertical shear of the zonal wind from P∼1 bar up to P∼7 bar in these jets is ∼15 m s⁻¹ per scale height. Intense vortices with tangential velocity at their periphery ∼100 m s⁻¹ tend to decay asymptotically to velocities ∼40 to 60 m s⁻¹ with a characteristic time that depends on the vortex intensity and static stability of the atmosphere. The vortices adjust their tangential velocity to the averaged peak to peak velocity of the opposed eastward and westward jets at their boundary. We show through our simulations that large-scale and long-lived vortices whose maximum tangential velocity is ∼100 m s⁻¹ can survive by absorbing smaller intense vortices.     

EPIC simulations of the merger of Jupiter's White Ovals BE and FA: altitude-dependent behavior

Observations of the merger of Jupiter's White Ovals BE and FA show altitude-dependent behavior that we seek to capture in numerical simulations. In particular, it was observed that the upper portions of the vortices orbited each other before merging, but the lower portions translated into each other without orbiting, a phenomenon we term the pair-orbit vertical dichotomy. To reproduce this dichotomy in the EPIC model, it is sufficient to have (i) a decrease with altitude of the background zonal winds above the cloud level with a scale height of ∼2.4, (ii) a height scale of the winds inside the vortices that is the same or larger, and (iii) a maximum tangential velocity in each vortex of ∼100 m s⁻¹ or larger. Condition (i) is expected from thermal-wind analyses, (ii) is consistent with thermal-wind and Shoemaker-Levy 9 debris-trajectory analyses, and (iii) is consistent with cloud-top wind tracking. The model generally does not reproduce the dichotomy for vortices with smaller vertical extent or weaker circulations. Our simulated mergers correctly reproduce the observed ∼9° separation at which vortices start to orbit in the upper layers before they merge and the ∼70% area ratio of the final vortex BA to the sum of BE and FA.     

In-shock cooling in numerical simulations

We model a one-dimensional shock-tube using smoothed particle hydrodynamics and investigate the consequences of having finite shock-width in numerical simulations caused by finite resolution of the codes. We investigate the cooling of gas during passage through the shock for three different cooling regimes.
For a theoretical shock temperature of 10⁵ K, the maximum temperature of the gas is much reduced. When the ratio of the cooling time to shock-crossing time was 8, we found a reduction of 25 per cent in the maximum temperature reached by the gas. When the ratio was reduced to 1.2, the maximum temperature reached dropped to 50 per cent of the theoretical value. In both cases the cooling time was reduced by a factor of 2.
At lower temperatures, we are especially interested in the production of molecular hydrogen, and so we follow the ionization level and H₂ abundance across the shock. The effect of in-shock cooling is substantial: the maximum temperature the gas reaches compared with the theoretical temperature is found to vary between 0.15 and 0.81, depending upon the shock strength and mass resolution. The downstream ionization level is reduced from the theoretical level by a factor of between 2.4 and 12.5, and the resulting H₂ abundance by a factor of 1.35 to 2.22.
At temperatures above 10⁵ K, radiative shocks are unstable and will oscillate. We find that the shock jump temperature varies by a factor of 20 because of these oscillations.
We conclude that extreme caution must be exercised when interpreting the results of simulations of galaxy formation.     

Jupiter’s South South Temperate Zone vortices: Observations and simulations

The region in Jupiter’s atmosphere with the highest density of anticyclonic spot-like vortices is the region known as the South South Temperate Zone (SSTZ), which is located between the eastward jet at ≈−42.9° latitude and the westward jet at ≈−39.2° latitude. We present a characterization of the spots found in this region based on ground-based and Hubble Space Telescope observations from the years 1993 to 2007. Mergers have been reported between spots in this region, similar to those observed for the White Ovals in the latitudinal domain immediately equatorward (northward). We use a multilayer model to perform numerical simulations that capture the details of a well-observed merger event involving multiple interacting vortices. We find that the vertical stratification has an important effect in the outcome of the interaction between spots. In particular it can play a determining role on whether or not a cyclone embedded between two approaching anticyclones can inhibit their merging. From our simulations we conclude that the background static stability of the atmosphere in the SSTZ is better characterized by an average value of .     

Dark matter subhaloes in numerical simulations

We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10¹¹ to  10¹⁴ M_⊙  at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation  d n /d v = (1/8)( v _cmax/ v _cmax,host)⁻⁴  . Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for   r ≳ 0.3 r _vir  , where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of   P ∝ kⁿ   , and demonstrate that a steeper spectral index, n , results in significantly less substructure.     

Hydrodynamics of hypersonic jets: experiments and numerical simulations

Stars form in regions of the galaxy that are denser and cooler than the mean interstellar medium. These regions are called Giant Molecular Clouds. At the beginning of their life, up to 10⁵–10⁶ years, stars accrete matter from their rich surrounding environment and are origin of a peculiar phenomenon that is the jet emission. Jets from Young Stellar Objects (YSOs) are intensively studied by the astrophysical community by observations at different wavelengths, analytical and numerical modeling and laboratory experiments. Indications about the jet propagation and its resulting morphologies are here obtained by means of a combined study of hypersonic jets carried out both in the laboratory and by numerical simulations.     

The thermal stability of coronal loops numerical simulations

We have studied the radiative stability of thermally isolated coronal loops with free-flow boundary conditions by nonlinear numerical simulation. We first establish a chromosphere-to-corona loop equilibrium (including the option of a deep chromosphere) by following the nonlinear evolution from an initial isothermal state with rigid boundaries. We then change the end conditions, to allow free flow and to fix the temperature, and investigate the response to non-isobaric perturbations. Within a family of loops of the same pressure, we find long hot loops to be stable and short cool loops to be unstable to the thermal chromosphericexpansion mode. The stable cases remain so, even when long chromospheric ends and/or gravity are added. In those cases which are unstable, we follow the subsequent nonlinear evolution which exhibits swelling of the chromosphere until the entire loop becomes cool and dense.     

Full numerical simulations of catastrophic small body collisions

The outcome of collisions between small icy bodies, such as Kuiper belt objects, is poorly understood and yet a critical component of the evolution of the trans-neptunian region. The expected physical properties of outer Solar System materials (high porosity, mixed ice-rock composition, and low material strength) pose significant computational challenges. We present results from catastrophic small body collisions using a new hybrid hydrocode to N-body code computational technique. This method allows detailed modeling of shock propagation and material modification as well as gravitational reaccumulation. Here, we consider a wide range of material strengths to span the possible range of Kuiper belt objects. We find that the shear strength of the target is important in determining the collision outcome for 2 to 50-km radius bodies, which are traditionally thought to be in a pure gravity regime. The catastrophic disruption and dispersal criteria, , can vary by up to a factor of three between strong crystalline and weak aggregate materials. The material within the largest reaccumulated remnants experiences a wide range of shock pressures. The dispersal and reaccumulation process results in the material on the surfaces of the largest remnants having experienced a wider range of shock pressures compared to material in the interior. Hence, depending on the initial structure and composition, the surface materials on large, reaccumulated bodies in the outer Solar System may exhibit complex spectral and albedo variations. Finally, we present revised catastrophic disruption criteria for a range of impact velocities and material strengths for outer Solar System bodies.     

Hydrodynamics of flaring loops: SMM observations and numerical simulations

The hydrodynamic response of confined magnetic structures to strong heating perturbations is investigated by means of a timedependent one-dimensional code which incorporates the energy, momentum and mass conservation equations. The entire atmospheric structure from the chromosphere to the corona is taken into account. The results of model calculations are compared with observations of flares obtained with the X-Ray Polychromator experiment on the Solar Maximum Mission.     

Asteroid rotation and shapes from numerical simulations of gravitational re-accumulation

We present simulations of the gravitational collapse of a mono-disperse set of spherical particles for studying shape and spin properties of re-accumulated members of asteroid families. Previous numerical studies have shown that these “gravitational aggregates” exhibit properties similar to granular continuum models described by Mohr-Coulomb theory. A large variety of shapes is thus possible, in principle consistent with the observed population of asteroid shapes.However, it remains to be verified that the re-accumulation following a catastrophic disruption is capable of naturally producing those shapes. Conversely, we find that fluid equilibrium shapes (flattened two-axis spheroids, in particular) are preferentially created by re-accumulation. This is rather unexpected, since the dynamical system used could allow for other stable configurations. Jacobi three-axial ellipsoids can also be created, but this seems to be a less common outcome.The results obtained so far seem to underline the importance of other non-disruptive shaping factors during the lifetime of rubble-pile asteroids.     

Application of a global polytropic model to the Jupiter's system of satellites: a numerical treatment

We study the so-called inverse planetary problem (i.e., given the distances from the centre, masses, and radii of, say, three planets of a planetary system, find the optimum polytropic index, mass, and radius of their star, and also other quantities of interest, which depend either explicitly or implicitly on the foregoing ones, e.g., central and mean density, central and mean pressure, central and mean temperature, etc.) for the system of satellites of Jupiter. In particular, Jupiter is considered as star and its satellites as planets of a proper planetary system, which is then treated numerically on the basis of the so-called global polytropic model, developed recently by the first author.     

Direct numerical simulations of the Blandford–Znajek effect

The time-dependent general relativistic equations of degenerate electrodynamics are solved numerically in order to study the mechanism of the electromagnetic extraction of the rotational energy of black holes. We performed a series of 2D runs for black holes with specific angular momentum, a , from 0.1 to 0.9 and for a monopole magnetic field assuming axisymmetry. In the inner region of the wind, the solution quickly settles to a steady state with an outgoing Poynting flux. In all cases the angular velocity of the magnetic field lines is almost half the angular velocity of the black hole. Thus, at least for the configuration considered, the Blandford–Znajek mechanism operates near its maximum power output.     

Jupiter's 24° N highest speed jet: Vertical structure deduced from nonlinear simulations of a large-amplitude natural disturbance

The evolution of a large-amplitude disturbance at cloud level in Jupiter's 24° N jet stream in 1990 is used to constrain the vertical structure of a realistic atmospheric model down to the 6 bar pressure level. We use the EPIC model (Dowling et al., 1998, The explicit planetary isentropic-coordinate (EPIC) atmospheric model, Icarus 132, 221-238) to perform long-term, three-dimensional, nonlinear simulations with a series of systematic variations in vertical structure and find that the details of the 1990 disturbance combine with the characteristics of the 24° N jet, the fastest on Jupiter, to yield a tight constraint on the solution space. The most important free parameters are the vertical dependence of the zonal-wind profile, and the thermal structure, below the cloud tops (p>0.7 bar) at the jet's central latitude. The temporal evolution of the disturbed cloud patterns, which spans more than 2 years, can be reproduced if the jet peak reaches ∼180 ms⁻¹ at the cloud level and increases to ∼210 ms⁻¹ at 1 bar and up to ∼240 ms⁻¹ at 6 bar; the observations were not reproduced for other configurations investigated. This trend is consistent with that measured by the Galileo Probe at 7° N; the implication is that this jovian jet extends well below the solar radiation penetration level situated near the 2 bar level.     

Constraints on interpretation of the Eltanin impact from numerical simulations

The results of numerical simulations of the Eltanin impact are combined with the available geological data in order to reconstruct the impact dynamics and to get some constraints on the impact parameters. Numerical simulations show that the Eltanin projectile size should be less than 2 km for a 45° oblique impact and less than 1.5 km for a vertical impact. On the other hand, we demonstrate that the projectile diameter cannot be considerably smaller than 1 km; otherwise, the impact‐induced water flow cannot transport eroded sediments across large distances. The maximum displacement approximately equals the water crater radius and rapidly decreases with increasing distances. Numerical simulations also show that ejecta deposits strongly depend on impact angle and projectile size and, therefore, cannot be used for reliable estimates of the initial projectile mass. The initial amplitudes of tsunami‐like waves are estimated. The presence of clay‐rich sediments, typical for the abyssal basins in cores PS2709 and PS2708 on the Freeden Seamounts (Bellingshausen Sea, Southern Ocean) combined with numerical data allow us to suggest a probable point of impact to the east of the seamounts. The results do not exclude the possibility that a crater in the ocean bottom may exist, but such a structure has not been found yet.     

Vorticity and astrophysical magnetism

Viscous resistance to differential rotation causes a current whose magnetic field is proportional to the vorticity of the medium. The magnetic fields of stars and galaxies could arise in this manner, provided that the time scale for development of the field is reasonable. The latter condition (assuming Ohmic rather than synchroton dissipation) requires that the scale length for a galactic field be less than 3×10¹³ cm. It is suggested that there may be continual generation of field within the core of a vortex of this dimension in the galactic nucleus, the field lines then being carried outwards by expanding plasma. The main observational evidence in connection with solar, stellar and galactic magnetic fields is appraised in the context of the above theory.     

Beaming of Jupiter's decametric emission

Dynamic spectra of a Jovian non-Io-A storm recorded simultaneously by the Voyager 1 spacecraft and by the Kiiminki radio spectrograph are compared. It seems that the emission beam of the storm co-rotates with the planet and has a sloped leading edge, in accordance with the result of Maeda and Carr (1984).     

Two- and three-dimensional numerical simulations of accretion discs in a close binary system

We perform 2D and 3D numerical simulations of an accretion disc in a close binary system using the simplified flux vector splitting (SFS) finite volume method. In our calculations, the gas is assumed to be ideal with γ =1.01, 1.05, 1.1 and 1.2 . The mass ratio of the mass-losing star to the mass-accreting star is unity. Our results show that spiral shocks are formed on the accretion disc in all cases. In 2D calculations we find that the smaller γ is, the more tightly the spiral winds. We observe this trend in 3D calculations as well in a somewhat weaker sense. Mach numbers in our discs are less than 10. These values are lower than the values in observed accretion discs in close binary systems.
Recently, Steeghs, Harlaftis & Horne found the first convincing evidence for spiral structure in the accretion disc of the eclipsing dwarf nova binary IP Pegasi, using the technique known as Doppler tomography. Although the Mach numbers in present calculations are rather low, we may claim that the spiral structure that we discovered in earlier numerical simulations is now found observationally.     

Scaling of melt production in hypervelocity impacts from high-resolution numerical simulations

The volume of melt produced in hypervelocity planetary impacts and the size and shape of the melted region are key to understanding the impact histories of solid planetary bodies and the geological effects of impacts on their surfaces and interiors. Prior work of Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) gave the first estimates of impact melt production in geological materials using a modern hydrocode and equation of state. However, computational limits at the time forced use of low resolution, which may have resulted in low melt volumes. Our simulations with 50 times higher resolution provide independent confirmation of the Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) melt volumes in aluminum, iron, dunite, and granite impacts at velocities between 20 and 80 km/s. In ice/ice impacts, we find that melt volumes depend on target temperature and are lower than predicted by Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423). Our melt volumes are directly proportional to impact energy for all materials, over a wide range of impact velocity. We also report new data for melt volume scalings for ice/dunite and iron/dunite impacts and the size and shape of melted region, valuable for interpretation of cratering records and studies of impact-induced differentiation.     

Development of an LENA instrument for planetary missions by numerical simulations

Low-energy neutral atom (LENA) observations bring us important information on particle environments around celestial objects such as Mercury and the Moon. In this paper, we report on new development of an LENA instrument for planetary explorations. The instrument is light weight (2 kg), and capable of mass and energy discrimination with a large sensitivity. The performance of the instrument is investigated by numerical simulations. By using our new computer code, we calculated 3D particle trajectories including ionization, neutralization, surface scattering, and secondary electron creation. This enables us to obtain detailed performance characterization of LENA measurements. We also made trajectory tracing of photons entering the instrument to acquire photon rejection capability. This LENA instrument has been selected for both the Indian lunar exploration mission Chandrayaan-1 and European–Japanese Mercury exploration mission BepiColombo.