Pressure and temperature dependence of the viscosity of a NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript> melt

The viscosity of a silicate melt of composition NaAlSi₂O₆ was measured at pressures from 1.6 to 5.5 GPa and at temperatures from 1,350 to 1,880°C. We employed in situ falling sphere viscometry using X-ray radiography. We found that the viscosity of the NaAlSi₂O₆ melt decreased with increasing pressure up to 2 GPa. The pressure dependence of viscosity is diminished above 2 GPa. By using the relationship between the logarithm of viscosity and the reciprocal temperature, the activation energies for viscous flow were calculated to be 3.7 ± 0.4 × 10² and 3.7 ± 0.5 × 10² kJ/mol at 2.2 and 2.9 GPa, respectively.     

Does the gas flow through a porous dust aggregate help its growth in a protoplanetary disk?

Sekiya and Takeda [2003, Earth Planets Space 55, 263-269] showed that the hydrodynamic gas flow around a dust aggregate larger than the mean free path of gas molecules prevents the growth of the body. In contrast to Wurm et al. [2004, Astrophys. J. 606, 983-987], we argue that this conclusion is not altered even if we take account of the effect of the flow through a porous dust aggregate.     

Sound velocity and elastic properties of Fe–Ni and Fe–Ni–C liquids at high pressure

The sound velocity (V _P) of liquid Fe–10 wt% Ni and Fe–10 wt% Ni–4 wt% C up to 6.6 GPa was studied using the ultrasonic pulse-echo method combined with synchrotron X-ray techniques. The obtained V _P of liquid Fe–Ni is insensitive to temperature, whereas that of liquid Fe–Ni–C tends to decrease with increasing temperature. The V _P values of both liquid Fe–Ni and Fe–Ni–C increase with pressure. Alloying with 10 wt% of Ni slightly reduces the V _P of liquid Fe, whereas alloying with C is likely to increase the V _P. However, a difference in V _P between liquid Fe–Ni and Fe–Ni–C becomes to be smaller at higher temperature. By fitting the measured V _P data with the Murnaghan equation of state, the adiabatic bulk modulus (K _S0) and its pressure derivative (K _S ^′ ) were obtained to be K _S0 = 103 GPa and K _S ^′  = 5.7 for liquid Fe–Ni and K _S0 = 110 GPa and K _S ^′  = 7.6 for liquid Fe–Ni–C. The calculated density of liquid Fe–Ni–C using the obtained elastic parameters was consistent with the density values measured directly using the X-ray computed tomography technique. In the relation between the density (ρ) and sound velocity (V _P) at 5 GPa (the lunar core condition), it was found that the effect of alloying Fe with Ni was that ρ increased mildly and V _P decreased, whereas the effect of C dissolution was to decrease ρ but increase V _P. In contrast, alloying with S significantly reduces both ρ and V _P. Therefore, the effects of light elements (C and S) and Ni on the ρ and V _P of liquid Fe are quite different under the lunar core conditions, providing a clue to constrain the light element in the lunar core by comparing with lunar seismic data.     

Melting of iron–silicon alloy up to the core–mantle boundary pressure: implications to the thermal structure of the Earth’s core

The melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell experiments. We have also investigated the subsolidus phase relations of Fe–18 wt% Si alloy by the in-situ X-ray diffraction method and confirmed that the bcc phase is stable at least up to 57 GPa and high temperature. The melting curve of the alloy was fitted by the Simon’s equation, P(GPa)/a = (T _m(K)/T ₀) ^c , with parameters, T ₀ = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. The melting temperature of bcc Fe–18 wt% Si alloy is comparable with that of pure iron in the pressure range of this work. The melting temperature of Fe–18 wt% Si alloy is estimated to be 3,300–3,500 K at 135 GPa, and 4,000–4,200 K at around 330 GPa, which may provide the lower bound of the temperatures at the core–mantle boundary and the inner core–outer core boundary if the light element in the core is silicon.     

Survival of a proto-atmosphere through the stage of giant impacts: the mechanical aspects

When a giant impact occurs, atmosphere loss may occur due to global ground motion excited by a strong shock wave traveling in the planetary interior. Here, the relations between the ground motion and the amount of the lost atmosphere are systematically investigated through calculations of a spherically one-dimensional atmospheric motion for various initial atmospheric conditions. The fraction of the lost atmosphere to the total mass of the atmosphere is found to be controlled only by the ground velocity and, insensitive to the initial atmospheric conditions. Unlike the previous studies (Ahrens, 1990, Origin of the Earth, H.E. Newson, J.H. Jones (Eds.), pp. 211-227; Ahrens, 1993, Annu. Rev. Earth Planet. Sci. 21, 525-555; Chen and Ahrens, 1997, Phys. Earth Planet. Inter. 100, 21-26); the estimated loss fraction for the giant impact is only 20%. Significant escape occurs only when the ground velocity is close to the escape velocity. Thus, most of the atmosphere should survive the giant impact. The cause of the difference from previous estimates is discussed from energetic and dynamic points of view. Moreover, if our estimates are applied to the atmosphere of the impactor planet, a significant fraction of it is carried to the target planet. Survival of the proto-atmosphere has very important effects on the origin and evolution of the terrestrial planets' volatile budget.     

Effect of hydrogen on the melting temperature of FeS at high pressure: Implications for the core of Ganymede

We have carried out in situ X-ray diffraction experiments on the FeS–H system up to 16.5 GPa and 1723 K using a Kawai-type multianvil high-pressure apparatus employing synchrotron X-ray radiation. Hydrogen was supplied to FeS from the thermal decomposition of LiAlH₄, and FeSH_x was formed at high pressures and temperatures. The melting temperature and phase relationships of FeSH_x were determined based on in situ powder X-ray diffraction data. The melting temperature of FeSH_x was reduced by 150–250 K comparing with that of pure FeS. The hydrogen concentration in FeSH_x was determined to be x = 0.2–0.4 just before melting occurred between 3.0 and 16.5 GPa. It is considered that sulfur is the major light element in the core of Ganymede, one of the Galilean satellites of Jupiter. Although the interior of Ganymede is differentiated today, the silicate rock and the iron alloy mixed with H₂O, and the iron alloy could react with H₂O (as ice or water) or the hydrous silicate before the differentiation occurred in an early period, resulting in a formation of iron hydride. Therefore, Ganymede's core may be composed of an Fe–S–H system. According to our results, hydrogen dissolved in Ganymede's core lowers the melting temperature of the core composition, and so today, the core could have solid FeSH_x inner core and liquid FeH_x–FeSH_x outer core and the present core temperature is considered to be relatively low.     

Maintenance of the mean kinetic energy in the global ocean by the barotropic and baroclinic energy routes: the roles of JEBAR and Ekman dynamics

In order to determine the maintenance mechanisms of the currents of the global ocean, this study investigates the budget of the annual mean kinetic energy (KE) in a high-resolution (0.1° × 0.1°) semi-global ocean simulation. The analysis is based on a separation of the mean KE using the barotropic (i.e., depth-averaged) and baroclinic (the residual) components of velocity. The barotropic and baroclinic KEs dominate in higher and lower latitudes, respectively, with their global average being comparable to each other. The working rates of wind forcing on the barotropic and baroclinic circulations in the global ocean are 243 and 747 gigawatts, respectively. This study presents at least three new results for the budget of the barotropic KE. Firstly, an energy diagram is rederived to show that the work of the barotropic component of the horizontal pressure gradient (HPG) is connected to the work related to the joint effect of baroclinicity and bottom relief (JEBAR), and then to the budget of potential energy (PE). Secondly, the model analysis shows that the globally averaged work of the barotropic HPG (which is connected to the work related to JEBAR and then to the budget of the PE) is nearly zero. This indicates that the wind- and buoyancy-induced barotropic circulations in the global ocean are of the same strength with opposite sign. Thirdly, it is found that the work of the wind forcing on the barotropic component of the simulated Antarctic Circumpolar Current (ACC) is canceled by the combined effect, in equal measure, of the work of the barotropic HPG and the work of dissipative processes for mean KE. This result makes a significant contribution to the discussion on the depth-integrated momentum balance of the ACC. The barotropic KE is dissipated by the effects of bottom frictional stress, lateral frictional stress, and the Reynolds stress, of which more than half is attributed to an unexpectedly large contribution from biharmonic horizontal friction. Future studies should pay more attention to the role of biharmonic friction used in high-resolution numerical models.     

Density measurements of liquid Fe–Si alloys at high pressure using the sink–float method

The compositional dependence on the density of liquid Fe alloys under high pressure is important for estimating the amount of light elements in the Earth’s outer core. Here, we report on the density of liquid Fe–Si at 4 GPa and 1,923 K measured using the sink–float method and our investigation on the effect of the Si content on the density of the liquid. Our experiments show that the density of liquid Fe–Si decreases from 7.43 to 2.71 g/cm³ non-linearly with increasing Si content (0–100 at%). The molar volume of liquid Fe–Si calculated from the measured density gradually decreases in the compositional range 0–50 at% Si, and increases in the range 50–100 at% Si. It should be noted that the estimated molar volume of the alloys shows a negative volume of mixing between Fe and Si. This behaviour is similar to Fe–S liquid (Nishida et al. in Phys Chem Miner 35:417–423, 2008). However, the excess molar volume of mixing for the liquid Fe–Si is smaller than that of liquid Fe–S. The light element contents in the outer core estimated previously may be an underestimation if we take into account the possible negative value of the excess mixing volume of iron–light element alloys in the outer core.     

Successive formation of planetary lenses in an intermediate layer

Abstract

We study the formation of lenses of the ocean's intermediate water using a 2.5-layerβ-plane primitive equation model with localized injection of water mass. For the injecting rate of 1.0 Sv, we have observed that strong vortices are shed regularly. These vortices propagate westward much faster than the second baroclinic long Rossby wave. They are totally isolated from each other and show strong baroclinicity as well. Moreover, they remain stable over a sufficiently long period of time. Regular formation of such strong vortices in the intermediate layer has not been reported previously. The translation speed is explained using the Euler's momentum integral theorem for the nonlinear baroclinic vortex on the β-plane. We have demonstrated that coupling between the primary motion in the intermediate layer and the secondary motion in the upper layer with a meridional shift is crucial to the fast westward translation of the intense vortices. A simple dispersion formula relating the zonal translation speed with the vortex radius is also derived under the assumption of quasi-geostrophy. It has turned out that the analytical relation explains the numerical results surprisingly well despite the limitation of its derivation.     

Thermal anomaly around the Nojima Fault as detected by fission-track analysis of Ogura 500 m borehole samples

Abstract To better understand heat generation and transfer along earthquake faults, this paper presents preliminary zircon fission-track (FT) length data from the Nojima Fault, Awaji Island, Japan, which was activated during the 1995 Kobe earthquake (Hyogo-ken Nanbu earthquake). Samples were collected of Cretaceous granitic rocks from the Ogura 500 m borehole as well as at outcrops adjacent to the borehole site. The Nojima Fault plane was drilled at a depth of 389.4 m (borehole apparent depth). Fission-track lengths in zircons from localities > 60 m distance from the fault plane, as well as those from outcrops, are characterized by the mean values of ≈10–11 μm and unimodal distributions with positive skewness, which show no signs of an appreciable reduction in FT length. In contrast, those from nearby the fault at depths show significantly reduced mean track lengths of ≈6–8 μm and distributions having a peak around 6–7 μm with rather negative skewness. In conjunction with other geological constraints, these results are best interpreted by a recent thermal anomaly around the fault, which is attributable to heat transfer via focused fluids from the deep interior of the crust and/or heat dispersion via fluids associated with frictional heating by fault motion.