Formation of early water oceans on rocky planets

Terrestrial planets, with silicate mantles and metallic cores, are likely to obtain water and carbon compounds during accretion. Here I examine the conditions that allow early formation of a surface water ocean (simultaneous with cooling to clement surface conditions), and the timeline of degassing the planetary interior into the atmosphere. The greatest fraction of a planet’s initial volatile budget is degassed into the atmosphere during the end of magma ocean solidification, leaving only a small fraction of the original volatiles to be released into the atmosphere through later volcanism. Rocky planets that accrete with water in their bulk mantle have two mechanisms for producing an early water ocean: First, if they accrete with at least 1 to 3 mass% of water in their bulk composition, liquid water may be extruded onto the planetary surface at the end of magma ocean solidification. Second, at initial water contents as low as 0.01 mass% or lower, during solidification a massive supercritical fluid and steam atmosphere is produced that collapses into a water ocean upon cooling. The low water contents required for this process indicate that rocky super-Earth exoplanets may be expected to commonly produce water oceans within tens to hundreds of millions of years of their last major accretionary impact, through collapse of their atmosphere.     

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.     

Radiative Transfer in Inhomogeneous Atmospheres. II

This paper is a continuation of a study of radiative transfer in one-dimensional inhomogeneous atmospheres. Two of the most important characteristics of multiple scattering in these media are calculated: the photon escape probability and the average number of scattering events. The latter is determined separately for photons leaving the medium and for photons that have undergone thermalization in the medium. The problem of finding the radiation field in an inhomogeneous atmosphere containing energy sources is also examined. It is assumed that the power of these sources, as well as the scattering coefficient, can vary arbitrarily with depth. It is shown that knowledge of the reflection and transmission coefficients of the atmosphere makes it possible to reduce all these problems to solving some first order linear differential equations with specified initial conditions. A series of new analytic results are obtained. Numerical calculations are done for two types of atmosphere with different depth dependences for the scattering coefficient. These are interpreted physically.     

Chemistry and evolution of Titan's atmosphere

The chemistry and evolution of Titan's atmosphere is reviewed in the light of the scientific findings from the Voyager mission. It is argued that the present N₂ atmosphere may be Titan's initial atmosphere rather than photochemically derived from an original NH₃ atmosphere. The escape rate of hydrogen from Titan is controlled by photochemical production from hydrocarbons. CH₄ is irreversibly converted to less hydrogen rich hydrocarbons, which over geologic time accumulate on the surface to a layer thickness of ～0.5 km. Magnetospheric electrons interacting with Titan's exosphere may dissociate enough N₂ into hot, escaping N atoms to remove ～0.2 of Titan's present atmosphere over geologic time. The energy dissipation of magnetospheric electrons exceeds solar e.u.v. energy deposition in Titan's atmosphere by an order of magnitude and is the principal driver of nitrogen photochemistry. The environmental conditions in Titan's upper atmosphere are favorable to building up complex molecules, particularly in the north polar cap region.     

Methane clathrate hydrates as a potential source for martian atmospheric methane

Small amounts of methane have been detected in the atmosphere of Mars, though the actual sources of the gas remain unknown. Thermodynamic conditions on Mars suggest that gas clathrate hydrate deposits might exist at the polar caps and in some areas of the planetary subsurface. We review the literature available on the detection of methane in the martian atmosphere and the presence of gas clathrate hydrates on Mars. The possibility of martian methane clathrate deposits is established, and initial sources for the sequestered methane are discussed. Based on correlated data and information from disparate sources, we conclude that subsurface methane clathrate deposits are a possible immediate source for the observed atmospheric methane on Mars.     

Numerical Simulations of Magnetoacoustic–Gravity Waves in the Solar Atmosphere

We investigate the excitation of magnetoacoustic–gravity waves generated from localized pulses in the gas pressure as well as in the vertical component of velocity. These pulses are initially launched at the top of the solar photosphere, which is permeated by a weak magnetic field. We investigate three different configurations of the background magnetic field lines: horizontal, vertical, and oblique to the gravitational force. We numerically model magnetoacoustic–gravity waves by implementing a realistic (VAL-C) model of the solar temperature. We solve the two-dimensional ideal magnetohydrodynamic equations numerically with the use of the FLASH code to simulate the dynamics of the lower solar atmosphere. The initial pulses result in shocks at higher altitudes. Our numerical simulations reveal that a small-amplitude initial pulse can produce magnetoacoustic–gravity waves, which are later reflected from the transition region due to the large-temperature gradient. The cavities in the lower solar atmosphere are found to have the best conditions to act as a resonator for various oscillations, including their trapping and leakage into the higher atmosphere. Our numerical simulations successfully model the excitation of such wave modes, their reflection and trapping, as well as the associated plasma dynamics.     

A hydrodynamic model for asymmetric explosions of rapidly rotating collapsing supernovae with a toroidal atmosphere

We numerically solved the two-dimensional axisymmetric hydrodynamic problem of the explosion of a low-mass neutron star in a circular orbit. In the initial conditions, we assumed a nonuniform density distribution in the space surrounding the collapsed iron core in the form of a stationary toroidal atmosphere that was previously predicted analytically and computed numerically. The configuration of the exploded neutron star itself was modeled by a torus with a circular cross section whose central line almost coincided with its circular orbit. Using an equation of state for the stellar matter and the toroidal atmosphere in which the nuclear statistical equilibrium conditions were satisfied, we performed a series of numerical calculations that showed the propagation of a strong divergent shock wave with a total energy of ～0.2×10⁵¹ erg at initial explosion energy release of ～1.0×10⁵¹ erg. In our calculations, we rigorously took into account the gravitational interaction, including the attraction from a higher-mass (1.9M_⊙) neutron star located at the coordinate origin, in accordance with the rotational explosion mechanism for collapsing supernovae. We compared in detail our results with previous similar results of asymmetric supernova explosion simulations and concluded that we found a lower limit for the total explosion energy.     

Stability of streams and lakes on Mars

Under present climatic conditions streams and lakes on Mars will freeze. Freezing is slow and would have a negligible effect in impeding flow of the large floods that are believed to have eroded the outflow channels. Valley networks are more difficult to form under current climatic conditions since they appear to have formed by slow erosion by streams of modest discharges. Freezing of small Martian streams was modeled for a variety of climatic conditions on the supposition that the Martian atmosphere may have been considerably thicker in the past when the valley networks formed. The modeling involves examination of the energy balance at the upper and lower surfaces of ice on streams to determine the rate at which the ice thickens with time. The results indicate that freezing rates are not strongly dependent on atmospheric pressure. With no wind, increasing the pressure by a factor of 10 cuts the time taken to freeze solid only by about a factor of about 2. Under windy conditions dependence on atmospheric pressure is even weaker. The distance that water could travel in a stream before flow is arrested by freezing is also calculated. The distances depend on the initial temperature of the stream and when icings develop, but in general, if a stream deeper than 2 m can be initiated and sustained, the water within it can survive long enough to cut most of the valley networks observed. The main problem with forming the valley is initiating the flow. Groundwater seepage alone appears inadequate because of the difficulty of recharging the groundwater system. Melting of ice precipitated onto the surface following injection of water into the atmosphere by large impacts is a possible source of water, but the climatic conditions under which the ice could melt and the water be collected into streams that can survive long enough to cut the valley is uncertain.     

Radiative hydrodynamic simulations of the spectral characteristics of solar white-light flares

As one of the most violent activities in the solar atmosphere,white-light flares(WLFs)are generally known for their enhanced white-light(or continuum)emission,which primarily originates in the solar lower atmosphere.However,we know little about how white-light emission is produced.In this study,we aim to investigate the response of the continua at 3600?and 4250?and also the Hαand Lyαlines during WLFs modeled using radiative hydrodynamic simulations.We take non-thermal electron beams as the energy source for the WLFs in two different initial atmospheres and vary their parameters.Our results show that the model with non-thermal electron beam heating clearly shows enhancements in the continua at 3600?and 4250?as well as in the Hαand Lyαlines.A larger electron beam flux,a smaller spectral index,or an initial penumbral atmosphere leads to a stronger emission increase at 3600?,4250?and in the Hαline.The Lyαline,however,is more obviously enhanced in a quiet-Sun initial atmosphere with a larger electron beam spectral index.It is also notable that the continua at 3600?and 4250?and the Hαline exhibit a dimming at the start of heating and reach their peak emissions after the peak time of the heating function,while the Lyαline does not show such behaviors.These results can serve as a reference for the analysis of future WLF observations.     

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

Natural superrotation of a rarefied planetary atmosphere

We consider the kinetics of a rarefied rotating planetary atmosphere. The spatial distributions of the atmospheric-gas density and mean angular velocity were determined by analyzing the exact solution of the two-dimensional kinetic equation. We show that the angular velocity of the gas at some distance from the planet could be higher than that in the initial layer starting from which the atmosphere is rarefied. Our model calculations elucidate the superrotation mechanism under consideration.     

彗木相撞的不可压缩分层流体模型

提出了一个彗木相撞的线性模型．在这个模型中，将木星大气看作是一个分层的、不可压缩和无粘滞的流体层，而与撞击相联的引力波则由一个初始冲力所造成．采用初始冲压P(r，z，0)代替初始表面形变作为初始条件．发现这种做法使得问题的数学处理更加方便，特别是在计算流体粒子的垂直位移和摄动势能方面，后者可以表为P(r，z，0)的有限傅立叶正弦和余弦变换．导出了一个联系彗星碰撞参数、木星大气参数和所设初始冲力之间的关系式．还对两种P(r，z，0)的假设形式分析地导出表面波波高．     

Hydrogen and helium abundances in neutron-star atmospheres

An analysis is presented of the burning and diffusion of hydrogen and helium in a neutron-star atmosphere. An initial two-component atmosphere of hydrogen and carbon and of helium and carbon is examined utilizing various photospheric temperatures. The hydrogen burns through the proton-proton reaction and the CN-cycle and the helium by the triple-alpha process and alpha capture on carbon. It is found that only a negligible proportion of hydrogen or helium can exist after a few years in the neutron-star atmosphere.     

Saltation impact as a means for raising dust on Mars

Experiments were conducted under atmospheric pressures appropriate for Earth and Mars to determine the efficiency of sand in saltation as a means for raising dust into the atmosphere under wind speeds which would otherwise be too low for dust entrainment. Experiments involving intimate mixtures of sand and dust (1:1 ratio by mass) showed that after an initial flurry of activity of a few seconds duration, the bed stabilized with little movement of either sand or dust. In contrast, sands set into saltation upwind from dust beds were efficient in injecting the dust into suspension, with low-pressure Martian conditions being some five times more efficient than terrestrial conditions. This result is attributed to the higher kinetic energies of the saltating grains on Mars, which is a consequence of the higher velocities of the grains. These results suggest that sands saltating across dust beds on Mars are an effective means for setting dust into suspension.     

Radiative Transfer in Inhomogeneous Atmospheres. III

The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented.     

An analytical model of the Comet's collision with Jupiter

An important feature observed in the wake of the Jupiter-comet clash was the appearance of the ring structure axisymmetrically positioned around the center of the impact. The persistent expansion of the dark rings and its speed indicated an outward propagating gravity wave (Benka, 1995). We employ an analytical model of constant density, uniform finite depth and inviscid fluid layer to investigate the wave motion produced by the impact of Comet Shoemaker-Levy 9 on the Jovian atmosphere. The relevant thermal effects are neglected and an explosion resulting from the collision is then described by an initial impulsive pressure at the surface of the Jovian atmosphere. Under the assumption that all the kinetic energy of a comet fragment is completely converted into the energy of wave motions in the Jovian atmosphere, an analytical formula describing the relationship between the resulting wave motion in the atmosphere and the parameters of a comet fragment (the radius, density and speed) is derived. Results from the present simple analytical model give a qualitative agreement with observations regarding the distance and speed of the waves.     

On penetration depth of the Shoemaker-Levy 9 fragments into the Jovian atmosphere

The actual penetration depth of the Shoemaker-Levy 9 fragments into the Jovian atmosphere is still an open question. From fundamental equations of meteoric physics with variable cross-section, a new analytic model of energy release of the fragments is presented. In use of reasonable parameters, a series of results are calculated for different initial mass of the fragments. The results show that the largest fragment explodes above pressure levels of 3 bars and does not penetrate into the H₂O cloud layer of the Jovian atmosphere, and that airburst of smaller fragments occur even above the upper cloud layer.     

The Canyon Diablo impact event: Projectile motion through the atmosphere

Abstract— Meteor Crater is one of the first impact structures systematically studied on Earth. Its location in arid northern Arizona has been ideal for the preservation of the structure and the surviving meteoric material. The recovery of a large amount of meteoritic material in and around the crater has allowed a rough reconstruction of the impact event: an iron object 50 m in diameter impacted the Earth's surface after breaking up in the atmosphere. The details of the disruption, however, are still debated. The final crater morphology (deep, bowl‐shaped crater) rules out the formation of the crater by an open or dispersed swarm of fragments, in which the ratio of swarm radius to initial projectile radius C_d is larger than 3 (the final crater results from the sum of the craters formed by individual fragments). On the other hand, the lack of significant impact melt in the crater has been used to suggest that the impactor was slowed down to 12 km/s by the atmosphere, implying significant fragmentation and fragments' separation up to 4 initial radii. This paper focuses on the problem of entry and motion through the atmosphere for a possible Canyon Diablo impactor as a first but necessary step for constraining the initial conditions of the impact event which created Meteor Crater. After evaluating typical models used to investigate meteoroid disruption, such as the pancake and separated fragment models, we have carried out a series of hydrodynamic simulations using the 3D code SOVA to model the impactor flight through the atmosphere, both as a continuum object and a disrupted swarm. Our results indicate that the most probable pre‐atmospheric mass of the Meteor Crater projectile was in the range of 4.10⁸to 1.2.10⁹kg (equivalent to a sphere 46–66 m in diameter). During the entry process the projectile lost probably 30% to 70% of its mass, mainly because of mechanical ablation and gross fragmentation. Even in the case of a tight swarm of particles (C_d < 3), small fragments can separate from the crater‐forming swarm and land on the plains (tens of km away from the crater) as individual meteorites. Starting from an impactor pre‐atmospheric velocity of ?18 km/s, which represents an average value for Earth‐crossing asteroids, we find that after disruption, the most probable impact velocity at the Earth's surface for a tight swarm is around 15 km/s or higher. A highly dispersed swarm would result in a much stronger deceleration of the fragments but would produce a final crater much shallower than observed at Meteor Crater.     

Magnetohydrodynamic behaviour of a finite amplitude disturbance in the solar magnetic field

In this paper, dynamic processes in the solar atmosphere are studied numerically from a complete set of MHD equations. Dynamic evolution of the non-linear magnetic field is produced by the finite amplitude of the azimuthai magnetic field at the base of the flux tube of the solar atmosphere. It is assumed that the initial configuration of the magnetic field is a force-free and potential field, the magnetic field is disturbed at the base, the plasma is driven and a part of the magnetic energy is transformed into the kinetic energy of the plasma.The compressed flow of the plasma has the features of fast MHD waves. The computation results give quantitatively the non-linear evolution of strong magnetic fields. These results could be used in an explanation of coronal transients, surge, spray and eruptive prominence events in the solar atmosphere, as well as in a modelling of plasma behaviour in high-β structure experiments in the laboratory.