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1.
In the present study, the temperature- and pressure-dependent transport and thermal properties, i.e., viscosity, phonon thermal conductivity, thermal expansivity and heat capacities, as well as electronic and radiative thermal conductivities, have been derived for the mantles of super-Earths. These properties are necessary to understand the interior dynamics and the thermal evolution of those planets. We assume that the mantles consist of MgSiO3 perovskite (pv), but we discuss the effects of the post-perovskite transition, and we elaborate on an addition of periclase MgO and incorporated Fe. However, MgO is found to only significantly influence the phonon thermal conductivity – the viscosities, heat capacities and thermal expansivities of pv and MgO remain comparable. We use the Keane theory of solids, which takes into account the behavior of solid matter at the infinite pressure limit, adopt the Keane equations of state, and adjust for pv and MgO by comparison with experimental high-pressure and high-temperature data. We find the theory of the infinite pressure limit of Keane to be in excellent agreement with recent ab initio studies and experiments. To calculate the melting curve, we further use the Lindemann–Stacey scaling law and fit it to available experimental data. The best data fitting melting temperature for pv reaches 5700 K at 135 GPa and increases to 20,000 K at 1.1 TPa, corresponding to the core-mantle boundary of a 10 Earth mass super-Earth (10MEarth). We find the pv adiabatic temperature (with a potential temperature of 1700 K) to reach 2570 K at 135 GPa and 5000 K at 1.1 TPa. To calculate the pressure-and temperature-dependent viscosity, we use the semi-empirical homologous temperature scaling to relate enthalpy change, and hence viscosity, to the melting temperature. We find that the resulting activation volume of pv decreases from 2.8 cm3/mol at 25 GPa to 1.4 cm3/mol at 1.1 TPa-resulting in a viscosity increase by ～15 orders of magnitude through the adiabatic mantle of a 10MEarth planet. Furthermore, the thermal expansivity (of pv and MgO) decreases by a factor of eight, and the total thermal conductivity (phonon, radiative and electronic) of an Earth-like pv/MgO composite increases by a factor of seven through an adiabatic mantle of a 10MEarth super-Earth. At higher temperatures, i.e., for super-adiabatic temperature profiles, the electronic and radiative thermal conductivities strongly increase and dominate the conductive heat transport. All findings indicate an increase of heat transfer solely by conduction in the lower mantles of super-Earths. Thus our results disagree with Earth-biased full-mantle convection assumptions made by previous models for super-Earths, and additionally raise questions about the differentiation of massive rocky exoplanets and their ability to generate magnetic fields or sustain plate tectonics.  相似文献   

2.
We model the internal thermal evolution of planets with Earth-like composition and masses ranging from 0.1 to 10 Earth masses over a period of 10 billion years. We also characterize the internal activity of the planets by the velocity of putative tectonic plates, the rate at which mantle material is processed through melting zones, and the time taken to process one mantle mass. The more massive the planet the larger its processing rate (?), which scales approximately as ?∝M0.8-1.0. The processing times for all the planets increase with time as they cool and become less active. As would be expected, the surface heat flow scales with planet mass. All planets have similar declines in mantle temperature except for the largest, in which pressure effects cause a larger decline. The larger planets have higher mantle temperatures over all times. The less massive the planet, the larger the decrease in core temperature with time. The core heat flow is also found to decrease more rapidly for smaller planet masses. Finally, rough predictions are made for the time required to generate an atmosphere from estimates of the time to degas water and carbon dioxide in mantle melting zones. The degassing times depend strongly on the initial temperature of the planet, but for the temperatures used in our model all the planets degas within ∼32 Ma after their formation.  相似文献   

3.
C. Sotin  O. Grasset  A. Mocquet 《Icarus》2007,191(1):337-351
By comparison with the Earth-like planets and the large icy satellites of the Solar System, one can model the internal structure of extrasolar planets. The input parameters are the composition of the star (Fe/Si and Mg/Si), the Mg content of the mantle (Mg# = Mg/[Mg + Fe]), the amount of H2O and the total mass of the planet. Equation of State (EoS) of the different materials that are likely to be present within such planets have been obtained thanks to recent progress in high-pressure experiments. They are used to compute the planetary radius as a function of the total mass. Based on accretion models and data on planetary differentiation, the internal structure is likely to consist of an iron-rich core, a silicate mantle and an outer silicate crust resulting from magma formation in the mantle. The amount of H2O and the surface temperature control the possibility for these planets to harbor an ocean. In preparation to the interpretation of the forthcoming data from the CNES led CoRoT (Convection Rotation and Transit) mission and from ground-based observations, this paper investigates the relationship between radius and mass. If H2O is not an important component (less than 0.1%) of the total mass of the planet, then a relation (R/REarth)=ab(M/MEarth) is calculated with (a,b)=(1,0.306) and (a,b)=(1,0.274) for 10−2MEarth<M<MEarth and MEarth<M<10MEarth, respectively. Calculations for a planet that contains 50% H2O suggest that the radius would be more than 25% larger than that based on the Earth-like model, with (a,b)=(1.258,0.302) for 10−2MEarth<M<MEarth and (a,b)=(1.262,0.275) for MEarth<M<10MEarth, respectively. For a surface temperature of 300 K, the thickness of the ocean varies from 150 to 50 km for planets 1 to 10 times the Earth's mass, respectively. Application of this algorithm to bodies of the Solar System provides not only a good fit to most terrestrial planets and large icy satellites, but also insights for discussing future observations of exoplanets.  相似文献   

4.
The search for rocky exoplanets plays an important role in our quest for extra-terrestrial life. Here, we discuss the extreme physical properties possible for the first characterised rocky super-Earth, CoRoT-7b (Rpl = 1.58 ± 0.10 REarth, Mpl = 6.9 ± 1.2 MEarth). It is extremely close to its star (a = 0.0171 AU = 4.48 Rst), with its spin and orbital rotation likely synchronised. The comparison of its location in the (Mpl, Rpl) plane with the predictions of planetary models for different compositions points to an Earth-like composition, even if the error bars of the measured quantities and the partial degeneracy of the models prevent a definitive conclusion. The proximity to its star provides an additional constraint on the model. It implies a high extreme-UV flux and particle wind, and the corresponding efficient erosion of the planetary atmosphere especially for volatile species including water. Consequently, we make the working hypothesis that the planet is rocky with no volatiles in its atmosphere, and derive the physical properties that result. As a consequence, the atmosphere is made of rocky vapours with a very low pressure (P ? 1.5 Pa), no cloud can be sustained, and no thermalisation of the planet is expected. The dayside is very hot (2474 ± 71 K at the sub-stellar point) while the nightside is very cold (50-75 K). The sub-stellar point is as hot as the tungsten filament of an incandescent bulb, resulting in the melting and distillation of silicate rocks and the formation of a lava ocean. These possible features of CoRoT-7b could be common to many small and hot planets, including the recently discovered Kepler-10b. They define a new class of objects that we propose to name “Lava-ocean planets”.  相似文献   

5.
Adam Edson  Sukyoung Lee 《Icarus》2011,212(1):1-13
Circulations and habitable zones of planets orbiting low-mass stars are investigated. Many of these planets are expected to rotate synchronously relative to their parent stars, thereby raising questions about their surface temperature distributions and habitability. We use a global circulation model to study idealized, synchronously rotating (tidally locked) planets of various rotation periods, with surfaces of all land or all water, but with an Earth-like atmosphere and solar insolation. The dry planets exhibit wide variations in surface temperature: >80 °C on the dayside to <−110 °C on the nightside for the 240-h rotator, for example. The water-covered aquaplanets are warmer and exhibit narrower ranges of surface temperatures, e.g., ∼40 °C to >−60 °C for the 240-h orbiter. They also have a larger habitable area, defined here as the region where average surface temperatures are between 0 °C and 50 °C. This concept has little relevance for either dry or aquaplanets, but might become relevant on a planet with both land area and oceans.The circulations on these tidally locked planets exhibit systematic changes as the rotation period is varied. However, they also reveal abrupt transitions between two different circulation regimes and multiple equilibria. For the dry planet, the transition occurs between a 4-day and a 5-day period, while for the aquaplanet, it occurs between a 3-day and a 4-day period. For both dry and aqua planets, this transition occurs when the Rossby deformation radius exceeds half the planetary radius. Further investigation on the dry planet reveals that multiple equilibria exist between 100- and 221-h periods. These multiple equilibria may be relevant for real planets within the habitable zones of late K and M stars, because these planets are expected to have rotation periods between 8 and 100 Earth days.  相似文献   

6.
R. Helled  P. Bodenheimer 《Icarus》2011,211(2):939-947
Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large (∼1 AU) and internal temperatures are low (<2000 K). The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of isolated, non-accreting planets of 3, 5, and 7 MJ. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.  相似文献   

7.
As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 107 years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System.  相似文献   

8.
Planetary formation models predict the existence of massive terrestrial planets and experiments are now being designed that should succeed in discovering them and measuring their masses and radii. We calculate internal structures of planets with one to ten times the mass of the Earth (Super-Earths) to obtain scaling laws for total radius, mantle thickness, core size and average density as a function of mass. We explore different compositions and obtain a scaling law of R∝M0.267-0.272 for Super-Earths. We also study a second family of planets, Super-Mercuries with masses ranging from one mercury-mass to ten mercury-masses with similar composition to the Earth's but with a larger core mass fraction. We explore the effect of surface temperature and core mass fraction on the scaling laws for these planets. The scaling law obtained for the Super-Mercuries is R∝M∼0.3.  相似文献   

9.
We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 107 years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 108 years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 106 years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 106 and 108 years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×106 years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10−4-10−3 times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.  相似文献   

10.
Andrew W. Smith 《Icarus》2009,201(1):381-58
An investigation of the stability of systems of 1 M⊕ (Earth-mass) bodies orbiting a Sun-like star has been conducted for virtual times reaching 10 billion years. For the majority of the tests, a symplectic integrator with a fixed timestep of between 1 and 10 days was employed; however, smaller timesteps and a Bulirsch-Stoer integrator were also selectively utilized to increase confidence in the results. In most cases, the planets were started on initially coplanar, circular orbits, and the longitudinal initial positions of neighboring planets were widely separated. The ratio of the semimajor axes of consecutive planets in each system was approximately uniform (so the spacing between consecutive planets increased slowly in terms of distance from the star). The stability time for a system was taken to be the time at which the orbits of two or more planets crossed. Our results show that, for a given class of system (e.g., three 1 M⊕ planets), orbit crossing times vary with planetary spacing approximately as a power law over a wide range of separation in semimajor axis. Chaos tests indicate that deviations from this power law persist for changed initial longitudes and also for small but non-trivial changes in orbital spacing. We find that the stability time increases more rapidly at large initial orbital separations than the power-law dependence predicted from moderate initial orbital separations. Systems of five planets are less stable than systems of three planets for a specified semimajor axis spacing. Furthermore, systems of less massive planets can be packed more closely, being about as stable as 1 M⊕ planets when the radial separation between planets is scaled using the mutual Hill radius. Finally, systems with retrograde planets can be packed substantially more closely than prograde systems with equal numbers of planets.  相似文献   

11.
William T. Reach 《Icarus》2010,209(2):848-850
Interplanetary dust particles from comets and asteroids pervade the Solar System and become temporarily trapped into orbital resonances with Earth, leading to a circumsolar dust ring. Using the unique vantage point of the Spitzer Space Telescope from its Earth-trailing solar orbit, we have measured for the first time the azimuthal structure of the Earth’s resonant dust ring. There is a relative paucity of particles within 0.1 AU of the Earth, followed by an enhancement in a cloud that is centered 0.2 AU behind Earth with a width of 0.08 AU along the Earth’s orbit. The North ecliptic pole is ∼3% brighter at 8 μm wavelength when viewed from inside the enhancement. The presence of azimuthal asymmetries in debris disks around other stars is considered strong evidence for planets. By measuring the properties of the Earth’s resonant ring, we can provide “ground truth” to models for interactions of planets and debris disks, possibly leading to improved predictions for detectability of life-bearing planets. The low amplitude of the azimuthal asymmetry in the Earth’s circumsolar ring suggests significant contributions to the zodiacal light from particles that are large (>30 μm) or have large orbital eccentricity that makes capture into mean motion resonances inefficient.  相似文献   

12.
Keiko Atobe 《Icarus》2007,188(1):1-17
We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ0), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ0∼1) are more likely to be produced than straight ones (sinγ0∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ0∼10° or the two-body planar problem in which γ0=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ0 (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ0 space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.  相似文献   

13.
L.A. Sromovsky  P.M. Fry 《Icarus》2010,210(1):230-257
The Cassini flyby of Jupiter in 2000 provided spatially resolved spectra of Jupiter’s atmosphere using the Visual and Infrared Mapping Spectrometer (VIMS). A prominent characteristic of these spectra is the presence of a strong absorption at wavelengths from about 2.9 μm to 3.1 μm, previously noticed in a 3-μm spectrum obtained by the Infrared Space Observatory (ISO) in 1996. While Brooke et al. (Brooke, T.Y., Knacke, R.F., Encrenaz, T., Drossart, P., Crisp, D., Feuchtgruber, H. [1998]. Icarus 136, 1-13) were able to fit the ISO spectrum very well using ammonia ice as the sole source of particulate absorption, Sromovsky and Fry (Sromovsky, L.A., Fry, P.M. [2010]. Icarus 210, 211-229), using significantly revised NH3 gas absorption models, showed that ammonium hydrosulfide (NH4SH) provided a better fit to the ISO spectrum than NH3, but that the best fit was obtained when both NH3 and NH4SH were present in the clouds. Although the large FOV of the ISO instrument precluded identification of the spatial distribution of these two components, the VIMS spectra at low and intermediate phase angles show that 3-μm absorption is present in zones and belts, in every region investigated, and both low- and high-opacity samples are best fit with a combination of NH4SH and NH3 particles at all locations. The best fits are obtained with a layer of small ammonia-coated particles (r ∼ 0.3 μm) overlying but often close to an optically thicker but still modest layer of much larger NH4SH particles (r ∼ 10 μm), with a deeper optically thicker layer, which might also be composed of NH4SH. Although these fits put NH3 ice at pressures less than 500 mb, this is not inconsistent with the lack of prominent NH3 features in Jupiter’s longwave spectrum because the reflectivity of the core particles strongly suppresses the NH3 absorption features, at both near-IR and thermal wavelengths. Unlike Jupiter, Saturn lacks the broad 3-μm absorption feature, but does exhibit a small absorption near 2.965 μm, which resembles a similar jovian feature and suggests that both planets contain upper tropospheric clouds of sub-micron particles containing ammonia as a minor fraction.  相似文献   

14.
We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489-496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10−4 times MMSN). However, in this case, on average, too many (?6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4-5 at 0.5-2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density (∼10−4-10−2 times MMSN).  相似文献   

15.
We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronology method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analytically, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth-Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Varying depths of this megaregolith between the mare and highlands is a plausible partial explanation for differences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.  相似文献   

16.
Althea V. Moorhead 《Icarus》2005,178(2):517-539
This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets.  相似文献   

17.
The known extrasolar planets exhibit a wide range of orbital eccentricities e. This has a profound influence on their rotations and climates. Because of tides in their interiors, mostly solid exoplanets are expected eventually to despin to a state of spin-orbit resonance, where the orbital period is some integer or half-integer times the rotation period. The most important of these resonances is the synchronous state, where the planet's spin period exactly equals its orbital period (like Earth's Moon, and indeed most of the regular satellites in the Solar System). Such planets seem doomed to roast on one side and freeze on the other. However, synchronous planets rock back and forth by an angle of ∼2Arcsine with respect to the sub-stellar point. For e=0.055 (as for the Moon), this optical libration amounts to only ∼6°; but for a synchronous planet with e=0.50, for example, it would rise to ∼59°. This greatly expands the temperate “twilight zone” near the terminator and considerably improves the planet's prospects for habitability. For e?0.72389, the optical libration exceeds 90°; for such planets, the sector of permanent night vanishes, while the sunniest region splits in two. Furthermore, the synchronous state is not the only possible spin resonance. For example, Mercury (with e≈0.206) has an orbital period exactly 1.5 times its rotation period. A terrestrial exoplanet with e=0.40, say, is liable to have an orbital period of 2.0, 2.5, or 3.0 times its spin period. The corresponding insolation patterns are generally complicated, and all different from the synchronous state. Yet these non-synchronous resonances also protect certain longitudes from the worst extremes of temperature and solar radiation, and improve the planet's habitability, compared to non-resonant rotation. These results also have implications for the direct detectability of extrasolar planets, and the interpretation of their thermal emissions.  相似文献   

18.
F.W. Wagner  F. Sohl  M. Grott 《Icarus》2011,214(2):366-376
The detection of low-mass extrasolar planets has initiated growing interest in massive rocky bodies (super-Earths) for which no Solar System analogue does exist. Here, we present a new model approach to investigate their interior structure and thermal state. We improve and extend previous interior models mainly in two areas: the first improvement is due to the consequent application of equations of state (EoS) that are compliant with the thermodynamics of the high-pressure limit and facilitate reinvestigating mass-radius relations for terrestrial-type exoplanets. To quantify the uncertainty due to extrapolation, we compare a generalized Rydberg and a Keane EoS, which are both consistent with the high-pressure limit. Furthermore, we consider a reciprocal K′ EoS that fits the seismologically obtained Preliminary Reference Earth Model (PREM), thereby accounting for the mineralogical composition of the Earth. As a result, the predicted planetary radii of terrestrial-type exoplanets of up to 10 Earth masses would differ by less than 2% between all three EoS, well within current observational limits. The second extension arises from the adoption of a mixing length formulation instead of the commonly used, more simplified parameterized approach to model convective heat transport in planetary mantles. In comparison to parameterized convection models, our results indicate generally hotter interiors with increasing planetary mass and a cumulative tendency to extended regimes of sluggish convection in the lowermost mantle. The latter is attributed to less efficient convective heat transport with increasing mantle pressures. An improved knowledge of the present thermal state is prerequisite to gain a better understanding of the pathways of internal evolution of terrestrial-type exoplanets.  相似文献   

19.
Planets less massive than about 10 MEarth are expected to have no massive H-He atmosphere and a cometary composition (∼50% rocks, 50% water, by mass) provided they formed beyond the snowline of protoplanetary disks. Due to inward migration, such planets could be found at any distance between their formation site and the star. If migration stops within the habitable zone, this may produce a new kind of planets, called ocean-planets. Ocean-planets typically consist in a silicate core, surrounded by a thick ice mantle, itself covered by a 100 km-deep ocean. The possible existence of ocean-planets raises important astrobiological questions: Can life originate on such body, in the absence of continent and ocean-silicate interfaces? What would be the nature of the atmosphere and the geochemical cycles? In this work, we address the fate of hot ocean-planets produced when migration ends at a closer distance. In this case the liquid/gas interface can disappear, and the hot H2O envelope is made of a supercritical fluid. Although we do not expect these bodies to harbor life, their detection and identification as water-rich planets would give us insight as to the abundance of hot and, by extrapolation, cool ocean-planets. The water reservoir of these planets seems to be weakly affected by gravitational escape, provided that they are located beyond some minimum distance, e.g. 0.04 AU for a 5-Earth-mass planet around a Sun-like star. The swelling of their water atmospheres by the high stellar flux is expected not to significantly increase the planets' radii. We have studied the possibility of detecting and characterizing these hot ocean-planets by measuring their mean densities using transit missions in space—CoRoT (CNES) and Kepler (NASA)—in combination with Doppler velocimetry from the ground—HARPS (ESO) and possible future instruments. We have determined the domain in the [stellar magnitude, orbital distance] plane where discrimination between ocean-planets and rocky planets is possible with these instruments. The brightest stars of the mission target lists and the planets closest to their stars are the most favorable cases. Full advantage of high precision photometry by CoRoT, and particularly Kepler, can be obtained only if a new generation of Doppler instruments is built.  相似文献   

20.
The propagation of ionizing radiation through model atmospheres of terrestrial-like exoplanets is studied for a large range of column densities and incident photon energies using a Monte Carlo code we have developed to treat Compton scattering and photoabsorption. Incident spectra from parent star flares, supernovae, and gamma-ray bursts are modeled and compared to energetic particles in importance. Large irradiation events with fluences of 106-109 erg cm−2 at the conventional habitable zone can occur at a rate from many per day (flares from young low-mass parent stars) to ∼100 per Gyr (supernovae and gamma-ray bursts). We find that terrestrial-like exoplanets with atmospheres thinner than about 100 g cm−2 block nearly all X-rays, but transmit and reprocess a significant fraction of incident γ-rays, producing a characteristic, flat surficial spectrum. Thick atmospheres (?100 g cm−2) efficiently block even γ-rays, but nearly all the incident energy is redistributed into diffuse UV and visible aurora-like emission, increasing the effective atmospheric transmission by many orders of magnitude. Depending on the presence of molecular UV absorbers and atmospheric thickness, up to 10% of the incident energy can reach the surface as UV reemission. For the Earth, between 2×10−3 and 4×10−2 of the incident flux reaches the ground in the biologically effective 200-320 nm range, depending on O2/O3 shielding. For atmospheres thicker than ∼50 g cm−2 in the case of pure Rayleigh scattering and ∼100 g cm−2 in the case of O2/O3 absorption, the UV reemission exceeds the surficial transmitted ionizing radiation. We also discuss the effects of angle of incidence and derive a modified two-stream approximation solution for the UV transfer. Finally, we suggest that transient atmospheric ionization layers can be frequently created at altitudes lower than the equilibrium layers that result from steady irradiation and winds from the parent star. We suggest that these events can produce frequent fluctuations in atmospheric ionization levels and surficial UV fluxes on terrestrial-like planets.  相似文献   

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