Runaway Phase Research Articles

Giant planet formation at the pressure maxima of protoplanetary disks

In the classical core-accretion planet formation scenario, rapid inward migration and accretion timescales of kilometer size planetesimals may not favor the formation of massive cores of giant planets before the dissipation of protoplanetary disks. On the other hand, the existence of pressure maxima in the disk could act as migration traps and locations for solid material accumulation, favoring the formation of massive cores. We aim to study the radial drift of pebbles and planetesimals and planet migration at pressure maxima in a protoplanetary disk and their implications for the formation of massive cores as triggering a gaseous runaway accretion phase. The time evolution of a viscosity driven accretion disk is solved numerically introducing a a dead zone as a low-viscosity region in the protoplanetary disk. A population of pebbles and planetesimals evolving by radial drift and accretion by the planets is also considered. Finally, the embryos embedded in the disk grow by the simultaneous accretion of pebbles, planetesimals and the surrounding gas. Our simulations show that the pressure maxima generated at the edges of the low-viscosity region of the disk act as planet migration traps, and that the pebble and planetesimal surface densities are significantly increased due to the radial drift towards pressure maxima locations. However, our simulations also show that migration trap locations and solid material accumulation locations are not exactly at the same positions. Thus, a planet's semi-major axis oscillations around zero torque locations, predicted by MHD and HD simulations, are needed for the planet to accrete all the available material accumulated at the pressure maxima. Pressure maxima generated at the edges of a low-viscosity region of a protoplanetary disk seem to be preferential locations for the formation and trap of massive cores.

In situ accretion of gaseous envelopes on to planetary cores embedded in evolving protoplanetary discs

The core accretion hypothesis posits that planets with significant gaseous envelopes accreted them from their protoplanetary discs after the formation of rocky/icy cores. Observations indicate that such exoplanets exist at a broad range of orbital radii, but it is not known whether they accreted their envelopes in situ, or originated elsewhere and migrated to their current locations. We consider the evolution of solid cores embedded in evolving viscous discs that undergo gaseous envelope accretion in situ with orbital radii in the range 0.1–10 au. Additionally, we determine the long-term evolution of the planets that had no runaway gas accretion phase after disc dispersal. We find the following. (i) Planets with 5 M⊕ cores never undergo runaway accretion. The most massive envelope contained 2.8 M⊕ with the planet orbiting at 10 au. (ii) Accretion is more efficient on to 10 M⊕ and 15 M⊕ cores. For orbital radii ap ≥ 0.5 au, 15 M⊕ cores always experienced runaway gas accretion. For ap ≥ 5 au, all but one of the 10 M⊕ cores experienced runaway gas accretion. No planets experienced runaway growth at ap = 0.1 au. (iii) We find that, after disc dispersal, planets with significant gaseous envelopes cool and contract on Gyr time-scales, the contraction time being sensitive to the opacity assumed. Our results indicate that Hot Jupiters with core masses ≲15 M⊕ at ≲0.1 au likely accreted their gaseous envelopes at larger distances and migrated inwards. Consistently with the known exoplanet population, super-Earths and mini-Neptunes at small radii during the disc lifetime, accrete only modest gaseous envelopes.

THE EVOLUTION OF GAS GIANT ENTROPY DURING FORMATION BY RUNAWAY ACCRETION

ABSTRACT We calculate the evolution of gas giant planets during the runaway gas accretion phase of formation, to understand how the luminosity of young giant planets depends on the accretion conditions. We construct steady-state envelope models, and run time-dependent simulations of accreting planets with the code Modules for Experiments in Stellar Astrophysics. We show that the evolution of the internal entropy depends on the contrast between the internal adiabat and the entropy of the accreted material, parametrized by the shock temperature T 0 and pressure P 0. At low temperatures ( – , depending on model parameters), the accreted material has a lower entropy than the interior. The convection zone extends to the surface and can drive a high luminosity, leading to rapid cooling and cold starts. For higher temperatures, the accreted material has a higher entropy than the interior, giving a radiative zone that stalls cooling. For , the surface–interior entropy contrast cannot be accommodated by the radiative envelope, and the accreted matter accumulates with high entropy, forming a hot start. The final state of the planet depends on the shock temperature, accretion rate, and starting entropy at the onset of runaway accretion. Cold starts with require low accretion rates and starting entropy, and the temperature of the accreting material needs to be maintained close to the nebula temperature. If instead the temperature is near the value required to radiate the accretion luminosity, , as suggested by previous work on radiative shocks in the context of star formation, gas giant planets form in a hot start with .

A Study of the Thermal Runaway Phase Generated During Cyclic Loading of Viscoelastic Materials Accounting for the Prestress

THE GOOD DAMPING PERFORMANCE AND INHERENT STABILITY OF VISCOELASTIC MATERIALS IN RELATIVELY BROAD FREQUENCY BANDS, BESIDES COST EFFECTIVE-NESS, OFFERS MANY POSSIBILITIES FOR PRACTICAL ENGINEERING APPLICATIONS. HOWEVER, FOR VISCOELASTIC DAMPERS SUBJECTED TO DYNAMIC LOADINGS SUPERIMPOSED ON STATIC PRELOADS, ESPECIALLY WHEN GOOD ISOLATION CHA-RACTERISTICS ARE REQUIRED AT HIGH FREQUENCIES, TRADITIONAL DESIGN GUIDELI-NES CAN LEAD TO POOR DESIGNS DUE TO THE RAPIDLY INCREASING RATE OF TEM-PERATURE CHANGE INSIDE THE MATERIAL. THIS PAPER IS DEVOTED TO THE NU-MERICAL AND EXPERIMENTAL INVESTIGATION IN THE DEGRADATION OF THE STIFFNESS AND CAPACITY OF A VISCOELASTIC MATERIAL INDUCED BY THE THERMAL RUNAWAY PHASE, WHEN IT IS SUBJECTED TO DYNAMIC AND STATIC LOADS SIMUL-TANEOUSLY. AFTER THE THEORETICAL BACKGROUND, THE OBTAINED RESULTS IN TERMS OF THE TEMPERATURE EVOLUTIONS AT DIFFERENT POINTS WITHIN THE VOLUME OF THE MATERIAL AND THE HYSTERESIS LOOPS FOR VARIOUS STATIC PRE-LOADS ARE COMPARED AND THE MAIN FEATURES OF THE PROPOSED STUDY ARE HIGHLIGHTED.

Water loss from terrestrial planets orbiting ultracool dwarfs: implications for the planets of TRAPPIST-1

Ultracool dwarfs (UCD; $T_{\rm eff}<\sim3000~$K) cool to settle on the main sequence after $\sim$1 Gyr. For brown dwarfs, this cooling never stops. Their habitable zone (HZ) thus sweeps inward at least during the first Gyr of their lives. Assuming they possess water, planets found in the HZ of UCDs have experienced a runaway greenhouse phase too hot for liquid water prior to entering the HZ. It has been proposed that such planets are desiccated by this hot early phase and enter the HZ as dry worlds. Here we model the water loss during this pre-HZ hot phase taking into account recent upper limits on the XUV emission of UCDs and using 1D radiation-hydrodynamic simulations. We address the whole range of UCDs but also focus on the planets recently found around the $0.08~M_\odot$ dwarf TRAPPIST-1. Despite assumptions maximizing the FUV-photolysis of water and the XUV-driven escape of hydrogen, we find that planets can retain significant amounts of water in the HZ of UCDs, with a sweet spot in the $0.04$-$0.06~M_\odot$ range. We also studied the TRAPPIST-1 system using observed constraints on the XUV-flux. We find that TRAPPIST-1b and c may have lost as much as 15 Earth Oceans and planet d -- which might be inside the HZ -- may have lost less than 1 Earth Ocean. Depending on their initial water contents, they could have enough water to remain habitable. TRAPPIST-1 planets are key targets for atmospheric characterization and could provide strong constraints on the water erosion around UCDs.

On the inward drift of runaway electrons during the plateau phase of runaway current

The well observed inward drift of current carrying runaway electrons during runaway plateau phase after disruption is studied by considering the phase space dynamic of runaways in a large aspect ratio toroidal system. We consider the case where the toroidal field is unperturbed and the toroidal symmetry of the system is preserved. The balance between the change in canonical angular momentum and the input of mechanical angular momentum in such a system requires runaways to drift horizontally in configuration space for any given change in momentum space. The dynamic of this drift can be obtained by integrating the modified Euler-Lagrange equation over one bounce time. It is then found that runaway electrons will always drift inward as long as they are decelerating. This drift motion is essentially non-linear, since the current is carried by runaways themselves, and any runaway drift relative to the magnetic axis will cause further displacement of the axis itself. A simplified analytical model is constructed to describe such inward drift both in the ideal wall case and no wall case, and the runaway current center displacement as a function of parallel momentum variation is obtained. The time scale of such displacement is estimated by considering effective radiation drag, which shows reasonable agreement with the observed displacement time scale. This indicates that the phase space dynamic studied here plays a major role in the horizontal displacement of runaway electrons during plateau phase.

Extreme water loss and abiotic O2 buildup on planets throughout the habitable zones of M dwarfs.

We show that terrestrial planets in the habitable zones of M dwarfs older than ∼1 Gyr could have been in runaway greenhouses for several hundred million years following their formation due to the star's extended pre-main sequence phase, provided they form with abundant surface water. Such prolonged runaway greenhouses can lead to planetary evolution divergent from that of Earth. During this early runaway phase, photolysis of water vapor and hydrogen/oxygen escape to space can lead to the loss of several Earth oceans of water from planets throughout the habitable zone, regardless of whether the escape is energy-limited or diffusion-limited. We find that the amount of water lost scales with the planet mass, since the diffusion-limited hydrogen escape flux is proportional to the planet surface gravity. In addition to undergoing potential desiccation, planets with inefficient oxygen sinks at the surface may build up hundreds to thousands of bar of abiotically produced O2, resulting in potential false positives for life. The amount of O2 that builds up also scales with the planet mass; we find that O2 builds up at a constant rate that is controlled by diffusion: ∼5 bar/Myr on Earth-mass planets and up to ∼25 bar/Myr on super-Earths. As a result, some recently discovered super-Earths in the habitable zone such as GJ 667Cc could have built up as many as 2000 bar of O2 due to the loss of up to 10 Earth oceans of water. The fate of a given planet strongly depends on the extreme ultraviolet flux, the duration of the runaway regime, the initial water content, and the rate at which oxygen is absorbed by the surface. In general, we find that the initial phase of high luminosity may compromise the habitability of many terrestrial planets orbiting low-mass stars.

ACCRETION OF JUPITER-MASS PLANETS IN THE LIMIT OF VANISHING VISCOSITY

In the core-accretion model the nominal runaway gas-accretion phase brings most planets to multiple Jupiter masses. However, known giant planets are predominantly Jupiter-mass bodies. Obtaining longer timescales for gas accretion may require using realistic equations of states, or accounting for the dynamics of the circumplanetary disk (CPD) in low-viscosity regime, or both. Here we explore the second way using global, three-dimensional isothermal hydrodynamical simulations with 8 levels of nested grids around the planet. In our simulations the vertical inflow from the circumstellar disk (CSD) to the CPD determines the shape of the CPD and its accretion rate. Even without prescribed viscosity Jupiter's mass-doubling time is $\sim 10^4$ years, assuming the planet at 5.2 AU and a Minimum Mass Solar Nebula. However, we show that this high accretion rate is due to resolution-dependent numerical viscosity. Furthermore, we consider the scenario of a layered CSD, viscous only in its surface layer, and an inviscid CPD. We identify two planet-accretion mechanisms that are independent of the viscosity in the CPD: (i) the polar inflow -- defined as a part of the vertical inflow with a centrifugal radius smaller than 2 Jupiter-radii and (ii) the torque exerted by the star on the CPD. In the limit of zero effective viscosity, these two mechanisms would produce an accretion rate 40 times smaller than in the simulation.

Planet formation models: the interplay with the planetesimal disc

According to the sequential accretion model, giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. In order to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. We compute the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. We compute the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate mass planets that have not started yet their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have either masses below 10 ME or above several Jupiter masses. To form giant planets before the dissipation of the disc, small planetesimals (~ 0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate mass planets. Other processes must therefore be at work in order to explain the population of extrasolar planets presently known.

SUBMILLIMETER ARRAY OBSERVATIONS OF THE RX J1633.9-2442 TRANSITION DISK: EVIDENCE FOR MULTIPLE PLANETS IN THE MAKING

We present continuum high resolution Submillimeter Array (SMA) observations of the transition disk object RX J1633.9-2442, which is located in the Ophiuchus molecular cloud and has recently been identified as a likely site of ongoing giant planet formation. The observations were taken at 340 GHz (880 micron) with the SMA in its most extended configuration, resulting in an angular resolution of 0.3" (35 AU at the distance of the target). We find that the disk is highly inclined (i ~50 deg) and has an inner cavity ~25 AU in radius, which is clearly resolved by our observations. We simultaneously model the entire optical to millimeter wavelength spectral energy distribution (SED) and SMA visibilities of RX J1633.9-2442 in order to constrain the structure of its disk. We find that an empty cavity ~25 AU in radius is inconsistent with the excess emission observed at 12, 22, and 24 micron. Instead, the mid-IR excess can be modeled by either a narrow, optically thick ring at ~10 AU or an optically thin region extending from ~7 AU to ~25 AU. The inner disk (r < 5 AU) is mostly depleted of small dust grains as attested by the lack of detectable near-IR excess. We also present deep Keck aperture masking observations in the near-IR, which rule out the presence of a companion up to 500 times fainter than the primary star (in K-band) for projected separations in the 5-20 AU range. We argue that the complex structure of the RX J1633.9-2442 disk is best explained by multiple planets embedded within the disk. We also suggest that the properties and incidence of objects such as RX J1633.9-2442, T Cha, and LkCa 15 (and those of the companions recently identified to these two latter objects) are most consistent with the runaway gas accretion phase of the core accretion model, when giant planets gain their envelopes and suddenly become massive enough to open wide gaps in the disk.

Simulation of the Breakdown Spots Spatial Distribution in High-K Dielectrics and Model Validation Using the Spatstat Package for R Language

The application of successive high-voltage sweeps to the gate electrode of metal/MgO/InP capacitors generates multiple breakdown spots distributed over the metal gate that can be regarded, from the spatial statistics viewpoint, as a point pattern set. The spots are associated with filamentary paths running across the oxide layer and are the result of important thermal effects occurring during the current runaway phase of the breakdown event. In this work, we analyze the spatial distribution of the spots using a software package specifically developed to that aim. The package is called Spatstat and forms part of the R language library.

The source of magnetic fields in (neutron-) stars

AbstractSome arguments, none entirely conclusive, are reviewed about the origin of magnetic fields in neutron stars, with emphasis of processes during and following core collapse in supernovae. Possible origins of the magnetic fields of neutron stars include inheritance from the main sequence progenitor and dynamo action at some stage of evolution of progenitor. Inheritance is not sufficient to explain the fields of magnetars. Energetic considerations point to differential rotation in the final stages of core collapse process as the most likely source of field generation, at least for magnetars. A runaway phase of exponential growth is needed to achieve sufficient field amplification during relevant phase of core collapse; it can probably be provided by a some form of magnetorotational instability. Once formed in core collapse, the field is in danger of decaying again by magnetic instabilities. The evolution of a magnetic field in a newly formed neutron star is discussed, with emphasis on the existence of stable equilibrium configurations as end products of this evolution, and the role of magnetic helicity in their existence. A particularly puzzling problem is the large range of field strengths observed in neutron stars (as well as in A stars and white dwarfs). It implies that a single, deterministic process is insufficient to explain the origin of the magnetic fields in these stars.

Dissipation of Magnetic Flux in Primordial Star Formation: From Run-away Phase to Mass-Accretion Phase

Abstract We investigate the dissipation of magnetic flux in primordial star-forming clouds throughout their collapse, including the run-away collapse phase as well as the accretion phase. We solve the energy equation and the non-equilibrium chemical reactions in the collapsing gas, in order to obtain the radial distribution of the ionized fraction during the collapse. As a result, we find that the ionized fraction is high enough for the magnetic field to couple with the gas throughout evolution of the cloud. This result suggests that the jet formation from protostars as well as the activation of magneto–rotational instability in the accretion disk are enabled in the presence of the cosmological seed magnetic flux proposed by Langer, Puget, and Aghanim (2003, Phys. Rev. D67, 43505).

H2 Line Emission Associated with the Formation of the First Stars

Abstract Molecular hydrogen ($\mathrm{H}_2$) line radiation emitted in the formation events of first-generation stars is evaluated in a discussion of its detectability by future observational facilities. $\mathrm{H}_2$ luminosity evolution from the onset of prestellar collapse until the formation of a $\sim 100 \,{{{M}_{\odot}}}$ protostar is followed. Calculations are extended not only to the early phase of the runaway collapse, but also to the later phase of accretion, whose observational features have not been studied before. Contrary to the runaway collapse phase, where the pure-rotational lines are always dominant, in the accretion phase rovibrational line emission becomes prominent. The maximum luminosity is also attained in the accretion phase for strong emission lines. The peak intensity of the strongest rovibrational line reaches $\sim 10^{-29} \,\mathrm{W} \,\mathrm{m}^{-2}$, corresponding to the flux density of $10^{-5} \,\mu\mathrm{Jy}$, for a source at the typical redshift of first-generation star formation, $1+z = 20$. Although the redshifted rovibrational $\mathrm{H}_2$ emission from such an epoch falls in the wavelength range of the next-generation infrared satellite, Space Infrared Telescope for Cosmology and Astrophysics, for exceeding the detection threshold, $10^7$ such protostars are required to reach the maximum luminosity simultaneously in a pregalactic cloud. It is improbable that this condition is satisfied in a realistic scenario of early structure formation.

Nuclear-reaction rates in the thermonuclear runaway phase of accreting neutron stars

Nuclear-reaction rates in the thermonuclear runaway phase of accreting neutron stars

Temporal and spatial correlations in a viscoelastic model of heterogeneous faults

We study the temporal and spatial correlations in a one-dimensional model of a heterogeneous fault zone, in the presence of visco-elastic effects. As a function of dynamical weakening and of dissipation, the system exhibits three different "phases" : one in which there are no time correlations between the events, a second, in which there are ``Omori's law'' type temporal correlations, and a third, runaway phase with quasiperiodic system size events.

Angular Momentum Transfer in Dynamically Collapsing Gaseous Disks

We investigate the angular momentum transfer in dynamically collapsing gaseous disks by using self-similar solutions for self-gravitating viscous disks. As for the mechanisms of angular momentum transfer, the turbulent viscosity and the gravitational torque are considered. We solved the self-similar equations to examine the effects of the angular momentum transfer in the disks in the runaway collapse phase, when a central core is not yet formed. As a result, the angular momentum transfer makes remarkable differences in rotational velocity distributions as compared with that of the disk with no angular momentum redistribution. In contrast, the distributions of surface density and infall velocity do not vary significantly, since the effect of the centrifugal force is small in this phase. Also, we find that the angular momentum transfer by gravitational torque tends to work more effectively than that due to turbulent viscosity. This is because the magnitude of effective viscosity of gravitational torque is superior to that of turbulent viscosity if the disk is unstable against self-gravity, which is satisfied in the disks in the runaway collapse phase. Finally, we discuss the angular momentum transfer in star-forming disk. From our estimations, we conclude that only a little angular momentum of the disk is transferred in the runaway phase compared with accretion phase before the classical T Tauri star formation. Meanwhile, the first core formation is significantly affected by the angular momentum redistribution in the runaway phase.

From Dust to Terrestrial Planets — Introduction

Terrestrial planets are accreted in a disk orbiting a central star. The basic challenge of their formation consists of assembling micron-sized or smaller dust grains to bodies with over 104 km in diameter. This formation process, ultimately based on collisions, occurs in three very different physical regimes depending upon the size of the bodies present: 1) Early on, micron- to mm-sized dust grains, chondrules and chondrites are strongly coupled to the gas. 2) As they grow larger, gravity increases the collisional cross section allowing runaway growth to occur. 3) After this runaway phase stops from exhaustion of matter in the immediate surroundings of the protoplanets, further growth occurs on timescales typical of mutual gravitational perturbations. The emphasis of this book is on the timescales corresponding to these formation phases as well as the characteristic chemical and isotopic composition of the bodies involved.

Gravitational Collapse of Spherical Interstellar Clouds

In this paper, the gravitational collapse of spherical interstellar clouds is discussed based on hydrodynamical simulations. The evolution is divided into two phases: former runaway collapse phase, in which the central density increases greatly on a finite time scale, and later contraction, associated with accretion onto a newborn star. The initial density distribution is expressed using a ratio of the gravitational force to the pressure force α. The equation of state for a polytropic gas is used. The central, high-density part of the solution converges on a self-similar solution, which was first derived for the runaway collapse by Larson and Penston (LP). In the later accretion phase, gas behaves like a particle, and the infall speed is accelerated by the gravity of the central object. The solution at this stage is qualitatively similar to the inside-out similarity solutions first found by Shu. However, it is shown that the gas-inflow (accretion) rate is time-dependent, in contrast to the constant rate of the inside-out similarity solutions. For isothermal models in which the pressure is important, 1 ≲ α ≲ 3.35, the accretion rate reaches its maximum when the central part, which obeys the LP solution, contracts and accretes. On the other hand, in isothermal models in which gravity is dominant, α ≳ 3.35, the accretion becomes most active at the epoch when the outer part of the cloud falls onto the center. The effect of the non-isothermal equation of state is discussed.

Critical Protoplanetary Core Masses in Protoplanetary Disks and the Formation of Short‐Period Giant Planets

We study a solid protoplanetary core undergoing radial migration in a protoplanetary disk. We con- sider cores in the mass range D1¨10 embedded in a gaseous protoplanetary disk at diUerent radial M ^ locations. We suppose that the core luminosity is generated as a result of planetesimal accretion and calculate the structure of the gaseous envelope assuming hydrostatic and thermal equilibrium. This is a good approximation during the early growth of the core, while its mass is less than the critical value, above which such static solutions can no longer be obtained and rapid gas accretion begins. The M crit , critical value corresponds to the crossover mass above which rapid gas accretion begins in time- dependent calculations. We model the structure and evolution of the protoplanetary nebula as an accre- tion disk with constant a. We present analytic —ts for the steady state relation between the disk surface density and the mass accretion rate as a function of radius. We calculate as a function of radial M crit location, gas accretion rate through the disk, and planetesimal accretion rate onto the core. For a —xed planetesimal accretion rate, is found to increase inward. On the other hand, it decreases with the M crit planetesimal accretion rate and hence with the core luminosity. We consider the planetesimal accretion rate onto cores migrating inward in a characteristic time of D103¨105 yr at 1 AU, as indicated by recent theoretical calculations. We —nd that the accretion rate is expected to be sufficient to prevent the attain- ment of during the migration process if the core starts oU signi—cantly below it. Only at those small M crit radii at which local conditions are such that dust, and accordingly planetesimals, no longer exist can be attained. At small radii, the runaway gas accretion phase may become longer than the disk M crit lifetime if the mass of the core is too small. However, within the context of our disk models, and if it is supposed that some process halts the migration, massive cores can be built up through the merger of additional incoming cores on a timescale shorter than for in situ formation. A rapid gas accretion phase may thus begin without an earlier prolonged phase in which planetesimal accretion occurs at a reduced rate because of feeding zone depletion in the neighborhood of a —xed orbit. Accordingly, we suggest that giant planets may begin to form through the above processes early in the life of the protostellar disk at small radii, on a timescale that may be signi—cantly shorter than that derived for in situ formation. Subject headings: accretion, accretion disksplanetary systemssolar system: formation