Long-Term Evolution of Objects in the Kuiper Belt Zone—Effects of Insolation and Radiogenic Heating

The Kuiper Belt zone is unique insofar as the major heat sources of objects a few tens of kilometers in size—solar radiation on the one hand and radioactive decay on the other—have comparable power. This leads to unique evolutionary patterns, with heat waves propagating inward from the irradiated surface and outward from the radioactively heated interior. A major radioactive source that is considered in this study is ²⁶Al. The long-term evolution of several models with characteristics typical of Kuiper Belt objects is followed by means of a 1-D numerical code that solves the heat and mass balance equations on a spherically symmetric grid. The free parameters considered are radius (10-500 km), heliocentric distance (30-120 AU), and initial ²⁶Al content (0-5×10⁻⁸ by mass). The initial composition assumed is a porous mixture of ices (H₂O, CO, and CO₂) and dust. Gases released in the interior are allowed to escape to the surface. It is shown that, depending on parameters, the interior may reach quite high temperatures (up to 180 K). The models suggest that Kuiper Belt objects are likely to lose the ices of very volatile species during early evolution; ices of less volatile species are retained in a surface layer, about 1 km thick. The models indicate that the amorphous ice crystallizes in the interior, and hence some objects may also lose part of the volatiles trapped in amorphous ice. Generally, the outer layers are far less affected than the inner part, resulting in a stratified composition and altered porosity distribution. These changes in structure and composition should have significant consequences for the short-period comets, which are believed to be descendants of Kuiper Belt objects.     

Combined modeling of thermal evolution and accretion of trans-neptunian objects—Occurrence of high temperatures and liquid water

We have calculated the early thermal evolution of trans-neptunian objects by means of a thermal evolution code that takes into account simultaneous accretion. The set of coupled partial differential equations for ²⁶Al radioactive heating, transformation of amorphous to crystalline ice and melting of water ice was solved numerically for small porous icy (cometary-like) bodies growing to final radii between 2 and 32 km and accreting between 20 and 44 AU. Accretion within a swarm of gravitationally interacting small bodies was calculated self-consistently with a simple accretion algorithm and thermal evolution of a typical member of the swarm was tracked in a parameter-space survey. We find that including accretion in numerical modeling of thermal evolution leads to a broad variety of thermally processed icy bodies and that the early occurrence of liquid water and extended crystalline ice interiors may be a very common phenomenon. The pristine nature of small icy bodies becomes thus restricted to a particular set of initial conditions. Generally, long-period comets should be more thermally affected than short-period ones.     

Growth and evolution of small porous icy bodies with an adaptive-grid thermal evolution code: I. Application to Kuiper belt objects and Enceladus

We present a new 1-dimensional thermal evolution code suited for small icy bodies of the Solar System, based on modern adaptive grid numerical techniques, and suited for multiphase flow through a porous medium. The code is used for evolutionary calculations spanning 4.6×¹⁰⁹ yr of a growing body made of ice and rock, starting with a 10 km radius seed and ending with an object 250 km in radius. Initial conditions are chosen to match two different classes of objects: a Kuiper belt object, and Saturn's moon Enceladus. Heating by the decay of ²⁶Al, as well as long-lived radionuclides is taken into account. Several values of the thermal conductivity and accretion laws are tested. We find that in all cases the melting point of ice is reached in a central core. Evaporation and flow of water and vapor gradually remove the water from the core and the final (present) structure is differentiated, with a rocky, highly porous core of 80 km radius (and up to 160 km for very low conductivities). Outside the core, due to refreezing of water and vapor, a compact, ice-rich layer forms, a few tens of km thick (except in the case of very high conductivity). If the ice is initially amorphous, as expected in the Kuiper belt, the amorphous ice is preserved in an outer layer about 20 km thick. We conclude by suggesting various ways in which the code may be extended.     

From KBOs to Centaurs: The thermal connection

Abstract— We present results of thermal evolution calculations for objects originating in the Kuiper belt and transferring inwards, to the region of the outer planets. Kuiper belt objects (KBOs) are considered to be part of a reservoir that supplies the flux of small icy bodies, mainly Centaurs and Jupiter‐family comets, to regions interior to the orbit of Neptune. We study the internal thermal evolution, for ?10⁸ yr, of three typical KBOs and use the end state of the simulation as initial conditions for evolutionary calculations of two typical Centaurs. Some evolutionary trends can be identified for the KBOs, depending on key physical parameters, such as size and composition. The subsequent evolution in the Centaur region results in both specific features for each modeled object (mainly surface and sub‐surface composition) and common characteristics of thermally evolved Centaurs.     

Thermal evolution of trans‐Neptunian objects,icy satellites,and minor icy planets in the early solar system

Numerical simulations are performed to understand the early thermal evolution and planetary scale differentiation of icy bodies with the radii in the range of 100–2500 km. These icy bodies include trans‐Neptunian objects, minor icy planets (e.g., Ceres, Pluto); the icy satellites of Jupiter, Saturn, Uranus, and Neptune; and probably the icy‐rocky cores of these planets. The decay energy of the radionuclides, ²⁶Al, ⁶⁰Fe, ⁴⁰K, ²³⁵U, ²³⁸U, and ²³²Th, along with the impact‐induced heating during the accretion of icy bodies were taken into account to thermally evolve these planetary bodies. The simulations were performed for a wide range of initial ice and rock (dust) mass fractions of the icy bodies. Three distinct accretion scenarios were used. The sinking of the rock mass fraction in primitive water oceans produced by the substantial melting of ice could lead to planetary scale differentiation with the formation of a rocky core that is surrounded by a water ocean and an icy crust within the initial tens of millions of years of the solar system in case the planetary bodies accreted prior to the substantial decay of ²⁶Al. However, over the course of billions of years, the heat produced due to ⁴⁰K, ²³⁵U, ²³⁸U, and ²³²Th could have raised the temperature of the interiors of the icy bodies to the melting point of iron and silicates, thereby leading to the formation of an iron core. Our simulations indicate the presence of an iron core even at the center of icy bodies with radii ≥500 km for different ice mass fractions.     

The early thermal evolution of Mars

Hf‐W isotopic systematics of Martian meteorites have provided evidence for the early accretion and rapid core formation of Mars. We present the results of numerical simulations performed to study the early thermal evolution and planetary scale differentiation of Mars. The simulations are confined to the initial 50 Myr (Ma) of the formation of solar system. The accretion energy produced during the growth of Mars and the decay energy due to the short‐lived radio‐nuclides ²⁶Al, ⁶⁰Fe, and the long‐lived nuclides, ⁴⁰K, ²³⁵U, ²³⁸U, and ²³²Th are incorporated as the heat sources for the thermal evolution of Mars. During the core‐mantle differentiation of Mars, the molten metallic blobs were numerically moved using Stoke's law toward the center with descent velocity that depends on the local acceleration due to gravity. Apart from the accretion and the radioactive heat energies, the gravitational energy produced during the differentiation of Mars and the associated heat transfer is also parametrically incorporated in the present work to make an assessment of its contribution to the early thermal evolution of Mars. We conclude that the accretion energy alone cannot produce widespread melting and differentiation of Mars even with an efficient consumption of the accretion energy. This makes ²⁶Al the prime source for the heating and planetary scale differentiation of Mars. We demonstrate a rapid accretion and core‐mantle differentiation of Mars within the initial ~1.5 Myr. This is consistent with the chronological records of Martian meteorites.     

Thermal evolution of Kuiper belt objects, with implications for cryovolcanism

We investigate the internal thermal evolution of Kuiper belt objects (KBOs), small (radii <1000 km), icy (mean densities ) bodies orbiting beyond Neptune, focusing on Pluto's moon Charon in particular. Our calculations are time-dependent and account for differentiation. We review evidence for ammonia hydrates in the ices of KBOs, and include their effects on the thermal evolution. A key finding is that the production of the first melt, at the melting point of ammonia dihydrate, ≈176 K, triggers differentiation of rock and ice. The resulting structure comprises a rocky core surrounded by liquids and ice, enclosed within a >100-km thick undifferentiated crust of rock and ice. This structure is especially conducive to the retention of subsurface liquid, and bodies the size of Charon or larger (radii >600 km) are predicted to retain some subsurface liquid to the present day. We discuss the possibility that this liquid can be brought to the surface rapidly via self-propagating cracks. We conclude that cryovolcanism is a viable process expected to affect the surfaces of large KBOs including Charon.     

Enceladus: Present internal structure and differentiation by early and long-term radiogenic heating

Pre-Cassini images of Saturn's small icy moon Enceladus provided the first indication that this satellite has undergone extensive resurfacing and tectonism. Data returned by the Cassini spacecraft have proven Enceladus to be one of the most geologically dynamic bodies in the Solar System. Given that the diameter of Enceladus is only about 500 km, this is a surprising discovery and has made Enceladus an object of much interest. Determining Enceladus' interior structure is key to understanding its current activity. Here we use the mean density of Enceladus (as determined by the Cassini mission to Saturn), Cassini observations of endogenic activity on Enceladus, and numerical simulations of Enceladus' thermal evolution to infer that this satellite is most likely a differentiated body with a large rock-metal core of radius about 150 to 170 km surrounded by a liquid water-ice shell. With a silicate mass fraction of 50% or more, long-term radiogenic heating alone might melt most of the ice in a homogeneous Enceladus after about 500 Myr assuming an initial accretion temperature of about 200 K, no subsolidus convection of the ice, and either a surface temperature higher than at present or a porous, insulating surface. Short-lived radioactivity, e.g., the decay of ²⁶Al, would melt all of the ice and differentiate Enceladus within a few million years of accretion assuming formation of Enceladus at a propitious time prior to the decay of ²⁶Al. Long-lived radioactivity facilitates tidal heating as a source of energy for differentiation by warming the ice in Enceladus so that tidal deformation can become effective. This could explain the difference between Enceladus and Mimas. Mimas, with only a small rock fraction, has experienced relatively little long-term radiogenic heating; it has remained cold and stiff and less susceptible to tidal heating despite its proximity to Saturn and larger eccentricity than Enceladus. It is shown that the shape of Enceladus is not that of a body in hydrostatic equilibrium at its present orbital location and rotation rate. The present shape could be an equilibrium shape corresponding to a time when Enceladus was closer to Saturn and spinning more rapidly, or more likely, to a time when Enceladus was spinning more rapidly at its present orbital location. A liquid water layer on Enceladus is a possible source for the plume in the south polar region assuming the survivability of such a layer to the present. These results could place Enceladus in a category similar to the large satellites of Jupiter, with the core having a rock-metal composition similar to Io, and with a deep overlying ice shell similar to Europa and Ganymede. Indeed, the moment of inertia factor of a differentiated Enceladus, C/MR², could be as small as that of Ganymede, about 0.31.     

Radiogenic heating of comets by 26Al and implications for their time of formation

The effect of radiogenic heating on the thermal evolution of spherical icy bodies with radii 1 km < R < 100 km was investigated. The radioisotopes considered were 26Al, 40K, 232Th, 235U, and 238U. Except for the 26Al abundance, which was varied, the other initial abundances were kept fixed, at values derived from those of chondritic meteorites and corresponding to a gas-to-dust ratio of 1. The initial models were homogeneous and isothermal (To = 10 K) amorphous ice spheres, in a circular orbit at 10(4) AU from the Sun. The main object of this study was to examine the conditions under which the transition temperature from amorphous into cubic ice (Ta = 137 K) would be reached. It was shown that the influence of the short-lived radionuclide 26Al dominates the effect of other radioactive species for bodies of radii up to approximately 50 km. Consequently, if we require comets to retain their ice in amorphous form, as suggested by observations, an upper limit of approximately 4 x 10(-9) is obtained for the initial 26Al abundance in comets, a factor of 100 lower than that of the inclusions in the Allende meteorite. A lower limit for the formation time of comets may thus be derived. The possibility of a coexistence of molten cometary cores and extended amorphous ice mantles is ruled out. Larger icy spheres (R > 100 km) reached Ta even in the absence of 26Al, due to the decay of the other radionuclides. As a result, a crystalline core formed whose relative size depended on the composition assumed. Thus the outermost icy satellites in the solar system, which might have been formed of ice in the amorphous state, have probably undergone crystallization and may have exhibited eruptive activity when the gas trapped in the amorphous ice was released (e.g., Miranda).     

Models of P/Wirtanen nucleus: active regions versus non-active regions

From the current understanding we know that comet nuclei have heterogeneous compositions and complex structures. It is believed that cometary activity is the result of a combination of physical processes in the nucleus, like sublimation and recondensation of volatile ices, dust grains release, phase transition of water ice, depletion of the most volatile components in the outer layers and interior differentiation.The evolution of the comet depends on the sublimation of ices and the release of different gases and dust grains: the formation of a dust crust, the surface erosion and the development of the coma are related to the gas fluxes escaping from the nucleus. New observations, laboratory experiments and numerical simulations suggest that the gas and dust emissions are locally generated, in the so-called active regions. This localized activity is probably superimposed to the global nucleus activity. The differences between active and inactive regions can be attributed to differences in texture and refractory material content of the different areas.In this paper we present the results of numerical models of cometary nucleus evolution, developed in order to understand which are the processes leading to the formation of active and non-active regions on the cometary surface. The used numerical code solves the equations of heat transport and gas diffusion within a porous nucleus composed of different ices—such as water (the dominant constituent), CO₂, CO- and of dust grains embedded in the ice matrix.By varying the set of physical parameters describing the initial properties of comet P/Wirtanen, the different behaviour of the icy and dusty areas can be followed.Comet P/Wirtanen is the target of the international ROSETTA mission, the cornerstone ESA mission to a cometary nucleus. The successful design of ROSETTA requires some knowledge of comet status and activity: surface temperatures, amount of active and inactive surface areas, gas production rate and dust flux.     

Iapetus' geophysics: Rotation rate, shape, and equatorial ridge

Iapetus has preserved evidence that constrains the modeling of its geophysical history from the time of its accretion until now. The evidence is (a) its present 79.33-day rotation or spin rate, (b) its shape that corresponds to the equilibrium figure for a hydrostatic body rotating with a period of ∼16 h, and (c) its high, equatorial ridge, which is unique in the Solar System. This paper reports the results of an investigation into the coupling between Iapetus' thermal and orbital evolution for a wide range of conditions including the spatial distributions with time of composition, porosity, short-lived radioactive isotopes (SLRI), and temperature. The thermal model uses conductive heat transfer with temperature-dependent conductivity. Only models with a thick lithosphere and an interior viscosity in the range of about the water ice melting point can explain the observed shape. Short-lived radioactive isotopes provide the heat needed to decrease porosity in Iapetus' early history. This increases thermal conductivity and allows the development of the strong lithosphere that is required to preserve the 16-h rotational shape and the high vertical relief of the topography. Long-lived radioactive isotopes and SLRI raise internal temperatures high enough that significant tidal dissipation can start, and despin Iapetus to synchronous rotation. This occurred several hundred million years after Iapetus formed. The models also constrain the time when Iapetus formed because the successful models are critically dependent upon having just the right amount of heat added by SLRI decay in this early period. The amount of heat available from short-lived radioactivity is not a free parameter but is fixed by the time when Iapetus accreted, by the canonical concentration of ²⁶Al, and, to a lesser extent, by the concentration of ⁶⁰Fe. The needed amount of heat is available only if Iapetus accreted between 2.5 and 5.0 Myr after the formation of the calcium aluminum inclusions as found in meteorites. Models with these features allow us to explain Iapetus' present synchronous rotation, its fossil 16-h shape, and the context within which the equatorial ridge arose.     

Geophysical evolution of Saturn’s satellite Phoebe,a large planetesimal in the outer Solar System

Saturn’s satellite Phoebe is the best-characterized representative of large outer Solar System planetesimals, thanks to the close flyby by the Cassini spacecraft in June 2004. We explore the information contained in Phoebe’s physical properties, density and shape, which are significantly different from those of other icy objects in its size range. Phoebe’s higher density has been interpreted as evidence that it was captured, probably from the proto-Kuiper-Belt. First, we demonstrate that Phoebe’s shape is globally relaxed and consistent with a spheroid in hydrostatic equilibrium with its rotation period. This distinguishes the satellite from ‘rubble-piles’ that are thought to result from the disruption of larger proto-satellites. We numerically model the geophysical evolution of Phoebe, accounting for the feedback between porosity and thermal state. We compare thermal evolution models for different assumptions on the formation of Phoebe, in particular the state of its water, amorphous or crystalline. We track the evolution of porosity and thermal conductivity as well as the destabilization of amorphous ice or clathrate hydrates. While rubble-piles may never reach temperatures suitable for porous ice to creep and relax, we argue that Phoebe’s shape could have relaxed due to heat from the decay of ²⁶Al, provided that this object formed less than 3 Myr after the production of the calcium–aluminum inclusions. This is consistent with the idea that Phoebe could be an exemplar of planetesimals that formed in the transneptunian region and later accreted onto outer planet satellites, either during the satellite’s formation stage, or still later, during the late heavy bombardment.     

Astronomical constraints on nebular temperatures: Implications for planetesimal formation

Abstract— Motivated by recent observations of T-Tauri stars and the interpretation of these observations in terms of the properties of circumstellar disks, we derive internal (midplane) temperatures for disks around mature (age ～1 Ma) T-Tauri stars. The estimates are obtained by combining published results for disk masses, sizes, accretion rates, and surface temperatures. For 26 stars (for which adequate data are available), we derive midplane temperatures at 1 AU primarily in the range 200–800 K, and 100–400 K at 2.5 AU. It is likely that the solar nebula, at the same stage of evolution, contained planetesimals and objects destined to become meteorite parent bodies. Observations of young stellar objects at earlier stages of evolution (age ～0.1 Ma) imply that accretion rates were, on the average, at least two orders of magnitude greater than the 10^?8 M_⊙/year rates typical for mature T-Tauri stars. Such high values would result in midplane temperatures at or near the silicate vaporization temperature in the terrestrial planet region. If cooling of the solar nebula from such a hot epoch was responsible for establishing the pervasive elemental fractionation patterns found in chondritic meteorites, then objects in the asteroid belt must have grown rapidly (within 0.1 Ma) to sizes of ～1 km, a conclusion consistent with current theories of planetesimal formation. However, the fact that primitive meteorite parent bodies escaped being melted by the decay of ²⁶Al then implies that further growth of at least some objects was essentially delayed for 2 Ma or more. Such a diminished growth rate appears to be consistent with simulations of the dynamics of solid bodies in the asteroid belt. Other hypotheses seem less attractive. One might assume that the final cooling occurred only after the decay of ²⁶Al (i.e., more than a million years after calcium-aluminum rich inclusion formation), or that ²⁶Al was not ubiquitous in the early solar system. But the first of these conjectures is incompatible with astronomical observations of T-Tauri systems, and the second appears to be contradicted by the evidence for ²⁶Al in diverse meteoritic components. The remaining alternative would then appear to be that, despite a lack of supporting evidence, chondritic fractionation patterns reflect the net effect of many local heating and cooling events and have nothing to do with global nebular cooling. We conclude that the most plausible hypothesis is that both nebular cooling and coagulation of solids to kilometer-sized objects occurred rapidly and that a substantial number of planetesimals in the asteroid belt remained smaller than a few kilometers in radius for at least 2 Ma.     

Accretion of the asteroids: Implications for their thermal evolution

Thermal models of asteroids generally assume that they accreted either instantaneously or over an extended interval with a prescribed growth rate. It is conventionally assumed that the onset of accretion of chondrite parent bodies was delayed until a substantial fraction of the initial ²⁶Al had decayed. However, this interval is not consistent with the early melting, and differentiation of parent bodies of iron meteorites. Formation time scales are tested by dynamical simulations of accretion from small primary planetesimals. Gravitational accretion yields rapid runaway growth of large planetary embryos until most smaller bodies are depleted. In a given simulation, all asteroid‐sized bodies have comparable growth times, regardless of size. For plausible parameters, growth times are shorter than the lifetime of ²⁶Al, consistent with thermal models that assume instantaneous accretion. Rapid growth after planetesimal formation is consistent with differentiation of parent bodies of iron meteorites, but not with the assumed delay in formation of chondritic bodies. After the initial growth stage, there is an interval of slower evolution until the belt is stirred and the embryos are dynamically removed. During this interval, a fraction of asteroid‐sized bodies experience large accretional impacts, allowing bodies of the same final size to have very different histories of radius versus time. Accretion from small primary planetesimals leaves some fraction of material in bodies small enough to preserve CAIs while avoiding heating by ²⁶Al. Unheated material can be a significant fraction of the mass that remains after large embryos are removed from the Main Belt.     

Simulations for the Original Distribution of KBOs

Using the N-body dynamical model that includes the sun, the 8 planets, Pluto, UB313 and massless particles, we simulate the orbital evolution of 551 Kuiper Belt Objects (KBOs) with known parameters. The initial conditions of the simulations are the currently observed orbital parameters. The integration backtracks from now to -10×10⁸ yr. The results show that about 10×10⁸ years ago, more than 1/3 of the presently observed KBOs resided in the region of the present Kuiper main belt, a few were located inside the Neptune orbit, and the rest were beyond 50AU; and that about 4.5×10⁸ years ago, all the objects in the Kuiper main belt exhibited a rather good normal distribution, without so many objects concentrated in the Neptune's 3:2 resonance region, as at present time.     

Radiation-induced amorphization of crystalline ice

We study radiation-induced amorphization of crystalline ice, analyzing the results of three decades of experiments with a variety of projectiles, irradiation energy, and ice temperature, finding a similar trend of increasing resistance of amorphization with temperature and inconsistencies in results from different laboratories. We discuss the temperature dependence of amorphization in terms of the ‘thermal spike’ model. We then discuss the common use of the 1.65 μm infrared absorption band of water as a measure of degree of crystallinity, an increasingly common procedure to analyze remote sensing data of astronomical icy bodies. The discussion is based on new, high quality near-infrared reflectance absorption spectra measured between 1.4 and 2.2 μm for amorphous and crystalline ices irradiated with 225 keV protons at 80 K. We found that, after irradiation with 10¹⁵ protons cm⁻², crystalline ice films thinner than the ion range become fully amorphous, and that the infrared absorption spectra show no significant changes upon further irradiation. The complete amorphization suggests that crystalline ice observed in the outer Solar System, including trans-neptunian objects, may results from heat from internal sources or from the impact of icy meteorites or comets.     

Prediction of deuterium abundance in comets

Using a chemical scheme based on ion-molecule reactions in cool interstellar clouds, the possibility of a deuterium enrichment of volatile material in comets is discussed. It is assumed that the hydrogen-containing molecules are deuterated before accretion and condensation on the coremantle dust particles from which the cometesimals are formed. The D/H ratio in comets may be enhanced in respect to the average value by a factor of 10². Therefore comets are not promising objects for testing the primordial deuterium abundance.     

Pressure dependent trace gas trapping in amorphous water ice at 77 K: Implications for determining conditions of comet formation

The nature of cometary volatile materials is subject to debate. Theoretical models of cometary nuclei and laboratory studies suggest that these objects could be made of amorphous water ice in addition to other volatile molecules and refractory grains. This water ice structure has the ability to encapsulate the gases of surrounding environment, reflecting the physical and chemical conditions during their deposition. Therefore, the knowledge of the chemical composition of volatile molecules trapped in amorphous water ice provides a tool for probing the formation environment of cometary ice grains. Experimental studies of gas trapping efficiency in amorphous water ice have been previously conducted mostly under kinetic conditions, where dynamic pumping and temperature gradients prevented rigorous calibrations. In this work, we investigated the trapping efficiencies of Ar, CO, CH₄, Kr and N₂ by depositing water vapor as ice in the presence of trace gases in a volume submerged in liquid nitrogen at 77 K. The gas trapping efficiencies were determined simply by monitoring the pressure difference of the trace gases before and after the deposition of a known amount of water molecules as amorphous ice.Our results show that the trapped gas to water molecule ratio in amorphous ice is controlled primarily by the partial pressure of the gas during water ice deposition, and is independent of the ice deposition rate as well as the gas to water ratio in the vapor phase. The trapping efficiencies of gases decrease in the order of Kr > CH₄ > CO > Ar > N₂ in accordance with previous studies. Assuming that the water ice structure of comets is at least partially amorphous water ice at the time of their formation, these results suggest that the total pressure and composition of the surrounding environment of amorphous ice formation are significant controlling factors of trace gas concentrations in cometary ice. This further indicates that the evolution of the solar nebula and timing of cometary ice condensation can also be important parameters in linking the volatile contents of comets and their formation process.     

SN 1987A: an investigation of the bolometric luminosity evolution and the interior neutron star

In this paper the contributions of various radioactive substances (⁵⁶Co, ⁵⁷Co, ⁴⁴Ti and ²²Na) in the envelope of the supernova SN 1987A to the evolution of the bolometric luminosity are calculated and the several types of radiation, which may probably exist in the interior neutron star, as well as their contributions to the bolometric luminosity are investigated. After comparison of the results of calculation with the observation of CTIO and ESO, it is believed that after about 900 days the nuclear decay energy is no longer the unique energy source which determines the bolometric luminosity evolution of SN 1987A, that the radiation coming from the interior neutron star begins to play a dominating role in the bolometric luminosity evolution and that the most important mechanism of radiation of the neutron star is accretion.     

Importance of the accretion process in asteroid thermal evolution: 6 Hebe as an example

Abstract— Widespread evidence exists for heating that caused melting, thermal metamorphism, and aqueous alteration in meteorite parent bodies. Previous simulations of asteroid heat transfer have assumed that accretion was instantaneous. For the first time, we present a thermal model that assumes a realistic (incremental) accretion scenario and takes into account the heat budget produced by decay of ²⁶Al during the accretion process. By modeling 6 Hebe (assumed to be the H chondrite parent body), we show that, in contrast to results from instantaneous accretion models, an asteroid may reach its peak temperature during accretion, the time at which different depth zones within the asteroid attain peak metamorphic temperatures may increase from the center to the surface, and the volume of high‐grade material in the interior may be significantly less than that of unmetamorphosed material surrounding the metamorphic core. We show that different times of initiation and duration of accretion produce a spectrum of evolutionary possibilities, and thereby, highlight the importance of the accretion process in shaping an asteroid's thermal history. Incremental accretion models provide a means of linking theoretical models of accretion to measurable quantities (peak temperatures, cooling rates, radioisotope closure times) in meteorites that were determined by their thermal histories.