Thermal evolution of Earth with magnesium precipitation in the core

In this paper, we investigate the cooling of neutron stars with relativistic and nonrelativistic models of dense nuclear matter. We focus on the effects of uncertainties originated from the nuclear models, the composition of elements in the envelope region, and the formation of superfluidity in the core and the crust of neutron stars. Discovery of [Formula: see text] neutron stars PSR J1614−2230 and PSR J0343[Formula: see text]0432 has triggered the revival of stiff nuclear equation of state at high densities. In the meantime, observation of a neutron star in Cassiopeia A for more than 10 years has provided us with very accurate data for the thermal evolution of neutron stars. Both mass and temperature of neutron stars depend critically on the equation of state of nuclear matter, so we first search for nuclear models that satisfy the constraints from mass and temperature simultaneously within a reasonable range. With selected models, we explore the effects of element composition in the envelope region, and the existence of superfluidity in the core and the crust of neutron stars. Due to uncertainty in the composition of particles in the envelope region, we obtain a range of cooling curves that can cover substantial region of observation data.

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Adiabatic Heat Flow in Mercury with a Fe-8.5wt%Si Core

10.5194/egusphere-egu21-1417 ◽

2021 ◽

Author(s):

Meryem Berrada ◽

Richard Secco ◽

Wenjun Yong

Keyword(s):

Thermal Conductivity ◽

Heat Flow ◽

Internal Structure ◽

High Pressures ◽

Inner Core ◽

Thermal Evolution ◽

The Core ◽

Thermally Driven ◽

Wire Method ◽

Core Conditions

Recent theoretical studies have tried to constrain Mercury&#8217;s internal structure and composition using thermal evolution models. The presence of a thermally stratified layer of Fe-S at the top of an Fe-Si core has been suggested, which implies a sub-adiabatic heat flow on the core side of the CMB. In this work, the adiabatic heat flow at the top of the core was estimated using the electronic component of thermal conductivity (kel), a lower bound for thermal conductivity. Direct measurements of electrical resistivity (&#961;) of Fe-8.5wt%Si at core conditions can be related to kel using the Wiedemann-Franz law. Measurements were carried out in a 3000 ton multi-anvil press using a 4-wire method. The integrity of the samples at high pressures and temperatures was confirmed with electron-microprobe analysis of quenched samples at various conditions. Unexpected behaviour at low temperatures between 6-8 GPa may indicate an undocumented phase transition. Measurements of &#961; at melting seem to remain constant at 127 &#181;&#937;&#183;cm from 10-24 GPa, on both the solid and liquid side of the melting boundary. The adiabatic heat flow at the core side of Mercury&#8217;s core-mantle boundary is estimated between 21.8-29.5 mWm-2, considerably higher than most models of an Fe-S or Fe-Si core yet similar to models of an Fe core. Comparing these results with thermal evolution models suggests that Mercury&#8217;s dynamo remained thermally driven up to 0.08-0.22 Gyr, at which point the core became sub-adiabatic and stimulated a change from dominant thermal convection to dominant chemical convection arising from the growth of an inner core. Simply considering the internal structure of Mercury, these results support the capture of Mercury into a 3:2 resonance orbit during the thermally driven era of the dynamo.

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Magneto–rotational and Thermal Evolution of Magnetars with Crustal Magnetic Fields

International Astronomical Union Colloquium ◽

10.1017/s0252921100060978 ◽

2000 ◽

Vol 177 ◽

pp. 681-684 ◽

Cited By ~ 2

Author(s):

U. Geppert ◽

D. Page ◽

M. Colpi ◽

T. Zannias

Keyword(s):

Magnetic Fields ◽

Binary Systems ◽

Thermal Evolution ◽

Linking the core heat content to Earth's accretion history

10.5194/egusphere-egu2020-10540 ◽

2020 ◽

Author(s):

Renaud Deguen ◽

Vincent Clési

Keyword(s):

Thermal State ◽

Thermal Evolution ◽

Heat Content ◽

Magma Ocean ◽

The Core ◽

Current State ◽

Partitioning Coefficients ◽

The Mean ◽

Mantle Diapirism ◽

Do So

The composition of Earth's mantle, when compared to experimentally determined partitioning coefficients, can be used to constrain the conditions of equilibration - pressure P, temperature T, and oxygen fugacity fO2 - of the metal and silicates during core-mantle differentiation. This places constraints on the thermal state of the planet during its accretion, and it is tempting to try to use these data to estimate the heat content of the core at the end of accretion. To do so, we develop an analytical model of the thermal evolution of the metal phase during its descent through the solid mantle toward the growing core, taking into account compression heating, &#160; viscous dissipation heating, and heat exchange with the surrounding silicates. For each impact, the model takes as initial condition the pressure and temperature at the base of the magma ocean, and gives the temperature of the metal when it reaches the core. The growth of the planet results in additional pressure increase and compression heating of the core. The thermal model is coupled to a Monte-Carlo inversion of the metal/silicates equilibration conditions (P, T, fO2) in the course of accretion from the abundance of Ni, Co, V and Cr in the mantle, and provides an estimate of the core heat content at the end of accretion for each geochemically successful accretion. The core heat content depends on the mean degree of metal-silicates equilibration, on the mode of metal/silicates separation in the mantle (diapirism, percolation, or dyking), but also very significantly on the shape of the equilibration conditions curve (equilibration P and T vs. fraction of Earth accreted). We find that many accretion histories which are successful in reproducing the mantle composition yield a core that is colder than its current state. Imposing that the temperature of the core at the end of accretion is higher than its current values therefore provides strong constraints on the accretion history. In particular, we find that the core heat content depends significantly on the last stages of accretion.&#160;

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Sculpting the valley in the radius distribution of small exoplanets as a by-product of planet formation: the core-powered mass-loss mechanism

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1230 ◽

2019 ◽

Vol 487 (1) ◽

pp. 24-33 ◽

Cited By ~ 53

Author(s):

Akash Gupta ◽

Hilke E Schlichting

Keyword(s):

Mass Loss ◽

Thermal Evolution ◽

Relative Magnitude ◽

Occurrence Rate ◽

Loss Mechanism ◽

Water Ice ◽

The Core ◽

Planetary Cores ◽

Short Period ◽

Atmospheric Mass

ABSTRACT Recent observations revealed a bimodal radius distribution of small, short-period exoplanets with a paucity in their occurrence, a radius ‘valley’, around 1.5–2.0 R⊕. In this work, we investigate the effect of a planet’s own cooling luminosity on its thermal evolution and atmospheric mass loss (core-powered mass-loss) and determine its observational consequences for the radius distribution of small, close-in exoplanets. Using simple analytical descriptions and numerical simulations, we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone (i.e. without any photoevaporation) can produce the observed valley in the radius distribution. Our results match the valley’s location, shape and slope in planet radius–orbital period parameter space, and the relative magnitudes of the planet occurrence rate above and below the valley. We find that the slope of the valley is, to first order, dictated by the atmospheric mass-loss time-scale at the Bondi radius and given by d logRp/d logP ≃ 1/(3(1 − β)) that evaluates to −0.11 for β ≃ 4, where Mc/M⊕ = (Rc/R⊕)β(ρc∗/ρ⊕)β/3 is the mass–radius relation of the core. This choice for β yields good agreement with observations and attests to the significance of internal compression for massive planetary cores. We further find that the location of the valley scales as $\rho _{\rm c*}^{-4/9}$ and that the observed planet population must have predominantly rocky cores with typical water–ice fractions of less than ${\sim } 20{{\, \rm per\, cent}}$. Furthermore, we show that the relative magnitude of the planet occurrence rate above and below the valley is sensitive to the details of the planet-mass distribution but that the location of the valley is not.

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Minimum heat flow from the core and thermal evolution of the Earth

Physics of The Earth and Planetary Interiors ◽

10.1016/j.pepi.2020.106457 ◽

2020 ◽

Vol 305 ◽

pp. 106457

Author(s):

V. Patočka ◽

O. Šrámek ◽

N. Tosi

Keyword(s):

Heat Flow ◽

Thermal Evolution ◽

The Core ◽

The Earth ◽

Minimum Heat

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Thermal Convection in the Core of Ganymede Inferred from Liquid Eutectic Fe-FeS Electrical Resistivity at High Pressures

Crystals ◽

10.3390/cryst11080875 ◽

2021 ◽

Vol 11 (8) ◽

pp. 875

Author(s):

Joshua A. H. Littleton ◽

Richard A. Secco ◽

Wenjun Yong

Keyword(s):

Electrical Resistivity ◽

Thermal Convection ◽

High Pressures ◽

Freezing Point ◽

Thermal Evolution ◽

Significant Proportion ◽

Freezing Point Depression ◽

The Core ◽

Liquid Transition ◽

End Members

The core of Ganymede is suggested to be mainly Fe but with a significant proportion of S. Effects of S as a core constituent are freezing-point depression, allowing for a molten core at relatively low core temperatures, and modification of transport properties that can influence the dynamo and thermal evolution. The electrical resistivity of solid and liquid Fe-FeS (~24–30 wt.% S) was measured up to 5 GPa and thermal conductivity was calculated using the Wiedemann–Franz law. These first well-constrained experimental data on near eutectic Fe-FeS compositions showed intermediate values of electrical and thermal conductivities compared to the end-members. Eutectic temperatures were delineated from the solid to liquid transition, inferred from sharp changes in electrical resistivity, at each pressure. Combined with thermal models, our calculated estimates of the adiabatic heat flow of a molten Fe-FeS eutectic composition core model of Ganymede showed that thermal convection is permissible.

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Effect of core electrical conductivity on core surface flow models

Earth Planets and Space ◽

10.1186/s40623-020-01269-0 ◽

2020 ◽

Vol 72 (1) ◽

Author(s):

Masaki Matsushima

Keyword(s):

Boundary Layer ◽

Electrical Conductivity ◽

Lorentz Force ◽

Thermal Evolution ◽

Surface Flow ◽

Core Flow ◽

Core Surface ◽

Flow Models ◽

The Core ◽

The Earth

AbstractThe electrical conductivity of the Earth’s core is an important physical parameter that controls the core dynamics and the thermal evolution of the Earth. In this study, the effect of core electrical conductivity on core surface flow models is investigated. Core surface flow is derived from a geomagnetic field model on the presumption that a viscous boundary layer forms at the core–mantle boundary. Inside the boundary layer, where the viscous force plays an important role in force balance, temporal variations of the magnetic field are caused by magnetic diffusion as well as motional induction. Below the boundary layer, where core flow is assumed to be in tangentially geostrophic balance or tangentially magnetostrophic balance, contributions of magnetic diffusion to temporal variation of the magnetic field are neglected. Under the constraint that the core flow is tangentially geostrophic beneath the boundary layer, the core electrical conductivity in the range from $${10}^{5} ~\mathrm{S}~{\mathrm{m}}^{-1}$$ 10 5 S m - 1 to $${10}^{7}~ \mathrm{S}~{\mathrm{m}}^{-1}$$ 10 7 S m - 1 has less significant effect on the core flow. Under the constraint that the core flow is tangentially magnetostrophic beneath the boundary layer, the influence of electrical conductivity on the core flow models can be clearly recognized; the magnitude of the mean toroidal flow does not increase or decrease, but that of the mean poloidal flow increases with an increase in core electrical conductivity. This difference arises from the Lorentz force, which can be stronger than the Coriolis force, for higher electrical conductivity, since the Lorentz force is proportional to the electrical conductivity. In other words, the Elsasser number, which represents the ratio of the Lorentz force to the Coriolis force, has an influence on the difference. The result implies that the ratio of toroidal to poloidal flow magnitudes has been changing in accordance with secular changes of rotation rate of the Earth and of core electrical conductivity due to a decrease in core temperature throughout the thermal evolution of the Earth.

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Long-term temperature evolution of neutron stars undergoing episodic accretion outbursts

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936035 ◽

2019 ◽

Vol 630 ◽

pp. A95 ◽

Cited By ~ 1

Author(s):

L. S. Ootes ◽

R. Wijnands ◽

D. Page

Keyword(s):

Neutron Star ◽

Equilibrium State ◽

Core Temperature ◽

Thermal Evolution ◽

Neutrino Emission ◽

Temperature Evolution ◽

The Core ◽

Heating And Cooling ◽

Nucleon Pairing

Context. Transient neutron star low-mass X-ray binaries undergo episodes of accretion, alternated with quiescent periods. During an accretion outburst, the neutron star heats up due to exothermic accretion-induced processes taking place in the crust. Besides the long-known deep crustal heating of nuclear origin, a likely non-nuclear source of heat, dubbed “shallow heating”, is present at lower densities. Most of the accretion-induced heat slowly diffuses into the core on a timescale of years. Over many outburst cycles, a state of equilibrium is reached when the core temperature is high enough that the heating and cooling (photon and neutrino emission) processes are in balance. Aims. We investigate how stellar characteristics and outburst properties affect the long-term temperature evolution of a transiently accreting neutron star. For the first time the effects of crustal properties are considered, particularly that of shallow heating. Methods. Using our code NSCool, we tracked the thermal evolution of a neutron star undergoing outbursts over a period of 105 yr. The outburst sequence is based on the regular outbursts observed from the neutron star transient Aql X-1. For each model we calculated the timescale over which equilibrium was reached and we present these timescales along with the temperature and luminosity parameters of the equilibrium state. Results. We performed several simulations with scaled outburst accretion rates, to vary the amount of heating over the outburst cycles. The results of these models show that the equilibrium core temperature follows a logarithmic decay function with the equilibrium timescale. Secondly, we find that shallow heating significantly contributes to the equilibrium state. Increasing its strength raises the equilibrium core temperature. We find that if deep crustal heating is replaced by shallow heating alone, the core would still heat up, reaching only a 2% lower equilibrium core temperature. Deep crustal heating may therefore not be vital to the heating of the core. Additionally, shallow heating can increase the quiescent luminosity to values higher than previously expected. The thermal conductivity in the envelope and crust, including the potentially low-conductivity pasta layer at the bottom of the crust, is unable to significantly alter the long-term internal temperature evolution. Stellar compactness and nucleon pairing in the core change the specific heat and the total neutrino emission rate as a function of temperature, with the consequences for the properties of the equilibrium state depending on the exact details of the assumed pairing models. The presence of direct Urca emission leads to the lowest equilibrium core temperature and the shortest equilibrium timescale.

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Mass Transfer and Stellar Evolution of the White Dwarfs in AM CVn Binaries

The Astrophysical Journal ◽

10.3847/1538-4357/ac2b2a ◽

2021 ◽

Vol 923 (1) ◽

pp. 125

Author(s):

Tin Long Sunny Wong ◽

Lars Bildsten

Keyword(s):

Mass Transfer ◽

Stellar Evolution ◽

White Dwarfs ◽

Thermal Evolution ◽

Mass Transfer Rate ◽

Adiabatic Evolution ◽

The Core ◽

Self Consistent ◽

Angular Momentum Loss ◽

Orbital Periods

Abstract We calculate the stellar evolution of both white dwarfs (WDs) in AM CVn binaries with orbital periods of P orb ≈ 5–70 minutes. We focus on the cases where the donor starts as a M He < 0.2M ⊙ helium WD and the accretor is a M WD > 0.6 M ⊙ WD. Using Modules for Experiments in Stellar Astrophysics, we simultaneously evolve both WDs assuming conservative mass transfer and angular momentum loss from gravitational radiation. This self-consistent evolution yields important feedback of the properties of the donor on the mass-transfer rate, M ̇ , as well as the thermal evolution of the accreting WD. Consistent with earlier work, we find that the high M ̇ 's at early times forces an adiabatic evolution of the donor for P orb < 30 minutes so that its mass–radius relation depends primarily on its initial entropy. As the donor reaches M He ≈ 0.02–0.03 M ⊙ at P orb ≃ 30 minutes, it becomes fully convective and could lose entropy and expand much less than expected under further mass loss. However, we show that the lack of reliable opacities for the donor’s surface inhibit a secure prediction for this possible cooling. Our calculations capture the core heating that occurs during the first ≈107 yr of accretion and continue the evolution into the phase of WD cooling that follows. When compared to existing data for accreting WDs, as seen by Cheng and collaborators for isolated WDs, we also find that the accreting WDs are not as cool as we would expect given the amount of time they have had to cool.

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