Applicability of isothermal unrealistic two-parameter equations of state for solids

Roy, Papiya Bose; Roy, Sushil Bose

doi:10.1088/0953-8984/18/46/015

Cited by 8 publications

(4 citation statements)

References 114 publications

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“…Regarding the structural properties of planets, although the polytropic model was considered as a first attempt to describe them, that equation of state does not incorporate the approximate incompressibility of solids and liquids at low pressures. To account for it, many different equations of state have been considered [115,[124][125][126][127][128][129][130][131][132][133][134]. The resulting shape of the JCAP05(2022)042 mass-radius relation, in the case of a homogeneous composition, is very similar for different materials, all cases presenting a maximum radius, with planets with heavier elements resulting in smaller radii [114,115].…”

Section: Planetary Bodiesmentioning

confidence: 99%

Evaporation of dark matter from celestial bodies

Garani

Palomares‐Ruiz

2022

J. Cosmol. Astropart. Phys.

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Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range [10-10 - 102] M⊙, for constant scattering cross sections and s-wave annihilations. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, at the local galactic position, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by Ec/Tχ ∼ 30, where Ec is the escape energy of DM particles at the core of the object and Tχ is their temperature. In that case, the minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, m evap ≃ 0.7 GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor smaller than three within the range 10-41 cm2 ≤ σp ≤ 10-31 cm2, where σp is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic, and details on the density and temperature profiles of celestial bodies have also a small impact.

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Section: Planetary Bodiesmentioning

confidence: 99%

Evaporation of dark matter from celestial bodies

Garani

Palomares‐Ruiz

2022

J. Cosmol. Astropart. Phys.

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show abstract

“…Regarding the structural properties of planets, although the polytropic model was considered as a first attempt to describe them, that equation of state does not incorporate the approximate incompressibility of solids and liquids at low pressures. To account for it, many different equations of state have been considered [114,[123][124][125][126][127][128][129][130][131][132][133]. The resulting shape of the mass-radius relation, in the case of a homogeneous composition, is very similar for different materials, all cases presenting a maximum radius, with planets with heavier elements resulting in smaller radii [113,114].…”

Section: Iii2 Planetary Bodiesmentioning

confidence: 99%

Evaporation of dark matter from celestial bodies

Garani,

Palomares-Ruiz

2021

Preprint

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Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range [10 −10 − 10 2 ] M . We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by Ec/Tχ ∼ 30, where Ec is the escape energy of DM particles at the core of the object and Tχ is the DM temperature. The minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, mevap 0.7 GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor of two or less within the range 10 −41 cm 2 ≤ σp ≤ 10 −31 cm 2 , where σp is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the local galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic.

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“…which we borrowed from Roy & Roy (2006). Thus for any given material there are only three parameters (ρ0, B0, and B ′ 0 ).…”

Section: Our Equation Of Statementioning

confidence: 99%

“…For all of our calculations above, which were cold curves, we fixed the product and sum of our parameters to A0 + A2 = n0 and A0A1 = n0. The sum is required for all curves, the product was a fortuitous choice suggested by Roy-Roy (2006) which worked well for cold curves, it controls the relative size of the second derivative…”

Section: Temperature Analysismentioning

confidence: 99%

A variable polytrope index applied to planet and material models

Weppner¹,

McKelvey²,

Thielen³

et al. 2015

Mon. Not. R. Astron. Soc.

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We introduce a new approach to a century old assumption which enhances not only planetary interior calculations but also high pressure material physics. We show that the polytropic index is the derivative of the bulk modulus with respect to pressure. We then augment the traditional polytrope theory by including a variable polytrope index within the confines of the Lane-Emden differential equation. To investigate the possibilities of this method we create a high quality universal equation of state, transforming the traditional polytrope method to a tool with the potential for excellent predictive power. The theoretical foundation of our equation of state is the same elastic observable which we found equivalent to the polytrope index, the derivative of the bulk modulus with respect to pressure. We calculate the density-pressure of six common materials up to 10 18 Pa, mass-radius relationships for the same materials, and produce plausible density-radius models for the rocky planets of our solar system. We argue that the bulk modulus and its derivatives have been under utilized in previous planet formation methods. We constrain the material surface observables for the inner core, outer core, and mantle of planet Earth in a systematic way including pressure, bulk modulus, and the polytrope index in the analysis. We believe this variable polytrope method has the necessary apparatus to be extended further to gas giants and stars. As supplemental material we provide computer code to calculate multi-layered planets.

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Applicability of isothermal unrealistic two-parameter equations of state for solids

Cited by 8 publications

References 114 publications

Evaporation of dark matter from celestial bodies

Evaporation of dark matter from celestial bodies

Evaporation of dark matter from celestial bodies

A variable polytrope index applied to planet and material models

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