Jeans Instability, Jeans Entropy and the Entropy Origin of Gravity

An entropic origin of gravity is re-visited. Isothermal self-gravitating cloud seen as an ideal gas is analyzed. Gravitational attraction within the isothermal cloud in equilibrium is balanced by the pressure, which is of a pure entropic nature. The notion of the Jeans entropy of the cloud corresponding to the entropy of the self-gravitating cloud in mechanical and thermal equilibrium is introduced. Balance of the gravitational compression and the entropic repulsion yields the scaling relation hinting to the entropic origin of the gravitational force. The analysis of the Jeans instability enables elimination of the “holographic screen” or “holographic principle” necessary for grounding of the entropic origin of gravity.

Thermal consequences of impact bombardments to silicate crusts of terrestrial-type exoplanets

<p><strong>Introduction. </strong>Post-accretionary impact bombardment is part of planet formation and leads to localized, regional [e.g., 1-3], or even wholesale global melting of silicate crust [e.g., 4]; less intense bombardment can also create hydrothermal oases favorable for life [e.g, 5]. Here, we generalize the effects of late accretion bombardments to extrasolar planets of different masses (0.1-10M<sub>⊕</sub>). One example is Proxima Centauri b, estimated at ~2× M<sub>⊕</sub> [6]. We model a 0.1M<sub>⊕ </sub>“mini-Earth”<sub></sub>and “super-Earth” at 10M<sub>⊕</sub>, the approximate upper limit for a “mini-Neptune” [7]. Output predicts lithospheric melting and subsurface habitable volumes.</p><p><strong>Methods. </strong>The model [1,2] consists of (i) stochastic cratering; (ii) analytical thermal expressions for each crater [e.g., 8,9]; and (iii) a 3-D thermal model of the lithosphere, where craters cool by conduction and radiation.</p><p>We analyze impact bombardments using our solar system’s mass production functions for the first 500 Myr [10]. Surface temperatures and geothermal gradients are set to 20 °C and 70 °C/km [2]. Total delivered mass for Earth is 7.8 × 10<sup>21</sup> kg, and scaled to other planets based on cross-sectional areas, with 1.7 × 10<sup>21</sup> kg for mini-Earth, 1.2 × 10<sup>22</sup> kg for Proxima Centauri b, and 3.6 × 10<sup>22</sup> kg for super-Earth. The impactors' SFD is based on our main asteroid belt [11]. Impactor and target densities are set to 3000 kg m<sup>-3</sup> and planetary bulk densities are assumed to be 5510 kg m<sup>-3</sup>, omitting gravitational compression [7]. Impactor velocity was estimated at 1.5 × v<sub>esc</sub> for each planet, with 7.8 km s<sup>-1</sup> for mini-Earth,  16.8 km s<sup>-1</sup> for the Earth, 21.1 km s<sup>-1</sup> for Proxima Centauri b, and 36.1 km s<sup>-1</sup> for super-Earth.</p><p><strong>Results. </strong>We assume fully formed crusts, so melt volume immediately increases due to impacts. Super-Earth reaches a maximum of ~45% of the lithosphere in molten state, whereas mini-Earth reaches a maximum of only ~5%.  This is due to much higher impact velocities and cratering densities on the super-Earth compared to mini-Earth. We also show the geophysical habitable volumes within the upper 4 km of a planet’s crust as the bombardment progresses. Impacts sterilize the majority of the habitable volume on super-Earth; however, due to its large total volume, the total habitable volume is still higher than on other planets despite the more intense bombardment in terms of energy delivered per unit area.</p><p><strong>References:</strong> [1] Abramov, O., and S.J. Mojzsis (2009) Nature, 459, 419-422. [2] Abramov et al. (2013) Chemie der Erde, 73, 227-248. [3] Abramov, O., and S. J. Mojzsis (2016) Earth Planet Sci. Lett., 442, 108-120. [4] Canup, R. M. (2004) Icarus, 168, 433-456. [5] Abramov, O., and D. A. Kring (2004) J. Geophys. Res., 109(E10). [6] Tasker, E. J. et al. (2020). Astronom. J., 159(2), 41. [7] Marcy, G. W. et al. (2014). PNAS, 111(35), 12655-12660. [8] Kieffer S. W. and Simonds C. H. (1980) Rev. Geophys. Space Phys., 18, 143-181. [9] Pierazzo E., and H.J. Melosh (2000). Icarus, 145, 252-261. [10] Mojzsis, S. J. et al. (2019). Astrophys. J., 881(1), 44. [11] Bottke, W. F. et al. (2010) Science, 330, 1527-1530.</p>

Compressive Biomechanics of the Reptilian Intervertebral Joint

This study compared the pre-sacral intervertebral joints of the American alligator (Alligator mississippiensis) with those from specimens of Varanus. These two taxa were chosen because they have similar number of pre-sacral vertebrae and similar body weights; however, Varanus can move bipedally and has diarthrotic intervertebral joints, whereas Alligator has intervertebral discs and cannot move bipedally. This study consisted of three objectives; 1) to document the anatomy of the intervertebral joint, 2) to quantify the compressive biomechanics of the intervertebral joints and explore which features contributed to compression resistance, and 3) to quantify the impact of compression on the intervertebral foramen and spinal nerves in these two taxa. The experimental results revealed that the diarthrotic intervertebral joints of Varanus were significantly (4x) stiffer than the intervertebral disc of Alligator, and that a significant component of this increased stiffness arose from the facet joints. Compressing the intervertebral joints of the two taxa caused a reduction in foraminal area, but the magnitude of this reduction was not significantly different. We hypothesize that the main factor preventing spinal nerve impingement in Varanus during gravitational compression is the relatively small size of the spinal ganglion/nerve relative to the foraminal area.

Jupiter's Interior as Revealed by Juno

Jupiter is in the class of planets that we call gas giants, not because they consist of gas but because they were primarily made from hydrogen-helium gas, which upon gravitational compression becomes a metallic fluid. Juno, in orbit about Jupiter since 2016, has changed our view: The gravity data are much improved, and the simplest interpretation of the higher order even harmonics implies that the planet may have a diluted central concentration of heavy elements. Jupiter has strong winds extending to perhaps ∼3,000-km depth that are evident in the odd zonal harmonics of the gravity field. Jupiter's distinctive magnetic field displays some limited local structure, most notably the Great Blue Spot (a region of downward flux near the equator), and some evidence for secular variation, possibly arising from the winds. However, Juno is ongoing; it has not answered all questions and has posed new ones. ▪ Juno's mission reveals Jupiter's interior. ▪ A core exists but is diluted by hydrogen. ▪ The mission revealed wind depth and magnetic field.

Rotation-Driven Phase Transitions in the Cores of Pulsars

In this paper, we discuss the impact of rotation on the particle composition of rotating neutron stars (pulsars). Particular emphasis is put on the formation of quark matter during stellar spin-down, driven by continuous gravitational compression. Our study is based on modern models for the nuclear equation of state whose parameters are tightly constrained by nuclear data, neutron star masses, and the latest estimates of neutron star radii.