Root mean squares of distance and geodesic between two constituent particles within fractal aggregates prepared by BCCA, DLA, and GSAW procedures

Understanding the geodesic properties of fractal aggregates is essential, as their thermal and mechanical properties are characterized by their geodesics. In this study, we investigate the root mean square (RMS) of the geodesic between two constituent particles within fractal aggregates prepared by ballistic cluster-cluster aggregation (BCCA), diffusion-limited aggregation (DLA), and growing self-avoiding walk (GSAW) processes in two- and three-dimensional spaces. We find that the dependence of the RMS of the geodesic on the number of constituent particles is given by the following equation: $N \approx k_{\rm g} {D_{\rm RMS}}^{d_{\rm g}}$, where $N$ is the number of constituent particles and $D_{\rm RMS}$ is the RMS of the geodesic. We numerically obtain the prefactor $k_{\rm g}$ and exponent $d_{\rm g}$ for these fractal aggregates. We name the exponent ``the geodesic dimension'', and it is compared with the fractal dimension. Our findings show that the difference between fractal and geodesic dimensions varies significantly depending on the preparation procedure for fractals.Comment: 8 pages, 15 figures. Accepted for publication in JPS

Thermal conductivity of porous aggregates

$\mathit{Context.}$ The thermal conductivity of highly porous dust aggregates is a key parameter for many subjects in planetary science; however, it is not yet fully understood. $\mathit{Aims.}$ In this study, we investigate the thermal conductivity of fluffy dust aggregates with filling factors of less than $10^{-1}$. $\mathit{Methods.}$ We determine the temperature structure and heat flux of the porous dust aggregates calculated by $N$-body simulations of static compression in the periodic boundary condition. $\mathit{Results.}$ We derive an empirical formula for the thermal conductivity through the solid network $k_{\rm sol}$ as a function of the filling factor of dust aggregates $\phi$. The results reveal that $k_{\rm sol}$ is approximately proportional to ${\phi}^{2}$, and the thermal conductivity through the solid network is significantly lower than previously assumed. In light of these findings, we must reconsider the thermal histories of small planetary bodies.Comment: 4 pages, 4 figures. Accepted for publication in Astronomy & Astrophysic

Survivability of Amorphous Ice in Comets Depends on the Latent Heat of Crystallization of Impure Water Ice

Comets would have amorphous ice rather than crystalline one at the epoch of their accretion. Cometary ice contains some impurities that govern the latent heat of ice crystallization, $L_{\rm cry}$. However, it is still controversial whether the crystallization process is exothermic or endothermic. In this study, we perform one-dimensional simulations of the thermal evolution of km-sized comets and investigate the effect of the latent heat. We find that the depth where amorphous ice can survive significantly depends on the latent heat of ice crystallization. Assuming the cometary radius of 2 km, the depth of the amorphous ice mantle is approximately 100 m when the latent heat is positive (i.e., the exothermic case with $L_{\rm cry} = + 9 \times 10^{4}$ J/kg). In contrast, when we consider the impure ice representing the endothermic case with $L_{\rm cry} = - 9 \times 10^{4}$ J/kg, the depth of the amorphous ice mantle could exceed 1 km. Although our numerical results indicate that these depths depend on the size and the accretion age of comets, the depth in a comet with the negative latent heat is a few to several times larger than the positive case for a given comet size. This work suggests that the spatial distribution of the ice crystallinity in a comet nucleus depends on the latent heat, which can be different from the previous estimates assuming pure water ice.Comment: 15 pages, 10 figures. Accepted for publication in PAS

On the Number of Stars in the Sun's Birth Cluster

The Sun is thought to be formed within a star cluster. The coexistence of $^{26}{\rm Al}$-rich and $^{26}{\rm Al}$-poor calcium--aluminum-rich inclusions indicates that a direct injection of $^{26}{\rm Al}$-rich materials from a nearby core-collapse supernova should occur in the first $10^5$ years of the solar system. Therefore, at least one core-collapse supernova should occur within the duration of star formation in the Sun's birth cluster. Here we revisit the number of stars in the Sun's birth cluster from the point of view of the probability for acquiring at least one core-collapse supernova within the finite duration of star formation in the birth cluster. We find that the number of stars in the birth cluster can be significantly larger than that previously considered, depending on the duration of star formation.Comment: 8 pages, 6 figures. Accepted for publication in A&