<p>The spin-axis orientations of asteroids encode key information about their dynamical evolution. This study analyzes the spin-axis ecliptic coordinates of 63 main belt asteroids grouped into three diameter-based clusters, along with approximately 150 members of four dynamical families (Athor, Eos, Zita, and “Lyka”). By mapping <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10569_2025_10257_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\((\lambda , \beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> into unit vectors on the celestial sphere, directional statistics were applied to characterize alignment and dispersion. A stochastic model was implemented to simulate 1&#xa0;Gyr of spin-axis evolution, incorporating YORP torques, secular precession, and collisional reorientations. Cluster&#xa0;2 (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10569_2025_10257_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\(D \le 210\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mo>≤</mo> <mn>210</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;km) exhibits a nearly isotropic spin distribution, consistent with strong dynamical reorientation. Cluster&#xa0;1 (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10569_2025_10257_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="109" /> </InlineMediaObject> <EquationSource Format="TEX">\(223 \le D \le 525\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>223</mn> <mo>≤</mo> <mi>D</mi> <mo>≤</mo> <mn>525</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;km) shows partial alignment not reproduced by either the solar-aligned or random initial conditions, suggesting an intermediate evolutionary state. Cluster&#xa0;0, represented by (1)&#xa0;Ceres, remains aligned with the ecliptic pole. Among the families, Athor and Eos display directional structures incompatible with the modeled reorientation rates, indicating distinct dynamical histories or classification uncertainties. In contrast, Zita and “Lyka” are better matched by the random hypothesis, despite residual angular offsets. The Rayleigh test confirms statistically significant alignment in “Lyka,” supporting a collisional origin followed by dynamical modification. These results indicate that asteroid spin-axis distributions reflect a size-dependent balance between primordial configurations and stochastic evolutionary processes.</p>

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Spatial distribution of asteroid spin-axes in diameter-based clusters

  • Alberto S. Betzler

摘要

The spin-axis orientations of asteroids encode key information about their dynamical evolution. This study analyzes the spin-axis ecliptic coordinates of 63 main belt asteroids grouped into three diameter-based clusters, along with approximately 150 members of four dynamical families (Athor, Eos, Zita, and “Lyka”). By mapping \((\lambda , \beta )\) ( λ , β ) into unit vectors on the celestial sphere, directional statistics were applied to characterize alignment and dispersion. A stochastic model was implemented to simulate 1 Gyr of spin-axis evolution, incorporating YORP torques, secular precession, and collisional reorientations. Cluster 2 ( \(D \le 210\) D 210  km) exhibits a nearly isotropic spin distribution, consistent with strong dynamical reorientation. Cluster 1 ( \(223 \le D \le 525\) 223 D 525  km) shows partial alignment not reproduced by either the solar-aligned or random initial conditions, suggesting an intermediate evolutionary state. Cluster 0, represented by (1) Ceres, remains aligned with the ecliptic pole. Among the families, Athor and Eos display directional structures incompatible with the modeled reorientation rates, indicating distinct dynamical histories or classification uncertainties. In contrast, Zita and “Lyka” are better matched by the random hypothesis, despite residual angular offsets. The Rayleigh test confirms statistically significant alignment in “Lyka,” supporting a collisional origin followed by dynamical modification. These results indicate that asteroid spin-axis distributions reflect a size-dependent balance between primordial configurations and stochastic evolutionary processes.