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Description
We numerically explore if and how the nature of dark energy affects the strength of the tendency that the shapes axes of galactic halos located on void surfaces have perpendicular alignments with the directions toward the void centers. The alignment tendency of void-surface halos is quantified by the correlation parameter, $d_{t}$, that enters the analytic formula derived by Lee (2018) for the probability density function of the cosines of the angles between the major principal axes of the halo inertia tensors and and local tidal tensors. This correlation parameter is numerically found to vary most strongly the amplitude of initial density fluctuations, $\sigma_{8}$ and linear growth rate, $f$. When the initial density fluctuations have lower amplitudes and grow at lower rates, the void-surface halos exhibit stronger perpendicular alignments with the directions toward the void centers. Our numerical analysis also reveals that at fixed $\sigma_{8}$ and $f$, the alignment tendency becomes stronger when the equation of state of dark energy $w$ and spectral index $n_{s}$ have lower values. Based on these numerical findings, we empirically determine
a non-parametric model for the cosmology dependence of $d_{t}$, which turns out to be valid for a wide range of the background cosmologies including the non-standard quintessence and thawing dark energy models. Our results imply that the perpendicular alignments of void-surface halos may be in principle useful as a complementary probe of the nature of dark energy.