Ensemble Of N-body Simulations Research Articles

System Architecture and Planetary Obliquity: Implications for Long-term Habitability

In the search for life beyond our solar system, attention should be focused on those planets that have the potential to maintain habitable conditions over the prolonged periods of time needed for the emergence and expansion of life as we know it. The observable planetary architecture is one of the determinants for long-term habitability as it controls the orbital evolution and ultimately the stellar fluxes received by the planet. With an ensemble of n-body simulations and obliquity models of hypothetical planetary systems, we demonstrate that the amplitude and period of the eccentricity, obliquity, and precession cycles of an Earth-like planet are sensitive to the orbital characteristics of a giant companion planet. A series of transient, ocean-coupled climate simulations show how these characteristics of astronomical cycles are decisive for the evolving surface conditions and long-term fractional habitability relative to the modern Earth. The habitability of Earth-like planets increases with the eccentricity of a Jupiter-like companion, provided that the mean obliquity is sufficiently low to maintain temperate temperatures over large parts of its surface throughout the orbital year. A giant companion closer in results in shorter eccentricity cycles of an Earth-like planet but longer, high-amplitude, obliquity cycles. The period and amplitude of obliquity cycles can be estimated to first order from the orbital pathways calculated by the n-body simulations. In the majority of simulations, the obliquity amplitude relates directly to the orbital inclination whereas the period of the obliquity cycle is a function of the nodal precession and the proximity of the giant companion.

Modelling large-scale halo bias using the bispectrum

We study the relation between the halo and matter density fields -- commonly termed bias -- in the LCDM framework. In particular, we examine the local model of biasing at quadratic order in the matter density. This model is characterized by parameters b_1 and b_2. Using an ensemble of N-body simulations, we apply several statistical methods to estimate the parameters. We measure halo and matter fluctuations smoothed on various scales and find that the parameters vary with smoothing scale. We argue that, for real-space measurements, owing to the mixing of wavemodes, no scale can be found for which the parameters are independent of smoothing. However, this is not the case in Fourier space. We measure halo power spectra and construct estimates for an effective large-scale bias. We measure the configuration dependence of the halo bispectra B_hhh and reduced bispectra Q_hhh for very large-scale k-space triangles. From this we constrain b_1 and b_2. Using the lowest-order perturbation theory, we find that for B_hhh the best-fit parameters are in reasonable agreement with one another as the triangle scale is varied, but that the fits become poor as smaller scales are included. The same is true for Q_hhh. The best-fit parameters depend on the discreteness correction. This led us to consider halo-mass cross-bispectra. The results from these statistics support our earlier findings. We develop a test to explore the importance of missing higher-order terms in the models. We prove that low-order expansions are not able to correctly model the data, even on scales k_1~0.04 h/Mpc. If robust inferences are to be drawn from galaxy surveys, then accurate models for the full nonlinear matter bispectrum and trispectrum will be essential.