Dynamics-based halo model for large scale structure (2406.04054v2)

Abstract: Accurate modelling of the one-to-two halo transition has long been difficult to achieve. We demonstrate that physically motivated halo definitions that respect the bimodal phase-space distribution of dark matter particles near halos resolves this difficulty. Specifically, the two phase-space components are overlapping and correspond to: 1) particles \it orbiting \rm the halo; and 2) particles \it infalling \rm into the halo for the first time. Motivated by this decomposition, Garc\'ia [R. Garc\'ia et. al., MNRAS 521, 2464 (2023)] advocated for defining haloes as the collection of particles orbiting their self-generated potential. This definition identifies the traditional one-halo term of the halo--mass correlation function with the distribution of orbiting particles around a halo, while the two-halo term governs the distribution of infalling particles. We use dark matter simulations to demonstrate that the distribution of orbiting particles is finite and can be characterised by a single physical scale $r_{\rm h}$, which we refer to as the \it halo radius. \rm The two-halo term is described using a simple yet accurate empirical model based on the Zel'dovich correlation function. We further demonstrate that the halo radius imprints itself on the distribution of infalling particles at small scales. Our final model for the halo--mass correlation function is accurate at the $\approx 2\%$ level for $r \in [0.1,50]\ h^{-1}\ Mpc$. The Fourier transform of our best fit model describes the halo--mass power spectrum with comparable accuracy for $k\in [0.06, 6.0]\ h\ Mpc^{-1}$.

• The paper proposes a novel dynamics-based halo model for large scale structure, redefining halos based on orbiting particles rather than static overdensities.
• This model distinguishes orbiting and infalling particles with distinct profiles and achieves approximately 2% accuracy for the halo-mass correlation function over large scales in simulations.
• The dynamics-based approach improves precision cosmology by accurately capturing the halo transition regime and facilitates the construction of bias-free halo catalogs.

Dynamics-Based Halo Model for Large Scale Structure

The paper "Dynamics-Based Halo Model for Large Scale Structure" presents a novel approach to modeling the transition between the one and two halo regimes in the context of large-scale structure. This work leverages a new definition of dark matter halos that respects the bimodal phase-space distribution of dark matter particles around halos. The authors propose that these particles can be segregated into two distinct components: those orbiting the halo and those infalling for the first time.

Methodology and Model Proposal

The authors advocate redefining halos as the collection of particles that are orbiting their self-generated potential. This redefinition leads to a more physically grounded description of the halo-mass correlation function, wherein the traditional one-halo term corresponds to orbiting particles, and the two-halo term corresponds to infalling particles. Utilizing this insight, the authors construct a model employing dark matter simulations, demonstrating that the distribution of orbiting particles can be characterized by a single physical scale termed the "halo radius."

This dynamics-based halo model is empirically validated using simulations, and the authors claim the model achieves approximately 2% accuracy over scales ranging from 0.1 to 50 Mpc/h for the halo-mass correlation function. The proposed model's primary components include:

• Orbiting Profile: Described by an exponentially truncated power-law function, characterized by the halo radius and a running power-law slope.
• Infall Profile: Represented through a modified large-scale bias function, incorporating a cored power-law that describes deviations from linear bias attributable to nonlinear growth.

The authors deploy the Zel'dovich approximation to model the larger-scale structure, further validated against extensive simulation data.

Numerical Results and Implications

The paper provides compelling numerical results, achieving percent-level precision in modeling the halo-mass correlation function. A significant implication of this work is its potential to enhance precision cosmology by reliably capturing the nuances of the halo transition regime. The work also underscores the practical feasibility of using the proposed halo definition in constructing halo catalogs devoid of exclusion biases.

Future Directions and Theoretical Speculations

The research opens avenues for further investigation into the dynamics of halo particle distributions and their influence over cosmological observations. Moreover, while the current work primarily focuses on applying the model within simulation contexts, the authors also suggest potential adaptability to observational data, assuming the development of appropriate observational tracers for the orbiting/infall dichotomy.

Future advancements might involve integrating this model with observational large-scale surveys or utilizing it to refine various cosmological parameters by constructing more accurate halo mass functions. This may also stimulate further theoretical discourse on the nature of dark matter and its interaction with visible matter across different cosmic scales.

In conclusion, this work presents an innovative recontextualization of halo models by integrating dynamics-based criteria, offering a fresh perspective on classical cosmological structures. The findings emphasize the importance of considering physical dynamics in halo definitions, potentially bridging theoretical and simulation-based approaches in cosmology.