Understanding the Core-Halo Relation of Quantum Wave Dark Matter, $ψ$DM, from 3D Simulations (1407.7762v2)

Abstract: We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter ($\psi$DM), described by the Schr\"{o}dinger-Poisson (SP) equation with a particle mass $\sim 10^{-22} {\rm eV}$. A distinct gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark matter scenarios. Furthermore, we show that each solitonic core is surrounded by an extended halo composed of large fluctuating dark matter granules which modulate the halo density on a scale comparable to the diameter of the solitonic core. The scaling symmetry of the SP equation and the uncertainty principle tightly relate the core mass to the halo specific energy, which, in the context of cosmological structure formation, leads to a simple scaling between core mass ($M_c$) and halo mass ($M_h$), $M_c \propto a^{-1/2} M_h^{1/3}$, where $a$ is the cosmic scale factor. We verify this scaling relation by (i) examining the internal structure of a statistical sample of virialized halos that form in our 3D cosmological simulations, and by (ii) merging multiple solitons to create individual virialized objects. Sufficient simulation resolution is achieved by adaptive mesh refinement and graphic processing units acceleration. From this scaling relation, present dwarf satellite galaxies are predicted to have kpc sized cores and a minimum mass of $\sim 10^8 {M_\odot}$, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of $2\times10^{12} {M_\odot}$ at $z=8$ should have massive solitonic cores of $\sim 2\times10^9 {M_\odot}$ within $\sim 60 {\rm pc}$. Such cores can provide a favorable local environment for funneling the gas that leads to the prompt formation of early stellar spheroids and quasars.

• The paper establishes a core-halo mass relation via high-resolution 3D simulations, demonstrating that M_c ∝ a^(-1/2) M_h^(1/3).
• The study utilizes adaptive mesh refinement and GPU acceleration to resolve halos down to ~10^8 M_☉, reinforcing the ψDM framework.
• The findings imply that dense solitonic cores in high-redshift galaxies can trigger rapid starbursts and early supermassive black hole growth.

Analyzing the Core-Halo Dynamics of Quantum Wave Dark Matter via 3D Simulations

The paper titled "Understanding the Core-Halo Relation of Quantum Wave Dark Matter, {\psiDM}, from 3D Simulations" by Schive et al. delivers an in-depth examination of the structural formations in wave-like cold dark matter, known specifically as {\psiDM}. The authors leverage the Schrödinger-Poisson equation to describe the dynamics involving ultra-light bosons with mass $m_{\psi} \sim 10^{-22}$ eV, offering a distinct perspective that potentially resolves longstanding issues in the standard cold dark matter (CDM) models.

The central feature of their approach is the 3D simulation of cosmological structure formations, resulting in the identification of a solitonic core at the center of gravitationally collapsed halos. Unlike the warm or self-interacting dark matter models, the soliton exhibits a unique density profile, intrinsically related to the scaling symmetry and the uncertainty principle inherent in the Schrödinger-Poisson equation. This work empirically establishes a core mass to halo mass relation: $M_c \propto a^{-1/2} M_h^{1/3}$, validated across various redshifts.

Through adaptive mesh refinement and GPU acceleration, these simulations achieve remarkable resolution, capable of resolving halos down to the dwarf galactic scale, with minimum mass estimates around $\sim 10^8 M_\odot$. Notably, applying their derived scaling law posits halo structures where dwarf galaxies manifest as kpc-sized cores, offering compelling resolutions to the "missing satellite" and "cusp-core" challenges faced by the CDM model. These findings suggest that structures at high redshifts, such as galaxies akin to $2 \times 10^{12} M_\odot$ at $z=8$, would contain massive cores $\sim 2 \times 10^9 M_\odot$ within a radius of $\sim 60$ pc.

The numerical viability of the {\psiDM} model is further supported with soliton collision experiments, which demonstrate the core-halo mass relationship as a non-trivial application of the uncertainty principle on a cosmological scale. The outcomes of these experiments reinforce the theoretical frameworks proposed by the authors, indicating that gravitational equilibrium outcomes are linearly dependent on core size inversely with halo-specific energy, as given by $M'_c = \alpha (|E'|/M')^{1/2}$.

This framework offers a substantial predictive power concerning the smallest halo mass, approximating $\sim 3 \times 10^8 M_\odot$ at $z=8$ for the boson mass $m_{\psi}=(8.0^{+1.8}_{-2.0}) \times 10^{-23}~\eV$. These results imply potential empirical testing in future large-scale sky surveys and high-redshift galaxy observations (e.g., JWST).

The implications extend into astrophysics, with anticipations of dense solitonic cores favorable to ultra-compact regions supportive of massive starbursts and rapid development of supermassive black holes. Such phenomena provide valuable insight into early universe conditions, particularly where quasars represent significant cosmic evolution markers.

In conclusion, the paper provides a rigorous examination of the quantum nature underlying dark matter structure formation, advocating {\psiDM} as a viable substitute to conventional paradigms, with attention to high-resolution cosmological simulation and adaptable theoretical construction. While speculative, it proposes a fascinating and plausible dynamical narrative for cosmic structure evolution, meriting further investigative inquiry and model refinement in future research trajectories.