Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes

Abstract: We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schr\"odinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic $r^{-3}$ NFW-like profile. We find a fundamental relation of the core=to-halo mass with the dimensionless invariant $\Xi \equiv \lvert E \rvert/M^3/(Gm/\hbar)^2$ or $M_{\rm c}/M \simeq 2.6 \Xi^{1/3}$, linking the soliton to global halo properties. For $r \geq 3.5 \,r_{\rm c}$ core radii, we find equipartition between potential, classical kinetic, and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behavior driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a $k^{-1.1}$ power-law. This suggests the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a $k^{-5/3}$ Kolmogorov power-law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying the soliton-sized granules carry most of the turbulent energy in BECDM haloes.

• The paper uses Schrödinger-Poisson simulations to study BECDM halo formation and dynamics, revealing distinct core and turbulent structures.
• Simulations show BECDM halos form a stable soliton core with a flat density profile, establishing a core-to-halo mass relation based on a dimensionless invariant.
• The outer halo exhibits turbulent dynamics driven by vortex reconnections, with a velocity power spectrum following a distinctive k^-1.1 power law.

Overview of Galaxy Formation with Bose-Einstein Condensate Dark Matter

The paper "Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes" presents a comprehensive investigation into the behavior of galaxy-scale haloes under the Bose-Einstein Condensate Dark Matter (BECDM) model. This form of dark matter considers ultralight bosonic scalar fields as a viable alternative to the Cold Dark Matter (CDM) paradigm. Researchers aim to address the shortcomings of CDM on small scales, particularly regarding core-cusp issues in dwarf galaxies, by leveraging the galaxy-scale de Broglie wavelength characteristic of BECDM.

Key Findings

1. Simulation Approach: The paper uses numerical simulations based on the Schrödinger-Poisson equations to explore the formation of BECDM haloes through mergers. These simulations allow for a detailed examination of soliton core behavior and surrounding halo structures.
2. Soliton Core Structure: The simulations reveal that BECDM haloes form with a stable soliton core, whose structure is supported by the quantum pressure tensor. The soliton exhibits a flat density profile at the center, contrasting sharply with the cuspy center of NFW profiles predicted by CDM.
3. Core-Halo Mass Relation: A noteworthy result is the established core-to-halo mass relation defined by the dimensionless invariant $\Xi$. The paper finds that $M_{\rm c}/M \simeq 2.6 \Xi^{1/3}$, thereby linking soliton core metrics to overall halo properties robustly.
4. Turbulent Dynamics: The outer regions of BECDM halos display significant turbulent behavior driven by vortex line reconnections. The velocity power spectrum follows a $k^{-1.1}$ power law, akin to thermally-driven turbulence seen in non-gravitational Bose-Einstein condensates, rather than a typical Kolmogorov $k^{-5/3}$ spectrum.

Implications

This study underscores the potential for BECDM to resolve standard CDM challenges, offering a plausible explanation for the distribution of mass in galactic cores. By suggesting a fundamental relation between core mass and halo energy, the paper provides a predictive framework that could be pivotal in future cosmological simulations.

The insights into turbulence suggest that BECDM halos have distinct dynamical properties that could affect their interaction with baryonic matter. This influence could be significant in refining models of galaxy formation and evolution.

Future Directions

The ongoing research aims to integrate BECDM dynamics with baryonic physics in fully cosmological simulations. Such coupled simulations will be crucial for assessing the impact of BECDM on cosmic structure formation and providing tighter constraints on the properties of ultralight bosonic particles. Future work will focus on understanding the interaction between BECDM and baryons in various cosmic environments, potentially offering deeper insights into the fundamental nature of dark matter.

These developments hold promise for advancing our understanding of the universe and resolving existing theoretical tensions with observational data. Continued investigation into BECDM's effects at both small and large scales will be essential for substantiating its viability as a cornerstone of modern cosmological models.