Axion dark matter, solitons, and the cusp-core problem (1502.03456v3)

Abstract: Self-gravitating bosonic fields can support stable and localised field configurations. For real fields, these solutions oscillate in time and are known as oscillatons. The density profile is static, and is soliton. Such solitons should be ubiquitous in models of axion dark matter, with the soliton characteristic mass and size depending on some inverse power of the axion mass. Stable configurations of non-relativistic axions are studied numerically using the Schr\"{o}dinger-Poisson system. This method, and the resulting soliton density profiles, are reviewed. Using a scaling symmetry and the uncertainty principle, the core size of the soliton can be related to the central density and axion mass, $m_a$, in a universal way. Solitons have a constant central density due to pressure-support, unlike the cuspy profile of cold dark matter (CDM). One consequence of this fact is that solitons composed of ultra-light axions (ULAs) may resolve the `cusp-core' problem of CDM. In DM halos, thermodynamics will lead to a CDM-like Navarro-Frenk-White profile at large radii, with a central soliton core at small radii. Using Monte-Carlo techniques to explore the possible density profiles of this form, a fit to stellar-kinematical data of dwarf spheroidal galaxies is performed. In order for ULAs to resolve the cusp-core problem (without recourse to baryon feedback or other astrophysical effects) the axion mass must satisfy $m_a<1.1\times 10^{-22}\text{ eV}$ at 95\% C.L. On the other hand, ULAs with $m_a\lesssim 1\times 10^{-22}\text{ eV}$ are in some tension with cosmological structure formation. An axion solution to the cusp-core problem thus makes novel predictions for future measurements of the epoch of reionisation. On the other hand, this can be seen as evidence that structure formation could soon impose a \emph{Catch 22} on axion/scalar field DM, similar to the case of warm DM.

• The paper demonstrates that ultra-light axions can form solitonic cores which address the cusp-core discrepancy in dwarf galaxies.
• It employs a combination of scaling symmetries and Monte Carlo analyses to derive an upper axion mass bound of 1.1×10⁻²² eV from stellar kinematics.
• The findings challenge conventional CDM models and propose a viable alternative framework for small-scale structure formation in cosmology.

Axion Dark Matter, Solitons, and the Cusp-Core Problem: A Technical Analysis

The paper under review investigates the intriguing potential of axions, particularly ultra-light axions (ULAs), as a dark matter (DM) candidate capable of addressing the cusp-core problem in dwarf spheroidal galaxies. The paper conducted by Marsh and Pop offers a mathematical and numerical approach to understanding how solitonic solutions form within the postulated axion dark matter framework and how these phenomena could be reconciled with observations.

Key Findings

The authors begin by framing the role of self-gravitating bosonic fields in achieving stable, solitonic configurations, particularly in models involving axion DM. They emphasize the scale-dependent nature of solitons, which are stabilized by axion quantum pressure. Notably, the paper introduces the relationship between soliton cores and central density through parameters like the axion mass $m_a$, employing a scaling symmetry to develop a universal relation applicable to ultra-light axions. This provides a stark contrast to the cold dark matter (CDM) prediction of cuspy density profiles.

The authors use a baseline derived from a Monte Carlo analysis of density profiles and successfully demonstrate that ULA models may inherently resolve the cusp-core problem observed in dark matter halos. Their findings are substantially rooted in a core size, density, and mass relationship inherent to solitons, which differs from CDM paradigms that lead to cuspy halo profiles. It is shown through numerical analysis and scaling arguments that the theoretical soliton model predicts core sizes akin to those deduced from actual astrophysical observations of dwarf spherical galaxies.

A crucial highlight of the paper is the derived constraint on the axion mass: $m_a < 1.1 \times 10^{-22}$ eV at a 95% confidence level. This upper bound is inferred directly from fitting the core density profiles using stellar-kinematic data, particularly from galaxies like Fornax and Sculptor, thereby merging theoretical prediction with astrophysical evidence. However, the mass range suggests tension with cosmological structure formation scenarios, necessitating further investigation into this apparent discord.

Implications and Speculative Advances

Practical Implications: The accurate alignment of a soliton-based approach with observed core structures of dwarf galaxies points towards ULAs as a conceivable dark matter candidate. This challenges standard CDM approaches, suggesting new mechanisms in small-scale structure formation, with implications for both fundamental physics and cosmology.

Theoretical Advances: The paper postulates that should axions contribute significantly to DM, major cosmological shifts would be observed. These include alterations in the reionization history due to their distinct cosmic structure formation patterns, implications that can be tested with forthcoming observational data. Such findings emphasize the essential nature of accurately modeling non-linear gravitational interactions in scalar field theories.

Future Developments: Considering a broader range of axion masses and exploring mixed DM models may help refine the existing constraints and mitigate the Catch 22 scenario posed by current structure formation limits. Also, advancements in observational technologies, such as JWST and Euclid, will be pivotal in constraining axion mass and, consequently, their role in DM cosmology.

In conclusion, Marsh and Pop's paper deepens the understanding of how scalar field dynamics can provide an alternative framework for explaining dark matter behavior on galactic scales. While the practical reconciliation of ULA models with all astrophysical observations remains an open challenge, the theoretical work presents crucial avenues for further exploration in the context of DM particle physics and cosmology.