The Core-Cusp Problem (0910.3538v1)

Abstract: This paper gives an overview of the attempts to determine the distribution of dark matter in low surface brightness disk and gas-rich dwarf galaxies, both through observations and computer simulations. Observations seem to indicate an approximately constant dark matter density in the inner parts of galaxies, while cosmological computer simulations indicate a steep power-law-like behaviour. This difference has become known as the "core/cusp problem", and remains one of the unsolved problems in small-scale cosmology.

• The paper highlights that observed constant-density cores in galaxies conflict with the steep cuspy profiles predicted by cold dark matter simulations.
• It employs high-resolution HI and Hα rotation curve analyses to compare observational data with theoretical models such as the NFW profile.
• The findings imply that baryonic processes or new dark matter physics may be necessary to reconcile the differences and refine galaxy evolution models.

The Core-Cusp Problem in Dark Matter Cosmology

The core-cusp problem represents one of the most persistent discrepancies in modern astrophysics, specifically concerning the distribution of dark matter in the inner regions of galaxies. The problem arises from the divergence between observational data and theoretical predictions driven by cosmological simulations of cold dark matter (CDM). While observations of low surface brightness (LSB) galaxies and gas-rich dwarf galaxies often reveal a consistent dark matter density, suggesting a "core" profile, CDM simulations predict a steep, power-law like "cusp" configuration at galaxy centers. This paper explores the intricacies of this problem, reviewing both observational studies and simulation results, along with proposed reconciliations.

Observational and Simulation Discrepancies

The divergence between observational and theoretical models first emerged through studies of the HI rotation curves of galaxies, which inferred discrepancies in dark matter intensity in the inner regions of galaxies. Observations tend to indicate a linear rise in rotation velocity, consistent with a mass density that is constant at the core. Conversely, CDM-based simulations, beginning with work from Dubinski (1991) and later by Navarro et al., suggested cuspy profiles with a steep density gradient described often by the Navarro-Frenk-White (NFW) model, and later by more complex profiles like those proposed by Moore et al.

Despite significant advances in the accuracy and resolution of numerical simulations over the years, no theoretical framework within the $\Lambda$CDM paradigm has yet replicated the apparently core-like behavior observed in galaxy rotation curves. This discrepancy is frequently termed the "small-scale crisis in cosmology."

Investigations into Dark Matter Density Profiles

Observational datasets comprising radio and optical evidence suggest that the distribution of dark matter is characterized by an approximately constant density core, in stark contrast to simulation-derived cusp models, which forecast a steep inner slope (typically $\alpha \sim -1.0$ to $\alpha \sim -1.5$). High-resolution HI and H$\alpha$ velocity fields have significantly bolstered the observational evidence for cores, reducing the likelihood of observational artifacts such as beam smearing or non-circular motions skewing results.

Several studies have attempted to reconcile theory with observation by suggesting that baryonic processes such as feedback from star formation or dynamical friction might alter halo structures post-formation. These processes might transform an initially cuspy profile to one resembling a core, though consensus remains elusive, and such models often struggle to account for the quiescent evolutionary history typical of LSB galaxies.

Theoretical and Practical Implications

From a theoretical standpoint, resolving the core-cusp problem is crucial for understanding the nature and behavior of dark matter, as well as the processes governing galaxy formation and evolution. If dark matter halos inherently lack cusps, it would indicate new physics potentially beyond the CDM paradigm. Alternatively, if interactions between baryons and dark matter evacuate cusps, it offers insights into feedback mechanisms and dark matter-baryon coupling.

Practically, understanding the accurate distribution of dark matter affects our capacity to predict galaxy dynamics, influence star formation, and track galaxy evolution over cosmic timescales. Model variations such as triaxiality, dynamical friction, or non-standard dark matter models (e.g., warm dark matter) may hold the key to resolving these differences.

Future Directions

Accurate modeling of the interaction between baryonic processes and dark matter distribution remains a frontier for future research. High-resolution simulations that increasingly incorporate full baryonic physics could offer new insights. Furthermore, observing galaxies with new-generation telescopes equipped with superior resolution and capabilities could refine our understanding of these dark matter distribution profiles.

In conclusion, the core-cusp problem remains an active area of research due to its implications for core cosmological models and galaxy dynamics. Future explorations taking full advantage of computational advances and observational technologies may offer the clarity needed in this crucial aspect of dark matter studies.