Constraining the mass of light bosonic dark matter using SDSS Lyman-$α$ forest

Abstract: If a significant fraction of the dark matter in the Universe is made of an ultra-light scalar field, named fuzzy dark matter (FDM) with a mass $m_a$ of the order of $10^{-22}-10^{-21}$ eV, then its de Broglie wavelength is large enough to impact the physics of large scale structure formation. In particular, the associated cut-off in the linear matter power spectrum modifies the structure of the intergalactic medium (IGM) at the scales probed by the Lyman-$\alpha$ forest of distant quasars. We study this effect by making use of dedicated cosmological simulations which take into account the hydrodynamics of the IGM. We explore heuristically the amplitude of quantum pressure for the FDM masses considered here and conclude that quantum effects should not modify significantly the non-linear evolution of matter density at the scales relevant to the measured Lyman-$\alpha$ flux power, and for $m_a \geq 10^{-22}$ eV. We derive a scaling law between $m_a$ and the mass of the well-studied thermal warm dark matter (WDM) model that is best adapted to the Lyman-$\alpha$ forest data, and differs significantly from the one infered by a simple linear extrapolation. By comparing FDM simulations with the Lyman-$\alpha$ flux power spectra determined from the BOSS survey, and marginalizing over relevant nuisance parameters, we exclude FDM masses in the range $10^{-22} \leq m_a < 2.3\times 10^{-21}$ eV at 95 % CL. Adding higher-resolution Lyman-$\alpha$ spectra extends the exclusion range up to $2.9\times 10^{-21}$ eV. This provides a significant constraint on FDM models tailored to solve the "small-scale problems" of $\Lambda$CDM.

• The paper constrains ultra-light bosonic dark matter by comparing detailed FDM simulations with SDSS Lyman-α forest observations.
• Dedicated hydrodynamical simulations reveal that quantum pressure effects are negligible for FDM masses mₐ ≥ 10⁻²² eV at non-linear scales.
• The study derives a scaling law between FDM and WDM models, establishing exclusion limits that refine viable dark matter models addressing small-scale structure issues.

Constraining Light Bosonic Dark Matter Using SDSS Lyman-α Forest Data

The paper by Armengaud et al. presents a detailed examination of ultra-light bosonic dark matter—also termed fuzzy dark matter (FDM)—using data from the SDSS Lyman-α forest of distant quasars. The authors aim to constrain the mass of FDM particles, which are characterized by masses in the range of $10^{-22}-10^{-21}$ eV. Such light scalar fields have a sufficiently large de Broglie wavelength, influencing the large scale structure formation by introducing a cutoff in the linear matter power spectrum.

Methodology

The authors employ dedicated cosmological simulations that incorporate the hydrodynamics of the intergalactic medium (IGM) to analyze the impact of FDM on the Lyman-α forest. By comparing FDM simulations with observed power spectra from the Baryon Oscillation Spectroscopic Survey (BOSS), they critically analyze the effect of varying mass ranges of FDM and their implications on structure formation.

To discern the contribution of quantum pressure—a characteristic of FDM due to its wave nature—the authors demonstrate through simulations that these quantum effects do not modify the non-linear evolution of matter density at scales relevant to the Lyman-α forest, particularly for masses $m_a \geq 10^{-22}$ eV.

Numerical Results and Constraints

A significant element of the study is the derivation of a scaling law that associates FDM masses with the thermal warm dark matter (WDM) model, adapting this scale appropriately for the Lyman-α forest data—a departure from simplistic linear extrapolation methods. The authors meticulously quantify these differences, finding that the linear power spectrum of FDM exhibits a more abrupt cutoff than WDM.

The comparison of simulations to observational data from the SDSS Lyman-α forest yields substantial constraints on FDM masses. Specifically, the study excludes FDM masses in the range $10^{-22} \leq m_a < 2.3 \times 10^{-21}$ eV at a 95% confidence level. With the integration of higher-resolution Lyman-α spectra, this exclusion range is extended, allowing the upper bound to increase up to $2.9 \times 10^{-21}$ eV. Consequently, these constraints limit the range of viable FDM models purportedly designed to address the small-scale issues associated with the conventional ΛCDM model.

Theoretical and Practical Implications

This research provides critical insights into the feasibility of Ultra-Light Bosons as dark matter candidates, potentially assisting in resolving observed discrepancies in small-scale cosmic structures when juxtaposed with ΛCDM predictions. It highlights the importance and utility of high-resolution astrophysical observations, like the Lyman-α forest, as powerful tools for probing the fundamental nature of dark matter.

Future Directions

The findings invite further theoretical development and observational validation of fuzzy dark matter models. A key avenue of exploration is improving the precision of quantum pressure effects in simulations, especially for FDM masses smaller than $10^{-22}$ eV, where such effects become significant. Additionally, future studies may leverage more comprehensive astrophysical data to refine these constraints, potentially extending the mass range further or ruling out light scalar fields altogether as fruitful dark matter candidates. Continued refinement in cosmological simulations and synergy with observational data will be critical in advancing our understanding of dark matter composition, influencing both theoretical and experimental physics domains.