The Impact of Fuzzy Dark Matter Dynamics on the Accumulation and Fragmentation of Primordial Gas

Abstract

Fuzzy Dark Matter (FDM), composed of ultra-light axions ($m_a \sim 1 \times 10^{-22}$ eV), exhibits wave-like properties that can significantly impact early-universe star formation. Using the arepo code with the axirepo module, we simulate the assembly of haloes across a range of axion masses ($1 \times 10^{-22}$ eV $\le m_a \le 7 \times 10^{-22} $ eV) and halo masses ($3 \times 10^{8} M_\odot \le M_h \le 8 \times 10^{9} M_\odot$). We investigate how small-scale dynamics of the FDM density field affect the accumulation of cold, dense gas. We find that the delay in star formation scales inversely with both halo mass and axion mass. While the static, cored geometry of the soliton primarily sets the timing of the initial collapse, we identify a secondary dynamical barrier driven by stochastic fluctuations that is most potent at the low-mass end of our parameter space. These dynamics dictate the spatial scale of dense gas by injecting kinetic energy and inducing significant angular momentum, which can rotationally stabilize gas out to the soliton radius. This wave-driven stirring leads to the formation of extended $\text{H}_2$ plumes and promotes dynamical mixing, effectively starving the central regions and forcing gas to cool in a more fragmented, diffuse manner. Our results indicate a shift from the monolithic central star formation seen in CDM toward lower-mass, fragmented clusters. These internal inefficiencies provide a physical mechanism for delaying Cosmic Dawn beyond the effects of the power spectrum cut-off, which is essential for refining observational constraints on the axion mass.

Figures (12)

• Figure 1: Dynamics of the solitonic core at the centre of a simulated FDM halo with a halo mass $M_{\mathrm{h}} = 3e9\Msun$ for axion mass $m_{\mathrm{a}} = e-22\eV$. The panels marked a) show the projected (log) density of the dark matter $\rho_{\mathrm{dm}}$ of a zoomed-in region at the centre of an FDM halo for a series of snapshots separated by $\sim 100\Myr$. The green line shows a track of the central density from its initial position at 0 Myr within the halo sampled with time resolution $\Delta t \approx 1\Myr$ at four snapshots throughout the simulation, spaced approximately 100 apart. The panel marked b) shows the order unity fluctuations of the central density along this track over time, with a characteristic period of $f \sim 0.02\per\Myr \Rightarrow \tau_\mathrm{osc} \sim 50\Myr$, which can be identified by the peak in the power spectral density of this oscillation in the bottom panel marked c). This lines up with the theoretical value for the period of oscillation $\tau_{\mathrm{osc}} \approx 65\Myr$ at the centre of the halo, shown by the dashed line.
• Figure 2: Top: Projected (log) density snapshots of the halo assembly starting from the initial conditions (the leftmost panel), followed by three intermediate steps at 117; 235; 469. The final halo used for our simulations is shown in the rightmost panel. Bottom: The total energy of the system (green, $E_{\mathrm{tot}}$) and energy components: potential energy (orange $W$), classical kinetic energy (purple $K_v$) and quantum kinetic energy (pink $K_\rho$) throughout the assembly timeline of the halo. The vertical dashed lines correspond to the three instances shown in the intermediate top panels. The total energy is clearly conserved throughout the simulation box. We highlight the horizontal axis at zero to show clearly that the total energy of our haloes is less than zero, i. e. the haloes are bound.
• Figure 3: Top: The time-averaged gravitational potential profiles of FDM haloes for different axion masses ($m_{\mathrm{a}} = \SIlist{2e-22; 3e-22; 7e-22}{\eV}$) and the corresponding CDM halo, all with a mass of $M_{\mathrm{h}} = 8e8\Msun$. Individual snapshots are shown by the translucent lines. The vertical dotted lines indicate the core radius ($r_{\mathrm{c}}$) for each FDM halo. The potential flattens inside the core radius for FDM haloes, a signature of quantum pressure. Bottom: The root-mean-square (RMS) fluctuation of the potential ($\delta V/ V$) for the same haloes. This quantifies the fluctuations of the solitonic core at the centre of each FDM halo. The fluctuations are most pronounced and extend to larger radii for smaller $m_{\mathrm{a}}$, and they decrease significantly outside the solitonic core radius.
• Figure 4: Gas density projections in the central region of each halo for a selection of our simulations with a halo mass of 8e8: FDM with $m_{\mathrm{a}} = 2e-22\eV$ (left), the "frozen" FDM with the same $m_{\mathrm{a}} = 2e-22\eV$ (centre), and a CDM case (right). The first row shows the gas state at the formation of the first sink. As the simulation proceeds, in the FDM cases, the gas is distributed more widely across the central region of the halo as it is affected by the dynamics of the central soliton. In the CDM case, gas remains tightly bound in the central region. The gray dots show the location of the sink particles, with the radius scaled by the sink mass $m_\mathrm{sink}^{1/3}$. The red circle shows the half-mass radius of the sink particles. There is no half mass radius shown for the "dynamic" FDM case for $t_\ast + 49\Myr$ as there was still only one sink formed at this time.
• Figure 5: Radial density profiles for the 8e8 halo at a late-time snapshot with $t \approx 250\Myr$ from the start of the simulations. The dashed lines show the "frozen" FDM cases while the dotted lines show the core radius $r_{\mathrm{c}}$. Top: Dark matter density profiles normalized by the core radius $r_{\mathrm{c}}$. For completeness we show CDM normalized with $r_{\mathrm{c}} = 1\kpc$. The FDM cases exhibit a flattened solitonic core, while the CDM shows a characteristic cusp. Middle: Gas density profiles. Bottom: Radial distribution of sink particles. In the FDM simulations, particularly at lower axion masses, the sinks are spatially dispersed and displaced from the halo centre. The vertical dotted lines indicate the core radius $r_{\mathrm{c}}$ for each respective FDM model.