Cosmic Structure as the Quantum Interference of a Coherent Dark Wave

Abstract

The conventional cold, particle interpretation of dark matter (CDM) still lacks laboratory support and struggles with the basic properties of common dwarf galaxies, which have surprisingly uniform central masses and shallow density profiles. In contrast, galaxies predicted by CDM extend to much lower masses, with steeper, singular profiles. This tension motivates cold, wavelike dark matter ($ψ$DM) composed of a non-relativistic Bose-Einstein condensate, so the uncertainty principle counters gravity below a Jeans scale. Here we achieve the first cosmological simulations of this quantum state at unprecedentedly high resolution capable of resolving dwarf galaxies, with only one free parameter, $\bf{m_B}$, the boson mass. We demonstrate the large scale structure of this $ψ$DM simulation is indistinguishable from CDM, as desired, but differs radically inside galaxies. Connected filaments and collapsed haloes form a large interference network, with gravitationally self-bound solitonic cores inside every galaxy surrounded by extended haloes of fluctuating density granules. These results allow us to determine $\bf{m_B=(8.1^{+1.6}_{-1.7})\times 10^{-23}~eV}$ using stellar phase-space distributions in dwarf spheroidal galaxies. Denser, more massive solitons are predicted for Milky Way sized galaxies, providing a substantial seed to help explain early spheroid formation. Suppression of small structures means the onset of galaxy formation for $ψ$DM is substantially delayed relative to CDM, appearing at $\bf{z\lesssim 13}$ in our simulations.

Figures (8)

• Figure 1: Comparison of cosmological large-scale structures formed by standard CDM and by wavelike dark matter, ${\psi}$DM. Panel (a) shows the structure created by evolving a single coherent wave function for ${\Lambda\psi}$DM calculated on AMR grids. Panel (b) is the structure simulated with a standard $\Lambda$CDM N-body code GADGET-2GADGET2 for the same cosmological parameters, with the high-k modes of the linear power spectrum intentionally suppressed in a way similar to the ${\psi}$DM model to highlight the comparison of large-scale features. This comparison clearly demonstrates that the large scale distribution of filaments and voids is indistinguishable between these two completely different calculations, as desired given the success of $\Lambda$CDM in describing the observed large scale structure. ${\psi}$DM arises from the low momentum state of the condensate so that it is equivalent to collisionless CDM well above the Jeans scale.
• Figure 2: A slice of density field of ${\psi}$DM simulation on various scales at $\bm{z=0.1}$. This scaled sequence (each of thickness 60 pc) shows how quantum interference patterns can be clearly seen everywhere from the large-scale filaments, tangential fringes near the virial boundaries, to the granular structure inside the haloes. Distinct solitonic cores with radius $\sim 0.3-1.6~\rm kpc$ are found within each collapsed halo. The density shown here spans over nine orders of magnitude, from $10^{-1}$ to $10^8$ (normalized to the cosmic mean density). The color map scales logarithmically, with cyan corresponding to density $\lesssim 10$.
• Figure 3: Radial density profiles of haloes formed in the ${\psi}$DM model. Dashed lines with various symbols show six examples of the halo profiles normalized to the cosmic mean density. All haloes are found to possess a distinct inner core fitted extremely well by the soliton solution (solid lines). A detailed soliton fit for the largest halo is inset, where the error is the root-mean-square scatter of density in each radial bin. An NFW profile representing standard CDM is also shown for comparison (black dot-dashed line, with a very large scale radius of $10~\rm kpc$), which fits well the profiles outside the cores. The yellow hatched area indicates the $\rho_{300}$ of the dSph satellites around Milky WayStrigari2008AE2011, which is consistent with the majority of galaxy haloes formed in the ${\psi}$DM simulations.
• Figure 4: Modeling the Fornax dSph galaxy with the soliton profile. Panel (a) shows the normalized stellar number density of the intermediate metallicity subpopulationAE2012a (symbols with 1-$\sigma$ error bars) and the best-fit soliton solution (red solid line) with $m_B=8.1\times 10^{-23}~\rm eV$, $r_c=0.92~\rm kpc$, and $\sigma_{||}=11.3~{\rm km/s}$. Also shown are the best-fit empirical formula of BurkertBurkert1995 (green dashed line) and the NFW profile (blue dot-dashed line) representing standard CDM. The scale radius of NFW is restricted to be no larger than $3.0~\rm kpc$ during the fit to exclude unreasonably small concentration parameters. Panel (b) shows the 1-$\sigma$ contours of the total enclosed mass estimated from each of the three subpopulationsAAE2013, overplotted with the model curves using the same best-fit parameters adopted in panel (a). Clearly, in both panels the soliton profile of ${\psi}$DM provides an accurate fit, matched only by the empirical fitting function of the Burkert profile, while NFW is not favoured by the data.
• Figure S1: Square wave function $\bm{\psi^2~(\equiv f^2e^{i2S})}$ in the ${\psi}$DM simulation. Panels (a) and (b) show a $2~\rm Mpc$ slice of phase ($sin(2S)$) and amplitude ($f^2$) of the wave function at $z=3.1$, respectively. The simulation challenge arises from the complexity of the wave function. Strong and rapid phase oscillations are common everywhere (even in the low-density background shown by the dark regions in the density plot), where sufficient spatial and temporal resolution is required to resolve each wavelength.