AxioNyx: Simulating Mixed Fuzzy and Cold Dark Matter

Goal:

  • AMR simulations for Mixed Dark Matter
  • CDM -> N-body scheme
  • FDM -> Spectral/Finite-difference method
  • Baryonic physics -> Nyx modules for hydrodynamics and feedback

Bodo Schwabe,  Mateja Gosenca, Christoph Behrens, Jens C. Niemeyer, and Richard Easther, Physical Review D, October 2020.

Spherical Collapse

v_c=\frac{2\pi}{7.5}\frac{\hbar}{mr_c}

Schroedinger-Vlasov correspondence:

  • Maxwellian FDM Powerspectrum of central region coincides well with particle velocity dispersion.
  • Outer radial density profiles have constant FDM/CDM density ratio

For f>0.1 a soliton forms with velocity                   close to maximum in spectrum indicated by dashed line

Spherical Collapse

Soliton amplitude grows linearly in time. Rate determined by FDM/CDM ratio

Peaks of velocity spectra:

  • Exceed virial velocity (horizontal line) for large FDM ratios.
  • Close to core velocities (solid line)
  • Core masses in isolated halos exceed core-halo mass relation

New Hybrid Method

Goal:

  • AMR simulation
  • Particle method on low resolution levels
  • Finite-difference method on finest level
  • Important: Boundary conditions between methods

Madelung transformation:

Initial phase:

Phase evolution:

Construction of wavefunction:

Gauss kernel:

\Psi = A\exp[-iSm/\hbar]
\nabla\cdot v_{0} = a^{-1}\nabla^{2} S_{0}
\frac{\text d S_{i}}{\text d t} = \frac{1}{2} {v_i}^2 - V({x_i})
\qquad \Psi({x}) = \sum_i W({x} - {x_i}) A_i e^{i(S_i + {v_i}\cdot a({x}-{x_i}))m/\hbar}

Goal:

  • AMR simulation
  • Particle method on low resolution levels
  • Finite-difference method on finest level
  • Important: Boundary conditions between methods
W(x-x_i) = \frac{\gamma^{3/2}\Delta^{3}x}{\pi^{3/2}}\exp\text{[}-\gamma(x-x_i)^{2}\text{]}\theta(x-x_i)

Agora Simulation

DM-only comparison run (60 Mpc/h) between various codes:

zoom-in simulation focusing on isolated halo

Axionyx N-body run with CDM initial conditions

Axionyx N-body run with FDM initial conditions

Gauss Beam Reconstruction

  • Restart FDM N-body simulation at z=3:
  • Reconstruct wavefunction at amr level 11 in the inner most halo region (virial radius at 50kpc)
  • Add 3 finite difference levels

The granular structure and central soliton is clearly visible

Agora Simulation

  • FDM Powerspectrum and underlying particle velocity dispersion correspond well to each other.
  • Halo velocities have not yet relaxed into Maxwell spectrum (but do so later on)
  • Soliton velocity (grey line) at peak in spectrum
  • FDM radial density profile with soliton core and NFW outer tail

New Hybrid Method

By bschwabe

New Hybrid Method

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