Benedikt Eggemeier & Bodo Schwabe

(University of Göttingen)

Simulations of Axion Stars and Miniclusters

Axion Miniclusters

  • Formation and mass growth
  • Equilibration in halo and the core-halo mass relation
  • Merger history

Axion Stars

  • Minicluster-Halo Mass Function
  • Minicluster morphology
  • CDM velocity dispersion vs. granular structure in miniclusters

Axion Minicluster Halos

A. Vaquero, J. Redondo, and J. Stadler, JCAP, April 2019

Initial conditions

evolved with Gadget3-code

BE, J. Redondo, K. Dolag, J.C. Niemeyer, A. Vaquero, arXiv: 1911.09417 

Minicluster Halo Mass Function

BE, J. Redondo, K. Dolag, J.C. Niemeyer, and A. Vaquero, arXiv: 1911.09417 

before

after

matter-radiation equality

MCH Numbers and Morphology

 

  • bound fraction at            ?
  • convergence of density profiles to NFW with decreasing redshift?
  • differences in morphology between MCHs and "canonical" MCs?

BE, J. Redondo, K. Dolag, J.C. Niemeyer, and A. Vaquero, arXiv: 1911.09417 

Future Work

r_\mathrm{vir} \in [12.7, 92.0]\,\mathrm{AU}
z=0
i\hbar\frac{\partial\psi}{\partial t} = -\frac{\hbar^{2}}{2ma^{2}}\nabla^{2}\psi+mV\psi
\nabla^{2}V = \frac{4\pi G}{a}\delta\rho
\delta\rho=|\psi|^{2}

FDM Structure Formation

H.-Y. Schive, T. Chiueh, and T. Broadhurst, Nature Physics, 2014

\lambda_{\rm dB}\sim \hbar/mv_{\rm vir}\sim(\hbar/m)(G\rho)^{-1/2}r^{-1}
\tau_{\rm dB}\sim \hbar/mv^{2}_{\rm vir}

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:

\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})
A({x}) = \sqrt{\sum_i W({x} - {x_i})}
\qquad S({x}) = \frac{\hbar}{m}\arg\left[\sum_i \sqrt{W({x} - {x_i})} e^{i(S_i + {v_i}\cdot a({x}-{x_i}))m/\hbar}\right]

Note: Classical density -> no gradient energy and interference effects

J. Veltmaat, J. C. Niemeyer, and BS, Physical Review D, August 2018.

Structure of FDM halos

f_{W}(v)=\frac{1}{N}\left|\int\exp\left[-imv\cdot x/\hbar\right]\Psi(x)\text{d}^{3}x\right|^{2}
f(v)\text{d}v = \frac{4}{\pi} \left(\frac{3}{2}\right)^{3/2} \frac{v^2}{v_\mathrm{rms}^3} \exp\left(-\frac{3}{2} \frac{v^2}{v_\mathrm{rms}^2}\right)\text{d}v

Velocity distribution:

Maxwellian distribution:

FDM dwarf galaxy with baryons

J. Veltmaat, J. C. Niemeyer, and BS, arXiv:1911.09614, November 2019.

Axion Stars in Axion Miniclusters

Initial conditions

  1. take subvolumes of initial conditions
  2. evolve axion density field with SP equations

BE, and J.C. Niemeyer, Phys. Rev. D, September 2019

overall structure similar to DM halos and their central cores in FDM simulations

A. Vaquero, J. Redondo, and J. Stadler, JCAP, April 2019

BE, and J.C. Niemeyer, Phys. Rev. D, September 2019

D.G. Levkov, A.G. Panin, I.I. Tkachev, Phys. Rev. Lett., October 2018

\tau\simeq \frac{1}{20}\frac{R}{v}(R/\lambda_{\rm dB})^{3}/\log(R/\lambda_{\rm dB})
M_{*}(t)\simeq M_{*,0}\left(\frac{t}{\tau}\right)^{1/2}
M_{*,{\rm sat}}\sim M_{h}^{1/3}

Mass Growth of Axion Stars in Axion Miniclusters

\rightarrow M_{*}(t)\simeq M_{*,{\rm sat}}\left(\frac{t}{\tau_{\rm sat}}\right)^{1/8}
M_{\ast,3} = \beta (M_{\ast,1} + M_{\ast,2})

Axion Star Mergers

\beta = 0.66

with

BE, and J.C. Niemeyer, Phys. Rev. D, September 2019

BS, J. C. Niemeyer, and J. F. Engels, Physical Review D, August 2016.

Binary Merger of Axion Stars

Recipe for Axion Star Evolution

  • Bound axion star mergers result in new axion star
  • Axion stars merge rapidly once they overlap
    • Merger history is a series of binary mergers
  • Only major mergers with mass ratio                                                        yield increased core mass
  • Minor mergers and smooth accretion leave heavier axion star unchanged
  • Numerically find
  • Recover the scaling relation                     found in cosmological simulations
\mu=M_{c1}/M_{c2}<\beta/(1-\beta)
M_{c}=\beta(M_{c1}+M_{c2})
\beta\simeq 0.7
M_{c}\sim M_{h}^{1/3}

BS, J. C. Niemeyer, and J. F. Engels, Physical Review D, August 2016.

X. Du, C. Behrens, J. C. Niemeyer, and BS, Physical Review D, February 2017.

Summary and Conclusions

  • Quantified abundance and morphology of axion miniclusters
  • Investigated evolution of axion stars in minicluster halos

Local dark matter density is not yet well constrained but important for haloscope experiments

-- Need further dedicated axion structure formation simulations --

Backup: Power Spectrum

Backup: Minicluster Data

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