Fuzzy Dark Matter on Galactic Scales
Bodo Schwabe
(University of Zaragoza)
credit: J.Veltmaat
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6553970/schive1.jpg)
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}
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6553976/schive2.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6554065/schive3.jpg)
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}
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6554522/mass_constraints.png)
in three different scenarios
- Pure FDM
- FDM + Baryons
- FDM + CDM
Quantifying FDM Halo Dynamics
- Radial density profiles
- CDM velocity dispersion vs. FDM granular structure
- Solitonic core dynamics
using
- AMR grid structures
- Hybrid particle+grid Methods
- Finite differencing
- Spectral codes
- N-body algorithms
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
Goal:
- AMR simulation
- Particle method on low resolution levels
- Finite-difference method on finest level
- Important: Boundary conditions between methods
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6554498/veltmaat3.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6554434/veltmaat1.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6554929/hybrid3.png)
J. Veltmaat, J. C. Niemeyer, and BS, Physical Review D, August 2018.
Structure of FDM Halos
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6585883/veltmaat4.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6586350/volumerendering-1.jpg)
FDM Dwarf Galaxy with Baryons
J. Veltmaat, BS, and J. C. Niemeyer, Physical Review D, April 2020.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6586303/densityprofilescomb-1.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6586304/velocities-1.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/6586302/coreoscillationswb-1.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/imports/1047496/AWQEc_h8/AWQEc_h8_001.jpg)
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
BS, Mateja Gosenca, Christoph Behrens, Jens C. Niemeyer, and Richard Easther, Physical Review D, October 2020.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/7529620/vel_prof2.png)
Spherical Collapse
v_c=\frac{2\pi}{7.5}\frac{\hbar}{mr_c}
f(\textbf{v}) = \frac{1}{N}\left|\int\text{d}^3 x\exp\left[-im\textbf{v}\cdot\textbf{x}/\hbar\right]\psi(\text{x})\right|^2
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/7529616/maxdens.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/7529615/maxamp2.png)
Spherical Collapse
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1047496/images/7529619/velocities2.png)
A(t) = A_{1}\cdot (t-t_{0})/\tau_{\text{gr}}+A_{0}f^{1/2}
\tau_{\text{gr}} = \frac{0.7\sqrt{2}}{12\pi^3}\frac{m^3v_c^6}{G^2\rho_{c}^2\Lambda}\simeq 0.015 \frac{t_c}{\Lambda}
Conclusions
-
Distinguishing features of FDM: Strong stochastic density fluctuations in halos on deBroglie length and time scales and formation of stable, oscillating soliton cores in center of halos
- Local FDM density important for experiments but not well constraint yet
- Heavier FDM mass can be best constrained on non-linear, galactic scales (soliton osc., soliton mergers, gravitational heating/cooling, tidal disruption,...)
-- Need further dedicated FDM simulations on galactic scales --
m<10^{-21}\,\text{eV}
- FDM structure formation similar to CDM on super deBroglie scales (except cut-off in initial power spectrum as for WDM)
- Weakly non-linear probes like Lyman-alpha exclude
Fuzzy Dark Matter on Galactic Scales (Saturnalia))
By bschwabe
Fuzzy Dark Matter on Galactic Scales (Saturnalia))
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