On the Random Motion of Nuclear Objects in a Fuzzy Dark Matter Halo
Dhruba Dutta Chowdhury, Frank C. van den Bosch, Victor H. Robles, Pieter van Dokkum, Hsi-Yu Schive, Tzihong Chiueh, Tom Broadhurst
Abstract
Abstract Fuzzy dark matter (FDM), consisting of ultralight bosons ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">b</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>22</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mspace width="0.25em"/> <mml:mi>eV</mml:mi> </mml:math> ), is an intriguing alternative to cold dark matter. Numerical simulations that solve the Schrödinger–Poisson (SP) equation show that FDM halos consist of a central solitonic core, which is the ground state of the SP equation, surrounded by an envelope of interfering excited states. These excited states also interfere with the soliton, causing it to oscillate and execute a confined random walk with respect to the halo center of mass. Using high-resolution numerical simulations of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>6.6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> FDM halo with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">b</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>8</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>23</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mspace width="0.25em"/> <mml:mi>eV</mml:mi> </mml:math> in isolation, we demonstrate that the wobbling, oscillating soliton gravitationally perturbs nuclear objects, such as supermassive black holes or dense star clusters, causing them to diffuse outwards. In particular, we show that, on average, objects with mass ≲0.3% of the soliton mass ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>sol</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) are expelled from the soliton in ∼3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mspace width="0.25em"/> <mml:mi>Gyr</mml:mi> </mml:math> , after which they continue their outward diffusion due to gravitational interactions with the soliton and the halo granules. More massive objects (≳ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mo>%</mml:mo> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>sol</mml:mi> </mml:mrow> </mml:msub> </mml:math> ), while executing a random walk, remain largely confined to the soliton due to dynamical friction. We also present an effective treatment of the diffusion, based on kinetic theory, that accurately reproduces the outward motion of low-mass objects and briefly discuss how the observed displacements of star clusters and active galactic nuclei from the centers of their host galaxies can be used to constrain FDM.