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Register a new userRelaxation in a Fuzzy Dark Matter Halo. II. Self-consistent kinetic equations
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Added by
Jean-Baptiste Fouvry
Publication date
2020
fields
Physics
and research's language is
English
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Fuzzy dark matter (FDM) is composed of ultra-light bosons having a de Broglie wavelength that is comparable to the size of the stellar component of galaxies at typical galactic velocities. FDM behaves like cold dark matter on large scales. However, on the scale of the de Broglie wavelength, an FDM halo exhibits density fluctuations that lead to relaxation, a process similar to the two-body relaxation that occurs in classical gravitational N-body systems and is described by the Fokker-Planck equation. We derive the FDM analog of that kinetic equation, and solve it to find the evolution of the velocity distribution in a spatially homogeneous FDM halo. We also determine the dielectric function and the dispersion relation for linear waves in an FDM halo.
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Fuzzy Dark Matter (FDM), consisting of ultralight bosons ($m_{rm b} sim 10^{-22} rm eV$), is an intriguing alternative to Cold Dark Matter. Numerical simulations that solve the Schrodinger-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 $6.6 times 10^9 M_{odot}$ FDM halo with $m_{rm b} = 8 times 10^{-23} rm eV$ 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 $lesssim 0.3 %$ of the soliton mass ($M_{rm sol}$) are expelled from the soliton in $sim 3 rm Gyr$, after which they continue their outward diffusion due to gravitational interactions with the soliton and the halo granules. More massive objects ($gtrsim 1 % M_{rm sol}$), 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.
The cusp-core problem is one of the main challenges of the cold dark matter paradigm on small scales: the density of a dark matter halo is predicted to rise rapidly toward the center as rho ~ r^alpha with alpha between -1 and -1.5, while such a cuspy profile has not been clearly observed. We have carried out the spatially-resolved mapping of gas dynamics toward a nearby ultra-diffuse galaxy (UDG), AGC 242019. The derived rotation curve of dark matter is well fitted by the cuspy profile as described by the Navarro-Frenk-White model, while the cored profiles including both the pseudo-isothermal and Burkert models are excluded. The halo has alpha=-(0.90+-0.08) at the innermost radius of 0.67 kpc, Mhalo=(3.5+-1.2)E10 Msun and a small concentration of 2.0+-0.36. AGC 242019 challenges alternatives of cold dark matter by constraining the particle mass of fuzzy dark matter to be < 0.11E-22 eV or > 3.3E-22 eV , the cross section of self-interacting dark matter to be < 1.63 cm2/g, and the particle mass of warm dark matter to be > 0.23 keV, all of which are in tension with other constraints. The modified Newtonian dynamics is also inconsistent with a shallow radial acceleration relationship of AGC 242019. For the feedback scenario that transforms a cusp to a core, AGC 242019 disagrees with the stellar-to-halo-mass-ratio dependent model, but agrees with the star-formation-threshold dependent model. As a UDG, AGC 242019 is in a dwarf-size halo with weak stellar feedback, late formation time, a normal baryonic spin and low star formation efficiency (SFR/gas).
A Fuzzy Dark Matter (FDM) halo consists of a soliton core close to the center and an NFW-like density profile in the outer region. Previous investigations found that the soliton core exhibits temporal oscillations and random walk excursions around the halo center. Analyzing a set of numerical simulations, we show that both phenomena can be understood as the results of wave interference -- a suitable superposition of the ground (solitonic) state and excited states in a fixed potential suffices to account for the main features of these phenomena. Such an eigenmode analysis can shed light on the evolution of a satellite halo undergoing tidal disruption. As the outer halo is stripped away, reducing the amplitudes of the excited states, the ground state evolves adiabatically. This suggests diminished soliton oscillations and random walk excursions, an effect to consider in deducing constraints from stellar heating.
We present an in-depth exploration of the phenomenon of dynamical friction in a universe where the dark matter is composed entirely of so-called Fuzzy Dark Matter (FDM), ultralight bosons of mass $msimmathcal{O}(10^{-22}),$eV. We review the classical treatment of dynamical friction before presenting analytic results in the case of FDM for point masses, extended mass distributions, and FDM backgrounds with finite velocity dispersion. We then test these results against a large suite of fully non-linear simulations that allow us to assess the regime of applicability of the analytic results. We apply these results to a variety of astrophysical problems of interest, including infalling satellites in a galactic dark matter background, and determine that emph{(1)}~for FDM masses $mgtrsim 10^{-21}, {rm eV}, c^{-2}$, the timing problem of the Fornax dwarf spheroidals globular clusters is no longer solved and emph{(2)}~the effects of FDM on the process of dynamical friction for satellites of total mass $M$ and relative velocity $v_{rm rel}$ should require detailed numerical simulations for $left(M/10^9~M_{odot}right) left(m/10^{-22}~{rm eV}right)left(100~{rm km}~{rm s}^{-1}/v_{rm rel}right) sim 1$, parameters which would lie outside the validated range of applicability of any currently developed analytic theory, due to transient wave structures in the time-dependent regime.
Recent studies have presented evidence that the Milky Way global potential may be nonspherical. In this case, the assembling process of the Galaxy may have left long lasting stellar halo kinematic fossils due to the shape of the dark matter halo, potentially originated by orbital resonances. We further investigate such possibility, considering now potential models further away from $Lambda$CDM halos, like scalar field dark matter halos, MOND, and including several other factors that may mimic the emergence and permanence of kinematic groups, such as, a spherical and triaxial halo with an embedded disk potential. We find that regardless of the density profile (DM nature), kinematic groups only appear in the presence of a triaxial halo potential. For the case of a MOND like gravity theory no kinematic structure is present. We conclude that the detection of these kinematic stellar groups could confirm the predicted triaxiality of dark halos in cosmological galaxy formation scenarios.
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