Fuzzy dark matter soliton cores around supermassive black holes

Abstract

We explore the effect of a supermassive black hole (SMBH) on the density profile of a fuzzy dark matter (FDM) soliton core at the centre of a dark matter halo. We numerically solve the Schrödinger-Poisson equations, treating the black hole as a gravitational point mass, and demonstrate that this additional perturbing term has a 'squeezing' effect on the soliton density profile, decreasing the core radius and increasing the central density. In the limit of large black hole mass, the solution approaches one akin to the hydrogen atom, with radius inversely proportional to the black hole mass. By applying our analysis to two specific galaxies (M87 and the Milky Way) and pairing it with known observational limits on the amount of centrally concentrated dark matter, we obtain a constraint on the FDM particle mass, finding that the range 10 −22.2 eV m 10 −21.7 eV should be forbidden (taking into account additional factors concerning the life-time of the soliton in the vicinity of a black hole). ; Einstein Fellow matter (FDM), this scalar field is assumed to have a particle mass of ∼ 10 −22 eV and a de Broglie wavelength of λ = 1.2 m 10 −22 eV 100 km s −1 v

Dynamical friction in a Fuzzy Dark Matter universe

“…1 it is clear that the exact solution approaches the perturbation theory result in the limit that M Q 1, as expected. We also refer the reader to calculations of a fixed point mass in a static FDM background with full self-gravity carried out in [49], which give rise to soliton-like solutions that resemble the ground state of the hydrogen atom in the limit that the point mass is large.…”

Astronomy with energy dependent flavour ratios of extragalactic neutrinos

“…[48] consider non-interacting BEC DM which forms solitonic core at the galactic centre in the absence of a BH. Therefore, this relation holds only in the case where solitonic cores are formed before SMBH [47,49,56]. Further, the M sol -M halo is valid for a very small range of m DM , around 10 −22 eV [49].…”

“…This has been confirmed by numerical simulations. Various analytical calculations of ultralight DM profile, both in the presence and the absence of a BH at the centre of the galaxy has been carried out [47][48][49]. While presenting our results we have considered following DM profile of the solitonic core, in the presence of a SMBH of mass M BH [47]:…”

“…halo [48,49]. There have also been attempts to predict the shape of the core using velocity dispersion [47,49]. Though we do not use these scaling relations while choosing the benchmark values of a and ρ 0 due to the caveats discussed later in this section.…”

“…The adiabatic propagation can also be achieved in the scenarios where the BH does not dominate the source [47]. For M BH < M halo the dark matter density profile at the core is given by [47,48] • In the case of neutrinos, for the benchmark a = 10 −5 pc, there is a significant violation of adiabaticity only for the jumping of ν 1 to ν 3 for E 1 PeV. Hence, the ratio of electron neutrinos at the detector is given as…”