We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic r −3 NFW-like profile. We find a fundamental relation of the core=to-halo mass with the dimensionless invariant Ξ ≡ |E|/M 3 /(Gm/ ) 2 or M c /M 2.6Ξ 1/3 , linking the soliton to global halo properties. For r ≥ 3.5 r c core radii, we find equipartition between potential, classical kinetic, and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behavior driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a k −1.1 power-law. This suggests the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a k −5/3 Kolmogorov power-law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying the soliton-sized granules carry most of the turbulent energy in BECDM haloes.

Accurate numerical solutions of the equations of hydrodynamics play an ever more important role in many fields of astrophysics. In this work, we reinvestigate the accuracy of the moving-mesh code Arepo and show how its convergence order can be improved for general problems. In particular, we clarify that for certain problems Arepo only reaches first-order convergence for its original formulation. This can be rectified by simple modifications we propose to the time integration scheme and the spatial gradient estimates of the code, both improving the accuracy of the code. We demonstrate that the new implementation is indeed second-order accurate under the L 1 norm, and in particular substantially improves conservation of angular momentum. Interestingly, whereas these improvements can significantly change the results of smooth test problems, we also find that cosmological simulations of galaxy formation are unaffected, demonstrating that the numerical errors eliminated by the new formulation do not impact these simulations. In contrast, simulations of binary stars followed over a large number of orbital times are strongly affected, as here it is particularly crucial to avoid a long-term build up of errors in angular momentum conservation.

The Schrödinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As /m → 0, m being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as /m → 0 due to interference and the uncertainty principle, the potential field converges to the classical answer as ( /m) 2 . Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as /m → 0. The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schrödinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultra-light axions, which in the classical limit ( /m → 0) is expected to manifest itself as collisionless cold dark matter.

We perform uniformly sampled large-scale cosmological simulations including magnetic fields with the moving mesh code arepo. We run two sets of MHD simulations: one including adiabatic gas physics only; the other featuring the fiducial feedback model of the illustris simulation. In the adiabatic case, the magnetic field amplification follows the B ∝ ρ 2/3 scaling derived from 'flux-freezing' arguments, with the seed field strength providing an overall normalization factor. At high baryon overdensities the amplification is enhanced by shear flows and turbulence. Feedback physics and the inclusion of radiative cooling change this picture dramatically. In haloes, gas collapses to much larger densities and the magnetic field is amplified strongly and to the same maximum intensity irrespective of the initial seed field of which any memory is lost. At lower densities a dependence on the seed field strength and orientation, which in principle can be used to constrain models of cosmic magnetogenesis, is still present. Inside the most massive haloes magnetic fields reach values of ∼ 10 − 100 µG, in agreement with galaxy cluster observations. The topology of the field is tangled and gives rise to rotation measure signals in reasonable agreement with the observations. However, the rotation measure signal declines too rapidly towards larger radii as compared to observational data.

In hierarchical models of structure formation, the first galaxies form in low-mass dark matter potential wells, probing the behavior of dark matter on kiloparsec (kpc) scales. Even though these objects are below the detection threshold of current telescopes, future missions will open an observational window into this emergent world. In this Letter we investigate how the first galaxies are assembled in a 'fuzzy' dark matter (FDM) cosmology where dark matter is an ultralight ∼ 10 −22 eV boson and the primordial stars are expected to form along dense dark matter filaments. Using a first-of-its-kind cosmological hydrodynamical simulation, we explore the interplay between baryonic physics and unique wavelike features inherent to FDM. In our simulation, the dark matter filaments show coherent interference patterns on the boson de Broglie scale and develop cylindrical solitonlike cores which are unstable under gravity and collapse into kpc-scale spherical solitons. Features of the dark matter distribution are largely unaffected by the baryonic feedback. On the contrary, the distributions of gas and stars, which do form along the entire filament, exhibit central cores imprinted by dark matter -a smoking gun signature of FDM.Introduction. The nearly century-old dark matter problem is one of the most intriguing mysteries in modern physics. We do not know the nature of 84 percent of matter in the Universe, yet it is thought to govern cosmic structure and hold galaxies and clusters together [1]. Observations show that on scales larger than a few megaparsecs (Mpc), the behavior of dark matter is consistent with it being collisionless [2,3]. However, on scales at and below the size of dwarf galaxies (few kpc) dark matter is not well constrained [4], allowing for many plausible theories with exotic small-scale physics and particle masses spanning over 30 orders of magnitude [5][6][7][8][9][10]. The first star-forming regions in the Universe -more susceptible to dark matter's small-scale behavior than much heavier present-day galaxies -will be revealed by next generation space telescopes and offer a unique probe of the nature of this elusive component.A leading hypothesis for the dark matter 'back-bone' of the Universe is cold dark matter (CDM), such as a thermally-produced weakly interacting massive particle (WIMP) of mass eV. CDM is collisionless and Jeans unstable to forming structure on all astrophysical scales down to a particle physics model-dependent small-scale

Star formation in our Galaxy occurs in molecular clouds that are self-gravitating, highly turbulent, and magnetized. We study the conditions under which cloud cores inherit large-scale magnetic field morphologies and how the field is governed by cloud turbulence. We present four moving-mesh simulations of supersonic, turbulent, isothermal, self-gravitating gas with a range of magnetic mean-field strengths characterized by the Alfvénic Mach number M A,0 , resolving pre-stellar core formation from parsec to a few AU scales. In our simulations with the turbulent kinetic energy density dominating over magnetic pressure (M A,0 > 1), we find that the collapse is approximately isotropic with B ∝ ρ 2/3 , core properties are similar regardless of initial mean-field strength, and the field direction on 100 AU scales is uncorrelated with the mean field. However, in the case of a dominant large-scale magnetic field (M A,0 = 0.35), the collapse is anisotropic with B ∝ ρ 1/2 . This transition at M A,0 ∼ 1 is not expected to be sharp, but clearly signifies two different paths for magnetic field evolution in star formation. Based on observations of different star forming regions, we conclude that star formation in the interstellar medium may occur in both regimes. Magnetic field correlation with the mean-field extends to smaller scales as M A,0 decreases, making future ALMA observations useful for constraining M A,0 of the interstellar medium.

In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one-and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfvén waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.

We investigate the formation, gravitational clustering, and interactions of solitons in a selfinteracting, non-relativistic scalar field in an expanding universe. Rapid formation of a large number of solitons is driven by attractive self-interactions of the field, whereas the slower clustering of solitons is driven by gravitational forces. Driven closer together by gravity, we see a rich plethora of dynamics in the soliton "gas" including mergers, scatterings and formation of soliton binaries. The numerical simulations are complemented by analytic calculations and estimates of (i) the relevant instability length and time scales, (ii) individual soliton profiles and their stability, (iii) number density of produced solitons, and (iv) the two-point correlation function of soliton positions as evidence for gravitational clustering. * mustafa.a.amin@gmail.com † philip.mocz@gmail.com; Einstein Fellow 1 Here, by cosmological initial conditions we mean an almost homogeneous field with small perturbations.