We examine four candidate mechanisms that could explain the high surface temperatures of magnetars.(1) Heat flux from the liquid core heated by ambipolar diffusion. It could sustain the observed surface luminosity L s ≈ 10 35 erg s −1 if core heating offsets neutrino cooling at a temperature T core > 6×10 8 K. This scenario is viable if the core magnetic field exceeds 10 16 G and the heat-blanketing envelope of the magnetar has a light element composition. We find however that the lifetime of such a hot core should be shorter than the typical observed lifetime of magnetars.(2) Mechanical dissipation in the solid crust. This heating can be quasi-steady, powered by gradual (or frequent) crustal yielding to magnetic stresses. We show that it obeys a strong upper limit. As long as the crustal stresses are fostered by the field evolution in the core or Hall drift in the crust, mechanical heating is insufficient to sustain persistent L s ≈ 10 35 erg s −1 . The surface luminosity is increased in an alternative scenario of mechanical deformations triggered by external magnetospheric flares. (3) Ohmic dissipation in the crust, in volume or current sheets. This mechanism is inefficient because of the high conductivity of the crust. Only extreme magnetic configurations with crustal fields B > 10 16 G varying on a 100 meter scale could provide L s ≈ 10 35 erg s −1 . (4) Bombardment of the stellar surface by particles accelerated in the magnetosphere. This mechanism produces hot spots on magnetars. Observations of transient magnetars show evidence for external heating.

We investigate nonlinear structure formation in the fuzzy dark matter (FDM) model using both numerical and perturbative techniques. On the numerical side, we examine the virtues and limitations of a Schrödinger-Poisson solver (wave formulation) versus a fluid dynamics solver (Madelung formulation). On the perturbative side, we carry out a computation of the one-loop mass power spectrum, i.e. up to third order in perturbation theory. We find that (1) in many situations, the fluid dynamics solver is capable of producing the expected interference patterns, but it fails in situations where destructive interference causes the density to vanish -a generic occurrence in the nonlinear regime.(2) The Schrödinger-Poisson solver works well in all test cases, but it is demanding in resolution: suppose one is interested in the mass power spectrum on large scales, it's not sufficient to resolve structure on those same scales; one must resolve the relevant de Broglie scale which is often smaller. The fluid formulation does not suffer from this issue. (3) We compare the one-loop mass power spectrum from perturbation theory against the mass power spectrum from the Schrödinger-Poisson solver, and find good agreement in the mildly nonlinear regime. We contrast fluid perturbation theory with wave perturbation theory; the latter has a more limited range of validity. (4) As an application, we compare the Lyman-alpha forest flux power spectrum obtained from the Schrödinger-Poisson solver versus one from an N-body simulation (the latter is often used as an approximate method to make predictions for FDM). At redshift 5, the two, starting from the same initial condition, agree to better than 10% on observationally relevant scales as long as the FDM mass exceeds 2 × 10 −23 eV. We emphasize that the so called quantum pressure is capable of both enhancing and suppressing fluctuations in the nonlinear regime -which dominates depends on the scale and quantity of interest.

In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about 100 eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves. This applies to, for instance, the QCD axion as well as to lighter axion-like particles such as fuzzy dark matter. We show that the interference of waves inside a halo inevitably leads to vortices, locations where chance destructive interference takes the density to zero. The phase of the wavefunction has nontrivial winding around these points. This can be interpreted as a non-zero velocity circulation, so that vortices are sites where the fluid velocity has a non-vanishing curl. Using analytic arguments and numerical simulations, we study the properties of vortices and show they have a number of universal features: (1) In three spatial dimensions, the generic defects take the form of vortex rings. (2) On average there is about one vortex ring per de Broglie volume and (3) generically only single winding (±1) vortices are found in a realistic halo. (4) The density near a vortex scales as r 2 while the velocity goes as 1/r, where r is the distance to vortex.(5) A vortex segment moves at a velocity inversely proportional to its curvature scale so that smaller vortex rings move faster, allowing momentary motion exceeding escape velocity. We discuss observational/experimental signatures from vortices and, more broadly, wave interference. In the ultra-light regime, gravitational lensing by interference substructures leads to flux anomalies of 5-10% in strongly lensed systems. For QCD axions, vortices lead to a diminished signal in some detection experiments but not in others. We advocate the measurement of correlation functions by axion detection experiments as a way to probe and capitalize on the expected interference substructures.