Hybrid model of condensate and particle Dark Matter: linear perturbations in the hydrodynamic limit

We analyse perturbations of self-interacting, scalar field dark matter that contains modes both in a coherent condensate state and an incoherent particle-like state. Starting from the coupled equations for the condensate, the particles and their mutual gravitational potential, first derived from first principles in earlier work by the authors, we derive a hydrodynamic limit of two coupled fluids and study their linearized density perturbations in an expanding universe. We find that away from the condensate-only or particle-only limits, and for certain ranges of the parameters, such self-interacting mixtures can significantly enhance the density power spectrum above the standard linear $\Lambda$CDM value at localised wavenumbers, even pushing structure formation into the non-linear regime earlier than expected in $\Lambda$CDM for these scales. We also note that such mixtures can lead to degeneracies between models with different boson masses and self-coupling strengths, in particular between self-coupled models and non-coupled Fuzzy Dark Matter made up of heavier bosons. These findings open up the possibility of a richer phenomenology in scalar field dark matter models and could further inform efforts to place observational limits on their parameters.Comment: 16 pages, 7 figures. v2: references adde

Unified description of corpuscular and fuzzy bosonic dark matter

We derive from first principles equations for bosonic, non-relativistic and self-interacting dark matter which can include both a condensed, low momentum "fuzzy" component and one with higher momenta that may be approximated as a collection of particles. The resulting coupled equations consist of a modified Gross-Pitaevskii equation describing the condensate and a kinetic equation describing the higher momentum modes, the "particles", along with the Poisson equation for the gravitational potential sourced by the density of both components. Our derivation utilizes the Schwinger-Keldysh path integral formalism and applies a semi-classical approximation which can also accommodate collisional terms amongst the particles and between the particles and the condensate to second order in the self-coupling strength. The equations can therefore describe both CDM and Fuzzy Dark Matter in a unified way, allowing for the coexistence of both phases and the inclusion of quartic self-interactions.Comment: 22 pages, 6 figures. V2: Final version, accepted in PR

Coherent and incoherent structures in fuzzy dark matter halos

We show that fuzzy dark matter halos exhibit spatial differentiation in the degree of coherence of the field configuration, ranging from completely coherent in the central solitonic core to incoherent outside it, with a crossover region in between the two phases. The solitonic core is indeed a pure condensate which overlaps almost perfectly with the Penrose-Onsager mode corresponding to the largest eigenvalue of the one-particle density matrix. The virialized outer halo surrounding the core exhibits no clear coherence as a whole upon radial and temporal averaging. However, when viewed locally and for short times, it can be described as a collection of quasi-condensate lumps exhibiting locally suppressed fluctuations which can be identified with the structures commonly referred to as granules. Phase coherence across the entire halo is inhibited by a dynamically evolving tangled web of vortices separating the localized quasi-condensate regions. Moreover, the dimensionless phase-space density in the outer halo drops significantly below its value at the core. We further examine the dynamics of this spatial structure and find that the oscillations of the core can be accurately described by two time-dependent parameters respectively characterizing the size of the core, $r_c(t)$, and the crossover region, $r_t(t)$. For the halos produced in our merger simulations this feature is reflected in the (anti-)correlated oscillation of the peak value of the field configuration's power-spectrum. The turbulent vortex tangle of the virialized halo appears to reach a quasi-equilibrium state over probed timescales, with the incompressible component of the kinetic energy exhibiting a characteristic $k^{-3}$ tail in its spectrum, indicative of a $\rho\sim r^2$ density profile around the quantum vortex cores. Comparison of the peak wavenumbers in the corresponding power-spectra shows that the inter-vortex..

Hip Disarticulation for Severe Lower Extremity Infections

Hip disarticulation is rarely performed for infections and variable mortality rates have been reported. We determined the number of deaths following hip disarticulation for severe lower extremity infections in 15 patients. Indications for hip disarticulation were necrotizing soft tissue infections in seven patients and persistent infections of the proximal thigh in eight patients. The most common microorganism was Staphylococcus aureus, present in eight patients. Hip disarticulation was performed emergently in seven patients and electively in eight patients. All patients survived the operation and at 1 month postoperatively 14 of 15 patients were alive. Hip disarticulation for these severe infections had high survival, even when performed emergently for life-threatening infections. We believe hip disarticulation is a reasonable option treating severe infections of the lower extremity and should be part of the armamentarium of the orthopaedic surgeon

Magnetic Resonance Imaging Findings in Hematogenous Osteomyelitis of the Hip in Adults

Hematogenous hip infections are rare in adults and the extent of infection into the bone or adjacent soft tissues may be underestimated, leading to inadequate surgical débridement. Using MRI, we sought to determine the extent of bone involvement and the presence of adjacent soft tissue abscesses in adults with hip osteomyelitis. We reviewed the records and MRIs in 11 adult patients (12 hips) with hematogenous osteomyelitis of the femoral head in 12 hips. Ten of 11 patients had one or more comorbidities. All patients underwent surgical débridement and received antibiotic therapy for 6 weeks. MRI revealed osteomyelitis distal to the femoral head in seven of 12 hips with extension into the medullary canal in three of these seven. Femoral head erosions were present in 10 hips, acetabulum osteomyelitis in 11, and acetabular erosions in six hips. Infection extended into adjacent soft tissues in eight of 12 hips. MRI demonstrated that the infection may extend distal to the femoral head or into the adjacent soft tissues. MRI may be useful for preoperative planning so that all regions affected by the infection can be treated