Conservation of radial actions in time-dependent spherical potentials

ABSTRACT In slowly evolving spherical potentials, Φ(r, t), radial actions are typically assumed to remain constant. Here, we construct dynamical invariants that allow us to derive the evolution of radial actions in spherical central potentials with an arbitrary time dependence. We show that to linear order, radial actions oscillate around a constant value with an amplitude $\propto \dot{\Phi }/\Phi \, P(E,L)$. Using this result, we develop a diffusion theory that describes the evolution of the radial action distributions of ensembles of tracer particles orbiting in generic time-dependent spherical potentials. Tests against restricted N-body simulations in a varying Kepler potential indicate that our linear theory is accurate in regions of phase-space in which the diffusion coefficient $\tilde {D}(J_r) \lt 0.01\, J_r^2$. For illustration, we apply our theory to two astrophysical processes. We show that the median mass accretion rate of a Milky Way (MW) dark matter (DM) halo leads to slow global time-variation of the gravitational potential, in which the evolution of radial actions is linear (i.e. either adiabatic or diffusive) for ∼84 per cent of the DM halo at redshift z = 0. This fraction grows considerably with look-back time, suggesting that diffusion may be relevant to the modelling of several Gyr old tidal streams in action-angle space. As a second application, we show that dynamical tracers in a dwarf-size self-interacting DM halo (with $\sigma /m_\chi = 1\, {\rm cm^2g^{-1}}$) have invariant radial actions during the formation of a cored density profile.

Wave Dark Matter

We review the physics and phenomenology of wave dark matter: a bosonic dark matter candidate lighter than about 30 eV. Such particles have a de Broglie wavelength exceeding the average interparticle separation in a galaxy like the Milky Way and are, thus, well described as a set of classical waves. We outline the particle physics motivations for such particles, including the quantum chromodynamics axion as well as ultralight axion-like particles such as fuzzy dark matter. The wave nature of the dark matter implies a rich phenomenology: ▪ Wave interference gives rise to order unity density fluctuations on de Broglie scale in halos. One manifestation is vortices where the density vanishes and around which the velocity circulates. There is one vortex ring per de Broglie volume on average. ▪ For sufficiently low masses, soliton condensation occurs at centers of halos. The soliton oscillates and undergoes random walks, which is another manifestation of wave interference. The halo and subhalo abundance is expected to be suppressed at small masses, but the precise prediction from numerical wave simulations remains to be determined. ▪ For ultralight ∼10−22 eV dark matter, the wave interference substructures can be probed by tidal streams or gravitational lensing. The signal can be distinguished from that due to subhalos by the dependence on stream orbital radius or image separation. ▪ Axion detection experiments are sensitive to interference substructures for wave dark matter that is moderately light. The stochastic nature of the waves affects the interpretation of experimental constraints and motivates the measurement of correlation functions. Current constraints and open questions, covering detection experiments and cosmological, galactic, and black hole observations, are discussed.

Seasonal Changes in the Drivers of Water Physico-Chemistry Variability of a Small Freshwater Tidal River

Where rivers meet the sea, tides can exert a physical and chemical influence on the lower reaches of a river. How tidal dynamics in these tidal river reaches interact with upstream hydrological drivers such as storm rainfall, which ultimately determines the quantity and composition of material transferred from watersheds to estuaries, is currently unknown. We monitored a small freshwater tidal river in the Pacific Northwest, United States in high resolution over 1 year to evaluate the relative importance of tides vs. upstream hydrological flows (i.e., base flow and precipitation events) on basic physico-chemical parameters (pH, dissolved oxygen, turbidity, specific conductivity, and temperature), and how these interactions relate to the downstream estuary. Tidal variability and diurnal cycles (i.e., solar radiation) dominated water physico-chemical variability in the summer, but the influence of these drivers was overshadowed by storm-driven sharp pulses in river physico-chemistry during the remainder of the year. Within such events, we found incidences of counterclockwise hysteresis of pH, counterclockwise hysteresis of dissolved oxygen, and clockwise hysteresis of turbidity, although systematic trends were not observed across events. The dominance of storm rainfall in the river’s physico-chemistry dynamics, and similar pulses of decreased pH observed in adjacent estuarine waters, suggest that the linkage between tidal streams and the broader system is variable throughout the year. High-frequency monitoring of tidal river biogeochemistry is therefore crucial to enable the assessment of how the relative strength of these drivers may change with future sea level rise and altered precipitation patterns to modulate biogeochemical dynamics across the land-ocean-atmosphere continuum.

On N-body simulations of globular cluster streams

ABSTRACT Stellar tidal streams are sensitive tracers of the properties of the gravitational potential in which they orbit and detailed observations of their density structure can be used to place stringent constraints on fluctuations in the potential caused by, e.g. the expected populations of dark matter subhaloes in the standard cold dark matter (CDM) paradigm. Simulations of the evolution of stellar streams in live N-body haloes without low-mass dark matter subhaloes, however, indicate that streams exhibit significant perturbations on small scales even in the absence of substructure. Here, we demonstrate, using high-resolution N-body simulations combined with sophisticated semi-analytical and simple analytical models, that the mass resolutions of 104–$10^5\, \rm {M}_{\odot }$ commonly used to perform such simulations cause spurious stream density variations with a similar magnitude on large scales as those expected from a CDM-like subhalo population and an order of magnitude larger on small, yet observable, scales. We estimate that mass resolutions of ${\approx}100\, \rm {M}_{\odot }$ (${\approx}1\, \rm {M}_{\odot }$) are necessary for spurious, numerical density variations to be well below the CDM subhalo expectation on large (small) scales. That streams are sensitive to a simulation’s particle mass down to such small masses indicates that streams are sensitive to dark matter clustering down to these low masses if a significant fraction of the dark matter is clustered or concentrated in this way, for example, in MACHO models with masses of 10–$100\, \rm {M}_{\odot }$.

The analytical and experimental study on the establishment of a tidal power plant in South Africa

The majority of South Africa’s electricity is generated from fossil-fuel plants that use mainly coal. In these power plants, the combustion of these fossil fuels liberates greenhouse gasses into the atmosphere that contribute to climate change. This problem coupled with the rapid depletion of fossil fuels has necessitated the need to explore the alternative form of energy such as renewable energy. Tidal energy is a form of ocean energy that can be considered as an alternative energy resource or renewable energy source. This form of energy has not been explored in South Africa, the only country in the world that is bounded by two oceans; the Indian and the Atlantic. Tidal energy can be harnessed from the movements of tides to generate electrical power. This study considered the possibility of harnessing tidal energy as the alternative energy source for power generation which can be used to mitigate the challenges associated with the energy crisis currently being experienced in the country. For this study, an extensive literature review was carried out to understand the tidal phenomenon, the concept of energy conversion from tides, the different techniques or technologies that can be used to generated power from tides. There are two main technologies used for converting tidal energy to electrical energy and these are the tidal barrage and the tidal streams. Based on the inferences drawn from the literature reviews concerning the tides experienced around the South Africa coastal region, it was identified that the tidal stream technique is applicable. Harmonic analysis of the tidal resource for four identified sites was conducted, from these analyses, Esikhawini was selected as an optimum site. Tidal streams extract the kinetic energy of tides and the mode of operation of tidal stream plants is determined by the type of tidal turbine employed. Several turbine designs were reviewed, a helical cross-flow turbine was selected due to its self-starting capability and its ability to operate in reverse stream flows. For this helical turbine, an analytical model using the blade element momentum theory (BEMT) was developed and was implemented on MATLAB environment. For the experimentation, a prototype was developed and tested in a laboratory concrete flume in the department of Civil Engineering at the University of KwaZulu-Natal. Based on the experimental results, an analysis of the unit turbine was done which was used to propose a conceptualized tidal power plant. Hence, the proposed tidal power plant was used to justify the reason for embarking on this study which is to ascertain the possibility of establishing a tidal power plant in South Africa.

The Fluid Mechanics of Tidal Stream Energy Conversion

Placing mechanical devices into fast-moving tidal streams to generate clean and predictable electricity is a developing technology. This review covers the fundamental fluid mechanics of this application, which is important for understanding how such devices work and how they interact with the tidal stream resource. We focus on how tidal stream turbines and energy generation are modeled analytically, numerically, and experimentally. Owing to the nature of the problem, our review is split into different scales—from turbine to array and regional—and we examine each in turn.