An unusual orbital element clustering of Kuiper belt objects (KBOs) has been observed. The most promising dynamic solution is the presence of a giant planet in the outer Solar system, Planet Nine. However, due to its extreme distance, intensive searches in optical have not been successful. We aim to find Planet Nine in the far-infrared, where it has the peak of the black body radiation, using the most sensitive all-sky far-infrared survey to date, AKARI. In contrast to optical searches, where the energy of reflected sunlight decreases by $d^{4}$, thermal radiation in the infrared decreases with the square of the heliocentric distance $d^{2}$. We search for moving objects in the AKARI Single Scan Detection List. We select sources from a promising region suggested by an N-body simulation from Millholland and Laughlin 2017: $30^{\circ}\lt$ R.A. $\lt50^{\circ}$ and $-20^{\circ}\lt$ Dec. $\lt20^{\circ}$. Known sources are excluded by cross-matching AKARI sources with 9 optical and infrared catalogues. Furthermore, we select sources with small background strength to avoid sources in the cirrus. Since Planet Nine is stationary in a timescale of hours but moves on a monthly scale, our primary strategy is to select slowly moving objects that are stationary in 24 h but not in six months, using multiple single scans by AKARI. The selected slowly moving AKARI sources are scrutinised for potential contamination from cosmic rays. Our analysis reveals two possible Planet Nine candidates whose positions and flux are within the theoretical prediction ranges. These candidates warrant further investigation through follow-up observations to confirm the existence and properties of Planet Nine.

We measured the harmonic-space power spectrum of Galaxy clustering auto-correlation from the Evolutionary Map of the Universe Pilot Survey 1 data (EMU PS1) and its cross-correlation with the lensing convergence map of cosmic microwave background (CMB) from Planck Public Release 4 at the linear scale range from $\ell=2$ to 500. We applied two flux density cuts at $0.18$ and $0.4$ mJy on the radio galaxies observed at 944MHz and considered two source detection algorithms. We found the auto-correlation measurements from the two algorithms at the 0.18 mJy cut to deviate for $\ell\gtrsim250$ due to the different criteria assumed on the source detection and decided to ignore data above this scale. We report a cross-correlation detection of EMU PS1 with CMB lensing at $\sim$5.5$\sigma$, irrespective of flux density cut. In our theoretical modelling we considered the SKADS and T-RECS redshift distribution simulation models that yield consistent results, a linear and a non-linear matter power spectrum, and two linear galaxy bias models. That is a constant redshift-independent galaxy bias $b(z)=b_g$ and a constant amplitude galaxy bias $b(z)=b_g/D(z)$. By fixing a cosmology model and considering a non-linear matter power spectrum with SKADS, we measured a constant galaxy bias at $0.18$ mJy ($0.4$ mJy) with $b_g=2.32^{+0.41}_{-0.33}$ ($2.18^{+0.17}_{-0.25}$) and a constant amplitude bias with $b_g=1.72^{+0.31}_{-0.21}$ ($1.78^{+0.22}_{-0.15}$). When $\sigma_8$ is a free parameter for the same models at $0.18$ mJy ($0.4$ mJy) with the constant model we found $\sigma_8=0.68^{+0.16}_{-0.14}$ ($0.82\pm0.10$), while with the constant amplitude model we measured $\sigma_8=0.61^{+0.18}_{-0.20}$ ($0.78^{+0.11}_{-0.09}$), respectively. Our results agree at $1\sigma$ with the measurements from Planck CMB and the weak lensing surveys and also show the potential of cosmology studies with future radio continuum survey data.

Before a binary system enters into a common envelope (CE) phase, accretion from the primary star onto the companion star through Roche Lobe overflow (RLOF) will lead to the formation of an accretion disk, which may generate jets. Accretion before and during the CE may alter the outcome of the interaction. Previous studies have considered different aspects of this physical mechanism. Here we study the properties of an accretion disk formed via 3D hydrodynamic simulations of the RLOF mass transfer between a 7 M$_{\odot}$, red supergiant star and a 1.4 M$_{\odot}$, neutron star companion. We simulate only the volume around the companion for improved resolution. We use a 1D implicit mesa simulation of the evolution of the system during 30 000 yr between the on-set of the RLOF and the CE to guide the binary parameters and the mass-transfer rate, while we simulate only 21 yr of the last part of the RLOF in 3D using an ideal gas quasi-isothermal equation of state. We expect that a pre-CE disk under these parameters will have a mass of $\sim 5\times 10^{-3}$ M$_{\odot}$ and a radius of $\sim40\ R_\odot$ with a scale height of $\sim 5\ R$$_{\odot}$. The temperature profile of the disk is shallower than that predicted by the formalism of Shakura and Sunyaev, but more reasonable cooling physics would need to be included. We stress test these results with respect to a number of physical and numerical parameters, as well as simulation choices, and we expect them to be reasonable within a factor of a few for the mass and 15% for the radius. We also contextualise our results within those presented in the literature, in particular with respect to the dimensionality of simulations and the adiabatic index. We discuss the measured accretion rate in the context of the Shakura and Sunyaev formalism and debate the viscous mechanisms at play, finishing with a list of prospects for future work.

The scatter in global atomic hydrogen (Hi) scaling relations is partly attributed to differences in how Hi and stellar properties are measured, with Hi reservoirs typically extending beyond the inner regions of galaxies where star formation occurs. Using pilot observations from the Widefield ASKAP L-band Legacy All-sky Blind Survey (WALLABY), we present the first measurements of Hi mass enclosed within the stellar-dominated regions of galaxies for a statistical sample of 995 local gas-rich systems, investigating the factors driving its variation. We examine how global Hi scaling relations change when measurements are restricted to $R_{\text{25}}$ and $R_{\text{24}}$ – the isophotal radii at 25 and 24 mag arcsec$^{-2}$ in the i-band – and explore how the fraction of Hi mass and Hi surface density within these radii correlate with other galaxy properties. On average, 68% of the total Hi mass is enclosed within $R_{\text{25}}$ and 54% within $R_{\text{24}}$, though significant variation exists between galaxies, ranging from $\sim$20% to 100%. The fraction of Hi mass within $R_{\text{25}}$ shows a mild correlation with stellar properties, with galaxies of higher stellar mass, greater stellar surface density, or redder colours enclosing a larger fraction of their Hi reservoirs. These correlations do not significantly strengthen when considering $R_{\text{24}}$. Conversely, global Hi surface densities show no significant correlation with stellar mass or stellar surface density, but trends start emerging when these are measured within the inner regions of galaxies. The strongest correlation is observed with optical colour, with bluer galaxies having higher average Hi surface densities within $R_{\text{25}}$. This trend of the average Hi surface density with optical colour strengthens when we restrict from $R_{\text{25}}$ to $R_{\text{24}}$, suggesting a closer connection between inner Hi reservoirs and star formation. This study underscores the value of (at least marginally) resolved Hi surveys of statistical samples for advancing our understanding of the gas-star formation cycle in galaxies.

Electron energisation by magnetic reconnection has historically been studied in the Lagrangian guiding-centre framework. Insights from such studies include that Fermi acceleration in magnetic islands can accelerate electrons to high energies. An alternative Eulerian fluid formulation of electron energisation was recently used to study electron energisation during magnetic reconnection in the absence of magnetic islands. Here, we use particle-in-cell simulations to compare the Eulerian and Lagrangian models of electron energisation in a set-up where reconnection leads to magnetic island formation. We find the largest energisation at the edges of magnetic islands. There, energisation related to the diamagnetic drift dominates in the Eulerian model, while the Fermi related term dominates in the Lagrangian model. The models predict significantly different energisation rates locally. A better agreement is found after integrating over the simulation domain. We show that strong magnetic curvature can break the magnetic moment conservation assumed by the Lagrangian model, leading to erroneous results. The Eulerian fluid model is a complete fluid description and accurately models bulk energisation. However, local measurements of its constituent energisation terms need not reflect locations where plasma is heated or accelerated. The Lagrangian guiding centre model can accurately describe the energisation of particles, but it cannot describe the evolution of the fluid energy. We conclude that while both models can be valid, they describe two fundamentally different quantities, and care should be taken when choosing which model to use.

Post-asymptotic giant branch (post-AGB) binaries are surrounded by dusty circumbinary disks and exhibit unexpected orbital properties resulting from poorly understood binary interaction processes. Re-accreted gas from the circumbinary disk alters the photospheric chemistry of the post-AGB star, producing a characteristic underabundance of refractory elements that correlates with condensation temperature – a phenomenon known as chemical depletion. This work investigates how re-accretion from a disk drives chemical depletion, and the impact accreted matter has on post-AGB evolution. We used the MESA code to evolve 0.55 and 0.60 M$_{\odot}$ post-AGB stars with the accretion of refractory element-depleted gas from a circumbinary disk. Our study adopts observationally-constrained initial accretion rates and disk masses to reproduce the chemical depletion patterns of six well-studied post-AGB binary stars: EP Lyr, HP Lyr, IRAS 17038-4815, IRAS 09144-4933, HD 131356, and SX Cen. We find high accretion rates ($\gt 10^{-7}$ M$_{\odot}\,\mathrm{yr}^{-1}$) and large disk masses ($\gtrsim10^{-2}$ M$_{\odot}$) necessary to reproduce observed depletion, particularly in higher-mass, hotter post-AGB stars ($T_{\textrm{eff}}\gtrsim$ 6 000 K). A slower evolution (lower core mass) is required to reproduce cooler ($T_{\textrm{eff}}\lesssim$ 5 000 K) depleted post-AGB stars. Rapid accretion significantly impacts post-AGB evolution, stalling stars at cooler effective temperatures and extending post-AGB lifetimes by factors of around 3 to 10. Despite this, extended post-AGB timescales remain within or below the planetary nebula visibility timescale, suggesting accretion cannot account for the observed lack of ionised PNe in post-AGB binaries. Our findings constrain accretion-flow parameters and advance our understanding of disk-binary interactions in post-AGB systems.

In their celebrated paper [CLR10], Caputo, Liggett and Richthammer proved Aldous’ conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality — a certain inequality of operators in the group ring $\mathbb{R}\left[{\mathrm{Sym}}_{n}\right]$ of the symmetric group. Here we generalise the Octopus Inequality and apply it to generalising the Caputo–Liggett–Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo.

Let M be a closed oriented 3-manifold equipped with an Euler structure e and an acyclic representation of its fundamental group. We define a twisted self-linking homology class of the diagonal of the two-point configuration space of M with respect to e. This twisted self-linking homology class appears as an obstruction in the Chern–Simons perturbation theory. When the representation is the maximal free abelian representation $\rho_0$, we prove that our self-linking class is a properly defined “logarithmic derivative” of the Reidemeister–Turaev torsion of $(M,\rho_0,e)$ equipped with the given Euler structure.

Optimal-mode theory (Landreman et al. 2015 J. Plasma Phys. 81, 905810501) can be used to derive upper bounds on growth rates of local gyrokinetic instabilities (Helander & Plunk 2021 Phys. Rev. Lett. 127, 155001). These bounds follow from thermodynamic principles (specifically on the Helmholtz free energy) (Helander & Plunk Phys. Rev. Lett. 127, 2021, p. 155001), and thus apply to any instability and geometry, independently of many plasma parameters. In this work, we compare these upper bounds with the growth rates of linear gyrokinetic eigenmodes. Experimentally relevant scenarios of density-gradient- and ion-temperature-gradient-driven instabilities are considered. The difference between the upper bounds and the numerically computed growth rates is always positive, as it must be, but depends strongly on the instability in question and on the geometry of the magnetic field. The nature of this difference can be analysed by examining the contributions of optimal modes to gyrokinetic eigenmodes. This approach exploits the completeness and orthogonality properties of optimal modes.

The bootstrap current in stellarators can be presented as a sum of a collisionless value given by the Shaing–Callen asymptotic formula and an off-set current, which non-trivially depends on plasma collisionality and radial electric field. Using NEO-2 modeling, analytical estimates and semi-analytical studies with the help of a propagator method, it is shown that the off-set current in the $1/\nu$ regime does not converge with decreasing collisionality $\nu _\ast$ but rather shows oscillations over $\log \nu _\ast$ with an amplitude of the order of the bootstrap current in an equivalent tokamak. The convergence to the Shaing–Callen limit appears in regimes with significant orbit precession, in particular, due to a finite radial electric field, where the off-set current decreases as $\nu _\ast ^{3/5}$. The off-set current strongly increases in case of nearly aligned magnetic field maxima on the field line where it diverges as $\nu _\ast ^{-1/2}$ in the $1/\nu$ regime and saturates due to the precession at a level exceeding the equivalent tokamak value by ${v_E^\ast }^{-1/2}$, where $v_E^\ast$ is the perpendicular Mach number. The latter off-set, however, can be minimized by further aligning the local magnetic field maxima and by fulfilling an extra integral condition of “equivalent ripples” for the magnetic field. A criterion for the accuracy of this alignment and of ripple equivalence is derived. In addition, the possibility of the bootstrap effect at the magnetic axis caused by the above off-set is also discussed.

We study a family of Thompson-like groups built as rearrangement groups of fractals introduced by Belk and Forrest in 2019, each acting on a Ważewski dendrite. Each of these is a finitely generated group that is dense in the full group of homeomorphisms of the dendrite (studied by Monod and Duchesne in 2019) and has infinite-index finitely generated simple commutator subgroup, with a single possible exception. More properties are discussed, including finite subgroups, the conjugacy problem, invariable generation and existence of free subgroups. We discuss many possible generalisations, among which we find the Airplane rearrangement group $T_A$. Despite close connections with Thompson’s group F, dendrite rearrangement groups seem to share many features with Thompson’s group V.

Accurate modelling of runaway electron generation and losses during tokamak disruptions is crucial for the development of reactor-scale tokamak devices. In this paper, we present a reduced model for runaway electron losses due to flux surface scrape-off caused by the vertical motion of the plasma. The model is made compatible with computationally inexpensive one-dimensional models averaging over a fixed flux-surface geometry, by formulating it as a loss term outside an estimated time-varying minor radius of the last closed flux surface. We then implement this model in the disruption modelling tool DREAM and demonstrate its impact on selected scenarios relevant for ITER. Our results indicate that scrape-off losses may be crucial for making complete runaway avoidance possible even in a $15\,\rm MA$ DT H-mode ITER scenario. The results are however sensitive to the details of the runaway electron generation and phenomena affecting the current density profile, such as the current profile relaxation at the beginning of the disruption.