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Magnetic fields remain one of the least understood aspects of exoplanetary systems. A deeper understanding of planetary dynamos and the evolution of surface magnetic properties throughout a planet's lifetime is a key scientific purpose, with implications for planetary evolution, habitability, and atmospheric dynamics. This study models the evolution of magnetic fields generated by dynamo action in cold giant gaseous planets. We solve the resistive magnetohydrodynamic (MHD) equations under anelastic approximation with a 3D pseudo-spectral spherical shell MHD code. We employ 1D thermodynamical hydrostatic profiles taken from gas giant evolutionary models as the background states of our MHD models. Numerical integration leads to saturated dynamo solutions. Such calculations are performed with radial profiles corresponding to different planetary ages so that we can interpret them as different snapshots of the magnetoconvection evolution during the long-term planetary evolution. We characterize magnetic fields across different evolutionary stages of a cold gaseous planet in terms of topology and strength. We find the occurrence of a transition from multipolar to dipolar-dominated dynamo regime throughout the life of a Jovian planet. During the planetary evolution and the cooling down phase, we observe a decrease in the average magnetic field strength near the dynamo surface as $\sim t^{-0.2}-t^{-0.3}$, a trend compatible with previously proposed scaling laws. We also find that some dimensionless parameters evolve differently for the multipolar to dipolar branch, possibly reflecting a force balance change. This approach can be extended to study hot gaseous planets, offering a versatile tool for interpreting the magnetic properties of giant planets., Comment: 19 pages, submitted for publication, comments are welcome

Scallop-shell stars, a recently discovered class of young M dwarfs, show complex optical light curves that are characterized by periodic dips as well as other features that are stable over tens to hundreds of rotation cycles. The origin of these features is not well-understood. 2MASS J05082729$-$2101444 is a $\sim$25 Myr old scallop-shell star that was identified using TESS data; it has a photometric period of 6.73h that has been attributed to rotation. Of the $\sim$50 recently confirmed scallop-shell stars, it is one of the few detected at radio frequencies between 1 and 8 GHz. We observed this rare system with the upgraded Giant Meterwave Radio Telescope at 575--720 MHz, covering 88% of the photometric period in each of the two observations scheduled almost a month apart in 2023. We detected $\sim$millijansky emission from the target in both epochs, with a significant circular polarization fraction: $|V/I|\sim$20--50%. The 3.5-min phase-folded light curves reveal unique variability in circular polarization, showing an $\sim$hour-long helicity reversal in both epochs, similar in amplitude, length, and (possibly) phase. These results suggest two emission components: The first is a persistent, moderately polarized component possibly ascribable to gyro-synchrotron emission driven by centrifugal breakout events. The second is a highly polarized, short burst-like component, likely due to an electron cyclotron maser (ECM), indicative of auroral emission and potentially responsible for the helicity reversal. To explain this, we discuss the different origins of the plasma responsible for the radio emission, including the possibility that the occulting material is acting as a plasma source. Future coordinated multifrequency radio and optical observations can further constrain the underlying scenario, as well as the magnetic geometry of the system, if we assume an ECM-like auroral emission., Comment: 9 pages, 5 figures, 1 table, Accepted for publication in Astronomy & Astrophysics Letters

People increasingly use digital platforms to exchange resources in accordance to some policies stating what resources users offer and what they require in return. In this paper, we propose a formal model of these environments, focussing on how users' policies are defined and enforced, so ensuring that malicious users cannot take advantage of honest ones. To that end, we introduce the declarative policy language MuAC and equip it with a formal semantics. To determine if a resource exchange is fair, i.e., if it respects the MuAC policies in force, we introduce the non-standard logic MuACL that combines non-linear, linear and contractual aspects, and prove it decidable. Notably, the operator for contractual implication of MuACL is not expressible in linear logic. We define a semantics preserving compilation of MuAC policies into MuACL, thus establishing that exchange fairness is reduced to finding a proof in MuACL. Finally, we show how this approach can be put to work on a blockchain to exchange non-fungible tokens.

Phishing is one of the most prolific cybercriminal activities, with attacks becoming increasingly sophisticated. It is, therefore, imperative to explore novel technologies to improve user protection across both technical and human dimensions. Large Language Models (LLMs) offer significant promise for text processing in various domains, but their use for defense against phishing attacks still remains scarcely explored. In this paper, we present APOLLO, a tool based on OpenAI's GPT-4o to detect phishing emails and generate explanation messages to users about why a specific email is dangerous, thus improving their decision-making capabilities. We have evaluated the performance of APOLLO in classifying phishing emails; the results show that the LLM models have exemplary capabilities in classifying phishing emails (97 percent accuracy in the case of GPT-4o) and that this performance can be further improved by integrating data from third-party services, resulting in a near-perfect classification rate (99 percent accuracy). To assess the perception of the explanations generated by this tool, we also conducted a study with 20 participants, comparing four different explanations presented as phishing warnings. We compared the LLM-generated explanations to four baselines: a manually crafted warning, and warnings from Chrome, Firefox, and Edge browsers. The results show that not only the LLM-generated explanations were perceived as high quality, but also that they can be more understandable, interesting, and trustworthy than the baselines. These findings suggest that using LLMs as a defense against phishing is a very promising approach, with APOLLO representing a proof of concept in this research direction.

In multiagent systems autonomous agents interact with each other to achieve individual and collective goals. Typical interactions concern negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose significant challenges, particularly in capturing the dynamic behaviour of agents, while ensuring that resources are correctly handled. Here, we propose exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return. Furthermore, we introduce a decidable extension of the computational fragment of linear logic as a fundamental tool for representing exchange environments and studying their dynamics in terms of provability.

Surgical procedures are often not "standardised" (i.e., defined in a unique and unambiguous way), but rather exist as implicit knowledge in the minds of the surgeon and the surgical team. This reliance extends to pre-surgery planning and effective communication during the procedure. We introduce a novel approach for the formal and automated analysis of surgical procedures, which we model as security ceremonies, leveraging well-established techniques developed for the analysis of such ceremonies. Mutations of a procedure are used to model variants and mistakes that members of the surgical team might make. Our approach allows us to automatically identify violations of the intended properties of a surgical procedure., Comment: This is an extended version of the paper "A Formal Approach For Modelling And Analysing Surgical Procedures" that appeared in the proceedings of The 20th International Workshop on Security and Trust Management (STM 2024). 25 pages, 7 figures

The young stellar object [BHB2007]-1 has been extensively studied in the past at radio, millimeter, and infrared wavelengths. It shows a gap in the disk and previous observations claimed the possible emission from a forming sub-stellar object, in correspondence to the disk gap. Here, we analyze a set of 8 Karl Jansky Very Large Array (VLA) observations at 15 GHz and spread over a month. We infer a slowly variable emission from the star, with a $\sim 15 \text{-} 20\%$ circular polarization detected in two of the eight observations. The latter can be related to the magnetic fields in the system, while the unpolarized and moderately varying component can be indicative of free-free emission associated with jet induced shocks or interaction of the stellar wind with dense surrounding material. We discard any relevant short flaring activities when sampling the radio light curves down to 10 seconds and find no clear evidence of emission from the sub-stellar object inferred from past observations, although deeper observations could shed further light on this., Comment: 9 pages, 6 figures, 2 tables, Accepted for publication in A&A

We analyze a long-lived hyper-massive neutron star merger remnant (post-merger lifetime $>250$ ms) that has been obtained via large eddy simulations with a gradient subgrid-scale model. We find a clear helicoidal magnetic field structure that is governed by the toroidal component of the magnetic field. Although no jet emerges during the simulation time, we observe at late times a significant increase of the poloidal component of the magnetic field at all scales. We also compare with the results of several binary neutron star simulations with moderate resolution of $120$~m, that are evolved up to $50$~ms after the merger, which differ in terms of the initial topology and strength of the magnetic field. We find that the best choice is an isotropic small-scale magnetic field distribution that mimics the turbulent state that generically develops during the merger. This initial configuration reaches a closer agreement with our high-resolution simulation results than the purely dipolar large-scale fields that are commonly employed in these type of simulations. This provides a recipe to perform such simulations avoiding the computationally expensive grids required to faithfully capture the amplification of the magnetic field by Kelvin-Helmholtz instabilities., Comment: 13 pages, 11 figures

Determining the full five-parameter grain boundary characteristics from experiments is essential for understanding grain boundaries impact on material properties, improving related models, and designing advanced alloys. However, achieving this is generally challenging, in particular at nanoscale, due to their 3D nature. In our study, we successfully determined the grain boundary characteristics of an annealed nickel-tungsten alloy (NiW) nanocrystalline needle-shaped specimen (tip) containing twins using Scanning Precession Electron Diffraction (SPED) Tomography. The presence of annealing twins in this face-centered cubic (fcc) material gives rise to common reflections in the SPED diffraction patterns, which challenges the reconstruction of orientation-specific virtual dark field (VDF) images required for tomographic reconstruction of the 3D grain shapes. To address this, an automated post-processing step identifies and deselects these shared reflections prior to the reconstruction of the VDF images. Combined with appropriate intensity normalization and projection alignment procedures, this approach enables high-fidelity 3D reconstruction of the individual grains contained in the needle-shaped sample volume. To probe the accuracy of the resulting boundary characteristics, the twin boundary surface normal directions were extracted from the 3D voxelated grain boundary map using a 3D Hough transform. For the sub-set of coherent Sigma 3 boundaries, the expected {111} grain boundary plane normals were obtained with an angular error of less than 3{\textdegree} for boundary sizes down to 400 nm${}^2$. This work advances our ability to precisely characterize and understand the complex grain boundaries that govern material properties.

Mutation testing consists of generating test cases that detect faults injected into software (generating mutants) which its original test suite could not. By running such an augmented set of test cases, it may discover actual faults that may have gone unnoticed with the original test suite. It is thus a desired practice for embedded software running in safety-critical cyber-physical systems (CPS). Unfortunately, the state-of-the-art tool targeting C, a typical language for CPS software, relies on symbolic execution, whose limitations often prevent its application. MOTIF overcomes such limitations by leveraging grey-box fuzzing tools to generate unit test cases in C that detect injected faults in mutants. Indeed, fuzzing tools automatically generate inputs by exercising the compiled version of the software under test guided by coverage feedback, thus overcoming the limitations of symbolic execution. Our empirical assessment has shown that it detects more faults than symbolic execution (i.e., up to 47 percentage points), when the latter is applicable., Comment: ICST2024. arXiv admin note: text overlap with arXiv:2308.07949

The amplification of astrophysical magnetic fields takes place via dynamo instability in turbulent environments. The presence of vorticity is crucial for the dynamo to happen. However, the role of vorticity is not yet fully understood. This work is an extension of previous research on the effect of an irrotational subsonic forcing on a magnetized medium in the presence of rotation or a differential velocity profile, aimed at exploring a wider parameter space in terms of Reynolds numbers, magnetic Prandtl number, forcing scale, cooling timescale in a Newtonian cooling. We study the effect of imposing either the acceleration or the velocity forcing function to be curl-free and evaluate the terms responsible for the evolution vorticity. We use Direct Numerical Simulations (DNS) to solve the fully compressible, resistive magnetohydrodynamical (MHD) equations with the Pencil Code. We study both isothermal and non-isothermal regimes and address the relative importance of different vorticity source terms.We report no small-scale dynamo for the models that do not include shear. We find a hydro instability, followed by a magnetic one, when a shearing velocity profile is applied. The vorticity production is found to be numerical in the purely irrotational case. Non-isothermality, rotation, shear or forcing in the form of a velocity curl-free, when included, contribute to increasing vorticity. Consistently with our previous study, we find that turbulence driven by subsonic expansion waves can amplify vorticity and magnetic field only in the presence of a background shearing profile. The presence of a cooling function make the instability happens on a shorter timescale. We estimate critical Reynolds and Magnetic Reynolds Numbes of 40 and 20, respectively., Comment: Submitted for publication. Comments are welcome

Neutron stars are the dense and highly magnetic relics of supernova explosions of massive stars. The quest to constrain the Equation of State (EoS) of ultra-dense matter and thereby probe the behavior of matter inside neutron stars, is one of the core goals of modern physics and astrophysics. A promising method involves investigating the long-term cooling of neutron stars, and comparing theoretical predictions with various sources at different ages. However, limited observational data, and uncertainties in source ages and distances, have hindered this approach. In this work, re-analyzing XMM-Newton and Chandra data from dozens of thermally emitting isolated neutron stars, we have identified three sources with unexpectedly cold surface temperatures for their young ages. To investigate these anomalies, we conducted magneto-thermal simulations across diverse mass and magnetic fields, considering three different EoS. We found that the "minimal" cooling model, failed to explain the observations, regardless the mass and the magnetic field, as validated by a machine learning classification method. The existence of these young cold neutron stars suggests that any dense matter EoS must be compatible with a fast cooling process at least in certain mass ranges, eliminating a significant portion of current EoS options according to recent meta-modelling analysis., Comment: 60 pages, 10 figures, 7 tables; Accepted for publication; first four authors are corresponding authors

This work presents a methodological approach to generate realistic $\gamma$-ray light curves of pulsars, resembling reasonably well the observational ones observed by the Fermi-Large Area Telescope instrument, fitting at the same time their high-energy spectra. The theoretical light curves are obtained from a spectral and geometrical model of the synchro-curvature emission. Despite our model relies on a few effective physical parameters, the synthetic light curves present the same main features observed in the observational $\gamma$-ray light curve zoo, such as the different shapes, variety in the number of peaks, and a diversity of peak widths. The morphological features of the light curves allows us to statistically compare the observed properties. In particular, we find that the proportion on the number of peaks found in our synthetic light curves is in agreement with the observational one provided by the third Fermi-LAT pulsar catalog. We also found that the detection probability due to beaming is much higher for orthogonal rotators (approaching 100%) than for small inclination angles (less than 20%).The small variation on the synthetic skymaps generated for different pulsars indicates that the geometry dominates over timing and spectral properties in shaping the gamma-ray light curves. This means that geometrical parameters like the inclination angle can be in principle constrained by gamma-ray data alone independently on the specific properties of a pulsar. At the same time, we find that $\gamma$-ray spectra seen by different observers can slightly differ, opening the door to constraining the viewing angle of a particular pulsar., Comment: 14 pages, 8 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society

The inflated radii observed in hundreds of Hot Jupiters represent a long-standing open issue. The observed correlation between radii and irradiation strength, and the occasional extreme cases, nearly double the size of Jupiter, remain without a comprehensive quantitative explanation. In this investigation, we delve into this issue within the framework of Ohmic dissipation, one of the most promising mechanisms for explaining the radius anomaly. Using the evolutionary code MESA, we simulate the evolution of irradiated giant planets, spanning the range 1 to 8 Jupiter masses, incorporating an internal source of Ohmic dissipation located beneath the radiative-convective boundary. Our modeling is based on physical parameters, and accounts for the approximated conductivity and the evolution of the magnetic fields, utilizing widely-used scaling laws. We compute the radius evolution across a spectrum of masses and equilibrium temperatures, considering varying amounts of Ohmic dissipation, calculated with the internal conductivity profile and an effective parametrization of the currents, based on the typical radius of curvature of the field lines. Our analysis reveals that this internal Ohmic dissipation can broadly reproduce the range of observed radii using values of radius of curvature up to about one order of magnitude lower than what we estimate from the Juno measurements of the Jovian magnetosphere and from MHD dynamo simulations presented herein. The observed trend with equilibrium temperature can be explained if the highly-irradiated planets have more intense and more small-scale magnetic fields. This suggests the possibility of an interplay between atmospherically induced currents and the interior, via turbulence, in agreement with recent box simulations of turbulent MHD in atmospheric columns., Comment: 13 pages, 14 figures

We evidence a family $\mathcal{X}$ of square matrices over a field $\mathbb{K}$, whose elements will be called X-matrices. We show that this family is shape invariant under multiplication as well as transposition. We show that $\mathcal{X}$ is a (in general non-commutative) subring of $GL(n,\mathbb{K})$. Moreover, we analyse the condition for a matrix $A \in \mathcal{X}$ to be invertible in $\mathcal{X}$. We also show that, if one adds a symmetry condition called here bi-symmetry, then the set $\mathcal{X}^b$ of bi-symmetric X-matrices is a commutative subring of $\mathcal{X}$. We propose results for eigenvalue inclusion, showing that for X-matrices eigenvalues lie exactly on the boundary of Cassini ovals. It is shown that any monic polynomial on $ \mathbb{R} $ can be associated with a companion matrix in $ \mathcal{X} $.

The thermal evolution of isolated neutron stars is a key element in unraveling their internal structure and composition and establishing evolutionary connections among different observational subclasses. Previous studies have predominantly focused on one-dimensional or axisymmetric two-dimensional models. In this study, we present the thermal evolution component of the novel three-dimensional magnetothermal code MATINS (MAgneto-Thermal evolution of Isolated Neutron Star). MATINS employs a finite volume scheme and integrates a realistic background structure, along with state-of-the-art microphysical calculations for the conductivities, neutrino emissivities, heat capacity, and superfluid gap models. This paper outlines the methodology employed to solve the thermal evolution equations in MATINS, along with the microphysical implementation which is essential for the thermal component. We test the accuracy of the code and present simulations with non-evolving magnetic fields of different configurations (all with electrical currents confined to the crust and a magnetic field that does not thread the core), to produce temperature maps of the neutron star surface. Additionally, for a specific magnetic field configuration, we show one fully coupled evolution of magnetic field and temperature. Subsequently, we use a ray-tracing code to link the neutron star surface temperature maps obtained by MATINS with the phase-resolved spectra and pulsed profiles that would be detected by distant observers. This study, together with our previous article focused on the magnetic formalism, presents in detail the most advanced evolutionary code for isolated neutron stars, with the aim of comparison with their timing properties, thermal luminosities and the associated X-ray light curves., Comment: 26 pages, 16 figures; published in MNRAS

Mutation testing can help reduce the risks of releasing faulty software. For such reason, it is a desired practice for the development of embedded software running in safety-critical cyber-physical systems (CPS). Unfortunately, state-of-the-art test data generation techniques for mutation testing of C and C++ software, two typical languages for CPS software, rely on symbolic execution, whose limitations often prevent its application (e.g., it cannot test black-box components). We propose a mutation testing approach that leverages fuzz testing, which has proved effective with C and C++ software. Fuzz testing automatically generates diverse test inputs that exercise program branches in a varied number of ways and, therefore, exercise statements in different program states, thus maximizing the likelihood of killing mutants, our objective. We performed an empirical assessment of our approach with software components used in satellite systems currently in orbit. Our empirical evaluation shows that mutation testing based on fuzz testing kills a significantly higher proportion of live mutants than symbolic execution (i.e., up to an additional 47 percentage points). Further, when symbolic execution cannot be applied, fuzz testing provides significant benefits (i.e., up to 41% mutants killed). Our study is the first one comparing fuzz testing and symbolic execution for mutation testing; our results provide guidance towards the development of fuzz testing tools dedicated to mutation testing., Comment: This article is the camera-ready version for ASE 2023

We perform a long and accurate Large-Eddy Simulation of a binary neutron star merger, following the newly formed remnant up to 110 milliseconds. The combination of high-order schemes, high-resolution and the gradient subgrid-scale model allow us to have among the highest effective resolutions ever achieved. Our results show that, although the magnetic fields are strongly amplified by the Kelvin-Helmholtz instability, they are coherent only over very short spatial scales until t \gtrsim 30 ms. Around that time, magnetic winding becomes more efficient leading to a linear growth of the toroidal component and slowly ordering the field to more axisymmetric, large scales. The poloidal component only starts to grow at small scales at much later times t \gtrsim 90 ms, in a way compatible with the magneto-rotational instability. No strong large-scale poloidal field or jet is produced in the timescales spanned by our simulation, although there is an helicoidal structure gradually developing at late times. We highlight that soon after the merger the topology is always strongly dominated by toroidal structures, with a complex distribution in the meridional plane and highly turbulent perturbations. Thus, starting with strong purely dipolar fields before the merger is largely inconsistent with the outcomes of a realistic evolution. Finally, we confirm the universality of the evolved topology, even when starting with very different magnetic fields confined to the outermost layers of each neutron star., Comment: 18 pages, 14 figures. arXiv admin note: text overlap with arXiv:2112.08413

X-ray Fluorescence Ghost Imaging (XRF-GI) was recently demonstrated for x-ray lab sources. It has the potential to reduce acquisition time and deposited dose by choosing their trade-off with spatial resolution, while alleviating the focusing constraints of the probing beam. Here, we demonstrate the realization of synchrotron-based XRF-GI: We present both an adapted experimental setup and its corresponding required computational technique to process the data. This extends the above-mentioned potential advantages of GI to synchrotron XRF imaging. In addition, it enables new strategies to improve resilience against drifts at all scales, and the study of previously inaccessible samples, such as liquids., Comment: 4 pages, 5 figures

In this paper, we construct exact rotating wormholes using Ehlers solution-generating technique. This is based on the Ernst description of four-dimensional, stationary, and axially symmetric solutions of the Einstein-Maxwell theory. We adopt the static Barcel\'o-Visser wormhole derived from the Einstein-Maxwell-conformal-scalar theory as a seed, and demonstrate, through the Ernst approach, how to construct two novel geometries of rotating wormholes. These geometries correspond to the Barcel\'o-Visser wormhole embedded within a rotating and a magnetic background, respectively. In the first case, the rotation is a result of a dragging force (due to the rotating background) acting on the initial static wormhole, while in the second case it is caused by the electromagnetic interaction between the electric charge of the static wormhole and the external magnetic field. We conduct a comprehensive analysis of the geometric properties of these configurations, and examine the new features introduced by rotation, such as the emergence of ergoregions. Recent evidence suggests that incorporating slow rotation can stabilise wormholes, rendering these exact, fully rotating solutions particularly appealing., Comment: Paper accepted by PRD on July 15. V3 matches published version

Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the other with powers of cyclic groups. We determine various combinatorial properties of these graphs through the spectral analysis of their adjacency matrices. In the case of symmetric groups, we establish a relation between the multiplicity of the null eigenvalue and longest increasing sub-sequences of permutations by means of the RSK correspondence. Finally, we consider dynamical arrangements of finitely many elements in finite spaces, which we refer to as particle-box systems. We apply the results obtained on binomial Cayley graphs in order to describe their degeneracy., Comment: 26 pages, 12 figures

We present the first 3D fully coupled magneto-thermal simulations of neutron stars (including the most realistic background structure and microphysical ingredients so far) applied to a very complex initial magnetic field topology in the crust, similar to what recently obtained by proto-neutron star dynamo simulations. In such configurations, most of the energy is stored in the toroidal field, while the dipolar component is a few percent of the mean magnetic field. This initial feature is maintained during the long-term evolution (1e6 yr), since the Hall term favours a direct cascade (compensating for Ohmic dissipation) rather than a strong inverse cascade, for such an initial field topology. The surface dipolar component, responsible for the dominant electromagnetic spin-down torque, does not show any increase in time, when starting from this complex initial topology. This is at contrast with the timing properties of young pulsars and magnetars which point to higher values of the surface dipolar fields. A possibility is that the deep-seated magnetic field (currents in the core) is able to self-organize in large scales (during the collapse or in the early life of a neutron star). Alternatively, the dipolar field might be lower than is usually thought, with magnetosphere substantially contributing to the observed high spin-down, via e.g., strong winds or strong coronal magnetic loops, which can also provide a natural explanation to the tiny surface hotspots inferred from X-ray data., Comment: 8 pages, 6 figures, submitted for publication in MNRAS, comments are welcome

This work concentrates on the effect of an irrotational forcing on a magnetized flow in the presence of rotation, baroclinicity, shear, or a combination of them. By including magnetic field in the model we can evaluate the occurrence of dynamo on both small and large scales. We aim at finding what are the minimum ingredients needed to trigger a dynamo instability and what is the relation between dynamo and the growth of vorticity. We use the Pencil code to run resistive MHD direct numerical simulations. We report no dynamo in all cases where only rotation is included, regardless on the equation of state. Conversely, the inclusion of a background sinusoidal shearing profile leads to an hydrodynamic instability that produces an exponential growth of the vorticity at all scales, starting from small ones. This is know as vorticity dynamo. The onset of this instability occurs after a rather long temporal evolution of several thousand turbulent turnover times. The vorticity dynamo in turn drives an exponential growth of the magnetic field, first at small scales, then also at large one. The instability then saturates and the magnetic field approximately reaches equipartition with the turbulent kinetic energy. During the saturation phase we can observe a winding of the magnetic field in the direction of the shearing flow. By varying the intensity of the shear we see that the growth rates of this instability change. The inclusion of the baroclinic term delays the onset of the vorticity dynamo but leads to a more rapid growth. We demonstrate how in the presence of shear, even a purely irrotational forcing amplifies the field to equipartition. At the same time, we confirm how this forcing alone does not lead to vorticity nor magnetic field growth, and this picture does not change in the presence of rotation or baroclinicity up to $256^3$ meshpoints., Comment: 14 pages, 8 figures, submitted for publication, comments welcome

While magnetism in exoplanets remains largely unknown, Hot Jupiters have been considered as natural candidates to harbour intense magnetic fields, both due to their large masses and their high energy budgets coming from irradiation as a consequence of their vicinity to their host stars. In this work we perform MHD simulations of a narrow day-side atmospheric column of ultra-hot Jupiters, suitable for very high local temperatures (T > 3000 K). Since the conductivity in this regime is very high, the dominant effect is winding due to the intense zonal winds. By including a forcing that mimics the wind profiles obtained in global circulation models, the shear layer induces a strong toroidal magnetic field (locally reaching hundreds of gauss), supported by meridional currents. Such fields and the sustaining currents don$'$t depend on the internally generated field, but are all confined in the thin (less than a scale-height) shear layer around 1 bar. Additionally, we add random perturbations that induce turbulent motions, which lead to further (but much smaller) magnetic field generation to a broader range of depths. These results allow an evaluation of the currents induced by the atmospheric dynamo. Although here we use ideal MHD and the only resistivity comes from the numerical scheme, we estimate a-posteriori the amount of Ohmic heat deposited in the outer layers, which could be employed in evolutionary models for Hot Jupiters' inflated radii., Comment: Accepted for publication in MNRAS

Detecting a planetary companion in a short-period orbit through radio emission from the interaction with its host star is a new prospect in exoplanet science. Recently, a tantalising signal was found close to the low-mass stellar system GJ 1151 using LOFAR observations. We studied spectroscopic time-series data of GJ 1151 in order to search for planetary companions, investigate possible signatures of stellar magnetic activity, and to find possible explanations for the radio signal. We used the combined radial velocities measured from spectra acquired with the CARMENES, HARPS-N, and HPF instruments, extracted activity indices from those spectra in order to mitigate the impact of stellar magnetic activity on the data, and performed a detailed analysis of Gaia astrometry and all available photometric time series coming from the MEarth and ASAS-SN surveys. We found a M$>$10.6 M$_{\oplus}$ companion to GJ 1151 in a 390d orbit at a separation of 0.57 au. Evidence for a second modulation is also present; this could be due to long-term magnetic variability or a second (substellar) companion. The star shows episodes of elevated magnetic activity, one of which could be linked to the observed LOFAR radio emission. We show that it is highly unlikely that the detected GJ 1151 b, or any additional outer companion is the source of the detected signal. We cannot firmly rule out the suggested explanation of an undetected short-period planet that could be related to the radio emission, as we establish an upper limit of 1.2 M$_{\oplus}$ for the minimum mass., Comment: 18 pages, 11 figures. Accepted version, A&A (2023)

Neutron stars cool down during their lifetime through the combination of neutrino emission from the interior and photon cooling from the surface. Strongly magnetised neutron stars, called magnetars, are no exception, but the effect of their strong fields adds further complexities to the cooling theory. Besides other factors, modelling the outermost hundred meters (the envelope) plays a crucial role in predicting their surface temperatures. In this letter, we revisit the influence of envelopes on the cooling properties of neutron stars, with special focus on the critical effects of the magnetic field. We explore how our understanding of the relation between the internal and surface temperatures has evolved over the past two decades, and how different assumptions about the neutron star envelope and field topology lead to radically different conclusions on the surface temperature and its cooling with age. In particular, we find that relatively old magnetars with core-threading magnetic fields are actually much cooler than a rotation-powered pulsar of the same age. This is at variance with what is typically observed in crustal-confined models. Our results have important implications for the estimates of the X-ray luminosities of aged magnetars, and the subsequent population study of the different neutron star classes., Comment: 5 pages, 4 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society

Multi-black hole solutions play a relevant role both from the theoretical and the phenomenological point of view. In this Thesis, we construct some regular multi-black hole spacetimes in pure Einstein's General Relativity with the aid of solution generating techniques. We begin with a perspective on the history of solution generating techniques, and then we explain in detail the Ernst formalism and the inverse scattering method. These are the techniques that are applied in the rest of the Thesis. Subsequently, we construct multi-black hole solutions embedded in an external gravitational field: it is possible to obtain an equilibrium configuration in many interesting cases, like a collection of collinear static black holes or a chain of accelerating black holes, by choosing appropriately the multipole parameters of the field. Then, we consider the expanding bubbles of nothing as a background for multi-black hole and black ring solutions. The expanding behaviour of the bubbles provides the force necessary to balance the gravitational attraction among the black holes, and hence to reach the equilibrium. Finally, we construct a solution that represents a black hole embedded in a "swirling" universe, which describes a spacetime whirlpool. Moreover, we discuss the possibility of implementing the swirling background in order to enforce the spin-spin configuration, and reach an equilibrium configuration in a double-Kerr spacetime., Comment: Ph.D. thesis (defended 25/10/2022, University of Milan). 158 pages, 26 figures. Based on arXiv:2104.07686, arXiv:2105.02894, arXiv:2106.02058, arXiv:2204.09690, arXiv:2205.13548

We observed the periodic radio transient GLEAM-X J162759.5-523504.3 (GLEAM-X J1627) using the Chandra X-ray Observatory for about 30-ks on January 22-23, 2022, simultaneously with radio observations from MWA, MeerKAT and ATCA. Its radio emission and 18-min periodicity led the source to be tentatively interpreted as an extreme magnetar or a peculiar highly magnetic white dwarf. The source was not detected in the 0.3-8 keV energy range with a 3-sigma upper-limit on the count rate of 3x10^{-4} counts/s. No radio emission was detected during our X-ray observations either. Furthermore, we studied the field around GLEAM-X J1627 using archival ESO and DECam data, as well as recent SALT observations. Many sources are present close to the position of GLEAM-X J1627, but only two within the 2" radio position uncertainty. Depending on the assumed spectral distribution, the upper limits converted to an X-ray luminosity of L_{X}<6.5x10^{29} erg/s for a blackbody with temperature kT=0.3 keV, or L_{X}<9x10^{29} erg/s for a power-law with photon index Gamma = 2 (assuming a 1.3 kpc distance). Furthermore, we performed magneto-thermal simulations for neutron stars considering crust- and core-dominated field configurations. Based on our multi-band limits, we conclude that: i) in the magnetar scenario, the X-ray upper limits suggest that GLEAM-X J1627 should be older than ~1 Myr, unless it has a core-dominated magnetic field or has experienced fast-cooling; ii) in the white dwarf scenario, we can rule out most binary systems, a hot sub-dwarf and a hot magnetic isolated white dwarf (T>10.000 K), while a cold isolated white dwarf is still compatible with our limits., Comment: 17 pages, 9 figures; ApJ accepted

For any complex K3 surface $X$, we construct a one-dimensional deformation in which all integers $\rho$ with $0 \leq \rho \leq 20$ occur as Picard numbers of some fibres. In contrast, we prove that the generic one-dimensional local family of K3 surfaces admits only $0$ and $1$ as Picard numbers of the fibres., Comment: 10 pages, 4 figures

The long-term evolution of the internal, strong magnetic fields of neutron stars needs a specific numerical modelling. The diversity of the observed phenomenology of neutron stars indicates that their magnetic topology is rather complex and three-dimensional simulations are required, for example, to explain the observed bursting mechanisms and the creation of surface hotspots. We present MATINS, a new three dimensions numerical code for magneto-thermal evolution in neutron stars, based on a finite-volume scheme that employs the cubed-sphere system of coordinates. In this first work, we focus on the crustal magnetic evolution, with the inclusion of realistic calculations for the neutron star structure, composition and electrical conductivity assuming a simple temperature evolution profile. MATINS follows the evolution of strong fields (1e14-1e15 Gauss) with complex non-axisymmetric topologies and dominant Hall-drift terms, and it is suitable for handling sharp current sheets. After introducing the technical description of our approach and some tests, we present long-term simulations of the non-linear field evolution in realistic neutron star crusts. The results show how the non-axisymmetric Hall cascade redistributes the energy over different spatial scales. Following the exploration of different initial topologies, we conclude that during a few tens of kyr, an equipartition of energy between the poloidal and toroidal components happens at small-scales. However, the magnetic field keeps a strong memory of the initial large-scales, which are much harder to be restructured or created. This indicates that large-scale configuration attained during the neutron star formation is crucial to determine the field topology at any evolution stage., Comment: 21 pages, 17 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society

Several important properties of rotation-powered millisecond pulsars (MSPs), such as their mass-radius ratio, equation of state and magnetic field topology, can be inferred from precise observations and modelling of their X-ray light curves. In the present study, we model the thermal X-ray signals originated in MSPs, all the way from numerically solving the surrounding magnetospheres up to the ray tracing of the emitted photons and the final computation of their light curves and spectra. Our modelled X-ray signals are then compared against a set of very accurate NICER observations of four target pulsars: PSR J0437-4715, PSR J1231-1411, PSR J2124-3358 and PSR J0030+0451. We find very good simultaneous fits for the light curve and spectral distribution in all these pulsars. The magnetosphere is solved by performing general relativistic force-free simulations of a rotating neutron star (NS) endowed with a simple centered dipolar magnetic field, for many different stellar compactness and pulsar misalignments. From these solutions, we derive an emissivity map over the surface of the star, which is based on the electric currents in the magnetosphere. In particular, the emission regions (ERs) are determined in this model by spacelike four-currents that reach the NS. We show that this assumption, together with the inclusion of the gravitational curvature on the force-free simulations, lead to non-standard ERs facing the closed-zone of the pulsar, in addition to other ERs within the polar caps. The combined X-ray signals from these two kinds of ERs (both antipodal) allow to approximate the non-trivial interpulses found in all the target MSPs light curves., Comment: 16 pages, 9 figures

The detected high-energy pulsars' population is growing in number, and thus, having agile and physically relevant codes to analyze it consistently is important. Here, we update our existing synchro-curvature radiation model by including a better treatment of the particle injection, particularly where the large pitch angle particles dominate the spectra, and by implementing a fast and accurate minimization technique. The latter allows a large improvement in computational cost, needed to test model enhancements and to apply the model to a larger pulsar population. We successfully fit the sample of pulsars with X-ray and $\gamma$-ray data. Our results indicate that, for every emitting particle, the spatial extent of their trajectory where the pitch angle is large and most of the detected X-ray radiation is produced is a small fraction of the light cylinder. We also confirm with this new approach that synchrotron radiation is not negligible for most of the gamma-ray pulsars detected. In addition, with the results obtained, we argue that J0357+3205 and J2055+2539 are MeV-pulsar candidates and are suggested for exhaustive observations in this energy band., Comment: 12 pages, 7 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society

In a decentralized environment, exchanging resources requires users to bargain until an agreement is found. Moreover, human agreements involve a combination of collaborative and selfish behavior and often induce circularity, complicating the evaluation of exchange requests. We introduce MuAC, a policy language that allows users to state in isolation under which conditions they are open to grant their resources and what they require in return. In MuAC, exchange requests are evaluated automatically with the guarantee that the only exchanges that will take place are those that mutually satisfy users' conditions. Moreover, MuAC can be used as an enforcement mechanism to prevent users from cheating. As a proof of concept, we implement a blockchain smart contract that allows users to exchange their non-fungible tokens.

The period and the period derivative of a pulsar are critical magnitudes for defining the properties of the magnetospheric size and plasma dynamics. The pulsar light cylinder, the magnetic field intensity nearby it, and the curvature radius all depend on these timing properties, and shape the observed high-energy synchro-curvature emission. Therefore, the radiative properties of pulsars are inextricably linked to them. This fact poses the question of how well does a given pulsar's spectral energy distribution embeds information of the timing parameters, and if so, whether we can deduce them if they have not been measured directly. This is relevant to possibly constrain the timing properties of potential pulsar candidates among unidentified $\gamma$-ray sources. We consider well-measured pulsar spectra blinding us from the knowledge of their timing properties, and address this question by using our radiative synchro-curvature model that was proven able to fit the observed spectra of the pulsar population. We find that in the majority of the cases studied (8/13), the spin period is constrained within a range of about one order of magnitude, within which the real period lies. In the other cases, there is degeneracy and no period range can be constrained. This can be used to facilitate the blind search of pulsed signals., Comment: 8 pages, 4 figures. Accepted for publication in The Astrophysical Journal

In prediction-based decision-making systems, different perspectives can be at odds: The short-term business goals of the decision makers are often in conflict with the decision subjects' wish to be treated fairly. Balancing these two perspectives is a question of values. However, these values are often hidden in the technicalities of the implementation of the decision-making system. In this paper, we propose a framework to make these value-laden choices clearly visible. We focus on a setting in which we want to find decision rules that balance the perspective of the decision maker and of the decision subjects. We provide an approach to formalize both perspectives, i.e., to assess the utility of the decision maker and the fairness towards the decision subjects. In both cases, the idea is to elicit values from decision makers and decision subjects that are then turned into something measurable. For the fairness evaluation, we build on well-known theories of distributive justice and on the algorithmic literature to ask what a fair distribution of utility (or welfare) looks like. This allows us to derive a fairness score that we then compare to the decision maker's utility. As we focus on a setting in which we are given a trained model and have to choose a decision rule, we use the concept of Pareto efficiency to compare decision rules. Our proposed framework can both guide the implementation of a decision-making system and help with audits, as it allows us to resurface the values implemented in a decision-making system.

The dissipation of intense crustal electric currents produces high Joule heating rates in cooling neutron stars. Here it is shown that Joule heating can counterbalance fast cooling, making it difficult to infer the presence of hyperons (which accelerate cooling) from measurements of the observed thermal luminosity $L_\gamma$. Models with and without hyperon cores match $L_{\gamma}$ of young magnetars (with poloidal-dipolar field $B_{\textrm{dip}} \gtrsim 10^{14}$ G at the polar surface and $L_{\gamma} \gtrsim 10^{34}$ erg s$^{-1}$ at $t \lesssim 10^5$ yr) as well as mature, moderately magnetized stars (with $B_{\textrm{dip}} \lesssim 10^{14}$ G and $10^{31} \ \textrm{erg s}^{-1} \lesssim L_{\gamma} \lesssim 10^{32}$ erg s$^{-1}$ at $t \gtrsim 10^5$ yr). In magnetars, the crustal temperature is almost independent of hyperon direct Urca cooling in the core, regardless of whether the latter is suppressed or not by hyperon superfluidity. The thermal luminosities of light magnetars without hyperons and heavy magnetars with hyperons have $L_{\gamma}$ in the same range and are almost indistinguishable. Likewise, $L_{\gamma}$ data of neutron stars with $B_{\textrm{dip}} \lesssim 10^{14}$ G but with strong internal fields are not suitable to extract information about the equation of state as long as hyperons are superfluid, with maximum amplitude of the energy gaps of the order $\approx 1$ MeV., Comment: 15 pages, 8 figures, 2 tables. Accepted for publication in MNRAS

We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst equations for stationary and axisymmetric spacetimes. This kind of the Ehlers transformation is able to embed any given solution into a rotating background, which is not of NUT type. We analyse the physical properties, ergoregions and geodesics of the new metric, which is regular outside the event horizon and has a well defined thermodynamics. We finally consider the Kerr generalisation., Comment: v4: 22 pages, 11 figures, updated pictures about geodesic motion

Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research. Recent works on mesh processing have concentrated on various kinds of natural symmetries, including translations, rotations, scaling, node permutations, and gauge transformations. To date, no existing architecture is equivariant to all of these transformations. In this paper, we present an attention-based architecture for mesh data that is provably equivariant to all transformations mentioned above. Our pipeline relies on the use of relative tangential features: a simple, effective, equivariance-friendly alternative to raw node positions as inputs. Experiments on the FAUST and TOSCA datasets confirm that our proposed architecture achieves improved performance on these benchmarks and is indeed equivariant, and therefore robust, to a wide variety of local/global transformations., Comment: Published in Transactions on Machine Learning Research (08/2022). Official code made available at https://github.com/gallego-posada/eman - For the OpenReview entry, see https://openreview.net/forum?id=3IqqJh2Ycy

A recent paper (Hedden 2021) has argued that most of the group fairness constraints discussed in the machine learning literature are not necessary conditions for the fairness of predictions, and hence that there are no genuine fairness metrics. This is proven by discussing a special case of a fair prediction. In our paper, we show that Hedden 's argument does not hold for the most common kind of predictions used in data science, which are about people and based on data from similar people; we call these human-group-based practices. We argue that there is a morally salient distinction between human-group-based practices and those that are based on data of only one person, which we call human-individual-based practices. Thus, what may be a necessary condition for the fairness of human-group-based practices may not be a necessary condition for the fairness of human-individual-based practices, on which Hedden 's argument is based. Accordingly, the group fairness metrics discussed in the machine learning literature may still be relevant for most applications of prediction-based decision making.

We argue that expanding bubbles of nothing are a widespread feature of systems of black holes with multiple or non-spherical horizons, appearing as a limit of regions that are narrowly enclosed by the horizons. The bubble is a minimal cycle that links the Einstein-Rosen bridges in the system, and its expansion occurs through the familiar stretching of space in black hole interiors. We demonstrate this idea (which does not involve any Wick rotations) with explicit constructions in four and five dimensions. The geometries of expanding bubbles in these dimensions arise as a limit of, respectively, static black hole binaries and black rings. The limit is such that the separation between the two black holes, or the inner hole of the black ring, becomes very small, and the horizons of the black holes correspond to acceleration horizons of the bubbles. We also explain how a five-dimensional black hole binary gives rise to a different type of expanding bubble. We then show that bubble spacetimes can host black hole binaries and black rings in static equilibrium, with their gravitational attraction being balanced against the background spacetime expansion. Similar constructions are expected in six or more dimensions, but most of these solutions can be obtained only numerically. Finally, we argue that the Nariai solution can be regarded as containing an expanding circular bubble of nothing., Comment: 23 pages, 11 figures. v2: minor changes (incl in the title); added discussion on Nariai solution as a bubble of nothing. v3: matches published version

We present a new family of exact four-dimensional Taub-NUT spacetimes in Einstein-$\Lambda$ theory supplemented with a conformally coupled scalar field exhibiting a power-counting super-renormalizable potential. The construction proceeds as follows: A solution of a conformally coupled theory with a conformal potential, henceforth the seed $(g_{\mu\nu},\phi)$, is transformed by the action of a specific change of frame in addition with a simultaneous shift of the seed scalar. The new configuration, $(\bar{g}_{\mu\nu},\bar{\phi})$, solves the field equations of a conformally coupled theory with the aforementioned super-renormalizable potential. The solution spectrum of the seed is notoriously enhanced. We highlight the existence of two types of exact black bounces given by de Sitter and anti-de Sitter geometries that transit across three different configurations each. The de Sitter geometries transit from a regular black hole with event and cosmological horizons to a bouncing cosmology connecting two de Sitter Universes with different values of the asymptotic cosmological constant. An intermediate phase represented by a de Sitter wormhole or by a bouncing cosmology that connects two de Sitter Universes is shown, this under the presence of a cosmological horizon. On the other hand, the anti-de Sitter geometries transit from a regular black hole with inner and event horizons to a wormhole that connects two asymptotic boundaries with different constant curvatures. The intermediate phase is given by an anti-de Sitter regular black hole with a single event horizon that appears in two different settings. As a regular anti-de Sitter black hole inside of an anti-de Sitter wormhole or as an anti-de Sitter regular black hole with an internal cosmological bounce. These geometries are smoothly connected by the mass parameter only. Other black holes, bouncing cosmologies and wormholes are also found., Comment: Published PRD version

Cyber-physical systems (CPSs) typically consist of a wide set of integrated, heterogeneous components; consequently, most of their critical failures relate to the interoperability of such components.Unfortunately, most CPS test automation techniques are preliminary and industry still heavily relies on manual testing. With potentially incomplete, manually-generated test suites, it is of paramount importance to assess their quality. Though mutation analysis has demonstrated to be an effective means to assess test suite quality in some specific contexts, we lack approaches for CPSs. Indeed, existing approaches do not target interoperability problems and cannot be executed in the presence of black-box or simulated components, a typical situation with CPSs. In this paper, we introduce data-driven mutation analysis, an approach that consists in assessing test suite quality by verifying if it detects interoperability faults simulated by mutating the data exchanged by software components. To this end, we describe a data-driven mutation analysis technique (DaMAT) that automatically alters the data exchanged through data buffers. Our technique is driven by fault models in tabular form where engineers specify how to mutate data items by selecting and configuring a set of mutation operators. We have evaluated DaMAT with CPSs in the space domain; specifically, the test suites for the software systems of a microsatellite and nanosatellites launched on orbit last year. Our results show that the approach effectively detects test suite shortcomings, is not affected by equivalent and redundant mutants, and entails acceptable costs., Comment: 19 pages

Magnetic fields are expected to play a key role in the dynamics and the ejection mechanisms that accompany the merger of two neutron stars. General relativistic magnetohydrodynamic (MHD) simulations offer a unique opportunity to unravel the details of the ongoing physical processes. Nevertheless, current numerical studies are severely limited by the fact that any affordable resolution remains insufficient to fully capture the small-scale dynamo, initially triggered by the Kelvin-Helmholtz instability, and later sourced by several MHD processes involving differential rotation. Here, we alleviate this limitation by using explicit large-eddy simulations, a technique where the unresolved dynamics occurring at the sub-grid scales (SGS) is modeled by extra terms, which are functions of the resolved fields and their derivatives. The combination of high-order numerical schemes, high resolutions, and the gradient SGS model allow us to capture the small-scale dynamos produced during the binary neutron star mergers. Here we follow the first 50 milliseconds after the merger and, for the first time, we find numerical convergence on the magnetic field amplification, in terms of integrated energy and spectral distribution over spatial scales. We also find that the average intensity of the magnetic field in the remnant saturates at $\sim 10^{16}$~G around $5$~ms after the merger. After $20-30$~ms, both toroidal and poloidal magnetic field components grow continuously, fed by the winding mechanism that provides a slow inverse cascade. We find no clear hints for magneto-rotational instabilities, and no significant impact of the magnetic field on the redistribution of angular momentum in the remnant in our simulations, probably due to the very turbulent and dynamical topology of the magnetic field at all stages, with small-scale components largely dominating over the large-scale ones., Comment: 22 pages, 17 figures, version matching the published article

The detection of a binary neutron star merger in 2017 through both gravitational waves and electromagnetic emission opened a new era of multimessenger astronomy. The understanding of the magnetic field amplification triggered by the Kelvin-Helmholtz instability during the merger is still a numerically unresolved problem because of the relevant small scales involved. One of the uncertainties comes from the simplifications usually assumed in the initial magnetic topology of merging neutron stars. We perform high-resolution, convergent large-eddy simulations of binary neutron star mergers, following the newly formed remnant for up to $30$ milliseconds. Here we specifically focus on the comparison between simulations with different initial magnetic configurations, going beyond the widespread-used aligned dipole confined within each star. The results obtained show that the initial topology is quickly forgotten, in a timescale of few miliseconds after the merger. Moreover, at the end of the simulations, the average intensity ($B\sim 10^{16}$ G) and the spectral distribution of magnetic energy over spatial scales barely depend on the initial configuration. This is expected due to the small-scale efficient dynamo involved, and thus it holds as long as: (i) the initial large-scale magnetic field is not unrealistically high (as often imposed in mergers studies); (ii) the turbulent instability is numerically (at least partially) resolved, so that the amplified magnetic energy is distributed across a wide range of scales and becomes orders-of-magnitude larger than the initial one., Comment: 8 pages, 5 figures

Neutron star models with maximum mass close to $2 \ M_{\odot}$ reach high central densities, which may activate nucleonic and hyperon direct Urca neutrino emission. To alleviate the tension between fast theoretical cooling rates and thermal luminosity observations of moderately magnetized, isolated thermally-emitting stars (with $L_{\gamma} \gtrsim 10^{31}$ erg s$^{-1}$ at $t \gtrsim 10^{5.3}$ yr), some internal heating source is required. The power supplied by the internal heater is estimated for both a phenomenological source in the inner crust and Joule heating due to magnetic field decay, assuming different superfluidity models and compositions of the outer stellar envelope. It is found that a thermal power of $W(t) \approx 10^{34}$ erg s$^{-1}$ allows neutron star models to match observations of moderately magnetized, isolated stars with ages $t \gtrsim 10^{5.3}$ yr. The requisite $W(t)$ can be supplied by Joule heating due to crust-confined initial magnetic configurations with (i) mixed poloidal-toroidal fields, with surface strength $B_{\textrm{dip}} = 10^{13}$ G at the pole of the dipolar poloidal component and $\sim 90$ per cent of the magnetic energy stored in the toroidal component; and (ii) poloidal-only configurations with $B_{\textrm{dip}} = 10^{14}$ G., Comment: 15 pages, 9 figures. Accepted for publication in MNRAS

In this paper we discuss the design, manufacturing and characterization of the feed horn array of the Strip instrument of the Large Scale Polarization Explorer (LSPE) experiment. Strip is a microwave telescope, operating in the Q- and W-band, for the observation of the polarized emissions from the sky in a large fraction (about 37%) of the Northern hemisphere with subdegree angular resolution. The Strip focal plane is populated by forty-nine Q-band and six W-band corrugated horns, each feeding a cryogenically cooled polarimeter for the detection of the Stokes $Q$ and $U$ components of the polarized signal from the sky. The Q-band channel is designed to accurately monitor Galactic polarized synchrotron emission, while the combination of Q- and W-band will allow the study of atmospheric effects at the observation site, the Observatorio del Teide, in Tenerife. In this paper we focus on the development of the Strip corrugated feed horns, including design requirements, engineering and manufacturing, as well as detailed characterization and performance verification., Comment: Version 1: This paper (28 pages, 25 figures) is part of the Special Issue "The LSPE/Strip instrument description and testing", being submitted to JINST. Version 2: Added new references. Splitting of design and specifications tables in Sec. 2.1. Other minor revisions included

An analytical metric of four-dimensional General Relativity, representing an array of collinear and accelerating black holes, is constructed with the inverse scattering method. The solution can be completely regularised from any conical singularity, thanks to the presence of an external gravitational field. Therefore the multi-black hole configuration can be maintained at equilibrium without the need of string or struts. Some notable subcases such as the accelerating distorted Schwarzschild black hole and the double distorted C-metric are explicitly presented. The Smarr law and the thermodynamics of these systems is studied. The Bonnor-Swaminarayan and the Bi\v{c}\'ak-Hoenselaers-Schmidt particle metrics are recovered, through appropriate limits, from the multi-black holes solutions., Comment: 19 pages, 5 figures. v2: minor corrections, references added