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We present a series of five new broadband X-ray observations of the ultraluminous X-ray source Holmberg IX X-1, performed by $XMM$-$Newton$ and $NuSTAR$ in coordination. The first three of these show high soft X-ray fluxes but a near total collapse of the high-energy ($\gtrsim$15 keV) emission, previously seen to be surprisingly stable across all prior broadband observations of the source. The latter two show a recovery in hard X-rays, remarkably once again respecting the same stable high-energy flux exhibited by all of the archival observations. We also present a joint analysis of all broadband observations of Holmberg IX X-1 to date (encompassing 11 epochs in total) in order to investigate whether it shows the same luminosity-temperature behaviour as NGC 1313 X-1 (which also shows a stable high-energy flux), whereby the hotter disc component in the spectrum exhibits two distinct, positively-correlated tracks in the luminosity-temperature plane. Holmberg IX X-1 may show similar behaviour, but the results depend on whether the highest energy emission is assumed to be an up-scattering corona or an accretion column. The strongest evidence for this behaviour is found in the former case, while in the latter the new 'soft' epochs appear distinct from the other high-flux epochs. We discuss possible explanations for these new 'soft' spectra in the context of the expected structure of super-Eddington accretion flows around black holes and neutron stars, and highlight a potentially interesting analogy with the recent destruction and re-creation of the corona seen in the AGN 1ES 1927+654., Comment: 15 pages, 5 figures, submitted for publication in MNRAS (comments welcome)

X-ray reverberation mapping is a powerful technique for probing the innermost accretion disk, whereas continuum reverberation mapping in the UV, optical, and infrared (UVOIR) reveals reprocessing by the rest of the accretion disk and broad-line region (BLR). We present the time lags of Mrk 817 as a function of temporal frequency measured from 14 months of high-cadence monitoring from Swift and ground-based telescopes, in addition to an XMM-Newton observation, as part of the AGN STORM 2 campaign. The XMM-Newton lags reveal the first detection of a soft lag in this source, consistent with reverberation from the innermost accretion flow. These results mark the first simultaneous measurement of X-ray reverberation and UVOIR disk reprocessing lags$\unicode{x2013}$effectively allowing us to map the entire accretion disk surrounding the black hole. Similar to previous continuum reverberation mapping campaigns, the UVOIR time lags arising at low temporal frequencies are longer than those expected from standard disk reprocessing by a factor of 2-3. The lags agree with the anticipated disk reverberation lags when isolating short-timescale variability, namely timescales shorter than the H$\beta$ lag. Modeling the lags requires additional reprocessing constrained at a radius consistent with the BLR size scale inferred from contemporaneous H$\beta$-lag measurements. When we divide the campaign light curves, the UVOIR lags show substantial variations, with longer lags measured when obscuration from an ionized outflow is greatest. We suggest that, when the obscurer is strongest, reprocessing by the BLR elongates the lags most significantly. As the wind weakens, the lags are dominated by shorter accretion disk lags., Comment: 28 pages, 11 figures, 3 tables. Accepted for publication in the Astrophysical Journal

Quasi-periodic eruptions (QPEs) are an extreme X-ray variability phenomenon associated with low-mass supermassive black holes. First discovered in the nucleus of the galaxy GSN 069, they have been so far securely detected in five other galaxies, including RX J1301.9+2747. When detected, the out-of-QPE emission (quiescence) is consistent with the high-energy tail of thermal emission from an accretion disk. We present the X-ray and radio properties of RX J1301.9+2747, both in quiescence and during QPEs. We analyse X-ray data taken during five XMM-Newton observations between 2000 and 2022. The last three observations were taken in coordination with radio observations with the Karl G. Jansky Very Large Array. We also make use of EXOSAT, ROSAT, and Chandra archival observations taken between 1983 and 2009. XMM-Newton detected 34 QPEs of which 8 have significantly lower amplitudes than the others. No correlated radio/X-ray variability was observed during QPEs. In terms of timing properties, the QPEs in RX J1301.9+2747 do not exhibit the striking regularity observed in the discovery source GSN 069. In fact there is no clear repetition pattern between QPEs: the average time separation between their peaks is about four hours, but it can be as short as one, and as long as six hours. The QPE spectral properties of RX J1301.9+2747 as a function of energy are however very similar to those of GSN 069 and of other QPE sources. The quiescent emission of RX J1301.9+2747 is more complex than that of GSN 069, as it requires a soft X-ray excess-like component in addition to the thermal emission from the accretion disk. Its long-term X-ray quiescent flux variations are of low-amplitude and not strictly monotonic, with a general decay over $\sim 22$ years. We discuss our observational results in terms of some of the ideas and models that have been proposed so far for the physical origin of QPEs., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages and 17 figures in the main text; 11 pages, 5 tables, and 4 figures in the Appendix. Abstract shortened to comply with arXiv requirements

'Bare' active galactic nuclei (AGN) are a subclass of Type 1 AGN that show little or no intrinsic absorption. They offer an unobscured view of the central regions of the AGN and therefore serve as ideal targets to study the relativistic reflection features originating from the innermost regions of the accretion disc. We present a detailed broadband spectral analysis ($0.3 - 70$ keV) of one of the most luminous bare AGN in the local universe, RBS 1124 ($z= 0.208$) using a new, co-ordinated high signal-to-noise observation obtained by $\textit{XMM-Newton}$ and $\textit{NuSTAR}$. The source exhibits a power-law continuum with $\Gamma \sim$ 1.8 along with a soft excess below 2 keV, a weak neutral iron line and curvature at high energies ($\sim 30$ keV). The broadband spectrum, including the soft excess and the high-energy continuum, is well fit by the relativistic reflection model when the accretion disc is allowed to have densities of log$(n_{\rm e}$/cm$^{-3}$) $\gtrsim 19.2$. Our analysis therefore suggests that when high-density effects are considered, relativistic reflection remains a viable explanation for the soft excess., Comment: 14 pages, 9 figures, accepted for publication in MNRAS

We observed the Seyfert 1 galaxy Mrk817 during an intensive multi-wavelength reverberation mapping campaign for 16 months. Here, we examine the behavior of narrow UV absorption lines seen in HST/COS spectra, both during the campaign and in other epochs extending over 14 years. We conclude that while the narrow absorption outflow system (at -3750 km/s with FWHM=177 km/s) responds to the variations of the UV continuum as modified by the X-ray obscurer, its total column density (logNH =19.5 cm-2) did not change across all epochs. The adjusted ionization parameter (scaled with respect to the variations in the Hydrogen ionizing continuum flux) is log UH =-1.0. The outflow is located at a distance smaller than 38 parsecs from the central source, which implies a hydrogen density of nH > 3000 cm-3. The absorption outflow system only covers the continuum emission source and not the broad emission line region, which suggests that its transverse size is small (< 1e16 cm), with potential cloud geometries ranging from spherical to elongated along the line of sight., Comment: 18 pages, 12 Figures, Accepted for publication in ApJ

X-ray binaries (XRBs) often exhibit spectral residuals in the 0.5 to 2 keV range, known as the "1 keV residual/1 keV feature", with variable centroid and intensity across different systems. Yet a comprehensive scientific explanation of the variability of the 1 keV feature has remained largely elusive. In this paper, we explain for the first time the origin and variability of the 1 keV feature in XRBs using the spectral synthesis code \textsc{Cloudy}. We constructed line blends for the emission and absorption lines and study the variability of these blends with ionization parameters, temperature, and column density. We conducted a sample study involving five XRBs including two ultraluminous X-ray sources (ULXs): NGC 247 ULX-1, NGC 1313 X-1, a binary X-ray pulsar: Hercules X-1, and two typical low-mass X-ray binaries (LMXBs): Cygnus X-2, and Serpens X-1, providing a comprehensive explanation of the 1 keV feature observed across these targets., Comment: 22 pages, 12 figures, Submitted to MNRAS

Quasi-periodic eruptions (QPEs) are high-amplitude, soft X-ray bursts recurring every few hours, associated with supermassive black holes. Many interpretations for QPEs were proposed since their recent discovery in 2019, including extreme mass ratio inspirals and accretion disk instabilities. But, as of today, their nature still remains debated. We perform the first high-resolution X-ray spectral study of a QPE source using the RGS gratings onboard XMM-Newton, leveraging nearly 2 Ms of exposure on GSN 069, the first discovered source of this class. We resolve several absorption and emission lines including a strong line pair near the N VII rest-frame energy, resembling the P-Cygni profile. We apply photoionization spectral models and identify the absorption lines as an outflow blueshifted by $1700-2900$ km/s, with a column density of about $10^{22}$ cm$^{-2}$ and an ionization parameter $\log (\xi$/erg cm s$^{-1})$ of $3.9-4.6$. The emission lines are instead redshifted by up to 2900 km/s, and likely originate from the same outflow that imprints the absorption features, and covers the full $4\pi$ sky from the point of view of GSN 069. The column density and ionization are comparable to the outflows detected in some tidal disruption events, but this outflow is significantly faster and has a strong emission component. The outflow is more highly ionized when the system is in the phase during which QPEs are present, and from the limits we derive on its location, we conclude that the outflow is connected to the recent complex, transient activity of GSN 069 which began around 2010., Comment: Submitted to ApJ. 26 pages, 10 figures, 4 tables

We present the results of the XMM-Newton and NuSTAR observations taken as part of the ongoing, intensive multi-wavelength monitoring program of the Seyfert 1 galaxy Mrk 817 by the AGN Space Telescope and Optical Reverberation Mapping 2 (AGN STORM 2) Project. The campaign revealed an unexpected and transient obscuring outflow, never before seen in this source. Of our four XMM-Newton/NuSTAR epochs, one fortuitously taken during a bright X-ray state has strong narrow absorption lines in the high-resolution grating spectra. From these absorption features, we determine that the obscurer is in fact a multi-phase ionized wind with an outflow velocity of $\sim$5200 km s$^{-1}$, and for the first time find evidence for a lower ionization component with the same velocity observed in absorption features in the contemporaneous HST spectra. This indicates that the UV absorption troughs may be due to dense clumps embedded in diffuse, higher ionization gas responsible for the X-ray absorption lines of the same velocity. We observe variability in the shape of the absorption lines on timescales of hours, placing the variable component at roughly 1000 $R_g$ if attributed to transverse motion along the line of sight. This estimate aligns with independent UV measurements of the distance to the obscurer suggesting an accretion disk wind at the inner broad line region. We estimate that it takes roughly 200 days for the outflow to travel from the disk to our line of sight, consistent with the timescale of the outflow's column density variations throughout the campaign.

This paper deals with a numerical analysis of plastic deformation under various conditions, utilizing Radial Basis Function (RBF) approximation. The focus is on the elasto-plastic von Mises problem under plane-strain assumption. Elastic deformation is modelled using the Navier-Cauchy equation. In regions where the von Mises stress surpasses the yield stress, corrections are applied locally through a return mapping algorithm. The non-linear deformation problem in the plastic domain is solved using the Picard iteration. The solutions for the Navier-Cauchy equation are computed using the Radial Basis Function-Generated Finite Differences (RBF-FD) meshless method using only scattered nodes in a strong form. Verification of the method is performed through the analysis of an internally pressurized thick-walled cylinder subjected to varying loading conditions. These conditions induce states of elastic expansion, perfectly-plastic yielding, and plastic yielding with linear hardening. The results are benchmarked against analytical solutions and traditional Finite Element Method (FEM) solutions. The paper also showcases the robustness of this approach by solving case of thick-walled cylinder with cut-outs. The results affirm that the RBF-FD method produces results comparable to those obtained through FEM, while offering substantial benefits in managing complex geometries without the necessity for conventional meshing, along with other benefits of meshless methods.

In this paper, two mesh-free CFD solvers for pore-scale fluid flow through porous media are considered, namely the Lattice Boltzmann Method with the two relaxation time collision term and the direct Navier-Stokes solver under the artificial compressibility limit. The porous media is built with a regular arrangement of spherical grains with variable radii, which allows control of the porosity. Both solvers use the same h-refined meshless spatial discretization to adequately capture the underlying geometry and the same Radial Basis Function (RBF) method to approximate the involved fields and partial differential operators. First, the results are compared with the data from the literature in terms of drag coefficient and permeability at different porosities achieving excellent agreement with the reported results. Next, the simulations are extended beyond the porosity range reported in the literature using proposed h-refined CFD solvers. The results are supported by convergence and timing analyses and discussions on meshless parameters such as stencil size and refinement settings.

In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with scattered nodes, only regions with geometric details are covered with scattered nodes, while the rest of the domain is discretized with regular nodes. A simpler approximation can be used in regions covered by regular nodes, effectively reducing the required stencil size and computational cost compared to the approximation on scattered nodes where a set of polyharmonic splines is added to ensure convergent behaviour. This paper is an extended version of conference paper entitled "Spatially-varying meshless approximation method for enhanced computational efficiency" [arXiv:2303.01760] presented at "International Conference on Computational Science (ICCS) 2023". The paper is extended with discussion on development and implementation of a hybrid regular-scattered node positioning algorithm (HyNP). The performance of the proposed HyNP algorithm is analysed in terms of separation distance and maximal empty sphere radius. Furthermore, it is demonstrated that HyNP nodes can be used for solving problems from fluid flow and linear elasticity, both in 2D and 3D, using meshless methods. The extension also provides additional analyses of computational efficiency and accuracy of the numerical solution obtained on the spatially-variable regularity of discretization nodes. In particular, different levels of refinement aggressiveness and scattered layer widths are considered to exploit the computational efficiency gains offered by such solution procedure., Comment: 36 pages, 23 figures; Submitted to the Journal of Computational Science as an extension of arXiv:2303.01760. arXiv admin note: text overlap with arXiv:2303.01760

When solving partial differential equations on scattered nodes using the Radial Basis Function-generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs with monomial augmentation, we observe that it affects the approximation accuracy in a particularly interesting way - the solution error oscillates under increasing stencil size. We find that we can connect this behaviour with the spatial dependence of the signed approximation error. Based on this observation we are able to introduce a numerical quantity that could indicate whether a given stencil size is locally optimal. This work is an extension of our ICCS 2023 conference paper., Comment: 41 pages, 18 Figures, Submitted to the Journal of Computational Science. arXiv admin note: text overlap with arXiv:2303.02252

Radial Basis Function-generated Finite Differences (RBF-FD) is a meshless method that can be used to numerically solve partial differential equations. The solution procedure consists of two steps. First, the differential operator is discretised on given scattered nodes and afterwards, a global sparse matrix is assembled and inverted to obtain an approximate solution. Focusing on Polyharmonic Splines as our Radial Basis Functions (RBFs) of choice, appropriately augmented with monomials, it is well known that the truncation error of the differential operator approximation is determined by the degree of monomial augmentation. Naively, one might think that the solution error will have the same order of convergence. We present a superconvergence result that shows otherwise - for some augmentation degrees, order of convergence is higher than expected., Comment: 6 pages, 4 figures. A preprint for the Eurotherm 2024 conference

The numerical stability of fluid flow is an important topic in computational fluid dynamics as fluid flow simulations usually become numerically unstable in the turbulent regime. Many mesh-based methods have already established numerical dissipation procedures that dampen the effects of the unstable advection term. When it comes to meshless methods, the prominent stabilisation scheme is hyperviscosity. It introduces numerical dissipation in the form of a higher-order Laplacian operator. Many papers have already discussed the general effects of hyperviscosity and its parameters. However, hyperviscosity in flow problems has not yet been analyzed in depth. In this paper, we discuss the effects of hyperviscosity on natural convection flow problems as we approach the turbulent regime., Comment: 6 pages, 4 figures, prepared for EUROTHERM 2024

Binaries containing a compact object orbiting a supermassive black hole are thought to be precursors of gravitational wave events, but their identification has been extremely challenging. Here, we report quasi-periodic variability in X-ray absorption which we interpret as quasi-periodic outflows (QPOuts) from a previously low-luminosity active galactic nucleus after an outburst, likely caused by a stellar tidal disruption. We rule out several models based on observed properties and instead show using general relativistic magnetohydrodynamic simulations that QPOuts, separated by roughly 8.3 days, can be explained with an intermediate-mass black hole secondary on a mildly eccentric orbit at a mean distance of about 100 gravitational radii from the primary. Our work suggests that QPOuts could be a new way to identify intermediate/extreme-mass ratio binary candidates., Comment: Accepted for publication in Science Advances. We report a new supermassive black hole phenomenon that we call quasi-periodic outflows (QPOuts)

X-ray binaries are known to launch powerful accretion disk winds that can have significant impact on the binary systems and their surroundings. To quantify the impact and determine the launching mechanisms of these outflows, we need to measure the wind plasma number density, an important ingredient in the theoretical disk wind models. While X-ray spectroscopy is a crucial tool to understanding the wind properties, such as their velocity and ionization, in nearly all cases, we lack the signal-to-noise to constrain the plasma number density, weakening the constraints on outflow location and mass outflow rate. We present a new approach to determine this number density in the X-ray binary Hercules X-1 by measuring the speed of the wind ionization response to time-variable illuminating continuum. Hercules X-1 is powered by a highly magnetized neutron star, pulsating with a period of 1.24 s. We show that the wind number density in Hercules X-1 is sufficiently high to respond to these pulsations by modeling the ionization response with the time-dependent photoionization model TPHO. We then perform a pulse-resolved analysis of the best-quality XMM-Newton observation of Hercules X-1 and directly detect the wind response, confirming that the wind density is at least $10^{12}$ cm$^{-3}$. Finally, we simulate XRISM observations of Hercules X-1 and show that they will allow us to accurately measure the number density at different locations within the outflow. With XRISM we will rule out $\sim3$ orders of magnitude in density parameter space, constraining the wind mass outflow rate, energetics, and its launching mechanism., Comment: Accepted in ApJ. 24 pages, 12 figures, 3 tables

The growth of dendritic grains during solidification is often modelled using the Grain Envelope Model (GEM), in which the envelope of the dendrite is an interface tracked by the Phase Field Interface Capturing (PFIC) method. In the PFIC method, an phase-field equation is solved on a fixed mesh to track the position of the envelope. While being versatile and robust, PFIC introduces certain numerical artefacts. In this work, we present an alternative approach for the solution of the GEM that employs a Meshless (sharp) Interface Tracking (MIT) formulation, which uses direct, artefact-free interface tracking. In the MIT, the envelope (interface) is defined as a moving domain boundary and the interface-tracking nodes are boundary nodes for the diffusion problem solved in the domain. To increase the accuracy of the method for the diffusion-controlled moving-boundary problem, an \h-adaptive spatial discretization is used, thus, the node spacing is refined in the vicinity of the envelope. MIT combines a parametric surface reconstruction, a mesh-free discretization of the parametric surfaces and the space enclosed by them, and a high-order approximation of the partial differential operators and of the solute concentration field using radial basis functions augmented with monomials. The proposed method is demonstrated on a two-dimensional \h-adaptive solution of the diffusive growth of dendrite and evaluated by comparing the results to the PFIC approach. It is shown that MIT can reproduce the results calculated with PFIC, that it is convergent and that it can capture more details in the envelope shape than PFIC with a similar spatial discretization., Comment: Revised version submitted to Journal of Computational Physics

Hercules X-1 is a nearly edge-on X-ray binary with a warped, precessing accretion disk, which manifests through a 35-day cycle of alternating High and Low flux states. This disk precession introduces a changing line of sight towards the X-ray source, through an ionized accretion disk wind. The sightline variation allows us to uniquely determine how the wind properties vary with height above the disk. All the previous wind measurements were made in the brighter Main High state of Her X-1. Here, we analyze the only Chandra observation during the fainter `Short' High state, and significantly detect blueshifted ionized absorption. We find a column density of $2.0_{-0.6}^{+1.1}\times10^{22}$ cm$^{-2}$, an ionization parameter $\log (\xi$/erg cm s$^{-1})=3.41_{-0.12}^{+0.15}$ and an outflow velocity of $380 \pm 40$ km/s. The properties of the outflow measured during the Short High state are in good agreement with those measured at equivalent precession phases during Main High. We conclude that we are sampling the same wind structure, seen during both Main and Short High, which is precessing alongside with the warped accretion disk every 35 days. Finally, the high spectral resolution of Chandra gratings above 1 keV in this observation enabled us to measure the abundances of certain elements in the outflow. We find Mg/O$=1.5_{-0.4}^{+0.5}$, Si/O$=1.5 \pm 0.4$ and S/O$=3.0_{-1.1}^{+1.2}$, whereas in our previous study of Her X-1 with XMM-Newton, we found an over-abundance of N, Ne and Fe compared with O. These peculiar abundance ratios were likely introduced by pollution of the donor by the supernova which created Her X-1., Comment: Accepted for publication in ApJ. 11 pages, 6 figures, 1 table

Tidal disruption events (TDEs) are exotic transients that can lead to temporary super-Eddington accretion onto a supermassive black hole. Such accretion mode is naturally expected to result in powerful outflows of ionized matter. However, to date such an outflow has only been directly detected in the X-ray band in a single TDE, ASASSN-14li. This outflow has a low velocity of just a few 100 km/s, although there is also evidence for a second, ultra-fast phase. Here we present the detection of a low-velocity outflow in a second TDE, ASASSN-20qc. The high-resolution X-ray spectrum reveals an array of narrow absorption lines, each blueshifted by a few 100 km/s, which cannot be described by a single photo-ionization phase. For the first time, we confirm the multiphase nature of a TDE outflow, with at least two phases and two distinct velocity components. One highly ionized phase is outflowing at $910^{+90}_{-80}$ km/s, while a lower ionization component is blueshifted by $400_{-120}^{+100}$ km/s. We perform time-resolved analysis of the X-ray spectrum and detect that, surprisingly, the mildly ionized absorber strongly varies in ionization parameter over the course of a single 60 ks observation, indicating that its distance from the black hole may be as low as 400 gravitational radii. We discuss these findings in the context of TDEs and compare this newly detected outflow with that of ASASSN-14li., Comment: Accepted for publication in ApJ. 12 pages, 4 figures, 2 tables

The accretion of matter onto black holes and neutron stars often leads to the launching of outflows that can greatly affect the environments surrounding the compact object. In supermassive black holes, these outflows can even be powerful enough to dictate the evolution of the entire host galaxy, and yet, to date, we do not understand how these so-called accretion disk winds are launched - whether by radiation pressure, magnetic forces, thermal irradiation, or a combination thereof. An important means of studying disk winds produced near the central compact object is through X-ray absorption line spectroscopy, which allows us to probe outflow properties along a single line of sight, but usually provides little information about the global 3D disk wind structure that is vital for understanding the launching mechanism and total wind energy budget. Here, we study Hercules X-1, a unique, nearly edge-on X-ray binary with a warped accretion disk precessing with a period of about 35 days. This disk precession results in changing sightlines towards the neutron star, through the ionized outflow. We perform time-resolved X-ray spectroscopy over the precession phase and detect a strong decrease in the wind column density by three orders of magnitude as our sightline progressively samples the wind at greater heights above the accretion disk. The wind becomes clumpier as it rises upwards and expands away from the neutron star. Modelling the warped disk shape, we create a 2D map of wind properties. This unique measurement of the vertical structure of an accretion disk wind allows direct comparisons to 3D global simulations to reveal the outflow launching mechanism., Comment: Published in Nature Astronomy on April 10, available at https://www.nature.com/articles/s41550-023-01929-7

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD) method and investigate its properties on a simple test problem., Comment: SpliTech 2023 Conference paper, 4 pages, 3 figures, preprint

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations (PDEs) within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences (RBF-FD) discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

When solving partial differential equations on scattered nodes using the Radial Basis Function generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs with monomial augmentation, we observe that it affects the approximation accuracy in a particularly interesting way - the solution error oscillates under increasing stencil size. We find that we can connect this behaviour with the spatial dependence of the signed approximation error. Based on this observation we are then able to introduce a numerical quantity that indicates whether a given stencil size is locally optimal., Comment: 8 pages, 6 figures, ICCS 2023 Conference Paper

In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatial variation of computational node regularity. Rather than covering the entire domain with scattered nodes, only regions with geometric details are covered with scattered nodes, while the rest of the domain is discretised with regular nodes. Consequently, in regions covered with regular nodes the approximation using solely the monomial basis can be performed, effectively reducing the required stencil size compared to the approximation on scattered nodes where a set of polyharmonic splines is added to ensure convergent behaviour. The performance of the proposed hybrid scattered-regular approximation approach, in terms of computational efficiency and accuracy of the numerical solution, is studied on natural convection driven fluid flow problems. We start with the solution of the de Vahl Davis benchmark case, defined on square domain, and continue with two- and three-dimensional irregularly shaped domains. We show that the spatial variation of the two approximation methods can significantly reduce the computational complexity, with only a minor impact on the solution accuracy., Comment: Preprint(reviewed)

A black hole can launch a powerful relativistic jet after it tidally disrupts a star. If this jet fortuitously aligns with our line of sight, the overall brightness is Doppler boosted by several orders of magnitude. Consequently, such on-axis relativistic tidal disruption events (TDEs) have the potential to unveil cosmological (redshift $z>$1) quiescent black holes and are ideal test beds to understand the radiative mechanisms operating in super-Eddington jets. Here, we present multi-wavelength (X-ray, UV, optical, and radio) observations of the optically discovered transient \target at $z=1.193$. Its unusual X-ray properties, including a peak observed luminosity of $\gtrsim$10$^{48}$ erg s$^{-1}$, systematic variability on timescales as short as 1000 seconds, and overall duration lasting more than 30 days in the rest-frame are traits associated with relativistic TDEs. The X-ray to radio spectral energy distributions spanning 5-50 days after discovery can be explained as synchrotron emission from a relativistic jet (radio), synchrotron self-Compton (X-rays), and thermal emission similar to that seen in low-redshift TDEs (UV/optical). Our modeling implies a beamed, highly relativistic jet akin to blazars but requires extreme matter-domination, i.e, high ratio of electron-to-magnetic field energy densities in the jet, and challenges our theoretical understanding of jets., Comment: To appear in Nature Astronomy on 30th November 2022. Also see here for an animation explaining the result: https://youtu.be/MQHdSbxuznY

Ultraluminous X-ray sources (ULXs) are extreme X-ray binaries shining above 10^39 erg/s, in most cases as a consequence of super-Eddington accretion onto neutron stars and stellar-mass black holes accreting above their Eddington limit. This was understood after the discovery of coherent pulsations, cyclotron lines and powerful winds. The latter was possible thanks to the high-resolution X-ray spectrometers aboard XMM-Newton. ULX winds carry a huge amount of power owing to their relativistic speeds (0.1-0.3 c) and are able to significantly affect the surrounding medium, likely producing the observed 100 pc ULX superbubbles, and limit the amount of matter that can reach the central accretor. The study of ULX winds is therefore quintessential to understand 1) how much and how fast can matter be accreted by compact objects and 2) how strong is their feedback onto the surrounding medium. This is also relevant to understand supermassive black holes growth. Here we provide an overview on this phenomenology, highlight some recent, exciting results and show how future missions such as XRISM, eXTP and ATHENA will improve our understanding., Comment: To appear in Astronomische Nachrichten / Astronomical Notes (AN)

We present an algorithm for $hp$-adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve-estimate-mark-refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning algorithm that supports variable node density. In the estimate phase, we introduce an Implicit-Explicit (IMEX) error indicator, which assumes that the error relates to the difference between the implicitly obtained solution (from the solve phase) and a local explicit re-evaluation of the PDE at hand using a higher order approximation. Based on the IMEX error indicator, the modified Texas Three Step marking strategy is used to mark the computational nodes for $h$-, $p$- or $hp$-(de-)refinement. Finally, in the refine phase, nodes are repositioned and the order of the method is locally redefined using the variable order of the augmenting monomials according to the instructions from the mark phase. The performance of the introduced $hp$-adaptive method is first investigated on a two-dimensional Peak problem and further applied to two- and three-dimensional contact problems. We show that the proposed IMEX error indicator adequately captures the global behaviour of the error in all cases considered and that the proposed $hp$-adaptive solution procedure significantly outperforms the non-adaptive approach. The proposed $hp$-adaptive method stands for another important step towards a fully autonomous numerical method capable of solving complex problems in realistic geometries without the user intervention., Comment: Preprint submitted to Computer Methods in Applied Mechanics and Engineering

Hercules X-1 is a nearly edge-on accreting X-ray pulsar with a warped accretion disk, precessing with a period of about 35 days. The disk precession allows for unique and changing sightlines towards the X-ray source. To investigate the accretion flow at a variety of sightlines, we obtained a large observational campaign on Her X-1 with XMM-Newton (380 ks exposure) and Chandra (50 ks exposure) for a significant fraction of a single disk precession cycle, resulting in one of the best datasets taken to date on a neutron star X-ray binary. Here we present the spectral analysis of the High State high-resolution grating and CCD datasets, including the extensive archival data available for this famous system. The observations reveal a complex Fe K region structure, with three emission line components of different velocity widths. Similarly, the high-resolution soft X-ray spectra reveal a number of emission lines of various widths. We correct for the uncertain gain of the EPIC-pn Timing mode spectra, and track the evolution of these spectral components with Her X-1 precession phase and observed luminosity. We find evidence for three groups of emission lines: one originates in the outer accretion disk (10^5 RG from the neutron star). The second line group plausibly originates at the boundary between the inner disk and the pulsar magnetosphere (10^3 RG). The last group is too broad to arise in the magnetically-truncated disk and instead must originate very close to the neutron star surface, likely from X-ray reflection from the accretion curtain (~10^2 RG)., Comment: Accepted for publication in ApJ. 26 pages, 17 figures, 4 tables

Despite two decades of studies, it is still not clear whether ULX spectral transitions are due to stochastic variability in the wind or variations in the accretion rate or in the source geometry. The compact object is also unknown for most ULXs. In order to place constraints onto such scenarios and on the structure of the accretion disc, we studied the temporal evolution of the spectral components of the variable source NGC 55 ULX-1. Using recent and archival data obtained with the XMM-Newton satellite, we modelled the spectra with two blackbody components which we interpret as thermal emission from the inner accretion flow and the regions around or beyond the spherization radius. The luminosity-temperature (L-T) relation of each spectral component agrees with the L proportional T^4 relationship expected from a thin disc model, which suggests that the accretion rate is close to the Eddington limit. However, there are some small deviations at the highest luminosities, possibly due to an expansion of the disc and a contribution from the wind at higher accretion rates. Assuming that such deviations are due to the crossing of the Eddington or supercritical accretion rate, we estimate a compact object mass of 6-14 Msun, favouring a stellar-mass black hole as the accretor., Comment: 12 pages, 9 figures, accepted for publication in MNRAS

Ultraluminous X-ray sources (ULXs) are a class of accreting compact objects with X-ray luminosities above 10$^{39}$ erg s$^{-1}$. The average number of ULXs per galaxy is still not well constrained, especially given the uncertainty on the fraction of ULX transients. Here, we report the identification of a new transient ULX in the galaxy NGC 55 (which we label as ULX-2), thanks to recent XMM-Newton and the Neil Gehrels Swift Observatory observations. This object was previously classified as a transient X-ray source with a luminosity around a few 10$^{38}$ erg s$^{-1}$ in a 2010 XMM-Newton observation. Thanks to new and deeper observations ($\sim$ 130 ks each), we show that the source reaches a luminosity peak $>1.6 \times 10^{39}$ erg s$^{-1}$. The X-ray spectrum of ULX-2 is much softer than in previous observations and fits in the class of soft ULXs. It can be well described using a model with two thermal components, as often found in ULXs. The time scales of the X-ray variability are of the order of a month and are likely driven by small changes in the accretion rate or due to super-orbital modulations, attributed to precession of the accretion disc, which is similar to other ULXs., Comment: 6 pages, including 4 figures and 2 tables, accepted for pubblication in MNRAS

1ES 1927+654 is a paradigm-defying AGN and one of the most peculiar X-ray nuclear transients. In early 2018, this well-known AGN underwent a changing-look event, in which broad optical emission lines appeared and the optical flux increased. Yet, by July 2018, the X-ray flux had dropped by over two orders of magnitude, indicating a dramatic change to the inner accretion flow. With three years of observations with NICER, XMM-Newton, and NuSTAR, we present the X-ray evolution of 1ES 1927+654, which can be broken into three phases-(1) an early super-Eddington phase with rapid variability in X-ray luminosity and spectral parameters, (2) a stable super-Eddington phase at the peak X-ray luminosity, and (3) a steady decline back to the pre-outburst luminosity and spectral parameters. For the first time, we witnessed the formation of the X-ray corona, as the X-ray spectrum transitioned from thermally-dominated to primarily Comptonized. We also track the evolution of the prominent, broad 1 keV feature in the early X-ray spectra and show that this feature can be modeled with blueshifted reflection (z = -0.33) from a single-temperature blackbody irradiating spectrum using xillverTDE, a new flavor of the xillver models. Thus, we propose that the 1 keV feature could arise from reflected emission off the base of an optically thick outflow from a geometrically thick, super-Eddington inner accretion flow, connecting the inner accretion flow with outflows launched during extreme accretion events (e.g. tidal disruption events). Lastly, we compare 1ES 1927+654 to other nuclear transients and discuss applications of xillverTDE to super-Eddington accretors., Comment: 25 pages, 10 figures, accepted for publication in ApJ

With the immense computing power at our disposal, the numerical solution of partial differential equations (PDEs) is becoming a day-to-day task for modern computational scientists. However, the complexity of real-life problems is such that tractable solutions do not exist. This makes it difficult to validate the numerically obtained solution, so good error estimation is crucial in such cases. It allows the user to identify problematic areas in the computational domain that may affect the stability and accuracy of the numerical method. Such areas can then be remedied by either \textit{h}- or \textit{p}-adaptive procedures. In this paper, we propose to estimate the error of the numerical solution by solving the same governing problem implicitly and explicitly, using a different approximation order in each case. We demonstrate the newly proposed error indicator on the solution of a synthetic two-dimensional Poisson problem with tractable solution for easier validation. We show that the proposed error indicator has good potential for locating areas of high error., Comment: preprint, splitech conference

We report on the discovery of an absorption line at $E=8.56^{+0.05}_{-0.11}$ keV detected with a significance of $>3.3\sigma$ in the NuSTAR and XMM-Newton spectra of a newly discovered hyperluminous X-ray source (HLX, $L_{\rm X}>10^{41}$ ergs$^{-1}$) in the galaxy NGC 4045 at a distance of 32 Mpc. The source was first discovered serendipitously in a Swift/XRT observation of the galaxy, and Swift monitoring reveals a highly variable source changing by over an order of magnitude from maximum to minimum. The origin of the absorption line appears likely to be by highly ionized iron with a blue shift of 0.19$c$, indicating an ultrafast outflow (UFO). However, the large equivalent width of the line (EW$=-0.22^{+0.08}_{-0.09}$ keV) paired with the lack of other absorption lines detected are difficult to reconcile with models. An alternative explanation is that the line is due to a cyclotron resonance scattering feature (CRSF), produced by the interaction of X-ray photons with the powerful magnetic field of a neutron star., Comment: Accepted for publication in ApJ

When the deformations of a solid body are sufficiently large, parts of the body undergo a permanent deformation commonly refereed to as plastic deformation. Several plasticity models describing such phenomenon have been proposed, e.g. von Mises, Tresca, etc. Traditionally, the finite element method (FEM) is the numerical tool of choice for engineers who are solving such problems. In this work, however, we present the implementation of the von Mises plasticity model with non-linear isotropic hardening in our in-house developed MEDUSA library, utilizing a variant of meshless methods -- namely the radial basis function-generated finite differences (RBF-FD). We define a simple plane stress case, where a 2D block is fixed at one edge, and a tensile force, which causes the block to deform, is applied to it at the opposite edge. We show that results are in good agreement with the numerical solution obtained by Abaqus FEA, a commercial FEM solver., Comment: MIPRO 2022, conference paper

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by using scalar reductions, which, however, come with a loss of spatial detail. Dynamic Mode Decomposition is a data-driven analysis method that solves this problem by identifying oscillating spatial structures and their corresponding frequencies. This paper presents the algorithm and provides a physical interpretation of the results by applying the decomposition method to a series of increasingly complex examples., Comment: 6 pages, 8 figures

Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local mesh-free strong-form method that combines the stability of Radial Basis Function-Generated Finite Differences (RBF-FD) with the computational effectiveness of Diffuse Approximation Method (DAM), forming a so-called hybrid method. To demonstrate the advantages of a hybrid method, we evaluate its computational complexity and accuracy of the obtained numerical solution by solving a two-dimensional Poisson problem with an exponentially strong source in the computational domain. Finally, we employ the hybrid method to solve a three-dimensional Boussinesq's problem on an isotropic half-space and show that the implementation overhead can be justified., Comment: Splitech 2022, Confernce paper

The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the approximation order and basis functions. In this paper we analyse two popular variants of local strong form meshless methods, namely the radial basis function-generated finite differences (RBF-FD) using polyharmonic splines (PHS) augmented with monomials, and the weighted least squares (WLS) approach using only monomials. Our analysis focuses on the accuracy and stability of the numerical solution computed on scattered nodes in a two- and three-dimensional domain. We show that while the WLS variant is a better choice when lower order approximations are sufficient, the RBF-FD variant exhibits a more stable behavior and a higher accuracy of the numerical solution for higher order approximations, but at the cost of higher computational complexity., Comment: Mipro conference paper

The grain envelope model (GEM) describes the growth of envelopes of dendritic crystal grains during solidification. Numerically the growing envelopes are usually tracked using an interface capturing method employing a phase field equation on a fixed grid. Such an approach describes the envelope as a diffuse interface, which can lead to numerical artefacts that are possibly detrimental. In this work, we present a sharp-interface formulation of the GEM that eliminates such artefacts and can thus track the envelope with high accuracy. The new formulation uses an adaptive meshless discretization method to solve the diffusion in the liquid around the grains. We use the ability of the meshless method to operate on scattered nodes to accurately describe the interface, i.e., the envelope. The proposed algorithm combines parametric surface reconstruction, meshless discretization of parametric surfaces, global solution construction procedure and partial differential operator approximation using monomials as basis functions. The approach is demonstrated on a two-dimensional h-adaptive solution of diffusive growth of dendrites and assessed by comparison to a conventional diffuse-interface fixed-grid GEM., Comment: 6 pages, conference preprint

In this paper we present a refined RBF-FD solution for a non-Newtonian fluid in a closed differentially heated cavity. The problem at hand is governed by three coupled nonlinear partial differential equations, namely heat transport, momentum transport and mass continuity. The non-Newtonian behaviour is modelled with the Ostwald-de Weele power law and the buoyancy with the Boussinesq approximation. The problem domain is discretised with scattered nodes without any requirement for a topological relation between them. This allows a trivial generalisation of the solution procedure to complex irregular 3D domains, which is also demonstrated by solving the problem in a 2D and 3D geometry mimicking the porous filter. The results in 2D are compared with two reference solutions that use the Finite volume method in a conjunction with two different stabilisation techniques (upwind and QUICK), where we achieved good agreement with the reference data. The refinement is implemented on top of a dedicated meshless node positioning algorithm using piecewise linear node density function that ensures sufficient node density in the centre of the domain while maximising the node density in a boundary layer where the most intense dynamic is expected. The results show that with a refined approach, up to 5 times fewer nodes are needed to obtain the results with the same accuracy compared to the regular discretisation. The paper also discusses the convergence for different scenarios for up to $2 \cdot 10^5$ nodes, the behaviour of the flow in the boundary layer, the behaviour of the viscosity and the geometric flexibility of the proposed solution procedure.

In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on Poisson disc sampling is parallelized for use on shared-memory computers, such as modern workstations with multi-core processors. The parallel algorithm uses a global spatial indexing method with its data divided into two levels, which allows for an efficient multi-threaded implementation. The addition of bootstrapping enables the algorithm to use any number of parallel threads while remaining as general as its sequential variant. We demonstrate the algorithm performance on six complex 2- and 3-dimensional domains, which are either of non-rectangular shape or have varying nodal spacing or both. We perform a run-time analysis of the algorithm, to demonstrate its ability to reach high speedups regardless of the domain and to show how well it scales on the experimental hardware with 16 processor cores. We also analyse the algorithm in terms of the effects of domain shape, quality of point placement, and various parallelization overheads.

Transmission system operators (TSOs) in recent years have faced challenges in order to ensure maximum transmission capacity of the system to satisfy market needs, while maintaining operational safety and permissible impact on the environment. A great help in the decision-making process was introduced with the Dynamic Thermal Rating (DTR) - an instrument to monitor and predict the maximal allowed ampacity of the power grid based on weather measurements and forecast. However, the introduction of DTR raises a number of questions related to the accuracy and uncertainty of the results of thermal assessment and the level of acceptable risk and its management. In this paper, we present a solution for estimating DTR uncertainty, appropriate for operational use at TSOs. With the help of conductor surface temperature measurements, weather measurements and predicted weather data, we also estimate the error of the weather forecast and the DTR itself. Following the results of the data analyses, we build an operative solution for estimating the ampacity uncertainty based on Monte Carlo random simulations and integrate it into the operational environment of ELES - the operator of the Slovenian electric power transmission network.

Ultra-fast outflows (UFOs) have been detected in the high-quality X-ray spectra of a number of active galactic nuclei (AGN) with fairly high accretion rates and are thought to significantly contribute to the AGN feedback. After a decade of dedicated study, their launching mechanisms and structure are still not well understood, but variability techniques may provide useful constraints. In this work, therefore, we perform a flux-resolved X-ray spectroscopy on a highly accreting and variable NLS1 AGN, 1H 0707-495, using all archival XMM-Newton observations to study the structure of the UFO. We find that the wind spectral lines weaken at higher luminosities, most likely due to an increasing ionization parameter as previously found in a few similar sources. Instead, the velocity is anticorrelated with the luminosity, which is opposite to the trend observed in the NLS1 IRAS 13224-3809. Furthermore, the detection of the emission lines, which are not observed in IRAS 13224-3809, indicates a wind with a larger opening angle in 1H 0707-495, presumably due to a higher accretion rate. The emitting gas is found to remain broadly constant with the luminosity. We describe the variability of the wind with a scenario where the strong radiation extends the launch radius outwards and shields the outer emitting gas, similarly to super-Eddington compact objects, although other possible explanations are discussed. Our work provides several hints for a multi-phase outflow in 1H 0707-495., Comment: 20 pages, 9 figures, accepted for publication in MNRAS

Most Ultraluminous X-ray sources (ULXs) are thought to be powered by super-Eddington accretion onto stellar-mass compact objects. Accretors in this extreme regime are naturally expected to ionise copious amounts of plasma in their vicinity and launch powerful radiation-driven outflows from their discs. High spectral resolution X-ray observations (with RGS gratings onboard XMM-Newton) of a few ULXs with the best datasets indeed found complex line spectra and confirmed such extreme (0.1-0.3c) winds. However, a search for plasma signatures in a large ULX sample with a rigorous technique has never been performed, thereby preventing us from understanding their statistical properties such as the rate of occurrence, to constrain the outflow geometry and its duty cycle. We developed a fast method for automated line detection in X-ray spectra and applied it to the full RGS ULX archive, rigorously quantifying the statistical significance of any candidate lines. Collecting the 135 most significant features detected in 89 observations of 19 objects, we created the first catalogue of spectral lines detected in soft X-ray ULX spectra. We found that the detected emission lines are concentrated around known rest-frame elemental transitions and thus originate from low-velocity material. The absorption lines instead avoid these transitions, suggesting they were imprinted by blueshifted outflows. Such winds therefore appear common among the ULX population. Additionally, we found that spectrally hard ULXs show fewer line detections than soft ULXs, indicating some difference in their accretion geometry and orientation, possibly causing over-ionisation of plasma by the harder spectral energy distributions of harder ULXs., Comment: Accepted for publication in MNRAS. 22 pages, 6 figures and 3 tables