Reviving stochasticity: uncertainty in SMBH binary eccentricity is unavoidable

We study supermassive black hole (SMBH) binary eccentricity of equal-mass galaxy mergers in $N$-body simulations with the KETJU code, which combines the GADGET-4 fast multipole gravity solver with accurate regularized integration and Post-Newtonian corrections around SMBHs. In simulations with realistic, high eccentricity galactic merger orbits, the binary eccentricity is found to be a non-linear function of the deflection angle in the SMBH orbit during the final, nearly radial close encounter between the SMBHs before they form a bound binary. This mapping between the deflection angle and the binary eccentricity has no apparent resolution dependence in our simulations spanning the resolution range of $1\times10^5 - 8\times10^6$ particles per galaxy. The mapping is also captured using a simple model with an analytic potential, indicating that it is driven by the interplay between a smooth asymmetric stellar background potential and dynamical friction acting on the SMBHs. Due to the non-linearity of this mapping, in certain merger configurations small, parsec-scale variations in the merger orbit can result in binary eccentricities varying in nearly the full possible range between $e=0$ and $e=1$. In idealized simulations, such variations are caused by finite resolution effects, and convergence of the binary eccentricity can be achieved with increasing resolution. However, in real galaxies, other mechanisms such as nuclear gas and substructure that perturb the merger orbit are likely to be significant enough for the binary eccentricity to be effectively random. Our results indicate that the distribution of these effectively random eccentricities can be studied using even moderate resolution simulations.Comment: 9 pages, 5 figure

Resolving the Complex Evolution of a Supermassive Black Hole Triplet in a Cosmological Simulation

We present here a self-consistent cosmological zoom-in simulation of a triple supermassive black hole (SMBH) system forming in a complex multiple galaxy merger. The simulation is run with an updated version of our code KETJU, which is able to follow the motion of SMBHs down to separations of tens of Schwarzschild radii while simultaneously modeling the large-scale astrophysical processes in the surrounding galaxies, such as gas cooling, star formation, and stellar and AGN feedback. Our simulation produces initially an SMBH binary system for which the hardening process is interrupted by the late arrival of a third SMBH. The KETJU code is able to accurately model the complex behavior occurring in such a triple SMBH system, including the ejection of one SMBH to a kiloparsec-scale orbit in the galaxy due to strong three-body interactions as well as Lidov-Kozai oscillations suppressed by relativistic precession when the SMBHs are in a hierarchical configuration. One pair of SMBHs merges similar to 3 Gyr after the initial galaxy merger, while the remaining binary is at a parsec-scale separation when the simulation ends at redshift z = 0. We also show that KETJU can capture the effects of the SMBH binaries and triplets on the surrounding stellar population, which can affect the binary merger timescales as the stellar density in the system evolves. Our results demonstrate the importance of dynamically resolving the complex behavior of multiple SMBHs in galactic mergers, as such systems cannot be readily modeled using simple orbit-averaged semianalytic models.Peer reviewe

MSTAR - a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates

We present the novel algorithmically regularized integration method MSTAR for high-accuracy (vertical bar Delta E/E vertical bar greater than or similar to 10(-14)) integrations of N-body systems using minimum spanning tree coordinates. The twofold parallelization of the O(N-part(2)) force loops and the substep divisions of the extrapolation method allow for a parallel scaling up to N-CPU = 0.2 x N-part. The efficient parallel scaling of MSTAR makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularization chain (AR-CHAIN) methods, e.g. N-part = 5000 particles on 400 CPUs for 1 Gyr in a few weeks of wall-clock time. We present applications of MSTAR on few particle systems, studying the Kozai mechanism and N-body systems like star clusters with up to N-part = 10(4) particles. Combined with a tree or fast multipole-based integrator, the high performance of MSTAR removes a major computational bottleneck in simulations with regularized subsystems. It will enable the next-generation galactic-scale simulations with up to 109 stellar particles (e.g. m(star) = 100 M-circle dot) for an M-star = 10(11) M-circle dot galaxy), including accurate collisional dynamics in the vicinity of nuclear supermassive black holes.Peer reviewe

Water and nitrogen processes along a typical water flowpath and streamwater exports from a forested catchment and changes after clear-cutting: a modelling study

International audienceA two dimensional model, FEMMA, to describe water and nitrogen (N) fluxes within and from a forested first-order catchment (Kangasvaara in Eastern Finland) was constructed by linking the most significant processes affecting the fluxes of water, ammonium, nitrate and dissolved organic nitrogen along a hillslope from the water divide to the stream. The hillslope represents the average flowpath of water in the catchment and the model was used to estimate the N fluxes for a catchment in eastern Finland before and after clear-cutting. The simulated results were in reasonable agreement with the nitrate, dissolved organic N and dissolved total N measurements from the study catchment and with other results in the literature. According to the simulations, the major sinks of N after clear-cutting were immobilisation by soil microbes, uptake by ground vegetation and sorption to soil. These sinks increased downslope from the clear-cut area, indicating the importance of an uncut buffer zone between the stream and the clear-cut area in reducing N exports. The buffer zone retained 76% of the N flux coming from the clear-cut area. Nitrification was a key process in controlling the N export after clear-cutting and N increases were mainly as nitrate. Most of the annual N export took place during the spring flood, when uptake of N by plants was minimal

Signatures of the Many Supermassive Black Hole Mergers in a Cosmologically Forming Massive Early-type Galaxy

We model here the merger histories of the supermassive black hole (SMBH) population in the late stages of a cosmological simulation of a similar to 2 x 10(13) M (circle dot) galaxy group. The gravitational dynamics around the several tens of SMBHs (M (center dot) > 7.5 x 10(7) M (circle dot)) hosted by the galaxies in the group is computed at high accuracy using regularized integration with the KETJU code. The 11 SMBHs that form binaries and a hierarchical triplet eventually merge after hardening through dynamical friction, stellar scattering, and gravitational wave (GW) emission. The binaries form at eccentricities of e similar to 0.3-0.9, with one system evolving to a very high eccentricity of e = 0.998, and merge on timescales of a few tens to several hundred megayears. During the simulation, the merger-induced GW recoil kicks eject one SMBH remnant from the central host galaxy. This temporarily drives the galaxy off the M (center dot)-sigma relation; however, the galaxy returns to the relation due to subsequent galaxy mergers, which bring in new SMBHs. This showcases a possible mechanism contributing to the observed scatter of the M (center dot)-sigma relation. Finally, we show that pulsar timing arrays and LISA would be able to detect parts of the GW signals from the SMBH mergers that occur during the similar to 4 Gyr time span simulated with KETJU.Peer reviewe

Barycentric interpolation on Riemannian and semi-Riemannian spaces

Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is a ubiquitous task in all of physics. In this work, we present a covariant generalization of the barycentric coordinates and the barycentric interpolation method for Riemannian and semi-Riemannian spaces of arbitrary dimension. We show that our new method preserves the linear accuracy property of barycentric interpolation in a coordinate-invariant sense. In addition, we show how the method can be used to interpolate constrained quantities so that the given constraint is automatically respected. We showcase the method with two astrophysics related examples situated in the curved Kerr space-time. The first problem is interpolating a locally constant vector field, in which case curvature effects are expected to be maximally important. The second example is a general relativistic magnetohydrodynamics simulation of a turbulent accretion flow around a black hole, wherein high intrinsic variability is expected to be at least as important as curvature effects.Peer reviewe

KETJU -- resolving small-scale supermassive black hole dynamics in GADGET-4

We present the new public version of the KETJU supermassive black hole (SMBH) dynamics module, as implemented into GADGET-4. KETJU adds a small region around each SMBH where the dynamics of the SMBHs and stellar particles are integrated using an algorithmically regularised integrator instead of the leapfrog integrator with gravitational softening used by GADGET-4. This enables modelling SMBHs as point particles even during close interactions with stellar particles or other SMBHs, effectively removing the spatial resolution limitation caused by gravitational softening. KETJU also includes post-Newtonian corrections, which allows following the dynamics of SMBH binaries to sub-parsec scales and down to tens of Schwarzschild radii. Systems with multiple SMBHs are also supported, with the code also including the leading non-linear cross terms that appear in the post-Newtonian equations for such systems. We present tests of the code showing that it correctly captures, at sufficient mass resolution, the sinking driven by dynamical friction and binary hardening driven by stellar scattering. We also present an example application demonstrating how the code can be applied to study the dynamics of SMBHs in mergers of multiple galaxies and the effect they have on the properties of the surrounding galaxy. We expect that the presented KETJU SMBH dynamics module can also be straightforwardly incorporated into other codes similar to GADGET-4, which would allow coupling small-scale SMBH dynamics to the rich variety of galactic physics models that exist in the literature.Comment: 21 pages, 19 figures. Code available from https://www.mv.helsinki.fi/home/phjohans/ketj

Topological Alterations of the Structural Brain Connectivity Network in Children with Juvenile Neuronal Ceroid Lipofuscinosis

BACKGROUND AND PURPOSE: We used diffusion MR imaging to investigate the structural brain connectivity networks in juvenile neuronal ceroid lipofuscinosis, a neurodegenerative lysosomal storage disease of childhood. Although changes in conventional MR imaging are typically not visually apparent in children agedPeer reviewe

Is the water footprint an appropriate tool for forestry and forest products: The Fennoscandian case

The water footprint by the Water Footprint Network (WF) is an ambitious tool for measuring human appropriation and promoting sustainable use of fresh water. Using recent case studies and examples from water-abundant Fennoscandia, we consider whether it is an appropriate tool for evaluating the water use of forestry and forest-based products. We show that aggregating catchment level water consumption over a product life cycle does not consider fresh water as a renewable resource and is inconsistent with the principles of the hydrologic cycle. Currently, the WF assumes that all evapotranspiration (ET) from forests is a human appropriation of water although ET from managed forests in Fennoscandia is indistinguishable from that of unmanaged forests. We suggest that ET should not be included in the water footprint of rain-fed forestry and forest-based products. Tools for sustainable water management should always contextualize water use and water impacts with local water availability and environmental sensitivity