Non-axisymmetric instabilities in self-gravitating tori around black holes, and solving Einstein constraints with superconvergent finite element methods

This thesis contains results on two related projects. In the first project, we explore non-axisymmetric instabilities in general relativistic accretion disks around black holes. Such disks are created as transient structures in several astrophysical scenarios, including mergers of compact objects and core collapse of massive stars. These disks are suggested for the role of cenral engines of gamma-ray bursts. We address the stability of these objects against the runaway and non-axisymmetric instabilities in the three-dimensional hydrodynamical fully general relativistic treatment. We explore three slender and moderately slender disk models with varying disk-to-black hole mass ratio. None of the models that we consider develop the runaway instability during the time span of the simulations, despite large radial axisymmetric oscillations, induced in the disks by the initial data construction procedure. All models develop unstable non-axisymmetric modes on a dynamical timescale. In simulations with dynamical general relativistic treatment, we observe two distinct types of instabilities: the Papaloizou-Pringle instability and the so-called Intermediate instability. The development of the nonaxisymmetric mode with azimuthal number m=1 is enhanced by the outspiraling motion of the black hole. The overall picture of the unstable modes in our disk models is similar to the Newtonian case. In the second project, we experiment with solving the Einstein constraint equations using finite elements on semistructured triangulations of multiblock grids. We illustrate our approach with a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor $\psi$. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, we evolve the constructed initial data using a high order finite-differencing multi-block approach and extract gravitational waves from the numerical solution

The long-term evolution of neutron star merger remnants - II. Radioactively powered transients

We use 3D hydrodynamic simulations of the long-term evolution of neutron star merger ejecta to predict the light curves of electromagnetic transients that are powered by the decay of freshly produced r-process nuclei. For the dynamic ejecta that are launched by tidal and hydrodynamic interaction, we adopt grey opacities of 10 cm$^2$/g, as suggested by recent studies. For our reference case of a 1.3-1.4 $M_\odot$ merger, we find a broad IR peak 2-4 d after the merger. The peak luminosity is $\approx 2\times 10^{40}$ erg/s for an average orientation, but increased by up to a factor of 4 for more favourable binary parameters and viewing angles. These signals are rather weak and hardly detectable within the large error box (~100 deg$^2$) of a gravitational wave trigger. A second electromagnetic transient results from neutrino-driven winds. These winds produce `weak' r-process material with $50 < A < 130$ and abundance patterns that vary substantially between different merger cases. For an adopted opacity of 1 cm$^2$/g, the resulting transients peak in the UV/optical about 6 h after the merger with a luminosity of $\approx 10^{41}$ erg/s (for a wind of 0.01 $M_\odot$) These signals are marginally detectable in deep follow-up searches (e.g. using Hypersuprime camera on Subaru). A subsequent detection of the weaker but longer lasting IR signal would allow an identification of the merger event. We briefly discuss the implications of our results to the recent detection of an nIR transient accompanying GRB 130603B.Comment: 14 pages, 11 figures, 5 tables, accepted to MNRA

Neutrino-driven winds in the aftermath of a neutron star merger: nucleosynthesis and electromagnetic transients

We present a comprehensive nucleosynthesis study of the neutrino-driven wind in the aftermath of a binary neutron star merger. Our focus is the initial remnant phase when a massive central neutron star is present. Using tracers from a recent hydrodynamical simulation, we determine total masses and integrated abundances to characterize the composition of unbound matter. We find that the nucleosynthetic yields depend sensitively on both the life time of the massive neutron star and the polar angle. Matter in excess of up to $9 \cdot 10^{-3} M_\odot$ becomes unbound until $\sim 200~{\rm ms}$. Due to electron fractions of $Y_{\rm e} \approx 0.2 - 0.4$ mainly nuclei with mass numbers $A < 130$ are synthesized, complementing the yields from the earlier dynamic ejecta. Mixing scenarios with these two types of ejecta can explain the abundance pattern in r-process enriched metal-poor stars. Additionally, we calculate heating rates for the decay of the freshly produced radioactive isotopes. The resulting light curve peaks in the blue band after about $4~{\rm h}$. Furthermore, high opacities due to heavy r-process nuclei in the dynamic ejecta lead to a second peak in the infrared after $3-4~{\rm d}$.Comment: 15 pages, 18 figures, 2 tables, accepted by Ap

Infrared emission from kilonovae: the case of the nearby short hard burst GRB 160821B

We present constraints on Ks-band emission from one of the nearest short hard gamma-ray bursts, GRB 160821B, at z=0.16, at three epochs. We detect a reddened relativistic afterglow from the jetted emission in the first epoch but do not detect any excess kilonova emission in the second two epochs. We compare upper limits obtained with Keck I/MOSFIRE to multi-dimensional radiative transfer models of kilonovae, that employ composition-dependent nuclear heating and LTE opacities of heavy elements. We discuss eight models that combine toroidal dynamical ejecta and two types of wind and one model with dynamical ejecta only. We also discuss simple, empirical scaling laws of predicted emission as a function of ejecta mass and ejecta velocity. Our limits for GRB 160821B constrain the ejecta mass to be lower than 0.03 Msun for velocities greater than 0.1c. At the distance sensitivity range of advanced LIGO, similar ground-based observations would be sufficiently sensitive to the full range of predicted model emission including models with only dynamical ejecta. The color evolution of these models shows that I-K color spans 7--16 mag, which suggests that even relatively shallow infrared searches for kilonovae could be as constraining as optical searches.Comment: Accepted for Publication in Astrophysical Journal Letter

Neutrino-driven winds from neutron star merger remnants

We present a detailed, 3D hydrodynamics study of the neutrino-driven winds that emerge from the remnant of a NS merger. Our simulations are performed with the Newtonian, Eulerian code FISH, augmented by a detailed, spectral neutrino leakage scheme that accounts for heating due to neutrino absorption in optically thin conditions. Consistent with the 2D study of Dessart et al. (2009), we find that a strong baryonic wind is blown out along the original binary rotation axis within $100$ ms after the merger. We compute a lower limit on the expelled mass of $3.5 \times 10^{-3} M_{\odot}$, large enough to be relevant for heavy element nucleosynthesis. The physical properties vary significantly between different wind regions. For example, due to stronger neutrino irradiation, the polar regions show substantially larger $Y_e$ than those at lower latitudes. This has its bearings on the nucleosynthesis: the polar ejecta produce interesting r-process contributions from $A\sim 80$ to about 130, while the more neutron-rich, lower-latitude parts produce also elements up to the third r-process peak near $A\sim 195$. We also calculate the properties of electromagnetic transients that are powered by the radioactivity in the wind, in addition to the macronova transient that stems from the dynamic ejecta. The high-latitude (polar) regions produce UV/optical transients reaching luminosities up to $10^{41} {\rm erg \, s^{-1}}$, which peak around 1 day in optical and 0.3 days in bolometric luminosity. The lower-latitude regions, due to their contamination with high-opacity heavy elements, produce dimmer and more red signals, peaking after $\sim 2$ days in optical and infrared. Our numerical experiments indicate that it will be difficult to infer the collapse time-scale of the HMNS to a BH based on the wind electromagnetic transient, at least for collapse time-scales larger than the wind production time-scale.Comment: 25 pages, 4 tables, 22 figures. Submitted to MNRA

Isotopic gamma lines for identification of shielding materials

Identifying the constituting materials of concealed objects is crucial in a wide range of sectors, such as medical imaging, geophysics, nonproliferation, national security investigations, and so on. Existing methods face limitations, particularly when multiple materials are involved or when there are challenges posed by scattered radiation and large areal mass. Here we introduce a novel brute-force statistical approach for material identification using high spectral resolution detectors, such as HPGe. The method relies upon updated semianalytic formulae for computing uncollided flux from source of gamma radiation, shielded by a sequence of nested spherical or cylindrical materials. These semianalytical formulae make possible rapid flux estimation for material characterization via combinatorial search through all possible combinations of materials, using a high-resolution HPGe counting detector. An important prerequisite for the method is that the geometry of the objects is known (for example, from X-ray radiography). We demonstrate the viability of this material characterization technique in several use cases with both simulated and experimental data.Comment: 16 pages; submitted to Nuclear Instruments and Methods in Physics Research; comments welcom

Modelling Populations of Kilonovae

The 2017 detection of a kilonova coincident with gravitational-wave emission has identified neutron star mergers as the major source of the heaviest elements, and dramatically constrained alternative theories of gravity. Observing a population of such sources has the potential to transform cosmology, nuclear physics, and astrophysics. However, with only one confident multi-messenger detection currently available, modelling the diversity of signals expected from such a population requires improved theoretical understanding. In particular, models which are quick to evaluate, and are calibrated with more detailed multi-physics simulations, are needed to design observational strategies for kilonovae detection, and to obtain rapid-response interpretations of new observations. We use grey-opacity models to construct populations of kilonovae, spanning ejecta parameters predicted by numerical simulations. Our modelling focuses on wavelengths relevant for upcoming optical surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST). In these simulations, we implement heating rates that are based on nuclear reaction network calculations. We create a Gaussian-process emulator for kilonova grey opacities, calibrated with detailed radiative transfer simulations. Using recent fits to numerical relativity simulations, we predict how the ejecta parameters from BNS mergers shape the population of kilonovae, accounting for the viewing-angle dependence. Our simulated population of binary neutron star (BNS) mergers produce peak i-band absolute magnitudes $-20 \leq M_i \leq -11$. A comparison with detailed radiative transfer calculations indicates that further improvements are needed to accurately reproduce spectral shapes over the full light curve evolution.Comment: 14 pages, 12 figures, 2 tables, matches version accepted to MNRAS. Fixes a software bug from previous versions which incorrectly determined the kilonovae ejecta velocitie