Semi-analytic Techniques Research Articles

Afterglows from Binary Neutron Star Postmerger Systems Embedded in Active Galactic Nuclei Disks

The observability of afterglows from binary neutron star mergers occurring within active galactic nuclei (AGN) disks is investigated. We perform 3D GRMHD simulations of a postmerger system and follow the jet launched from the compact object. We use semianalytic techniques to study the propagation of the blast wave powered by the jet through an AGN disk-like external environment, extending to distances beyond the disk scale height. The synchrotron emission produced by the jet-driven forward shock is calculated to obtain the afterglow emission. The observability of this emission at different frequencies is assessed by comparing it to the quiescent AGN emission. In the scenarios where the afterglow could temporarily outshine the AGN, we find that detection will be more feasible at higher frequencies (≳1014 Hz) and the electromagnetic counterpart could manifest as a fast variability in the AGN emission, on timescales less than a day.

Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems

Abstract In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.

Field Line Universal relaXer (FLUX): A Fluxon Approach to Coronal Magnetic Field Modeling

We describe a novel method for modeling the global, steady solar wind using photospheric magnetic fields as a driving boundary condition. Prior wind models in this class include both rapid heuristic methods that use potential field extrapolation and variants thereof, trading rigor for computation speed, and detailed 3D magnetohydrodynamic (MHD) models that attempt to simulate the entire solar corona with a degree of physical rigor, but require large amounts of computation. The Field Line Universal relaXer, an open-source numerical code that implements the “fluxon” semi-Lagrangian approach to MHD modeling, provides an intermediate approach between these two general classes. In particular, the fluxon approach to MHD describes the magnetic field through discrete analogs of magnetic field lines, relaxing these structures to a stationary state of force balance. In this work we introduce a 1D solar wind solution along each field line, providing an ensemble of solutions that are interpolated back onto a uniform grid at an outer boundary surface. This provides advantages in physical rigor over heuristic semianalytic techniques, and in computational efficiency over full 3D MHD techniques. Here we describe the underlying methodology and the FLUXPipe modeling pipeline process.

Tomography of stellar halos: what does anisotropy in a stellar halo tell us?

The stellar halo of the Milky Way is known to have a highly lumpy structure due to the presence of tidal debris and streams accreted from the satellite galaxies. The abundance and distribution of these substructures can provide a wealth of information on the assembly history of the Milky Way. We use some information-theoretic measures to study the anisotropy in a set of Milky Way-sized stellar halos from the Bullock & Johnston suite of simulations that uses a hybrid approach coupling semi-analytic and N-body techniques. Our analysis shows that the whole-sky anisotropy in each stellar halo increases with the distance from its centre and eventually plateaus out beyond a certain radius. All the stellar halos have a very smooth structure within a radius of ∼ 50 kpc and a highly anisotropic structure in the outskirts. At a given radius, the anisotropies at a fixed polar or azimuthal angle have two distinct components: (i) an approximately isotropic component and (ii) a component with large density fluctuations on small spatial scales. We remove the contributions of the substructures and any non-spherical shape of the halo by randomizing the polar and azimuthal coordinates of the stellar particles while keeping their radial distances fixed. We observe that the fluctuating part of the anisotropy is completely eliminated, and the approximately uniform component of the anisotropy is significantly reduced after the sphericalization. A comparison between the original halos and their sphericalized versions reveals that the approximately uniform part of the anisotropy originates from the discreteness noise and the non-spherical shape of the halo whereas the substructures contribute to the fluctuating part. We show that such distinction between the anisotropies has the potential to constrain the shape of the stellar halo and its substructures.

Blandford-Znajek monopole expansion revisited: novel non-analytic contributions to the power emission

The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas et al. put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations.Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole.We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter.We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter.The resulting formula for the energy extractionimproves the agreement with numerical simulations at finite spin.Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well.Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.

Moving Taylor series for solving one-dimensional one-phase Stefan problem

In this work, a modified form of Taylor series is proposed which we call the moving Taylor series. We prove theorems that formulate coefficients of the proposed series along with the formula of its time-derivatives. This new form of power series is applied solve one-dimensional one-phase Stefan problem which is an important model for describing heat applications with a moving boundary. Some examples are presented to demonstrate steps of the proposed technique and the results illustrate its efficiency when compared to other semi-analytic techniques.

Semi-analytic forecasts for JWST – V. AGN luminosity functions and helium reionization at z = 2–7

ABSTRACT Active galactic nuclei (AGN) forming in the early universe are thought to be the primary source of hard ionizing photons contributing to the reionization of intergalactic helium. However, the number density and spectral properties of high-redshift AGN remain largely unconstrained. In this work, we make use of physically informed models calibrated with a wide variety of available observations to provide estimates for the role of AGN throughout the Epoch of Reionization. We present AGN luminosity functions in various bands between z = 2 and 7 predicted by the well-established Santa Cruz semi-analytic model, which includes modelling of black hole accretion and AGN feedback. We then combine the predicted AGN populations with a physical spectral model for self-consistent estimates of ionizing photon production rates, which depend on the mass and accretion rate of the accreting supermassive black hole. We then couple the predicted comoving ionizing emissivity with an analytic model to compute the subsequent reionization history of intergalactic helium and hydrogen. This work demonstrates the potential of coupling physically motivated analytic or semi-analytic techniques to capture multiscale physical processes across a vast range of scales (here, from AGN accretion discs to cosmological scales). Our physical model predicts an intrinsic ionizing photon budget well above many of the estimates in the literature, meaning that helium reionization can comfortably be accomplished even with a relatively low escape fraction. We also make predictions for the AGN populations that are expected to be detected in future James Webb Space Telescope surveys.

Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit

<p style='text-indent:20px;'>We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barriers are time-dependent. We managed to show that these solutions are systematically more efficient for pricing and calibration than, e.g., the corresponding finite-difference solvers. In this paper we extend this technique to pricing double barrier options and present two approaches to solving it: the General Integral transform method and the Heat Potential method. Our results confirm that for double barrier options these semi-analytic techniques are also more efficient than the traditional numerical methods used to solve this type of problems.</p>

Pseudo-parameter Iteration Method (PIM): A semi-analytic solution procedure for nonlinear problems

We present an iterative semi-analytical method for solving not only nonlinear ordinary differential equations but partial differential equations. In this method, a system of nonlinear integral equations, equivalent to an original differential equation together with (initial and) boundary conditions, is constructed based on an artificially introduced (non-zero) parameter. The method finds a solution for the differential equation with the conditions by solving the integral equation system via the Banach contraction principle. The parameter, referred to as the pseudo-parameter, is a non-zero auxiliary (non-physical) parameter that provides a key to arrive at the integral equations from the differential equation. Further, the parameter can be viewed as a control parameter, which can control the performance of the method, e.g., its accuracy and convergence speed, etc. Especially, the present method, different from other nonlinear semi-analytic techniques such as the perturbation approach, does not depend on a small (perturbation) parameter, so that it can find a wide application in (strongly) nonlinear physical problems without a proper linearization strategy under small perturbations.

Accelerated HPSTM: An efficient semi-analytical technique for the solution of nonlinear PDE’s

AbstractIn this paper a novel technique i.e. accelerated homotopy perturbation Sumudu transformation method (AHPSTM), which is a hybrid of accelerated homotopy perturbation method and Sumudu transformation to obtain an approximate analytic solution of nonlinear partial differential equation (PDE) with proportional delay, is used. This approach is based on the new form of calculating He’s polynomial, which accelerates the convergence of the series solution. The series solutions obtained from the proposed method are found to converge rapidly to exact solution. In order to affirm the effectiveness and legitimacy of proposed method, the proposed technique is implemented on nonlinear partial differential equation (PDE) with proportional delay. The condition of convergence of series solution is analyzed. Moreover, statistical analysis has been performed to analyze the outcome acquired by AHPSTM and other semi-analytic techniques.

Preheating after multifield inflation with nonminimal couplings. II. Resonance structure

This is the second in a series of papers on preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. In this paper, we work in the rigid-spacetime approximation and consider field trajectories within the single-field attractor, which is a generic feature of these models. We construct the Floquet charts to find regions of parameter space in which particle production is efficient for both the adiabatic and isocurvature modes, and analyze the resonance structure using analytic and semi-analytic techniques. Particle production in the adiabatic direction is characterized by the existence of an asymptotic scaling solution at large values of the nonminimal couplings, $\xi_I \gg 1$, in which the dominant instability band arises in the long-wavelength limit, for comoving wavenumbers $k \rightarrow 0$. However, the large-$\xi_I$ regime is not reached until $\xi_I \geq {\cal O} (100)$. In the intermediate regime, with $\xi_I \sim {\cal O}(1 - 10)$, the resonance structure depends strongly on wavenumber and couplings. The resonance structure for isocurvature perturbations is distinct and more complicated than its adiabatic counterpart. An intermediate regime, for $\xi_I \sim {\cal O} (1 - 10)$, is again evident. For large values of $\xi_I$, the Floquet chart consists of densely spaced, nearly parallel instability bands, suggesting a very efficient preheating behavior. The increased efficiency arises from features of the nontrivial field-space manifold in the Einstein frame, which itself arises from the fields' nonminimal couplings in the Jordan frame, and has no analogue in models with minimal couplings. Quantitatively, the approach to the large-$\xi_I$ asymptotic solution for isocurvature modes is slower than in the case of the adiabatic modes.

Exploring SMBH assembly with semi-analytic modelling

We develop a semi-analytic model to explore different prescriptions of supermassive black hole (SMBH) fuelling. This model utilises a merger-triggered burst mode in concert with two possible implementations of a long-lived steady mode for assembling the mass of the black hole in a galactic nucleus. We improve modelling of the galaxy-halo connection in order to more realistically determine the evolution of a halo's velocity dispersion. We use four model variants to explore a suite of observables: the M-sigma relation, mass functions of both the overall and broad-line quasar population, and luminosity functions as a function of redshift. We find that "downsizing" is a natural consequence of our improved velocity dispersion mappings, and that high-mass SMBHs assemble earlier than low-mass SMBHs. The burst mode of fuelling is sufficient to explain the assembly of SMBHs to z=2, but an additional steady mode is required to both assemble low-mass SMBHs and reproduce the low-redshift luminosity function. We discuss in detail the trade-offs in matching various observables and the interconnected modelling components that govern them. As a result, we demonstrate the utility as well as the limitations of these semi-analytic techniques.

Semi-analytic techniques for calculating bubble wall profiles

We present semi-analytic techniques for finding bubble wall profiles during first order phase transitions with multiple scalar fields. Our method involves reducing the problem to an equation with a single field, finding an analytic solution and perturbing around it. The perturbations can be written in a semi-analytic form. We argue that our technique lacks convergence problems and demonstrate the speed of convergence on an example potential.

From discs to bulges: effect of mergers on the morphology of galaxies

We study the effect of mergers on the morphology of galaxies by means of the simulated merger tree approach first proposed by Moster et al. This method combines N-body cosmological simulations and semi-analytic techniques to extract realistic initial conditions for galaxy mergers. These are then evolved using high resolution hydrodynamical simulations, which include dark matter, stars, cold gas in the disc and hot gas in the halo. We show that the satellite mass accretion is not as effective as previously thought, as there is substantial stellar stripping before the final merger. The fraction of stellar disc mass transferred to the bulge is quite low, even in the case of a major merger, mainly due to the dispersion of part of the stellar disc mass into the halo. We confirm the findings of Hopkins et al., that a gas rich disc is able to survive major mergers more efficiently. The enhanced star formation associated with the merger is not localised to the bulge of galaxy, but a substantial fraction takes place in the disc too. The inclusion of the hot gas reservoir in the galaxy model contributes to reducing the efficiency of bulge formation. Overall, our findings suggest that mergers are not as efficient as previously thought in transforming discs into bulges. This possibly alleviates some of the tensions between observations of bulgeless galaxies and the hierarchical scenario for structure formation.

Galaxy formation on the largest scales: the impact of astrophysics on the baryonic acoustic oscillation peak

We investigate the effects of galaxy formation on the baryonic acoustic oscillations (BAO) peak by applying semi-analytic modelling techniques to the Millennium-XXL, a $3 \times 10^{11}$ particle N-body simulation of similar volume to the future EUCLID survey. Our approach explicitly incorporates the effects of tidal fields and stochasticity on halo formation, as well as the presence of velocity bias, spatially correlated merger histories, and the connection of all these with the observable and physical properties of galaxies. We measure significant deviations in the shape of the BAO peak from the expectations of a linear bias model built on top of the nonlinear dark matter distribution. We find that the galaxy correlation function shows an excess close to the maximum of the BAO peak ($r\sim110 Mpc/h$) and a deficit at $r\sim90 Mpc/h$. Depending on the redshift, selection criteria and number density of the galaxy samples, these bias distortions can be up to 5% in amplitude. They are, however, largely absorbed by marginalization over nuisance parameters in current analytical modelling of the BAO peak in configuration space, in particular into the parameter that controls the broadening due to nonlinear evolution. As a result, the galaxy formation effects detected here are unlikely to bias the high-precision measurements planned by the upcoming generation of wide-field galaxy surveys.

Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both its (complex) permittivity and permeability tensors. Among the salient features of our formulation are (i) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (ii) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly evanescent spectra contributions, and (iii) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena (e.g., mode coupling at interfaces and nonreciprocal mode propagation). Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

ON THE ASSEMBLY HISTORY OF STELLAR COMPONENTS IN MASSIVE GALAXIES

Matsuoka & Kawara (2010) showed that the number density of the most massive galaxies (log M/M_sun=11.5-12.0) increases faster than that of the next massive group (log M/M_sun=11.0-11.5) during 0 < z < 1. This appears to be in contradiction to the apparent "downsizing effect". We attempt to understand the two observational findings in the context of the hierarchical merger paradigm using semi-analytic techniques. Our models closely reproduce the result of Matsuoka & Kawara (2010). Downsizing can also be understood as larger galaxies have, on average, smaller assembly ages but larger stellar ages. Our fiducial models further reveal details of the history of the stellar mass growth of massive galaxies. The most massive galaxies (log M/M_sun=11.5-12.0 at z=0), which are mostly brightest cluster galaxies, obtain roughly 70% of their stellar components via merger accretion. The role of merger accretion monotonically declines with galaxy mass: 40% for log M/M_sun=11.0-11.5 and 20% for log M/M_sun=10.5-11.0 at z=0. The specific accreted stellar mass rates via galaxy mergers decline very slowly during the whole redshift range, while specific star formation rates sharply decrease with time. In the case of the most massive galaxies, merger accretion becomes the most important channel for the stellar mass growth at z~2. On the other hand, in-situ star formation is always the dominant channel in L* galaxies.

The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate their identification. Second, we present a practical solution to the problem of multi-loop analytical tensor reduction. Finally, we discuss the partial fractioning of polynomials with external linear relations between the variables. All algorithms have been tested and used in real calculations.

The environmental history of group and cluster galaxies in a Λ cold dark matter universe

We use publicly available galaxy merger trees, obtained applying semi-analytic techniques to a large high resolution cosmological simulation, to study the environmental history of group and cluster galaxies. Our results highlight the existence of an intrinsic history bias which makes the nature versus nurture (as well as the mass versus environment) debate inherently ill posed. In particular we show that: (i) surviving massive satellites were accreted later than their less massive counterparts, from more massive haloes; (ii) the mixing of galaxy populations is incomplete during halo assembly, which creates a correlation between the time a galaxy becomes satellite and its present distance from the parent halo centre. The weakest trends are found for the most massive satellites, as a result of efficient dynamical friction and late formation times of massive haloes. A large fraction of the most massive group/cluster members are accreted onto the main progenitor of the final halo as central galaxies, while about half of the galaxies with low and intermediate stellar mass are accreted as satellites. Large fractions of group and cluster galaxies (in particular those of low stellar mass) have therefore been `pre-processed' as satellites of groups with mass ~10^13 Msun. To quantify the relevance of hierarchical structure growth on the observed environmental trends, we have considered observational estimates of the passive galaxy fractions, and their variation as a function of halo mass and cluster-centric distance. Comparisons with our theoretical predictions require relatively long times (~5-7 Gyr) for the suppression of star formation in group and cluster satellites. [abridged]

The population of Milky Way satellites in the Λ cold dark matter cosmology

We present a model for the satellites of the Milky Way in which galaxy formation is followed using semi-analytic techniques applied to the six high-resolution N-body simulations of galactic halos of the Aquarius project. The model, calculated using the Galform code, incorporates improved treatments of the relevant physics in the LambdaCDM cosmogony, particularly a self-consistent calculation of reionization by UV photons emitted by the forming galaxy population, including the progenitors of the central galaxy. Along the merger tree of each halo, the model calculates gas cooling (by Compton scattering off cosmic microwave background photons, molecular hydrogen and atomic processes), gas heating (from hydrogen photoionization and supernova energy), star formation and evolution. The evolution of the intergalactic medium is followed simultaneously with that of the galaxies. Star formation in the more massive progenitor subhalos is suppressed primarily by supernova feedback, while for smaller subhalos it is suppressed primarily by photoionization due to external and internal sources. The model is constrained to match a wide range of properties of the present day galaxy population as a whole, but at high redshift it requires an escape fraction of UV photons near unity in order completely to reionize the universe by redshift z ~ 8. In the most successful model the local sources photoionize the pre-galactic region completely by z ~ 10. In addition to the luminosity function of Milky Way satellites, the model matches their observed luminosity-metallicity relation, their radial distribution and the inferred values of the mass within 300 pc, which in the models increase slowly but significantly with luminosity. There is a large variation in satellite properties from halo to halo, with the luminosity function, for example, varying by a factor of ~ 2 among the six simulations.