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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

TURBULENT CONVECTION MODEL IN THE OVERSHOOTING REGION. II. THEORETICAL ANALYSIS

Turbulent convection models (TCMs) are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied to calculations of stellar structure and evolution. In order to understand the physical processes of the convective overshooting and to simplify the application of TCMs, a semi-analytic solution is necessary. We obtain the approximate solution and asymptotic solution of the TCM in the overshooting region, and find some important properties of the convective overshooting. (1) The overshooting region can be partitioned into three parts: a thin region just outside the convective boundary with high efficiency of turbulent heat transfer, a power-law dissipation region of turbulent kinetic energy in the middle, and a thermal dissipation area with rapidly decreasing turbulent kinetic energy. The decaying indices of the turbulent correlations k, u{sub r}'T'-bar, and T'T'-bar are only determined by the parameters of the TCM, and there is an equilibrium value of the anisotropic degree {omega}. (2) The overshooting length of the turbulent heat flux u{sub r}'T'-bar is about 1H{sub k} (H{sub k} = |dr/dln k|). (3) The value of the turbulent kinetic energy at the convective boundary k{sub C} can be estimated by a method called the maximum of diffusion. Turbulent correlations in the overshooting region can be estimated by using k{sub C} and exponentially decreasing functions with the decaying indices.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

AN INTEGRATED MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS AND QUIESCENT SPECTRA FROM HOMOGENEOUS AND INHOMOGENEOUS BLACK HOLE ACCRETION CORONAE

Many accreting black holes manifest time lags during outbursts, in which the hard Fourier component typically lags behind the soft component. Despite decades of observations of this phenomenon, the underlying physical explanation for the time lags has remained elusive, although there are suggestions that Compton reverberation plays an important role. However, the lack of analytical solutions has hindered the interpretation of the available data. In this paper, we investigate the generation of X-ray time lags in Compton scattering coronae using a new mathematical approach based on analysis of the Fourier-transformed transport equation. By solving this equation, we obtain the Fourier transform of the radiation Green’s function, which allows us to calculate the exact dependence of the time lags on the Fourier frequency, for both homogeneous and inhomogeneous coronal clouds. We use the new formalism to explore a variety of injection scenarios, including both monochromatic and broadband (bremsstrahlung) seed photon injection. We show that our model can successfully reproduce both the observed time lags and the time-averaged (quiescent) X-ray spectra for Cyg X-1 and GX 339-04, using a single set of coronal parameters for each source. The time lags are the result of impulsive bremsstrahlung injection occurring near the outer edge of the corona, while the time-averaged spectra are the result of continual distributed injection of soft photons throughout the cloud.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Hydrodynamic Simulations of Moonlet-induced Propellers in Saturn’s Rings: Application to Blériot

One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn’s A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Blériot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Blériot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν {sub 0} = 340 cm{sup 2} s{sup −1}, a dispersion velocity in the range of 0.3 cm s{sup −1} < c {sub 0} < 1.5 cm s{sup −1}, and a fairly high bulk viscosity 7 < ξ {sub 0}/ν {sub 0} < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

A GENERAL RELATIVISTIC RAY-TRACING METHOD FOR ESTIMATING THE ENERGY AND MOMENTUM DEPOSITION BY NEUTRINO PAIR ANNIHILATION IN COLLAPSARS

Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ({nu}+{nu}-bar{yields}e{sup -}+e{sup +}) in the vicinity of an accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic (GR) neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. We employ the Fehlberg (4,5) adaptive integrator in the Runge-Kutta method to perform the numerical integration accurately. For the neutrino opacity, the charged-current {beta}-processes, which are dominant in the vicinity of the accretion tori, are taken into account. The numerical accuracy of the developed code is certified by several tests in which we show comparisons with the corresponding analytical solutions. In order to solve the energy-dependent ray-tracing transport, we propose that an adaptive-mesh-refinement approach, which we take for the two radiation angles ({theta}, {phi}) and the neutrino energy, is useful in reducing the computational cost significantly. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the GR effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percent. After the accretion disk settles into a stationary state (typically later than {approx}9 s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest that the neutrino pair annihilation is potentially as important as the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Generation of scale invariant magnetic fields in bouncing universes

We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution. For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic field can arise before the bounce for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape after the bounce. However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain. In this work, with the help of a new time variable that we introduce, which we refer to as the e-N-fold, we investigate these scenarios numerically. Imposing the initial conditions on the modes in the contracting phase, we numerically evolve the modes across the bounce and evaluate the spectra of the electric and magnetic fields at a suitable time after the bounce. As one could have intuitively expected, though the complete spectra depend on the details of the bounce, we find that, under the original conditions, scale invariant spectra of the magnetic fields do arise for wavenumbers much smaller than the scale associated with the bounce. We also show that magnetic fields which correspond to observed strengths today can be generated for specific values of the parameters. But, we find that, at the bounce, the backreaction due to the electromagnetic modes that have been generated can be significantly large calling into question the viability of the model. We briefly discuss the implications of our results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets

An approximate analytical solution is presented, along with numerical calculations, for a system of two single-photon wave packets interacting via an ideal, localized Kerr medium. It is shown that, because of spontaneous emission into the initially unoccupied temporal modes, the cross-phase-modulation in the Schroedinger picture is very small as long as the spectral width of the single-photon pulses is well within the medium's bandwidth. In this limit, the Hamiltonian used can be derived from the 'giant Kerr effect' for a four-level atom, under conditions of electromagnetically induced transparency; it is shown explicitly that the linear absorption in this system increases as the pulse's spectral width approaches the medium's transparency bandwidth, and hence, as long as the absorption probability remains small, the maximum cross-phase-modulation is limited to essentially useless values. These results are in agreement with the general, causality-based, and unitarity-based arguments of Shapiro and Razavi [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. H. Shapiro and M. Razavi, New J. Phys. 9, 16 (2007)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Electron cyclotron harmonic resonances in high-frequency heating of the ionosphere

Electron acceleration by upper hybrid waves under cyclotron harmonic resonance interaction is studied. Theory is formulated; the analytical solutions in the second and fourth harmonic cyclotron resonance cases are obtained, and in the third harmonic case, a first order differential equation governing the evolution of the electron energy is derived. The theory is applied for explaining the generation of artificial ionization layers observed in high-frequency (HF) ionospheric heating experiments. The upper hybrid waves are assumed to be excited parametrically by the O-mode HF heating wave. As the decay mode is the lower hybrid wave, the excited upper hybrid waves have wavelengths ranging from 0.25 to 0.5 m, which are short enough to effectively incorporate the finite Larmour radius effect for the harmonic cyclotron resonance interactions as well as have a frequency bandwidth of about 20 kHz, which provides an altitude region of about 10 km for continuous harmonic cyclotron resonance interaction between electrons and descending waves in the slightly inhomogeneous geomagnetic field. The numerical results on electron acceleration show that electron fluxes with energies larger than 14 eV are generated in the three harmonic cases. These energetic electrons cause impact ionizations, which are descending to form artificial ionization layers at the bottom of the ionospheric F region.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

THE HYDROMAGNETIC INTERIOR OF A SOLAR QUIESCENT PROMINENCE. I. COUPLING BETWEEN FORCE BALANCE AND STEADY ENERGY TRANSPORT

This series of papers investigates the dynamic interiors of quiescent prominences revealed by recent Hinode and SDO/AIA high-resolution observations. This first paper is a study of the static equilibrium of the Kippenhahn-Schlueter diffuse plasma slab, suspended vertically in a bowed magnetic field, under the frozen-in condition and subject to a theoretical thermal balance among an optically thin radiation, heating, and field-aligned thermal conduction. The everywhere-analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system. For most values of the total mass frozen into a given bowed field, force balance and steady energy transport cannot both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness, within which the frozen-in condition must break down. An exact, resistive hydromagnetic extension of the Kippenhahn-Schlueter slab is also presented, resolving the mass-sheet singularity into a finite-thickness layer of steadily falling dense fluid. Our hydromagnetic result suggests that the narrow, vertical prominence H{sub {alpha}} threads may be falling across magnetic fields, with optically thick cores much denser and ionized to much lower degrees than conventionally considered. This implication is discussed in relation to (1) the recent SDO/AIA observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors, (2) the canonical range of 5-60 G determined from spectral polarimetric observations of prominence magnetic fields over the years, and (3) the need for a more realistic multi-fluid treatment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Nonequilibrium spin transport through a diluted magnetic semiconductor quantum dot system with noncollinear magnetization

The spin-dependent transport through a diluted magnetic semiconductor quantum dot (QD) which is coupled via magnetic tunnel junctions to two ferromagnetic leads is studied theoretically. A noncollinear system is considered, where the QD is magnetized at an arbitrary angle with respect to the leads' magnetization. The tunneling current is calculated in the coherent regime via the Keldysh nonequilibrium Green's function (NEGF) formalism, incorporating the electron-electron interaction in the QD. We provide the first analytical solution for the Green's function of the noncollinear DMS quantum dot system, solved via the equation of motion method under Hartree-Fock approximation. The transport characteristics (charge and spin currents, and tunnel magnetoresistance (TMR)) are evaluated for different voltage regimes. The interplay between spin-dependent tunneling and single-charge effects results in three distinct voltage regimes in the spin and charge current characteristics. The voltage range in which the QD is singly occupied corresponds to the maximum spin current and greatest sensitivity of the spin current to the QD magnetization orientation. The QD device also shows transport features suitable for sensor applications, i.e., a large charge current coupled with a high TMR ratio. - Highlights: Black-Right-Pointing-Pointer The spin polarized transport through a diluted magnetic quantum dot is studied. Black-Right-Pointing-Pointer The model is based on the Green's function and the equation of motion method. Black-Right-Pointing-Pointer The charge and spin currents and tunnel magnetoresistance (TMR) are investigated. Black-Right-Pointing-Pointer The system is suitable for current-induced spin-transfer torque application. Black-Right-Pointing-Pointer A large tunneling current and a high TMR are possible for sensor application.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2017

Equilibrium and Sudden Events in Chemical Evolution

We present new analytic solutions for one-zone (fully mixed) chemical evolution models that incorporate a realistic delay time distribution for Type Ia supernovae (SNe Ia) and can therefore track the separate evolution of αelements produced by core collapse supernovae (CCSNe) and iron peak elements synthesized in both CCSNe and SNe Ia. Our solutions allow constant, exponential, or linear–exponential (te{sup -t/τsfh}) star formation histories, or combinations thereof. In generic cases, α and iron abundances evolve to an equilibrium at which element production is balanced by metal consumption and gas dilution, instead of continuing to increase over time. The equilibrium absolute abundances depend principally on supernova yields and the outflow mass loading parameter η, while the equilibrium abundance ratio [α/Fe] depends mainly on yields and secondarily on star formation history. A stellar population can be metal-poor either because it has not yet evolved to equilibrium or because high outflow efficiency makes the equilibrium abundance itself low. Systems with ongoing gas accretion develop metallicity distribution functions (MDFs) that are sharply peaked, while “gas starved” systems with rapidly declining star formation, such as the conventional “closed box” model, have broadly peaked MDFs. A burst of star formation that consumes a significant fraction of a system’s available gas and retains its metals can temporarily boost [α/Fe] by 0.1–0.3 dex, a possible origin for rare, α-enhanced stars with intermediate age and/or high metallicity. Other sudden transitions in system properties can produce surprising behavior, including backward evolution of a stellar population from high to low metallicity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Peculiarities of Forming a Multiband Transmission Function Based on Multifrequency Acousto-Optic Diffraction

An analytical solution for the transmission function of noncoherent wideband radiation is obtained under acousto-optic (AO) filtering using a discrete set of monochromatic AO waves with a small spectral overlap. We studied characteristics of the AO transformation of a continuous spectrum of noncoherent radiation into a given set of discrete narrow bands of spectral transmission by excitation of a discrete set of sound frequencies. We carried out the analysis of transmission functions of individual channels taking into account a partial overlap of their spectra and possible intermodulation distortions. It is shown that a stationary value of the root-mean-square light power is found at the electronic output due to the photoelectric transformation and detecting diffracted light. Based on this, a necessary stationary, multiband, and nearly equidistant transmission function of a device can be formed by using a relevant spectrum of acoustic excitation. Peculiarities of this way of forming the multiband transmission function are revealed: the limitation of diffraction efficiency for an individual channel, the possibility of decoupling side lobes of adjacent channels, etc. A multiband acousto-optic filter (MAOF) was simulated that was based on a paratellurite monocrystal (TeO{sub 2}), which was previously used for experimental optical encoding. The theoretical and experimental results are in gratifying agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The origin of the plateau and late rebrightening in the afterglow of GRB 120326A

GRB 120326A is an unusual gamma-ray burst (GRB) that has a long plateau and a very late rebrightening in both X-ray and optical bands. The similar behavior of the optical and X-ray light curves suggests that they may share a common origin. The long plateau starts at several hundred seconds and ends at tens of thousands of seconds, and the peak time of the late rebrightening is about 30,000 s. We analyze the energy injection model by means of numerical and analytical solutions, considering both the wind environment and the interstellar medium environment for GRB afterglows. We particularly study the influence of the injection starting time, ending time, stellar wind density (or density of the circumburst environment), and injection luminosity on the shape of the afterglow light curves, respectively. In the wind model, we find that the light curve is largely affected by the parameters and that there is a 'bump' in the late stage. In the wind environment, we found that the longer the energy is injected, the more obvious the rebrightening will be. We also find that the peak time of the bump is determined by the stellar wind density. We use the late continuous injection model to interpret the unusual afterglow of GRB 120326A. The model fits the observational data well; however, we find that the timescale of the injection must be higher than 10,000 s, which implies that the timescale of the central engine activity must also be more than 10,000 s. This information can give useful constraints on the central engines of GRBs—we consider a newborn millisecond pulsar with a strong magnetic field to be the central engine. On the other hand, our results suggest that the circumburst environment of GRB 120326A is very likely a stellar wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Does administering iodine in radiological procedures increase patient doses?

Purpose: The authors investigated the changes in the pattern of energy deposition in tissue equivalent phantoms following the introduction of iodinated contrast media. Methods: The phantom consisted of a small “contrast sphere,” filled with water or iodinated contrast, located at the center of a 28 cm diameter water sphere. Monte Carlo simulations were performed using MCNP5 codes, validated by simulating irradiations with analytical solutions. Monoenergetic x-rays ranging from 35 to 150 keV were used to simulate exposures to spheres containing contrast agent with iodine concentrations ranging from 1 to 100 mg/ml. Relative values of energy imparted to the contrast sphere, as well as to the whole phantom, were calculated. Changes in patterns of energy deposition around the contrast sphere were also investigated. Results: Small contrast spheres can increase local absorbed dose by a factor of 13, but the corresponding increase in total energy absorbed was negligible (<1%). The highest localized dose increases were found to occur at incident photon energies of about 60 keV. For a concentration of about 10 mg/ml, typical of clinical practice, localized absorbed doses were generally increased by about a factor of two. At this concentration of 10 mg/ml, the maximum increase in total energy deposition in the phantom was only 6%. These simulations demonstrated that increases in contrast sphere doses were offset by corresponding dose reductions at distal and posterior locations. Conclusions: Adding iodine can result in values of localized absorbed dose increasing by more than an order of magnitude, but the total energy deposition is generally very modest (i.e., <10%). Their data show that adding iodine primarily changes the pattern of energy deposition in the irradiated region, rather than increasing patient doses per se.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

SELF-GRAVITATING BODY WITH AN INTERNAL MAGNETIC FIELD. I. NEW ANALYTICAL EQUILIBRIA

We construct exact analytical solutions of the equations describing the equilibrium of a self-gravitating magnetized fluid body, possibly rigidly rotating, by superposing two solutions of finite energy defined in the whole space, one describing a non-magnetized gravitating equilibrium (ST1) and the other describing a magnetized non-gravitating equilibrium (ST2). A large number of ST1s can be found in the literature and directly used for our constructions, and we thus concentrate on ST2s, which are difficult to obtain. We derive some of their general properties and exhibit two explicit classes of axisymmetric 'elementary' such equilibria. The first one is extracted from the stellar models proposed by Prendergast and by Kutvitskii and Solov'ev, respectively. The second one is constructed by using Palumbo's theory of isodynamic equilibria, for which the magnetic pressure is constant on each flux surface. Both types of ST2s have their magnetic field confined within a bounded region, respectively, of spherical and toroidal shapes. A much more general ST2 can be obtained by juxtaposing n+q elementary ST2s, with n of the first type and q of the second type, in such a way that the magnetic regions do not pairwise overlap. The specific equilibria we obtain by superposition thus have no external field extending to infinity, and may be three dimensional (3D), which invalidates a recent nonexistence conjecture. Moreover, they may be arranged to contain force-free regions. Our superposition method can be considered as a 3D generalization of the axisymmetric splitting method previously developed by Kutvitskii and Solov'ev.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

RADIONUCLIDE IONIZATION IN PROTOPLANETARY DISKS: CALCULATIONS OF DECAY PRODUCT RADIATIVE TRANSFER

We present simple analytic solutions for the ionization rate ζ{sub SLR} arising from the decay of short-lived radionuclides (SLRs) within protoplanetary disks. We solve the radiative transfer problem for the decay products within the disk, and thereby allow for the loss of radiation at low disk surface densities; energy loss becomes important outside R ∼> 30 AU for typical disk masses M{sub g} = 0.04 M{sub ☉}. Previous studies of chemistry/physics in these disks have neglected the impact of ionization by SLRs, and often consider only cosmic rays (CRs), because of the high CR-rate present in the interstellar medium. However, recent work suggests that the flux of CRs present in the circumstellar environment could be substantially reduced by relatively modest stellar winds, resulting in severely modulated CR ionization rates, ζ{sub CR}, equal to or substantially below that of SLRs (ζ{sub SLR} ∼< 10{sup –18} s{sup –1}). We compute the net ionizing particle fluxes and corresponding ionization rates as a function of position within the disk for a variety of disk models. The resulting expressions are especially simple for the case of vertically Gaussian disks (frequently assumed in the literature). Finally, we provide a power-law fit to the ionization rate in the midplane as a function of gas disk surface density and time. Depending on location in the disk, the ionization rates by SLRs are typically in the range ζ{sub SLR} ∼ (1-10) × 10{sup –19} s{sup –1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

An adaptive multi-level simulation algorithm for stochastic biological systems

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, “Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics,” SIAM Multiscale Model. Simul. 10(1), 146–179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the efficiency of our method using a number of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Black hole and galaxy coevolution from continuity equation and abundance matching

We investigate the coevolution of galaxies and hosted supermassive black holes (BHs) throughout the history of the universe by a statistical approach based on the continuity equation and the abundance matching technique. Specifically, we present analytical solutions of the continuity equation without source terms to reconstruct the supermassive BH mass function from the active galactic nucleus (AGN) luminosity functions. Such an approach includes physically motivated AGN light curves tested on independent data sets, which describe the evolution of the Eddington ratio and radiative efficiency from slim- to thin-disk conditions. We nicely reproduce the local estimates of the BH mass function, the AGN duty cycle as a function of mass and redshift, along with the Eddington ratio function and the fraction of galaxies with given stellar mass hosting an AGN with given Eddington ratio. We exploit the same approach to reconstruct the observed stellar mass function at different redshift from the ultraviolet and far-IR luminosity functions associated with star formation in galaxies. These results imply that the build-up of stars and BHs in galaxies occurs via in situ processes, with dry mergers playing a marginal role at least for stellar masses ≲3×10{sup 11} M{sub ⊙} and BH masses ≲10{sup 9} M{sub ⊙}, where the statistical data are more secure and less biased by systematic errors. In addition, we develop an improved abundance matching technique to link the stellar and BH content of galaxies to the gravitationally dominant dark matter (DM) component. The resulting relationships constitute a testbed for galaxy evolution models, highlighting the complementary role of stellar and AGN feedback in the star formation process. In addition, they may be operationally implemented in numerical simulations to populate DM halos or to gauge subgrid physics. Moreover, they may be exploited to investigate the galaxy/AGN clustering as a function of redshift, mass, and/or luminosity. In fact, the clustering properties of BHs and galaxies are found to be in full agreement with current observations, thus further validating our results from the continuity equation. Finally, our analysis highlights that (i) the fraction of AGNs observed in the slim-disk regime, where most of the BH mass is accreted, increases with redshift; and (ii) already at z≳6 a substantial amount of dust must have formed over timescales ≲10{sup 8} yr in strongly star-forming galaxies, making these sources well within the reach of ALMA surveys in (sub)millimeter bands.

79 ASTRONOMY AND ASTROPHYSICS↗