arXiv subjects

Edmund Bertschinger

Publications and source records attributed to Edmund Bertschinger.

At least 19 recordsLinked to original sources

arXiv2019

Astro2020 APC White Paper: Providing a Timely Review of Input Demographics to Advisory Committees

Organizations that support science (astronomy) such as federal agencies, research centers, observatories, academic institutions, societies, etc. employ advisory committees and boards as a mechanism for reviewing their activities and giving advice on practices, policies and future directions. As with any scientific endeavor, there is concern over complementing these committees with enough members who have as broad a range of expertise and understanding as possible, so that bias is mitigated. However, for a number of reasons (logistical, practical, financial, etc.), committees can also not be infinitely large and thus trade-offs must be made. It is often recognized that conflicts of interest must be acknowledged within these committees, but what is not often recognized it the potential for unmitigated biases and "group think" that can be introduced as part of these committees. In this white paper, we recommend that advisory committees that collect community input, (e.g., the Decadal Survey review committee), also collect, compile and review input demographic data before finalizing reports, (e.g., the final 2020 Decadal Survey Report). A summary of these data should be released alongside the final survey report. This information would enable the committee to understand potential "blind spots" and biases of the data collection phase and inform future data collections of any barriers that affect the omission of perspectives from various demographics.

astro-ph.IM↗

arXiv2018

Time-symmetric integration in astrophysics

Calculating the long term solution of ordinary differential equations, such as those of the $N$-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally no analytic solution exists to these equations, researchers rely on numerical methods which are prone to various errors. In an effort to mitigate these errors, powerful symplectic integrators have been employed. But symplectic integrators can be severely limited because they are not compatible with adaptive stepping and thus they have difficulty accommodating changing time and length scales. A promising alternative is time-reversible integration, which can handle adaptive time stepping, but the errors due to time-reversible integration in astrophysics are less understood. The goal of this work is to study analytically and numerically the errors caused by time-reversible integration, with and without adaptive stepping. We derive the modified differential equations of these integrators to perform the error analysis. As an example, we consider the trapezoidal rule, a reversible non-symplectic integrator, and show it gives secular energy error increase for a pendulum problem and for a Hénon---Heiles orbit. We conclude that using reversible integration does not guarantee good energy conservation and that, when possible, use of symplectic integrators is favored. We also show that time-symmetry and time-reversibility are properties that are distinct for an integrator.

astro-ph.IM↗

arXiv2016

Women in physics in the United States: recruitment and retention

Initiatives to increase the number, persistence, and success of women in physics in the US reach pre-teen girls through senior women. Programs exist at both the local and national levels. In addition, researchers have investigated issues related to gender equity in physics and physics education. Anecdotal evidence suggests increased media coverage of the underrepresentation of women in science. All of these efforts are both motivated and made more effective by the collection and presentation of data on the presence, persistence, and promise of women in physics.

physics.ed-ph↗

arXiv2015

Symplectic integration for the collisional gravitational $N$-body problem

We present a new symplectic integrator designed for collisional gravitational $N$-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves 9 integrals of motion of the $N$-body problem to machine precision. The integrator is second order, but the order can easily be increased by the method of \citeauthor{yos90}. We use fixed time step in all tests studied in this paper to ensure preservation of symplecticity. We study small $N$ collisional problems and perform comparisons with typically used integrators. In particular, we find comparable or better performance when compared to the 4th order Hermite method and much better performance than adaptive time step symplectic integrators introduced previously. We find better performance compared to SAKURA, a non-symplectic, non-time-reversible integrator based on a different two-body decomposition of the $N$-body problem. The integrator is a promising tool in collisional gravitational dynamics.

astro-ph.IM↗

arXiv2015

An Extension of the Faddeev-Jackiw Technique to Fields in Curved Spacetimes

The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev-Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating a Hamiltonian paired with a well-defined initial value problem when working with a singular Lagrangian. This phase space coordinate reduction was generalized by Barcelos-Neto and Wotzasek to simplify its application. We present an extension of the Faddeev-Jackiw technique for constraint reduction in gauge field theories and non-gauge field theories that are coupled to a curved spacetime that is described by General Relativity. A major difference from previous formulations is that we do not explicitly construct the symplectic matrix, as that is not necessary. We find that the technique is a useful tool that avoids some of the subtle complications of the Dirac approach to constraints. We apply this formulation to the Ginzburg-Landau action and provide a calculation of its Hamiltonian and Poisson brackets in a curved spacetime.

hep-th↗

arXiv2012

Scale-Dependent Growth from a Transition in Dark Energy Dynamics

We investigate the observational consequences of the quintessence field rolling to and oscillating near a minimum in its potential, "if" it happens close to the present epoch (z<0.2). We show that in a class of models, the oscillations lead to a rapid growth of the field fluctuations and the gravitational potential on subhorizon scales. The growth in the gravitational potential occurs on timescales << H^(1). This effect is present even when the quintessence parameters are chosen to reproduce an expansion history consistent with observations. For linearized fluctuations, we find that although the gravitational potential power spectrum is enhanced in a scale-dependent manner, the shape of the dark matter/galaxy power spectrum is not significantly affected. We find that the best constraints on such a transition in the quintessence field is provided via the integrated Sachs-Wolfe (ISW) effect in the CMB temperature power spectrum. Going beyond the linearized regime, the quintessence field can fragment into large, localized, long lived excitations (oscillons) with sizes comparable to galaxy clusters; this fragmentation could provide additional observational constraints. Two quoted "signatures" of modified gravity are a scale-dependent growth of the gravitational potential and a difference between the matter power spectrum inferred from measurements of lensing and galaxy clustering. Here, both effects are achieved by a minimally coupled scalar field in general relativity with a canonical kinetic term.

astro-ph.CO↗

arXiv2011

One Gravitational Potential or Two? Forecasts and Tests

The metric of a perturbed Robertson-Walker spacetime is characterized by three functions: a scale-factor giving the expansion history and two potentials which generalize the single potential of Newtonian gravity. The Newtonian potential induces peculiar velocities and, from these, the growth of matter fluctuations. Massless particles respond equally to the Newtonian potential and to a curvature potential. The difference of the two potentials, called the gravitational slip, is predicted to be very small in general relativity but can be substantial in modified gravity theories. The two potentials can be measured, and gravity tested on cosmological scales, by combining weak gravitational lensing or the Integrated Sachs-Wolfe effect with galaxy peculiar velocities or clustering.

astro-ph.CO↗

arXiv2010

Self-Similar Spherical Collapse with Tidal Torque

N-body simulations have revealed a wealth of information about dark matter halos however their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by N-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We choose torque parameters motivated by tidal torque theory and N-body simulations and analytically calculate the structure of the halo in different radial regimes. We find that angular momentum plays an important role in determining the density profile at small radii. For cosmological initial conditions, the density profile on small scales is set by the time rate of change of the angular momentum of particles as well as the halo mass. On intermediate scales, however, $ρ\propto r^{-2}$, while $ρ\propto r^{-3}$ close to the virial radius.

astro-ph.CO↗

arXiv2010

Velocity Structure of Self-Similar Spherically Collapsed Halos

Using a generalized self-similar secondary infall model, which accounts for tidal torques acting on the halo, we analyze the velocity profiles of halos in order to gain intuition for N-body simulation results. We analytically calculate the asymptotic behavior of the internal radial and tangential kinetic energy profiles in different radial regimes. We then numerically compute the velocity anisotropy and pseudo-phase-space density profiles and compare them to recent N-body simulations. For cosmological initial conditions, we find both numerically and analytically that the anisotropy profile asymptotes at small radii to a constant set by model parameters. It rises on intermediate scales as the velocity dispersion becomes more radially dominated and then drops off at radii larger than the virial radius where the radial velocity dispersion vanishes in our model. The pseudo-phase-space density is universal on intermediate and large scales. However, its asymptotic slope on small scales depends on the halo mass and on how mass shells are torqued after turnaround. The results largely confirm N-body simulations but show some differences that are likely due to our assumption of a one-dimensional phase space manifold.

astro-ph.CO↗

arXiv2010

Seen and unseen tidal caustics in the Andromeda galaxy

Indirect detection of high-energy particles from dark matter interactions is a promising avenue for learning more about dark matter, but is hampered by the frequent coincidence of high-energy astrophysical sources of such particles with putative high-density regions of dark matter. We calculate the boost factor and gamma-ray flux from dark matter associated with two shell-like caustics of luminous tidal debris recently discovered around the Andromeda galaxy, under the assumption that dark matter is its own supersymmetric antiparticle. These shell features could be a good candidate for indirect detection of dark matter via gamma rays because they are located far from the primary confusion sources at the galaxy's center, and because the shapes of the shells indicate that most of the mass has piled up near apocenter. Using a numerical estimator specifically calibrated to estimate densities in N-body representations with sharp features and a previously determined N-body model of the shells, we find that the largest boost factors do occur in the shells but are only a few percent. We also find that the gamma-ray flux is an order of magnitude too low to be detected with Fermi for likely dark matter parameters, and about 2 orders of magnitude less than the signal that would have come from the dwarf galaxy that produces the shells in the N-body model. We further show that the radial density profiles and relative radial spacing of the shells, in either dark or luminous matter, is relatively insensitive to the details of the potential of the host galaxy but depends in a predictable way on the velocity dispersion of the progenitor galaxy.

astro-ph.GA↗

arXiv2009

Hierarchy in the Phase Space and Dark Matter Astronomy

We develop a theoretical framework for describing the hierarchical structure of the phase space of cold dark matter haloes, due to gravitationally bound substructures. Because it includes the full hierarchy of the cold dark matter initial conditions and is hence complementary to the halo model, the stable clustering hypothesis is applied for the first time here to the small-scale phase space structure. As an application, we show that the particle dark matter annihilation signal could be up to two orders of magnitude larger than that of the smooth halo within the Galactic virial radius. The local boost is inversely proportional to the smooth halo density, and thus is O(1) within the solar radius, which could translate into interesting signatures for dark matter direct detection experiments: The temporal correlation of dark matter detection can change by a factor of 2 in the span of 10 years, while there will be significant correlations in the velocity space of dark matter particles. This can introduce O(1) uncertainty in the direction of local dark matter wind, which was believed to be a benchmark of directional dark matter searches or the annual modulation signal.

astro-ph.CO↗

arXiv2008

Hierarchical Phase Space Structure of Dark Matter Haloes: Tidal debris, Caustics, and Dark Matter annihilation

Most of the mass content of dark matter haloes is expected to be in the form of tidal debris. The density of debris is not constant, but rather can grow due to formation of caustics at the apocenters and pericenters of the orbit, or decay as a result of phase mixing. In the phase space, the debris assemble in a hierarchy which is truncated by the primordial temperature of dark matter. Understanding this phase structure can be of significant importance for the interpretation of many astrophysical observations and in particular dark matter detection experiments. With this purpose in mind, we develop a general theoretical framework to describe the hierarchical structure of the phase space of cold dark matter haloes. We do not make any assumption of spherical symmetry and/or smooth and continuous accretion. Instead, working with correlation functions in the action-angle space, we can fully account for the hierarchical structure (predicting a two-point correlation function ~ (ΔJ)^{-1.6} in the action space), as well as the primordial discreteness of the phase space. As an application, we estimate the boost to the dark matter annihilation signal due to the structure of the phase space within virial radius: the boost due to the hierarchical tidal debris is of order unity, whereas the primordial discreteness of the phase structure can boost the total annihilation signal by up to an order of magnitude. The latter is dominated by the regions beyond 20% of the virial radius, and is largest for the recently formed haloes with the least degree of phase mixing.

astro-ph↗

arXiv2008

Kinematic Density Waves in Accretion Disks

When thin accretion disks around black holes are perturbed, the main restoring force is gravity. If gas pressure, magnetic stresses, and radiation pressure are neglected, the disk remains thin as long as orbits do not intersect. Intersections would result in pressure forces which limit the growth of perturbations. We find that a discrete set of perturbations is possible for which orbits remain non-intersecting for arbitrarily long times. These modes define a discrete set of frequencies. We classify all long-lived perturbations for arbitrary potentials and show how their mode frequencies are related to pattern speeds computed from the azimuthal and epicyclic frequencies. We show that modes are concentrated near radii where the pattern speed has vanishing radial derivative. We explore these modes around Kerr black holes as a possible explanation for the high-frequency quasi-periodic oscillations of black hole binaries such as GRO J1655-40. The long-lived modes are shown to coincide with diskoseismic waves in the limit of small sound speed. While the waves have long lifetime, they have the wrong frequencies to explain the pairs of high-frequency quasi-periodic oscillations observed in black hole binaries.

astro-ph↗

arXiv2008

Distinguishing Modified Gravity from Dark Energy

The acceleration of the universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark energy models. Modifications of general relativity are expected to be scale-independent on super-horizon scales and scale-dependent on sub-horizon scales. For scale-independent modifications, utilizing the conservation of the curvature scalar and a parameterized post-Newtonian formulation of cosmological perturbations, we derive results for large scale structure growth, weak gravitational lensing, and cosmic microwave background anisotropy. For scale-dependent modifications, inspired by recent $f(R)$ theories we introduce a parameterization for the gravitational coupling $G$ and the post-Newtonian parameter $γ$. These parameterizations provide a convenient formalism for testing general relativity. However, we find that if dark energy is generalized to include both entropy and shear stress perturbations, and the dynamics of dark energy is unknown a priori, then modified gravity cannot in general be distinguished from dark energy using cosmological linear perturbations.

astro-ph↗

arXiv2007

Variational Integrators for the Gravitational N-Body Problem

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.

astro-ph↗

arXiv2006

Effects of cold dark matter decoupling and pair annihilation on cosmological perturbations

Weakly interacting massive particles are part of the lepton-photon plasma in the early universe until kinetic decoupling, after which time the particles behave like a collisionless gas with nonzero temperature. The Boltzmann equation for WIMP-lepton collisions is reduced to a Fokker-Planck equation for the evolution of the WIMP distribution including scalar density perturbations. This equation and the Einstein and fluid equations for the plasma are solved numerically including the acoustic oscillations of the plasma before and during kinetic decoupling, the frictional damping occurring during kinetic decoupling, and the free-streaming damping occurring afterwards and throughout the radiation-dominated era. An excellent approximation reduces the solution to quadratures for the cold dark matter density and velocity perturbations. The subsequent evolution is followed through electron pair annihilation and the radiation-matter transition; analytic solutions are provided for both large and small scales. For a 100 GeV WIMP with bino-type interactions, kinetic decoupling occurs at a temperature $T_d=23$ MeV. The transfer function in the matter-dominated era leads to an abundance of small cold dark matter halos; with a smooth window function the Press-Schechter mass distribution is $dn/d\ln M\propto M^{-1/3}$ for $M<10^{-4} (T_d/$10 MeV)$^{-3}$ M$_\odot$.

astro-ph↗

arXiv2006

Brownian Motion of Stars, Dust, and Invisible Matter

Treating the motion of a dust particle suspended in a liquid as a random walk, Einstein in 1905 derived an equation describing the diffusion of the particle's probability distribution in configuration space. Fokker and Planck extended this work to describe the velocity distribution of the particles. Their equation and its solutions have been applied to many problems in nature starting with the motion of Brownian particles in a liquid. Chandrasekhar derived the Fokker-Planck equation for stars and showed that long-range gravitational encounters provide a drag force, dynamical friction, which is important in the evolution of star clusters and the formation of galaxies. In certain circumstances, Fokker-Planck evolution also describes the evolution of dark (invisible) matter in the universe. In the early universe, the thermal decoupling of weakly interacting massive particles from the plasma of relativistic leptons and photons is governed by Fokker-Planck evolution. The resulting dissipation imprints a minimum length scale for cosmic density fluctuations. Still later, these density fluctuations produce stochastic gravitational forces on the dark matter as it begins to cluster under gravity. The latter example provides an exact derivation of the Fokker-Planck equation without the usual assumption of Markovian dynamics.

astro-ph↗

arXiv2006

On the Growth of Perturbations as a Test of Dark Energy

The strongest evidence for dark energy comes presently from geometric techniques such as the supernova distance-redshift relation. By combining the measured expansion history with the Friedmann equation one determines the energy density and its time evolution, hence the equation of state of dark energy. Because these methods rely on the Friedmann equation which has not been independently tested it is desirable to find alternative methods that work for both general relativity and other theories of gravity. Assuming that sufficiently large patches of a perturbed Robertson-Walker spacetime evolve like separate Robertson-Walker universes, that shear stress is unimportant on large scales and that energy and momentum are locally conserved, we derive several relations between long-wavelength metric and matter perturbations. These relations include generalizations of the initial-value constraints of general relativity. For a class of theories including general relativity we reduce the long-wavelength metric, density, and velocity potential perturbations to quadratures including curvature perturbations, entropy perturbations, and the effects of nonzero background curvature. When combined with the expansion history measured geometrically, the long-wavelength solution provide a test that may distinguish modified gravity from other explanations of dark energy.

astro-ph↗