arXiv subjects

Viktor T. Toth

Publications and source records attributed to Viktor T. Toth.

At least 55 records · Page 3Linked to original sources

arXiv2019

Imaging extended sources with the solar gravitational lens

We investigate the optical properties of the solar gravitational lens (SGL) with respect to an extended source located at a large but finite distance from the Sun. The static, spherically symmetric gravitational field of the Sun is modeled within the first post-Newtonian approximation of the general theory of relativity. We consider the propagation of monochromatic electromagnetic (EM) waves near the Sun. We develop, based on a Mie theory, a vector theory of diffraction that accounts for the refractive properties of the solar gravitational field. The finite distance to a point source can be accounted for using a rotation of the coordinate system to align its polar axis with the axis directed from the point source to the center of the Sun, which we call the optical axis. We determine the EM field and study the key optical properties of the SGL in all four regions formed behind the Sun by an EM wave diffracted by the solar gravity field: the shadow, geometric optics, and weak and strong interference regions. Extended sources can then be represented as collections of point sources. We present the power density of the signal received by a telescope in the image plane. Our discussion concludes with considering the implications for imaging with the SGL.

gr-qc↗

arXiv2019

Diffraction of light by plasma in the solar system

We study the propagation of electromagnetic (EM) waves in the solar system and develop a Mie theory that accounts for the refractive properties of the free electron plasma in the extended solar corona. We use a generic model for the electron number density distribution and apply the eikonal approximation to find a solution in terms of Debye potentials, which is then used to determine the EM field both within the inner solar system and at large heliocentric distances. As expected, the solution for the EM wave propagating through the solar system is characterized by a plasma-induced phase shift and related change in the light ray's direction of propagation. Our approach quantitatively accounts for these effects, providing a wave-optical treatment for diffraction in the solar plasma. As such, it may be used in practical applications involving big apertures, large interferometric baselines or otherwise widely distributed high-precision astronomical instruments.

physics.optics↗

arXiv2019

Optical properties of the solar gravitational lens in the presence of the solar corona

We investigate the optical properties of the solar gravitational lens (SGL) in the presence of the solar corona. For this, we consider the combined influence of the static spherically symmetric gravitational field of the Sun---modeled within the first post-Newtonian approximation of the general theory of relativity---and of the solar corona---modeled as a generic, static, spherically symmetric free electron plasma. We study the propagation of monochromatic electromagnetic (EM) waves through the solar system and develop a Mie theory that accounts for the refractive properties of the gravitational field of the Sun and that of the free electron plasma in the extended solar system. We establish a compact, closed-form solution to the boundary value problem and demonstrate that the presence of the solar plasma affects all characteristics of an incident unpolarized light. The affected properties include the direction of the EM wave propagation, its amplitude and its phase, leading to a reduction of the light amplification of the SGL and to a broadening of the corresponding point spread function. The wavelength-dependent plasma effect is critically important at radio frequencies, where it drastically reduces both the amplification factor of the SGL and also its angular resolution. However, for optical and shorter wavelengths, the plasma's contribution to the EM wave leaves the plasma-free optical properties of the SGL practically unaffected. We discuss the applicability of the SGL for direct high-resolution multipixel imaging and spatially-resolved spectroscopy of exoplanets

gr-qc↗

arXiv2019

Diffraction of light by the gravitational field of the Sun and the solar corona

We study the optical properties of the solar gravitational lens (SGL) under the combined influence of the static spherically symmetric gravitational field of the Sun---modeled within the first post-Newtonian approximation of the general theory of relativity---and of the solar corona---modeled as a generic, steady-state, spherically symmetric free electron plasma. For this, we consider the propagation of monochromatic electromagnetic (EM) waves near the Sun and develop a Mie theory that accounts for the refractive properties of the gravitational field of the Sun and that of the free electron plasma in the extended solar system. We establish a compact, closed-form solution to the boundary value problem, which extends previously known results into the new regime where gravity and plasma are both present. Relying on the wave-optical approach, we consider three different regions of practical importance for the SGL, including the shadow region directly behind the Sun, the region of geometrical optics and the interference region. We demonstrate that the presence of the solar plasma affects all characteristics of an incident unpolarized light, including the direction of the EM wave propagation, its amplitude and its phase. We show that the presence of the solar plasma leads to a reduction of the light amplification of the SGL and to a broadening of its point spread function. We also show that the wavelength-dependent plasma effect is important at radio frequencies, where it drastically reduces both the amplification factor of the SGL and also its angular resolution. However, for optical and shorter wavelengths, the plasma's contribution to the EM wave is negligibly small, leaving the plasma-free optical properties of the SGL practically unaffected.

gr-qc↗

arXiv2018

Wave-optical treatment of the shadow cast by a large gravitating sphere

We study the shadow cast by a large gravitating sphere, similar to our Sun. For this, we consider the gravitational field produced by a static mass monopole within the first post-Newtonian approximation of the general theory of relativity. We study the propagation of a monochromatic electromagnetic wave in the vicinity of a large, opaque, gravitating sphere. To treat the opaque nature of the body and its physical size, we implement fully absorbing boundary conditions and develop a wave-optical treatment of the shadow formed by this object. Based on this approach, we demonstrate that the structure of the shadow is determined by the Schwarzschild radius of the body and its physical size. The shadow's boundary has the shape of a concave rotational hyperboloid bent inward due to the refractive properties of the curved spacetime. We show that there is no light in the shadow. However, even in the presence of gravity and related gravitational bending of photon trajectories there is the bright spot of Arago that is formed behind a perfectly spherical obscuration.

gr-qc↗

arXiv2018

Wave-optical treatment of the shadow cast by a large sphere

We study the electromagnetic (EM) field in the shadow cast by a large opaque sphere. For this, we consider the scattering of a high frequency monochromatic EM wave by the large sphere and develop a Mie theory that accounts for the presence of this obscuration. Applying fully absorbing boundary conditions, we find a solution for the Debye potentials, which we use to determine the EM field in the shadow in the wave zone at large distances from the sphere. We use the standard tools available from the nuclear scattering theory to develop the wave-optical treatment of the problem. Based on this treatment, we demonstrate that there is no EM field deep in the shadow, except for the field that is diffracted into the shadow by the edges of the sphere, as anticipated.

physics.optics↗

arXiv2018

Diffraction of electromagnetic waves in the gravitational field of the Sun

We consider the propagation of electromagnetic (EM) waves in the gravitational field of the Sun within the first post-Newtonian approximation of the general theory of relativity. We solve Maxwell's equations for the EM field propagating on the background of a static mass monopole and find an exact closed form solution for the Debye potentials, which, in turn, yield a solution to the problem of diffraction of EM waves in the gravitational field of the Sun. The solution is given in terms of the confluent hypergeometric function and, as such, it is valid for all distances and angles. Using this solution, we develop a wave-theoretical description of the solar gravitational lens (SGL) and derive expressions for the EM field and energy flux in the immediate vicinity of the focal line of the SGL. Aiming at the potential practical applications of the SGL, we study its optical properties and discuss its suitability for direct high-resolution imaging of a distant exoplanet.

gr-qc↗

arXiv2018

Recognizing the Value of the Solar Gravitational Lens for Direct Multipixel Imaging and Spectroscopy of an Exoplanet

The Solar Gravitational Lens (SGL) allows for major brightness amplification ($\sim 10^{11}$ at wavelength of $1~μ$m) and extreme angular resolution ($\sim10^{-10}$ arcsec) within a narrow field of view. A meter-class telescope, with a modest coronagraph to block solar light with 1e-6 suppression placed in the focal area of the SGL, can image an exoplanet at a distance of 30 parsec with few kilometer-scale resolution on its surface. Notably, spectroscopic broadband SNR is $\sim 10^{-6}$ in two weeks of integration time, providing this instrument with incredible remote sensing capabilities. A mission capable of exploiting the remarkable optical properties of the SGL allows for direct high-resolution imaging/spectroscopy of a potentially habitable exoplanet. Such missions could allow exploration of exoplanets relying on the SGL capabilities decades, if not centuries, earlier than possible with other extant technologies.

astro-ph.IM↗

arXiv2018

Direct Multipixel Imaging and Spectroscopy of an Exoplanet with a Solar Gravity Lens Mission

The remarkable optical properties of the solar gravitational lens (SGL) include major brightness amplification (~1e11 at wavelength of 1 um) and extreme angular resolution (~1e-10 arcsec) in a narrow field of view. A mission to the SGL carrying a modest telescope and coronagraph opens up a possibility for direct megapixel imaging and high-resolution spectroscopy of a habitable Earth-like exoplanet at a distance of up to 100 light years. The entire image of such a planet is compressed by the SGL into a region with a diameter of ~1.3 km in the vicinity of the focal line. The telescope, acting as a single pixel detector while traversing this region, can build an image of the exoplanet with kilometer-scale resolution of its surface, enough to see its surface features and signs of habitability. We report here on the results of our initial study of a mission to the deep outer regions of our solar system, with the primary mission objective of conducting direct megapixel high-resolution imaging and spectroscopy of a potentially habitable exoplanet by exploiting the remarkable optical properties of the SGL. Our main goal was to investigate what it takes to operate spacecraft at such enormous distances with the needed precision. Specifically, we studied i) how a space mission to the focal region of the SGL may be used to obtain high-resolution direct imaging and spectroscopy of an exoplanet by detecting, tracking, and studying the Einstein ring around the Sun, and ii) how such information could be used to detect signs of life on another planet. Our results indicate that a mission to the SGL with an objective of direct imaging and spectroscopy of a distant exoplanet is challenging, but possible. We composed a list of recommendations on the mission architectures with risk and return tradeoffs and discuss an enabling technology development program.

astro-ph.IM↗

arXiv2016

Self-gravitating Bose-Einstein condensates and the Thomas-Fermi approximation

Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson equations (the GPP system). In the analysis of these hypothetical objects, the Thomas-Fermi (TF) approximation is widely used. This approximation is based on the assumption that in the presence of a large number of particles, the kinetic term in the Gross-Pitaevskii energy functional can be neglected, yet it is well known that this assumption is violated near the condensate surface. We also show that the total energy of the self-gravitating condensate in the TF-approximation is positive. The stability of a self-gravitating system is dependent on the total energy being negative. Therefore, the TF-approximation is ill suited to formulate initial conditions in numerical simulations. As an alternative, we offer an approximate solution of the full GPP system.

gr-qc↗

arXiv2016

Sparse Representations of Clifford and Tensor algebras in Maxima

Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an extensive demonstration of the applications of Clifford algebras in electromagnetism using the geometric algebra G3 = Cl(3,0) as a computational model in the Maxima computer algebra system. We compare the geometric algebra-based approach with conventional symbolic tensor calculations supported by Maxima, based on the itensor package. The Clifford algebra functionality of Maxima is distributed as two new packages called clifford - for basic simplification of Clifford products, outer products, scalar products and inverses; and cliffordan - for applications of geometric calculus.

cs.SC↗

arXiv2016

General relativistic observables for the ACES experiment

We develop a high-precision model for relativistic observables of the Atomic Clock Ensemble in Space (ACES) experiment on the International Space Station (ISS). We develop all relativistic coordinate transformations that are needed to describe the motion of ACES in Earth orbit and to compute observable quantities. We analyze the accuracy of the required model as it applies to the proper-to-coordinate time transformations, light time equation, and spacecraft equations of motion. We consider various sources of nongravitational noise and their effects on ACES. We estimate the accuracy of orbit reconstruction that is needed to satisfy the ACES science objectives. Based on our analysis, we derive models for the relativistic observables of ACES, which also account for the contribution of atmospheric drag on the clock rate. We include the Earth's oblateness coefficient $J_2$ and the effects of major nongravitational forces on the orbit of the ISS. We demonstrate that the ACES reference frame is pseudo-inertial at the level of accuracy required by the experiment. We construct a Doppler-canceled science observable representing the gravitational redshift. We derive accuracy requirements for ISS navigation. The improved model is accurate up to $<1$ ps and $\sim 4\times 10^{-17}$ for time and frequency transfers, correspondingly. These limits are determined by the higher order harmonics in Earth's gravitational potential.

gr-qc↗

arXiv2015

TianQin: a space-borne gravitational wave detector

TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiment's error budget and discuss the project's overall feasibility. Given the current level of technology readiness, we expect TianQin to be flown in the second half of the next decade.

astro-ph.IM↗

arXiv2015

New perturbative method for solving the gravitational N-body problem in the general theory of relativity

We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using an arbitrary energy-momentum tensor and assumed to possess any number of internal multipole moments. The solution of the gravitational field equations in any reference frame is presented as a sum of three terms: i) the inertial flat spacetime in that frame, ii) unperturbed solutions for each body in the system that is covariantly transformed to the coordinates of this frame, and iii) the gravitational interaction term. We use the harmonic gauge conditions that allow reconstruction of a significant part of the structure of the post-Galilean coordinate transformation functions relating global coordinates of the inertial reference frame to the local coordinates of the non-inertial frame associated with a particular body. The remaining parts of these functions are determined from dynamical conditions, obtained by constructing the relativistic proper reference frame associated with a particular body. In this frame, the effect of external forces acting on the body is balanced by the fictitious frame-reaction force that is needed to keep the body at rest with respect to the frame, conserving its relativistic three-momentum. The resulting post-Galilean coordinate transformations have an approximate group structure that extends the Poincar'e group of global transformations to the case of accelerating observers in a gravitational field of $N$-body system. We present and discuss the structure of the metric tensors corresponding to the reference frames involved, the rules for transforming relativistic gravitational potentials, the coordinate transformations between frames and the resulting relativistic equations of motion.

gr-qc↗

arXiv2014

Evolution and dynamical properties of Bose-Einstein condensate dark matter stars

Using recently developed nonrelativistic numerical simulation code, we investigate the stability properties of compact astrophysical objects that may be formed due to the Bose-Einstein condensation of dark matter. Once the temperature of a boson gas is less than the critical temperature, a Bose-Einstein condensation process can always take place during the cosmic history of the universe. Due to dark matter accretion, a Bose-Einstein condensed core can also be formed inside massive astrophysical objects such as neutron stars or white dwarfs, for example. Numerically solving the Gross-Pitaevskii-Poisson system of coupled differential equations, we demonstrate, with longer simulation runs, that within the computational limits of the simulation the objects we investigate are stable. Physical properties of a self-gravitating Bose-Einstein condensate are examined both in non-rotating and rotating cases.

hep-ph↗

arXiv2014

Accelerating classical charges and the equivalence principle

We compare the behavior of a charged particle in a gravitational field and empty space. We resolve the apparent conflict between the Lorentz-Dirac equation and Larmor's formula of radiation by noting that the former describes an electron that is itself accelerated by an electromagnetic field. If instead, a hypothetical particle is considered that is accelerated by a non-electromagnetic force, Larmor's formula is found to be consistent with the accelerating particle's equation of motion. We consider the consequences concerning the equivalence principle and find that it is indeed violated if one demands that the same electromagnetic field be present in both the gravitational and accelerating cases; however, if one allows for the external electromagnetic fields to be different, the validity of the equivalence principle is restored. In either case, the basic idea behind the equivalence principle, which leads to a geometrized theory of gravity, remains unaffected.

gr-qc↗

arXiv2014

General relativistic laser interferometric observables of the GRACE-Follow-On mission

We develop a high-precision model for laser ranging interferometric (LRI) observables of the GRACE Follow-On (GRACE-FO) mission. For this, we study the propagation of an electromagnetic wave in the gravitational field in the vicinity of an extended body, in the post-Newtonian approximation of the general theory of relativity. We present a general relativistic model for the phase of a plane wave that accounts for contributions of all the multipoles of the gravitating body, its angular momentum, as well as the contribution of tidal fields produced by external sources. We develop a new approach to model a coherent signal transmission in the gravitational field of the solar system that relies on a relativistic treatment of the phase. We use this approach to describe high-precision interferometric measurements on GRACE-FO and formulate the key LRI observables, namely the phase and phase rate of a coherent laser link between the two spacecraft. We develop a relativistic model for the LRI-enabled range between the two GRACE-FO spacecraft, accurate to less than 1 nm, and a high-precision model for the corresponding range rate, accurate to better than 0.1 nm/s. We also formulate high-precision relativistic models for the double one-way range (DOWR) and DOWR-enabled range rate observables originally used on GRACE and now studied for interferometric measurements on GRACE-FO. Our formulation justifies the basic assumptions behind the design of the GRACE-FO mission and highlights the importance of achieving nearly circular and nearly identical orbits for the GRACE-FO spacecraft.

gr-qc↗

arXiv2013

Numerical simulation code for self-gravitating Bose-Einstein condensates

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson's equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 1E9 years using a finer (100x100x100) spatial grid, in less than a day of processor time on a contemporary desktop computer.

astro-ph.GA↗