arXiv subjects

Carl R. Gwinn

Publications and source records attributed to Carl R. Gwinn.

At least 19 recordsLinked to original sources

arXiv2024

An Electromagnetic Plane Wave in the Spacetime of a Plane Gravitational Wave

I find nearly plane-wave solutions for the Gauss-Ampere law for the 4-vector potential, subject to the Lorenz gauge condition, in the spacetime of a plane gravitational plane wave. I assume that the gravitational wave is weak, in the sense that the dimensionless strain amplitude h is much less than 1. I find a solution for the homogeneous scalar wave equation in this spacetime, and then find a 4-vector potential that solves the Gauss-Ampere law and Lorenz gauge condition in the absence of sources. The solutions are plane waves in Minkowski spacetime, plus additional scattered waves of order h. The problem is analogous to diffraction from a transmission grating, or Brillouin scattering from sound waves in matter. The corrections solve the inhomogeneous wave equation in Minkowski spacetime, with a "distributed source" of order h comprised of terms arising from the non-Minkowski metric and the zero-order solution. The scalar wave solution requires two scattered waves, which can be combined to form a phase correction h phi that varies at the gravitational-wave frequency. This phase correction yields the same time delay and deflection at the observer as for propagation along null geodesics, in the ray approximation. The electromagnetic-wave solution requires four scattered waves. Two correspond to the phase correction h phi found for the scalar field. The other two scattered waves introduce amplitude and polarization changes of order h to the electromagnetic wave. The time delay and deflection match those for the scalar waves. The solution predicts variations of the intensity of the electromagnetic wave of first order in h, at the wavenumber of the gravitational wave. These arise from interference of the first-order scattered waves and the zero-order solution. I briefly discuss possible observations of this effect.

gr-qc↗

arXiv2021

First Space-VLBI Observations of Sagittarius A*

We report results from the first Earth-space VLBI observations of the Galactic Center supermassive black hole, Sgr A*. These observations used the space telescope Spektr-R of the RadioAstron project together with a global network of 20 ground telescopes, observing at a wavelength of 1.35cm. Spektr-R provided baselines up to 3.9 times the diameter of the Earth, corresponding to an angular resolution of approximately 55 microarcseconds and a spatial resolution of $5.5 R_{\rm Sch}$ at the source, where $R_{\rm Sch} \equiv 2 G M/c^2$ is the Schwarzschild radius of Sgr A*. Our short ground baseline measurements (<80 Mλ) are consistent with an anisotropic Gaussian image, while our intermediate ground baseline measurements (100-250 Mλ) confirm the presence of persistent image substructure in Sgr A*. Both features are consistent with theoretical expectations for strong scattering in the ionized interstellar medium, which produces Gaussian scatter-broadening on short baselines and refractive substructure on long baselines. We do not detect interferometric fringes on any of the longer ground baselines or on any ground-space baselines. While space VLBI offers a promising pathway to sharper angular resolution and the measurement of key gravitational signatures in black holes, such as their photon rings, our results demonstrate that space VLBI studies of Sgr A* will require sensitive observations at submillimeter wavelengths.

astro-ph.GA↗

arXiv2019

Scintillation Arc Brightness and Electron Density for an Analytical Noodle Model

We show that narrow filaments or sheets of over- or under-dense plasma, or "noodles," with fluctuations of scattering phase of less than a radian, can form the scintillation arcs seen for many pulsars. The required local fluctuations of electron density are indefinitely small. We assume a cosine profile for the electron column and find the scattered field by analytic Kirchhoff integration. For a large electron column, corresponding to large amplitude of phase variation, the stationary-phase approximation is accurate; we call this regime "ray optics". For smaller-amplitude phase variation, the stationary-phase approximation is inaccurate or inapplicable; we call this regime "wave optics". We show that scattering is most efficient when the width of the strip equals that of one pair of Fresnel zones, and in the wave-optics regime. We show that the resolution of present observations is about 100 Fresnel zones on the scattering screen. Incoherent superposition of strips within a resolution element tends to increase the scattered field. We find that observations match a single noodle per resolution element with phase of up to 12 radians; or many noodles per resolution element with arbitrarily small phase variation each, for net phase of less than a radian. Observations suggest a minimum radius for noodles of about 650 km, comparable to the ion inertial scale or the ion cyclotron radius in the scattering plasma.

astro-ph.GA↗

arXiv2019

Noodle Model for Scintillation Arcs

I show that narrow, parallel strips of phase-changing material, or "noodles," generically produce parabolic structures in the delay-rate domain. Such structures are observed as "scintillation arcs" for many pulsars. The model assumes the strips have widths of a few Fresnel zones or less, and are much longer than they are wide. I use the Kirchhoff integral to find the scattered field. Along the strips, integration leads to a stationary-phase point where the strip is closest to the line of sight. Across the strip, the integral leads to a 1D Fourier transform. In the limit of narrow bandwidth and short integration time, the integral reproduces the observed scintillation arcs and secondary arclets. The set of scattered paths follows the pulsar as it moves. Cohorts of noodles parallel to different axes produce multiple arcs, as often observed. A single strip canted with respect to the rest produces features off the main arc. I present calculations for unrestricted frequency ranges and integration times; behavior of the arcs matches that observed, and can blur the arcs. Physically, the noodles may correspond to filaments or sheets of over- or under-dense plasma, with a normal perpendicular to the line of sight. The noodles may lie along parallel magnetic field lines that carry density fluctuations, perhaps in reconnection sheets. If so, observations of scintillation arcs would allow visualization of magnetic fields in reconnection regions.

astro-ph.GA↗

arXiv2018

The Scattering and Intrinsic Structure of Sagittarius A* at Radio Wavelengths

Radio images of the Galactic Center supermassive black hole, Sagittarius A* (Sgr A*), are dominated by interstellar scattering. Previous studies of Sgr A* have adopted an anisotropic Gaussian model for both the intrinsic source and the scattering, and they have extrapolated the scattering using a purely $λ^2$ scaling to estimate intrinsic properties. However, physically motivated source and scattering models break all three of these assumptions. They also predict that refractive scattering effects will be significant, which have been ignored in standard model fitting procedures. We analyze radio observations of Sgr A* using a physically motivated scattering model, and we develop a prescription to incorporate refractive scattering uncertainties when model fitting. We show that an anisotropic Gaussian scattering kernel is an excellent approximation for Sgr A* at wavelengths longer than 1cm, with an angular size of $(1.380 \pm 0.013) λ_{\rm cm}^2\,{\rm mas}$ along the major axis, $(0.703 \pm 0.013) λ_{\rm cm}^2\,{\rm mas}$ along the minor axis, and a position angle of $81.9^\circ \pm 0.2^\circ$. We estimate that the turbulent dissipation scale is at least $600\,{\rm km}$, with tentative support for $r_{\rm in} = 800 \pm 200\,{\rm km}$, suggesting that the ion Larmor radius defines the dissipation scale. We find that the power-law index for density fluctuations in the scattering material is $β< 3.47$, shallower than expected for a Kolmogorov spectrum ($β=11/3$), and we estimate $β= 3.38^{+0.08}_{-0.04}$ in the case of $r_{\rm in} = 800\,{\rm km}$. We find that the intrinsic structure of Sgr A* is nearly isotropic over wavelengths from 1.3mm to 1.3cm, with a size that is roughly proportional to wavelength. We discuss implications for models of Sgr A*, for theories of interstellar turbulence, and for imaging Sgr A* with the Event Horizon Telescope.

astro-ph.GA↗

arXiv2016

Extreme Brightness Temperatures and Refractive Substructure in 3C273 with RadioAstron

Earth-space interferometry with RadioAstron provides the highest direct angular resolution ever achieved in astronomy at any wavelength. RadioAstron detections of the classic quasar 3C273 on interferometric baselines up to 171,000 km suggest brightness temperatures exceeding expected limits from the "inverse-Compton catastrophe" by two orders of magnitude. We show that at 18 cm, these estimates most probably arise from refractive substructure introduced by scattering in the interstellar medium. We use the scattering properties to estimate an intrinsic brightness temperature of 7*10^12 K, which is consistent with expected theoretical limits, but which is ~15 times lower than estimates that neglect substructure. At 6.2 cm, the substructure influences the measured values appreciably but gives an estimated brightness temperature that is comparable to models that do not account for the substructure. At 1.35 cm, the substructure does not affect the extremely high inferred brightness temperatures, in excess of 10^13 K. We also demonstrate that for a source having a Gaussian surface brightness profile, a single long-baseline estimate of refractive substructure determines an absolute minimum brightness temperature, if the scattering properties along a given line of sight are known, and that this minimum accurately approximates the apparent brightness temperature over a wide range of total flux densities.

astro-ph.HE↗

arXiv2016

Theory and Simulations of Refractive Substructure in Resolved Scatter-Broadened Images

At radio wavelengths, scattering in the interstellar medium distorts the appearance of astronomical sources. Averaged over a scattering ensemble, the result is a blurred image of the source. However, Narayan & Goodman (1989) and Goodman & Narayan (1989) showed that for an incomplete average, scattering introduces refractive substructure in the image of a point source that is both persistent and wideband. We show that this substructure is quenched but not smoothed by an extended source. As a result, when the scatter-broadening is comparable to or exceeds the unscattered source size, the scattering can introduce spurious compact features into images. In addition, we derive efficient strategies to numerically compute realistic scattered images, and we present characteristic examples from simulations. Our results show that refractive substructure is an important consideration for ongoing missions at the highest angular resolutions, and we discuss specific implications for RadioAstron and the Event Horizon Telescope.

astro-ph.IM↗

arXiv2014

Imaging an Event Horizon: Mitigation of Scattering Toward Sagittarius A*

The image of the emission surrounding the black hole in the center of the Milky Way is predicted to exhibit the imprint of general relativistic (GR) effects, including the existence of a shadow feature and a photon ring of diameter ~50 microarcseconds. Structure on these scales can be resolved by millimeter-wavelength very long baseline interferometry (VLBI). However, strong-field GR features of interest will be blurred at lambda >= 1.3 mm due to scattering by interstellar electrons. The scattering properties are well understood over most of the relevant range of baseline lengths, suggesting that the scattering may be (mostly) invertible. We simulate observations of a model image of Sgr A* and demonstrate that the effects of scattering can indeed be mitigated by correcting the visibilities before reconstructing the image. This technique is also applicable to Sgr A* at longer wavelengths.

astro-ph.IM↗

arXiv2013

Interferometric Visibility of a Scintillating Source: Statistics at the Nyquist Limit

We derive the distribution of interferometric visibility for a source exhibiting strong diffractive scintillation, with particular attention to spectral resolution at or near the Nyquist limit. We also account for arbitrary temporal averaging, intrinsic variability within the averaging time, and the possibility of spatially-extended source emission. We demonstrate that the interplay between scintillation and self-noise induces several remarkable features, such as a broad "skirt" in the visibility distribution. Our results facilitate the interpretation of interferometric observations of pulsars at meter and decimeter wavelengths.

astro-ph.IM↗

arXiv2012

Optimal Correlation Estimators for Quantized Signals

Using a maximum-likelihood criterion, we derive optimal correlation strategies for signals with and without digitization. We assume that the signals are drawn from zero-mean Gaussian distributions, as is expected in radio-astronomical applications, and we present correlation estimators both with and without a priori knowledge of the signal variances. We demonstrate that traditional estimators of correlation, which rely on averaging products, exhibit large and paradoxical noise when the correlation is strong. However, we also show that these estimators are fully optimal in the limit of vanishing correlation. We calculate the bias and noise in each of these estimators and discuss their suitability for implementation in modern digital correlators.

astro-ph.IM↗

arXiv2012

Constraining the Vela Pulsar's Radio Emission Region Using Nyquist-Limited Scintillation Statistics

Using a novel technique, we achieve ~100 picoarcsecond resolution and set an upper bound of less than 4 km for the characteristic size of the Vela pulsar's emission region. Specifically, we analyze flux-density statistics of the Vela pulsar at 760 MHz. Because the pulsar exhibits strong diffractive scintillation, these statistics convey information about the spatial extent of the radio emission region. We measure both a characteristic size of the emission region and the emission sizes for individual pulses. Our results imply that the radio emission altitude for the Vela pulsar at this frequency is less than 340 km.

astro-ph.SR↗

arXiv2012

Ultra-High Resolution Intensity Statistics of a Scintillating Source

We derive the distribution of flux density of a compact source exhibiting strong diffractive scintillation. Our treatment accounts for arbitrary spectral averaging, spatially-extended source emission, and the possibility of intrinsic variability within the averaging time, as is typical for pulsars. We also derive the modulation index and present a technique for estimating the self-noise of the distribution, which can be used to identify amplitude variations on timescales shorter than the spectral accumulation time. Our results enable a for direct comparison with ultra-high resolution observations of pulsars, particularly single-pulse studies with Nyquist-limited resolution, and can be used to identify the spatial emission structure of individual pulses at a small fraction of the diffractive scale.

astro-ph.IM↗

arXiv2011

Noise and Signal for Spectra of Intermittent Noiselike Emission

We show that intermittency of noiselike emission, after propagation through a scattering medium, affects the distribution of noise in the observed correlation function. Intermittency also affects correlation of noise among channels of the spectrum, but leaves the average spectrum, average correlation function, and distribution of noise among channels of the spectrum unchanged. Pulsars are examples of such sources: intermittent and affected by interstellar propagation. We assume that the source emits Gaussian white noise, modulated by a time-envelope. Propagation convolves the resulting time series with an impulse-response function that represents effects of dispersion, scattering, and absorption. We assume that this propagation kernel is shorter than the time for an observer to accumulate a single spectrum. We show that rapidly-varying intermittent emission tends to concentrate noise near the central lag of the correlation function. We derive mathematical expressions for this effect, in terms of the time envelope and the propagation kernel. We present examples, discuss effects of background noise, and compare our results with observations.

astro-ph.GA↗

arXiv2005

Radio-wave propagation in the non-Gaussian interstellar medium

Radio waves propagating from distant pulsars in the interstellar medium (ISM), are refracted by electron density inhomogeneities, so that the intensity of observed pulses fluctuates with time. The theory relating the observed pulse time-shapes to the electron-density correlation function has developed for 30 years, however, two puzzles have remained. First, observational scaling of pulse broadening with the pulsar distance is anomalously strong; it is consistent with the standard model only when non-uniform statistics of electron fluctuations along the line of sight are assumed. Second, the observed pulse shapes are consistent with the standard model only when the scattering material is concentrated in a narrow slab between the pulsar and the Earth. We propose that both paradoxes are resolved at once if one assumes stationary and uniform, but non-Gaussian statistics of the electron-density distribution. Such statistics must be of Levy type, and the propagating ray should exhibit a Levy flight. We propose that a natural realization of such statistics may be provided by the interstellar medium with random electron-density discontinuities. We develop a theory of wave propagation in such a non-Gaussian random medium, and demonstrate its good agreement with observations. The qualitative introduction of the approach and the resolution of the anomalous-scaling paradox was presented earlier in [PRL 91, 131101 (2003); ApJ 584, 791 (2003)].

astro-ph↗

arXiv2003

Levy model for interstellar scintillations

Observations of radio signals from distant pulsars provide a valuable tool for investigation of interstellar turbulence. The time-shapes of the signals are the result of pulse broadening by the fluctuating electron density in the interstellar medium. While the scaling of the shapes with the signal frequency is well understood, the observed anomalous scaling with respect to the pulsar distance has remained a puzzle for more than 30 years. We propose a new model for interstellar electron density fluctuations, which explains the observed scaling relations. We suggest that these fluctuations obey Levy statistics rather than Gaussian statistics, as assumed in previous treatments of interstellar scintillations.

astro-ph↗

arXiv2000

Sub-Microarcsecond Astrometry and New Horizons in Relativistic Gravitational Physics

Attaining the limit of sub-microarcsecond optical resolution will completely revolutionize fundamental astrometry by merging it with relativistic gravitational physics. Beyond the sub-microarcsecond threshold, one will meet in the sky a new population of physical phenomena caused by primordial gravitational waves from early universe and/or different localized astronomical sources, space-time topological defects, moving gravitational lenses, time variability of gravitational fields of the solar system and binary stars, and many others. Adequate physical interpretation of these yet undetectable sub-microarcsecond phenomena can not be achieved on the ground of the "standard" post-Newtonian approach (PNA), which is valid only in the near-zone of astronomical objects having a time-dependent gravitational field. We describe a new, post-Minkowskian relativistic approach for modeling astrometric observations having sub-microarcsecond precision and briefly discuss the light-propagation effects caused by gravitational waves and other phenomena related to time-dependent gravitational fields. The domain of applicability of the PNA in relativistic space astrometry is explicitly outlined.

gr-qc↗

arXiv1999

Astrometric and Timing Effects of Gravitational Waves from Localized Sources

A consistent approach for an exhaustive solution of the problem of propagation of light rays in the field of gravitational waves emitted by a localized source of gravitational radiation is developed in the first post-Minkowskian and quadrupole approximation of General Relativity. We demonstrate that the equations of light propagation in the retarded gravitational field of an arbitrary localized source emitting quadrupolar gravitational waves can be integrated exactly. The influence of the gravitational field on the light propagation is examined not only in the wave zone but also in cases when light passes through the intermediate and near zones of the source. Explicit analytic expressions for light deflection and integrated time delay (Shapiro effect) are obtained accounting for all possible retardation effects and arbitrary relative locations of the source of gravitational waves, that of light rays, and the observer. It is shown that the ADM and harmonic gauge conditions can both be satisfied simultaneously outside the source of gravitational waves. Their use drastically simplifies the integration of light propagation equations and those for the motion of light source and observer in the field of the source of gravitational waves, leading to the unique interpretation of observable effects. The two limiting cases of small and large values of impact parameter are elaborated in more detail. Explicit expressions for Shapiro effect and deflection angle are obtained in terms of the transverse-traceless part of the space-space components of the metric tensor. We also discuss the relevance of the developed formalism for interpretation of radio interferometric and timing observations, as well as for data processing algorithms for future gravitational wave detectors.

gr-qc↗

arXiv1996

Quasar Proper Motions and Low-Frequency Gravitational Waves

We report observational upper limits on the mass-energy of the cosmological gravitational-wave background, from limits on proper motions of quasars. Gravitational waves with periods longer than the time span of observations produce a simple pattern of apparent proper motions over the sky, composed primarily of second-order transverse vector spherical harmonics. A fit of such harmonics to measured motions yields a 95%-confidence limit on the mass-energy of gravitational waves with frequencies <2e-9 Hz, of <0.11/h*h times the closure density of the universe.

astro-ph↗