Interferometric Signatures Research Articles

Interferometric signatures of black holes with multiple photon spheres

Interferometric signatures of black holes with multiple photon spheres

Spatio-temporal analysis and volumetric characterization of interferometric synthetic aperture radar-observed deformation signatures related to underground and in situ leach mining

Spatio-temporal analysis and volumetric characterization of interferometric synthetic aperture radar-observed deformation signatures related to underground and in situ leach mining

Human Activity Classification Based on Dual Micro-Motion Signatures Using Interferometric Radar

Micro-Doppler signatures obtained from the Doppler radar are generally used for human activity classification. However, if the angle between the direction of motion and radar antenna broadside is greater than 60°, the micro-Doppler signatures generated by the radial motion of human body reduce significantly, thereby degrading the performance of the classification algorithm. For the accurate classification of different human activities irrespective of trajectory, we propose a new algorithm based on dual micro-motion signatures, namely, the micro-Doppler and interferometric micro-motion signatures, using an interferometric radar. First, the motion of different parts of the human body is simulated using motion capture (MOCAP) data, which is further utilized for radar echo signal generation. Second, time-varying Doppler and interferometric spectrograms obtained from time-frequency analysis of a single Doppler receiver and interferometric output data, respectively, are fed as input to the deep convolutional neural network (DCNN) for feature extraction and the training/testing process. The performance of the proposed algorithm is analyzed and compared with a micro-Doppler signatures-based classifier. Results show that a dual micro-motion-based DCNN classifier using an interferometric radar is capable of classifying different human activities with an accuracy level of 98%, where Doppler signatures diminish considerably, providing insufficient information for classification. Verification of the proposed classification algorithm based on dual micro-motion signatures is also performed using a real radar test dataset of different human walking patterns, and a classification accuracy level of approximately 90% is achieved.

Interference Measurements of Non-Abelian e/4 & Abelian e/2 Quasiparticle Braiding

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. The non-Abelian statistics of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$. At both $\nu=5/2$ and $7/2$ we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with either fermion parity change or change in the number of the enclosed $e/4$ quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

Spectroscopic and interferometric signatures of magnetospheric accretion in young stars

Aims. We aim to assess the complementarity between spectroscopic and interferometric observations in the characterisation of the inner star-disc interaction region of young stars. Methods. We used the MCFOST code to solve the non-local thermodynamic equilibrium problem of line formation in non-axisymmetric accreting magnetospheres. We computed the Brγ line profile originating from accretion columns for models with different magnetic obliquities. We also derived monochromatic synthetic images of the Brγ line-emitting region across the line profile. This spectral line is a prime diagnostic of magnetospheric accretion in young stars and is accessible with the long baseline near-infrared interferometer GRAVITY installed at the ESO Very Large Telescope Interferometer. Results. We derive Brγ line profiles as a function of rotational phase and compute interferometric observables, visibilities, and phases, from synthetic images. The line profile shape is modulated along the rotational cycle, exhibiting inverse P Cygni profiles at the time the accretion shock faces the observer. The size of the line’s emission region decreases as the magnetic obliquity increases, which is reflected in a lower line flux. We apply interferometric models to the synthetic visibilities in order to derive the size of the line-emitting region. We find the derived interferometric size to be more compact than the actual size of the magnetosphere, ranging from 50 to 90% of the truncation radius. Additionally, we show that the rotation of the non-axisymmetric magnetosphere is recovered from the rotational modulation of the Brγ-to-continuum photo-centre shifts, as measured by the differential phase of interferometric visibilities. Conclusions. Based on the radiative transfer modelling of non-axisymmetric accreting magnetospheres, we show that simultaneous spectroscopic and interferometric measurements provide a unique diagnostic to determine the origin of the Brγ line emitted by young stellar objects and are ideal tools to probe the structure and dynamics of the star-disc interaction region.

Differential Interferometric Signatures of Close Binaries of Supermassive Black Holes in Active Galactic Nuclei. II. Merged Broad-line Regions

Pairs of supermassive black holes (SMBHs) at different stages are the natural results of galaxy mergers in the hierarchical framework of galaxy formation and evolution. However, identification of close binaries of SMBHs (CB-SMBHs) with sub-parsec separations in observations are still elusive. Recently, unprecedented spatial resolutions achieved by GRAVITY/GRAVITY+ on board the Very Large Telescope Interferometer through spectroastrometry (SA) provide new opportunities to resolve CB-SMBHs. Differential phase curves of CB-SMBHs with two independent broad-line regions (BLRs) are found to have distinguished characteristic structures from a single BLR. Once the CB-SMBH evolves to the stage where BLRs merge to form a circumbinary BLR, it will hopefully be resolved by the pulsar timing array in the near future as sources of nanohertz gravitational waves. In this work, we use a parameterized model for circumbinary BLRs to calculate line profiles and differential phase curves for SA observations. We show that both profiles and phase curves exhibit asymmetries caused by the Doppler boosting effect of accretion disks around individual black holes, depending on the orbital parameters of the binary and geometries of the BLR. We also generate mock SA data using the model and then recover orbital parameters by fitting the mock data. Degeneracies between parameters contribute greatly to uncertainties of parameters but can be eased through joint analysis of multiple-epoch SA observations and reverberation mappings.

Adaptive analytical ray tracing of black hole photon rings

Recent interferometric observations by the Event Horizon Telescope have resolved the horizon-scale emission from sources in the vicinity of nearby supermassive black holes. Future space-based interferometers promise to measure the ''photon ring''--a narrow, ring-shaped, lensed feature predicted by general relativity, but not yet observed--and thereby open a new window into strong gravity. Here we present AART: an Adaptive Analytical Ray-Tracing code that exploits the integrability of light propagation in the Kerr spacetime to rapidly compute high-resolution simulated black hole images, together with the corresponding radio visibility accessible on very long space-ground baselines. The code samples images on a nonuniform adaptive grid that is specially tailored to the lensing behavior of the Kerr geometry and is therefore particularly well-suited to studying photon rings. This numerical approach guarantees that interferometric signatures are correctly computed on long baselines, and the modularity of the code allows for detailed studies of equatorial sources with complex emission profiles and time variability. To demonstrate its capabilities, we use AART to simulate a black hole movie of a stochastic, non-stationary, non-axisymmetric equatorial source; by time-averaging the visibility amplitude of each snapshot, we are able to extract the projected diameter of the photon ring and recover the shape predicted by general relativity.

The GRAVITY young stellar object survey

Context. Hot atomic hydrogen emission lines in pre-main sequence stars serve as tracers for physical processes in the innermost regions of circumstellar accretion disks, where the interaction between a star and disk is the dominant influence on the formation of infalls and outflows. In the highly magnetically active T Tauri stars, this interaction region is particularly shaped by the stellar magnetic field and the associated magnetosphere, covering the inner five stellar radii around the central star. Even for the closest T Tauri stars, a region as compact as this is only observed on the sky plane at sub-mas scales. To resolve it spatially, the capabilities of optical long baseline interferometry are required. Aims. We aim to spatially and spectrally resolve the Brγ hydrogen emission line with the methods of interferometry in order to examine the kinematics of the hydrogen gas emission region in the inner accretion disk of a sample of solar-like young stellar objects. The goal is to identify trends and categories among the sources of our sample and to discuss whether or not they can be tied to different origin mechanisms associated with Brγ emission in T Tauri stars, chiefly and most prominently magnetospheric accretion. Methods. We observed a sample of seven T Tauri stars for the first time with VLTI GRAVITY, recording spectra and spectrally dispersed interferometric quantities across the Brγ line at 2.16 µm in the near-infrared K-band. We used the visibilities and differential phases to extract the size of the Brγ emission region and the photocentre shifts on a channel-by-channel basis, probing the variation of spatial extent at different radial velocities. To assist in the interpretation, we also made use of radiative transfer models of magnetospheric accretion to establish a baseline of expected interferometric signatures if accretion is the primary driver of Brγ emission. Results. From among our sample, we find that five of the seven T Tauri stars show an emission region with a half-flux radius in the four to seven stellar radii range that is broadly expected for magnetospheric truncation. Two of the five objects also show Brγ emission primarily originating from within the co-rotation radius, which is an important criterion for magnetospheric accretion. Two objects exhibit extended emission on a scale beyond 10 R*, one of them is even beyond the K-band continuum half-flux radius of 11.3 R*. The observed photocentre shifts across the line can be either similar to what is expected for disks in rotation or show patterns of higher complexity. Conclusions. Based on the observational findings and the comparison with the radiative transfer models, we find strong evidence to suggest that for the two weakest accretors in the sample, magnetospheric accretion is the primary driver of Brγ radiation. The results for the remaining sources imply either partial or strong contributions coming from additional, spatially extended emission components in the form of outflows, such as stellar or disk winds. We expect that in actively accreting T Tauri stars, these phenomena typically occur simultaneously on different spatial scales. Through more advanced modelling, interferometry will be a key factor in disentangling their distinct contributions to the total Brγ flux arising from the innermost disk regions.

Photon ring test of the Kerr hypothesis: Variation in the ring shape

Context. The Event Horizon Telescope (EHT) collaboration recently released horizon-scale images of the supermassive black hole M87*. These images are consistently described by an optically thin, lensed accretion flow in the Kerr spacetime. General relativity (GR) predicts that higher-resolution images of such a flow would present thin, ring-shaped features produced by photons on extremely bent orbits. Recent theoretical work suggests that these “photon rings” produce clear interferometric signatures that depend very little on the astrophysical configuration and whose observation could therefore provide a stringent consistency test of the Kerr hypothesis. Aims. We wish to understand how the photon rings of a Kerr black hole vary with its surrounding emission. Gralla, Lupsasca, and Marrone (GLM) found that the shape of high-order photon rings follows a specific functional form that is insensitive to the details of the astrophysical source, and proposed a method for measuring this GR-predicted shape via space-based interferometry. We wish to assess the robustness of this prediction by checking it for a variety of astrophysical profiles, black hole spins, and observer inclinations. Methods. We use the ray tracing code Gyoto to simulate images of thin equatorial disks accreting onto a Kerr black hole. We extract the shape of the resulting photon rings from their interferometric signatures using a refinement of the method developed by GLM. We repeat this analysis for hundreds of models with different emission profiles, black hole spins, and observer inclinations. Results. We identify the width of the photon ring and its angular variation as a main obstacle to the method’s success. We qualitatively describe how this width varies with the emission profile, black hole spin, and observer inclination. At low inclinations, our improved method is robust enough to confirm the shape prediction for a variety of emission profiles; however, the choice of baseline is critical to the method’s success. At high inclinations, we encounter qualitatively new effects that are caused by the ring’s non-uniform width and require further refinements to the method. We also explore how the photon ring shape could constrain black hole spin and inclination.

Interferometry of quantum revivals.

It has recently been shown that an interferometric approach can be used to obtain Auger lifetimes in molecules in certain point groups. Here, we extend this concept to those molecular states for which Auger decay is energetically forbidden and which exhibit initial quasi-exponential decay followed by quantum revivals. We demonstrate that this allows us to extract the quasi-exponential decay rate and the revival timescale. We solve analytically a model containing a state coupled to the idealized Bixon-Jortner quasicontinuum, and we obtain an interferometric signature of revival, which can be easily generalized to realistic systems. Moreover, we analyze how this revival signature is influenced by the system parameters, and we suggest optimal conditions for its observation. We, therefore, show that our new approach allows population revivals of a molecular state to be detected interferometrically.

Interferometric signature of different spectral symmetries of biphoton states

In this paper, we investigate the influence of the symmetry of the biphoton wave function on the coincidence measurement of the generalized Mach-Zehnder (MZ) interferometer, where there are a temporal and frequency shift operations between the two beam splitters. We show that the generalized MZ interferometer allows the measurement of the short-time Fourier transform of the function modeling the energy conservation of a spontaneous parametric down-conversion process if the full biphoton state is symmetric, and of the symmetric characteristic distribution of the phase-matching function if the state is antisymmetric. Thus, this technique is phase sensitive to the spectral distribution of the photon pairs. Finally, we investigate in detail the signature of a pair of anyons whose peculiar statistics can be simulated by engineering the spectrum of photon pairs.

Numerical calibration method for a multiple spectrometer-based OCT system.

The present paper introduces a numerical calibration method for the easy and practical implementation of multiple spectrometer-based spectral-domain optical coherence tomography (SD-OCT) systems. To address the limitations of the traditional hardware-based spectrometer alignment across more than one spectrometer, we applied a numerical spectral calibration algorithm where the pixels corresponding to the same wavelength in each unit are identified through spatial- and frequency-domain interferometric signatures of a mirror sample. The utility of dual spectrometer-based SD-OCT imaging is demonstrated through in vivo retinal imaging at two different operation modes with high-speed and dual balanced acquisitions, respectively, in which the spectral alignment is critical to achieve improved retinal image data without any artifacts caused by misalignment of the spectrometers.

Black Hole Shadow Drift and Photon Ring Frequency Drift

The apparent angular size of the shadow of a black hole in an expanding Universe is redshift-dependent. Since cosmological redshifts change with time - known as the redshift drift - all redshift-dependent quantities acquire a time dependence, and _a fortiori_ so do black hole shadows. We find a mathematical description of the black hole shadow drift and show that the amplitude of this effect is of order $10^{-16}$ per day for M87$^{\star}$. While this effect is small, we argue that its non-detection can be used to constrain the accretion rate around supermassive black holes, as well as a novel probe of the equivalence principle. If general relativity is assumed, we infer from the data obtained by the Event Horizon Telescope for M87$^{\star}$ a maximum accretion rate of $|\dot{M}/{M}| \leq 10^5 M_{\odot}$ per year. On the other hand, in the case of an effective gravitation coupling, we derive a constraint of $|\dot{G}/G| \leq 10^{-3}-10^{-4}$ per year. The effect of redshift drift on the visibility amplitude and frequency of the universal interferometric signatures of photon rings is also discussed, which we show to be very similar to the shadow drift. This is of particular interest for future experiments involving spectroscopic and interferometric techniques, which could make observations of photon rings and their frequency drifts viable.

The Impact of Phenological Developments on Interferometric and Polarimetric Crop Signatures Derived from Sentinel-1: Examples from the DEMMIN Study Site (Germany)

This study explores the potential of Sentinel-1 Synthetic Aperture Radar (SAR) to identify phenological phases of wheat, sugar beet, and canola. Breakpoint and extreme value analyses were applied to a dense time series of interferometric (InSAR) and polarimetric (PolSAR) features recorded during the growing season of 2017 at the JECAM site DEMMIN (Germany). The analyses of breakpoints and extrema allowed for the distinction of vegetative and reproductive stages for wheat and canola. Certain phenological stages, measured in situ using the BBCH-scale, such as leaf development and rosette growth of sugar beet or stem elongation and ripening of wheat, were detectable by a combination of InSAR coherence, polarimetric Alpha and Entropy, and backscatter (VV/VH). Except for some fringe cases, the temporal difference between in situ observations and breakpoints or extrema ranged from zero to five days. Backscatter produced the signature that generated the most breakpoints and extrema. However, certain micro stadia, such as leaf development of BBCH 10 of sugar beet or flowering BBCH 69 of wheat, were only identifiable by the InSAR coherence and Alpha. Hence, it is concluded that combining PolSAR and InSAR features increases the number of detectable phenological events in the phenological cycles of crops.

Ground-Based Radar Interferometry of Sea Ice

In light of recent Arctic change, there is a need to better understand sea ice dynamic processes at the floe scale to evaluate sea ice stability, deformation, and fracturing. This work investigates the use of the Gamma portable radar interferometer (GPRI) to characterize sea ice displacement and surface topography. We find that the GPRI is best suited to derive lateral surface deformation due to mm-scale horizontal accuracy. We model interferometric phase signatures from sea ice displacement and evaluate possible errors related to noise and antenna motion. We compare the analysis with observations acquired during a drifting ice camp in the Beaufort Sea. We used repeat-scan and stare-mode interferometry to identify two-dimensional shear and to track continuous uni-directional convergence. This paper demonstrates the capacity of the GPRI to derive surface strain on the order of 10−7 and identify different dynamic regions based on sub-mm changes in displacement. The GPRI is thus a promising tool for sea ice applications due to its high accuracy that can potentially resolve pre- and post-fracture deformation relevant to sea ice stability and modeling.

Observable shape of black hole photon rings

Motivated by the prospect of measuring a black hole photon ring, in previous work we explored the interferometric signature produced by a bright, narrow curve in the sky. Interferometric observations of such a curve measure its "projected position function" $\mathbf{r}\cdot\hat{\mathbf{n}}$, where $\mathbf{r}$ parameterizes the curve and $\hat{\mathbf{n}}$ denotes its unit normal vector. In this paper, we show by explicit construction that a curve can be fully reconstructed from its projected position, completing the argument that space interferometry can in principle determine the detailed photon ring shape. In practice, near-term observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or "widths") of the shape. We explore the freedom in reconstructing a convex curve from its widths, giving insight into the shape information probed by technically plausible future astronomical measurements. Finally, we consider the Kerr "critical curve" in this framework and present some new results on its shape. We analytically show that the critical curve is an ellipse at small spin or inclination, while at extremal spin it becomes the convex hull of a Cartesian oval. We find a simple oval shape, the "phoval", which reproduces the critical curve with high fidelity over the whole parameter range.

The shape of the black hole photon ring: A precise test of strong-field general relativity

We propose a new test of strong-field general relativity (GR) based on the universal interferometric signature of the black hole photon ring. The photon ring is a narrow ring-shaped feature, predicted by GR but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. We show that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of GR. We forecast that a tailored space-based interferometry experiment targeting M87* could test the Kerr nature of the source to the sub-sub-percent level.

Measuring the shape of a black hole photon ring

General relativity predicts that gravitational lensing near black holes will produce narrow "photon rings" on images. Building on recent work of Johnson, Lupsasca et al. focusing on circular rings, I calculate the long-baseline interferometric signature of a narrow feature of arbitrary shape and intensity. The shape information is contained in the oscillation frequencies of the complex visibility as a function of baseline length, for each baseline angle. These results raise the possibility of measuring the detailed shape of a photon ring and comparing to the precise predictions of general relativity.

Opposite-Side Ambiguities in Radar Sounding Interferometry

We report the analysis of opposite-side ambiguities in single-pass radar sounding interferometry. Nadir pointing radar sounders suffer inherent cross track ambiguities that cannot be separated with the power image alone. Interferometry can be used to interpret these ambiguities when data are collected with multichannel receivers. However, opposite-side surface clutter, volume scattering, and cross track range misalignment create unique interferometric phase and correlation signatures. Such signatures are observed experimentally in data collected by the Polarimetric Airborne Radar Ice Sounder (POLARIS) P-band multichannel radar sounder. We derive analytic expressions to predict the observations and validate them with simulation. In addition, we observe and explain a correlation dropout feature that is due to volume scattering competing with surface clutter in the null of the cross track antenna pattern. The purpose of this article is to explain opposite-side ambiguity signatures in radar sounder interferometry and provide models and techniques for scientific interpretation of interferograms.

Interferometric Signatures of Electron Transfer through Majorana Bound States

Interferometric Signatures of Electron Transfer through Majorana Bound States