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We give a graphical theory of integral indefinite binary Hamiltonian forms f analogous to the one by Conway for binary quadratic forms and the one of Bestvina-Savin for binary Hermitian forms. Given a maximal order O in a definite quaternion algebra over Q, we define the waterworld of f, analogous to Conway's river and Bestvina-Savin's ocean, and use it to give a combinatorial description of the values of f on O×O. We use an appropriate normalisation of Busemann distances to the cusps (with an algebraic description given in an independent appendix), and the SL2(O)-equivariant Ford-Voronoi cellulation of the real hyperbolic 5-space.
The nearby radio galaxy M87 is a prime target for studying black hole accretion and jet formation1,2. Event Horizon Telescope observations of M87 in 2017, at a wavelength of 1.3 mm, revealed a ring-like structure, which was interpreted as gravitationally lensed emission around a central black hole3. Here we report images of M87 obtained in 2018, at a wavelength of 3.5 mm, showing that the compact radio core is spatially resolved. High-resolution imaging shows a ring-like structure of [Formula: see text] Schwarzschild radii in diameter, approximately 50% larger than that seen at 1.3 mm. The outer edge at 3.5 mm is also larger than that at 1.3 mm. This larger and thicker ring indicates a substantial contribution from the accretion flow with absorption effects, in addition to the gravitationally lensed ring-like emission. The images show that the edge-brightened jet connects to the accretion flow of the black hole. Close to the black hole, the emission profile of the jet-launching region is wider than the expected profile of a black-hole-driven jet, suggesting the possible presence of a wind associated with the accretion flow.
The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.
Ultra-high angular resolution in astronomy has always been an important vehicle for making fundamental discoveries. Recent results in direct imaging of the vicinity of the supermassive black hole in the nucleus of the radio galaxy M87 by the millimeter VLBI system Event Horizon Telescope and various pioneering results of the Space VLBI mission RadioAstron provided new momentum in high angular resolution astrophysics. In both mentioned cases, the angular resolution reached the values of about 10–20 microarcseconds (0.05–0.1 nanoradian). Further developments towards at least an order of magnitude “sharper” values, at the level of 1 microarcsecond are dictated by the needs of advanced astrophysical studies. The paper emphasis that these higher values can only be achieved by placing millimeter and submillimeter wavelength interferometric systems in space. A concept of such the system, called Terahertz Exploration and Zooming-in for Astrophysics, has been proposed in the framework of the ESA Call for White Papers for the Voyage 2050 long term plan in 2019. In the current paper we present new science objectives for such the concept based on recent results in studies of active galactic nuclei and supermassive black holes. We also discuss several approaches for addressing technological challenges of creating a millimeter/sub-millimeter wavelength interferometric system in space. In particular, we consider a novel configuration of a space-borne millimeter/sub-millimeter antenna which might resolve several bottlenecks in creating large precise mechanical structures. The paper also presents an overview of prospective space-qualified technologies of low-noise analogue front-end instrumentation for millimeter/sub-millimeter telescopes. Data handling and processing instrumentation is another key technological component of a sub-millimeter Space VLBI system. Requirements and possible implementation options for this instrumentation are described as an extrapolation of the current state-of-the-art Earth-based VLBI data transport and processing instrumentation. The paper also briefly discusses approaches to the interferometric baseline state vector determination and synchronisation and heterodyning system. The technology-oriented sections of the paper do not aim at presenting a complete set of technological solutions for sub-millimeter (terahertz) space-borne interferometers. Rather, in combination with the original ESA Voyage 2050 White Paper, it sharpens the case for the next generation microarcsecond-level imaging instruments and provides starting points for further in-depth technology trade-off studies.
The black hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center of the M87 galaxy, this timescale (5-61 days) is comparable to the 6 day extent of the 2017 EHT observations. Closure phases along baseline triangles are robust interferometric observables that are sensitive to the expected structural changes of the images but are free of station-based atmospheric and instrumental errors. We explored the day-to-day variability in closure-phase measurements on all six linearly independent nontrivial baseline triangles that can be formed from the 2017 observations. We showed that three triangles exhibit very low day-to-day variability, with a dispersion of ∼3°-5°. The only triangles that exhibit substantially higher variability (∼90°-180°) are the ones with baselines that cross the visibility amplitude minima on the u-v plane, as expected from theoretical modeling. We used two sets of general relativistic magnetohydrodynamic simulations to explore the dependence of the predicted variability on various black hole and accretion-flow parameters. We found that changing the magnetic field configuration, electron temperature model, or black hole spin has a marginal effect on the model consistency with the observed level of variability. On the other hand, the most discriminating image characteristic of models is the fractional width of the bright ring of emission. Models that best reproduce the observed small level of variability are characterized by thin ring-like images with structures dominated by gravitational lensing effects and thus least affected by turbulence in the accreting plasmas.
At the beginning of 2020, COVID-19 became a global problem. Despite all the efforts to emphasize the relevance of preventive measures, not everyone adhered to them. Thus, learning more about the characteristics determining attitudinal and behavioral responses to the pandemic is crucial to improving future interventions. In this study, we applied machine learning on the multinational data collected by the International Collaboration on the Social and Moral Psychology of COVID-19 (N = 51,404) to test the predictive efficacy of constructs from social, moral, cognitive, and personality psychology, as well as socio-demographic factors, in the attitudinal and behavioral responses to the pandemic. The results point to several valuable insights. Internalized moral identity provided the most consistent predictive contribution—individuals perceiving moral traits as central to their self-concept reported higher adherence to preventive measures. Similar results were found for morality as cooperation, symbolized moral identity, self-control, open-mindedness, and collective narcissism, while the inverse relationship was evident for the endorsement of conspiracy theories. However, we also found a non-neglible variability in the explained variance and predictive contributions with respect to macro-level factors such as the pandemic stage or cultural region. Overall, the results underscore the importance of morality-related and contextual factors in understanding adherence to public health recommendations during the pandemic.
In 2017 the Event Horizon Telescope (EHT) observed the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), at a frequency of 228.1 GHz (λ = 1.3 mm). The fundamental physics tests that even a single pulsar orbiting Sgr A* would enable motivate searching for pulsars in EHT data sets. The high observing frequency means that pulsars—which typically exhibit steep emission spectra—are expected to be very faint. However, it also negates pulse scattering, an effect that could hinder pulsar detections in the Galactic center. Additionally, magnetars or a secondary inverse Compton emission could be stronger at millimeter wavelengths than at lower frequencies. We present a search for pulsars close to Sgr A* using the data from the three most sensitive stations in the EHT 2017 campaign: the Atacama Large Millimeter/submillimeter Array, the Large Millimeter Telescope, and the IRAM 30 m Telescope. We apply three detection methods based on Fourier-domain analysis, the fast folding algorithm, and single-pulse searches targeting both pulsars and burst-like transient emission. We use the simultaneity of the observations to confirm potential candidates. No new pulsars or significant bursts were found. Being the first pulsar search ever carried out at such high radio frequencies, we detail our analysis methods and give a detailed estimation of the sensitivity of the search. We conclude that the EHT 2017 observations are only sensitive to a small fraction (≲2.2%) of the pulsars that may exist close to Sgr A*, motivating further searches for fainter pulsars in the region.
Synchrotron radiation from hot gas near a black hole results in a polarized image. The image polarization is determined by effects including the orientation of the magnetic field in the emitting region, relativistic motion of the gas, strong gravitational lensing by the black hole, and parallel transport in the curved spacetime. We explore these effects using a simple model of an axisymmetric, equatorial accretion disk around a Schwarzschild black hole. By using an approximate expression for the null geodesics derived by Beloborodov and conservation of the Walker-Penrose constant, we provide analytic estimates for the image polarization. We test this model using currently favored general relativistic magnetohydrodynamic simulations of M87∗, using ring parameters given by the simulations. For a subset of these with modest Faraday effects, we show that the ring model broadly reproduces the polarimetric image morphology. Our model also predicts the polarization evolution for compact flaring regions, such as those observed from Sgr A∗ with GRAVITY. With suitably chosen parameters, our simple model can reproduce the EVPA pattern and relative polarized intensity in Event Horizon Telescope images of M87∗. Under the physically motivated assumption that the magnetic field trails the fluid velocity, this comparison is consistent with the clockwise rotation inferred from total intensity images.
The Event Horizon Telescope (EHT) provides the unprecedented ability to directly resolve the structure and dynamics of black hole emission regions on scales smaller than their horizons. This has the potential to critically probe the mechanisms by which black holes accrete and launch outflows, and the structure of supermassive black hole spacetimes. However, accessing this information is a formidable analysis challenge for two reasons. First, the EHT natively produces a variety of data types that encode information about the image structure in nontrivial ways; these are subject to a variety of systematic effects associated with very long baseline interferometry and are supplemented by a wide variety of auxiliary data on the primary EHT targets from decades of other observations. Second, models of the emission regions and their interaction with the black hole are complex, highly uncertain, and computationally expensive to construct. As a result, the scientific utilization of EHT observations requires a flexible, extensible, and powerful analysis framework. We present such a framework, Themis, which defines a set of interfaces between models, data, and sampling algorithms that facilitates future development. We describe the design and currently existing components of Themis, how Themis has been validated thus far, and present additional analyses made possible by Themis that illustrate its capabilities. Importantly, we demonstrate that Themis is able to reproduce prior EHT analyses, extend these, and do so in a computationally efficient manner that can efficiently exploit modern high-performance computing facilities. Themis has already been used extensively in the scientific analysis and interpretation of the first EHT observations of M87.
The COVID-19 pandemic has affected all domains of human life, including the economic and social fabric of societies. One of the central strategies for managing public health throughout the pandemic has been through persuasive messaging and collective behaviour change. To help scholars better understand the social and moral psychology behind public health behaviour, we present a dataset comprising of 51,404 individuals from 69 countries. This dataset was collected for the International Collaboration on Social & Moral Psychology of COVID-19 project (ICSMP COVID-19). This social science survey invited participants around the world to complete a series of moral and psychological measures and public health attitudes about COVID-19 during an early phase of the COVID-19 pandemic (between April and June 2020). The survey included seven broad categories of questions: COVID-19 beliefs and compliance behaviours; identity and social attitudes; ideology; health and well-being; moral beliefs and motivation; personality traits; and demographic variables. We report both raw and cleaned data, along with all survey materials, data visualisations, and psychometric evaluations of key variables.
3C 279 is an archetypal blazar with a prominent radio jet that show broadband flux density variability across the entire electromagnetic spectrum. We use an ultra-high angular resolution technique - global Very Long Baseline Interferometry (VLBI) at 1.3mm (230 GHz) - to resolve the innermost jet of 3C 279 in order to study its fine-scale morphology close to the jet base where highly variable-ray emission is thought to originate, according to various models. The source was observed during four days in April 2017 with the Event Horizon Telescope at 230 GHz, including the phased Atacama Large Millimeter/submillimeter Array, at an angular resolution of ∼20 μas (at a redshift of z = 0:536 this corresponds to ∼0:13 pc ∼ 1700 Schwarzschild radii with a black hole mass MBH = 8 × 108 M⊙). Imaging and model-fitting techniques were applied to the data to parameterize the fine-scale source structure and its variation.We find a multicomponent inner jet morphology with the northernmost component elongated perpendicular to the direction of the jet, as imaged at longer wavelengths. The elongated nuclear structure is consistent on all four observing days and across diffierent imaging methods and model-fitting techniques, and therefore appears robust. Owing to its compactness and brightness, we associate the northern nuclear structure as the VLBI "core". This morphology can be interpreted as either a broad resolved jet base or a spatially bent jet.We also find significant day-to-day variations in the closure phases, which appear most pronounced on the triangles with the longest baselines. Our analysis shows that this variation is related to a systematic change of the source structure. Two inner jet components move non-radially at apparent speeds of ∼15 c and ∼20 c (∼1:3 and ∼1:7 μas day-1, respectively), which more strongly supports the scenario of traveling shocks or instabilities in a bent, possibly rotating jet. The observed apparent speeds are also coincident with the 3C 279 large-scale jet kinematics observed at longer (cm) wavelengths, suggesting no significant jet acceleration between the 1.3mm core and the outer jet. The intrinsic brightness temperature of the jet components are ≤1010 K, a magnitude or more lower than typical values seen at ≥7mm wavelengths. The low brightness temperature and morphological complexity suggest that the core region of 3C 279 becomes optically thin at short (mm) wavelengths.