Prediction for the interferometric shape of the first black hole photon ring

Black hole images are theoretically predicted (under mild astrophysical assumptions) to display a stack of lensed "photon rings" that carry information about the underlying spacetime geometry. Despite vigorous efforts, no such ring has been observationally resolved thus far. However, planning is now actively under way for space missions targeting the first (and possibly the second) photon rings of the supermassive black holes M87* and Sgr A*. In this work, we study interferometric photon ring signatures in time-averaged images of Kerr black holes surrounded by different astrophysical profiles. We focus on the first, most easily accessible photon ring, which has a larger width-to-diameter ratio than subsequent rings and whose image consequently lacks a sharply defined diameter. Nonetheless, we show that it does admit a precise angle-dependent diameter in visibility space, for which the Kerr metric predicts a specific functional form that tracks the critical curve. We find that a measurement of this interferometric ring diameter is possible for most astrophysical profiles, paving the way for precision tests of strong-field general relativity via near-future observations of the first photon ring.Comment: 16 pages, 6 figures. V2: Minor changes to match the published versio

Probing the regular nature of the spacetime by direct measurement of black hole properties

In the following years Very Long Baseline Interferometry (VLBI) facilities will be able to directly image the accretion flow around the supermassive black hole candidate at the center of the Milky Way, Sgr A*. They will also be able to observe its shadow: an optical property which appears as a consequence of the strong gravitational field around it and which thus depends only on the physical parameters of the black hole. While there is no definitive evidence of the nature of the spacetime geometry around Sgr A*, it has been usually modeled by a Kerr black hole, by virtue of the no-hair theorem, which asserts that all uncharged black holes in 4-dimensional general relativity are described by this metric and thus completely specified by two parameters, the mass M and the spin parameter a. As a consequence, testing the no-hair theorem in nature with future observations allows us to not only verify that black holes in our universe are Kerr black holes, but to test the strong field predictions of general relativity In this work I investigate if the shadow, image and spectrum of a non-Kerr regular black hole inspired by noncommutative geometry may provide a measurement of the parameters characterizing Kerr and non-Kerr regular black holes to distinguish one from the other. Specifically, the non-Kerr solution studied here is the rotating black hole found by Smailagic and Spallucci in 2010 and known as the “Kerrr” black hole, where the third “r” stands for regular, in the sense of a pathology-free rotating black hole. The general strategy to derive this generalized solution consists of prescribing an improved form of the energy-momentum tensor, which accounts, at least phenomenologically, for the noncommutative fluctuations of the manifold at the origin and which vanishes for large distances with respect to the noncommutative geometry scale, l_{0}. Abstract The image and spectrum of Sgr A*, as the case of study, was modeled using the relativistic ray-tracing code GYOTO, assuming an optically thin, constant angular momentum torus in hydrodynamic equilibrium around the Kerr and "Kerrr" geometries. The model used includes a toroidal magnetic field and radiative cooling by bremsstrahlung, synchrotron, and inverse Compton processes. The assumptions provided here, for drawing the shadow and to model the accretion disk, do not provide a realistic scenario, but an easily accessible yet powerful analytical analogy. Then comparisons with the Kerr geometry are calculated by using the observables defined by Hioki and Maeda and the distortion parameter introduced by Tsukamoto, Li and Bambi. This work confirms that it is definitely challenging to test this kind of regular metric solely from observations of the shadow or accretion structures in the near future.Resumen. En los próximos años las estaciones de interferometría de base ancha, Very Long Baseline Interferometry (VLBI), serán capaces de obtener imágenes de la acreción alrededor del candidato a agujero negro supermasivo en el centro de la Vía Láctea, Sgr A*. Los resultados de estas campañas de observación permitirán observar también su sombra: un propiedad óptica que se genera como consecuencia del fuerte campo gravitacional alrededor del agujero negro y que depende solamente de los parámetros físicos del agujero negro. Actualmente no hay evidencia definitiva sobre la naturaleza del espacio-tiempo alrededor de Sgr A* y usualmente ha sido modelado como un agujero negro de Kerr en virtud de los teoremas del no pelo, los cuales afirman que todos los agujeros negros sin carga, en cuatro dimensiones descritos por la relatividad general, dependen únicamente de los dos parámetros de esa métrica; la masa y el parámetro de rotación. Por tal razón, probar la validez de este teorema en la naturaleza a través de observaciones nos permitirá, no solamente verificar si los agujeros negros del Universo están descritos por la métrica de Kerr, sino además probar las predicciones de la relatividad general en el campo fuerte. En este trabajo investigo si la sombra, imagen y espectro de un agujero negro regular diferente de Kerr, inspirado de la geometría no conmutativa, permite medir los parámetros que caracterizan los agujeros negros y distinguir sus diferencias. Específicamente, la solución estudiada acá es la rotante encontrada por Smailagic y Spallucci en 2010 conocida como el agujero negro de "Kerrr", en donde la tercera "r" simboliza la naturaleza regular de esa solución. La forma general de obtener ese tipo de soluciones consiste en modificar el tensor de momento y energía de tal manera que codifique, al menos de forma fenomenológica, las fluctuaciones no conmutativas de la variedad en el origen y que desaparecen a grandes distancias, con respecto a la escala de la geometría no conmutativa. La imagen y el espectro de Sgr A*, como caso de estudio, fueron modeladas usando el código de trazado de rayos GYOTO, asumiendo un toro ópticamente delgado con momento angular constante en equilibrio hidrodinámico, alrededor de las geometrías de Kerr y "Kerrr". El modelo usado incluye un campo magnético toroidal y enfriamientos radiativos por bremsstrahlung, synchroton y procesos de Compton inverso. Las simplificaciones hechas acá, para dibujar la sombre y modelar el disco de acreción, no representan un escenario real, pero son buenas analogías analíticas. Las comparaciones son hechas a través de los observables definidos por Hioki y Maeda y el parámetro de distorsión de Tsukamoto, Li y Bambi. Este trabajo confirma la complejidad y dificultad de probar este tipo de soluciones a través de únicamente mediciones de la sombra y estructura de acreción en el futuro próximo.Maestrí

Challenges in Quasinormal Mode Extraction: Perspectives from Numerical solutions to the Teukolsky Equation

The intricacies of black hole ringdown analysis are amplified by the absence of a complete set of orthogonal basis functions for quasinormal modes. Although damped sinusoids effectively fit the ringdown signals from binary black hole mergers, the risk of overfitting remains, due to initial transients and nonlinear effects. In light of this challenge, we introduce two methods for extracting quasinormal modes in numerical simulations and qualitatively study how the transient might affect quasinormal mode fitting. In one method, we accurately fit quasinormal modes by using their spatial functional form at constant time hypersurfaces, while in the other method, we exploit both spatial and temporal aspects of the quasinormal modes. Both fitting methods leverage the spatial behavior of quasinormal eigenfunctions to enhance accuracy, outperforming conventional time-only fitting techniques at null infinity. We also show that we can construct an inner product for which the quasinormal eigenfunctions form an orthonormal (but not complete) set. We then conduct numerical experiments involving linearly perturbed Kerr black holes in horizon penetrating, hyperboloidally compactified coordinates, as this setup enables a more precise isolation and examination of the ringdown phenomenon. From solutions to the Teukolsky equation, describing scattering of an ingoing gravitational wave pulse, we find that the contributions from early-time transients can lead to large uncertainties in the fit to the amplitudes of higher overtones ($n\geq 3$) when the signal is fitted over a short time interval. While the methods we discuss here cannot be applied directly to data from merger observations, our findings underscore the persistence of ambiguities in interpreting ringdown signals, even with access to both temporal and spatial information

Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy

We present the first X-ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the Kerr solution. We employ the formalism of the transfer function proposed by Cunningham. The calculations of the reflection spectrum of a thin accretion disk are split into two parts: the calculation of the transfer function and the calculation of the local spectrum at any emission point in the disk. The transfer function only depends on the background metric and takes into account all the relativistic effects (gravitational redshift, Doppler boosting, and light bending). Our code computes the transfer function for a spacetime described by the Johannsen metric and can easily be extended to any stationary, axisymmetric, and asymptotically flat spacetime. Transfer functions and single line shapes in the Kerr metric are compared to those calculated from existing codes to check that we reach the necessary accuracy. We also simulate some observations with NuSTAR and LAD/eXTP and fit the data with our new model to show the potential capabilities of current and future observations to constrain possible deviations from the Kerr metric

Astrobites as a Community-led Model for Education, Science Communication, and Accessibility in Astrophysics

Support for early career astronomers who are just beginning to explore astronomy research is imperative to increase retention of diverse practitioners in the field. Since 2010, Astrobites has played an instrumental role in engaging members of the community -- particularly undergraduate and graduate students -- in research. In this white paper, the Astrobites collaboration outlines our multi-faceted online education platform that both eases the transition into astronomy research and promotes inclusive professional development opportunities. We additionally offer recommendations for how the astronomy community can reduce barriers to entry to astronomy research in the coming decade

Funciones Especiales I

Presentación netamente práctica que expone el tema propuesto en la presentación por medio de las diferentes demostraciones de Riemann.This presentation presents different special functions that handle great proximity and relation with prime numbers such as the Riemann zeta function, the roots of the Riemann zeta function, the functional equation of the Riemann zeta function, among others.En esta presentación se exponen diferentes funciones especiales que manejan gran proximidad y relación con los números primos como la función zeta de Riemann, las raíces de la función zeta de Riemann, la ecuación funcional de la función zeta de Riemann entre otras.1. Introducción2. Función3. Las raíces4. La hipótesis5. Actividad6. Referencias1.0MatemáticoPregrad

Propiedades de los Números Primos

Presentación que continúa el tema de los números primos, pero en esta ocasión haciendo énfasis en la criba de Eratóstenes, método usado para hallar los números primos.El método más conocido de obtener todos los números primos menores que un entero dado n es la criba de Eratóstenes, método inventado por el matemático griego del mismo nombre en el siglo III a.C. Consiste en disponer en una tabla todos los enteros entre 2 y n. Luego se eliminan de la tabla todos los múltiplos de 2. El siguiente paso se hace igual con los múltiplos de 3, luego con los múltiplos de 5, etc. Los números que finalmente queden en dicha tabla serán todos números primos, entre 2 y n.1. Introducción2. Preguntas fundamentales sobre los números primos3. Criba de Eratóstenes4. Actividad5. Referencias1.0The best known method of obtaining all primes less than a given n integer is the Eratosthenes sieve, a method invented by the Greek mathematician of the same name in the 3rd century B.C. It consists in having all integers between 2 and n in a table. Then all multiples of 2 are removed from the table. The next step becomes the same with multiples of 3, then with multiples of 5, etc. The numbers that finally remain in that table will all be prime numbers, between 2 and n.MatemáticoPregrad

Thermal Accretion Disk Spectra Based Tests of General Relativity

The continuous X-ray flux of stellar-mass black holes provides an excellent source of data to learn about the astrophysics of accretion disks and about the spacetime itself. The extraction of information, however, depends heavily on our ability to correctly model the astrophysics and the theory of gravity, and the quality of the data. By combining a relativistic ray-tracing and Markov-Chain Monte-Carlo sampling technique, I show that the incorporation of the spin parameter through a slowly-rotating approximation, is not able to break the complex degeneracies of the model and therefore, when introducing modifications beyond general relativity it is very challenging to perform tests of general relativity with this type of observations. As a particular case, I show that it not possible to distinguish the small-coupling, slow-rotation black hole solution of dynamical Chern–Simons gravity from the Kerr solution with current instruments