Galactic Black Hole Research Articles

The X-ray variability of active galactic nuclei: Power spectrum and variance analysis of the Swift/BAT light curves

Aims. We study the X-ray power spectrum of active galactic nuclei (AGN) in order to investigate whether Seyfert I and II power spectra are similar or not and whether AGN variability depends on the mass and accretion rate of black holes as well as to compare the power spectra of AGN with the power spectra of Galactic X-ray black hole binaries. Method. We used 14–195 keV band light curves from the 157-month Swift/BAT hard X-ray survey, and we computed the mean power spectrum and excess variance of AGN in narrow black hole mass and AGN luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on the black hole mass, luminosity, and accretion rate of AGN. Results. We found the Seyfert I and Seyfert II power spectra to be identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same power-law like shape, with a slope of −1 in all AGN irrespective of their luminosity and black hole mass. We did not detect any flattening to a slope of zero at frequencies as low as 10−9 Hz. We detected an anti-correlation between the power spectral density function (PSD) amplitude and the accretion rate, similar to what has been seen in the past in the 2–10 keV band. This implies that the variability amplitude in AGN decreases with an increasing accretion rate. The universal AGN power spectrum is consistent with the mean 2–9 keV band Cyg X-1 power spectrum in its soft state. We detected a small difference in amplitude, but this is probably due to the difference in energy. Conclusions. The mean low-frequency AGN X-ray power spectrum is consistent with the extension of the mean 0.01–25 Hz Cyg X-1 power spectrum in its soft state to lower frequencies. We cannot prove that the mean AGN PSD is analogous to the mean Cyg X-1 PSD in its soft state, as we do not know the location of the high-frequency break in the hard X-ray AGN PSDs. However, if this is the case, then the accretion disc in AGN probably extends to the radius of the innermost circular stable orbit (as is probably the case with the black hole binaries in their soft state). The X-ray corona will then be located on top, illuminating the disc and producing the X-ray reflection and disc reverberation phenomena commonly observed in these objects. Furthermore, the agreement between the PSD amplitude in AGN and the Cyg X-1 (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.

Discovery of a dormant 33 solar-mass black hole in pre-release Gaia astrometry

Gravitational waves from black-hole (BH) merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models -- and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source BH3, implies the presence of a $32.70 BH in a binary system with a period of 11.6 yr. radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way.

Testing gravitational lensing effects by supermassive massive black holes with superstring theory metric: Astrophysical implications and EHT constraints

We investigate gravitational lensing, both strong and weak, induced by charged black holes within heterotic superstring theory – α′-corrected Reissner-Nordström (RN) black holes characterized by an additional parameter, denoted as α, in addition to mass M and charge Q. Our findings reveal that as the parameter α increases, various crucial parameters such as the unstable photon orbit radius rph, critical impact parameter uph, deflection angle αD(θ), and angular position θ∞ also increase. Concurrently, the angular separation s decreases, while the relative magnitude rmag increases with the growing value of α. Utilizing supermassive black holes (SMBH) Sgr A* and M87* as gravitational lenses, the deflection angle resulting from the α′-corrected RN black hole, in both strong and weak field limits, surpasses that of the RN black holes (α=0) and falls below that of Schwarzschild black holes (α′=0, Q=0.5). For Sgr A*, the angular position θ∞ lies within (24.08, 26.38) μas, while for M87* it ranges from (18.23, 19.96) μas. Estimating the time delay between the first and second relativistic images using twenty supermassive galactic center black holes as lenses, we find, for instance, that the time delay for Sgr A* and M87*, with Q=0.5 and α=5, can reach approximately 9.81 min and 14835.6 min, respectively. Remarkably, the EHT results for Sgr A* impose more stringent limits on the parameter space of α′-corrected RN black holes compared to those established by the EHT results for M87*. Our analysis deduces that, within the 1σ region, a substantial portion of the parameter space for α′-corrected RN black holes aligns with the Event Horizon Telescope (EHT) results for M87* and Sgr A*, and that and one cannot rule out the possibility of that heterotic superstring theory’s α′-corrected RN black holes being strong candidates for astrophysical black holes.

Polarized signatures of orbiting hot spots: Special relativity impact and probe of spacetime curvature

Context. The Galactic Center supermassive black hole is well known to exhibit transient peaks of flux density on a daily basis across the spectrum. Recent infrared and millimeter observations have strengthened the case for the association between these flares and circular orbital motion in the vicinity of the event horizon. The strongly polarized synchrotron radiation associated with these events leads to specific observables called QU loops, that is, looping motion in the Stokes QU plane of linear polarization. These patterns have been observed by the Submillimeter Array, VLTI/GRAVITY, and ALMA. Aims. We want to deepen the understanding of the QU loops associated with orbiting hot spots. To this end, we computed such loops in Minkowski and Schwarzschild spacetimes in order to determine which aspects of the observed patterns are due to special- or general-relativistic phenomena. Methods. We considered a parcel of energized plasma in circular motion in Minkowski spacetime and in Keplerian orbit in the Schwarzschild spacetime. We computed, using the GYOTO ray-tracing code, the polarized radiative transfer associated with this orbiting hot spot and derived the evolution of the flux density, astrometry, and Stokes Q and U parameters. Results. We show that QU loops in Minkowski spacetime at low or moderate inclination i ≲ 45° (where i = 0° is a face-on view) share all the qualitative features of Schwarzschild QU loops. There exist QU loops for all setups considered (including for the face-on view and vertical magnetic field), there may be one or two QU loops per orbital period for a vertical magnetic field configuration, and there are always two QU loops in case of a toroidal magnetic field. The simplicity of Minkowski spacetime is a key asset for allowing us to provide analytical formulas that explain the details of this behavior. Moreover, we analyzed the flux variation of the hot spot and show that it is dictated either by the angular dependence of the radiative transfer coefficients or by relativistic beaming. In the former case, this can lead to extreme flux ratios, even at a moderate inclination. Finally, we highlight the increasing mirror asymmetry of the Schwarzschild QU track with increasing inclination and show that this behavior is a specific Schwarzschild feature caused by light bending. Conclusions. Although special-relativistic effects have not been extensively discussed in this context, they are a crucial part in generating the observed QU loops. However, general-relativistic light bending leads to a specific observable feature encoded in the asymmetry of the observed loops, and this feature might allow the spacetime curvature to be quantified.

Toward More Accurate Synthetic Reflection Spectra: Improving the Calculations of Returning Radiation

We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation. Assuming a lamppost coronal geometry, we simulate simultaneous observations of NICER and NuSTAR of bright Galactic black holes and we fit the simulated data with the latest version of relxill (modified to read the table of reflionx, which is the nonrelativistic reflection model used in our calculations). We find that relxill with returning radiation cannot fit well the simulated data when the black hole spin parameter is very high and the coronal height and disk’s ionization parameter are low, and some parameters can be significantly overestimated or underestimated. We can find better fits and recover the correct input parameters as the value of the black hole spin parameter decreases and the value of the coronal height increases.

First Sagittarius A* Event Horizon Telescope Results. VII. Polarization of the Ring

The Event Horizon Telescope observed the horizon-scale synchrotron emission region around the Galactic center supermassive black hole, Sagittarius A* (Sgr A*), in 2017. These observations revealed a bright, thick ring morphology with a diameter of 51.8 ± 2.3 μas and modest azimuthal brightness asymmetry, consistent with the expected appearance of a black hole with mass M ≈ 4 × 106 M ⊙. From these observations, we present the first resolved linear and circular polarimetric images of Sgr A*. The linear polarization images demonstrate that the emission ring is highly polarized, exhibiting a prominent spiral electric vector polarization angle pattern with a peak fractional polarization of ∼40% in the western portion of the ring. The circular polarization images feature a modestly (∼5%–10%) polarized dipole structure along the emission ring, with negative circular polarization in the western region and positive circular polarization in the eastern region, although our methods exhibit stronger disagreement than for linear polarization. We analyze the data using multiple independent imaging and modeling methods, each of which is validated using a standardized suite of synthetic data sets. While the detailed spatial distribution of the linear polarization along the ring remains uncertain owing to the intrinsic variability of the source, the spiraling polarization structure is robust to methodological choices. The degree and orientation of the linear polarization provide stringent constraints for the black hole and its surrounding magnetic fields, which we discuss in an accompanying publication.

Dark matter condensates as highly nonlocal solitons: instability in the Schwarzschild metric and laboratory analog

Theories on the bosonic nature of dark matter are a promising alternative to the cold dark matter model. Here we consider a dark matter halo in the state of a Bose–Einstein condensate (BEC), subject to the gravitation of a black hole. In the low energy limit, we bring together the general relativity in the Schwarzschild metric and the quantum description of the BEC. The model is solvable in the Fermi normal coordinates with the so called highly nonlocal approximation and describes tidal deformations in the condensate wave function. The black hole deforms the localized condensate until the attraction of the compact object overcomes the self-gravitation and destabilizes the solitonic dark matter. Moreover, the model can be implemented as a gravitational analog in the laboratory; the time-dependent potential generated by the galactic black hole can be mimicked by an optical trap acting on a conventional condensate. The results open the way to new laboratory simulators for quantum gravitational effects.

The internal Faraday screen of Sagittarius A*

We report on 85−101 GHz light curves of the Galactic Center supermassive black hole, Sagittarius A* (Sgr A*), observed in April 2017 with the Atacama Large Millimeter/submillimeter Array (ALMA). This study of high-cadence full-Stokes data provides new measurements of the fractional linear polarization at a 1−2% level resolved in 4 s time segments, and stringent upper limits on the fractional circular polarization at 0.3%. We compare these findings to ALMA light curves of Sgr A* at 212−230 GHz observed three days later, characterizing a steep depolarization of the source at frequencies below about 150 GHz. We obtain time-dependent rotation measure (RM) values, with the mean RM at 85−101 GHz being a factor of two lower than that at 212−230 GHz. Together with the rapid temporal variability of the RM and its different statistical characteristics in both frequency bands, these results indicate that the Faraday screen in Sgr A* is largely internal, with about half of the Faraday rotation taking place inside the inner 10 gravitational radii, contrary to the common external Faraday screen assumption. We then demonstrate how this observation can be reconciled with theoretical models of radiatively inefficient accretion flows for a reasonable set of physical parameters. Comparisons with numerical general relativistic magnetohydrodynamic simulations suggest that the innermost part of the accretion flow in Sgr A* is much less variable than these models predict; in particular, the observed magnetic field structure appears to be coherent and persistent.

Chasing the Break: Tracing the Full Evolution of a Black Hole X-Ray Binary Jet with Multiwavelength Spectral Modeling

Black hole (BH) X-ray binaries (XRBs) are ideal targets to study the connection between accretion inflow and jet outflow. Here we present quasi-simultaneous, multiwavelength observations of the Galactic BH system MAXI J1820+070, throughout its 2018–2019 outburst. Our data set includes coverage from the radio through X-ray bands from 17 different instruments/telescopes, and encompasses 19 epochs over a 7 month period, resulting in one of the most well-sampled multiwavelength data sets of a BH XRB outburst to date. With our data, we compile and model the broadband spectra of this source using a phenomenological model that includes emission from the jet, a companion star, and an accretion flow. This modeling allows us to track the evolution of the spectral break in the jet spectrum, a key observable that samples the jet launching region. We find that the spectral break location changes over at least ≈3 orders of magnitude in electromagnetic frequency over this period. Using these spectral break measurements, we link the full cycle of jet behavior, including the rising, quenching, and reignition, to the changing accretion flow properties as the source evolves through its different accretion states. Our analysis shows consistent jet behavior with other sources in similar phases of their outbursts, reinforcing the idea that jet quenching and recovery may be a global feature of BH XRB systems in outburst. Our results also provide valuable evidence supporting a close connection between the geometry of the inner accretion flow and the base of the jet.

Galactic pure Lovelock black holes: Geometry, stability, and Hawking temperature

Galactic pure Lovelock black holes: Geometry, stability, and Hawking temperature

Origin of an orbiting star around the galactic supermassive black hole.

The tremendous tidal force that is linked to the supermassive black hole (SMBH) at the center of our galaxy is expected to strongly subdue star formation in its vicinity. Stars within 1'' from the SMBH thus likely formed further from the SMBH and migrated to their current positions. In this study, spectroscopic observations of the star S0-6/S10, one of the closest (projected distance from the SMBH of ≈0''.3) late-type stars were conducted. Using metal absorption lines in the spectra of S0-6, the radial velocity of S0-6 from 2014 to 2021 was measured, and a marginal acceleration was detected, which indicated that S0-6 is close to the SMBH. The S0-6 spectra were employed to determine its stellar parameters including temperature, chemical abundances ([M/H], [Fe/H], [α/Fe], [Ca/Fe], [Mg/Fe], [Ti/Fe]), and age. As suggested by the results of this study, S0-6 is very old (≳10 Gyr) and has an origin different from that of stars born in the central pc region.

The high energy X-ray probe (HEX-P): probing the physics of the X-ray corona in active galactic nuclei

The hard X-ray emission in active galactic nuclei (AGN) and black hole X-ray binaries is thought to be produced by a hot cloud of electrons referred to as the corona. This emission, commonly described by a power law with a high-energy cutoff, is suggestive of Comptonization by thermal electrons. While several hypotheses have been proposed to explain the origin, geometry, and composition of the corona, we still lack a clear understanding of this fundamental component. NuSTAR has been playing a key role improving our knowledge of X-ray coronæ thanks to its unprecedented sensitivity above 10 keV. However, these constraints are limited to bright, nearby sources. The High Energy X-ray Probe (HEX-P) is a probe-class mission concept combining high spatial resolution X-ray imaging and broad spectral coverage (0.2–80 keV) with a sensitivity superior to current facilities. In this paper, we highlight the major role that HEX-P will play in further advancing our insights of X-ray coronæ notably in AGN. We demonstrate how HEX-P will measure key properties and track the temporal evolution of coronæ in unobscured AGN. This will allow us to determine their electron distribution and test the dominant emission mechanisms. Furthermore, we show how HEX-P will accurately estimate the coronal properties of obscured AGN in the local Universe, helping address fundamental questions about AGN unification. In addition, HEX-P will characterize coronæ in a large sample of luminous quasars at cosmological redshifts for the first time and track the evolution of coronæ in transient systems in real time. We also demonstrate how HEX-P will enable estimating the coronal geometry using spectral-timing techniques. HEX-P will thus be essential to understand the evolution and growth of black holes over a broad range of mass, distance, and luminosity, and will help uncover the black holes’ role in shaping the Universe.

Black Hole Ultracompact X-Ray Binaries as Galactic Low-frequency Gravitational Wave Sources: The He Star Channel

Black hole (BH) ultracompact X-ray binaries (UCXBs) are potential Galactic low-frequency gravitational wave (GW) sources. As an alternative channel, BH UCXBs can evolve from BH+He star binaries. In this work, we perform a detailed stellar evolution model for the formation and evolution of BH UCXBs evolving from the He star channel to diagnose their detectability as low-frequency GW sources. Our calculations found that some nascent BH+He star binaries after the common-envelope (CE) phase could evolve into UCXB-LISA sources with a maximum GW frequency of ∼5 mHz, which can be detected in a distance of 10 kpc (or 100 kpc). Once BH+He star systems become UCXBs through mass transfer, they would emit X-ray luminosities of ∼1038 erg s−1, making them ideal multimessenger objects. If the initial He-star masses are ≥0.7 M ⊙, those systems are likely to experience two Roche lobe overflows, and the X-ray luminosity can reach a maximum of 3.5 × 1039 erg s−1 in the second mass-transfer stage. The initial He-star masses and initial orbital periods of progenitors of Galactic BH UCXB-LISA sources are in the range of 0.32–2.9 M ⊙ and 0.02–0.19 days, respectively. Nearly all BH+He star binaries in the above parameter space can evolve into GW sources whose chirp masses can be accurately measured. Employing a population synthesis simulation, we predict the birthrate and detection number of Galactic BH UCXB-LISA sources evolving from the He star channel are R = 2.2 × 10−6 yr−1 and 33 for an optimistic CE parameter, respectively.

High-resolution, Mid-infrared Color Temperature Mapping of the Central 10″ of the Galaxy

The neighborhood of the Galactic black hole boasts a plethora of extended interstellar gas and dust features, as well as populations of compact (unresolved or marginally resolved) features such as the G objects. Most are well manifested in the infrared. To disentangle and characterize the infrared structure of the extended features and identify compact sources, we used 3.8 μm (L′ filter) data from the NIRC2 imager at the Keck Observatory and 8.6 μm (PAH1 filter) data from the VISIR imager at the Very Large Telescope to produce the highest-resolution mid-IR color temperature map of the inner half-parsec of the Galactic center to date. From this map, we compile a catalog of features that stand out from their background. In particular, we identify 33 compact sources that stand out against the local background temperature, 11 of which are newly identified and candidates for being members of the G object population. Additionally, we resolve and newly characterize the morphology of several known extended features. These results prepare the way for ongoing and future JWST studies that have access to a greater range of mid-infrared wavelengths and thus will allow for refined estimation of the trends of dust temperatures.

Pair Plasma Cascade in Rotating Black Hole Magnetospheres with a Split Monopole Flux Model

An electron-positron cascade in the magnetospheres of Kerr black holes (BHs) is a fundamental ingredient to fueling the relativistic γ-ray jets seen at the polar regions of galactic supermassive BHs (SMBHs). This leptonic cascade occurs in the spark gap region of a BH magnetosphere where the unscreened electric field parallel to the magnetic field is present; hence, it is affected by the magnetic field structure. A previous study explored the case of a thin accretion disk, representative of active galactic nuclei. Here we explore the case of a quasi-spherical gas distribution, as is expected to be present around the SMBH Sgr A* in the center of our Milky Way galaxy, for example. The properties and efficiency of the leptonic cascade are studied. The findings of our study and the implications for SMBH systems in various spectral and accretion states are discussed. The relationships and scalings derived from varying the mass of the BH and background photon spectra are further used to analyze the leptonic cascade process to power jets seen in astronomical observations. In particular, one finds the efficiency of the cascade in a quasi-spherical gas distribution peaks at the jet axis. Observationally, this should lead to a more prominent jet core, in contrast to the thin disk accretion case, where it peaks around the jet–disk interface. One also finds the spectrum of the background photons plays a key role. The cascade efficiency is maximum for a spectral index of 2, while harder and softer spectra lead to a less efficient cascade.

The Solar Particle Acceleration Radiation and Kinetics (SPARK) Mission Concept

Particle acceleration is a fundamental process arising in many astrophysical objects, including active galactic nuclei, black holes, neutron stars, gamma-ray bursts, accretion disks, solar and stellar coronae, and planetary magnetospheres. Its ubiquity means energetic particles permeate the Universe and influence the conditions for the emergence and continuation of life. In our solar system, the Sun is the most energetic particle accelerator, and its proximity makes it a unique laboratory in which to explore astrophysical particle acceleration. However, despite its importance, the physics underlying solar particle acceleration remain poorly understood. The SPARK mission will reveal new discoveries about particle acceleration through a uniquely powerful and complete combination of γ-ray, X-ray, and EUV imaging and spectroscopy at high spectral, spatial, and temporal resolutions. SPARK’s instruments will provide a step change in observational capability, enabling fundamental breakthroughs in our understanding of solar particle acceleration and the phenomena associated with it, such as the evolution of solar eruptive events. By providing essential diagnostics of the processes that drive the onset and evolution of solar flares and coronal mass ejections, SPARK will elucidate the underlying physics of space weather events that can damage satellites and power grids, disrupt telecommunications and GPS navigation, and endanger astronauts in space. The prediction of such events and the mitigation of their potential impacts are crucial in protecting our terrestrial and space-based infrastructure.

Constraining a Companion of the Galactic Center Black Hole Sgr A*

We use 23 yr of astrometric and radial velocity data on the orbit of the star S0-2 to constrain a hypothetical intermediate-mass black hole orbiting the massive black hole Sgr A* at the Galactic center. The data place upper limits on variations of the orientation of the stellar orbit at levels between 0.°02 and 0.°07 per year. We use a combination of analytic estimates and full numerical integrations of the orbit of S0-2 in the presence of a black hole binary. For a companion intermediate-mass black hole outside the orbit of S0-2 (1020 au), we find that a companion black hole with mass m c between 103 and 105 M ⊙ is excluded, with a boundary behaving as . For a companion with a c < 1020 au, a black hole with mass between 103 and 105 M ⊙ is excluded, with . These bounds arise from quadrupolar perturbations of the orbit of S0-2. Significantly stronger bounds on an inner companion arise from the fact that the location of S0-2 is measured relative to the bright emission of Sgr A* and that separation is perturbed by the “wobble” of Sgr A* about the center of mass between it and the companion. The result is a set of bounds as small as 400 M ⊙ at 200 au; the numerical simulations suggest a bound from these effects varying as . We compare and contrast our results with those from a recent analysis by the GRAVITY collaboration.

First detection of soft-lag in GRS 1915 + 105 at HFQPO using AstroSat observations

ABSTRACT The Galactic black hole GRS 1915 + 105 exhibits generic high-frequency quasi-periodic oscillations (HFQPOs) at ∼ 67 Hz only during the radio-quiet ‘softer’ variability classes. We present the time-lag properties associated with HFQPOs in the wide energy band (3–60 keV) using all AstroSat observations. For the first time, we detect soft-lag of 6–25 keV band w.r.t. 3–6 keV band for all ‘softer’ variability classes (δ, ω, κ, and γ). Moreover, our findings reveal that soft-lag increases gradually with the energy of the photons. These features are entirely opposite to the previous report of hard-lag obtained with the RXTE observations. The energy-dependent time-lag study exhibits a maximum soft-lag of ∼ 3 and ∼ 2.5 ms for the δ and ω classes, respectively, whereas the κ and γ classes both exhibit a maximum soft-lag of ∼2.1 ms. We find a coherent lag-energy correlation for all four variability classes, where the amplitude of soft-lag increases with energy and becomes maximum at ∼18 keV. We interpret this observed soft-lag as the reflection of hard photons in the ‘cooler’ accretion disc. A generic lag-rms correlation implies that the soft-lag increases with the rms amplitude of the HFQPO. The wideband (0.7–50 keV) spectral study suggests a high value of the optical depth (τ ∼ 6.90–12.55) of the Comptonized medium and the magnitude of the soft-lag increases linearly with the increase in optical depth (τ). We explain the observed time-lag features at the HFQPOs in the context of a possible accretion disc scenario.

Strong gravitational lensing by loop quantum gravity motivated rotating black holes and EHT observations

We investigate gravitational lensing in the strong deflection regime by loop quantum gravity (LQG)-motivated rotating black hole (LMRBH) metrics with an additional parameter l besides mass M and rotation a. The LMRBH spacetimes are regular everywhere, asymptotically encompassing the Kerr black hole as a particular case and, depending on the parameters, describe black holes with one horizon only (BH-I), black holes with an event horizon and a Cauchy horizon (BH-II), black holes with three horizons (BH-III), or black holes with no horizons (NH) spacetime. 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The angular separation s, for SMBHs Sgr A* and M87*, differs significantly, with values ranging ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.008–0.376) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as for Sgr A* and ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.006–0.282) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as for M87*. The deviations of the lensing observables Δθ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \ heta _{\\infty }$$\\end{document} and Δs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta s$$\\end{document} for LMRBH (a=0.80,l=2.0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a=0.80,l=2.0$$\\end{document}) from Kerr black holes can reach up to 10.22μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10.22\\,\\upmu $$\\end{document}as and 0.241μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.241~\\upmu $$\\end{document}as for Sgr A*, and 7.683μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.683~\\upmu $$\\end{document}as and 0.181μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.181~\\upmu $$\\end{document}as for M87*. The relative magnitude rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document}∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.047, 1.54). We estimate the time delay between the first and second relativistic images using twenty supermassive galactic centre black holes as lenses to find, for example, the time delay for Sgr A* and M87* can reach approximately 23.26 min and 33,261.8 min, respectively. Our analysis concludes that, within the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\sigma $$\\end{document} region, a significant portion of the BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. The possibility of LMRBH being a BH-III with three horizons has been almost ruled out, except for a small portion of parameter space, by θsh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{sh}$$\\end{document} bounds of Sgr A* and M87* measured by EHT. In contrast, NH without a horizon is completely ruled out. We discover that the EHT results of Sgr A* place more stringent limits on the parameter space of LMRBH black holes than those established by the EHT results of M87*.

MAXI J0637–430: A Possible Candidate for Bulk Motion Comptonization?

The transient Galactic black hole candidate MAXI J0637–430 went through an outburst in 2019–2020 for the very first time. This outburst was active for almost 6 months from 2019 November to 2020 May. We study the spectral properties of this source during that outburst using archival data from NICER/XTI, Swift/XRT, and NuSTAR/FPM satellites/instruments. We have analyzed the source during six epochs on which simultaneous NICER–NuSTAR and Swift/XRT–NuSTAR data were available. Using both phenomenological and physical model fitting approaches, we analyzed the spectral data in the broad 0.7–70 keV energy band. We first used a combination of disk blackbody with power-law, disk blackbody with broken power-law, and disk blackbody with power-law and bulk motion Comptonization (BMC) models. For a better understanding of the accretion picture, e.g., understanding how the accretion rates change with the changing size of the perceived Compton cloud, we used the two-component advective flow (TCAF) model with the broken power-law, and TCAF with the combined power-law, BMC models. For the last three epochs, the diskbb+power-law and TCAF models were able to spectrally fit the data for acceptable χ 2/degrees of freedom (dof). However, for the first three epochs, we needed an additional component to fit spectra for acceptable χ 2/dof. From our analysis, we reported on the possible presence of another component during these first three epochs when the source was in the high soft state. This additional component in this state is best described by the BMC phenomenon. From the TCAF model fitting, we estimated the average mass of the source as .