Relativistic Precession Research Articles

F(R)gravity after the detection of the orbital precession of the S2 star around the Galactic Center massive black hole

The GRAVITY Collaboration achieved the remarkable detection of the orbital precession of the S2 star around the Galactic centre supermassive black hole, providing yet another proof of the validity of the General Relativity. The departure from the Schwarzschild precession is encoded in the parameter $f_{\rm SP}$ which multiplies the predicted general relativistic precession. Such a parameter results to be $f_{\rm SP}=1.10\pm0.19$, which is consistent with General Relativity ($f_{\rm SP}=1$) at 1$\sigma$ level. Nevertheless, this parameter may also hide an effect of modified theories of gravity. Thus, we consider the orbital precession due to the Yukawa-like gravitational potential arising in the weak field limit of $f(R)$-gravity, and we use the current bound on the $f_{\rm SP}$ to constrain the strength and the scale length of the Yukawa-like potential. No deviation from GR are revealed at scale of $\lambda<6300$ AU with the strength of the Yukawa potential restricted to $\delta = -0.01_{-0.14}^{+0.61}$.

Two regimes of tidal-stream circularization by supermassive black holes

Stars that approach a supermassive black hole (SMBH) too closely can be disrupted by the tidal gravitational field of the SMBH. The resulting debris forms a tidal stream orbiting the SMBH which can collide with itself due to relativistic apsidal precession. These self-collisions dissipate energy, causing the stream to circularize. We perform kinematic simulations of these stream self-collisions to estimate the efficiency of this circularization as a function of SMBH mass $M_\bullet$ and penetration factor $\beta$, the ratio of the tidal radius to the pericenter distance. We uncover two distinct regimes depending on whether the time $t_c$ at which the most tightly bound debris circularizes is greater or less than the time $t_{\rm fb}$ at which the mass fallback rate peaks. The bolometric light curve of energy dissipated in the stream self-collisions has a single peak at $t > t_{\rm fb}$ in the slow circularization regime ($t_c > t_{\rm fb}$), but two peaks (one at $t < t_{\rm fb}$ and a second at $t_{\rm fb}$) in the fast circularization regime ($t_c < t_{\rm fb}$). Tidal streams will circularize in the slow (fast) regime for apsidal precession angles less (greater) than 0.2 radians which occur for $\beta \lesssim (\gtrsim) (M_\bullet/10^6M_\odot)^{-2/3}$. The observation of prominent double peaks in bolometric TDE light curves near the transition between these two regimes would strongly support our model of tidal-stream kinematics.

Testing Kerr black hole mimickers with quasi-periodic oscillations from GRO J1655-40

The measurements of quasi-periodic oscillations (QPOs) provide a quite powerful tool to test the nature of astrophysical black hole candidates in the strong gravitational field regime. In this paper, we use QPOs within the relativistic precession model to test a recently proposed family of rotating black hole mimickers, which reduce to the Kerr metric in a limiting case, and can represent traversable wormholes or regular black holes with one or two horizons, depending on the values of the parameters. In particular, assuming that the compact object of GRO J1655-40 is described by a rotating black hole mimicker, we perform a chi -square analysis to fit the parameters of the mimicker with two sets of observed QPO frequencies from GRO J1655-40. Our results indicate that although the metric around the compact object of GRO J1655-40 is consistent with the Kerr metric, a regular black hole with one horizon is favored by the observation data of GRO J1655-40.

Signs of Eccentricity in Two Gravitational-wave Signals May Indicate a Subpopulation of Dynamically Assembled Binary Black Holes

Abstract The orbital eccentricity of a merging binary black hole leaves an imprint on the associated gravitational-wave signal that can reveal whether the binary formed in isolation or in a dynamical environment, such as the core of a dense star cluster. We present measurements of the eccentricity of 26 binary black hole mergers in the second LIGO–Virgo gravitational-wave transient catalog, updating the total number of binary black holes analyzed for orbital eccentricity to 36. Using the SEOBNRE waveform, we find the data for GW190620A are poorly explained by the zero-eccentricity hypothesis (frequentist p-value ≲0.1%). Using a log-uniform prior on eccentricity, the eccentricity at 10 Hz for GW190620A is constrained to e 10 ≥ 0.05 (0.1) at 74% (65%) credibility. With this log-uniform prior, we obtain a 90% credible lower eccentricity limit of 0.001, while assuming a uniform prior leads the data to prefer e 10 ≥ 0.11 at 90% credibility. This is the second measurement of a binary black hole system with statistical support for nonzero eccentricity; the intermediate-mass black hole merger GW190521 was the first. Interpretation of these two events is currently complicated by waveform systematics; we are unable to simultaneously model the effects of relativistic precession and eccentricity. However, if these two events are, in fact, eccentric mergers, then there are potentially many more dynamically assembled mergers in the LIGO–Virgo catalog without measurable eccentricity; ≳27% of the observed LIGO–Virgo binaries may have been assembled dynamically in dense stellar environments (95% credibility).

On the Origin of Late-time X-Ray Flares in UV/optically Selected Tidal Disruption Events

Abstract We propose a model to explain the time delay between the peak of the optical and X-ray luminosity, Δt O−X hereafter, in UV/optically selected tidal disruption events (TDEs). The following picture explains the observed Δt O−X in several TDEs as a consequence of the circularization and disk accretion processes as long as the sub-Eddington accretion. At the beginning of the circularization, the fallback debris is thermalized by the self-crossing shock caused by relativistic precession, providing the peak optical emission. During the circularization process, the mass fallback rate decreases with time to form a ring around the supermassive black hole (SMBH). The formation timescale corresponds to the circularization timescale of the most tightly bound debris, which is less than a year to several decades, depending mostly on the penetration factor, the circularization efficiency, and the black hole mass. The ring will subsequently evolve viscously over the viscous diffusion time. We find that it accretes onto the SMBH on a fraction of the viscous timescale, which is 2 years for the typical given parameters, leading to X-ray emission at late times. The resultant Δt O−X is given by the sum of the circularization timescale and the accretion timescale and significantly decreases with increasing penetration factor to several to ∼10 yr typically. Since the X-ray luminosity substantially decreases as the viewing angle between the normal to the disk plane and line of sight increases from 0° to 90°, a low late-time X-ray luminosity can be explained by an edge-on view. We also discuss the super-Eddington accretion scenario, where Δt O−X is dominated by the circularization timescale.

Distinguishing regular and singular black holes in modified gravity

This paper is devoted to investigate the possible ways of distinguishing regular and singular black holes (BHs) in modified gravity (MOG) called regular MOG (RMOG) and Schwarzschild MOG (SMOG) BHs through observational data from twin peak quasiperiodic oscillations (QPOs) which are generated by test particles in stable orbits around the BHs. The presence of MOG field causes to sufficiently the mpeak in effective potential for a radial motion of test particles. The effect of MOG parameter on specific angular momentum and energy has also studied. As a main part of the paper, we focus on investigations of QPOs around SMOG and RMOG BHs in RP model and the relations of upper and lower frequencies of twin peak QPOs in SMOG and RMOG BH models together with extreme rotating Kerr and Schwarzschild BH. Moreover, possible parameters for the central BHs of the objects GRS J1915 + 105 and XTE 1550 – 564 have also obtained numerically in the relativistic precession (RP) model. Finally, we provide comparisons of the innermost stable circular orbit (ISCO) and the orbits where twin peak QPOs with the ratio 3:2 taken place and show that QPOs can not be generated at/inside ISCO and there is a correlation between the radius of ISCO and QPO orbits.

A timing-based estimate of the spin of the black hole in MAXI J1820+070

ABSTRACT MAXI J1820+070 (ASSASN-18ey) is a black hole (BH) X-ray binary discovered in 2018. The brightness of the source triggered multi-wavelength campaigns of this source from different observatories. We analyse the power density spectra (PDS) obtained from NICER high cadence observations of the source in the hard state. We obtain the evolution of the characteristic frequencies by modelling the PDS. We interpret the characteristic frequencies of various PDS components (both QPOs and broad-band noise components) as variability occurring at a particular radius, and explain them in the context of the Relativistic Precession Model (RPM). We estimate the dimensionless spin of the BH at $0.799^{+0.016}_{-0.015}$ by fitting the RPM.

Testing no-hair theorem by quasi-periodic oscillations: thequadrupole of GRO J1655–40

We perform an observational test of no-hair theorem usingquasi-periodic oscillations within the relativistic precession model. Twowell motivated metrics we apply are Kerr-Q and Hartle-Thorne metrics inwhich the quadrupole is the parameter that possibly encodes deviations fromthe Kerr black hole. The expressions for the quasi-periodic frequencies arederived before comparing the models with the observation. We encounter adegeneracy in constraining spin and quadrupole parameters that makes itdifficult to measure their values. In particular, we here propose a noveltest of no-hair theorem by adapting the Hartle-Thorne metric. We complement our study by doing a model comparison. We findthat there is strong evidence that Kerr black hole is the source of the central object in GROJ1655–40 given the present observational precisions.

The Impact of Classical and General Relativistic Obliquity Precessions on the Habitability of Circumstellar Neutron Stars’ Planets

Abstract Recently, it has been shown that rocky planets orbiting neutron stars can be habitable under plausible circumstances. If a distant, point-like source of visible light, such as a Sun-like main-sequence star or the gravitationally-lensed accretion disk of a supermassive black hole is present, possible temporal variations Δ ε p t of the planet’s axial tilt ε p to the ecliptic plane should be included in the overall habitability budget since the obliquity determines the insolation at a given latitude on a body’ s surface. I point out that, for rather generic initial spin–orbit initial configurations, general relativistic and classical spin variations induced by the post-Newtonian de Sitter and Lense–Thirring components of the field of the host neutron star and by its pull to the planetary oblateness J 2 p may induce huge and very fast variations of ε p that would likely have an impact on the habitability of such worlds. In particular, for a planet’s distance of, say, 0.005 au from a 1.4 M ⊙ neutron star corresponding to an orbital period P b = 0.109 day, obliquity shifts Δε p as large as ε p max − ε p min ≃ 50 ° – 100 ° over characteristic timescales as short as 10 days ( J 2 p ) to 3 Myr (Lense–Thirring) may occur for arbitrary orientations of the orbital and spin angular momenta L , S ns, S p of the planet-neutron star system. In view of this feature of their spins, I dub such hypothetical planets as “nethotrons.”

Testing gravity of a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories by quasi-periodic oscillations

By using the relativistic precession model, we have studied frequencies of quasi-periodic oscillations in the spacetime of a disformal Kerr black hole. This black hole owns an extra disformal parameter and belongs to a class of non-stealth solutions in quadratic degenerate higher-order scalar-tensor (DHOST) theories. Our result shows that only the periastron precession frequency is related to the disformal parameter, while the azimuthal frequency and the nodal precession frequency are identical with those in the usual Kerr black hole in general relativity. Combing with the observation data of GRO J1655-40, we fit parameters of the disformal Kerr black hole, and find that the disformal parameter α is almost negative in the range of 1 σ, which implies the negative disformal parameter α is favored by the observation data of GRO J1655-40.

Regular nonminimal magnetic black hole as a source of quasiperiodic oscillations

We study the properties of the spacetime around a regular nonminimal magnetic black hole (BH) together with the dynamics of the neutral, magnetized, and magnetically charged particles in its vicinity. The dependence of the values of curvature invariants and the outer event horizon corresponding to the extreme charge of the BH from the coupling parameter are studied in detail. Our study of the test particle motion shows that the innermost stable circular orbit (ISCO) radius decreases with the increase of the magnetic charge of the nonminimal regular magnetic BH. We show that the increase of the ISCO radius with the increase of the coupling parameter is due to the decrease of the extreme value of the BH charge. In particular, when the coupling parameter $q\ensuremath{\rightarrow}\ensuremath{\infty}$ the ISCO radius tends to the value ${r}_{\mathrm{ISCO}}=4.5M$. The effect of the magnetic charge parameter on ISCO radius can mimic the effect due to the spin parameter of the rotating Kerr BH, and the mimicking values of the spin parameter decreases with the increase of the coupling parameter. We also explore the possible mimicking of the parameters through the observations of twin-peak quasiperiodic oscillations (QPOs). Our analysis shows that the Reissner-Nordstr\"om (RN) charge can mimic the spin parameter of the Kerr BH up to $a/M\ensuremath{\simeq}0.51$ provided that there is the same relation between the upper and lower frequencies of the twin-peak QPOs. On the other hand, the nonminimal regular magnetic BH coupling parameter may mimic the spin parameter up to $a/M\ensuremath{\simeq}0.215$ in the relativistic precession model.

Hinting a dark matter nature of Sgr A* via the S-stars

ABSTRACT The motion data of the S-stars around the Galactic Centre gathered in the last 28 yr imply that Sgr A* hosts a supermassive compact object of about $4 \times 10^6\, {\rm M}_{\odot }$, a result awarded with the Nobel Prize in Physics 2020. A non-rotating black hole (BH) nature of Sgr A* has been uncritically adopted since the S-star orbits agree with Schwarzschild geometry geodesics. The orbit of S2 has served as a test of general relativity predictions such as the gravitational redshift and the relativistic precession. The central BH model is, however, challenged by the G2 post-peripassage motion and by the lack of observations on event-horizon-scale distances robustly pointing to its univocal presence. We have recently shown that the S2 and G2 astrometry data are better fitted by geodesics in the spacetime of a self-gravitating dark matter core–halo distribution of 56 keV-fermions, ‘darkinos’, which also explains the outer halo Galactic rotation curves. This letter confirms and extends this conclusion using the astrometry data of the 17 best-resolved S-stars, thereby strengthening the alternative nature of Sgr A* as a dense core of darkinos.

Detecting general relativistic orbital precession in transiting hot Jupiters

ABSTRACT Both classical and relativistic weak-field and slow-motion perturbations to planetary orbits can be treated as perturbative corrections to the Keplerian model. In particular, tidal forces and General Relativity (GR) induce small precession rates of the apsidal line. Accurate measurements of these effects in transiting exoplanets could be used to test GR and to gain information about the planetary interiors. Unfortunately, models for transiting planets have a high degree of degeneracy in the orbital parameters that, combined to the uncertainties of photometric transit observations, results in large errors on the determinations of the argument of periastron and precludes a direct evaluation of the apsidal line precession. Moreover, tidal and GR precession time-scales are many order of magnitudes larger than orbital periods, so that on the observational time-spans required to cumulate a precession signal enough strong to be detected, even small systematic errors in transit ephemerides add up to cancel out the tiny variations due to precession. Here we present a more feasible solution to detect tidal and GR precession rates through the observation of variations of the time interval (Δτ) between primary and secondary transits of hot Jupiters and propose the most promising target for such detection, WASP-14 b. For this planet we expect a cumulated $\Delta \tau \, \approx$ −250 s, due to tidal and relativistic precession, since its first photometric observations.

Resolving the Complex Evolution of a Supermassive Black Hole Triplet in a Cosmological Simulation

Abstract We present here a self-consistent cosmological zoom-in simulation of a triple supermassive black hole (SMBH) system forming in a complex multiple galaxy merger. The simulation is run with an updated version of our code KETJU, which is able to follow the motion of SMBHs down to separations of tens of Schwarzschild radii while simultaneously modeling the large-scale astrophysical processes in the surrounding galaxies, such as gas cooling, star formation, and stellar and AGN feedback. Our simulation produces initially an SMBH binary system for which the hardening process is interrupted by the late arrival of a third SMBH. The KETJU code is able to accurately model the complex behavior occurring in such a triple SMBH system, including the ejection of one SMBH to a kiloparsec-scale orbit in the galaxy due to strong three-body interactions as well as Lidov–Kozai oscillations suppressed by relativistic precession when the SMBHs are in a hierarchical configuration. One pair of SMBHs merges ∼3 Gyr after the initial galaxy merger, while the remaining binary is at a parsec-scale separation when the simulation ends at redshift z = 0. We also show that KETJU can capture the effects of the SMBH binaries and triplets on the surrounding stellar population, which can affect the binary merger timescales as the stellar density in the system evolves. Our results demonstrate the importance of dynamically resolving the complex behavior of multiple SMBHs in galactic mergers, as such systems cannot be readily modeled using simple orbit-averaged semianalytic models.

Very low-frequency oscillations from the 11 Hz pulsar in Terzan 5: frame dragging back on the table.

ABSTRACT We present a re-analysis of 47 Rossi X-ray Timing Explorer observations of the 11 Hz accreting pulsar IGR J17480-2446 in Terzan 5 during its 2010 outburst. We studied the fast-time variability properties of the source and searched for quasi-periodic oscillations (QPOs) in a large-frequency range. General relativity predicts that frame dragging occurs in the vicinity of a spinning compact object and induces the precession of matter orbiting said object. The relativistic precession model predicts that this frame dragging can be observed as QPOs with a characteristic frequency in the light curves of accreting compact objects. Such QPOs have historically been classified as horizontal branch oscillations in neutron star (NS) systems, and for a NS spinning at 11 Hz, these oscillations are expected at frequencies below 1 Hz. However, previous studies of IGR J17480-2446 have classified QPOs at 35–50 Hz as horizontal branch oscillations, thus casting doubts on the frame-dragging nature of such QPOs. Here, we report the detection of seven very low-frequency QPOs, previously undetected, with centroid frequencies below 0.3 Hz, and which can be ascribed to frame dragging. We also discuss the possible nature of the QPOs detected at 35–50 Hz in this alternative scenario.

First light from tidal disruption events

ABSTRACT When a star comes too close to a supermassive black hole, it gets torn apart by strong tidal forces in a tidal disruption event, or TDE. Half of the elongated stream of debris comes back to the stellar pericentre where relativistic apsidal precession induces a self-crossing shock. As a result, the gas gets launched into an outflow that can experience additional interactions, leading to the formation of an accretion disc. We carry out the first radiation–hydrodynamics simulations of this process, making use of the same injection procedure to treat the self-crossing shock as in our previous adiabatic study. Two sets of realistic parameters of the problem are considered that correspond to different strengths of this initial interaction. In both cases, we find that the injected matter has its trajectories promptly circularized by secondary shocks taking place near the black hole. However, the generated internal energy efficiently diffuses away in the form of radiation, which results in a thin vertical profile of the formed disc. The diffusing photons promptly irradiate the surrounding debris until they emerge with a bolometric luminosity of $L\approx 10^{44} \, \rm erg\, s^{-1}$. Towards the self-crossing shock, diffusion is, however, slowed that results in a shallower luminosity increase, with a potentially significant component in the optical band. Matter launched to large distances continuously gains energy through radiation pressure, which can cause a significant fraction to become unbound. This work provides direct insight into the origin of the early emission from TDEs, which is accessed by a rapidly increasing number of observations.

Formation of an Accretion Flow

After a star has been tidally disrupted by a black hole, the debris forms an elongated stream. We start by studying the evolution of this gas before its bound part returns to the original stellar pericenter. While the axial motion is entirely ballistic, the transverse directions of the stream are usually thinner due to the confining effects of self-gravity. This basic picture may also be influenced by additional physical effects such as clump formation, hydrogen recombination, magnetic fields and the interaction with the ambient medium. We then examine the fate of this stream when it comes back to the vicinity of the black hole to form an accretion flow. Despite recent progress, the hydrodynamics of this phase remains uncertain due to computational limitations that have so far prevented us from performing a fully self-consistent simulation. Most of the initial energy dissipation appears to be provided by a self-crossing shock that results from an intersection of the stream with itself. The debris evolution during this collision depends on relativistic apsidal precession, expansion of the stream from pericenter, and nodal precession induced by the black hole spin. Although the combined influence of these effects is not fully understood, current works suggest that this interaction is typically too weak to significantly circularize the trajectories, with its main consequence being an expansion of the shocked gas. Global simulations of disc formation performed for simplified initial conditions find that the debris experiences additional collisions that cause its orbits to become more circular until eventually settling into a thick and extended structure. These works suggest that this process completes faster for more relativistic encounters due to the stronger shocks involved. It is instead significantly delayed if weaker shocks take place, allowing the gas to retain large eccentricities during multiple orbits. Radiation produced as the matter gets heated by circularizing shocks may leave the system through photon diffusion and participate in the emerging luminosity. This current picture of accretion flow formation results from recent theoretical works synthesizing the interplay between different aspects of physics. In comparison, early analytical works correctly identified the essential processes involved in disc formation, but had difficulty developing analytic frameworks that accurately combined non-linear hydrodynamical processes with the underlying relativistic dynamics. However, important aspects still remain to be understood at the time of writing, due to numerical challenges and the complexity of this process.

Doppler Boosting of the S-stars in the Galactic Center

Abstract Astrometry and spectroscopy of the S-stars in the Galactic Center provide a unique way to probe the properties of the central supermassive black hole, as well as the post-Newtonian effects caused by its gravity, e.g., gravitational redshift and general relativistic precession. It has also been suggested that the photometry of S-stars can be used for studying the properties of the gaseous environment of Sgr A*. Due to the high velocities of the S-stars, sometimes approaching 0.1c, their photometric signal should be considerably affected by the Doppler boosting. We calculate this relativistic effect for several S-stars closely approaching the central black hole (most of them recently announced) and show that the amplitude of the photometric variability due to the Doppler boosting for some of them (S62 and S4714) exceeds 6%; for the well-studied star S2 it is about 2%. Measurement of the Doppler boosting can confirm the existence and help refine orbital parameters of the S-stars with noisy spectroscopy and astrometry. This effect should be explicitly accounted for when the photometry of S-stars is used for probing the medium around the Sgr A*. We discuss the observability of the Doppler boosting given the complications typical for the Galactic Center and conclude, in particular, that the purely photometric detection of the higher-order relativistic corrections to the Doppler-boosting signal (due to the gravitational redshift and transverse Doppler shift, which we also calculate) is hardly possible for the S-stars.

Tidal Disruptions of Main-sequence Stars. V. The Varieties of Disruptions

Abstract Tidal disruption events (TDEs) are generally imagined as the complete disruption of a star when it passes close to a supermassive black hole (SMBH). Relativistic apsidal precession is thought to quickly “circularize” the bound debris, forming a compact accretion disk, which then emits a flare of standardized light curve and spectrum. We show here that this picture holds in only a minority of cases. TDEs are more diverse and can be grouped into several categories distinguished by stellar pericenter distance r p ; we estimate the relative frequency of these categories. Rapid circularization is rare both because it requires ( ) and because most events with lead to direct capture. For larger pericenter distances, (for M BH = 106 M ⊙), main-sequence stars with M * ≲ 3 are completely disrupted, but the bound debris orbits are highly eccentric and possess semimajor axes ∼100× the scale of the expected compact disk. Partial disruptions with fractional mass loss ≳10% occur with a rate similar to that of total disruptions; for fractional mass loss ≳50%, the rate is ≈1/3 as large. Partial disruptions—which must precede total disruptions when the stars’ angular momenta evolve in the “empty loss-cone” regime—change the orbital energy by factors ≳O(1). Partial disruption remnants are in general far from thermal equilibrium. Depending on its orbital energy and conditions within the stellar cluster surrounding the SMBH, a remnant may return after ∼O(100)–O(1000) yr and be fully disrupted, or it may rejoin the stellar cluster.

A Geometric Origin for Quasi-periodic Oscillations in Black Hole X-Ray Binaries

Abstract We expand the relativistic precession model to include nonequatorial and eccentric trajectories and apply it to quasi-periodic oscillations (QPOs) in black hole X-ray binaries (BHXRBs) and associate their frequencies with the fundamental frequencies of the general case of nonequatorial (with Carter's constant, ) and eccentric ( ) particle trajectories, around a Kerr black hole. We study cases with either two or three simultaneous QPOs and extract the parameters {e, r p , a, Q}, where r p is the periastron distance of the orbit, and a is the spin of the black hole. We find that the orbits with should have e ≲ 0.5 and r p ∼ 2–20 for the observed range of QPO frequencies, where a ∈ [0, 1], and that the spherical trajectories {e = 0, } with Q = 2–4 should have r s ∼ 3–20. We find nonequatorial eccentric solutions for both M82 X-1 and GROJ 1655-40. We see that these trajectories, when taken together, span a torus region and give rise to a strong QPO signal. For two simultaneous QPO cases, we found equatorial eccentric orbit solutions for XTEJ 1550-564, 4U 1630-47, and GRS 1915+105, and spherical orbit solutions for BHXRBs M82 X-1 and XTEJ 1550-564. We also show that the eccentric orbit solution fits the Psaltis–Belloni–Klis correlation observed in BHXRB GROJ 1655-40. Our analysis of the fluid flow in the relativistic disk edge suggests that instabilities cause QPOs to originate in the torus region. We also present some useful formulae for trajectories and frequencies of spherical and equatorial eccentric orbits.