Perihelion Precession Research Articles

Spin contributions to the alternate correction to the perihelion precession of binary systems such as OJ287

Spin contributions to the alternate correction to the perihelion precession of binary systems such as OJ287

Orbital precession of stars in the Galactic Centre

ABSTRACT The region around the centre of our Galaxy is very dense of stars. The kinematics of inner moving stars in the Galaxy (the so-called S-stars) has been deeply studied by different research groups leading to the conclusion of the existence of a very compact object (Sgr A*, likely a supermassive black hole) responsible for their high speed. Here, we start from the observational evidence of orbital apsidal line precession for the S2 (also called S0-2) star to investigate on a theoretical side what level of quality in such regime of relatively strong gravitational field is reached in the orbit angular precession determination when using a direct orbital integration of the star motion subjected to an acceleration computed in the post-Newtonian (PN) scheme up to different orders. This approach, although approximated and limited to particle speed not exceeding ∼ 0.3c, allows the inclusion of various effects, like that of a possible spin of the central massive object. Our results show that the inclusion of PN terms above the standard 1PN term (the one corresponding to the classic Einstein–Schwarzschild estimate of pericenter advance) is compulsory to determine angular precession at sufficient level of accuracy for those penetrating stars that would allow to pick contemporary the value of the mass and of the spin of a rotating (Kerr-like) supermassive black hole (SMBH). We discuss how future observational data, together with a proper modelization, could allow the determination of both mass and spin of the SMBH of our Galaxy.

Steeper Scattered Disks Buckle Faster

Disks of low-mass bodies scattered by giant planets to large semimajor axis and constant periapsis orbits are vulnerable to a buckling instability. This instability exponentially grows orbital inclinations, raises periapsis distances, and coherently tilts orbits resulting in clustering of arguments of periapsis. The dynamically hot system is then susceptible to the formation of a lopsided mode. Here we show that the timescale of the buckling instability decreases as the radial surface density of the population becomes more centrally dense, i.e., steeper scattered disks buckle faster. Accounting for differential apsidal precession driven by giant planets, we find that ∼10 M ⊕ is sufficient for a primordial scattered disk in the trans-Neptunian region to have been unstable if .

Gravitational-wave imprints of compact and galactic-scale environments in extreme-mass-ratio binaries

Circumambient and galactic-scale environments are intermittently present around black holes that reside in active galactic nuclei. As supermassive black holes impart energy on their host galaxy, so the galactic environment affects the dynamics of solar-mass objects around black holes and the gravitational waves emitted from non-vacuum asymmetric binaries. Only recently an exact general-relativistic solution has been found that describes a Schwarzschild black hole immersed in a dark matter halo of the Hernquist type. We perform an extensive analysis of generic geodesics delving in such non-vacuum spacetimes and compare our results with those obtained in Schwarzschild, as well as calculate their gravitational-wave emission. Our findings indicate that the radial and polar oscillation frequency ratios descend deeper into the strong gravity region as the compactness of the halo increases. This translates to a redshift of non-vacuum geodesics and their resulting waveforms with respect to the vacuum ones. We calculate the overlap between waveforms resulting from Schwarzschild and non-vacuum geometries and find that it decreases as the halo compactness grows, meaning that dark matter environments should be distinguishable by space-borne detectors. For compact environments, we find that the apsidal precession is strongly affected due to the gravitational pull of dark matter; the orbit's axis can rotate in the opposite direction as that of the orbital motion, leading to a retrograde precession drift that depends on the halo mass, as opposed to the typical prograde precession transpiring in galactic-scale environments. Gravitational waves in retrograde-to-prograde alterations demonstrate transient frequency phenomena around critical non-precessing turning points, thus they may serve as `smoking guns' for the presence of compact dark matter environments around supermassive black holes.

Constraining deviations from spherical symmetry using γ -metric

The $\ensuremath{\gamma}$-spacetime metric is a static and axially symmetric vacuum solution of the Einstein equation. This spacetime represents a naked singularity and it has an extra parameter $\ensuremath{\gamma}$ which signifies deviations from spherical symmetry. In this work, we study the possibility of constraining the deformation parameter with astrophysical observations. We start with gravitational lensing in the weak- and strong-field limits and calculate the respective deflection angles to show that only strong-field lensing observations will be able to constrain $\ensuremath{\gamma}$ independently. Later we study two other classical tests of gravity: Shapiro time delay and precession of perihelion. We show that, out of these two experiments, the deformation parameter affects the observables only in perihelion shift.

Alternate method of correction to the perihelion precession of binary systems

Alternate method of correction to the perihelion precession of binary systems

Coplanar Circumbinary Planets Can Be Unstable to Large Tilt Oscillations in the Presence of an Inner Polar Planet

Mutually misaligned circumbinary planets may form in a warped or broken gas disk or from later planet–planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semimajor axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect—it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.

Improving circumbinary planet detections by fitting their binary’s apsidal precession

ABSTRACT Apsidal precession in stellar binaries is the main non-Keplerian dynamical effect impacting the radial-velocities of a binary star system. Its presence can notably hide the presence of orbiting circumbinary planets because many fitting algorithms assume perfectly Keplerian motion. To first order, apsidal precession ($\dot{\omega }$) can be accounted for by adding a linear term to the usual Keplerian model. We include apsidal precession in the kima package, an orbital fitter designed to detect and characterize planets from radial velocity data. In this paper, we detail this and other additions to kima that improve fitting for stellar binaries and circumbinary planets including corrections from general relativity. We then demonstrate that fitting for $\dot{\omega }$ can improve the detection sensitivity to circumbinary exoplanets by up to an order of magnitude in some circumstances, particularly in the case of multiplanetary systems. In addition, we apply the algorithm to several real systems, producing a new measurement of aspidal precession in KOI-126 (a tight triple system), and a detection of $\dot{\omega }$ in the Kepler-16 circumbinary system. Although apsidal precession is detected for Kepler-16, it does not have a large effect on the detection limit or the planetary parameters. We also derive an expression for the precession an outer planet would induce on the inner binary and compare the value this predicts with the one we detect.

Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?

We investigate a nonsingular black hole spacetime representing a strong deformation of the Schwarzschild solution with mass $M$ by an additional hair $\ensuremath{\ell}$, which may be hierarchically larger than the Planck scale. The spacetime is an exact solution of Einstein's equations sourced by an anisotropic fluid. The model presents a de Sitter core and $\mathcal{O}({\ensuremath{\ell}}^{2}/{r}^{2})$ slow-decaying corrections to the Schwarzschild solution. These solutions are thermodynamically preferred when $0.2\ensuremath{\lesssim}\ensuremath{\ell}/GM\ensuremath{\lesssim}0.3$ and are characterized by strong deviations in the orbits of test particles from the Schwarzschild case. In particular, we find corrections to the perihelion precession angle scaling linearly with $\ensuremath{\ell}$. We test our model using the available data for the orbits of the S2 star around ${\text{SgrA}}^{*}$. These data strongly constrain the value of the hair $\ensuremath{\ell}$, casting an upper bound on it of $\ensuremath{\sim}0.47GM$ but do not rule out the possible existence of regular black holes with super-Planckian hair.

The study on transiting systems HAT-P-13, HAT-P-16, and WASP-32 through combining ground-based and TESS photometry

ABSTRACT High-precision transit photometry supplies ideal opportunities for detecting new exoplanets and characterizing their physical properties, which usually encode valuable information for unveiling the planetary structure, atmosphere, and dynamical history. We present revised properties of three transiting systems (i.e. HAT-P-13, HAT-P-16, and WASP-32) through analyzing TESS photometry and ground-based transit observations, which were obtained at the 1-m and 2.4-m telescopes of Yunnan Observatories, China, and the 1.2-m telescope of Hamburg Observatory, Germany, as well as the data in the literature. During modelling the transit light curves, Gaussian process is employed to account for the potential systematic errors. Through comprehensive timing analysis, we find that both HAT-P-13b and HAT-P-16b show significant timing variations (TTVs) that can be explained by apsidal precession. TTVs of WASP-32b may be led by a decaying orbit due to tidal dissipation or apsidal precession. However, the current observations can not rule out the origins of three systems’ TTVs from gravitational perturbations of close planetary companions conclusively.

Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

The Hermean average perihelion rate ω˙2PN, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from −18 to −4 microarcseconds per century μascty−1, depending on the true anomaly at epoch f0. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun’s gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury’s perihelion rate ω˙exp recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is σω˙exp≃8μascty−1, corresponding to a relative accuracy of 2×10−7 for the combination 2+2γ−β/3 of the PPN parameters β and γ scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to ≃10–50 times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recently improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a ≃10−7 accuracy level in constraining β and γ in an extended mission, despite ≃10−6 seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not-too-distant future, it will be necessary to include the 2PN acceleration in the Solar System’s dynamics as well.

Examining the orbital decay targets KELT-9 b, KELT-16 b, and WASP-4b, and the transit-timing variations of HD 97658 b

Context. Tidal orbital decay is suspected to occur for hot Jupiters in particular, with the only observationally confirmed case of this being WASP-12b. By examining this effect, information on the properties of the host star can be obtained using the so-called stellar modified tidal quality factor Q*′, which describes the efficiency with which the kinetic energy of the planet is dissipated within the star. This can provide information about the interior of the star. Aims. In this study, we aim to improve constraints on the tidal decay of the KELT-9, KELT-16, and WASP-4 systems in order to find evidence for or against the presence of tidal orbital decay. With this, we want to constrain the Q*′ value for each star. In addition, we aim to test the existence of the transit timing variations (TTVs) in the HD 97658 system, which previously favoured a quadratic trend with increasing orbital period. Methods. Making use of newly acquired photometric observations from CHEOPS (CHaracterising ExOplanet Satellite) and TESS (Transiting Exoplanet Survey Satellite), combined with archival transit and occultation data, we use Markov chain Monte Carlo (MCMC) algorithms to fit three models to the data, namely a constant-period model, an orbital-decay model, and an apsidal-precession model. Results. We find that the KELT-9 system is best described by an apsidal-precession model for now, with an orbital decay trend at over 2 σ being a possible solution as well. A Keplerian orbit model with a constant orbital period provides the best fit to the transit timings of KELT-16 b because of the scatter and scale of their error bars. The WASP-4 system is best represented by an orbital decay model at a 5 σ significance, although apsidal precession cannot be ruled out with the present data. For HD 97658 b, using recently acquired transit observations, we find no conclusive evidence for a previously suspected strong quadratic trend in the data.

On the Dynamics of the Solar System III: Perihelion Precession and Eccentricity Variation

On the Dynamics of the Solar System III: Perihelion Precession and Eccentricity Variation

On the Attribution of Mercury’s Perihelion Precession

Although Newtonian gravity and general relativity predicted the precession of Mercury perihelion historically, many improved methods continue to predict the precession of Mercury during recent decades of years. Uncertainties in various predictions and observations suggest that the attribution of Mercury’s precession is still not well understood. This paper argues that the cause of Mercury’s precession is not gravity, but the inertia of material motion left over from the formation of the solar system. According to this inertia theory, the planetary precession is associated with the ratio of total mass-energy density of the system to the mass-energy of the Sun and its change over time. If other factors are not changed with time, the perihelion precession of planets per orbit is proportional to his distance relative to the Sun. The conclusions of this paper can provide more effective factor considerations for the complete description of various astronomical events and phenomena using general relativity equations.

Polar Circumtriple Planets and Disks Can Only Form Close to a Triple Star

Observations of protoplanetary disks around binary and triple star systems suggest that misalignments between the orbital plane of the stars and the disks are common. Motivated by recent observations of polar circumbinary disks, we explore the possibility of polar circumtriple disks and therefore polar circumtriple planets that could form in such a disk. With n-body simulations and analytic methods, we find that the inclusion of a third star, and the associated apsidal precession, significantly reduces the radial range of polar orbits so that circumtriple polar disks and planets can only be found close to the stellar system. Outside of a critical radius that is typically in the range of 3–10 times the outer binary separation, depending upon the binary parameters, the orbits behave the same as they do around a circular orbit binary. For some observed systems that have shorter-period inner binaries, the critical radius is considerably larger. If polar circumtriple planets can form, we suggest that it is likely that they form in a disk that was subject to breaking.

The Perihelion Precession of the Planets Indicates a Variability of the Gravitational Constant

The gravitational constant G according to the theory of NEWTON is the most imprecise constant of all physical constants. Moreover, there are a number of phenomena which suggest that this is caused by its invariant nature and the gravitation constant might be in fact a variable. In this article, a possible dependence of the gravitational constant on the distance between the two mass points is determined from the observed values of the perihelion displacement of the planets. However, to fit the observed measurements the 1/r2 dependence is modified to a 1/r2+1/R dependence with “R” as the Rydberg constant. With the proposed new power function, the perihelion precessions of the planets are recalculated and then compared with previous observations as well as the postulated anomaly of Saturn.

Bounds on graviton mass and constraining Yukawa-like gravitational potential from planetary motion in the solar system

In this study we used the observed perihelion precession of planetary orbits in the Solar System in order to constrain theory of Yukawa-type gravity, and to bound mass of graviton. For that purpose we assumed that the precession angles of the planets in Yukawa-type gravity should be equal to their observed values, as well as to the corresponding predictions of General Relativity (GR). Starting from these requests we constrain Yukawa-like gravitational potential. The obtained results showed that our estimates for the range of Yukawa interaction ? at the Solar System scales are in good agreement with recent experimental constrains. Assuming that the estimated value of the range of ? corresponds to the Compton wavelength of graviton ?1, we then estimate the upper bound for its mass m1. We found that these estimates were in agreement with our previous results obtained from the observed stellar orbits around the Galactic Center (GC).

Exploring the Temporal Variation of the Solar Quadrupole Moment J 2

Recently, Rozelot & Eren pointed out that the first solar gravitational moment (J 2) might exhibit a temporal variation. The suggested explanation is through the temporal variation of the solar rotation with latitude. This issue is deeper developed due to an accurate knowledge of the long-term variations in solar differential rotation regarding solar activity. Here we analyze solar cycles 12–24, investigating the long-term temporal variations in solar differential rotation. It is shown that J 2 exhibits a net modulation over the 13 studied cycles of ≈(89.6 ± 0.1) yr, with a peak-to-peak amplitude of ≈0.1 × 10−7 for a reference value of 2.07 × 10−7). Moreover, J 2 exhibits a positive linear trend in the period of minima solar activity (sunspot number up to around 40) and a marked declining trend in the period of maxima (sunspot number above 50). In absolute magnitude, the mean value of J 2 is more significant during periods of minimum than in periods of maximum. These findings are based on observational results that are not free of errors and can be refined further by considering torsional oscillations for example. They are comforted by identifying a periodic variation of the J 2 term evidenced through the analysis of the perihelion precession of planetary orbits either deduced from ephemerides or computed in the solar equatorial coordinate system instead of the ecliptic coordinate one usually used.

The Quasi-Keplerian Motion of the Charged Test Particle in Reissner-Nordström Spacetime under the Wagoner-Will-Epstein-Haugan Representation

We present the post-Newtonian solution for the quasi-Keplerian motion of a charged test particle in the field of Reissner-Nordström black hole under the Wagoner-Will-Epstein-Haugan representation. The explicit formulations for the charge effects on perihelion precession and the orbital period are achieved, which may be useful not only in the comparisons with astronomical observations but also in calculating the waveform of the gravitational wave from this kind of system.

Uncovering a hidden black hole binary from secular eccentricity variations of a tertiary star

We study the dynamics of a solar-type star orbiting around a black hole binary (BHB) in a nearly coplanar system. We present a novel effect that can prompt a growth and significant oscillations of the eccentricity of the stellar orbit when the system encounters an ``apsidal precession resonance,'' where the apsidal precession rate of the outer stellar orbit matches that of the inner BHB. The eccentricity excitation requires the inner binary to have a nonzero eccentricity and unequal masses, and can be created even in noncoplanar triples. We show that the secular variability of the stellar orbit's apocenter, induced by the changing eccentricity, could be potentially detectable by Gaia. Detection is favorable for BHBs emitting gravitational waves in the frequency band of the Laser Interferometer Space Antenna, hence providing a distinctive, multimessenger probe of the existence of stellar-mass BHBs in the Milky Way.