Periastron Precession Research Articles

Periastron shift for a spinning test particle around naked singularities

In the present article, we investigate the Periastron precession for a spinning test particle moving in nearly circular orbits around naked singularities. We consider two well-known solutions that can produce a spacetime with naked singularity---(a) first, the Reissner-Nordstr\om metric, which is a static charged solution with spherical symmetry, and (b) second, the stationary, axisymmetric Kerr metric. For simplicity, we only consider the motion confined on the equatorial plane in both these cases and solve exactly the Mathisson-Papapetrou equations. In addition, we analytically compute the Periastron precession within the framework of linear spin approximation. The inclusion of the spin parameter modifies the results with nonspinning particles and also reflects some interesting properties of the naked geometries. Furthermore, we carried out a numerical approach without any assumptions to probe the large order spin values. The implication of the spin-curvature coupling in connection with the naked geometries is also discussed.

Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order

In this paper, we revisit and complete our preceding work on the Fokker Lagrangian describing the dynamics of compact binary systems at the fourth post-Newtonian (4PN) order in harmonic coordinates. We clarify the impact of the non-local character of the Fokker Lagrangian or the associated Hamiltonian on both the conserved energy and the relativistic periastron precession for circular orbits. We show that the non-locality of the action, due to the presence of the tail effect at the 4PN order, gives rise to an extra contribution to the conserved integral of energy with respect to the Hamiltonian computed on shell, which was not taken into account in our previous work. We also provide a direct derivation of the periastron advance by taking carefully into account this non-locality. We then argue that the infra-red (IR) divergences in the calculation of the gravitational part of the action are problematic, which motivates us to introduce a second ambiguity parameter, in addition to the one already assumed previously. After fixing these two ambiguity parameters by requiring that the conserved energy and the relativistic periastron precession for circular orbits are in agreement with numerical and analytical gravitational self-force calculations, valid in the limiting case of small mass ratio, we find that our resulting Lagrangian is physically equivalent to the one obtained in the ADM Hamiltonian approach.

Analysis of the orbital evolution of exoplanets

An exoplanet, or extrasolar planet, is a planet that does not orbit the Sun, but is around a different star, stellar remnant, or brown dwarf. Up to now, about 1900 exoplanets were discovered. To better understand the dynamics of these exoplanets, a study with respect to possible collisions of the planet with the central star is shown here. We present an expanded model in a small parameter that takes into account up to the fifth order to analyze the effect of this potential in the orbital elements of the extrasolar planet. Numerical simulations were also performed using the N-body simulations, using the software Mercury, to compare the results with the ones obtained by the analytical model. The numerical simulations are presented in two stages: one considering the celestial bodies as point masses and the other one taking into account their dimensions. This analysis showed that the planet collided with the central star in the moment of the first inversion for orbits with high inclinations in various situations. The results of the simulations of the equations developed in this study are consistent with the N-body numerical simulations. We analyze also the flip of the inclination taking into account the coupling of the perturbations of the third body, effect due to the precession of periastron and the tide effect. In general, we find that such perturbations combined delay the time of first inversion, but do not keep the planet in a prograde or retrograde orbit.

CONSTRAINTS ON THE ATMOSPHERIC CIRCULATION AND VARIABILITY OF THE ECCENTRIC HOT JUPITER XO-3b

We report secondary eclipse photometry of the hot Jupiter XO-3b in the 4.5~$\mu$m band taken with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. We measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses. We fit these data simultaneously with two transits observed in the same band in order to obtain a global best-fit secondary eclipse depth of $0.1580\pm 0.0036\%$ and a center of eclipse phase of $0.67004\pm 0.00013 $. We assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05$\%$. The new secondary eclipse observations extend the total baseline from one and a half years to nearly three years, allowing us to place an upper limit on the periastron precession rate of $2.9\times 10^{-3}$ degrees/day the tightest constraint to date on the periastron precession rate of a hot Jupiter. We use the new transit observations to calculate improved estimates for the system properties, including an updated orbital ephemeris. We also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit-to-orbit variability of an eccentric hot Jupiter and demonstrate the consistency of multiple-epoch Spitzer observations.

IMPORTANCE OF TIDES FOR PERIASTRON PRECESSION IN ECCENTRIC NEUTRON STAR-WHITE DWARF BINARIES

Although not nearly as numerous as binaries with two white dwarfs, eccentric neutron star-white dwarf (NS-WD) binaries are important gravitational-wave (GW) sources for the next generation of space-based detectors sensitive to low frequency waves. Here we investigate periastron precession in these sources as a result of general relativistic, tidal, and rotational effects; such precession is expected to be detectable for at least some of the detected binaries of this type. Currently, two eccentric NS-WD binaries are known in the galactic field, PSR J1141-6545 and PSR B2303+46, both of which have orbits too wide to be relevant in their current state to GW observations. However, population synthesis studies predict the existence of a significant Galactic population of such systems. Though small in most of these systems, we find that tidally induced periastron precession becomes important when tides contribute to more than 3% of the total precession rate. For these systems, accounting for tides when analyzing periastron precession rate measurements can improve estimates of the WD component mass inferred and, in some cases, will prevent us from misclassifying the object. However, such systems are rare due to rapid orbital decay. To aid the inclusion of tidal effects when using periastron precession as a mass measurement tool, we derive a function that relates the WD radius and periastron precession constant to the WD mass.

ORBITAL DYNAMICS OF MULTI-PLANET SYSTEMS WITH ECCENTRICITY DIVERSITY

Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Amongst these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single planet but several have been found to also contain a longer period planet in a near-circular orbit. Here we use the latest Keplerian orbital solutions to investigate four known systems which exhibit this extreme eccentricity diversity; HD 37605, HD 74156, HD 163607, and HD 168443. We place limits on the presence of additional planets in these systems based on the radial velocity residuals. We show that the two known planets in each system exchange angular momentum through secular oscillations of their eccentricities. We calculate the amplitude and timescale for these eccentricity oscillations and associated periastron precession. We further demonstrate the effect of mutual orbital inclinations on the amplitude of high-frequency eccentricity oscillations. Finally, we discuss the implications of these oscillations in the context of possible origin scenarios for unequal eccentricities.

Isofrequency pairing of geodesic orbits in Kerr geometry

Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain "synchronized" in phase.

HIGH-FIDELITY RADIO ASTRONOMICAL POLARIMETRY USING A MILLISECOND PULSAR AS A POLARIZED REFERENCE SOURCE

A new method of polarimetric calibration is presented in which the instrumental response is derived from regular observations of PSR J0437-4715 based on the assumption that the mean polarized emission from this millisecond pulsar remains constant over time. The technique is applicable to any experiment in which high-fidelity polarimetry is required over long time scales; it is demonstrated by calibrating 7.2 years of high-precision timing observations of PSR J1022+1001 made at the Parkes Observatory. Application of the new technique followed by arrival time estimation using matrix template matching yields post-fit residuals with an uncertainty-weighted standard deviation of 880 ns, two times smaller than that of arrival time residuals obtained via conventional methods of calibration and arrival time estimation. The precision achieved by this experiment yields the first significant measurements of the secular variation of the projected semi-major axis, the precession of periastron, and the Shapiro delay; it also places PSR J1022+1001 among the ten best pulsars regularly observed as part of the Parkes Pulsar Timing Array (PPTA) project. It is shown that the timing accuracy of a large fraction of the pulsars in the PPTA is currently limited by the systematic timing error due to instrumental polarization artifacts. More importantly, long-term variations of systematic error are correlated between different pulsars, which adversely affects the primary objectives of any pulsar timing array experiment. These limitations may be overcome by adopting the techniques presented in this work, which relax the demand for instrumental polarization purity and thereby have the potential to reduce the development cost of next-generation telescopes such as the Square Kilometre Array.

New tests of local Lorentz invariance of gravity with small-eccentricity binary pulsars

Some alternative gravity theories allow the Universal matter distribution to single out the existence of a preferred frame, which breaks the symmetry of local Lorentz invariance (LLI) for the gravitational interaction. In the post-Newtonian parametrization of semi-conservative gravity theories, LLI violation is characterized by two parameters, α1 and α2. In binary pulsars, the isotropic violation of Lorentz invariance in the gravitational sector should lead to characteristic preferred frame effects (PFEs) in the orbital dynamics, if the barycenter of the binary is moving relative to the preferred frame with a velocity w. For small-eccentricity binaries, the effects induced by and (the hat indicates possible modifications by strong-field effects) decouple, and can therefore be tested independently. We use recent timing results of two compact pulsar-white dwarf binaries with known three-dimensional velocity, PSRs J1012+5307 and J1738+0333 to constrain PFEs for strongly self-gravitating bodies, by assuming the isotropic cosmic microwave background to single out a preferred frame. The time derivative of the projected semi-major axis is used to constrain a precession of the orbital plane around w due to PFEs. From this, we derive a limit at 95% confidence level, which is the most constraining limit for strongly self-gravitating systems up to now, however, still three orders of magnitude weaker than the best Solar system limit for the corresponding weak-field parameter α2. Concerning , we propose a new, robust method to constrain this parameter, which avoids the probabilistic considerations inherent in previous methods. This method is based on the fact that a PFE-induced intrinsic eccentricity cannot stay unobserved during a long-term observation due to the significant precession of periastron in binary pulsar with short orbital periods. Our most conservative result, at 95% confidence level from PSR J1738+0333, constitutes a significant improvement compared to current most stringent limits obtained both in the Solar system and binary pulsar tests. We also derive corresponding limits for and for a preferred frame that is at rest with respect to our Galaxy, and preferred frames that locally co-move with the rotation of our Galaxy. These limits will continue to improve significantly with future pulsar timing observations conducted at large radio telescopes.Communicated by C M Will

Constraints on a scalar-tensor theory with an intermediate-range force by binary pulsars

Searching for an intermediate-range force has been considerable interests in gravity experiments. In this paper, aiming at a scalar-tensor theory with an intermediate-range force, we have derived the metric and equations of motion (EOMs) in the first post-Newtonian (1PN) approximation for general matter without specific equation of state and N point masses firstly. Subsequently, the secular periastron precession (omega) over dot of binary pulsars in harmonic coordinates is given. After that, (omega) over dot of four binary pulsars data (PSR B1913 + 16, PSR B1534 + 12, PSR J0737-3039 and PSR B2127 + 11C) have been used to constrain the intermediate-range force, namely, the parameters alpha and lambda. alpha and lambda respectively represent the strength of the intermediate-range force coupling and its length scale. The limits from four binary pulsars data are respectively lambda = (4.95 +/- 0.02) x 10(8) m and alpha = (2.30 +/- 0.01) x 10(-8) if beta = 1, where beta is a parameter like standard parametrized post-Newtonian parameter beta(PPN). When three degrees of freedom (alpha, lambda and (beta) over bar beta - 1) in 1 sigma confidence level are considered, it yields alpha = (4.21 +/- 0.01) x 10(-4), lambda = (4.51 +/- 0.01) x 10(7) m and (beta) over bar = (-3.30 +/- 0.01) x 10(-3). Through our research on the scalar-tensor theory with the intermediate-range force, it shows that the parameter a is directly related to the parameter gamma (alpha = (1 - gamma)/(1 + gamma)). Thus, this presents the constraints on 1 - gamma by binary pulsars which is about 10(-4) for three degrees of freedom.

Inspiral of generic black hole binaries: spin, precession and eccentricity

Given the absence of observations of black hole binaries, it is critical that the full range of accessible parameter space be explored in anticipation of future observation with gravitational-wave detectors. To this end, we compile the Hamiltonian equations of motion describing the conservative dynamics of the most general black hole binaries and incorporate an effective treatment of dissipation through gravitational radiation, as computed by Will and collaborators. We evolve these equations for systems with orbital eccentricity and precessing spins. We find that, while spin–spin coupling corrections can destroy constant radius orbits in principle, the effect is so small that orbits will reliably tend to quasi-spherical orbits as angular momentum and energy are lost to gravitational radiation. Still, binaries that are initially highly eccentric may retain eccentricity as they pass into the detectable bandwidth of ground-based gravitational-wave detectors. We also show that a useful set of natural frequencies for an orbit demonstrating both spin precession and periastron precession is comprised of (1) the frequency of angular motion in the orbital plane, (2) the frequency of the plane precession and (3) the frequency of radial oscillations. These three natural harmonics shape the observed waveform.

Revisiting the double-binary-pulsar probe of nondynamical Chern-Simons gravity

One of the popular modifications to the theory of general relativity is nondynamical Chern-Simons (CS) gravity, in which the metric is coupled to an externally prescribed scalar field. Setting accurate constraints to the parameters of the theory is important owing to their implications for the scalar field and/or the underlying fundamental theory. The current best constraints rely on measurements of the periastron precession rate in the double-binary-pulsar system and place a very tight bound on the characteristic CS length scale ${k}_{\mathrm{cs}}^{\ensuremath{-}1}\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{km}$. This paper considers several effects that were not accounted for when deriving this bound and lead to a substantial suppression of the predicted rate of periastron precession. It is shown, in particular, that the point-mass approximation for extended test bodies does not apply in this case. The constraint to the characteristic CS length scale is revised to ${k}_{\mathrm{cs}}^{\ensuremath{-}1}\ensuremath{\lesssim}0.4\text{ }\text{ }\mathrm{km}$, 8 orders of magnitude weaker than what was previously found.

Ruling out Kozai resonance in highly eccentric galactic binary millisecond pulsar PSR J1903+0327

Abstract We investigate the observational signatures associated with one of the proposed formation scenario for the recently discovered highly eccentric binary millisecond pulsar (MSP) PSR J1903+0327 in the galactic plane. The scenario requires that the MSP to be part of a hierarchical triple (HT), consisting of inner and outer binaries, experiencing the Kozai resonance. Numerical modelling of a bound point-mass HT, while incorporating the effects due to the quadrupolar interactions between the binary orbits and dominant contributions to the general relativistic periastron precession in the inner binary, reveals that, at the present epoch, the orbital eccentricity of the binary MSP should decrease for reasonable ranges in the HT parameters. The estimated decrements in the orbital eccentricity of the inner binary are few parts in 105, substantially higher than the reported accuracies in the estimation of the orbital eccentricity of the binary MSP, while employing various general relativistic timing models for isolated binary pulsars. For wide ranges in the allowed orbital parameters, the estimated rate of change in the eccentricity of the inner binary is orders of magnitude higher than the value recently measured by the pulsar timing analysis. Therefore, we rule out the scenario that the MSP is part of an HT undergoing the Kozai oscillations. The origin of this system in a typical globular cluster is also shown to be less likely than inferred in the discovery paper.

Double-binary-pulsar test of Chern-Simons modified gravity

Chern-Simons modified gravity is a string-theory and loop-quantum-gravity inspired effective theory that modifies General Relativity by adding a parity-violating Pontryagin density to the Einstein-Hilbert action multiplied by a coupling scalar. We strongly constrain non-dynamical Chern-Simons modified gravity with a timelike Chern-Simons scalar through observations of the double binary pulsar PSR J0737-3039A/B. We first calculate Chern-Simons corrections to the orbital evolution of binary systems. We find that the ratio of the correction to periastron precession to the general relativistic prediction scales quadratically with the semi-major axis and inversely with the square of the object's radius. Binary pulsar systems are thus ideal to test this theory, since periastron precession can be measured with sub-degree accuracies and the semi-major axis is millions of times larger than the stellar radius. Using data from PSR J0737-3039A/B we dramatically constrain the non-dynamical Chern-Simons coupling to $M_{\CS} := 1/|\dot{\vartheta}| > 33 {\textrm{meV}}$, approximately a hundred billion times better than current Solar System tests.

Gravitomagnetic effects in Kerr-de Sitter space-time

We explicitly worked out the orbital effects induced on thetrajectory of a test particle by the the weak-field approximationof the Kerr-de Sitter metric. It results that thenode, the pericentre and the mean anomaly undergo secularprecessions proportional to k. We used such theoretical predictions andthe latest observational determinations of the non-standardprecessions of the perihelia of the inner planets of the SolarSystem to put a bound on k getting k ⩽ 10−29 m−2. The node rate of the LAGEOS Earth's satellite yieldsk ⩽ 10−26 m−2. The periastron precession of the double pulsar PSR J0737-3039A/B allows to obtain k ⩽ 3 × 10−21 m−2.Interpreting k as a cosmological constant Λ, it turns out that such constraints are weaker than those obtained from the Schwarzschild-de Sitter metric.

Modified scalar-tensor-vector gravity theory and the constraint on its parameters

A gravity theory called scalar-tensor-vector gravity (STVG) has been recently developed and succeeded in solar system, astrophysical, and cosmological scales without dark matter 1. However, two assumptions have been used: (i) B(r)=A(-1)(r), where B(r) and A(r) are g(00) and g(rr) in the Schwarzschild coordinates (static and spherically symmetric); (ii) scalar field G=Const. in the solar system. These two assumptions actually imply that the standard parametrized post-Newtonian parameter gamma=1. In this paper, we relax these two assumptions and study STVG further by using the post-Newtonian approximation approach. With abandoning the assumptions, we find gamma not equal 1 in general cases of STVG. Then, a version of modified STVG is proposed through introducing a coupling function of scalar field G: theta(G). We have derived the metric and equations of motion in 1PN for general matter without specific equation of state and N point masses firstly. Subsequently, the secular periastron precession omega of binary pulsars in harmonic coordinates is given. After discussing two parametrized post-Newtonian parameters (gamma and beta) and two Yukawa parameters (alpha and lambda), we use omega of four binary pulsars data (PSR B1913+16, PSR B1534+12, PSR J0737-3039, and PSR B2127+11C) to constrain the Yukawa parameters for modified STVG: lambda=(3.97 +/- 0.01)x10(8) m and alpha=(2.40 +/- 0.02)x10(-8) if we fix |2 gamma-beta-1|=0.

Periastron precession measurements in transiting extrasolar planetary systems at the level of general relativity

Transiting exoplanetary systems are surpassingly important among the planetary systems since they provide the widest spectrum of information for both the planet and the host star. If a transiting planet is on an eccentric orbit, the duration of transits T_D is sensitive to the orientation of the orbital ellipse relative to the line of sight. The precession of the orbit results in a systematic variation in both the duration of individual transit events and the observed period between successive transits, P_obs. The periastron of the ellipse slowly precesses due to general relativity and possibly the presence of other planets in the system. This secular precession can be detected through the long-term change in P_obs (transit timing variations, TTV) or in T_D (transit duration variations, TDV). We estimate the corresponding precession measurement precision for repeated future observations of the known eccentric transiting exoplanetary systems (XO-3b, HD 147506b, GJ 436b and HD 17156b) using existing or planned space-borne instruments. The TDV measurement improves the precession detection sensitivity by orders of magnitude over the TTV measurement. We find that TDV measurements over a ~4 year period can typically detect the precession rate to a precision well exceeding the level predicted by general relativity.

Prospects for measuring the moment of inertia of pulsar J0737-3039A

Here we consider the possibility-envisaged by many authors as feasible in the near future-of measuring at 10% or better the moment of inertia I of the pulsar J0737-3039A via the gravitomagnetic spin–orbit periastron precession (analogous to the Lense–Thirring pericentre precession in the case of a test-particle orbiting a central spinning mass). Such a gravitomagnetic effect is expected to be of the order of 10 - 4 deg yr - 1 and the present-day precision in measuring the periastron precession of J0737-3039A via pulsar timing is 6.8 × 10 - 4 deg yr - 1 . However the systematic uncertainty in the much larger first-order post-Newtonian (1PN) gravitoelectric precession (analogous to the Einstein Mercury’s perihelion precession in the weak-field and slow-motion approximation), which should be subtracted from the measured one in order to pick up the gravitomagnetic rate, is of primary importance. Indeed, by determining the sum of the masses by means of the third Kepler law, such a bias amounts to 0.03165 deg yr −1, according to the current level of accuracy in knowing the parameters of the J0737-3039 system. The major sources of uncertainty are the Keplerian projected semimajor axis x B of the component B and the post-Keplerian parameter s, identified with sin i ; their knowledge should be improved by three orders of magnitude at least; the bias due to the Keplerian projected semimajor axis x A of the component A amounts to ≈ 10 % today. The present-day level of accuracy in the eccentricity e would affect the investigated measurement at a percent level, while the impact of the orbital period P b is completely negligible. If, instead, the sum of the masses is measured by means of the post-Keplerian parameters r and s, it turns out that r should be measured five orders of magnitude better than now: according to the present-day level of accuracy, the total uncertainty in the 1PN periastron rate is, in this case, 2.11819 deg yr −1. In conclusion, the prospect of measuring the moment of inertia of PSR J0737-3039A at 10% accuracy or better seems unlikely given the limitations to the precision with which the system’s basic binary and post-Keplerian parameters can be measured via radio timing.

Probing White Dwarf Interiors with LISA: Periastron Precession in Eccentric Double White Dwarfs

In globular clusters, dynamical interactions give rise to a population of eccentric double white dwarfs detectable by the Laser Interferometer Space Antenna (LISA) up to the Large Magellanic Cloud. In this Letter, we explore the detectability of periastron precession in these systems with LISA. Unlike previous investigations, we consider contributions due to tidal and rotational distortions of the binary components in addition to general relativistic contributions to the periastron precession. At orbital frequencies above a few mHz, we find that tides and stellar rotation dominate, opening up a possibly unique window to the study of the interior and structure of white dwarfs.

Determination of tidal distortion in the eclipsing binary system V621 Cen by means of deviations from the third Kepler law

In this paper we determine the tidal distortion parameter k m of the secondary partner (mass loser) of the semi-detached eclipsing binary system V621 Cen by comparing the phenomenologically determined orbital period P b = 3.683549 ( 11 ) d to the Keplerian one P Kep computed with the values of the relevant system’s parameters determined independently of the third Kepler law itself. Our result is k m = - 1.5 ± 0.6 . Using the periastron precession, as traditionally done with other eclipsing binaries in eccentric orbits, would have not been possible because of the circularity of the V621 Cen path.