Perihelion Precession Research Articles

SECULAR DYNAMICS OF THE TRIPLE SYSTEM HARBORING PSR J0337+1715 AND IMPLICATIONS FOR THE ORIGIN OF ITS ORBITAL CONFIGURATION

We explore secular dynamics of a recently discovered hierarchical triple system consisting of the radio pulsar PSR J0337+1715 and two white dwarfs (WDs). We show that three body interactions endow the inner binary with a large forced eccentricity and suppress its apsidal precession, to about 24% of the rate due to the general relativity. However, precession rate is still quite sensitive to the non-Newtonian effects and may be used to constrain gravity theories if measured accurately. Small value of the free eccentricity of the inner binary $e_{i}^{free}\approx 2.6\times 10^{-5}$ and vanishing forced eccentricity of the outer, relatively eccentric binary naturally result in their apsidal near-alignment. In addition, this triple system provides a unique opportunity to explore excitation of both eccentricity and inclination in neutron star-WD binaries, e.g. due to random torques caused by convective eddies in the WD progenitor. We show this process to be highly anisotropic and more effective at driving eccentricity rather than inclination. The outer binary eccentricity as well as $e_{i}^{free}$ exceed by more than an order of magnitude the predictions of the eccentricity-period relation of Phinney (1992), which is not uncommon. We also argue that the non-zero mutual inclination of the two binaries emerges at the end of the Roche lobe overflow of the outer (rather than the inner) binary.

Planet X revamped after the discovery of the Sedna-like object 2012 VP113?

Abstract The recent discovery of the Sedna-like dwarf planet 2012 VP113 by Trujillo and Sheppard has revamped the old-fashioned hypothesis that a still unseen trans-Plutonian object of planetary size, variously dubbed over the years as Planet X, Tyche and Telisto, might lurk in the distant peripheries of the Solar system. This time, the presence of a super-Earth with mass mX =2–15 m⊕ at a distance dX ≈ 200–300 astronomical units (au) has been proposed to explain the observed clustering of the arguments of perihelion ω near ω ≈ 0° but not ω ≈ 180° for Sedna, 2012 VP113 and other minor bodies of the Solar system with perihelion distances q > 30 au and semimajor axes a > 150 au. Actually, such a scenario is strongly disfavoured by the latest constraints $\Delta \dot{\varpi }$ on the anomalous perihelion precessions of some Solar system planets obtained with the INPOP and EPM ephemerides. Indeed, they yield dX ≳ 496–570 au (mX = 2 m⊕) and dX ≳ 970–1111 au (mX = 15 m⊕). Much tighter constraints could be obtained in the near future from the New Horizons mission to Pluto.

SECULAR EVOLUTION OF THE PULSAR TRIPLE SYSTEM J0337+1715

The pulsar triple system, J0337+1715, is remarkably regular and highly hierarchical. Secular dynamics controls its long term evolution with orbital commensurability having negligible effect. Secular interactions transfer angular momentum between inner and outer orbits unless their apsidal lines are parallel or anti-parallel. These choices correspond, respectively, to orthogonal eigenmodes p and a. Each is characterized by an eccentricity ratio set by the masses and semi-major axes, i.e., $e_{p, 1}/e_{p, 2}\sim a_1/a_2$ while $e_{a, 1}/e_{a, 2}\sim (a_1/a_2)^{-3/2}(m_2/m_1)$. Mode p dominates the system's current state so $e_1/e_2$ always remains close to $e_{p, 1}/e_{p, 2}$. A small contribution by Mode a causes $e_1$ and $e_2$ to oscillate with period $\sim 10^3\,\yr$. Orbital changes should be apparent in a few years. These will reveal the forcing of the apsidal precession of the inner orbit by general relativity (GR), and possibly also the smaller contribution due to the tidal and rotational distortion of the inner white dwarf (WD). Phinney (1992) proposes that the epicyclic energy of a WD-pulsar binary reaches equipartition with the kinetic energy of a single convective eddy when the WD's progenitor fills its Roche lobe. We extend Phinney's theory to apply to modes rather than individual orbits. Thus we predict that Mode p and Mode a achieved equipartition with eddies in the giant envelopes of the progenitors of the outer and inner WD, respectively. The most effective eddies are those with lifetimes closest to the orbit period. These were more energetic in the progenitor of the outer WD. This explains why Mode p overwhelms Mode a, and also why the inner binary's orbit is far more eccentric than other WD-pulsar binaries with similar orbit periods. Mode a's small but finite amplitude places a lower bound of $Q\sim 10^6$ on the tidal quality parameter of the inner WD.

Dark energy, paradigm shifts, and the role of evidence

We comment on cases in the history of Astronomy, which may shed some light on the current established but enigmatic concordance model of Cosmology. Should the model be understood by adding new entities such as Dark Matter and Dark Energy, or by modifying the underlying theory? For example, the prediction and discovery of planet Neptune can be regarded as analogous to finding a dark component; while explaining the anomalous perihelion precession of Mercury by General Relativity can be taken as analogous to the possibility that modified gravity is an alternative to dark components of the universe. In this paper, we revise this analogy coming from the history of astronomy with an eye to illustrating some of the similarities and differences between the two cases.

SHORT APSIDAL PERIOD OF THREE ECCENTRIC ECLIPSING BINARIES DISCOVERED IN THE LARGE MAGELLANIC CLOUD

We present new elements of apsidal motion in three eccentric eclipsing binaries located in the Large Magellanic Cloud. The apsidal motions of the systems were analyzed using both light curves and eclipse timings. The OGLE-III data obtained during the long period of 8 yr (2002-2009) allowed us to determine the apsidal motion period from their analyses. The existence of third light in all selected systems was investigated by light curve analysis. The O – C diagrams of EROS 1018, EROS 1041, and EROS 1054 were analyzed using the 30, 44, and 26 new times of minimum light, respectively, determined from full light curves constructed from EROS, MACHO, OGLE-II, OGLE-III, and our own observations. This enabled a detailed study of the apsidal motion in these systems for the first time. All of the systems have a significant apsidal motion below 100 yr. In particular, EROS 1018 shows a very fast apsidal period of 19.9 ± 2.2 yr in a detached system.

Modified theories of gravity with nonminimal coupling and orbital particle dynamics

We consider a non-rotating, massive test particle acted upon by a ‘pressure’-type, non-geodesic acceleration arising from a certain general class of gravitational theories with nonminimal coupling between the matter and the metric. The resulting orbital perturbations for a two-body system are investigated both analytically and numerically. Remarkably, a secular increase of the two-body relative distance occurs. In principle, it may yield a physical mechanism for the steady recession of the Earth from the Sun recently proposed to explain the Faint Young Sun Paradox in the Archean eon. At present, the theorists have not yet derived explicit expressions for some of the key parameters of the model, such as the integrated ‘charge’ ξ, depending on the matter distribution of the system, and the 4-vector connected with the nonminimal function F. Thus, we phenomenologically treat them as free parameters, and preliminarily infer some indications on their admissible values according to the most recent Solar System’s planetary ephemerides. From the latest determinations of the corrections to the standard perihelion precessions, estimated by the astronomers who produced the EPM2011 ephemerides without modeling the theory considered here, we preliminarily obtain |ξK| ≲ 0.1 kg s−1 for the Sun and Mars. From guesses on what could be the current bounds on the secular rates of change of the planetary semimajor axes, we get |ξK0| ≲ 1249 kg s−1 for Mars. More effective constraints could be posed by reprocessing the same planetary data sets with dedicated dynamical models including the effects studied here, and explicitly estimating the associated parameters. The Earth and the COBE and GP-B satellites yield |ξK| ≲ 2 × 10−4 kg s−1 and |ξK0| ≲ 2 × 10−10 kg s−1, respectively .

Illustrating the covariances of general relativity by perihelion precession

We calculate the perihelion precession of a test particle in the Edditington-Robertson parameterized metric via the rate of change of the Runge-Lenz vector. It is shown that the calculation results are the same as in the standard, isotropic and harmonic coordinates. These results provide concrete illustrations of the covariances of general relativity. In addition, we find some typos in the derivation of the perihelion precession via the Runge-Lenz vector in Weinberg's classic general relativity textbook, and this finding might also be useful for the beginners who are reading the textbook.

Revised physical elements of the astrophysically important O9.5+O9.5V eclipsing binary system Y Cygni

Thanks to its long and rich observational history and rapid apsidal motion, the massive eclipsing binary Y Cyg represents one of the cornestones to critical tests of stellar evolution theory for massive stars. Yet, the determination of the basic physical properties is less accurate than it could be given the existing number of spectral and photometric observations. Our goal is to analyze all these data simultaneously with the new dedicated series of our own spectral and photometric observations from observatories widely separated in longitude. We obtained new series of UBV observations at three observatories separated in local time to obtain complete light curves of Y Cyg for its orbital period close to 3 days. This new photometry was reduced and carefully transformed to the standard UBV system using the HEC22 program. We also obtained new series of red spectra secured at two observatories and re-analyzed earlier obtained blue electronic spectra. Our analyses provide the most accurate so far published value of the apsidal period of 47.805 +/- 0.030 yrs and the following physical elements: M1=17.72+/-0.35$ Msun, M2=17.73+/-0.30 Msun, R1=5.785+/-0.091 Rsun, and R2=5.816+/-0.063 Rsun. The disentangling thus resulted in the masses, which are somewhat higher than all previous determinations and virtually the same for both stars, while the light curve implies a slighly higher radius and luminosity for star 2. The above empirical values imply the logarithm of the internal structure constant log k2 = -1.937. A comparison with Claret's stellar interior models implies an age close to 2 millions yrs for both stars. The claimed accuracy of modern element determination of 1-2 per cent seems still a bit too optimistic and obtaining new high-dispersion and high-resolution spectra is desirable.

Coupling between corotation and Lindblad resonances in the presence of secular precession rates

We investigate the dynamics of two satellites with masses \(\mu _s\) and \(\mu '_s\) orbiting a massive central planet in a common plane, near a first order mean motion resonance \(m+1{:}m\) (m integer). We consider only the resonant terms of first order in eccentricity in the disturbing potential of the satellites, plus the secular terms causing the orbital apsidal precessions. We obtain a two-degrees-of-freedom system, associated with the two critical resonant angles \(\phi = (m+1)\lambda ' -m\lambda - \varpi \) and \(\phi '= (m+1)\lambda ' -m\lambda - \varpi '\), where \(\lambda \) and \(\varpi \) are the mean longitude and longitude of periapsis of \(\mu _s\), respectively, and where the primed quantities apply to \(\mu '_s\). We consider the special case where \(\mu _s \rightarrow 0\) (restricted problem). The symmetry between the two angles \(\phi \) and \(\phi '\) is then broken, leading to two different kinds of resonances, classically referred to as corotation eccentric resonance (CER) and Lindblad eccentric Resonance (LER), respectively. We write the four reduced equations of motion near the CER and LER, that form what we call the CoraLin model. This model depends upon only two dimensionless parameters that control the dynamics of the system: the distance \(D\) between the CER and LER, and a forcing parameter \(\epsilon _L\) that includes both the mass and the orbital eccentricity of the disturbing satellite. Three regimes are found: for \(D=0\) the system is integrable, for \(D\) of order unity, it exhibits prominent chaotic regions, while for \(D\) large compared to 2, the behavior of the system is regular and can be qualitatively described using simple adiabatic invariant arguments. We apply this model to three recently discovered small Saturnian satellites dynamically linked to Mimas through first order mean motion resonances: Aegaeon, Methone and Anthe. Poincaré surfaces of section reveal the dynamical structure of each orbit, and their proximity to chaotic regions. This work may be useful to explore various scenarii of resonant capture for those satellites.

Non-circular features in Saturn’s D ring: D68

D68 is a narrow ringlet located only 67,627km (1.12 planetary radii) from Saturn’s spin axis. Images of this ringlet obtained by the Cassini spacecraft reveal that this ringlet exhibits persistent longitudinal brightness variations and a substantial eccentricity (ae=25±1km). By comparing observations made at different times, we confirm that the brightness variations revolve around the planet at approximately the local orbital rate (1751.6°/day), and that the ringlet’s pericenter precesses at 38.243±0.008°/day, consistent with the expected apsidal precession rate at this location due to Saturn’s higher-order gravitational harmonics. Surprisingly, we also find that the ringlet’s semi-major axis appears to be decreasing with time at a rate of 2.4±0.4km/year between 2005 and 2013. A closer look at these measurements, along with a consideration of earlier Voyager observations of this same ringlet, suggests that the mean radius of D68 moves back and forth, perhaps with a period of around 15 Earth years or about half a Saturn year. These observations could place important constraints on both the ringlet’s local dynamical environment and the planet’s gravitational field.

Atlantic overturning responses to obliquity and precession over the last 3 Myr

This study analyzes 39 Atlantic and seven Pacific benthic δ13C records to characterize obliquity and precession responses in Atlantic overturning since 3 Ma. Regional benthic δ13C stacks are also analyzed. A major transition in orbital responses is observed at 1.5–1.6 Ma coincident with the first glacial shoaling of Northern Component Water. Since ∼1.5 Ma, the phases of Atlantic benthic δ13C records from 2300 to 4000 m depth lag maximum obliquity by 59° (6.7 kyr) and June perihelion precession forcing by 133° (8.5 kyr). Comparison with North Atlantic sea surface temperature suggests that these orbital responses (particularly precession) in middle deep Atlantic δ13C are associated with changes in ocean heat transport and overturning rates. The mid-Pleistocene transition had little effect on the obliquity and precession phases of benthic δ13C but did result in a ∼50% decrease in the obliquity power of middle deep Atlantic δ13C at 0.6 Ma.

Solar system constraints on alternative gravity theories

The perihelion precession of planetary orbits and the bending angle of null geodesics are estimated for different gravity theories in string-inspired models. It is shown that, for dilaton coupled gravity, the leading order measure in the angle of bending of light comes purely from vacuum expectation value of the dilaton field which may be interpreted as an indicator of a dominant stringy effect over the curvature effect. We arrive at similar results for spherically symmetric solution in quadratic gravity. We also present the perihelion shift and bending of light in the Einstein-Maxwell-Gauss-Bonnet theory with special reference to the Casimir effect and Damour-Polyakov mechanism. Numerical bounds to different coupling parameters in these models are estimated.

Perihelion Precession and Deflection of Light in the General Spherically Symmetric Spacetime

The perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, and the master equation is obtained. As the application of this master equation, the Reissner-Nordstorm-AdS solution and Clifton-Barrow solution inf(R)gravity have been taken as examples. We find that both the electric charge andf(R)gravity can affect the perihelion precession and deflection of light, while the cosmological constant can only effect the perihelion precession. Moreover, we clarify a subtlety in the deflection of light in the solar system that the possible sun’s electric charge is usually used to interpret the gap between the experiment data and theoretical result. However, after also considering the effect from the sun’s same electric charge on the perihelion precession of Mercury, we can find that it is not the truth.

CONSTRAINING THE PREFERRED-FRAME α1, α2 PARAMETERS FROM SOLAR SYSTEM PLANETARY PRECESSIONS

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the Parametrized Post-Newtonian (PPN) parameters α1, α2. Preliminary constraints on α1, α2 are inferred from the latest determinations of the observationally admitted ranges [Formula: see text] for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint [Formula: see text] based on an interpretation of the current close alignment of the Sun's equator with the invariable plane of the Solar System in terms of the action of a α2-induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions [Formula: see text] of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield α1 = (0.8±4) × 10-6 and α2 = (4±6) × 10-6, respectively. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a priori bias of unmodeled/mismodeled standard effects such as the general relativistic Lense–Thirring precessions and the classical rates due to the Sun's oblateness J2, allows to infer α1 = (-1 ± 6) × 10-6, α2 = (-0.9 ± 3.5) × 10-5. Such figures are obtained by assuming that the ranges of values for the anomalous perihelion precessions are entirely due to the unmodeled effects of α1 and α2. Our bounds should be improved in the near-mid future with the MESSENGER and, especially, BepiColombo spacecrafts. Nonetheless, it is worthwhile noticing that our constraints are close to those predicted for BepiColombo in two independent studies. In further dedicated planetary analyses, PFE may be explicitly modeled to estimate α1, α2 simultaneously with the other PPN parameters as well.

Study of the Apsidal Precession of the Physical Symmetrical Pendulum

We study the apsidal precession of a physical symmetrical pendulum (PSP) (Allais’ precession) as a generalization of the precession corresponding to the ideal spherical pendulum (ISP) (Airy’s precession). Based on the Hamilton–Jacobi formalism and using the techniques of variation of parameters along with the averaging method, we obtain approximate analytical solutions, in terms of which the motion of both systems admits a simple geometrical description. The method developed in this paper is considerably simpler than the standard one in terms of elliptical functions, and the numerical agreement with the exact solutions is excellent. In addition, the present procedure permits to show clearly the origin of the Airy’s and Allais’ precession, as well as the effect of the spin of the physical pendulum on the Allais’ precession. Further, the method could be extended to the study of the asymmetrical pendulum in which an exact analytical solution is not possible anymore.

Timing variations in the secondary eclipse of NN Ser

Abstract The eclipsing white dwarf plus main-sequence binary NN Serpentis provides one of the most convincing cases for the existence of circumbinary planets around evolved binaries. The exquisite timing precision provided by the deep eclipse of the white dwarf has revealed complex variations in the eclipse arrival times over the last few decades. These variations have been interpreted as the influence of two planets in orbit around the binary. Recent studies have proved that such a system is dynamically stable over the current lifetime of the binary. However, the existence of such planets is by no means proven and several alternative mechanisms have been proposed that could drive similar variations. One of these is apsidal precession, which causes the eclipse times of eccentric binaries to vary sinusoidally on many year time-scales. In this Letter, we present timing data for the secondary eclipse of NN Ser and show that they follow the same trend seen in the primary eclipse times, ruling out apsidal precession as a possible cause for the variations. This result leaves no alternatives to the planetary interpretation for the observed period variations, although we still do not consider their existence as proven. Our data limit the eccentricity of NN Ser to e < 10−3. We also detect a 3.3 ± 1.0 s delay in the arrival times of the secondary eclipses relative to the best planetary model. This delay is consistent with the expected 2.84 ± 0.04 s Rømer delay of the binary, and is the first time this effect has been detected in a white dwarf plus M dwarf system.

Preliminary bounds of the gravitational local position invariance from Solar system planetary precessions

In the framework of the Parameterized Post-Newtonian (PPN) formalism, we calculate the long-term Preferred Location (PL) effects, proportional to the Whitehead parameter $\xi$, affecting all the Keplerian orbital elements of a localized two-body system, apart from the semimajor axis $a$. They violate the gravitational Local Position Invariance (LPI), fulfilled by General Relativity (GR). We obtain preliminary bounds on $\xi$ by using the latest results in the field of the Solar System planetary ephemerides. The non-detection of any anomalous perihelion precession for Mars allows us to indirectly infer $|\xi|\leq 5.8\times 10^{-6}$. \textcolor{black}{Such a bound is close to the constraint, of the order of $10^{-6}$, expected from the future BepiColombo mission to Mercury. As a complementary approach, the PL effects should be explicitly included in the dynamical models fitted to planetary data sets to estimate $\xi$ in a least-square fashion in a dedicated ephemerides orbit solution.} The ratio of the anomalous perihelion precessions for Venus and Jupiter, determined with the EPM2011 ephemerides at the $<3\sigma$ level, if confirmed as genuine physical effects needing explanation by future studies, rules out the hypothesis $\xi \neq 0$. A critical discussion of the $|\xi| \lesssim 10^{-6}-10^{-7}$ upper bounds obtained in the literature from the close alignment of the Sun's spin axis and the total angular momentum of the Solar System is presented.

Galileon forces in the Solar System

We consider the challenging problem of obtaining an analytic understanding of realistic astrophysical dynamics in the presence of a Vainshtein screened fifth force arising from infrared modifications of General Relativity. In particular, we attempt to solve -- within the most general flat spacetime galileon model -- the scalar force law between well separated bodies located well within the Vainshtein radius of the Sun. To this end, we derive the exact static Green's function of the galileon wave equation linearized about the background field generated by the Sun, for the minimal cubic and maximally quartic galileon theories, and then introduce a method to compute the general leading order force law perturbatively away from these limits. We also show that the same nonlinearities which produce the Vainshtein screening effect present obstacles to an analytic calculation of the galileon forces between closely bound systems within the solar system, such as that of the Earth and Moon. Within the test mass approximation, we deduce that a large enough quartic galileon interaction would suppress the effect on planetary perihelion precession below the level detectable by even the next-generation experiments.

Noncircular features in Saturn’s rings I: The edge of the B ring

A comprehensive investigation of all available radio and stellar occultation data for the outer edge of Saturn’s B ring, spanning the period 1980–2010, confirms that the m=2 distortion due to the strong Mimas 2:1 inner Lindblad resonance circulates slowly relative to Mimas in a prograde direction, with a frequency ΩL=0.1819°d−1. Our best-fitting model implies that the radial amplitude of this distortion ranges from a minimum of 3km to a maximum of 71km, with short-lived minima recurring every 5.42yrs. In addition to the dominant m=2 pattern, the edge of the B ring also exhibits at least four other perturbations. An m=1 component with a radial amplitude of ∼20km rotates at a rate very close to the expected local apsidal precession rate of ϖ̇B∼5.059°d−1, while smaller perturbations are seen with m=3 (amplitude 12.5km), m=4 (5.9km), and m=5 (5.6km), each of which has a pattern speed consistent with that expected for a spontaneously-generated “normal mode” (French, R.G. et al. [1988]. Icarus 73, 349–378). Our results for m=1, m=2 and m=3 are compatible with those obtained by Spitale and Porco (Spitale, J.N., Porco, C.C. [2010]. Astron. J. 140, 1747–1757), which were based on Cassini imaging data. The pattern speed of each normal mode slightly exceeds that expected at the mean edge radius, supporting their conclusion that they may represent a series of free modes, each of which is trapped in a narrow region between the mode’s resonant radius and the ring’s edge. However, both our model and that of Spitale and Porco fail to provide complete descriptions of this surprisingly complex feature, with post-fit root-mean-square residuals of ∼8km considerably exceeding typical measurement errors of 1km or less.

THE IMPACT OF BOUND STELLAR ORBITS AND GENERAL RELATIVITY ON THE TEMPORAL BEHAVIOR OF TIDAL DISRUPTION FLARES

We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound orbit with moderate eccentricity instead of a parabolic orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time ~ the original stellar orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes. The detection triggers for future surveys should be extended to capture such "non-standard" short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.