Post-Newtonian effects on some characteristic timescales of transiting exoplanets

Abstract

Some measurable characteristic timescales $\left\{t_{\mathrm{trn}}\right\}$ of transiting exoplanets are investigated in order to check preliminarily if their cumulative shifts over the years induced by the post-Newtonian (pN) gravitoelectric (Schwarzschild) and gravitomagnetic (Lense-Thirring) components of the stellar gravitational field are, at least in principle, measurable. Both the primary (planet in front of the star) and the secondary (planet behind the star) transits are considered along with their associated characteristic time intervals: the total transit duration $t_D$, the ingress/egress transit duration $\tau$, the full width at half maximum primary transit duration $t_H$, and also the time of conjunction $t_{\mathrm{cj}}$. For each of them, the net changes per orbit $⟨\Delta t_D⟩,⟨\Delta \tau ⟩,⟨\Delta t_H⟩,⟨\Delta t_{\mathrm{cj}}⟩$ induced by the aforementioned pN accelerations are analytically obtained; also the Newtonian effect of the star's quadrupole mass moment $J_2^{\star }$ is worked out. They are calculated for a fictitious Sun-Jupiter system in an edge-on elliptical orbit, and the results are compared with the present-day experimental accuracies for the HD 286123 b exoplanet. Its pN gravitoelectric shift $⟨\Delta t_{\mathrm{cj}}^{1pN}⟩$ may become measurable, at least in principle, at a $\simeq 8\times 10^{-5}$ level of (formal) relative accuracy after about 30 years of continuous monitoring corresponding to about 1000 transits. Systematics like, e.g., confusing time standards, neglecting star spots, neglecting clouds, would likely deteriorate the actual accuracy. The method presented is general enough to be applied also to modified models of gravity.

arXiv commentLaTex2e, 27 pages, 2 figures, no tables. Remark about the temporal features of the pN signatures added

References in corpus (38)

• The Transiting Exoplanet Survey Satellite
• The K2 Mission: Characterization and Early results
• The Kilodegree Extremely Little Telescope (KELT): A Small Robotic Telescope for Large-Area Synoptic Surveys
• Evidence of Possible Spin-Orbit Misalignment Along the Line of Sight in Transiting Exoplanet Systems
• Transit Timing Observations from Kepler: IV. Confirmation of 4 Multiple Planet Systems by Simple Physical Models
• 55 Cancri (Copernicus): A Multi-Planet System with a Hot Super-Earth and a Jupiter Analogue
• Probing the Interiors of Very Hot Jupiters Using Transit Light Curves
• Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations
• Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances
• Long Term Evolution of Close Planets Including the Effects of Secular Interactions
• The Detection and Characterization of a Nontransiting Planet by Transit Timing Variations
• KOI-142, the King of Transit Variations, is a Pair of Planets near the 2:1 Resonance
• Characterizing the Orbital Eccentricities of Transiting Extrasolar Planets with Photometric Observations
• Observability of the General Relativistic Precession of Periastra in Exoplanets
• Periastron Precession Measurements in Transiting Extrasolar Planetary Systems at the Level of General Relativity
• Transit Timing Observations from Kepler: VI. Potentially interesting candidate systems from Fourier-based statistical tests
• Effects of Secular Interactions in Extrasolar Planetary Systems
• On the (im)possibility of testing new physics in exoplanets using transit timing variations: deviation from inverse-square law of gravity
• Are we far from testing general relativity with the transiting extrasolar planet HD 209458b `Osiris'?
• K2-137 b: an Earth-sized planet in a 4.3-hour orbit around an M-dwarf
• Accurate characterization of the stellar and orbital parameters of the exoplanetary system WASP-33 b from orbital dynamics
• Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them
• HAT-P-31b,c: A Transiting, Eccentric, Hot Jupiter and a Long-Period, Massive Third-Body
• Classical and relativistic long-term time variations of some observables for transiting exoplanets
• Retrieval of the fluid Love number $k_2$ in exoplanetary transit curves
• EPIC247098361b: a transiting warm Saturn on an eccentric $P=11.2$ days orbit around a $V=9.9$ star
• Extrasolar planets as a probe of modified gravity
• Relativistic Effects in Extrasolar Planetary Systems
• Constraining the Kehagias-Sfetsos solution in the Horava-Lifshitz gravity with extrasolar planets
• Post-Keplerian effects on radial velocity in binary systems and the possibility of measuring General Relativity with the S2 star in 2018
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• Detecting the General Relativistic Orbital Precession of the Exoplanet HD 80606b
• Probing a $r^{-n}$ modification of the Newtonian potential with Exoplanets
• Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the Galactic Center
• Two warm, low-density sub-Jovian planets orbiting bright stars in K2 campaigns 13 and 14
• Parametrized Post-Newtonian Orbital Effects in Extrasolar Planets
• Post-Keplerian corrections to the orbital periods of a two-body system and their measurability
• Detecting General Relativistic Orbital Precession in Transiting Hot Jupiters

Cited by in corpus (1)

• General Relativity Can Prevent a Runaway Greenhouse on Potentially Habitable Planets Orbiting White Dwarfs