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.

LaTex2e, 27 pages, 2 figures, no tables. Remark about the temporal features of the pN signatures added

References in corpus (16)

• The Transiting Exoplanet Survey Satellite
• The K2 Mission: Characterization and Early results
• Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances
• Long Term Evolution of Close Planets Including the Effects of Secular Interactions
• 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
• Effects of Secular Interactions in Extrasolar Planetary Systems
• Are we far from testing general relativity with the transiting extrasolar planet HD 209458b `Osiris'?
• Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them
• 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
• Relativistic Effects in Extrasolar Planetary Systems
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• Parametrized Post-Newtonian Orbital Effects in Extrasolar Planets
• 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