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Prospecting transit duration variations in extrasolar planetary systems

In transiting planetary systems, the angle between the orbital angular momentum and the stellar spin is usually constrained through the Rossiter-McLaughlin effect observed in radial velocity and can be subject to large uncertainties, especially for hot stars (T_eff > 6250 K). It is thus interesting to have an alternative method to constrain the value of the obliquity and to detect companions that might have disturbed the orbit of the planet. We show how the long-term variations in the transit duration (TDV) can be used to constrain the obliquity of the stellar rotation axis. We introduce a simple theory to express the secular variations in the orbital elements and their effects on the TDVs with a general formulation valid for both oblique and eccentric systems. Parameters or orbital elements that cannot be directly measured, such as the longitude of the ascending node of the orbit, are avoided thus allowing us a straightforward application. We compute the expected TDVs for the presently known transiting systems, adopting their parameters found in the literature. Considering the capabilities of the present or next generation space-borne telescopes, we point out the systems that could be readily observed and discuss the constraints derivable on their fundamental parameters. TDVs can be used to constrain the obliquity of the stars (and possibly of the planets in systems younger than 10 -- 100 Myr), giving information about the formation scenarios, the strength of the tidal coupling, and the internal structure of both the stars and the planets. Moreover, they can provide an indirect indication of the presence of other bodies, even with a mass comparable with that of the Earth, because they give rise to additional contributions to the nodal precession.