Center of Light Curves for Whitney Fold and Cusp

The generic, qualitative, local behavior of center-of-light curves near folds and cusps are studied. The results apply to any finite number of lens planes.Comment: 2 pages, 1 figure, to appear in the ``Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity,'' eds. V. Gurzadyan, R. Jantzen, & R. Ruffini, World Scientific (Singapore

Achieving better than 1 minute accuracy in the Heliocentric and Barycentric Julian Dates

As the quality and quantity of astrophysical data continue to improve, the precision with which certain astrophysical events can be timed becomes limited not by the data themselves, but by the manner, standard, and uniformity with which time itself is referenced. While some areas of astronomy (most notably pulsar studies) have required absolute time stamps with precisions of considerably better than 1 minute for many decades, recently new areas have crossed into this regime. In particular, in the exoplanet community, we have found that the (typically unspecified) time standards adopted by various groups can differ by as much as a minute. Left uncorrected, this ambiguity may be mistaken for transit timing variations and bias eccentricity measurements. We argue that, since the commonly-used Julian Date, as well as its heliocentric and barycentric counterparts, can be specified in several time standards, it is imperative that their time standards always be reported when accuracies of 1 minute are required. We summarize the rationale behind our recommendation to quote the site arrival time, in addition to using BJD_TDB, the Barycentric Julian Date in the Barycentric Dynamical Time standard for any astrophysical event. The BJD_TDB is the most practical absolute time stamp for extra-terrestrial phenomena, and is ultimately limited by the properties of the target system. We compile a general summary of factors that must be considered in order to achieve timing precisions ranging from 15 minutes to 1 microsecond. Finally, we provide software tools that, in principal, allow one to calculate BJD_TDB to a precision of 1 microsecond for any target from anywhere on Earth or from any spacecraft.Comment: Online BJD_TDB calculator at http://astroutils.astronomy.ohio-state.edu/time/utc2bjd.html. PASP accepted, 11 pages, 6 figures, updated to match published versio