The transits of a planet on a Keplerian orbit occur at time intervals exactly equal to the period of the orbit. If a second planet is introduced the orbit is not Keplerian and the transits are no longer exactly periodic. We compute the magnitude of these variations in the timing of the transits, dt. We investigate analytically several limiting cases: (i) interior perturbing planets with much smaller periods; (ii) exterior perturbing planets on eccentric orbits with much larger periods; (iii) both planets on circular orbits with arbitrary period ratio but not in resonance; and (iv) planets on initially circular orbits locked in resonance. Case (iv) is perhaps the most interesting case since some systems are known to be in resonances and the perturbations are the largest. As long as the perturber is more massive than the transiting planet, the timing variations would be of order of the period regardless of the perturber mass! For lighter perturbers, we show that the timing variations are smaller than the period by the perturber to transiting planet mass ratio. An earth mass planet in 2:1 resonance with a 3-day period transiting planet (e.g. HD 209458b) would cause timing variations of order 3 minutes, which would be accumulated over a year. These are easily detectable with current ground-based measurements. For the case of both planets on eccentric orbits, we compute numerically the transit timing variations for several cases of known multiplanet systems assuming they were edge-on. Transit timing measurements may be used to constrain the masses and radii of the planetary system and, when combined with radial velocity measurements, to break the degeneracy between mass and radius of the host star. (abstract truncated)Comment: 21 pages, 9 figures, submitted to MNRA

The SuperWASP Cameras are wide-field imaging systems sited at the Observatorio del Roque de los Muchachos on the island of La Palma in the Canary Islands, and the Sutherland Station of the South African Astronomical Observatory. Each instrument has a field of view of some ~482 square degrees with an angular scale of 13.7 arcsec per pixel, and is capable of delivering photometry with accuracy better than 1% for objects having V ~ 7.0 - 11.5. Lower quality data for objects brighter than V ~15.0 are stored in the project archive. The systems, while designed to monitor fields with high cadence, are capable of surveying the entire visible sky every 40 minutes. Depending on the observational strategy, the data rate can be up to 100GB per night. We have produced a robust, largely automatic reduction pipeline and advanced archive which are used to serve the data products to the consortium members. The main science aim of these systems is to search for bright transiting exo-planets systems suitable for spectroscopic followup observations. The first 6 month season of SuperWASP-North observations produced lightcurves of ~6.7 million objects with 12.9 billion data points.Comment: 42 pages, 2 plates, 5 figures PASP in pres

We present significantly improved proper motion measurements of the Milky Way's central stellar cluster. These improvements are made possible by refining our astrometric reference frame with a new geometric optical distortion model for the W. M. Keck II 10 m telescope's Adaptive Optics camera (NIRC2) in its narrow field mode. For the first time, this distortion model is constructed from on-sky measurements, and is made available to the public in the form of FITS files. When applied to widely dithered images, it produces residuals in the separations of stars that are a factor of ∼3 smaller compared to the outcome using previous models. By applying this new model, along with corrections for differential atmospheric refraction, to widely dithered images of SiO masers at the Galactic center, we improve our ability to tie into the precisely measured radio Sgr A*-rest frame. The resulting infrared reference frame is ∼2-3 times more accurate and stable than earlier published efforts. In this reference frame, Sgr A* is localized to within a position of 0.6 mas and a velocity of 0.09 mas yr −1 , or ∼3.4 km s −1 at 8 kpc (1σ). Also, proper motions for members of the central stellar cluster are more accurate, although less precise, due to the limited number of these wide field measurements. These proper motion measurements show that, with respect to Sgr A*, the central stellar cluster has no rotation in the plane of the sky to within 0.3 mas yr −1 arcsec −1 , has no net translational motion with respect to Sgr A* to within 0.1 mas yr −1 , and has net rotation perpendicular to the plane of the sky along the Galactic plane, as has previously been observed. While earlier proper motion studies defined a reference frame by assuming no net motion of the stellar cluster, this approach is fundamentally limited by the cluster's intrinsic dispersion and therefore will not improve with time. We define a reference frame with SiO masers and this reference frame's stability should improve steadily with future measurements of the SiO masers in this region (∝ t 3/2 ). This is essential for achieving the necessary reference frame stability required to detect the effects of general relativity and extended mass on short-period stars at the Galactic center.

We present stellar proper motions in the Galactic bulge from the Sagittarius Window Eclipsing Extrasolar Search (SWEEPS) project using ACS WFC on HST. Proper motions are extracted for more than 180,000 objects, with >81,000 measured to accuracy better than 0.3 mas yr À1 in both coordinates. We report several results based on these measurements: (1) Kinematic separation of bulge from disk allows a sample of >15,000 bulge objects to be extracted based on !6 detections of proper motion, with <0.2% contamination from the disk. This includes the first detection of a candidate bulge blue straggler population. (2) Armed with a photometric distance modulus on a star-by-star basis, and using the large number of stars with high-quality proper-motion measurements to overcome intrinsic scatter, we dissect the kinematic properties of the bulge as a function of distance along the line of sight. This allows us to extract the stellar circular speed curve from proper motions alone, which we compare with the circular speed curve obtained from radial velocities. (3) We trace the variation of the fl; bg velocity ellipse as a function of depth. (4) Finally, we use the density-weighted fl; bg proper-motion ellipse produced from the tracer stars to assess the kinematic membership of the 16 transiting planet candidates discovered in the Sagittarius Window; the kinematic distribution of the planet candidates is consistent with that of the disk and bulge stellar populations.