An Analysis of Jitter and Transit Timing Variations in the HAT-P-13 System

If the two planets in the HAT-P-13 system are coplanar, the orbital states provide a probe of the internal planetary structure. Previous analyses of radial velocity and transit timing data of the system suggested that the observational constraints on the orbital states were rather small. We reanalyze the available data, treating the jitter as an unknown MCMC parameter, and find that a wide range of jitter values are plausible, hence the system parameters are less well constrained than previously suggested. For slightly increased levels of jitter ($\sim 4.5\,m\,s^{-1}$) the eccentricity of the inner planet can be in the range $0<e_{inner}<0.07$, the period and eccentricity of the outer planet can be $440<P_{outer}<470$ days and $0.55<e_{outer}<0.85$ respectively, while the relative pericenter alignment, $\eta$, of the planets can take essentially any value $-180^{\circ}<\eta<+180^{\circ}$. It is therefore difficult to determine whether $e_{inner}$ and $\eta$ have evolved to a fixed-point state or a limit cycle, or to use $e_{inner}$ to probe the internal planetary structure. We perform various transit timing variation (TTV) analyses, demonstrating that current constraints merely restrict $e_{outer}<0.85$, and rule out relative planetary inclinations within $\sim 2^{\circ}$ of $i_{rel}=90^{\circ}$, but that future observations could significantly tighten the restriction on both these parameters. We demonstrate that TTV profiles can readily distinguish the theoretically favored inclinations of i_{rel}=0^{\circ}\,&\,45^{\circ}, provided that sufficiently precise and frequent transit timing observations of HAT-P-13b can be made close to the pericenter passage of HAT-P-13c. We note the relatively high probability that HAT-P-13c transits and suggest observational dates and strategies.Comment: Published in Ap

Integrating an Android Device into Embedded Computer Systems

An embedded system is a computer system designed to perform a specific set of tasks such as a GPS device or a digital camera. An embedded system is composed of three major parts: a processor (CPU), input devices, and output devices. The input devices are peripherals to take user command (switches and keypad) and sensors to measure environmental conditions (barometer and accelerometer). The output devices are actuators that generate light and sound (LED display and amplified speaker) and moving parts (servo motor). An important step in prototyping an embedded system is to design the input subsystem. It is traditionally done by selecting input modules and then developing hardware and software interfaces for each individual module. The undergraduate summer research is to use an inexpensive, entry-level, Android phone as a universal programmable sensor module. It provides a single unified interface and can be configured to replace a dozen commonly used input devices.https://engagedscholarship.csuohio.edu/u_poster_2015/1058/thumbnail.jp

Integrating an Android Device into Embedded Computer Systems

An embedded system is a computer system designed to perform a specific set of tasks such as a GPS device or a digital camera. An embedded system is composed of three major parts: a processor (CPU), input devices, and output devices. The input devices are peripherals to take user command (switches and keypad) and sensors to measure environmental conditions (barometer and accelerometer). The output devices are actuators that generate light and sound (LED display and amplified speaker) and moving parts (servo motor). An important step in prototyping an embedded system is to design the input subsystem. It is traditionally done by selecting input modules and then developing hardware and software interfaces for each individual module. The undergraduate summer research is to use an inexpensive, entry-level, Android phone as a universal programmable sensor module. It provides a single unified interface and can be configured to replace a dozen commonly used input devices.https://engagedscholarship.csuohio.edu/u_poster_2015/1058/thumbnail.jp

Quantifying the challenges of detecting unseen planetary companions with transit timing variations

Both ground and space-based transit observatories are poised to significantly increase the number of known transiting planets and the number of precisely measured transit times. The variation in a planet's transit times may be used to infer the presence of additional planets. Deducing the masses and orbital parameters of such planets from transit time variations (TTVs) alone is a rich and increasingly relevant dynamical problem. In this work, we evaluate the extent of the degeneracies in this process, systematically explore the dependence of TTV signals on several parameters and provide phase space plots that could aid observers in planning future observations. Our explorations are focused on a likely-to-be prevalent situation: a known transiting short-period Neptune or Jupiter-sized planet and a suspected external low-mass perturber on a nearly-coplanar orbit. Through approximately 10^7 N-body simulations, we demonstrate how TTV signal amplitudes may vary by orders of magnitude due to slight variations in any one orbital parameter (0.001 AU in semimajor axis, 0.005 in eccentricity, or a few degrees in orbital angles), and quantify the number of consecutive transit observations necessary in order to obtain a reasonable opportunity to characterize the unseen planet (approximately greater or equal to 50 observations). Planets in or near period commensurabilities of the form p:q, where p < 21 and q < 4, produce distinct TTV signatures, regardless of whether the planets are actually locked in a mean motion resonance. We distinguish these systems from the secular systems in our explorations. Additionally, we find that computing the autocorrelation function of a TTV signal can provide a useful diagnostic for identifying possible orbits for additional planets and suggest that this method could aid integration of TTV signals in future studies of particular exosystems.Comment: 53 pages total, including 18 figures, 1 table, and 1 appendix. Accepted for publication in ApJ. Better resolution plots will appear in online journa