Tidally Distorted Exoplanets: Density Corrections for Short-period Hot-Jupiters Based Solely on Observable Parameters

The close proximity of short-period hot-Jupiters to their parent star means they are subject to extreme tidal forces. This has a profound effect on their structure and, as a result, density measurements that assume that the planet is spherical can be incorrect. We have simulated the tidally distorted surface for 34 known short-period hot-Jupiters, assuming surfaces of constant gravitational equipotential for the planet, and the resulting densities have been calculated based only on observed parameters of the exoplanet systems. Comparing these results to the density values, assuming the planets are spherical, shows that there is an appreciable change in the measured density for planets with very short periods (typically less than two days). For one of the shortest-period systems, WASP-19b, we determine a decrease in bulk density of 12% from the spherical case and, for the majority of systems in this study, this value is in the range of 1%-5%. On the other hand, we also find cases where the distortion is negligible (relative to the measurement errors on the planetary parameters) even in the cases of some very short period systems, depending on the mass ratio and planetary radius. For high-density gas planets requiring apparently anomalously large core masses, density corrections due to tidal deformation could become important for the shortest-period systems.

Investigation of Machining Parameters for Multiple Response Optimization in Microelectrodischarge Milling

This paper investigated the influence of three micro electrodischarge milling process parameters, which were feed rate, capacitance, and voltage. The response variables were average surface roughness (R a ), maximum peak-to-valley roughness height (R y ), tool wear ratio (TWR), and material removal rate (MRR). Statistical models of these output responses were developed using three-level full factorial design of experiment. The developed models were used for multiple-response optimization by desirability function approach to obtain minimum R a , R y , TWR, and maximum MRR. Maximum desirability was found to be 88%. The optimized values of R a , R y , TWR, and MRR were 0.04, 0.34 μm, 0.044, and 0.08 mg min−1, respectively for 4.79 μm s−1 feed rate, 0.1 nF capacitance, and 80 V voltage. Optimized machining parameters were used in verification experiments, where the responses were found very close to the predicted values.