http://arxiv.org/abs/2112.07667
Mapping exoplanets across phases and during secondary eclipse is a powerful technique for characterizing Hot Jupiters in emission. Since these planets are expected to rotate about axes normal to their orbital planes, with rotation periods synchronized with their orbital periods, mapping provides a direct correspondence between orbital phase and planetary longitude. For planets with fewer constraints on their spin properties, the relationship between the shape of the eclipse light curve and the visible portion of the surface is more complex. We develop a framework to understand the information content of planets where the rotation rate and/or axis orientation are not well constrained, by constructing a basis of emission time series (“light curves”) that are orthogonal in integrated flux across secondary eclipse. The most orthogonal bases in eclipse consist of periodic functions – akin to sinusoids – and at slow enough rotation rates these follow a monotonic series in frequency. If only data during eclipse are considered, we show that very similar light curves at a given frequency can be generated by maps of similar complexity at a wide range of spin axis orientations. Constraining spin axis orientations from eclipse data alone may therefore depend on strong prior knowledge of plausible emission map structures and/or rotation rates. When the planetary rotation period becomes shorter than the total eclipse duration, there will be an additional ambiguity between the complexity of the emission map and observable variations due to rotation, as both can in principle generate similar signals. By modeling example eclipse observations of the Warm Jupiter HAT-P-18 b, we demonstrate that the available signal-to-noise for $\sim 10$ orbits is just sufficient to derive map structure beyond the eclipse depth.
A. Adams and E. Rauscher
Wed, 15 Dec 21
12/85
Comments: 28 pages, 22 figures. Submitted to AAS Journals
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