Abstract
We investigate 1D exoplanetary distributions using a novel analysis algorithm based on the continuous wavelet transform. The analysis pipeline includes an estimation of the wavelet transform of the probability density function (p.d.f.) without pre-binning, use of optimized wavelets, a rigorous significance testing of the patterns revealed in the p.d.f., and an optimized minimum-noise reconstruction of the p.d.f. via matching pursuit iterations.
In the distribution of orbital periods, \(P\), our analysis revealed a narrow subfamily of exoplanets within the broad family of “warm Jupiters”, or massive giants with \(P\gtrsim 300~\mbox{d}\), which are often deemed to be related with the iceline accumulation in a protoplanetary disk. We detected a p.d.f. pattern that represents an upturn followed by an overshooting peak spanning \(P\sim 300\mbox{--}600~\mbox{d}\), right beyond the “period valley”. It is separated from the other planets by p.d.f. concavities from both sides. It has at least 2-sigma significance.
In the distribution of planet radii, \(R\), and using the California Kepler Survey sample properly cleaned, we confirm the hints of a bimodality with two peaks about \(R=1.3R_{\oplus }\) and \(R=2.4R_{ \oplus }\), and the “evaporation valley” between them. However, we obtain just a modest significance for this pattern, 2-sigma only at the best. Besides, our follow-up application of the Hartigan and Hartigan dip test for unimodality returns 3 per cent false alarm probability (merely 2.2-sigma significance), contrary to 0.14 per cent (or 3.2-sigma), as claimed by Fulton et al. (2017).
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Notes
Since we analyze the distribution of \(\log P\) actually, \(a\) has the meaning of a relative scale. That is, \(a=0.3\) infers about \(\pm 15\) per cent range from a given \(P\).
Note that details in the \(A\)-distribution should be always blurred additionally, because \(M_{\star }\) often involves remarkable uncertainties. But this effect is smaller than the scatter of \(M_{\star }\) in the sample.
We used a public python implementation of the test, available at https://github.com/alimuldal/diptest.
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Acknowledgements
V.Sh. Shaidulin was supported by the Russian Foundation for Basic Research grant 17-02-00542 A. R.V. Baluev was supported by the Presidium of Russian Academy of Sciences programme P-28, subprogram “The space: investigating fundamental processes and their interrelations”. We thank the anonymous referee for their suggestions regarding this manuscript.
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Baluev, R.V., Shaidulin, V.S. Fine-resolution analysis of exoplanetary distributions by wavelets: hints of an overshooting iceline accumulation. Astrophys Space Sci 363, 192 (2018). https://doi.org/10.1007/s10509-018-3416-9
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DOI: https://doi.org/10.1007/s10509-018-3416-9