Abstract
I begin this review by first defining what is meant by exoplanet demographics, and then motivating why we would like as broad a picture of exoplanet demographics as possible. I then outline the methodology and pitfalls to measuring exoplanet demographics in practice. I next review the methods of detecting exoplanets, focusing on the ability of these methods to detect wide separation planets. For the purposes of this review, I define wide separation as separations beyond the “snow line” of the protoplanetary disk, which is at \(\simeq 3\mathrm{au}\) for a sun-like star. I note that this definition is somewhat arbitrary, and the practical boundary depends on the host star mass, planet mass and radius, and detection method. I review the approximate scaling relations for the signal-to-noise ratio for the detectability of exoplanets as a function of the relevant physical parameters, including the host star properties. I provide a broad overview of what has already been learned from the transit, radial velocity, direct imaging, and microlensing methods. I outline the challenges to synthesizing the demographics using different methods and discuss some preliminary first steps in this direction. Finally, I describe future prospects for providing a nearly complete statistical census of exoplanets.
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Notes
- 1.
I note that in systems with multiple planets, any apsidal alignment can be inferred by the individual values of \(\omega \). The existence of an apsidal alignment (or alignments) can provide constraints on the formation and/or evolution of that system. See, e.g., Chiang et al. (2001).
- 2.
I note that the posterior distribution of \(M_\mathrm{p}\) given a measurement \(M_\mathrm{p}\sin {i}\) is often estimated by simply assuming that \(\cos {i}\) is uniformly distributed. This leads to the familiar result that the median of the true mass is only \((\sin {[\text {arccos}{(0.5)}]})^{-1}{\simeq }1.15\) larger than the minimum mass. Unfortunately, this is only correct if the distribution of true planet masses is such that \(d N/d \log {M_\mathrm{p}}\) is a constant (Ho and Turner 2011; Stevens and Gaudi 2013). For other distributions, the true mass can be larger or smaller than this naive estimate.
- 3.
Again, one might instead wish to instead transform \(\mathbf {\beta }_\mathcal{I} \rightarrow \mathbf {\alpha }\) and then constrain \(d^n N_\mathrm{pl}/d\mathbf {\alpha }\). For brevity, I will no longer specifically call out this alternate method.
- 4.
In general this method works only if the majority of the targets do not have a planetary signal that is significant compared to the intrinsic noise distribution in the data.
- 5.
Fortunately, with the availability of near-UV to near-IR absolute broadband photometry, combined with Gaia parallaxes and stellar atmosphere models, it is possible to measure the radii of most bright stars nearly purely empirically to relatively high precision (Stassun et al. 2017; Stevens et al. 2017).
- 6.
Formally, the minimum detectable \(M_\mathrm{p}\sin {i}\).
- 7.
I note that a common alternative parameterization is to use \(T_{14}\), the time between first and fourth contact, and \(T_{23}\), the time between second and third contact (also referred to as \(T_\mathrm{full}\) and \(T_\mathrm{flat}\)). I strongly advise against adopting this parameterization, for several reasons. First, the algebra required to transform from this parameterization to the physical parameters is significantly more complicated (compare Seager and Mallén-Ornelas 2003 and Carter et al. 2008). Second, \(T_{14}\) and \(T_{23}\) are generally much more highly correlated than T and \(\tau \), making the analytical interpretation of fits using the former parameterization much more difficult than using the latter parameters. Finally, the timescale estimated from the Boxcar Least Squares algorithm (Kovács et al. 2002) is much more well approximated by T than \(T_{14}\) or \(T_{23}\).
- 8.
I note that, in some cases, it is possible to disambiguate free-floating planets from bound planets by detecting (or excluding) light from the host.
- 9.
I note that in the microlensing literature, this variable is typically simply referred to as \(\alpha \). Since I have already defined \(\alpha \) above, I adopt the form \(\alpha _{\mu \mathrm{L}}\) to avoid confusion.
- 10.
Note that, with only astrometric observations, there is a two-fold ambiguity in \(\Omega \).
- 11.
As noted in Chap. 3, Sect. 3.1 and Fig. 4.12, Wittenmyer et al. (2020) find instead that long-period giant planet frequency beyond the snowline does not appear to decline, while Fulton et al. (2021) provide evidence that the turnover in occurrence rate of gas giants might start closer to 10 au, and it might be mass-dependent.
- 12.
- 13.
Formally, the condition for runaway growth is that the mass of the gaseous envelop becomes larger than that of the core, leading to a Jeans-like instability and rapid gas accretion (e.g., Mizuno 1980; Stevenson 1982; Pollack et al. 1996). However, the simplest models of protoplanetary disks generally predict core masses of \({\sim }10~M_\oplus \), and thus the total critical mass for runaway accretion of \({\sim }20~M_\oplus \), e.g., somewhat larger than the masses of the ice giants.
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Acknowledgements
I would like to thank the organizers of the 3rd Advanced School on Exoplanetary Science: Demographics of Exoplanetary Systems for inviting me to attend a very enjoyable school held at an extraordinarily beautiful venue, and for giving me the opportunity to present on the topic of “Wide-Separation Exoplanets”. I am very much indebted to the editors of the proceedings (L. Mancini, K. Biazzo, V. Bozza, and A. Sozzetti) for their exceptional patience as I wrote this chapter. I would like to thank the many people who have shaped my thinking about exoplanet demographics over the past 20+ years, including (but not limited to) Thomas Beatty, Chas Beichman, David Bennett, Gary Blackwood, Brendan Bowler, Chris Burke, Jennifer Burt, Dave Charbonneau, Jesse Christiansen, Christian Clanton, Andrew Cumming, Martin Dominik, Subo Dong, Courtney Dressing, Debra Fischer, Eric Ford, Andrew Gould, Calen Henderson, Andrew Howard, Marshall Johnson, Bruce Macintosh, Eric Mamajek, Michael Meyer, Matthew Penny, Michael Perryman, Peter Plavchan, Radek Poleski, Aki Roberge, Penny Sackett, Sara Seager, Yossi Shvartzvald, Karl Stapelfeldt, Christopher Stark, Keivan Stassun, Takahiro Sumi, Andrzej Udalski, Steven Villanueva, Jr., Ji Wang, Josh Winn, Jennifer Yee, Andrew Youdin, and Wei Zhu. Apologies to those I forgot to include in this list and those I forgot to cite in this review. Finally, I recognize the support from the Thomas Jefferson Chair for Space Exploration endowment from the Ohio State University, and the Jet Propulsion Laboratory. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.
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Scott Gaudi, B. (2022). The Demographics of Wide-Separation Planets. In: Biazzo, K., Bozza, V., Mancini, L., Sozzetti, A. (eds) Demographics of Exoplanetary Systems. Astrophysics and Space Science Library, vol 466. Springer, Cham. https://doi.org/10.1007/978-3-030-88124-5_4
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