Abstract
Abstract We examine whether various characteristics of planet-driven spiral arms can be used to constrain the masses of unseen planets and their positions within their disks. By carrying out two-dimensional hydrodynamic simulations varying planet mass and disk gas temperature, we find that a larger number of spiral arms form with a smaller planet mass and a lower disk temperature. A planet excites two or more spiral arms interior to its orbit for a range of disk temperatures characterized by the disk aspect ratio , whereas exterior to a planet’s orbit multiple spiral arms can form only in cold disks with . Constraining the planet mass with the pitch angle of spiral arms requires accurate disk temperature measurements that might be challenging even with ALMA. However, the property that the pitch angle of planet-driven spiral arms decreases away from the planet can be a powerful diagnostic to determine whether the planet is located interior or exterior to the observed spirals. The arm-to-arm separations increase as a function of planet mass, consistent with previous studies; however, the exact slope depends on disk temperature as well as the radial location where the arm-to-arm separations are measured. We apply these diagnostics to the spiral arms seen in MWC 758 and Elias 2–27. As shown in Bae et al., planet-driven spiral arms can create concentric rings and gaps, which can produce a more dominant observable signature than spiral arms under certain circumstances. We discuss the observability of planet-driven spiral arms versus rings and gaps.
Highlights
Recent observations with state-of-the-art telescopes have imaged multi-armed spirals in protoplanetary disks (e.g., MWC 758, Grady et al 2013; Benisty et al 2015; Reggiani et al 2018; SAO 206462, Muto et al 2012; Garufi et al 2013; Stolker et al 2016; Maire et al 2017; Elias 2–27, Pérez et al 2016; AB Aur, Tang et al 2017)
An important feature in the planet-driven spiral arm formation mechanism is that the formation of both primary and additional arms can be understood as a linear process when the planet mass is sufficiently small
In order to examine which characteristics of spiral arms can be used, we carry out a suite of two-dimensional isothermal hydrodynamic simulations varying planet mass and disk temperature
Summary
Recent observations with state-of-the-art telescopes have imaged multi-armed spirals in protoplanetary disks (e.g., MWC 758, Grady et al 2013; Benisty et al 2015; Reggiani et al 2018; SAO 206462, Muto et al 2012; Garufi et al 2013; Stolker et al 2016; Maire et al 2017; Elias 2–27, Pérez et al 2016; AB Aur, Tang et al 2017). In the companion paper (Bae & Zhu 2018, hereafter Paper I), we described the mechanism by which a planet excites multiple spiral arms in the underlying protoplanetary disk. Spiral arms driven by smaller-mass planets may not be directly detectable They still can create observable signatures: concentric rings and gaps. In disks with a low viscosity, it is possible that low-mass planets not capable of generating observable spiral arms can still induce sufficient trapping of solid particles that can be observable (Bae et al 2017, see Section 5.2 of the present paper).
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