The Astrophysical Journal Letters, 837:L6 (7pp), 2017 March 1 https://doi.org/10.3847/2041-8213/aa61a7 © 2017. The American Astronomical Society. All rights reserved. HD 106906: A Case Study for External Perturbations of a Debris Disk Erika R. Nesvold1, Smadar Naoz2,3, and Michael P. Fitzgerald2 1 Department of Terrestrial Magnetism, Carnegie Institution for Science, 5241 Broad Branch Road, Washington, DC 20015, USA 2 Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, CA 90095, USA 3 Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA Received 2017 February 10; revised 2017 February 17; accepted 2017 February 17; published 2017 March 1 Abstract Models of debris disk morphology are often focused on the effects of a planet orbiting interior to or within the disk. Nonetheless, an exterior planetary-mass perturber can also excite eccentricities in a debris disk, via Laplace– Lagrange secular perturbations in the coplanar case or Kozai–Lidov perturbations for mutually inclined companions and disks. HD 106906 is an ideal example of such a a system, as it harbors a confirmed exterior 11 MJup companion at a projected separation of 650 au outside a resolved, asymmetric disk. We use collisional and dynamical simulations to investigate the interactions between the disk and the companion, and to use the disk’s observed morphology to place constraints on the companion’s orbit. We conclude that the disk’s observed morphology is consistent with perturbations from the observed exterior companion. Generalizing this result, we suggest that exterior perturbers, as well as interior planets, should be considered when investigating the cause of observed asymmetries in a debris disk. Key words: celestial mechanics – circumstellar matter – methods: numerical – planetary systems – planet–disk interactions – stars: individual (HD 106906) 1. Introduction grains (Kalas et al. 2015; Lagrange et al. 2016). These Circumstellar debris disks are produced by the rocky and icy observations noted four major features of the disk morphology material leftover from the formation of the star and any planets and system geometry: in the system. To date, over 1700 debris disks have been 1. The position angle (PA) of the disk is oriented ~21 detected via the excess infrared emission in their star’s spectral counterclockwise from the PA of the companion, which energy distribution (Cotten & Song 2016), and over 40 have constrains the orbit of the companion relative to the disk. been resolved with optical or infrared imaging (http:// 2. The inner disk has little to no vertical extension. While ) circumstellardisks.org . The architecture of the underlying Kalas et al. (2015) tentatively suggested the presence of a planetary system can leave a distinct imprint on the morph- “warp” in the disk’s vertical structure on the west side of ( ology of a debris disk Mouillet et al. 1997; Wyatt et al. 1999; the disk, this warp was not confirmed by Lagrange et al. Matthews et al. 2014; Nesvold & Kuchner 2015b; Lee & (2016). This lack of vertical extension indicates that the Chiang 2016; Nesvold et al. 2016). inclinations of the disk particles have not been excited. Modeling debris disk morphology is often focused on the 3. The east side of the disk is brighter than the west side in effects of a planetary-mass perturber orbiting interior to or GPI and SPHERE near-infrared images. within the disk (Mouillet et al. 1997; Chiang et al. 2009; 4. Kalas et al. (2015) observed a faint extension on the west Nesvold & Kuchner 2015a; Pearce & Wyatt 2015). None- theless, exterior companions have been detected and inferred side of the disk out to nearly 500 au, but only diffuse for several systems (Rodriguez & Zuckerman 2012; Bailey emission on the east side. et al. 2014; Mawet et al. 2015), and dynamical modeling These latter two features indicate that the disk may be an suggests that an exterior perturber can also excite eccentricities eccentric ring, which will exhibit a brightness asymmetry – of the particles in a debris disk, via Laplace Lagrange secular toward the pericenter side (“pericenter glow”; Wyatt ( ) perturbations in the near-coplanar case Thébault et al. 2012 or et al. 1999) and a faint, extended tail toward the apocenter Kozai–Lidov perturbations for mutually inclined companions ( ) ( ) side Lee & Chiang 2016 . and disks Nesvold et al. 2016 , inducing asymmetries in the We modeled the HD 106906 system to demonstrate that the disk and triggering a collisional cascade. Collisions between observed exterior companion can shape the disk into a flat, the disk particles produce smaller dust grains whose thermal eccentric ring, and that all four of these morphological features emission or scattered light can then be spatially resolved with can be reproduced without invoking the presence of a second infrared or optical imaging (Wyatt 2008). HD 106906 is an ideal example of a system with an exterior companion. We also used the observed features and asymme- perturber, as it harbors a confirmed exterior companion with a tries of the HD 106906 disk to place constraints on the orbit of the observed companion. In Section 2, we describe the model-atmosphere-derived mass of 11 MJup at a projected separation of 650 au outside a resolved disk (Bailey collisional and dynamical simulations we performed on the et al. 2014). Scattered-light imaging of the disk with the parent bodies and dust grains in the HD 106906 disk. In Gemini Planet Imager (GPI), the Hubble Space Telescope’s Section 3, we present the simulated brightness images Advanced Camera for Surveys (HST/ACS), and SPHERE has produced by our simulations for comparison with observations. revealed that the disk is a ring viewed nearly edge-on In 4, we discuss the implication of these results and show how (inclination ~85), with a inner region cleared of small dust they can be used to constrain the orbit of HD 106906b. In 1 The Astrophysical Journal Letters, 837:L6 (7pp), 2017 March 1 Nesvold, Naoz, & Fitzgerald Table 1 such that the simulated companion’s orbit could reproduce the Initial Conditions of the Disk and Companion for the Simulation position of the observed companion. Parameter Initial Disk Values HD 106906b 2.2. SMACK versus Collisionless N-body Semimajor Axis (au) 65–85 700 Eccentricity 0–0.01 0.7 To measure the effects of collisions on the dynamics of the Inclination (°) 0–0.29 8.5 disk particles, we also performed a collisionless N-body Longitude of Nodes (°) 0–360 90 simulation of the disk using the Wisdom–Holman integrator Argument of Pericenter (°) 0–360 −90 of REBOUND with collision detection and resolution turned Optical Depth 1.4´ 10-3 L off. The collisionless N-body simulation used the same ( −3) L Density gcm 1.0 companion and disk parameters as the SMACK simulation (Table 1), with 10,000 test particles to represent the disk. Figure 1 shows the time evolution of the simulated disk’s Section 5, we summarize our conclusions and suggest average eccentricity, inclination, longitude of nodes, and opportunities for future work. argument of pericenter. Although there are small variations, most notably in the average eccentricity, between the SMACK 2. Simulations simulation and the collisionless N-body simulation, the maximum difference for each parameter is 10%, indicating Given that collisions between particles in a disk with that fragmenting collisions have a minimal effect on the fi ( -3 suf ciently high optical depth LIR L* »´1.4 10 for HD dynamics of this system. 106906 Chen et al. 2011) will both produce the small grains seen in observations and may affect the dynamics of the disk, 2.3. Dust Model we simulated the HD 106906 system using the Superparticle- Method Algorithm for Collisions in Kuiper belts and debris To generate the simulated images of the dust grains in the disks (SMACK; Nesvold et al. 2013). We then recorded the HD 106906 system, we adapted the method of Lee & Chiang dust-producing encounters between parent bodies, simulated (2016), which extended the dust orbit calculations of Wyatt the orbits of the generated dust grains under the influence of et al. (1999) to include estimates of the surface brightness. Our radiative forces following the method of Lee & Chiang (2016), SMACK simulation output the locations of dust-producing then simulated the surface brightness of the dust using a collisions during the 15 Myr simulation, as well as the orbits of Henyey–Greenstein scattering phase function (Henyey & the parent bodies producing the dust. We selected the first 104 Greenstein 1941). dust production events occurring after time t=5 Myr. For each dust production event, we generated 10 dust orbits, each with a β value randomly chosen from a power-law distribution 2.1. SMACK Model with an index 3/2 (where b » FFrad grav represents the ratio of SMACK is based on the N-body integrator REBOUND the radiative and gravitational forces acting on a dust grain). (Rein & Liu 2012), but approximates each particle in the The maximum possible value for the β value was set by the integrator as a collection of bodies with a range of sizes parent body’s orbit: between 1 mm and 10 cm in diameter, traveling on the same “ ” 1 - ep orbit. This group of bodies is called a superparticle and is bmax = ,1() characterized by a size distribution, position, and velocity. The 21()+ efp cosp superparticles act as test particles in the integration, and orbit where e and f are the parent body’s eccentricity and true the star under the influence of perturbations by any planets in p p the simulation. Each superparticle is approximated as a sphere anomaly, respectively. The semimajor axis a, eccentricity e, with some finite radius.