Mind the Gap: Secular Dynamics of Self-gravitating Debris Disks Antranik A. Sefilian1†, Roman R. Rafikov1, Mark C. Wyatt2 1 DAMTP, University of Cambridge; 2 Institute of Astronomy, University of Cambridge; †[email protected] ABSTRACT Spatially resolved images of debris disks frequently reveal complex morphologies such as gaps, spirals, and warps. Most existing models for explaining such morphologies focus on the role of massive perturbers (i.e. planets, stellar companions), ignoring the gravitational effects of the disk itself. Here we investigate the secular interaction between an eccentric planet and a massive, external using a simple analytical model. Our framework accounts for both the gravitational coupling between the disk and the planet, as well as the disk self-gravity – with the limitation that it ignores the non-axisymmetric component of the disk (self-)gravity. We find generally that even when the disk is less massive than the planet, the system may feature secular resonances within the disk, where planetesimal eccentricities get significantly excited. Given this outcome we propose that gapped debris disks, such as those around HD 107146 and HD 92945, could be the result of secular resonances with a yet-undetected planet interior to the disk. We characterize the dependence of the properties of the secular resonances (i.e. locations, timescales, and widths) on the planet and disk parameters, finding that the mechanism is robust provided the disk is massive enough. As an example, we apply our results to HD 107146 and find that this mechanism readily produces ~20 au wide non-axisymmetric gaps. Our results may be used to set constraints on the total of gapped debris disks. We demonstrate this for HD 206893, for which we infer a disk mass of ≈ 170 by considering perturbations from the known brown dwarf companion. BACKGROUND TYPICAL EVOLUTION OF THE DISK STRUCTURE • To date, four debris disks are known to exhibit double-belt structures that are separated by depleted gaps in their dust distribution as traced by ALMA.

HD 206893

• The most accepted explanation for the observed gaps is the presence of yet unseen planets orbiting within the gaps (i.e. at ~ 100 au).

MODEL • We study the secular gravitational interaction between an eccentric planet and a coplanar, initially axisymmetric, external debris disk by including, for the first time, the effects of disk (self)-gravity.

• For simplicity, we only account for the axisymmetric component of the disk (self)- figure. this of version animated the download to gravity, ignoring its non-axisymmetric contribution. ain aout >ain here

→ Linear Laplace-Lagrange theory Click Click

Ask for details! PRECESSIONAL RATES

Fiducial parameters:

• Planet: mp = 0.6 MJ ap = 20 au eP = 0.05 ϖP(0) = 0

• Disk: ain = 30 au aout= 150 au p = 1

Md = 20 ME

We identified 3 evolutionary stages occurring on timescales measured relative to the planet’s precession period, 휏푠푒푐.

SECULAR RESONANCE •At early times (푡 ≲ 휏푠푒푐; panels a, b), •By the time the planet has • Further into the evolution (푡 ≥ Planetesimal precession: A(a) = Ad(a) + AP(a) the disk quickly evolves away from completed around one precession 휏푠푒푐, panels d–f), the structure of • The planet induces prograde precession of planetesimal orbits, AP(a) > 0 its initial axisymmetric state by cycle (푡~휏푠푒푐 panel c), a crescent- the gap practically remains • The disk induces retrograde precession of planetesimal orbits, Ad(a) < 0 developing a trailing spiral structure. shaped ~20 au wide gap forms invariant: the gap maintains its Note: these two rates are comparable in absolute value when Md < mP This spiral structure initially starts off around the secular resonance (at 70 crescent shape along with its

Planetary precession: Ad,P at the inner disk edge and propagates au). The gap is asymmetric such that alignment with the planet as it • The disk induces prograde precession of the planet’s orbit, A > 0 radially outwards with time as it it is both wider and deeper in the co-precesses with the planetary d,P wraps around the (★). direction of planet’s pericenter (●). It apsidal line. Note the offset has a fractional depth of about 0.5. between the disk parts interior PLANETESIMAL DYNAMICS and exterior to the gap. • Planet-dominated regime in the • Disk-dominated regime in the inner disk parts, where A(a)>Ad,P outer disk parts, where A(a)

SECULAR RESONANCES AND GAPS DISK MASS ESTIMATION • The transition between the two regimes occurs via a secular resonance, Our results provide a unique way to indirectly measure the total mass of debris disks e.g. if a planet interior where to the disk is detected. A case in point: HD 206893 and planetesimal eccentricities are forced to arbitrarily large values. Our model requires • Planetesimals on eccentric orbits spend most of their time near their • Star: F-type, 50 – 700 Myr old apocenter, further away from their orbital semimajor axis → We expect • Brown dwarf: a = 11 au, m = 12 MJ , e = 0.15 surface density depletion at and around the resonance where e →1 • Disk: 30 – 180 au, with a ~25 au wide gap centred at ~75 au No need for additional planets

PROPERTIES OF THE SECULAR RESONANCES SUMMARY • For the first time, we studied the long-term evolution of massive debris disks in planetary systems. Resonance Location (or mass): • When the disk is less massive than the planet, the combined gravity of a “single planet + external disk” system mediates the establishment of secular eccentricity resonances in the disk. <<1 • This leads to the formation of an observable gap within the disk, akin to those in HD 107146 and HD 92945, over a broad region of parameter space. Timescale for e-excitation: • Our results may be used (i) to set constraints on the total masses of gapped debris disks, and (ii) to infer the presence and parameters of planets based on observed gap features. - Inclusion of non-axisymmetric component of disk gravity using a FUTURE WORK “softened N-ring” model in preparation Resonance width: - Collisional depletion of planetesimals Ask for details!

Sefilian et al. 2020, ApJ (in press), arXiv: 2010.15617 Marino et al. 2019, MNRAS, 484, 1257 Sefilian & Rafikov, 2019, MNRAS, 489, 4176 Marino et al. 2020, MNRAS, 498, 1319 The mechanism is robust over a REFERENCES Sefilian & Touma, 2019, AJ, 157, 59 Pearce & Wyatt, 2015, MNRAS, 453,3329 broad region of parameter space Delorme et al. 2017, A&A, 608, A79 Shannon et al. 2016, MNRAS, 462, L116 Marino et al. 2018, MNRAS, 479, 5423 Yelverton & Kennedy, 2018, MNRAS, 479, 2673