Location
Physics : 401
Date & Time
June 12, 2015, 10:00 am – 12:00 pm
Description
TITLE: Modeling Collisions in Circumstellar Debris Disks
ABSTRACT: Observations of resolved debris disks show a spectacular variety of features and asymmetries, including inner cavities and gaps, inclined secondary disks or warps, and eccentric, sharp-edged rings. Embedded exoplanets could create many of these features via gravitational perturbations, which sculpt the disk directly and by generating planetesimal collisions. In this thesis, I present the Superparticle Model/Algorithm for Collisions in Kuiper belts and debris disks (SMACK), a new method for simultaneously modeling, in 3-D, the collisional and dynamical evolution of planetesimals in a debris disk with planets. SMACK can simulate azimuthal asymmetries and how these asymmetries evolve over time. I show that SMACK is stable to numerical viscosity and numerical heating over 10 Myr, and that it can reproduce analytic models of disk evolution. As an example of the algorithm's capabilities, I use SMACK to model the evolution of a debris ring containing a planet on an eccentric orbit and demonstrate that differential precession creates a spiral structure as the ring evolves, but collisions subsequently break up the spiral, leaving a narrower eccentric ring.
To demonstrate SMACK's utility in studying debris disk physics, I apply SMACK to simulate a planet on a circular orbit near a ring of planetesimals that are experiencing destructive collisions. Previous simulations of a planet opening a gap in a collisionless debris disk have found that the width of the gap scales as the planet mass to the 2/7th power (alpha=2/7). I find that gap sizes in a collisional disk still obey a power law scaling with planet mass, but that the index alpha of the power law depends on the age of the system $t$ relative to the collisional timescale t_coll of the disk by alpha = 0.32 (t/t_coll)^(-0.04), with inferred planet masses up to five times smaller than those predicted by the classical gap law. The increased gap sizes likely stem from the interaction between collisions and the mean motion resonances near the chaotic zone. I investigate the effects of the initial eccentricity distribution of the disk particles and find a negligible effect on the gap size at Jovian planet masses, since collisions tend to erase memory of the initial particle eccentricity distributions. I also find that the presence of Trojan analogs is a potentially powerful diagnostic of planets in the mass range ~1-10 M_Jup. I apply my model to place new upper limits on planets around Fomalhaut, HR 4796 A, HD 202628, HD 181327, and beta Pictoris.
Finally, to show how SMACK can be used to analyze a single debris disk in detail, I present a new model of the beta Pictoris disk and planet system that, for the first time, combines simulations of the colliding planetesimals and the dynamics of the dust grains, allowing me to model features and asymmetries in both submillimeter and scattered light images of the disk. I combine a 100,000 superparticle SMACK simulation with N-body integrations of the dust produced by the simulated collisions. I find that secular perturbations of the planet's measured inclination and eccentricity can explain the observed warp and planetesimal ring, while collisions between planetesimals shape the disk by eroding close-in material. The complex 3D structure of the disk due to the perturbations from the planet creates an azimuthally asymmetric spatial distribution of collisions, which could contribute to the observed azimuthal clump of CO gas seen with ALMA. My simulations of the small dust grains produced by collisions demonstrate that the "birth ring'' approximation for beta Pictoris fails to account for the ~54% of dust mass produced outside of the planetesimal ring. I also reproduce the gross morphology of high-resolution scattered light images of the disk, including the two-disk "x"-pattern seen in scattered light, which has not been replicated by previous dust dynamics models.
ABSTRACT: Observations of resolved debris disks show a spectacular variety of features and asymmetries, including inner cavities and gaps, inclined secondary disks or warps, and eccentric, sharp-edged rings. Embedded exoplanets could create many of these features via gravitational perturbations, which sculpt the disk directly and by generating planetesimal collisions. In this thesis, I present the Superparticle Model/Algorithm for Collisions in Kuiper belts and debris disks (SMACK), a new method for simultaneously modeling, in 3-D, the collisional and dynamical evolution of planetesimals in a debris disk with planets. SMACK can simulate azimuthal asymmetries and how these asymmetries evolve over time. I show that SMACK is stable to numerical viscosity and numerical heating over 10 Myr, and that it can reproduce analytic models of disk evolution. As an example of the algorithm's capabilities, I use SMACK to model the evolution of a debris ring containing a planet on an eccentric orbit and demonstrate that differential precession creates a spiral structure as the ring evolves, but collisions subsequently break up the spiral, leaving a narrower eccentric ring.
To demonstrate SMACK's utility in studying debris disk physics, I apply SMACK to simulate a planet on a circular orbit near a ring of planetesimals that are experiencing destructive collisions. Previous simulations of a planet opening a gap in a collisionless debris disk have found that the width of the gap scales as the planet mass to the 2/7th power (alpha=2/7). I find that gap sizes in a collisional disk still obey a power law scaling with planet mass, but that the index alpha of the power law depends on the age of the system $t$ relative to the collisional timescale t_coll of the disk by alpha = 0.32 (t/t_coll)^(-0.04), with inferred planet masses up to five times smaller than those predicted by the classical gap law. The increased gap sizes likely stem from the interaction between collisions and the mean motion resonances near the chaotic zone. I investigate the effects of the initial eccentricity distribution of the disk particles and find a negligible effect on the gap size at Jovian planet masses, since collisions tend to erase memory of the initial particle eccentricity distributions. I also find that the presence of Trojan analogs is a potentially powerful diagnostic of planets in the mass range ~1-10 M_Jup. I apply my model to place new upper limits on planets around Fomalhaut, HR 4796 A, HD 202628, HD 181327, and beta Pictoris.
Finally, to show how SMACK can be used to analyze a single debris disk in detail, I present a new model of the beta Pictoris disk and planet system that, for the first time, combines simulations of the colliding planetesimals and the dynamics of the dust grains, allowing me to model features and asymmetries in both submillimeter and scattered light images of the disk. I combine a 100,000 superparticle SMACK simulation with N-body integrations of the dust produced by the simulated collisions. I find that secular perturbations of the planet's measured inclination and eccentricity can explain the observed warp and planetesimal ring, while collisions between planetesimals shape the disk by eroding close-in material. The complex 3D structure of the disk due to the perturbations from the planet creates an azimuthally asymmetric spatial distribution of collisions, which could contribute to the observed azimuthal clump of CO gas seen with ALMA. My simulations of the small dust grains produced by collisions demonstrate that the "birth ring'' approximation for beta Pictoris fails to account for the ~54% of dust mass produced outside of the planetesimal ring. I also reproduce the gross morphology of high-resolution scattered light images of the disk, including the two-disk "x"-pattern seen in scattered light, which has not been replicated by previous dust dynamics models.
