Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA new inclination instability reshapes Keplerian disks into cones: application to the outer Solar System
118
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between bodies in the disk drive exponential growth of their orbital inclinations and clustering in their angles of pericenter, expanding an initially thin disk into a conical shape by giving each orbit an identical tilt with respect to the disk plane. This new instability dynamically produces the unusual distribution of orbits observed for minor planets beyond Neptune, suggesting that the instability has shaped the outer Solar System. It also implies a large initial disk mass (1-10 Earth masses) of scattered bodies at hundreds of AU; we predict increasing numbers of detections of minor planets clustered in their angles of pericenter with high inclinations.
rate research
Read More
Three-body interactions are ubiquitous in astrophysics. For instance, Kozai-Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly-hierarchical triples also play an important role, but they are less explored. In this work we consider the secular dynamics of a test particle in a mildly-hierarchical configuration. We find the limit within which the secular approximation is reliable, present resonances and chaotic regions using surface of sections, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer solar system. We focus on the distribution of extreme trans-neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet-9), and find that in addition to a low inclination Planet-9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations.
Axisymmetric disks of eccentric Kepler orbits are vulnerable to an instability which causes orbits to exponentially grow in inclination, decrease in eccentricity, and cluster in their angle of pericenter. Geometrically, the disk expands to a cone shape which is asymmetric about the mid-plane. In this paper, we describe how secular gravitational torques between individual orbits drive this inclination instability. We derive growth timescales for a simple two-orbit model using a Gauss $N$-ring code, and generalize our result to larger $N$ systems with $N$-body simulations. We find that two-body relaxation slows the growth of the instability at low $N$ and that angular phase coverage of orbits in the disk is important at higher $N$. As $N to infty$, the e-folding timescale converges to that expected from secular theory.
The magnetorotational instability (MRI) drives vigorous turbulence in a region of protoplanetary disks where the ionization fraction is sufficiently high. It has recently been shown that the electric field induced by the MRI can heat up electrons and thereby affect the ionization balance in the gas. In particular, in a disk where abundant dust grains are present, the electron heating causes a reduction of the electron abundance, thereby preventing further growth of the MRI. By using the nonlinear Ohms law that takes into account electron heating, we investigate where in protoplanetary disks this negative feedback between the MRI and ionization chemistry becomes important. We find that the e-heating zone, the region where the electron heating limits the saturation of the MRI, extends out up to 80 AU in the minimum-mass solar nebula with abundant submicron-sized grains. This region is considerably larger than the conventional dead zone whose radial extent is $sim20$ AU in the same disk model. Scaling arguments show that the MRI turbulence in the e-heating zone should have a significantly lower saturation level. Submicron-sized grains in the e-heating zone are so negatively charged that their collisional growth is unlikely to occur. Our present model neglects ambipolar and Hall diffusion, but our estimate shows that ambipolar diffusion would also affect the MRI in the e-heating zone.
The invariance of the Lagrangian under time translations and rotations in Keplers problem yields the conservation laws related to the energy and angular momentum. Noethers theorem reveals that these same symmetries furnish generalized forms of the first integrals in a special nonconservative case, which approximates various physical models. The system is perturbed by a biparametric acceleration with components along the tangential and normal directions. A similarity transformation reduces the biparametric disturbance to a simpler uniparametric forcing along the velocity vector. The solvability conditions of this new problem are discussed, and closed-form solutions for the integrable cases are provided. Thanks to the conservation of a generalized energy, the orbits are classified as elliptic, parabolic, and hyperbolic. Keplerian orbits appear naturally as particular solutions to the problem. After characterizing the orbits independently, a unified form of the solution is built based on the Weierstrass elliptic functions. The new trajectories involve fundamental curves such as cardioids and logarithmic, sinusoidal, and Cotes spirals. These orbits can represent the motion of particles perturbed by solar radiation pressure, of spacecraft with continuous thrust propulsion, and some instances of Schwarzschild geodesics. Finally, the problem is connected with other known integrable systems in celestial mechanics.
A foundational goal of the Large Synoptic Survey Telescope (LSST) is to map the Solar System small body populations that provide key windows into understanding of its formation and evolution. This is especially true of the populations of the Outer Solar System -- objects at the orbit of Neptune $r > 30$AU and beyond. In this whitepaper, we propose a minimal change to the LSST cadence that can greatly enhance LSSTs ability to discover faint distant Solar System objects across the entire wide-fast-deep (WFD) survey area. Specifically, we propose that the WFD cadence be constrained so as to deliver least one sequence of $gtrsim 10$ visits per year taken in a $sim 10$ day period in any combination of $g, r$, and $i$ bands. Combined with advanced shift-and-stack algorithms (Whidden et al. 2019) this modification would enable a nearly complete census of the outer Solar System to $sim 25.5$ magnitude, yielding $4-8$x more KBO discoveries than with single-epoch baseline, and enabling rapid identification and follow-up of unusual distant Solar System objects in $gtrsim 5$x greater volume of space. These increases would enhance the science cases discussed in Schwamb et al. (2018) whitepaper, including probing Neptunes past migration history as well as discovering hypothesized planet(s) beyond the orbit of Neptune (or at least placing significant constraints on their existence).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
