An official website of the United States government
Abstract Previously we demonstrated that the magnetorotational instability (MRI) grows vigorously in eccentric disks, much as it does in circular disks, and we investigated the nonlinear development of the eccentric MRI without vertical gravity. Here we explore how vertical gravity influences the magnetohydrodynamic (MHD) turbulence stirred by the eccentric MRI. Similar to eccentric disks without vertical gravity, the ratio of Maxwell stress to pressure, or the Shakura–Sunyaevαparameter, remains ∼10−2, and the local sign flip in the Maxwell stress persists. Vertical gravity also introduces two new effects. Strong vertical compression near pericenter amplifies reconnection and dissipation, weakening the magnetic field. Angular momentum transport by MHD stresses broadens the mass distribution over eccentricity at much faster rates than without vertical gravity; as a result, spatial distributions of mass and eccentricity can be substantially modified in just ∼5 to 10 orbits. MHD stresses in the eccentric debris of tidal disruption events may power emission ≳1 yr after disruption.
more »
« less
Nonlinear Evolution of the Magnetorotational Instability in Eccentric Disks
Abstract The magnetorotational instability (MRI) has been extensively studied in circular magnetized disks, and its ability to drive accretion has been demonstrated in a multitude of scenarios. There are reasons to expect eccentric magnetized disks to also exist, but the behavior of the MRI in these disks remains largely uncharted territory. Here we present the first simulations that follow the nonlinear development of the MRI in eccentric disks. We find that the MRI in eccentric disks resembles circular disks in two ways, in the overall level of saturation and in the dependence of the detailed saturated state on magnetic topology. However, in contrast with circular disks, the Maxwell stress in eccentric disks can be negative in some disk sectors, even though the integrated stress is always positive. The angular momentum flux raises the eccentricity of the inner parts of the disk and diminishes the same of the outer parts. Because material accreting onto a black hole from an eccentric orbit possesses more energy than material tracing the innermost stable circular orbit, the radiative efficiency of eccentric disks may be significantly lower than circular disks. This may resolve the “inverse energy problem” seen in many tidal disruption events.
more »
« less
- Award ID(s):
- 2009260
- PAR ID:
- 10444325
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 933
- Issue:
- 1
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 81
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital distances are well-separated. However, instability, which is often associated with significant energy exchange between orbits, takes time to develop. Assuming two massive objects in a circular orbit and a test particle in an eccentric orbit, we develop an analytical formula estimating the time it takes for the test particle’s orbital energy to change by an order of itself. We show its consistency with results from N -body simulations. For eccentric orbits in particular, the instability is primarily driven not by close encounters of the test particle with one of the other bodies, but by the fundamental susceptibility of eccentric orbits to exchange energy at their periapsis. Motivated by recent suggestions that the galactic center may host an intermediate-mass black hole (IMBH) as a companion to the massive black hole Sgr A*, we use our timescale to explore the parameter space that could harbor an IMBH for the lifetime of the S-cluster of stars surrounding Sgr A*. Furthermore, we show that the orbit of an S-star can be stable for long timescales in the presence of other orbital crossing stars, thus suggesting that the S-cluster may be stable for the lifetimes of its member stars.more » « less
-
Abstract Axisymmetric disks of eccentric orbits in near-Keplerian potentials are unstable and undergo exponential growth in inclination. Recently, Zderic et al. showed that an idealized disk then saturates to a lopsided mode. Here we show, using N -body simulations, that this apsidal clustering also occurs in a primordial Scattered Disk in the outer solar system, which includes the orbit-averaged gravitational influence of the giant planets. We explain the dynamics using Lynden-Bell's mechanism for bar formation in galaxies. We also show surface density and line-of-sight velocity plots at different times during the instability, highlighting the formation of concentric circles and spiral arms in velocity space.more » « less
-
ABSTRACT Spirals in protoplanetary discs have been used to locate the potential planet in discs. Since only the spiral shape from a circularly orbiting perturber is known, most previous works assume that the planet is in a circular orbit. We develop a simple semi-analytical method to calculate the shape of the spirals launched by an eccentric planet. We assume that the planet emits wavelets during its orbit, and the wave fronts of these propagating wavelets form the spirals. The resulting spiral shape from this simple method agrees with numerical simulations exceptionally well. The spirals excited by an eccentric planet can detach from the planet, bifurcate, or even cross each other, which are all reproduced by this simple method. The spiral’s bifurcation point corresponds to the wavelet that is emitted when the planet’s radial speed reaches the disc’s sound speed. Multiple spirals can be excited by an eccentric planet (more than five spirals when e ≳ 0.2). The pitch angle and pattern speed are different between different spirals and can vary significantly across one spiral. The spiral wakes launched by high-mass eccentric planets steepen to spiral shocks and the crossing of spiral shocks leads to distorted or broken spirals. With the same mass, a more eccentric planet launches weaker spirals and induces a shallower gap over a long period of time. The observed unusually large/small pitch angles of some spirals, the irregular multiple spirals, and the different pattern speeds between different spirals may suggest the existence of eccentric perturbers in protoplanetary discs.more » « less
-
The free energy of a ternary system, such as a triblock copolymer, is a sum of two parts: an interface energy determined by the size of the interfaces separating the micro-domains of the three constituents, and a long range interaction energy that serves to prevent unlimited micro-domain growth. In two dimensions a parameter range is identified where the system admits stable stationary disk assemblies. Such an assembly consists of perturbed disks made from either type-I constituent or type-II constituent. All the type-I disks have approximately the same radius and all the type-II disks also have approximately the same radius. The locations of the disks are determined by minimization of a function. Depending on the parameters, the disks of the two types can be mixed in an organized way, or mixed in a random way. They can also be fully separated. The first scenario offers a mathematical proof of the existence of a morphological phase for triblock copolymers conjectured by polymer scientists. The last scenario shows that the ternary system is capable of producing two levels of structure. The primary structure is at the microscopic level where disks form near-perfect lattices. The secondary structure is at the macroscopic level forming two large regions, one filled with type-I disks and the other filled with type-II disks. A macroscopic, circular interface separates the two regions.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.3847/1538-4357/ac68f3
