skip to main content

Title: Eccentricity evolution in gaseous dynamical friction

We analyse how drag forces modify the orbits of objects moving through extended gaseous distributions. We consider how hydrodynamic (surface area) drag forces and dynamical friction (gravitational) drag forces drive the evolution of orbital eccentricity. While hydrodynamic drag forces cause eccentric orbits to become more circular, dynamical friction drag can cause orbits to become more eccentric. We develop a semi-analytic model that accurately predicts these changes by comparing the total work and torque applied to the orbit at periapse and apoapse. We use a toy model of a radial power-law density profile, ρ ∝ r−γ, to determine that there is a critical γ = 3 power index, which separates the eccentricity evolution in dynamical friction: orbits become more eccentric for γ < 3 and circularize for γ > 3. We apply these findings to the infall of a Jupiter-like planet into the envelope of its host star. The hydrostatic envelopes of stars are defined by steep density gradients near the limb and shallower gradients in the interior. Under the influence of gaseous dynamical friction, an infalling object’s orbit will first decrease in eccentricity and then increase. The critical separation that delineates these regimes is predicted by the local density slope and is more » linearly dependent on polytropic index. More broadly, our findings indicate that binary systems may routinely emerge from common envelope phases with non-zero eccentricities that were excited by the dynamical friction forces that drove their orbital tightening.

« less
; ;
Award ID(s):
Publication Date:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range or eLocation-ID:
p. 5465-5473
Oxford University Press
Sponsoring Org:
National Science Foundation
More Like this
  1. ABSTRACT Tidal dissipation due to turbulent viscosity in the convective regions of giant stars plays an important role in shaping the orbits of pre-common-envelope systems. Such systems are possible sources of transients and close compact binary systems that will eventually merge and produce detectable gravitational wave signals. Most previous studies of the onset of common envelope episodes have focused on circular orbits and synchronously rotating donor stars under the assumption that tidal dissipation can quickly spin-up the primary and circularize the orbit before the binary reaches Roche lobe overflow (RLO). We test this assumption by coupling numerical models of the post-main-sequence stellar evolution of massive stars with the model for tidal dissipation in convective envelopes developed in Vick & Lai – a tidal model that is accurate even for highly eccentric orbits with small pericentre distances. We find that, in many cases, tidal dissipation does not circularize the orbit before RLO. For a $10\, {\rm M}_{\odot }$ ($15\, {\rm M}_{\odot }$) primary star interacting with a $1.4\, {\rm M}_{\odot }$ companion, systems with pericentre distances within 3 au (6 au) when the primary leaves the main sequence will retain the initial orbital eccentricity when the primary grows to the Roche radius. Even inmore »systems that tidally circularize before RLO, the donor star may be rotating subsynchronously at the onset of mass transfer. Our results demonstrate that some possible precursors to double neutron star systems are likely eccentric at the Roche radius. The effects of pre-common-envelope eccentricity on the resulting compact binary merit further study.« less
  2. Abstract Highly eccentric orbits are one of the major surprises of exoplanets relative to the solar system and indicate rich and tumultuous dynamical histories. One system of particular interest is Kepler-1656, which hosts a sub-Jovian planet with an eccentricity of 0.8. Sufficiently eccentric orbits will shrink in the semimajor axis due to tidal dissipation of orbital energy during periastron passage. Here our goal was to assess whether Kepler-1656b is currently undergoing such high-eccentricity migration, and to further understand the system’s origins and architecture. We confirm a second planet in the system with M c = 0.40 ± 0.09 M jup and P c = 1919 ± 27 days. We simulated the dynamical evolution of planet b in the presence of planet c and find a variety of possible outcomes for the system, such as tidal migration and engulfment. The system is consistent with an in situ dynamical origin of planet b followed by subsequent eccentric Kozai–Lidov perturbations that excite Kepler-1656b’s eccentricity gently, i.e., without initiating tidal migration. Thus, despite its high eccentricity, we find no evidence that planet b is or has migrated through the high-eccentricity channel. Finally, we predict the outer orbit to be mutually inclined in a nearlymore »perpendicular configuration with respect to the inner planet orbit based on the outcomes of our simulations and make observable predictions for the inner planet’s spin–orbit angle. Our methodology can be applied to other eccentric or tidally locked planets to constrain their origins, orbital configurations, and properties of a potential companion.« less
  3. ABSTRACT We examine massive black hole (MBH) mergers and their associated gravitational wave signals from the large-volume cosmological simulation Astrid . Astrid includes galaxy formation and black hole models recently updated with an MBH seed population between 3 × 104h−1M⊙ and 3 × 105h−1M⊙ and a sub-grid dynamical friction (DF) model to follow the MBH dynamics down to 1.5 ckpc h−1. We calculate the initial eccentricities of MBH orbits directly from the simulation at kpc-scales, and find orbital eccentricities above 0.7 for most MBH pairs before the numerical merger. After approximating unresolved evolution on scales below ${\sim 200\, \text{pc}}$, we find that the in-simulation DF on large scales accounts for more than half of the total orbital decay time ($\sim 500\, \text{Myr}$) due to DF. The binary hardening time is an order of magnitude longer than the DF time, especially for the seed-mass binaries (MBH < 2Mseed). As a result, only $\lesssim 20{{\rm per \,cent}}$ of seed MBH pairs merge at z > 3 after considering both unresolved DF evolution and binary hardening. These z > 3 seed-mass mergers are hosted in a biased population of galaxies with the highest stellar masses of $\gt 10^9\, {\rm M}_\odot$. With the higher initial eccentricity prediction from Astrid , we estimate anmore »expected merger rate of 0.3−0.7 per year from the z > 3 MBH population. This is a factor of ∼7 higher than the prediction using the circular orbit assumption. The Laser Interferometer Space Antenna events are expected at a similar rate, and comprise $\gtrsim 60\,{\rm{per\,cent}}$ seed-seed mergers, $\sim 30\,{\rm{per\,cent}}$ involving only one seed-mass MBH, and $\sim 10\,{\rm{per\,cent}}$ mergers of non-seed MBHs.« less
  4. ABSTRACT Common envelope (CE) evolution is a critical but still poorly understood progenitor phase of many high-energy astrophysical phenomena. Although 3D global hydrodynamic CE simulations have become more common in recent years, those involving an asymptotic giant branch (AGB) primary are scarce, due to the high computational cost from the larger dynamical range compared to red giant branch (RGB) primaries. But CE evolution with AGB progenitors is desirable to simulate because such events are the likely progenitors of most bi-polar planetary nebulae (PNe), and prominent observational testing grounds for CE physics. Here we present a high-resolution global simulation of CE evolution involving an AGB primary and 1-$\mathrm{M_\odot }$ secondary, evolved for 20 orbital revolutions. During the last 16 of these orbits, the envelope unbinds at an almost constant rate of about 0.1–$0.2\, \mathrm{M_\odot \, yr^{-1}}$. If this rate were maintained, the envelope would be unbound in less than $10\, {\rm yr}$. The dominant source of this unbinding is consistent with inspiral; we assess the influence of the ambient medium to be subdominant. We compare this run with a previous run that used an RGB phase primary evolved from the same 2-$\mathrm{M_\odot }$ main-sequence star to assess the influence of themore »evolutionary state of the primary. When scaled appropriately, the two runs are quite similar, but with some important differences.« less
  5. Abstract

    We examine the origin of dynamical friction using a nonperturbative, orbit-based approach. Unlike the standard perturbative approach, in which dynamical friction arises from the LBK torque due to pure resonances, this alternative, complementary view nicely illustrates how a massive perturber significantly changes the energies and angular momenta of field particles on near-resonant orbits, with friction arising from an imbalance between particles that gain energy and those that lose energy. We treat dynamical friction in a spherical host system as a restricted three-body problem. This treatment is applicable in the “slow” regime, in which the perturber sinks slowly and the standard perturbative framework fails due to the onset of nonlinearities. Hence, it is especially suited to investigate the origin of core-stalling: the cessation of dynamical friction in central constant-density cores. We identify three different families of near-corotation-resonant orbits that dominate the contribution to dynamical friction. Their relative contribution is governed by the Lagrange points (fixed points in the corotating frame). In particular, one of the three families, which we call Pac-Man orbits because of their appearance in the corotating frame, is unique to cored density distributions. When the perturber reaches a central core, a bifurcation of the Lagrange points drasticallymore »changes the orbital makeup, with Pac-Man orbits becoming dominant. In addition, due to relatively small gradients in the distribution function inside a core, the net torque from these Pac-Man orbits becomes positive (enhancing), thereby effectuating a dynamical buoyancy. We argue that core-stalling occurs where this buoyancy is balanced by friction.

    « less