On the orbital evolution of binaries with polar circumbinary disks

TL;DR

The paper addresses how a polar circumbinary disk influences the orbital evolution of an eccentric binary. It employs 3D Smoothed Particle Hydrodynamics simulations (PHANTOM) with mass injection to explore a parameter space including $e_{ m b}$, $q_{ m b}$, and $R_{ m acc}$, treating the disk as polar to the binary plane and allowing back-reaction after reaching a steady state. The main finding is robust: all modeled systems experience binary shrinkage, with rates typically larger than those for aligned or retrograde disks of comparable disk mass and viscosity; unequal-mass cases can form a long-lived circumprimary disk, and the overall results hold across variations in $e_{ m b}$ and $R_{ m acc}$, though ZKL oscillations in CPDs are not clearly observed under the chosen resolution and viscosity. These results have broad implications, including potential polar-planet formation in young polar disks and enhanced SMBH binary mergers in galactic centers, highlighting polar CBDs as a significant channel in binary evolution models.

Abstract

Binaries occur in many astrophysical systems, from young protostellar binaries in star forming regions to supermassive black hole binaries in galaxy centers. In many cases, a circumbinary disk of gas forms around the binary with an orbit that may be misaligned to the binary plane. Misaligned disks around nearly circular binaries evolve into disks that are either aligned or counteraligned with the binary orbit. However, if the binary is sufficiently eccentric, then it can be more likely that the disk ends up in a polar-aligned configuration in which the disk angular momentum vector aligns with the binary eccentricity vector. We use Smoothed Particle Hydrodynamics simulations, evolved to an approximate steady state under mass injection, to determine the orbital evolution of a binary with a polar-aligned disk for a range of binary-disk parameters. We find that, in all of the cases we have simulated, the binary shrinks with time. The decay rate is larger than for binaries surrounded by aligned or retrograde disks with matched disk parameters. The rate of shrinkage is largely unaltered by the size of the sink radii employed for the binary stars, but for small enough sink radii some of the models exhibit long-lived polar circumprimary disks, which are continually fed mass from the circumbinary disk. We discuss our results in the contexts of planet formation in young polar-aligned disks and merging supermassive black holes in galaxy centers.

Figures (8)

• Figure 1: Column density plots for the models A (top panels), B (middle panels) and C (lower panels) in the $y$-$z$ plane and the $x$-$z$ plane. The disks are shown once they have reached a steady state. Red circles mark the binary locations, with sizes equal to the accretion radii for each star. The unit of the axis is $a_{\rm b}$, and the color bars are the same for all of the panels with the density in arbitrary units.
• Figure 2: The semi-major axis and the eccentricity of the binary with time measured in binary orbits, $T_{\rm b}$, of models A -- D after we turn on the live binary. The blue, yellow, green and red lines represent models A, B, C and D, respectively. The left panels show cases with $R_{\rm acc} = 0.4 a_{\rm b}$ and the right panels show cases with smaller $R_{\rm acc}$.
• Figure 3: Same as Fig. \ref{['fig:1']} except $R_{\rm acc}=0.025\ a_{\rm b}$.
• Figure 4: Column density plots for model D with $R_{\rm acc}$ = 0.4 $a_{\rm b}$ (top panels) and $0.1\times R_{\rm RL}$ (lower panel) as they reach the steady state. Two red circles represent the location of the binary stars (sink particles) with sizes equal to the size of the accretion radius of each star. The unit of the axis is $a_{\rm b}$ and the color bars are the same for all of the panels with the density in arbitrary units.
• Figure 5: The time evolution of the test particle's $e_{\rm p}$ (top panel) and $i_{\rm p}$ (lower panel) around the CPD with the same binary parameters to model D.