Mutual Orbit Alignment in Resolved Triple Systems

TL;DR

This study analyzes mutual orbital alignment in 278 resolved triple systems with outer separations $<\sim 300$ au, using relative-motion measurements and sign-correlation diagnostics to infer the average mutual inclination when full orbital solutions are unavailable. It finds that orbital alignment strengthens for closer, more compact hierarchies and for lower-mass primaries, with an average mutual inclination around $40^\circ$ for the full sample and ~ $10^\circ$ in a low-mass, tight subset; inner eccentricities are typically smaller in aligned systems. A second sample of 371 hierarchies with outer orbits and inner eclipsing subsystems shows only $\sim 22\%$ alignment within $\sim 20^\circ$, indicating a predominantly random orientation for many compact systems as well. The results support a qualitative two-regime formation framework: gas-dominated accretion and migration imprint alignment at small separations, while N-body dynamics dominate at larger scales; fragmentation of isolated cores appears to produce predominantly aligned, low-mass hierarchies. The work highlights the role of mass, separation, and dynamical history in shaping hierarchical architectures and motivates targeted simulations and extended surveys.

Abstract

A sample of 278 triple systems with outer separations under 300 au and resolved inner pairs is studied, focusing on the mutual alignment between inner and outer orbits. The degree of alignment increases with (i) decreasing outer separation, (ii) decreasing ratio of outer and inner separations, (iii) decreasing mass of the inner primary component, and (iv) increasing inner mass ratio. There is no dependence on the outer mass ratio. The average mutual inclination is ~40deg for the full sample and ~10deg for 38 triples with primary components less massive than 1 solar and outer separations below 50 au. Inner eccentricities in aligned triples are smaller compared to misaligned ones. In another sample of 371 hierarchies with known outer orbits and inner eclipsing subsystems, only 22% show mutual alignment within 20deg, while the rest are aligned randomly. These findings match qualitatively current understanding of the formation of hierarchical systems, where the N-body dynamics dominates at large scales, while the accretion and migration shape systems closer than $\sim$100 au. Fragmentation of isolated cores apparently produces approximately aligned low-mass hierarchies.

Figures (9)

• Figure 1: Observed orbital motions in the low-mass triple system 00247$-$2653 (LHS 1070) are approximated by two Keplerian orbits, highlighting the decade of monitoring at SOAR. The positions of the inner pair B,C are plotted by magenta triangles, and the positions of A,B by green squares. The solid line shows the outer orbit with wobble, the dashed line is the outer orbit of the center of mass BC around A.
• Figure 2: Relative motions in a triple system of hierarchy AB--C (section \ref{['sec:meth']}). AB is the center of mass of the inner subsystem A,B. Blue arrows indicate the motion directions. The angle between the radius-vector joing the components and the motion direction is $\gamma$.
• Figure 3: Observed relative motions in three selected low-mass triples. The coordinate origin is marked by a large asterisk. Relative positions of the inner and outer pairs are plotted by solid lines, with the times of the first and last observations indicated. The brown numbers are component's masses. The outer positions refer to the center of mass of the inner pair. The first positions of the inner and outer pairs are marked by the square and triangle, respectively. The inserts show the speckle images of these triples from the latest observations at SOAR. In 06460$-$6624, the observed part of the 11.7 yr inner orbit of B,C is plotted; note the opposite motion sense of the inner and outer pairs in this triple.
• Figure 4: Top: periods of the inner and outer subsystems in multiple stars. Small blue crosses denote hierarchies within 200 pc with primary masses less than 1.5 $M_\odot$ . Large red symbols mark our sample of triples with (asterisks) or without (squares) known orbits. The thin red line denotes the imposed limits on periods, and the thick solid diagonal line plots the nominal dynamical stability criterion $P_{\rm out}/P_{\rm in} > 4.7$Mardling2001. Bottom: comparison between mass ratios in the inner and outer subsystems of our sample (squares). In 106 triples located to the right of the line, the tertiary is the most massive star.
• Figure 5: Top: comparison of the cosines of inner and outer orbital inclinations for 76 triples where both orbits are known. Middle: the angle $\gamma$ in the outer pair vs. inclination of the inner orbit for 85 triples; the dotted line is $90^\circ \cos i_{\rm in}$. In both plots, red asterisks mark systems with inner primary mass below 0.8 $M_\odot$ . Bottom: position angle of the outer pair vs. position angle of the inner pair for edge-on inner orbits; both angles are folded in the $(0,90\degr)$ interval. Squares and asterisks plot the nodal angles of 16 pairs with known outer orbits and the position angles of 14 outer companions with linear models, respectively.