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  • Planes toy models

    Left panel: Number of co-rotating satellite pairs (green line) and counter-rotating satellite pairs (orange line) with \(\alpha {<}35^{\circ}\) as a function of \(\alpha\). Right panel: Fraction of satellite pairs that are co-rotating as a function of \(\alpha\). For hosts with two satellites, there is a significant excess of co-rotating pairs over counter-rotating pairs at small \(\alpha\) (i.e. in satellites that are nearly diametrically opposed to each other). The suggests the possibile presence of coherently rotating planar satellite structures.

    \label{fig:zoom}

    Definition of the opening angle between satellite pairs, \(\alpha\). Each unique satellite pair (here, S1 and S2) has a uniquely defined \(\alpha\).

    \ref{fig:alpha}

    Left panel: Number of co-rotating satellite pairs (green line) and counter-rotating satellite pairs (orange line) as a function of \(\alpha\) over the full \(180^{\circ}\) domain. Right panel: Fraction of satellite pairs that are co-rotating as a function of \(\alpha\). Viewed over this domain, the data seems more consistent with a flat line, which would indicate satellite velocities oriented independently along the line-of-sight and a lack of coherent rotation.

    \label{fig:full}