We study the dynamical interaction in which the two single runaway stars AE~ { } Aurig \ae and \mu \thinspace Columb \ae and the binary \iota \thinspace Orionis acquired their unusually high space velocity .
The two single runaways move in almost opposite directions with a velocity greater than 100 { \thinspace km s ^ { -1 } } away from the Trapezium cluster .
The star \iota \thinspace Orionis is an eccentric ( e \simeq 0.8 ) binary moving with a velocity of about 10 { \thinspace km s ^ { -1 } } at almost right angles with respect to the two single stars .
The kinematic properties of the system suggest that a strong dynamical encounter occurred in the Trapezium cluster about 2.5 \thinspace Myr ago .
Curiously enough , the two binary components have similar spectral type but very different masses , indicating that their ages must be quite different .
This observation leads to the hypothesis that an exchange interaction occurred in which an older star was swapped into the original \iota \thinspace Orionis binary .
We test this hypothesis by a combination of numerical and theoretical techniques , using N-body simulations to constrain the dynamical encounter , binary evolution calculations to constrain the high orbital eccentricity of \iota \thinspace Orionis and stellar evolution calculations to constrain the age discrepancy of the two binary components .
We find that an encounter between two low eccentricity ( 0.4 { \thinspace \hbox to 0.0 pt { \raise 2.15 pt \hbox { $ \scriptstyle { < } $ } } { \lower 1.2 % 9 pt \hbox { $ \scriptstyle { \sim } $ } } \thinspace } e { \thinspace \hbox to 0.0 pt { \raise 2. % 15 pt \hbox { $ \scriptstyle { < } $ } } { \lower 1.29 pt \hbox { $ \scriptstyle { \sim } $ } } % \thinspace } 0.6 ) binaries with comparable binding energy , leading to an exchange and the ionization of the wider binary , provides a reasonable solution to this problem .