tokens: quantities ( α , δ , , μ δ , D (SpT), v rad ) by adopting their uncertainties and relevant correlations. We drew 10 000 initial conditions, which were evolved for 10 Gyr in the future and traced back in the past for a sufficiently long time (i.e., up to τ evo ). For each star, we note the rest-frame velocity, v rf , the past and future Galactic Cartesian coordinates, and the corresponding velocity components. We estimated the escape probability from the Milky Way, P esc , for each star as the fraction of initial conditions where ( v rf − v esc ) > 0. We determined the vertical component of the angular momentum, L Z , which indicates the direction towards which the star has been ejected. We also numerically estimated the eccentricity, e , the median orbital apocenter and pericenter, R apo and R peri , and the maximum vertical displacement, Z max . The most recent Galactic plane crossings, R ( Z = 0), were recorded and used to determine the flight time from such locations, τ flight . The ejection velocity, v ej , was determined as the velocity possessed by the star at R ( Z = 0), which was corrected for the solar motion and the Galactic rotation. Table 5 lists the relevant orbital quantities for the 12 MS runaway candidates in a Galactocentric reference system that is left-handed, that is, with the x - and y -axis pointing, respectively, from the Milky Way’s center towards the Sun and along the direction of the Galactic rotation. Table 5. Orbital parameters of our MS candidates. Notes. The meaning of the columns from left to right is as follows: current X Y Z Galactocentric Cartesian coordinates, vertical component of Galactocentric rest-frame velocity, Galactocentric rest-frame velocity, escape probability, orbit eccentricity, vertical component of the angular momentum, median pericenter and apocenter, maximum vertical displacement from the plane, Galactocentric radius at the most recent intersection of past trajectories with the Z = 0 plane, ejection velocity from Z = 0, and flight time from Z = 0. 6. Properties of the runaway candidates 6.1. Orbit analysis As expected for nearby runaway MS stars, all but one candidate are bound to the Milky Way’s potential, since they have v rf that is on average two times smaller than v esc at their Galactic coordinates. The only exception is 2207−4329 that has an escape probability of P esc = 0.4, which is defined as the fraction of simulated trajectories with v rest > v esc . Due to our selection cut of v tan > 150 km s −1 (Eq. ( 1 )), all stars in our sample (both the MS and BHB candidates) ended up having | v rad |≲ v tan within the error bars. Three stars, 2034−5307, 2207−4329, and 2259−4931, have the largest v tan ≳ 450 km s −1 of all MS candidates. This unusual feature can also be noted in the Toomre diagram of Fig. 11 , where the three stars have large negative Galactic Cartesian V components (i.e., they lag behind the Milky Way’s rotation), as it is more typically seen for the majority of BHB
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