HVS outer turnaround as a function of the ejection speed, v_ej, in Newtonian gravity with different shapes of the dark matter halo and in QUMOND with γ = 1 and γ = 2; models and symbols are detailed in the inset. The scatter of the points originates from the random initial directions of the HVS ejection velocities. The Newtonian gravitational potential is dominated by the dark matter halo that becomes approximately spherical at large radii and makes the scatter of the points decrease with increasing v_ej. The vertical dotted lines mark the thresholds v_ej = 710 km s⁻¹ for QUMOND with γ = 2 and v_ej = 750 km s⁻¹ for all the other models; the horizontal line marks the minimum galactocentric distance of 15 kpc, appropriate for 4 M_⊙ HVSs. Less massive stars have larger velocity thresholds and larger minimum galactocentric distances.