Notes. Barycentres of the M 81 complex assuming M 81 (first row) and the next three brightest central galaxies (accumulating one galaxy after the other from the second to the fourth row) constrain its position (α_c, δ_c, and the distance, r_c, of the barycentre to us as observers) and its line-of-sight velocity component (v_helc). Uncertainties in the distance (Δr_c) and line-of-sight velocity (Δv_helc) are given by linear propagation of independent uncertainties. The latter only contain measurement imprecisions and no systematic biases due to potential offsets between dark and luminous matter. The last three columns show the three-dimensional distance between r_c and r_{M 81}, the line-of-sight velocity corrected for the sun’s motion in the LG, v_LG, and its uncertainty, Δv_LG. The last row lists the barycentre properties for a varying mass-to-light ratio; see the text.

^* determined from distance uncertainties only, assuming 10% or 20% uncertainty in the L_K, changes in Δr_c remain below the precision given here. Uncertainties in the mass-to-light ratio in the last row, as given by Karachentsev & Kashibadze (2021), were taken into account.

^† determined from distance uncertainties only, assuming 10% uncertainty in the L_K: Δv_helc = [1,7,7,6] km/s, for 20%, we obtain: Δv_helc = [1,13,13,13] km/s, analogously for 10% uncertainty in L_K: Δv_LGc = [10,12,12,12] km/s, for 20%: Δv_LGc = [10,17,16,16] km/s. Including the uncertainties in the mass-to-light ratio in the last row, assuming additional 10% uncertainty in the L_K: Δv_helc = 6 km/s and Δv_LGc = 11 km/s, and for 20%: Δv_helc = 7 km/s and Δv_LGc = 12 km/s.