Table A.1.

Cluster parameters of the synthetic demo clusters. The cluster position was fixed at (−8300,0,0) pc with zero velocity. The inclination (i) was measured from the line of sight. All rotation axes are in the Galactocentric XY plane. The velocity noise is composed of typical internal velocity dispersion in OCs (0.5 km s⁻¹; Choudhuri 2010) and typical errors in the Gaia DR3 observations for a cluster at 300 pc (Gaia Collaboration 2021: RV_error ≈1.3 km s⁻¹; Fabricius et al. 2021: PM_error ≈0.02 km s⁻¹). The meanings of the suffixes are as follows: sb: solid body, dr: differential rotation, vir: virialised, unvir: non-virialised, n: noise included.

Name	i	ω	Apeak	Rpeak	Velocity noise	n_stars
	[°]	[cy Gyr−1]	[km s−1]	[pc]	[km s−1]
Demo clusters in Figure 1
demo_i90_sb	90	40	-	-	0	500
demo_i90_dr_unvir	90	-	2	2	0	500
demo_i90_dr_vir	90	-	2	10	0	500
demo_i90_dr_unvir_n	90	-	2	2	$\sqrt{0.5^2+1.3^2}$	500
demo_i90_dr_vir_n	90	-	2	10	$\sqrt{0.5^2+1.3^2}$	500
Demo clusters in Figure 2
demo_i0_sb	0	40	-	-	0	100
demo_i0_dr_unvir	0	-	2	2	0	100
demo_i0_dr_vir	0	-	2	10	0	100
demo_i0_dr_unvir_n	0	-	2	2	$\sqrt{0.5^2+0.{02}^2}$	100
demo_i0_dr_vir_n	0	-	2	10	$\sqrt{0.5^2+0.{02}^2}$	100