The evolution of velocity dispersion in the Sco-Cen OB association

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Table 1

Linear fitting results (slope, a, intercept, b) of the speed (v) versus time (t) and radial-motion (v_r) versus distance (r) relations when using three different reference points (see Figs. 4, 5, and B.2).

	Speed–time relation			Radial-motion–distance relation
	v = b + a · t			v_r = b + a · r
	$a = \frac{d v}{d t}$ $Mathematical equation: $a = \frac{dv}{dt}$$	b	b	$a = \frac{d v_{r}}{d r}$ $Mathematical equation: $a = \frac{dv_\mathrm{r}}{dr}$$	b	a⁻¹
Reference Point	[km s⁻¹ Myr⁻¹]	[km s⁻¹]	[pc Myr⁻¹]	[km s⁻¹ pc⁻¹]	[km s⁻¹]	[Myr]
e Lup (20.9 Myr)	${0.45}_{- 0.07}^{+ 0.08}$ $Mathematical equation: $0.45^{+0.08}_{-0.07}$$	${10.55}_{- 0.84}^{+ 0.87}$ $Mathematical equation: $10.55^{+0.87}_{-0.84}$$	10.8±0.9	${0.092}_{- 0.009}^{+ 0.009}$ $Mathematical equation: $0.092^{+0.009}_{-0.009}$$	$- {2.02}_{- 0.60}^{+ 0.56}$ $Mathematical equation: $-2.02^{+0.56}_{-0.60}$$	${10.6}_{- 1.0}^{+ 1.2}$ $Mathematical equation: $10.6^{+1.2}_{-1.0}$$
φ Lup (16.9 Myr)	${0.42}_{- 0.06}^{+ 0.07}$ $Mathematical equation: $0.42^{+0.07}_{-0.06}$$	${9.54}_{- 0.82}^{+ 0.84}$ $Mathematical equation: $9.54^{+0.84}_{-0.82}$$	9.8±0.9	${0.082}_{- 0.010}^{+ 0.010}$ $Mathematical equation: $0.082^{+0.010}_{-0.010}$$	$- {1.31}_{- 0.54}^{+ 0.58}$ $Mathematical equation: $-1.31^{+0.58}_{-0.54}$$	${11.9}_{- 1.3}^{+ 1.6}$ $Mathematical equation: $11.9^{+1.6}_{-1.3}$$
SC15 (>15 Myr)	${0.34}_{- 0.06}^{+ 0.06}$ $Mathematical equation: $0.34^{+0.06}_{-0.06}$$	${8.44}_{- 0.71}^{+ 0.71}$ $Mathematical equation: $8.44^{+0.71}_{-0.71}$$	8.6±0.7	${0.071}_{- 0.010}^{+ 0.011}$ $Mathematical equation: $0.071^{+0.011}_{-0.010}$$	$- {0.91}_{- 0.66}^{+ 0.58}$ $Mathematical equation: $-0.91^{+0.58}_{-0.66}$$	${13.7}_{- 1.8}^{+ 2.4}$ $Mathematical equation: $13.7^{+2.4}_{-1.8}$$

Notes. Col. 1 lists the three chosen reference points, with the cluster age in brackets or the age limit in the case of SC15. The slope of the speed-time relation gives the expansion over time (Col. 2). The intercept of the speed-time relation gives the expansion speed of Sco-Cen at the present day, given in kilometres per second in Col. 3, and converted to parsec per million year in Col. 4. In Col. 7, the inverse of the slope of the radial-motion-distance relation gives the time of the possible onset of the expansion.

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