On the shape of the spectrum of cosmic rays accelerated inside superbubbles

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Table 1:

Physical parameters for well observed massive-star forming regions in the Galaxy and in the LMC.
		Cluster			Superbubble		$\theta_{\star}$ ^d
Name	$N_{\star }$ ^a	Age	Distance	Size^b	Size^b	Density^c	$B=1~\mu\rm {G}$	$B=1~\mu\rm {G}$	$B=10~\mu\rm {G}$	$B=10~\mu\rm {G}$
		(Myr)	(kpc)	(pc)	(pc)	( $\rm cm^{-3}$ )	q=5/3	q=3/2	q=5/3	q=3/2
Cygnus OB1/3	38⁽¹⁶⁾	2-6⁽¹²⁾	1.8⁽¹⁹⁾	24	80-100⁽¹⁴⁾	0.01?	$5\times 10^4$	$4\times 10^2$	$4\times 10^{0}$	$2\times 10^{-2}$
							$5\times 10^5$	$3\times 10^3$	$4\times 10^{1}$	$1\times 10^{-1}$
Cygnus OB2	750⁽⁵⁾	3-4⁽¹²⁾	1.4-1.7⁽¹⁰⁾	60⁽¹¹⁾	450?⁽⁵⁾	0.02⁽⁵⁾	$2\times 10^4$	$9\times 10^1$	$1\times 10^0$	$4\times 10^{-3}$
							$2\times 10^5$	$7\times 10^2$	$2\times 10^1$	$3\times 10^{-2}$
Orion OB1	30-100⁽³⁾	12⁽²⁾	0.45⁽²⁾	10⁽²⁾	$140\times 300$ ⁽³⁾	0.02-0.03⁽⁴⁾	$3\times 10^3$	$4\times 10^{1}$	$3\times 10^{-1}$	$1\times 10^{-3}$
							$2\times 10^6$	$7\times 10^3$	$2\times 10^2$	$3\times 10^{-1}$
Carina nebula	?	3⁽²³⁾	2.3⁽⁸⁾	20	110⁽²³⁾	0.01?	$2\times 10^4$	$1\times 10^2$	$1\times 10^0$	$5\times 10^{-3}$
							$2\times 10^6$	$7\times 10^3$	$1\times 10^2$	$3\times 10^{-1}$
Westerlund 1	450⁽¹⁾	3.3⁽¹⁾	3.9⁽¹³⁾	1⁽¹⁾	40?⁽¹³⁾	0.01?	$2\times 10^3$	$5\times 10^1$	$2\times 10^{-1}$	$2\times 10^{-3}$
						$3\times 10^6$	$2\times 10^4$	$3\times 10^2$	$8\times 10^{-1}$
Westerlund 2	14⁽²¹⁾	2⁽²¹⁾	8⁽²¹⁾	1⁽⁶⁾	100^(21,6)	0.0015⁽²⁴⁾	$1\times 10^2$	$2\times 10^0$	$9\times 10^{-3}$	$1\times 10^{-4}$
							$5\times 10^4$	$2\times 10^2$	$4\times 10^{0}$	$1\times 10^{-2}$
DEM L192	135	3⁽²⁰⁾	50	60⁽²⁰⁾	$120 \times135$ ⁽⁹⁾	0.03⁽⁷⁾	$3\times 10^5$	$2\times 10^3$	$2\times 10^1$	$6\times 10^{-2}$
							$1\times 10^6$	$4\times 10^3$	$9\times 10^1$	$2\times 10^{-1}$
30 Doradus	>400⁽²²⁾	2⁽¹⁷⁾	50	40⁽²⁵⁾	200⁽²⁵⁾	0.09⁽²⁷⁾	$2\times 10^5$	$1\times 10^3$	$2\times 10^1$	$6\times 10^{-2}$
							$2\times 10^6$	$7\times 10^3$	$2\times 10^2$	$3\times 10^{-1}$
N11	130	5⁽²⁶⁾	50	$15\times 30$ ⁽¹⁸⁾	$100\times 150^{(9)}$	0.08⁽¹⁵⁾	$9\times 10^4$	$9\times 10^2$	$8\times 10^0$	$3\times 10^{-2}$
							$4\times 10^6$	$2\times 10^4$	$4\times 10^2$	$8\times 10^{-1}$

Notes. ^(a) $N_{\star }$ is the number of stars with mass $\ge$ $8~M_{\odot}$ (a Salpeter IMF has been assumed, expected for N11 where an index of 2.4 has been used). ^(b) Sizes are either the diameter if the region is spherical, or the large and small semi-axis if the region is ellipsoidal. ^(c) The density is the Hydrogen nuclei density. ^(d) Estimates of $\theta_{\star}$ are calculated from Eq. (25), as explained in Sect. 4.1. The range of values of $\theta_{\star}$ given for each object and for each magnetic configuration reflects uncertainties in the actual values of bubble density, accelerator size and turbulence scale.

References. (1) Brandner et al. (2008); (2) Brown et al. (1994); (3) Brown et al. (1995); (4) Burrows et al. (1993); (5) Cash et al. (1980); (6) Conti & Crowther (2004); (7) Cooper et al. (2004); (8) Davidson & Humphreys (1997); (9) Dunne et al. (2001); (10) Hanson (2003); (11) Knödlseder (2000); (12) Knödlseder et al. (2002); (13) Kothes & Dougherty (2007); (14) Lozinskaya et al. (1998); (15) Maddox et al. (2009); (16) Massey et al. (1995); (17) Massey & Hunter (1998); (18) Nazé et al. (2004); (19) Nichols-Bohlin & Fesen (1993); (20) Oey & Smedley (1998); (21) Rauw et al. (2007); (22) Selman et al. (1999); (23) Smith et al. (2000); (24) Tsujimoto et al. (2007); (25) Walborn (1991); (26) Walborn & Parker (1992); (27) Wang & Helfand (1991).

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