The relation for planetary nebulae | Astronomy & Astrophysics (A&A)

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Table 1:

The results of the $\Sigma -D$ and L-D fits.
No.	Sample^a	$\beta_{_{\Sigma - D}}^b$	$r_{_{\Sigma- D}}^b$	$\alpha_{_{L-D}}^b$	r_{_L-D}^b	N^b
01	SSV d<1.0	$2.61\pm0.21$	-0.97	00.61 $\pm$ 0.21	-0.67	013
02	SSV $1.0\leq d < 2.0$	$1.89 \pm 0.43$	-0.78	- $0.11\pm0.43$	00.08	015
03	SSV $d\geq2.0$	$3.96\pm0.62$	-0.91	01.97 $\pm$ 0.61	-0.73	011
04	SSV	2.56 $\pm$ 0.22	-0.89	00.56 $\pm$ 0.22	-0.40	039
05	SSV + Ph02 $d\leq0.4$	$1.47\pm0.40$	-0.74	- $0.53\pm0.40$	00.38	013
06	SSV + Ph02 $0.4<d\leq0.6$	$2.18\pm0.22$	-0.91	00.18 $\pm$ 0.22	-0.17	023
07	SSV + Ph02 $0.6<d\leq1.0$	$2.37\pm0.20$	-0.95	00.37 $\pm$ 0.20	-0.43	018
08	SSV + Ph02 $1.0<d\leq2.0$	$2.64\pm0.40$	-0.88	00.64 $\pm$ 0.40	-0.41	015
09	SSV + Ph02 d>2.0	$4.44\pm$ 0.47	-0.96	02.44 $\pm$ 0.47	-0.90	009
10	SSV + Ph02	$2.40\pm0.17$	-0.86	00.40 $\pm$ 0.17	-0.27	078
11	SSV + Ph02 $d\leq0.4$ $\dag$	$2.31\pm0.38$	-0.90	00.31 $\pm$ 0.38	-0.26	011
12	SSV + Ph02 $0.4<d\leq0.6$ $\dag$	$2.33\pm0.15$	-0.96	00.33 $\pm$ 0.15	-0.44	022
13	SSV + Ph02 $\dag$	$2.57\pm0.14$	-0.92	00.57 $\pm0.14$	-0.45	075
14	B&L	$2.31 \pm 0.11$	-0.90	00.31 $\pm0.11$	-0.26	109
15	Zhang (1995)	$2.17 \pm0.14$	-0.80	00.17 $\pm0.14$	-0.10	132
16	Van de Steene & Zijlstra (1995)	$2.41 \pm 0.34$	-0.84	00.41 $\pm0.34$	-0.26	023
17	Van de Steene & Zijlstra (1995)	$2.24 \pm 0.09$	-0.92	00.24 $\pm0.09$	-0.24	132
18	Van de Steene & Zijlstra (1995) (stronger criteria by B&L)	$2.21\pm0.09$	-0.94	00.21 $\pm0.09$	-0.25	088

^a SSV stands for Stanghellini et al. 2008, B&L for Bensby & Lundström (2001) and Ph02 for Phillips (2002). PNe from Ph02 are included in the sample sets (5-13) as additional, if they were not extracted by the SSV in their sample; d<1 denotes that a set of PNe have distances less than 1 kpc, $1\leq d < 2$ , between 1 and 2 kpc, etc.; ^b the parameters of the fit ( $\beta$ and $\alpha$ , respectively) and the correlation coefficient r are given for each sample. The number of PNe in the sample is given in the last column (N); $\dag$ - 3 PNe (He 1-5, HDW 6 and HaWe 5) are removed (see text).

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