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Table 6

Modeled parameters of the three different mass model approaches. Top – model with Faber-Jackson scaling relation, middle – model with fundamental plane scaling relation and bottom – our final model with explicitly included X-rays gas mass plus fundamental plane scaling relations.

System Δα Δδ ϵ θ a r core r cut σ 0
(′′) (′′) (kpc) (′′) (km s-1)
FJ log(Evidence) = –35.1 rmsFJ = 0.197 ′′
DM 1 8.3 ± 0.3 −2.5 ± 0.8 0.64 ± 0.05 72.0 ± 2.1 117.4 ± 5.9 [1000.0] 884.2 ± 31.9
DM 2 24.2 ± 1.0 28.3 ± 1.2 0.13 ± 0.11 56.6 ± 1.0 127.3 ± 17.1 [1000.0] 840.2 ± 37.5
DM 3 185.9 ± 0.3 50.1 ± 0.1 0.46 ± 0.05 5.2 ± 0.5 47.3 ± 0.9 [1000.0] 795.7 ± 18.9
BCG 1 [0.00] [0.00] [0.26] [43.5] [0.3] 150.0 ± 2.1 255.9 ± 39.3
BCG 2 [24.05] [29.13] [0.20] [37.4] [0.2] 112.2 ± 1.8 201.6 ± 2.4
Gal A [51.94] [48.93] [0.13] [9.9] [0.1] 60.0 ± 0.9 199.3 ± 3.9
Gal B [5.23] [23.01] [0.10] [−49.0] [0.1] 53.3 ± 1.3 105.1 ± 1.6
... ... ... ... [0.1] 48.6 ± 8.5 119.2 ± 5.1
FP log(Evidence) = –34.0 rmsFP = 0.160 ′′
DM 1 8.2 ± 0.3 −2.3 ± 0.7 0.56 ± 0.07 72.4 ± 2.6 125.8 ± 7.0 [1000.0] 938.1 ± 39.0
DM 2 24.8 ± 0.8 27.9 ± 1.0 0.23 ± 0.09 55.4 ± 1.1 133.4 ± 7.6 [1000.0] 847.0 ± 42.0
DM 3 186.0 ± 0.4 50.1 ± 0.1 0.44 ± 0.04 4.8 ± 0.5 50.0 ± 3.0 [1000.0] 815.2 ± 16.8
BCG 1 [0.00] [0.00] [0.26] [43.5] [0.3] 50.5 ± 12.3 201.8 ± 32.0
BCG 2 [24.05] [29.13] [0.20] [37.4] [0.2] 48.8 ± 5.8 212.7 ± 7.2
Gal A [51.94] [48.93] [0.13] [9.9] [0.1] 48.1 ± 10.1 230.5 ± 4.9
Gal B [5.23] [23.01] [0.10] [−49.0] [0.1] 48.5 ± 2.2 117.2 ± 13.1
S FP ... ... ... ... [0.1] 71.1 ± 5.1 1.16 ± 0.14b
FP log(Evidence) = –31.7 rmsFP + X = 0.147 ′′
DM 1 9.6 ± 0.4 −1.6 ± 1.6 0.41 ± 0.06 81.7 ± 3.8 131.2 ± 12.3 [1000.0] 918.6 ± 49.6
DM 2 21.6 ± 1.2 25.6 ± 2.1 0.43 ± 0.07 64.5 ± 1.8 108.5 ± 12.5 [1000.0] 733.0 ± 54.9
DM 3 185.6 ± 0.3 50.1 ± 0.1 0.30 ± 0.02 3.5 ± 0.7 58.9 ± 1.2 [1000.0] 862.2 ± 7.0
BCG 1 [0.00] [0.00] [0.26] [43.5] [0.3] 49.2 ± 5.8 302.3 ± 10.5
BCG 2 [24.05] [29.13] [0.20] [37.4] [0.2] 50.3 ± 7.2 215.5 ± 7.6
Gal A [51.94] [48.93] [0.13] [9.9] [0.1] 49.5 ± 6.8 224.4 ± 5.8
Gal B [5.23] [23.01] [0.10] [−49.0] [0.1] 51.4 ± 7.0 117.5 ± 13.5
SFP ... ... ... ... [0.1] 93.1 ± 59.3 1.19 ± 0.76b

Notes. Values quoted within brackets were kept fixed in the optimization. The error bars correspond to 68% confidence levels. The location and the ellipticity of the matter clumps associated with the cluster galaxies were kept fixed according to the light distribution. The ellipticity ϵ is the one of the mass distribution, expressed as a2−b2/a2 + b2. The center is defined at α = 104.6588589δ = −55.9571863 in J2000 coordinates corresponding to the center of the first BCG.

(a)

Position angle of the potential distribution expressed in degree, 90° relative to PA. It corresponds to the direction of the semi-minor axis of the isopotential counted from the horizontal axis, counterclockwise.

(b)

This is fundamental plane parameter described in Eq. (4), it is a factor S that translates σFP into σdPIE.

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