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Table 5.

Estimates of various timescales and their ratios.

Source Cooling time/Free-fall time Cooling time/Eddy turnover time


σ* Rmin tcool/tff Length amaj σv teddy tcool/teddy
(km s−1) (kpc) [at Rmin] (kpc) (kpc) (km s−1) (108 yr)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
M 87 189 (e) 3.8 19.5 ± 1.0 3.8 0.7–1.1 153 ± 11 1.62 1.64 ± 0.57
Centaurus 254 (a) 6.0 15.7 ± 1.0 6 1.2–2.9 127 ± 10 2.88 1.10 ± 0.69
Abell 262 189 (d) 3.8 21.2 ± 1.3 3.9 3.7–4.2 110 ± 10 1.34 1.50 ± 0.90
Abell 3581 195 (d) 16.2 17.5 ± 1.8 14 3–4.2 104 ± 8 7.01 1.30 ± 0.84
2A0335+096 220 (d) 21.2 8.0 ± 1.0 18 6.3–9.6 183 ± 3 6.16 0.80 ± 0.86
Hydra-A 237 (d) 18.4 16.5 ± 1.0 20 15.3–16.4 142 ± 4 9.65 1.08 ± 0.88
Abell S1101 219 (c) 30.0 13.5 ± 0.9 38 6.2–20.5 158 ± 10 14.21 0.90 ± 0.90
Abell 1795 221 (c) 20.1 17.8 ± 1.8 54 18.5 151 ± 10 19.33 1.40 ± 0.93
RXJ1539.5 242 (b) 44.4 16.8 ± 2.9 50
Abell 2597 218 (d) 25.0 12.0 ± 1.0 23 3.1–14.0 175 ± 15 11.28 0.89 ± 0.53
PKS 0745−191 290 (d) 14.0 10.0 ± 1.0 34 9.9–11.6 196 ± 10 7.09 0.84 ± 0.85
RXJ0821+0752 247 (d)
Abell 1664 267 (d) 39.4 18.3 ± 1.9 61
Abell 1835 486 (d) 28.0 12.6 ± 1.7 45 5.8–16.9 120 ± 4 21.51 0.63 ± 0.66
Phoenix-A

Notes. (1) Source name. (2) Stellar velocity dispersions of the galaxies. The references are indicated by the superscript by each value and the corresponding references are: (a)Bernardi et al. (2002); (b)Hamer et al. (2016); (c)Hogan et al. (2017); (d)Pulido et al. (2018); (e)Smith et al. (1990). (3) Radius of the minimum of tcool/tff. (4) Ratio between tcool and tff at Rmin. (5) Maximum radial extent of the filaments, measured from MUSE Hα maps or [CII] for M 87 (Werner et al. 2014). (6) Half of the value of the injection scale, i.e., X-ray major axis of the cavities taken from the literature (Shin et al. 2016; Bîrzan et al. 2004). (7) Velocity dispersion of the warm or cold phase. For Centaurus, Abell S1101, PKS 0745−191, Hydra-A, 2A0335+096, Abell 1795, Abell 3581, Abell 1664 and Abell 1835 we used Hα emission lines. For Abell 2597 we used HI broad absorption lines from ALMA and VLBA observations taken from Gaspari et al. (2018). For Abell 262 we used CO(3-2) ALMA observations. For M 87 we used [CII] from Herschel (Werner et al. 2013). (8) Eddy turnover time estimated using the Eq. (5). (9) Condensation time, i.e., the ratio of the cooling time over the eddy turnover time at maximum projected radial extension of the filaments (Gaspari et al. 2018).

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