Astronomy & Astrophysics

All Tables

Table 1: The radius at the center of the last radial bin considered in the temperature fits and the best-fit parameters from fitting Eqs. (1) and (2) to the data ( $1\sigma$ errors in parenthesis). Here, $\mu =2$ in Eq. (1) is used and, for both fitting functions, T(r=0) is set equal to the temperature of the central bin.
Table 2: The radius at the center of the last radial bin considered in the gas density fits and the best-fit parameters from fitting Eq. (3) to the data ( $1\sigma$ errors in parenthesis).
Table 3: Cooling radius $R_{{\rm cool}}$ and the results for the effervescent heating model with no mass dropout ( $\dot M=0$ ). For each model, i.e. for a fixed conduction efficiency $0<f_{{\rm c}}< 1/3$ , the extra heating curve H derived from Eqs. (4)-(6) is fitted using Eq. (11) over the radial range $0<r<R_{{\rm cool}}$ , and the best-fit values for L and r₀ are derived. Only models with $f_{{\rm c}}$ between $f_{{\rm c}}^{{\rm min}}$ and $f_{{\rm c}}^{{\rm max}}$ can be fitted. The corresponding minimum and maximum values of the time-averaged luminosity Land the inner cutoff radius r₀ are given. For most of the clusters, both best-fit parameters for time-averaged luminosity and inner cutoff radius decrease monotonically with increasing $f_{{\rm c}}$ . These are labeled by an asterisk in the column trend. $\tilde{L}$ and $\tilde{r}_0$ are the time-averaged luminosity and the inner cutoff radius for the model with the smallest reduced $\chi ^2$ and $\tilde{f}_{\rm c}$ is the corresponding conduction efficiency. The minimum and maximum values of the time-averaged luminosity $L^{{\rm min,max}}_{{\rm fin}}$ for finite integration limits (see Sect. 4.5) are also listed. No result is found for A399.
Table 4: Results for the effervescent heating model with mass dropout or outflow. The minimum and maximum values of the time-averaged luminosity L and the inner cutoff radius r₀ are computed from the results of models with conduction efficiency $0<f_{{\rm c}}< 1/3$ and $-\dot{M}^{{\rm max}}/10<\dot{M}< + \dot{M}^{{\rm max}}/10$ . The minimum and maximum values of the time-averaged luminosity $L^{{\rm min,max}}_{{\rm fin}}$ for finite integration limits (see Sect. 4.5) are also listed. As for the $\dot M=0$ models, no result is found for A399.