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Astron. Astrophys. 321, 64-70 (1997)

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5. Pressure balance

5.1. Thermal pressure

The thermal pressure due to the intracluster medium can be calculated from the PSPC X-ray data by assuming that the gas is isothermal and that the ion and electron temperatures are the same. Thus the thermal pressure is approximated by [FORMULA], where [FORMULA] and [FORMULA] are estimated from the X-ray surface brightness profile and the X-ray spectra in Sect.  2. Fig. 6 shows the thermal pressure as a function of radius.

[FIGURE] Fig. 6. A comparison of the thermal X-ray pressure (solid curve) with that of the minimum radiation pressure. The filled triangles show the minimum pressure for each slice of the western jet and the open circles are for that of the eastern jet.

5.2. Minimum radiation pressure

The radio data enable the minimum internal pressure of the tails to be calculated (Burbidge 1958). The tails would be at a minimum pressure when the equipartition condition is satisfied, namely the energy density of the relativistic particles is equal to that of the magnetic field (Pacholczyk 1970). Indeed given the thermal pressure of the surronding medium, we can verify if the tails are in equipartition. We have adopted the method given by Killeen et al. (1988) for calculating the minimum pressure. The following assumption were made: 1) the jets are perpendicular to the line of sight and the magnetic field lines are perpendicular to the line of sight; 2) the energy ratio k between relativistic electrons and relativistic protons plus thermal particles is 1; 3) the source spectra is a power law extending from 10 MHz to 100 GHz with a spectral index of [FORMULA] ; 4) the filling factor is 1. Amongst the above assumptions, the two most uncertain factors are k and the filling factor. The parameter k can range from 1 to 2000 (Pacholczyk 1970) and a factor of 100 in k produces roughly an order of magnitude difference in [FORMULA]. The filling factor can easily be [FORMULA]. However, an increase in k increases [FORMULA] and a decrease in the filling factor increases [FORMULA]. Thus by choosing [FORMULA] and filling factor [FORMULA], we have really calculated the minimum [FORMULA].

In order to calculate the internal pressure exerted by the particles in the radio source, the 1.4 GHz image was smoothed with a circular beam of [FORMULA] and Gaussians were fit to slices perpendicular to the jet to estimate the peak flux density and size of each slice. The minimum radiation pressure was calculated for each slice using a program kindly supplied by Geoff Bicknell (see Fig. 6). An average spectral index of [FORMULA] was used for each slice of the tails. Given the uncertainties involved, Fig. 6 shows that the minimum pressure deduced from the radio data is in good agreement with the X-ray pressure, i.e. within a factor of 2-3. This suggests that the tails are likely to be in equipartition, if we assume that the tails are in pressure equilibrium with the X-ray gas. Note that the minimum pressure plotted are truly the lower limits, due to the choice of k and filling factor. Feretti et al. (1992) showed in a study of [FORMULA] tailed radio sources, including WATs and NATs, that the thermal pressure is always either comparable to or higher than the minimum [FORMULA]. A study of 22 low radio luminosity sources by Morganti et al. (1988) had found a similar result, suggesting that low luminosity radio sources can be confined by thermal pressure alone.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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