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Astron. Astrophys. 363, L17-L20 (2000)

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4. Physical parameters

Recently, Ishwara-Chandra & Saikia (1999) have published very interesting statistics of some physical parameters calculated for 44 known giants exceeding 1 Mpc, and compared them with the corresponding parameters of smaller 3CR radio sources. Following Ishwara-Chandra and Saikia, we calculate the equipartition magnetic field [FORMULA] and minimum energy density [FORMULA] in J1343+3758 using the standard method (e.g. Miley 1980), as well as the ratio [FORMULA], where [FORMULA] nT is the equivalent magnetic field of the microwave background radiation, and [FORMULA], which represents the ratio of the energy losses by synchrotron radiation to the total energy losses due to the synchrotron and inverse Compton processes. Following their analysis and assuming: a cylindrical geometry of the source with a base diameter of 298 kpc (which is the mean of the deconvolved widths of the lobes derived in Sect. 2) and the projected length of 3140 kpc, the filling factor of unity, and equal energy distribution between relativistic electrons and protons, we found the total radio luminosity of the source between 10 MHz and 10 GHz [FORMULA] erg s-1 and the source volume of [FORMULA] cm3. Since the parabolic fit of the spectrum may underestimate fluxes (and thus the source luminosity) at frequencies below 151 MHz, we also calculated [FORMULA] for constant spectral slope of -0.45 at [FORMULA] MHz and found only 8 per cent increase of [FORMULA]. Then we found [FORMULA] nT, [FORMULA] erg cm-3, [FORMULA], and [FORMULA]. The errors in [FORMULA] and [FORMULA] are calculated adopting errors of 15 per cent in the integral luminosity, 0.2 in spectral index, and 50 per cent in the volume.

The equipartition magnetic field and energy density found for J1343+3758 are extremely low. Only two giants in the sample of Ishwara-Chandra & Saikia have their parameters comparable to the above values. The respective parameters are compared in Table 2.


Table 2. Comparison of the physical parameters derived for J1343+3758 and NGC6251 and DA240. The respective parameters of these two latter giants have extremal values in the sample of Ishwara-Chandra & Saikia

The age of relativistic electrons in the radio lobes [FORMULA] radiating at a given frequency [FORMULA] can be deduced from the values of [FORMULA] and [FORMULA]. Again following the analysis of Ishwara-Chandra & Saikia, we have calculated [FORMULA] at [FORMULA] MHz. Using their expression (cf. also Alexander & Leahy 1987 and Liu, Pooley & Riley 1992) which is derived under assumption that electrons are isotropized on time-scales much shorter than their radiative lifetime (JP model: Jaffe & Perola 1974), we found [FORMULA] yr. It is somehow lower than [FORMULA] yr for Ishwara-Chandra & Saikia's giants with [FORMULA], and closer to [FORMULA] yr for those at [FORMULA].

However, this is worth to emphasize that the JP model predicts the fastest steepening of synchrotron spectrum at high frequencies, while its slowest steepening is provided in the case of continuous injection of energetic particles (CI model); for the detailed description cf. Myers & Spangler (1985). Because of very limited observational data, one cannot distinguish which model of the radiative losses would be plausible for J1343+3758, but this model-dependent uncertainty of the synchrotron lifetime of particles in its lobes is less than that introduced by other effects like unknown filling factor, energy distribution between electrons and protons, or uncertain volume.

If the main axis of the source is close to the plane of the sky, the distance from the core to the brightest regions in the lobes will be within 1.4 Mpc and 1.8 Mpc. Relating [FORMULA] yr to any distance between the above values, the advance speed of the lobes material should be about [FORMULA]. This value is still within the speed range found for much smaller, double 3CR radio sources (e.g. Alexander & Leahy; Liu et al.). This advance speed can suggest that the source achieved its present size due to expansion in a low-density environment. To check this, we followed Hill & Lilly (1991) and estimated the environment density by simple counts of galaxies around the identified galaxy. We define [FORMULA] as the net excess number of galaxies with R magnitude from [FORMULA] to [FORMULA] and within 1.5 Mpc radius around our galaxy. Using the DSS data base and adopting [FORMULA] mag, we found 30 galaxies to meet the above criterium. However, the number of galaxies with [FORMULA] mag can be underestimated in the DSS as they can be seen at the POSS E-plates only, therefore we adopt [FORMULA]. The relevant number of background galaxies, [FORMULA] was found using the differential counts [FORMULA] deg-2mag-1] (Tyson 1988). Resultant negative net value [FORMULA] indicates that J1343+3758 lies in a distinctly poor region of intergalactic medium. This conclusion is further supported by an estimate of the particle density around the lobes. Following Lacy et al. (1993), we assume that the heads of lobes are ram-pressure confined. Taking the deconvolved diameter of the hotspot in the NE lobe as 3 arc sec, we can estimate the ambient density [FORMULA] g cm-3. This estimate is lower by an order than that found for the other giants (cf. Parma et al. 1996: Mack et al. 1998; Schoenmakers et al. 1998).

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000