3.1. Morphological structure of the radio halo
At 1.4 GHz, the diffuse radio halo Coma C reveals a butterfly-like shape with an angular extent down to noise of more than along the east-west direction and of about in north-south direction, corresponding to 3.2 Mpc 1.8 Mpc respectively. The 1.4 GHz aperture synthesis map of Coma C recently obtained by Kim et al. (1990) shows an angular size of the radio halo down to noise of only , due to the low sensitivity to the very large scale radio emission.
An even more striking feature is the close resemblance of the spatial structure of the halo source at 1.4 GHz and the smooth, extended X-ray halo of Coma (Briel et al. 1992; White et al. 1993). The X-ray emission is thermal bremsstrahlung originating from the hot ( K) intracluster gas (Sarazin 1988). Both the X-ray halo and the 1.4 GHz radio halo are elongated approximately east-west. Both the ROSAT PSPC X-ray image (White et al. 1993) and our 1.4 GHz halo map (Fig. 2) reveal a narrow extension towards the galaxy group associated with NGC 4839 south-west of the Coma cluster. Our radio map actually shows that this extended structure represents a narrow, low-brightness bridge of diffuse radio emission connecting the radio source Coma C with the peripheral extended complex of radio emission, Coma A. This bridge was also detected at 326 MHz by Venturi et al. (1990).
Fig. 3 shows the azimuthally averaged surface brightness distribution of the 1.4 GHz map of the halo centered at , (1950). For comparison, we plotted the model function (normalized to 200 mJy) given by Briel et al. (1992) which fits the azimuthally averaged surface brightness distribution of the X-ray halo observed with ROSAT. As a model function, Briel et al. (1992) adopted a modified isothermal King profile (King 1966) , where denotes the projected radius, a is the core radius, is the density slope parameter, and is the central surface brightness. The radial profile of the X-ray surface brightness distribution is fitted best adopting a and a core radius (Briel et al. 1992). The galaxy distribution of the cluster is more centrally concentrated having a core radius of 6-8 arcmin (Sarazin 1988, and references therein). The FWHM of the X-ray halo is , while one infers a from the azimuthally averaged, deconvolved brightness distribution at 1.4 GHz. This shows that the scale size of the diffuse radio halo source at 1.4 GHz is similar to that of the X-ray halo. However, the radio emission declines more rapidly in the outer regions of the cluster.
As has already been noted by Kim et al. (1990), the positions of the two sources are significantly displaced. On the largest scale, we find the radio source to be about 3-4 arcmin west of the X-ray source. The location of the peak surface brightness in our map (Fig. 2) seems to be even more displaced. This must not be taken too seriously, considering i) the low angular resolution of the observation, and ii) the sensitivity of the result of the removal procedure concerning the proper positioning of the strong radio sources 5C4.85 and 5C4.81 in the center region of the cluster. Inspecting the 2.7 GHz map of the diffuse radio halo obtained by Schlickeiser et al. (1987), one finds that also at this high frequency the halo source reveals a positional offset of 2-3 armin to the west relativ to the X-ray source. From the existence of the positional offset between radio halo and X-ray halo, Kim et al. (1990) concluded that the relativistic particles in the radio halo may not be directly responsible for the heating of the X-ray emitting gas. Since, if the relativistic particles were the main heating source of the hot gas, the two sources should be precisely coextensive. Nevertheless, the close morphological correspondence between thermal X-ray bremsstrahlung and non-thermal synchrotron radiation suggests that the existence of the diffuse radio emission is based on the physical condition of the hot thermal gas.
3.2. Integrated diffuse flux from Coma C
Performing the procedure described in Sect. 2 we obtained an integrated diffuse flux density from Coma C of mJy. Kim et al. (1990) derived an integrated diffuse flux of mJy at 1380 MHz using the DRAO Synthesis Telescope and the NRAO Very Large Array. Our single-dish observation, however, indicates that the radio halo at 1.4 GHz is much more extended than it is suggested by the DRAO image, which accounts for the increased integrated flux at that frequency. Fig. 4 shows the integrated diffuse flux from Coma C at various frequencies. The data set used (see Table 1) comprises our measurement together with data used by Schlickeiser et al. (1987) and by Giovannini et al. (1993). Our measurement seems to fit rather neatly a power law extrapolation from lower frequencies. The data points in the frequency range GHz may be fitted by a power law with index . If we take all data into account a power-law fit gives .
Table 1. Integrated flux densities from Coma C. References: (1) Henning 1989; (2) Hanisch & Erickson 1980; (3) Cordey 1985; (4) Venturi et al. 1990; (5) Kim et al. 1990; (6) Hanisch 1980; (7) Giovannini et al. 1993; (8) present paper; (9) Schlickeiser et al. 1987; (10) Waldthausen et al. 1980
3.3. Scale-size-vs.-frequency relation
Our value for the FWHM of the halo at 1.4 GHz (15:02) is in agreement with the scale size obtained by Kim et. (1990) (), who fitted the brightness distribution with a two-dimensional Gaussian. At 326 MHz, Venturi et al. (1990) inferred a . Henning (1989) derived the scale size of the radio halo at an even lower frequency (30.9 MHz). She found . In order to obtain a rough estimate of the halo's FWHM at 2.7 GHz, we azimuthally averaged the 2.7 GHz map given by Schlickeiser et al. (1987) and inferred a FWHM from that radial distribution. This yields a which may be regarded as an upper limit, since we did not deconvolve the original map. In any case, this is significantly smaller than the scale size of the halo at 1.4 GHz. Hence, there appear to be strong observational evidences that the scale size of the radio halo is a monotonically decreasing function of frequency. This supports the suggestion made by Giovannini et al. (1993) that in the external regions of the cluster the diffuse radio halo exhibits a steeper spectrum than in the core region. Comparing surface brightness measurements at 326 MHz and 1.4 GHz, performed with synthesis aperture telescopes, Giovannini et al. (1993) derived a spectral index distribution which shows an almost constant index of within a cluster radius of and a strong increase of the index up to values higher than 1.8 outside this central "plateau". However, our single-dish observations indicate that at larger spatial scales there is much more diffuse radio power at 1.4 GHz than it is suggested by the synthesis aperture measurements. Thus, the increase of the spectral index may be weaker than claimed by Giovannini et al. (1993). A smaller spectral index implies a weaker net energy loss of the relativistic electrons in the peripheral region of the cluster.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998