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Astron. Astrophys. 332, 395-409 (1998)

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6. Other relics

6.1. General remarks

A handful of other cluster relics are known. Their properties and that of their host clusters are collected in the upper part of Tab. 1. According to the theory discussed in this paper other quantities are calculated and given in the lower part of Tab. 1. Average values for 1253+275 are also given in Tab. 1, but the very recently discovered relic 2010-57 (Röttgering et al. 1997) is only discussed in the text.


Table 1. The upper part of the table is a collection of measurements of properties of cluster radio relics and their host clusters. The references are indicated in the third column in the sequence of the eight examples. The lower part gives estimates, using the above properties and the formulae of this paper, as indicated in the third column. A discussion of the individual sources and various assumptions made in order to get the given values can be found in Sect. 6.

For four relics, namely 0917+75, 1253+27, 1712+64, and 1706+78, polarization measurements are available. In three cases these polarizations fit well into the prediction of the accretion shock theory (see Fig. 3). In the case of 1706+78 in A2256 the observed polarization is much higher than expected. This can be understood if the shock is due to an on-going merger event (Fabian & Daines 1991), and therefore located at a smaller cluster radius. The accretion shock theory predicts a polarization of 28% for the relic 2006-56, 10% for 2010-57, 4% for 1140+203 and 1401-33, and 1% for 0038-096.

The predicted shock velocity [FORMULA] is in all accretion shock examples lower than that of the accretion shock theory of Kang et al. (1997) by 16% on average. This could be due to an assumed temperature drop of a factor of less than two from the cluster center to the accretion shock radius, or due to the need of some recalibration of the accretion shock parameters.

Looking at the distribution of the predicted viewing angle [FORMULA] one recognizes that large angles are underrepresented. In an isotropic distribution half of the relics should be seen at a viewing angle above [FORMULA]. This is clearly a selection effect, since the sensitive radio surveys of clusters with good angular resolution which are needed for the detection of these sources, usually do not reach projected radii of 5 Mpc, as would be necessary in order to include the whole accretion shock. We expect therefore that undiscovered relics, with strong radio polarizations, are waiting in these outer regions of clusters for their exploration.

6.2. Abell 85: 0038-096

The spectral index of 0038-096 is not settled in the literature: Slee & Siegman (1983) give [FORMULA], Reynolds (1986) gives [FORMULA], Slee et al. (1994) 2.37, Joshi et al. (1986) 3.03 above a break at 300 MHz, whereas Feretti & Giovannini (1996) state that [FORMULA]. We base our estimates mainly on the numbers of the latter authors. It is possible that the observed strong steepening is in fact a smeared-out cutoff, resulting from the limited acceleration power of a weak accretion shock. Since the projected relic position is close to the cluster center the viewing angle is close to zero and therefore no visible polarization resulting from field compression is expected. The necessary radio efficiency [FORMULA] of the shock is [FORMULA] and thus reasonable. The predicted magnetic field strength [FORMULA] G [FORMULA] from assuming pressure equilibrium between the post-shock gas and the relic is again higher than the equipartition (or minimum energy) value given by Feretti & Giovannini (1996) [FORMULA] G [FORMULA] (corrected by [FORMULA]). Lima Neto et al. (1997) report the appearance of an X-ray blob in the X-ray image of A85 centered on 0038-096, possibly inverse-Compton scattered microwave background photons. If so, the magnetic field strength could be derived directly from an estimate of this X-ray excess.

6.3. Abell 786: 0917+75

The megaparsec cluster radio relic 0917+75 is located 5 Mpc [FORMULA] away from the center of A786 within the plane of sky. Unfortunately no temperature or velocity dispersion of A786 is available in the literature. Thus, the expected shock radius and therefore the polarization cannot be predicted. However the very peripheral position indicates a large viewing angle, consistent with the high degree of the observed polarization of [FORMULA]. A viewing angle of [FORMULA] corresponding to an accretion shock radius of [FORMULA] Mpc [FORMULA] would be in agreement with this polarization. Such a large shock radius indicates a deep gravitational potential. The corresponding virial temperature [FORMULA] keV (Eq. 1) is in the upper range of observed temperatures of clusters, and therefore possible. However the shock structure might in fact be also due to an accretion flow, which is centered on and stops at the boundary of the supercluster Rood #27, which A786 is a member of. This could explain the large projected shock radius.

The direction of the projected magnetic field observed by radio polarization is mainly perpendicular to the axis connecting the center of A786 and 0917+75, as it should be if the field is compressed at a spherical shock centered on the cluster. But a weakly visible spiral structure in the projected fields could result from an intrinsic order which the magnetic fields had before they passed the shock.

The relic 0917+75 exhibits a break in its spectrum (Harris et al. 1993). Below 300 MHz the spectral index is 0.6 and above it is steeper by the canonical value 0.5, as is expected from a steepening of the spectral index of the electron population by 1, predicted in Sect. 2.4. The corresponding compression ratio of [FORMULA] is close to the maximum possible value [FORMULA] of a strong nonrelativistic shock.

The projected peripheral position of 0917+75 allows a sensitive search for inverse-Compton scattered microwave background photons in the X-ray range. Harris et al. (1995) observed the relic with the PSPC instrument on the ROSAT satellite and got an upper limit to the flux in the 0.5-2.0 keV band of [FORMULA]. This implies that the magnetic field strength must be [FORMULA] G, slightly larger than [FORMULA] G [FORMULA] derived from minimum energy considerations and various assumptions, which were discussed in Harris et al. (1995) and Sect. 5.1of this article.

6.4. Abell 1367: 1140+203

The diffuse radio source found in A1367 is usually called a halo, but it is more probably a cluster relic because of its noncentral location and asymmetric shape. The distance to the center of the galaxy distribution is [FORMULA] (Gavazzi 1978), but to that of the X-ray emission it is [FORMULA] (see map in Gavazzi et al. 1995). We use the latter distance, since the X-ray emission should be a better tracer of the gravitational potential. The X-ray emission is elongated into the direction of the relic, possibly tracing the influence of the large-scale structure potential, or the main direction of the accretion flow onto the cluster, or both. The radio relic could be contaminated or related to three close irregular galaxies, which have radio trails behind them (Gavazzi & Jaffe 1987), indicating that they are falling inwards. Strong on-going star formation, a recent supernova in one of them, and young and abundant H II regions, which are aligned as if they were formed by bow shocks (Gavazzi et al. 1995), could be triggered by the sudden change of the environment of these galaxies during the passage of the accretion shock. A starburst might increase the accretion within these galaxies onto a possible central black hole (similar to the argumentation of Wang & Biermann 1998) and therefore can trigger the ejection of radio plasma.

The measurements of the spectral index and radio flux of the relic differ in the literature (compare Gavazzi 1987, Hanisch 1980, and Gavazzi & Trinchieri 1983) and therefore any derived numbers have to be used with care. Especially the radio power [FORMULA] is an extrapolation of a very steep spectrum ([FORMULA]) down to 10 MHz and probably an overestimate. Due to the low expected viewing angle only a small polarization of 4% is expected. Gavazzi & Trinchieri (1983) detected some X-ray emission from the region of the relic. Assuming this to result from inverse Compton emission they estimate a magnetic field strength of [FORMULA] G, of the same order as the equipartition value of [FORMULA] G [FORMULA] and the predicted strength of [FORMULA] G [FORMULA] for pressure equilibrium with the surrounding.

6.5. Abell 2255: 1712+64

The cluster A2255 has a number of similarities to the Coma cluster: there is evidence that the cluster is in a state of merging (Burns et al. 1995), a radio halo is present, and also a peripheral radio relic without any obvious parent galaxy (Feretti et al. 1997). The spectral index of the relic is fairly constant along the structure. The upper limits to the polarization of 9% at 20 cm and 2% at 90 cm do not contradict the predicted polarization of 3% seriously, taking into account e.g. the rough assumptions which entered the estimate of the shock radius, and the possibility that external Faraday depolarization has lowered the degree of the radio polarization if the relic is seen through the denser magnetized central intra-cluster medium. This relic therefore fits also well into the accretion shock theory.

6.6. Abell 2256: 1706+78

The radio emission reveals a very complex situation within A2256: a mini-halo is visible in the map of Bridle & Fomalont (1976), and several head-tail radio galaxies can be found. One NAT source (in the notation of Bridle & Fomalont (1976): source C) is one of the longest head-tail sources known. The tail extends over 700 kpc [FORMULA], is slightly bent and exhibits a kink 570 kpc [FORMULA] behind the head (Röttgering 1994). The bending can be understood as the gravitational influence of the cluster mass to the trajectory of a fast moving radio galaxy, at which the tail traces the path. The kink might result from a sudden change of the surrounding density or velocity field of the background gas (Röttgering et al. 1994), as it might happen if the radio galaxy passes a shock. The projected position of the kink is within a very extended irregular and sharp-edged region of diffuse radio emission in the north-west region of the cluster. This region consists of two extended sources (G and H in the notation of Bridle & Fomalont (1976)), which might be two independent relic sources with similar properties.

The spectral index of 0.8 of these possible cluster relics indicates that the injection electron spectrum below the break in the momentum distribution is observed. The spectral index of the synchrotron emission above the break should be [FORMULA]. The break momentum (Eq. 12) is highest for a large shock velocity [FORMULA] and a thin magnetized post-shock region (small D). The latter could explain why the emission region is relatively sharp-edged. If the thickness D is much smaller than we assumed, the kinematic age of the relic [FORMULA] would be much smaller than [FORMULA] yr, in accordance with [FORMULA] yr. The polarization of 20% is much too high for the expected viewing angle [FORMULA] of a relic located at the canonical radius of the accretion shock [FORMULA], which predicts only 1% polarization. A consistent viewing angle of [FORMULA] would imply that if the normal of the shock front is pointing to the cluster center, the shock radius is [FORMULA]. This would be in agreement with the average direction of the polarization, which is oriented roughly perpendicular to this assumed normal of the shock front. A shock in the interior of the cluster can only be explained by a merger event. Independent evidence for such a collision can be found in the X-ray morphology, in the complex temperature structure and in the elongated galaxy distribution. An extensive discussion of the observational signs reported in the literature is given by Roettiger et al. (1995). They compare these observations with simulations of cluster mergers and conclude that the entire data are best reproduced by a merger of two clusters with mass ratio 1:2 and a relative velocity of 3000 km/s. The separation of the cluster centers is 0.75 Mpc [FORMULA]. The smaller cluster is infalling from the north-west and is approaching the observer. The angle between the line-of-sight and the merger axis is in the best-fit model in the range of [FORMULA] to [FORMULA], in agreement with [FORMULA] estimated from polarization, without taking any possible influence of external Faraday depolarization into account.

The temperature [FORMULA] given in Tab. 1 is an average value of a complex distribution, biased by the heat production of the shock. Since the infalling subcluster has a much higher temperature ([FORMULA] keV; [FORMULA] is assumed here) than the accretion streams hitting all other known cluster relics ([FORMULA] keV), the moderate shock compression ratio [FORMULA] at this shock, which has the highest shock velocity of our sample, can be understood to result from the high pressure of the upstream matter.

The predicted shock velocity derived from the up-stream temperature and pressure jump is [FORMULA], being in agreement, and completely independent of the above mentioned merger velocity from the hydrodynamic simulations. The merger velocity corresponds to the infall velocity measured in the cluster rest frame [FORMULA], which is usually lower by [FORMULA] than the shock velocity [FORMULA]. But in case of a massive merger it is unrealistic to believe that A2256 behaves like a single body, the downstream flow does surely not rest in the cluster reference frame. We therefore use a realistic velocity of [FORMULA] km/s.

The line-of-sight velocities of the head-tail radio galaxies also point towards the observer, and especially the obviously fast moving source C seems to originate from the infalling cluster. Röttgering et al. (1994) have fitted trajectories, calculated for a gravitational potential derived from X-ray data to the tail of source C, and concluded that the initial velocity had to be in the range of 2000-3500 km/s, in accordance with the value of the relative cluster velocity given by Roettiger et al. (1995). From the undisturbed straightness of the source Röttgering et al. (1994) derive that the turbulent motion of the cluster medium has a velocity [FORMULA] km/s, much too low to explain the diffuse emission resulting from large-scale turbulent motion. However, this is not in contradiction to the merger shock model for this relic, where violent velocity changes occur only in the thin shock region, which might have distorted the tail of source C at the position of the kink. We note, that a brightening of the radio tail is visible there, as expected to result from the action of the shock onto the tail (Röttgering et al. 1994). Source C should have moved from the kink within [FORMULA] years to its present day position. This is comparable or higher than a typical cooling time of radio emitting electron, and explains the observed fading of the tail.

The details of the complex scenario might differ from the above picture in that the shock might be oblique (Roettiger et al. 1995), or the impact parameter of the merging clusters is non-zero (Briel et al. 1991).

6.7. Abell 3667: 2006-56 and 2010-57

The giant cluster radio relic 2006-56 is peripherally located within the direction of the elongation of A3667. This elongation is seen in X-rays, but also contains a subgroup of galaxies (Knopp et al. 1996). Because of the low X-ray background, 2006-56 would be an ideal candidate for a future sensitive search for inverse Compton flux (by, e.g., AXAF, XMM). Goss et al. (1982) separated two extended radio sources at this position, located close to each other: 2006-56 and a diffuse ridge. A recent sensitive observation by Röttgering et al. (1997) shows that there is in fact a single Z-shaped structure, extending over [FORMULA], with constant spectral index along the main axis of the relic. The Z-shape might be the structure of the radio plasma, since we do not see the relic edge-on. The side more distant from the cluster center is sharply edged and has a flatter spectral index, as is expected to happen on the upstream side as explained in Sect. 2.1. The spectral index drops from [FORMULA] in the central region of the relic to [FORMULA] at this edge. This indicates strongly the presence of particle acceleration, so that we can use the thickness of the rim of lower spectral index in order to estimate the thickness of the relic. The projected thickness derived from the rim is approximately [FORMULA]. The region with steeper spectral index on the inner side has also a projected thickness of [FORMULA]. Assuming a viewing angle of [FORMULA], deprojection gives [FORMULA]. The projected area of the relic is [FORMULA]. A stripe of [FORMULA] belongs to one edge. Deprojecting the remaining area gives a relic surface of [FORMULA]. The infalling gas seems to be relatively cool, with [FORMULA] keV, but this number has a large error since the temperature jump is very sensitive to small variations in R, since R is close to its maximum value (see Eq. 4or Fig. 4).

[FIGURE] Fig. 4. Central cluster temperatures vs. spectral index of the radio relics. The dotted lines are temperature-spectral index relations, computed from the temperature jump given by Eq. 4, which for a given temperature of the infalling gas [FORMULA] (and assuming [FORMULA]) is a function of the spectral index [FORMULA] only. The temperature of the infalling gas [FORMULA] is indicated for the curves.

Röttgering et al. (1997) report a pressure imbalance of one to two orders of magnitude, between the gas pressure at the projected cluster radius of the relic and its equipartition pressure. This discrepancy should vanish if the lower gas pressure at the shock radius and the higher radio plasma pressure of a compressed, flattened structure is taken into account. Therefore we find good agreement between equipartition field strength and predicted field strength.

Surprisingly, the radio image of Röttgering et al. (1997) reveals a second cluster radio relic on the other side of the cluster (2010-57). These authors mention that both relics might be the two lobes of a former, now inactive, radio galaxy, possibly the cD galaxy. This must have been gigantic, since the projected distance is [FORMULA]. The expected diameter of the accretion shock sphere of [FORMULA] would be a lower limit to the extent of this radio galaxy in our scenario, since nowadays we would see a backflow of the radio lobe from larger distances. In order to achive such an extent, the radio galaxy must have been very powerful and the ambient medium more tenuous than today. If both structures are really produced by one galaxy, this should have happened during the early period of violent quasar activity, when the intra-cluster medium was thinner.

If the two relics are independent, in the sense that their radio plasma is from different sources, but their positions are correlated due to the membership of A3667 to a large-scale filament, then the head-tail radio galaxy B2007-569 can be the source of the shocked radio plasma in 2006-56. It is located between the cluster center and the relic and is moving towards us with a speed of 1200 km/s ([FORMULA] ; Sodreé et al. 1992). If it is on a radially falling orbit, which traversed the shock sphere at the location of the present day relic, it should have a velocity of 1800 km/s (using [FORMULA]), higher than the expected infall velocity of matter (measured in the cluster rest frame) at the higher radius of the shock. Travelling with this velocity it should have passed the shock a Gyr ago. This is an order of magnitude longer than a typical cooling time of radio emitting electrons and therefore the expected trace of radio plasma on the path of that galaxy became invisible. It is amazing that Röttgering et al. (1997) found marginal evidence for a bridge between this galaxy and the relic, which might indicate reacceleration.

We predict a polarization in 2006-56 of 28% from our accretion shock model, and 10% in 2010-57 due to its smaller expected viewing angle of [FORMULA], assuming the same spectral index and shock compression ratio as for 2006-56. The observation of these polarizations would be an independent test of the theory, and therefore could verify general assumptions made about large-scale flows in the Universe.

6.8. Abell S753: 1401-33

S753 is a poor cluster. Its low velocity dispersion of 536 km/s (Fadda et al. 1996) indicates a low central gas temperature of [FORMULA] keV, applying the dispersion-temperature relation given in Bird et al. (1995), and therefore a flat gravitational potential compared to the other clusters. The spectral index [FORMULA] of the relic 1401-33 corresponds to a shock compression ratio of [FORMULA]. This relatively strong shock at this poor cluster can be understood if the accreting matter has a temperature of [FORMULA] keV. This is lower than what seems to be typical for the other clusters ([FORMULA] keV, see Fig. 4). The lower preheating of the flow onto this cluster might indicate a poorer cosmological environment. Since the sky position of the relic 1401-33 is close to the center of S753, the viewing angle should be small and only 4% polarization is predicted.

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Online publication: March 23, 1998