What causes diffuse radio emission?

Introduction

The development of this field of research has been based around the idea of a `radio relic' which is the remains of a once active galaxy. This term is misleading, as current evidence in the literature suggests strongly that many of the diffuse emission regions are the result of cluster mergers, accretion shocks and extreme turbulence. Far from being old, fading remains they are the products of the most powerful dynamic events in the universe.

The field has evolved to the point where there are now around 30 examples of diffuse cluster emission, some of them with vastly different properties. We have found another 14 candidate sources, a significant contribution considering the low number of these sources known already. We believe that the sources can be categorized into distinct groups rather than in a single group with a large range of properties. By distinguishing these different types it is possible to resolve some of the apparent contradictions in the observations and models of the mechanisms which create and sustain the sources.

Much of the theoretical research in this field is concerned with the mechanisms of shock acceleration. Until recently the focus has been on cluster mergers as the cause of cluster-wide shocks but a new area of interest is cluster accretion shocks. Cluster mergers have been discussed in Section 1.1.3. Below we briefly outline cluster accretion and the standard theory of diffusive shock acceleration. We then discuss mechanisms which could cause diffuse radio emission and relate them to our results in this project.

Accretion Shocks

Both numerical and observational evidence shows that the large-scale structure of the universe consists of sheet-like and filamentary structures. Clusters of galaxies form at the vertices where several filaments intersect and the density, gravitational potential and temperature are the highest. Hydrodynamic simulations of large-scale structure formation [Kang et al.1994,Cen and Ostriker1994] show that shocks will form and heat the cluster gas as matter accretes towards the dense vertex regions. [Kang et al.1996] suggest that the accretion shocks around clusters could be as fast as 1000-3000 kms^-1 and so are the fastest known shocks, generated by very deep potential wells. Hence accretion shocks are excellent candidates for the acceleration of particles to very high energies.

Diffusive Shock Acceleration

The theory of planar shock waves is well understood in the context of solar system physics, and so a natural extension is to apply it to large scale extragalactic astrophysics.

A shock wave is produced when a disturbance moves through a fluid faster that the characteristic propagation speed of small amplitude waves in the fluid (sound waves in unmagnetized plasma and Alfven waves in magnetized plasma). The shock front is a boundary between two plasmas whose properties such as mass density, temperature and magnetic field change discontinuously at the shock front. The plasma parameters ahead of the shock (upstream) and behind the shock (downstream) can be related by the jump conditions or Rankine-Hugoniot relations.

Diffusive shock acceleration is an example of an energy changing mechanism first described by Fermi in 1949. A particle reflected from an approaching surface gains energy resulting in a net acceleration. A quantitative treatment of diffusive shock acceleration predicts that, given a mono-energetic spectrum of injected particles, the downstream spectrum of accelerated particles follows a power law form $f(p) \propto p^{-b}$ where b = 3r/(r-1) is the compression ratio and $r=\eta_{down}/\eta_{up}$ is the density jump across the shock [Cairns1999].

Some of the predictions that can be used to compare the theory with observations are radio polarization of the sources, magnetic field strength, diffusion coefficient in the post-shock region, density and temperature of infalling gas, spectral index of the radio spectrum and whether the shock has the necessary power to produce the observed sources.

   
Relic Radio Galaxies

Some diffuse sources are `genuine' radio relics as described by [Komissarov and Gubanov1994], that is, they are the remains of massive lobes from radio galaxies. When activity in the nuclei of radio galaxies ceases, they stop producing the characteristic plasma outflows. Compact components such as the radio core and the jets dissipate and eventually disappear. However, the radio lobes could remain powerful sources, maintained by high pressure in the cluster environment and losing energy only by synchrotron emission and inverse Compton scattering of 3K microwave background photons. The higher energy electrons lose energy quicker than the lower energy ones ( $dE/dt \propto -E^2$) which causes the spectrum of the relic sources to be steeper than the spectrum of the original radio galaxy.

Examples of these Very Steep Spectrum Radio Sources (VSSRSs) are the diffuse sources in A85 [Slee and Reynolds1984], A133 and A2626 [Rizza et al.1998], A566 [Harris et al.1982] and A1914 [Baldwin and Scott1973]. These sources have exceptionally steep spectral indices ( $\alpha \le -2$) and relatively compact, although elongated, radio morphologies. In our sample we have at least one radio relic source, Src 3 in A3266, and several other candidates (A3093, A3505, A3351, A3553). As discussed in Section 5.3.3, Src 3 has an exceptionally steep spectral index ( $\alpha \sim -2.8$) which steepens with distance from the possible host galaxy. Since we only have single frequency (MOST) observations of the other sources, we can not estimate their spectral indices.

If the above picture of radio relics is accurate, the detection rate of these sources would depend on how well the emission regions are contained by the cluster environment. In a more rarefied environment the regions would dissipate away and lose energy quickly, falling below the flux limit of radio surveys. Hence radio relics either must originate from only the most powerful cluster radio galaxies, or the electrons must be reaccelerated in some way, such as by cluster-wide shocks or turbulence. If the radio spectra of the relic source exhibits a frequency cutoff it is probable that it is simply the remains of an old, powerful radio galaxy. However, if no such cutoff is observed, particle acceleration of some form must be taking place. We believe that shock acceleration, either bow shocks from cluster mergers or accretion shocks from large scale structure formation, is the most likely explanation for the presence of radio relic sources with no cutoff.

Diffuse Emission

As discussed in Section 1.2, diffuse sources have traditionally been classified into relics -- peripherally located, irregularly shaped, polarized sources -- and halos -- large regions of unpolarized radio emission, centrally located and with radio structures similar to the thermal X-ray emission.

The only characteristics that distinguish these sources are radio morphology, position in the cluster and polarization. We propose that none of these features is sufficient to distinguish between the two types of source for the following reasons: projection effects mean that it is not possible to distinguish a source at the centre of a cluster from a source at the projected centre of a cluster; the analysis of [Enßlin et al.1998] shows that observed polarization is correlated with viewing angle; observed morphology is clearly dependent on viewing angle. For example, it has been suggested (eg. [Sakelliou and Merrifield1999]) that wide-angle tailed and narrow-angle tailed sources could be the same type of source viewed at a different orientation to the line of sight.

We believe the most plausible explanation for the presence of diffuse emission regions, which do not have the characteristics of radio relic sources (Section 6.2) is particle acceleration due to cluster mergers and/or accretion shocks. In general, a source located at a shock front should exhibit different properties on the inner edge (where the radio plasma is further from the shock front) and outer edge. The outer edge should be sharper due to a better confined plasma and should have a flatter than average spectral index since the electrons have been accelerated more recently [Enßlin et al.1998]. The diffuse source in A3376 and Src 13 in A3266 are probably the most convincing examples of this in our sample. However, this interpretation is of course highly dependent on the orientation of the source with respect to the observer.

   
A Case Study of A3266

[Kang et al.1997] model the collapse of clusters as the collapse of an initially overdense point-mass perturbation followed by the secondary infall of the background medium. This is based on similar models studied semi-analytically [Bertschinger1985] and numerically [Ryu and Kang1997]. The infalling baryonic matter forms an accretion shock, with the magnetic field strength in equipartition with the post shock thermal energy. [Kang et al.1997] relate the accretion shock parameters to physically observable quantities. Hence the shock radius, r_s, and velocity, V_s, can be calculated using the following equations

$$r_s = 3.03 \mbox{ Mpc} \left(\frac{kT_{obs}}{6.06 \mbox{keV}}\right)^{1/2} (1+z)^{-3/2}$$ (6.1)

$$V_s = 1750 \mbox{ kms}^{-1} \left(\frac{kT_{obs}}{6.06 \mbox{keV}}\right)^{1/2}$$ (6.2)

These equations assume spherical flow and a polytropic gas index of $\gamma_{gas} = 5/3$.

Substituting the redshift and observed temperature of A3266 (z = 0.0545, kT_obs = 6.2 keV) into these equations gives a shock radius of r_s = 2.8 Mpc and velocity of V_s = 1770 kms^-1. The projected distance of Src 3 from the centre of A3266 is 0.45 Mpc, so if Src 3 is at the position of the shock this implies a viewing angle (angle between line of sight and shock normal) of $\theta = 9^\circ$. This implies that Src 3 would be much larger than its projected linear extent of 0.41 Mpc. [Enßlin et al.1998] derive the expected polarization of relic sources as a function of viewing angle. For both the weak and strong magnetic field cases, they find observed polarization is negligible for viewing angles of $\theta \le 10^\circ$ which is in agreement with our non-detection of polarization for Src 3 in A3266.

Summary

We have found 14 candidate diffuse sources in a distance limited sample of southern Abell clusters. We have compiled a web based catalogue of the 92 clusters in our sample, bringing together optical, radio and X-ray data from a range of surveys. Statistical analysis of the sample confirmed previous research that there is no correlation between the richness of clusters and the radio source count. We found that clusters containing diffuse sources did not have a higher than average optical richness or radio source count. We also found no evidence of a correlation between the presence of a diffuse source and X-ray luminosity. Our results suggest a tendency for diffuse sources to be found in B-M type II-III clusters which could be a result of a disturbed cluster morphology due to shocks and/or turbulence.

Our detailed study of A3266 revealed a new diffuse source (Src 13), as well as providing more information on the radio relic source that has already been identified (Src 3). We found that Src 3 had an exceptionally steep spectrum that steepened with distance from the possible host galaxy and hence classified it as a Very Steep Spectrum Radio Source (VSSRS). There is evidence from N-body simulations that A3266 is undergoing a cluster-subcluster merger and it could be a shock associated with this that caused Src 13 and sustained Src 3.

Traditionally diffuse sources have been classified according to their location in the cluster, their morphology and their polarization. We propose that none of these are reasonable distinctions as they all depend on the viewing angle of the observer, rather than any intrinsic properties of the sources. We think that the most useful distinction at this time is between genuine `relic' radio galaxies and regions of diffuse emission that are caused by particle acceleration due to cluster merger or accretion shocks.

Future Research

We plan to re-observe several of the candidate diffuse sources to get a better quality images and possibly data at different frequencies so that spectral indices can be calculated. It would also be beneficial to re-reduce or re-observe the clusters that were rejected from our sample because of poor quality MOST images.

In a broader context, it is essential to combine the information from all the studies of diffuse sources done so far into one statistical study. This would help to characterize the sources in a more quantitative way and provide a stronger basis for finding more sources. It would also allow some of the theoretical models to be compared to a wider range of empirical data.

By characterizing diffuse sources on the basis of the physical processes that create them, we may be able to solve the mystery of these sources, which may be the products of some of the most powerful dynamic events in the universe.

Acknowledgments

I wish to thank the following people:

Richard Hunstead, my supervisor, for his understanding and enthusiasm throughout the year, valuable suggestions and extensive help with the project and for the most comprehensive proof-reading I have ever seen; Vince McIntyre, for helping to produce the polarization images, explaining some of the technical aspects of data reduction and answering my many questions about UNIX and Miriad in particular; the rest of the astrophysics department, especially Lawrence Cram and Gordon Robertson, for their help and suggestions; Feraz Azhar, for comparing our measured flux densities with the NVSS values, as part of his 3rd Year Special Project; and Julian Berengut, Steven Fuerst, Katherine Manson and Michael Shuter for helping to observe A3266 as part of the ATNF Vacation Scholarship program;

Finally I would like to thank James Curran, for writing a secure cgi script for the web page, convincing me at the beginning of the year that `AWK scripts will save time', proof-reading many draft literature reviews and being great fun to work with all year.