Particle Acceleration on Megaparsec Scales in a Merging Galaxy Cluster

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Science  15 Oct 2010:
Vol. 330, Issue 6002, pp. 347-349
DOI: 10.1126/science.1194293


Galaxy clusters form through a sequence of mergers of smaller galaxy clusters and groups. Models of diffusive shock acceleration suggest that in shocks that occur during cluster mergers, particles are accelerated to relativistic energies, similar to conditions within supernova remnants. In the presence of magnetic fields, these particles emit synchrotron radiation and may form so-called radio relics. We detected a radio relic that displays highly aligned magnetic fields, a strong spectral index gradient, and a narrow relic width, giving a measure of the magnetic field in an unexplored site of the universe. Our observations show that diffusive shock acceleration also operates on scales much larger than in supernova remnants and that shocks in galaxy clusters are capable of producing extremely energetic cosmic rays.

In the universe, structure forms hierarchically, with smaller structures merging to form bigger ones. On the largest scales, clusters of galaxies merge, releasing energies on the order of 1064 ergs on time scales of 1 billion to 2 billion years (1, 2). During such merger events, large-scale shock waves with moderate Mach numbers of 1 to 5 should be created. In such shocks, diffusive shock acceleration is expected to accelerate electrons to high energies; in the presence of a magnetic field, these particles are expected to form large regions emitting synchrotron radiation at radio wavelengths (24). The accelerated particles at the shock front have a power-law energy distribution, which directly translates into an integrated power-law radio spectrum (flux ∝ να, where α is the spectral index and ν is frequency). The slope of the particle distribution s in the linear test particle regime, and thus the radio spectral index [α = (1 − s)/2], depends only on the compression ratio r of the shock (5, 6), with s = (r + 2)/(r − 1). At the shock front, the intracluster medium (ICM) is compressed such that magnetic fields align parallel to the shock front (7). These ordered and aligned magnetic fields cause the radio emission to be highly polarized. Synchrotron and inverse Compton losses cool the radio plasma behind the shock, creating a strong spectral index gradient in the direction toward the cluster center. It has been suggested that such synchrotron-emitting regions from shocks can be identified with radio relics (3, 7). These are elongated radio sources located mostly in the outskirts of massive merging galaxy clusters (814).

We detected a 2-Mpc radio relic (Figs. 1 and 2) located in the northern outskirts of the galaxy cluster CIZA J2242.8+5301 (redshift z = 0.1921). This x-ray luminous cluster (15) (Lx = 6.8 × 1044 erg s−1, between 0.1 and 2.4 keV) shows a disturbed elongated morphology in Röntgen Satellite (ROSAT) x-ray images (16), indicative of a major merger event. The relic is located at a distance of 1.5 Mpc from the cluster center. Unlike other known radio relics, the northern relic is extremely narrow with a width of 55 kpc. Deep Westerbork Synthesis Radio Telescope (WSRT), Giant Metrewave Radio Telescope (GMRT), and Very Large Array (VLA) observations (see supporting online material) show a clear unambiguous spectral index gradient toward the cluster center (Fig. 3). The spectral index, measured over a range of frequencies between 2.3 and 0.61 GHz, decreases from −0.6 to −2.0 across the width of the narrow relic. The gradient is visible over the entire 2-Mpc length of the relic, constituting clear evidence for shock acceleration and spectral aging of relativistic electrons in an outward-moving shock. The relic’s integrated radio spectrum is a single power law, with α = −1.08 ± 0.05, as predicted (5, 6). The relic is strongly polarized at the 50 to 60% level, indicating a well-ordered magnetic field, and polarization magnetic field vectors are aligned with the relic. In the southern part of the cluster, located symmetrically with respect to the cluster center and the northern relic, there is a second fainter broader relic. The elongated radio relics are orientated perpendicular to the major axis of the cluster’s elongated x-ray–emitting ICM, as expected for a binary cluster merger event in which the second southern relic traces the opposite shock wave (1). Furthermore, there is a faint halo of diffuse radio emission extending all the way toward the cluster center connecting the two radio relics (Fig. 1). This emission extends over 3.1 Mpc.

Fig. 1

WSRT radio image at 1.4 GHz. The image has a resolution of 16.5 arc sec × 12.9 arc sec and the root-mean-square (RMS) noise is 19 μJy beam−1. Colors represent intensity of radio emission; red contours (linearly spaced) represent the x-ray emission from ROSAT showing the hot ICM.

Fig. 2

GMRT 610-MHz radio image. The image has a RMS noise of 23 μJy beam−1 and a resolution of 4.8 arc sec × 3.9 arc sec. Colors represent intensity of radio emission.

Fig. 3

Radio spectral index and polarization maps. (A) The spectral index was determined using matched observations at 2.3, 1.7, 1.4, 1.2, and 0.61 GHz, fitting a power-law radio spectrum to the flux density measurements. The map has a resolution of 16.7 arc sec × 12.7 arc sec. Contours are from the WSRT 1.4-GHz image and are drawn at levels of 1, 4, 16, … × 36 μJy per beam. (B) The polarization electric field vector map was obtained with the VLA at a frequency of 4.9 GHz and has a resolution of 5.2 arc sec × 5.1 arc sec. The contours are from Fig. 2 and are drawn at levels of 1, 4, 16, … × 70 μJy per beam. The length of the vectors is proportional the polarization fraction, which is the ratio between the total intensity and total polarized intensity. A reference vector for 100% polarization is shown in the upper left corner. The vectors were corrected for the effects of Faraday rotation using a Faraday depth of −140 rad m−2 determined from WSRT observations at 1.2 to 1.8 GHz.

The source cannot be a gravitational lens, because it is too large and located too far from the cluster center. The morphology, spectral index, and association with a cluster exclude the possibility of the source being a supernova remnant. The source is also not related to the radio AGN (active galactic nucleus) located at the eastern end of the relic. High-resolution observations show this source to be detached from the relic (Fig. 2). The spectral and polarization properties are also unlike that of any known tailed radio sources (17, 18). The power-law radio spectral index, clear spectral index gradient, and enormous extent exclude the possibility that the source is tracing (compressed) fossil radio plasma from a radio source whose jets are now off (19, 20). The integrated radio spectra of such fossil sources are very steep (α < −1.5) and curved, because the radio-emitting plasma is old and has undergone synchrotron and inverse Compton losses. In addition, the shell-like (and not lobe-like) morphology does not support the above scenario.

Instead, all the observed properties of the relic perfectly match those of electrons accelerated at large-scale shocks via diffusive shock acceleration. The characteristics of the bright relic provide evidence that (at least some) relics are direct tracers of shock waves; moreover, the narrow width of the relic provides a way to determine the magnetic field strength at the location of the shock, using arguments similar to those that have been used for supernova remnants (21).

The configuration of the relic arises naturally for a head-on binary cluster merger of roughly equal masses, without much substructure, in the plane of the sky with the shock waves seen edge-on. The polarization fraction of 50% or larger can only be explained by an angle of less than 30° between the line of sight and the shock surface (10). Moreover, because there is evidence for spectral aging across the relic, only part of the width can be caused by projection effects.

The amount of spectral aging by synchrotron and inverse Compton losses is determined by the magnetic field strength B, the equivalent magnetic field strength of the cosmic microwave background BCMB, and the observed frequency. The result is a downward spectral curvature resulting in a steeper spectral index in the post-shock region (i.e., lower α). For a relic seen edge-on, the downstream luminosity and spectral index profiles thus directly reflect the aging of the relativistic electrons (22). To first approximation, the width of the relic (lrelic) is determined by a characteristic time scale (tsync) due to spectral aging, and by the downstream velocity (vd): lrelictsync × vd, where tsync ∝ [B1/2/(B2 + BCMB2)] × [ν(1 + z)]−1/2. Conversely, from the width of the relic and its downstream velocity, a direct measurement of the magnetic field at the location of the shock can be obtained. Using standard shock jump conditions, it is possible to determine the downstream velocity from the Mach number and the downstream plasma temperature.

The spectral index at the front of the relic is −0.6 ± 0.05, which gives a Mach number of 4.60.9+1.3 for the shock (14) in the linear regime. Using the LxT scaling relation for clusters (23), we estimate the average temperature of the ICM to be ~9 keV. Behind the shock front, the temperature is likely to be higher. Temperatures in the range of 1.5 to 2.5 times the average value have previously been observed (24). The derived Mach number and the advocated temperature range imply downstream velocities between 900 and 1200 km s−1 (we used an adiabatic exponent of 5/3). For the remainder we adopt a value of 1000 km s−1. Using the redshift, downstream velocity, spectral index, and characteristic synchrotron time scale, the width of the relic (in kpc) can be derived aslrelic,610MHz1.2×103B1/2B2+BCMB2(1)where B and BCMB are in units of μG. Because BCMB is known, the measurement of lrelic from the radio maps directly constrains the magnetic field. From the 610-MHz image (the image with the best signal-to-noise ratio and highest angular resolution), the relic has a deconvolved width (full width at half maximum) of 55 kpc (Fig. 4). Because Eq. 1 has two solutions, the strength of the magnetic field is 5 or 1.2 μG. However, projection effects can increase the observed width of the relic and affect the derived magnetic field strength. Therefore, the true intrinsic width of the relic could be smaller, which implies that B ≥ 5 μG or ≤ 1.2 μG (Eq. 1). We investigated the effects of projection using a curvature radius of 1.5 Mpc, the projected distance from the cluster center. Instead of using Eq. 1, we computed full radio profiles (25) for different angles subtended by a spherical shock front into the plane of the sky (Ψ; the total angle subtended is 2Ψ for a shell-like relic). The profile for Ψ = 10° and B = 5 μG agrees best with the observations (Fig. 4). For Ψ = 15°, B is 7 μG or 0.6 μG. Values of Ψ larger than ~15° are ruled out. Lower limits placed on the inverse Compton emission (26, 27) and measurements of Faraday rotation (28) indicate magnetic fields higher than ~2 μG. We therefore exclude the lower solutions for the magnetic field strength and conclude that the magnetic field at the location of the bright radio relic is between 5 and 7 μG.

Fig. 4

The deconvolved profile at 610 MHz, averaged over the full length of the relic, is shown by the solid black line and dots. Models for different magnetic field strengths and projection angles (Ψ; i.e., the angle subtended by the relic into the plane of the sky) are overlaid. We used an equivalent magnetic field strength of the CMB at z = 0.1921 of 4.6 μG and a downstream velocity of 1000 km s−1. The model (red) for Ψ = 10° and B = 5 μG provides the best fit. A model for B = 5 μG without any projection effects is overlaid in blue. For Ψ > 15°, no good fit to the data could be obtained; as an example, we have plotted the profile (gray) for Ψ = 20° and B = 10 μG. Inset: The intrinsic width of the relic as a function of magnetic field strength (Eq. 1); for a given width, usually two solutions for the magnetic field strength can be obtained.

Magnetic fields within the ICM are notoriously difficult to measure. No methods have yielded precise magnetic field strengths as far from the center as the virial radius; only lower limits using limits on inverse Compton emission have been placed. Equipartition arguments have been used as a method to determine the magnetic field strength (9, 10, 12, 14), but this method gives only a rough estimate for the magnetic field strength and relies on various assumptions that cannot be verified. The value of 5 to 7 μG we find shows that a substantial magnetic field exists even far out from the cluster center.

Because radio relics directly pinpoint the location of shock fronts, they can be used to obtain a complete inventory of shocks and their associated properties in galaxy clusters. Such an inventory helps to clarify the impact of shocks and mergers on the general evolution of clusters. Because less energetic mergers are more common and have lower Mach numbers, there should be many fainter relics with steep spectra that have escaped detection by current instruments. Interestingly, these large-scale shocks in galaxy clusters have been suggested as acceleration sites for highly relativistic cosmic rays (29). As the radiation losses for relativistic cosmic ray protons are negligible, the maximum energy to which they can be accelerated is only limited by the lifetime of the shock, which can last for at least 109 years. This means that in merging clusters, protons can be accelerated up to extreme energies of 1019 eV, much higher than particles accelerated in supernova remnants.

Supporting Online Material

SOM Text

Figs. S1 and S2


References and Notes

  1. The WSRT is operated by ASTRON (Netherlands Institute for Radio Astronomy) with support from the Netherlands Foundation for Scientific Research (NWO). We thank the staff of the GMRT who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities Inc. Supported by the Royal Academy of Arts and Sciences (KNAW) (R.J.v.W.). We thank G. Brunetti for discussions.
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