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Astrophysics and Space Science

DOI 10.1007/s•••••-•••-••••-•

Shock Waves in the Large-Scale Structure of the Universe

Dongsu Ryu • Hyesung Kang

c Springer-Verlag ••••

draft of June 12, 2008

Abstract

Cosmological shock waves are induced during hierar-chical formation of large-scale structure in the universe.Like most astrophysical shocks, they are collisionless,since they form in the tenuous intergalactic mediumthrough electromagnetic viscosities. The gravitationalenergy released during structure formation is trans-ferred by these shocks to the intergalactic gas as heat,cosmic-rays, turbulence, and magnetic fields. Here webriefly describe the properties and consequences of theshock waves in the context of the large-scale structureof the universe.

Keywords Cosmic-rays · Large-scale structure of uni-verse · Magnetic fields · Shock waves · Turbulence

1 Introduction

Shock waves are ubiquitous in astrophysical environ-ments; from solar winds to the largest scale of theuniverse (Ryu et al. 2003). In the current paradigmof the cold dark matter (CDM) cosmology, the large-scale structure of the universe forms through hierarchi-cal clustering of matter. Deepening of gravitational po-tential wells causes gas to move supersonically. Cosmo-logical shocks form when the gas accretes onto clusters,filaments, and sheets, or as a consequence of the chaotic

Dongsu Ryu

Department of Astronomy and Space Science, Chungnam Na-tional University, Daejeon 305-764, Koreaemail: ryu@canopus.cnu.ac.kr

Hyesung Kang

Department of Earth Sciences, Pusan National University, Pusan609-735, Koreaemail: kang@uju.es.pusan.ac.kr

flow motions of the gas inside the nonlinear structures.The gravitational energy released during the formation

of large-scale structure in the universe is transferred bythese shocks to the intergalactic medium (IGM).

Cosmological shocks are collisionless shocks whichform in a tenuous plasma via collective electromagneticinteractions between baryonic particles and electromag-netic fields (Quest 1988). They play key roles in gov-erning the nature of the IGM through the following pro-cesses: in addition to the entropy generation, cosmic-rays (CRs) are produced via diffusive shock accelera-tion (DSA) (Bell 1978; Blandford and Ostriker 1978),magnetic fields are generated via the Biermann batterymechanism (Kulsrud et al. 1997) and Weibel instability

(Medvedev et al. 2006) and also amplified by streamingCRs (Bell 2004), and vorticity is generated at curvedshocks (Binney 1974).

Cosmological shocks in the intergalactic space havebeen studied in details using various hydrodynamic sim-ulations for the cold dark matter cosmology with cos-mological constant (ΛCDM) (Ryu et al. 2003; Pfrom-mer et al. 2006; Kang et al. 2008). In this contribution,we describe the properties of cosmological shocks andtheir implications for the intergalactic plasma from asimulation using a PM/Eulerian hydrodynamic cosmol-ogy code (Ryu et al. 1993) with the following param-eters: ΩBM = 0.043, ΩDM = 0.227, and ΩΛ = 0.73,

h ≡ H 0/(100 km/s/Mpc) = 0.7, and σ8 = 0.8. A cu-bic region of comoving size 100 h−1 Mpc was simulatedwith 10243 grid zones for gas and gravity and 5123 par-ticles for dark matter, allowing a uniform spatial resolu-tion of ∆l = 97.7h−1 kpc. The simulation is adiabaticin the sense that it does not include radiative cooling,galaxy/star formation, feedbacks from galaxies/stars,and reionization of the IGM. A temperature floor wasset to be the temperature of cosmic background radia-tion.

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Fig. 1 Two-dimensional images showing x-ray emissivity (top left), locations of shocks with color-coded shock speed V s(top right), perpendicular component of vorticity (bottom left), and magnitude of vorticity (bottom right) in the region of (25 h−1Mpc)2 around a galaxy cluster at present (z = 0). Color codes V s from 15 (green) to 1,800 km s−1 (red).

2 Properties of Cosmological Shocks

As a post-processing step, shocks in the simulated vol-ume are identified by a set of criteria based on the shock

jump conditions. Then the locations and properties of the shocks such as shock speed (V s), Mach number (M ),and kinetic energy flux (f kin) are calculated.

In the top panels of Figure 1, we compare the loca-tions of cosmological shocks with the x-ray emissivityin the region around a cluster of galaxies, both of whichare calculated from the simulation data at redshiftz = 0. External shocks encompass this complex nonlin-ear structure and define the outermost boundaries upto ∼ 10 h−1 Mpc from the cluster core, far beyond theregion observable with x-ray of size ∼ 1 h−1 Mpc. In-

ternal shocks are found within the region bounded byexternal shocks. External shocks have high Mach num-bers of up to M ∼ 103 due to the low temperature of the accreting gas in the void region. Internal shocks,

on the other hand, have mainly low Mach numbers of M 3, because the gas inside nonlinear structures hasbeen previously heated by shocks and so has high tem-perature.

The frequency of cosmological shocks in the simu-lated volume is represented by the quantity S , the areaof shock surfaces per unit comoving volume, in otherwords, the reciprocal of the mean comoving distancebetween shock surfaces. In the top left panel of Figure2, we show S (V s) per unit logarithmic shock speed in-terval at z = 0. We note that the frequency of low speed

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Shock Waves in the Large-Scale Structure of the Universe 3

Fig. 2 (Top left) Reciprocal of the mean comoving distancebetween shock surfaces at z = 0 in units of 1/(h−1Mpc).(Top right) Kinetic energy flux passing through shock sur-faces per unit comoving volume at z = 0 in units of 1040 ergss−1 (h−1Mpc)−3. (Bottom left) Thermal energy dissipated(dotted line) and CR energy generated (solid line) at shocksurfaces, integrated from z = 5 to 0. (Bottom right) Cu-mulative energy distributions. The energies in the bottompanels are normalized to the total thermal energy at z = 0.All quantities are plotted as a function of shock speed V s.

shocks with V s < 15 km s−1 is overestimated here,

since the temperature of the intergalactic medium isunrealistically low in the adiabatic simulation withoutthe cosmological reionization process. Although shockswith V s ∼ a few × 10 km s−1 are most common, thosewith speed up to several ×103 km s−1 are present atz = 0. The mean comoving distance between shock sur-faces is 1/S ∼ 3 h−1Mpc when averaged over the entireuniverse, while it is ∼ 1 h−1Mpc inside the nonlinearstructures of clusters, filaments, and sheets.

In order to evaluate the energetics of cosmologicalshocks, the incident shock kinetic energy flux, f kin =(1/2)ρ1V 3

s , is calculated. Here ρ1 is the preshock gas

density. Then the average kinetic energy flux throughshock surfaces per unit comoving volume, F , is calcu-lated. The top right panel of Figure 2 shows F (V s)per unit logarithmic shock speed interval. Energeti-cally the shocks with V s > 103 km s−1, which form inthe deepest gravitation potential wells in and aroundclusters of galaxies, are most important. Those respon-sible for most of shock energetics are the internal shockswith relatively low Mach number of M ∼ 2 − 4 in thehot IGM, because they form in the high-density gas in-side nonlinear structures. On the other hand, external

Fig. 3 Gas thermalization efficiency, δ(M ), and CR ac-celeration efficiency, η(M ), as a function of Mach number.Symbols are the values estimated from numerical simula-tions based on a DSA model and dotted and dashed linesare the fits. Solid line is for the gas thermalization efficiencyfor shocks without CRs.

shocks typically form in accretion flows with the low-

density gas in voids, so the amount of the kinetic energypassed through the external shocks is rather small.

3 Energy Dissipation at Cosmological Shocks

In addition to the gas entropy generation, the accelera-tion of CRs is an integral part of collisionless shocks, inwhich electromagnetic interactions between plasma andmagnetic fields provide the necessary viscosities. Supra-thermal particles are extracted from the shock-heatedthermal particle distribution (Malkov and Drury 2001).With 10−4 − 10−3 of the particle flux passing throughthe shocks injected into the CR population, up to ∼60%of the kinetic energy of strong quasi-parallel shocks canbe converted into CR ions and the nonlinear feedback tothe underlying flow can be substantial (Kang and Jones2005). At perpendicular shocks, however, the CR in-

jection and acceleration are expected to be much lessefficient, compared to parallel shocks, since the trans-port of low energy particles normal to the average fielddirection is suppressed. So the CR acceleration dependssensitively on the mean magnetic field orientation.

Time-dependent simulations of DSA at quasi-parallelshocks with a thermal leakage injection model and a

Bohm-type diffusion coefficient have shown that theevolution of CR modified shocks becomes self-similar,after the particles are accelerated to relativistic en-ergies and the precursor compression reaches a time-asymptotic state (Kang and Jones 2005, 2007). Theself-similar evolution of CR modified shocks dependssomewhat weakly on the details of various particle-waveinteractions, but it is mainly determined by the shockMach number. Based on this self-similar evolution, wecan estimate the gas thermalization efficiency, δ(M ),and the CR acceleration efficiency, η(M ), as a function

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Shock Waves in the Large-Scale Structure of the Universe 5

can be regarded as the turbulence energy, εturb. Asshown in Ryu et al. (2008), εturb < εtherm in clus-ters/groups. In particular, the mass-averaged valueis εturb/εthermmass = 0.1 − 0.3 in the intraclustermedium (ICM), which is in good agreement with the

observationally inferred values in cluster core regions(Schuecker et al. 2004). In filaments and sheets, thisratio is estimated to be 0.5 εturb/εtherm 2 and itincreases with decreasing temperature.

5 Intergalactic Magnetic Field

How have the intergalactic magnetic fields (IGMFs)arisen? The general consensus is that there was no vi-able mechanism to produce strong, coherent magneticfields in the IGM prior to the formation of large-scalestructure and galaxies (Kulsrud and Zweibel 2008).

However, it is reasonable to assume that weak seedfields were created in the early universe. A num-ber of mechanisms, including the Biermann batterymechanism (Kulsrud et al. 1997) and Weibel instabil-ity (Medvedev et al. 2006) working at early cosmologi-cal shocks, have been suggested (Kulsrud and Zweibel2008). The turbulence described in §4 then can am-plify the seed fields in the IGM through the stretch-ing of field lines, a process known as the turbulencedynamo. In this scenario the evolution of the IGMFsshould go through three stages: (i) the initial exponen-tial growth stage, when the back-reaction of magnetic

fields is negligible; (ii) the linear growth stage, whenthe back-reaction starts to operate; and (iii) the finalsaturation stage (Cho and Vishniac 2000; Cho et al.2008).

In order to estimate the strength of the IGMFs re-sulted from the dynamo action of turbulence in theIGM, we model the growth and saturation of magneticenergy as:

εBεturb

=

0.04 × exp[(t − 4)/0.36] for t < 4,

(0.36/41) × (t − 4) + 0.04 for 4 < t < 45,

0.4 for t > 45,

based on a simulation of incompressible magnetohydro-dynamic turbulence (Ryu et al. 2008; Cho et al. 2008).Here t = t/teddy is the number of eddy turnovers. Thisprovides a functional fit for the fraction of the turbu-lence energy, εturb, transfered to the magnetic energy,εB, as a result of the turbulence dynamo.

The above formula is convoluted to the data of thesimulation described in §1, setting t ≡ ω ×tage, and thestrength of the IGMFs is calculated as B = (8πεB)1/2.The resulting magnetic field strength is presented inthe bottom panels of Figure 4. On average the IGMFs

are stronger in hotter and denser regions. The strengthof the IGMFs is B 1µG inside clusters/groups (themass-averaged value for T > 107 K), ∼ 0.1µG aroundclusters/groups (the volume-averaged value for T > 107

K), and ∼ 10 nG in filaments (with 105 < T < 107

K) at present. The IGMFs should be much weakerin sheetlike structures and voids. But as noted above,turbulence has not developed fully in such low densityregions, so our model is not adequate to predict thefield strength there.

We note that in addition to the turbulence dynamo,other processes such as galactic winds driven by super-nova explosions and jets from active galactic nuclei canfurther strengthen the magnetic fields to the IGM (forreferences, see Ryu et al. 2008)

6 Conclusion

Shocks are inevitable consequences of the formationof large-scale structure in the universe. They heatgas, accelerate cosmic-ray particles, produce vortic-ity and turbulence, and generate and amplify mag-netic fields in the IGM. By applying detailed mod-els of the DSA and the turbulence dynamo to thedata of a cosmological hydrodynamic simulation of aconcordance ΛCDM universe, we have made the fol-lowing quantitative estimates: εCRp/εtherm ∼ 0.4 inthe IGM, εturb/εthermmass = 0.1 − 0.3 in the ICM,εturb/εtherm ∼ 0.5 − 2 in filaments and sheets, B

1µG inside clusters/groups, B ∼ 0.1µG around clus-ters/groups, and B ∼ 10 nG in filaments at present.Our results suggest that the non-thermal componentscan be energetically significant in the intergalacticplasma of large-scale structure, as in the interstellarplasma inside Our Galaxy.

Acknowledgements The work of DR was supportedby the Korea Research Foundation Grant funded bythe Korean Government (MOEHRD) (KRF-2007-341-C00020). The work of HK was supported for two yearsby Pusan National University Research Grant.

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References

Bell, A. R.: The acceleration of cosmic rays in shock fronts.I. Mon. Not. Roy. Astron. Soc. 182, 147-156 (1978)

Bell, A. R.: Turbulent amplification of magnetic field anddiffusive shock acceleration of cosmic rays. Mon. Not.

Roy. Astron. Soc. 353, 550-558 (2004)Binney, J.: Galaxy formation without primordial turbu-

lence: mechanisms for generating cosmic vorticity. Mon.

Not. Roy. Astron. Soc. 168, 73-92 (1974)Blandford, R. D., Ostriker, J. P.: Particle acceleration by

astrophysical shocks. Astrophys. J. 221, L29-L32 (1978)Cho, J., Vishniac, E. T.: The generation of magnetic fields

through driven turbulence. Astrophys. J. 538, 217-225(2000)

Cho, J., Vishniac, E. T., Beresnyak, A., Lazarian, A., Ryu,D.: Growth of magnetic fields induced by turbulent mo-tions. Astrophys. J. submitted (2008)

Kang, H., Jones, T. W.: Efficiency of nonlinear particle ac-celeration at cosmic structure shocks. Astrophys. J. 620,

44-58 (2005)Kang, H., Jones, T. W.: Self-similar evolution of cosmic-ray-modified quasi-parallel plane shocks. Astropart. Phys. 28,232-246 (2007)

Kang, H., Ryu, D., Cen, R., Ostriker, J. P.: Propagation of ultra-high-energy protons through the magnetized cosmicweb. Astrophys. J. 669, in press (2008)

Kang, H., Ryu, D., Cen, R., Song, D.: Shock-heated gasin the large-scale structure of the universe. Astrophys. J.

620, 21-30 (2005)Kulsrud, R. M., Cen, R., Ostriker, J. P., Ryu, D.: The

Protogalactic origin for cosmic magnetic fields. Astrophys.

J. 480, 481-491 (1997)Kulsrud, R. M., Zweibel, E. G.; On the origin of cosmic

magnetic fields. Rep. Prog. Phys. 71, 046901, 1-33 (2008)Malkov M. A., Drury, L. O’ C.: Nonlinear theory of diffusive

acceleration of particles by shock waves. Rep. Prog. Phys.

64, 429-481 (2001)Medvedev, M. V., Silva, L. O., Kamionkowski, M.: Clus-

ter magnetic fields from large-scale structure and galaxycluster shocks. Astrophys. J. 642, L1-L4 (2006)

Pfrommer, C., Springel, V., Enßlin, T. A., Jubelgas, M.:Detecting shock waves in cosmological smoothed particlehydrodynamics simulations. Mon. Not. Roy. Astron. Soc.

367, 113-131 (2006)Quest, K. B.: Theory and simulation of collisionless parallel

shocks. J. Geophys. Res. 93, 9649-9680 (1988)Ryu, D., Kang, H., Cho, J., Das, S.: Turbulence and mag-

netic fields in the large-scale structure of the universe.

Science 320, 909-912 (2008)Ryu, D., Kang, H., Hallman, E., Jones, T. W.: Cosmologi-

cal shock waves and their role in the large-scale structureof the universe. Astrophys. J. 593, 599-610 (2003)

Ryu, D., Ostriker, J. P., Kang, H., Cen, R.: A cosmologicalhydrodynamic code based on the total variation dimin-ishing scheme. Astrophys. J. 414, 1-19 (1993)

Schuecker, P., Finoguenov, A., Miniati, F., Bohringer, H.,Briel, U. G.: Probing turbulence in the Coma galaxy clus-ter. Astron. Astrophys. 426, 387-397 (2004)

This manuscript was prepared with the AAS LATEX macros v5.2.