Dongsu Ryu and Hyesung Kang- Cosmic Rays Accelerated at Shock Waves in Large Scale Structures

8/3/2019 Dongsu Ryu and Hyesung Kang- Cosmic Rays Accelerated at Shock Waves in Large Scale Structures

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Journal of The Korean Astronomical Society

37: 477 482, 2004

COSMIC RAYS ACCELERATED AT SHOCK WAVES IN LARGE SCALE

STRUCTURE

Dongsu Ryu1 and Hyesung Kang2

1Department of Astronomy & Space Science, Chungnam National University, Daejon 305-764, Korea2Department of Earth Sciences, Pusan National University, Pusan 609-735, Korea

E-mail: [email protected], [email protected]

ABSTRACT

Shock waves form in the intergalactic space as an ubiquitous consequence of cosmic structure forma-tion. Using N-body/hydrodynamic simulation data of a CDM universe, we examined the propertiesof cosmological shock waves including their morphological distribution. Adopting a diffusive shock ac-celeration model, we then calculated the amount of cosmic ray energy as well as that of gas thermalenergy dissipated at the shocks. Finally, the dynamical consequence of those cosmic rays on clusterproperties is discussed.

Key words : cosmic rays large scale structure of universe shock waves

I. INTRODUCTION

Intergalactic shock waves develop as a consequenceof the large scale structure formation of the universe(see, e.g., Ryu & Kang, 1998; Quilis et al., 1998; Miniatiet al., 2000; Ryu et al., 2003; Gabici & Blasi, 2003).Those cosmological shock waves, like most astrophys-ical shocks, are collisionless features mediated by col-lective, electromagnetic viscosities. Through dissipa-tion the cosmological shock waves convert a part of the

gravitational energy associated with structure forma-tion into heat. At the same time, due to incompleteplasma thermalization at collisionless shocks, a sizableportion of the shock energy can be converted into cos-mic ray (CR) energy (mostly ionic) via diffusive shockacceleration (Kang et al., 1996; Miniati et al., 2001b,a;Ryu et al., 2003; Gabici & Blasi, 2003) (see, also Blasi,2004; Miniati, 2004).

Diffuse synchrotron radio halos or/and radio relicshave been observed in a number of clusters, indicat-ing the existence of CR electrons as well as magneticfield in the intracluster medium (ICM) (Feretti et al.,2004; Giovannini & Feretti, 2004). In addition, EUVand/or hard X-ray radiation excesses over the thermal

X-ray from hot gas has been reported in some clus-ters, which are due to inverse-Compton scattering ofcosmic background radiation photons by CR electrons(Bowyer, 2004; Henriksen & Hudson, 2004). If some ofthose CR electrons have been energized at cosmologicalshock waves, the same process should have produced agreater CR proton population, although the existenceof CR protons in the ICM is yet to be confirmed by ob-servations of -rays by inelastic collisions between CRand thermal-gas protons (Reimer, 2004).

In this paper, first we describe the distribution andproperties of cosmological shock waves, studied in a

Proceedings of The 3rd Korean Astrophysics Workshop onCosmic Rays and Magnetic Fields in Large Scale Structure

numerical simulation of the CDM cosmology. Then,we present an estimate for the amount of CR protonsthat should have been accelerated in those shocks. Wefind that the energy of the CR protons in the ICMcould be a significant fraction of gas thermal energy.Finally, we describe the possible influence of such CRson the properties of clusters/groups, again studied withnumerical simulations of the CDM cosmology.

II. SHOCK WAVES IN LARGE SCALE

STRUCTURE

To study the distribution and properties of cosmo-logical shock waves, the data from an N-body/hydrody-namic simulation of a CDM universe with radiativecooling were used. The simulation was performedusing a PM+Eulerian hydrodynamic cosmology codethat was specifically designed to capture shocks with ahigh accuracy (Ryu et al., 1993). The CDM modeladopted the currently favored values of the followingcosmology parameters: BM = 0.043, DM = 0.227, = 0.73 (BM + DM + = 1), h H0/(100km/s/Mpc) = 0.7, and 8 = 0.8. These values are con-sistent with those fitted with the recent WMAP data

(see, e.g., Spergel et al., 2003). A cubic region of sizeL = 100h1Mpc at present was simulated inside thecomputational box with 10243 grid zones for gas andgravity and with 5123 particles for dark matter.

Shock waves, which were created by supersonic flowmotion in the course of large scale structure formation,were identified in the simulation and their character-istics were quantified (see Ryu et al., 2003; Kang etal., 2005, for details). Based on close examination ofshock locations and the properties of the shocks andtheir associated flows, we classified cosmological shockwaves into two categories, externaland internal shocks.External shocks surround sheets, filaments and knots,forming when never-shocked, low density, void gas ac-cretes onto those nonlinear structures. Internal shocks

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Fig. 1. Time evolution of shock wave distributionaround a cluster complex in a two-dimensional slice of28h1 37h1 Mpc2. Color indicates shocks of differentcategories: black - external shocks with vsh < 150 km s

1,red - external shocks with 150 < vsh < 700 km s

1, blue -external shocks with vsh > 700 km s

1, magenta - internalshocks with vsh < 150 km s

1, yellow - internal shocks with150 < vsh < 700 km s

1, and cyan - internal shocks withvsh > 700 km s

1.

form and are distributed within the regions boundedby external shocks. Figure 1 shows in a two dimen-sional slice the time evolution of shock waves identifiedaround a cluster complex. It plots the distributions ofexternal and internal shocks, which were coded withdifferent colors depending on shock speed.

It is expected that the speed of cosmological shockwaves reflects the depth of gravitational potentialwells of nonlinear structures, and hence their mor-phology. In the simulation, 1) high-speed shocks withvsh > 700 km s

1 are found mostly around and in-side knot-like structures of clusters/groups, 2) shockswith 150 km s1 < vsh < 700 km s

1 mostly around

and inside filamentary structures, and 3) low-speedshocks with vsh < 150 km s

1 mostly around and in-side sheet-like structures. Figure 2 display the volumerendering images of shock waves with three ranges ofspeed in small regions of computational box. The figuredemonstrates clearly that the morphology of nonlinearstructures can be revealed through the distributions ofshocks with different speeds.

In order to quantify the occurrence of shocks, thesurface area of identified shocks per logarithmic Machnumber interval, dS(M, z)/d log M, normalized by thevolume of the simulation box, was calculated. Fig-ure 3 shows dS(M, z)/d log M for external and internalshocks at several epochs. A few points are noticed. 1)

Fig. 2. Volume rendering of three-dimensional shockwave distribution at z = 0. Top panel: shock waves withvsh < 150 km s

1 in a region of (25 h1Mpc)3. Middlepanel: shock waves with 150 < vsh < 700 km s

1 in aregion of (31 h1Mpc)3. Bottom panel: shock waves with

vsh > 700 km s1

in a region of (25 h1

Mpc)3

.


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CRS AT COSMOLOGICAL SHOCKS 479

At present, the mean distance between shock surfacesover all the computational volumes is 3h1 Mpc.The mean distance between shock surfaces inside non-

linear structures is 1h1

Mpc. 2) At present, exter-nal shocks are more common than internal shocks. Thetotal surface area of external shocks is about twice ofthat of internal shocks. 3) External shocks are strongerwith Mach number extending up to several hundreds,while internal shocks are weaker with Mach numbermostly less than 10. It is because the preshock gashas T 104 K for external shocks, but it is much hot-ter for internal shocks. However, although the meanMach number is higher for external shocks, the meanshock speed is actually larger for internal shock. In ad-dition, the preshock gas density is significantly higherfor internal shocks.

III. CRS ACCELERATED AT COSMOLOG-ICAL SHOCKS

To estimate the amount of CR protons acceleratedat cosmological shock waves, we calculated the follow-ing energy fluxes through shock surfaces: 1) the ki-netic energy flux, f = (1/2)1v

3sh; 2) the thermal

energy flux generated at shocks, fth; 3) the CR en-ergy extracted, i.e., nonthermal dissipation, at shocks,fCR. The thermal energy flux was computed from theRankine-Hugoniot jump condition. Then, the ratiofth/f (M) can be defined as the efficiency of shockthermalization. Similarly, the efficiency of CR acceler-ation, fCR/f (M), can be defined as well. The

efficiency (M) can be estimated with nonlinear nu-merical models of diffusive shock acceleration (DSA) atquasi-parallel shocks. We computed the values of(M)using one-dimensional simulations of CR proton accel-eration and accompanying CR-modified flow evolutionfor shocks with vsh = 1500 3000 km s

1 propagatinginto media of T = 104 108 K, assuming Bohm-typediffusion for CRs (Kang & Jones, 2004).

The thermal and CR energies dissipated at shocksurfaces can be calculated by convolving the shockMach number distribution in Figure 3 with (M) and(M). To measure the dissipations at shocks as well asthe kinetic energy flux through shocks over the cosmo-

logical time scale, we integrated those quantities fromz = 2 to z = 0, dYi(M)/d log M, with i (for ki-netic energy flux), th, and CR. We also summed thesetime-integrated quantities to calculate the associatedglobal shock-processed quantities, Yi(> M). Figure4 shows dYi(M)/d log M and Yi(> M) for externaland internal shocks. The figure indicates that ener-getically internal shocks are more important than ex-ternal shocks, although they are less common. It isbecause internal shocks have higher preshock densityand velocity, as noted in the previous section. Specif-ically, internal shocks with 2 < M < 5 are most im-portant, accounting for 1/2 of CR energy genera-tion. With the DSA model we adopted, the ratio of

the CR to thermal energies dissipated at cosmological

shock waves with the Mach number greater than 1.5 isYCR( 1.5)/Yth( 1.5) 1/2.

IV. DYNAMICAL INFLUENCE OF CRS ONCLUSTERS

The time scales of CR proton trapping and energyloss are larger than the Hubble time scale in most en-ergy range. Hence, once generated, CR protons shouldfill the volume inside filaments and sheets as well as inclusters/groups. The existence of substantial CR pro-tons should have affected the evolution and the dynam-ical status of the large scale structure of the universe.

To study the influence of such CRs, we performedan additional set of numerical simulations, where thedynamical effects of CRs were included explicitly. Thesimulations employed the CDM cosmology same as

that described in II. But a cubic region of size 75h1Mpc at the current epoch was simulated inside a com-putational box with 5123 gas, CR and gravity zonesand 2563 dark matter particles. Two simulations weredone, one with CRs included and the other withoutCRs. The convection equation for the CR energy wassolved explicitly in a two-fluid approximation, in addi-tion to the standard set of equations for dark matterand gas. It was assumed that the sources (AGNs),which deposit CRs into the ICM, form at 40 differentepochs after the redshift z = 10, if the following criteriaare satisfied in each grid zone

Mgas 4 1010

(1 + z)1/5 h1

M,ukxk < 0, (1)

where Mgas is the total gas mass inside the zone and ukis the flow velocity. It was further assumed that eachsource ejects the following amount of CR energy intothe ICM

ECR = 3 104h1M c

2. (2)

Note that at z = 0 this translates into the CR efficiency,ECR/Mgasc

2 = 7.5 107. With the above model forCR deposit, the CR energy density in the ICM becomes 1/2 of the gas thermal energy density at z 1 andstays constant afterwards.

The global effect of CRs on the growth of the largescale structure is exhibited in Figure 5. With ECR 1/2Eth on average, the power of density perturbationwas decreased by 50% at the present epoch on thecluster scale of 1h1 Mpc. However, the structuresof scales larger than the cluster scale have been lessaffected. It is because the sources formed mostly at thehighest density peaks within clusters/groups, but alsoit is expected that the dynamical effects of CR pressureas well as thermal pressure are most important in theICM.

In order to examine the dynamical effects of CRs onindividual clusters/groups, we identified them in simu-lation data and calculated their properties, such as X-

ray luminosity, Lx, gas mass, Mgas, temperature, Tx,


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Fig. 3. Inverse of the mean comoving distance between shock surfaces with Mach number between log M and log M +d(log M) at different redshifts, dS(M, z), for external shocks (left panel) and internal shocks (right panel).

Fig. 4. Left panel: kinetic energy, dY(M), thermal energy, dYth(M), and CR energy, dYCR(M), processed throughsurfaces of external and internal shocks with Mach number between log M and log M+ d(log M), from z = 2 to z = 0. Rightpanel: same energies, Y(> M), Yth(> M), YCR(> M), processed through surfaces of external and internal shocks withMach number greater than M, from z = 2 to z = 0. The energies are normalized to the total gas thermal energy, Eth, insidesimulation box at z = 0.


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CRS AT COSMOLOGICAL SHOCKS 481

Fig. 5. Power spectrum of gas density perturbations atthree different epochs. Solid lines are from the simulationwith CRs and dotted lines are from the simulation withoutCRs. Vertical line marks the scale of 1h1 Mpc.

gas thermal energy, Eth and CR energy ECR. We foundthat the slopes of the Lx Tx and Mgas Tx relationsdo not change noticeably. However, the additional CRpressure reduces Lx, Mgas, and Tx of identified clus-ters/groups. Quantitative estimates of changes in thesecluster properties can be seen in Figure 6, which showsthe ratios of Lx, Mgas, and Tx for the same clusterswithout/with CRs, as a function of ECR/Eth. Here,

Eth is the gas thermal energy of clusters with CRs.Clusters have the values of ECR/Eth between 0.1 to 2due to statistical fluctuation of CR sources. In the clus-ters with ECR/Eth 1/2, we can see that Mgas and Txare reduced by 15% due to CRs, while Lx is reducedby 30%.

ACKNOWLEDGEMENTS

DR and HK acknowledge P. L. Biermann, T. W.Jones, E. Hallman for collaborations and discussions.DR was supported in part by a grant of the ChungnamNational University 2004 R&D Project. HK was sup-

ported in part by KOSEF through Astrophysical Re-

Fig. 6. Ratios of X-ray luminosity (top panel), mass(middle panel) and temperature (bottom panel) for the sameclusters/groups but with/without CRs, as a function of theratio of CR to thermal energies. 50 clusters/groups areshown. Solid lines represent the least square fits. Vertical

lines mark ECR

/Eth

= 0.2, 0.5, and 1.

search Center for the Structure and Evolution of Cos-mos (ARCSEC)

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Dongsu Ryu and Hyesung Kang- Cosmic Rays Accelerated at Shock Waves in Large Scale Structures

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