Nonthermal Emission Associated with Strong AGN Outbursts at the Centers of Galaxy Clusters
aa r X i v : . [ a s t r o - ph ] M a y Nonthermal Emission Associated with Strong AGN Outbursts atthe Centers of Galaxy Clusters
Yutaka Fujita , Kazunori Kohri , , Ryo Yamazaki , and Motoki Kino , ABSTRACT
Recently, strong AGN outbursts at the centers of galaxy clusters have beenfound. Using a simple model, we study particle acceleration around a shockexcited by an outburst and estimate nonthermal emission from the acceleratedparticles. We show that emission from secondary electrons is consistent with theradio observations of the minihalo in the Perseus cluster, if there was a strongAGN outburst & yrs ago with an energy of ∼ . × erg. The validityof our model depends on the frequency of the large outbursts. We also estimategamma-ray emission from the accelerated particles and show that it could bedetected with GLAST . Subject headings: acceleration of particles — radiation mechanisms: non-thermal– galaxies: active — galaxies: clusters: general — galaxies: clusters: individual:Perseus (A426)
1. Introduction
Diffuse synchrotron radio emission is often found in the intracluster medium (ICM)of galaxy clusters (e.g., Kim et al. 1990; Giovannini et al. 1993; Giovannini & Feretti 2000;Kempner & Sarazin 2001). These radio sources in clusters are often classified as either Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan; [email protected] Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, MS-51, 60 GardenStreet, Cambridge, MA 02138 Physics Department, Lancaster University, Lancaster LA1 4YB, UK; [email protected] Department of Physics, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan;[email protected] Institute of Space and Astronautical Science, JAXA, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510,Japan; [email protected] ∼ erg. The examplesare MS 0735.6+7421 (McNamara et al. 2005; Gitti et al. 2007), Hercules A (Nulsen et al.2005a), and Hydra-A (Nulsen et al. 2005b; Wise et al. 2007). Such an intensive outburstshould excite a shock in the ICM. In fact, weak shocks have been found in those clusters.In the early stage of the evolution of the shock, the Mach number is expected to be large.Therefore, particles would be accelerated at the shock as in the case of a supernova remnant.In this letter, we consider particle acceleration at the shock generated by an intensiveoutburst of the AGN at the cluster center. We study nonthermal emission from the accel-erated particles. In particular, we focus on nonthermal radio emission of secondary origin.Recently, Hinton & Domainko (2007) estimated gamma-ray emission associated with AGNoutbursts, assuming that the hot cavity behind a shock is entirely filled with high-energyprotons. This assumption may be too simple, and they did not discuss the acceleration andenergy spectrum of protons. However, motivated by this study, we also estimate the gamma-ray emission using our model. We take the Perseus cluster as a model cluster, because thiscluster has a well-studied minihalo. 3 –
2. Models
We assume that the duration of an AGN outburst is ∼ yr. Since we are interestedin the evolution of a shock for t & yr, where t = 0 corresponds to the ignition of theoutburst, the evolution can be approximated by that of an instant explosion with an energyof E at t = 0.For the sake of simplicity, we assume that the cluster is spherically symmetric and thedensity profile of the ICM has a form of a power-law: ρ ICM ( r ) = ρ ( r/r ) − ω . (1)We take ρ = 5 . × − g cm − , r = 10 kpc, and ω = 1 .
43, based on the density profileof the Perseus cluster for 70 < r <
300 kpc (Fig. 8 in Churazov et al. 2003). We takethat region because our model is correct for t & × yr, and the radius of the shock at t ∼ yr is R s ∼
70 kpc for parameters we adopt in § R s = ξ (cid:18) E ρ r ω (cid:19) / (5 − ω ) t / (5 − ω ) , (2)where ξ = "(cid:18) − ω (cid:19) π ( γ + 1) ( γ − − ω )9 γ − − ω ( γ + 1) / (5 − ω ) , (3)and γ (= 5 /
3) is the adiabatic index. The Mach number of the shock gradually decreases. Theshock stops expanding when its Mach number approaches to one. At this point, the cavityfilled with hot gas inside the shock becomes in pressure equilibrium with the surroundingICM. Since we stop calculation before the radiative cooling of the shock becomes effective( & Gyr), we do not need to consider the radiative cooling.Following Yamazaki et al. (2006), we assume that particles are accelerated at the shockvia diffusive shock acceleration (i.e., first-order Fermi acceleration) and that their energyspectra are given by N ( E ) ∝ E − x e − E/E max , (4)where E max is the maximum energy of the protons or electrons. The index is given by x = ( r b + 2) / ( r b − r b is the compression ratio of the shock (Blandford & Eichler1987). We estimate the maximum energies of the protons and electrons using the relationsof t acc = min { t pp , t } , t acc = min { t syn , t } , (5) 4 –respectively. Here, t acc , t pp , t and t syn are the acceleration time, the lifetime of high-energyprotons through pion production, the age of the shock wave, and the synchrotron coolingtime, respectively.Assuming the standard manner for the diffusion coefficient, the acceleration time isgiven by t acc = 20 hcE max eB d V s , (6)where c is the speed of light, − e is the electron charge, and V s (= dR s /dt ) is the shockvelocity (Jokipii 1987; Yamazaki et al. 2004). The correction factor h depends on the meanfree path of particles and the angle between the shock and the magnetic field. Since h ∼ h = 1 from now on. The downstream magnetic fieldis given by B d = r b B , where B is the magnetic field strength of the unperturbed ICM. Weestimate t pp as t pp = 5 . × yr ( n ICM / cm − ) − , (7)where n ICM is the number density of the ICM. Since the shock is in pressure equilibrium in ∼ yr (see §
3) and n ICM . . − , the cooling is not effective. Thus, the maximumenergy of protons is determined by the age of the shock. On the other hand, the synchrotroncooling time for electrons is given by t syn = 1 . × yr (cid:18) E max , e
10 TeV (cid:19) − (cid:18) B d µ G (cid:19) − , (8)and is shorter than the age of the shock. Thus, using relations (5), we obtain E max , p ∼ . × (cid:18) V s km s − (cid:19) (cid:18) B d µ G (cid:19) (cid:18) t yr (cid:19) TeV , (9) E max , e ∼ (cid:18) V s km s − (cid:19) (cid:18) B d µ G (cid:19) − / TeV . (10)We assume that the minimum electron and proton energies are their rest masses. Forgiven proton and electron spectra, we calculate radiation from them. We consider the syn-chrotron, bremsstrahlung, and inverse Compton emissions from primary electrons that aredirectly accelerated at the shock, the π -decay gamma-ray through proton-proton collisions,and the synchrotron, bremsstrahlung, and inverse Compton emissions from secondary elec-trons created through the decay of charged pions that are also generated through proton-proton collisions (Sturner et al. 1997; Kohri, Yamazaki, & Bamba 2007). The density oftarget protons for the proton-proton interaction is given by r b ρ ICM ( R s ) / (1 . m p ), where m p is the proton mass. We assume that the spectrum from secondary electrons is stationary 5 –if the lifetime of the electrons is smaller than the age of the system. On the other hand,if the lifetime is larger than the system age, we calculate the evolution according to §
3. Results
In our model, the evolution of a shock is determined by ρ ICM and E (equation [2]). TheMach number also depends on the ICM temperature, T . The energy spectrum of particlesdepends on the evolution of the shock and the magnetic field, B . The luminosity of nonther-mal emission from the shock depends on the total energy of high-energy ( > m p c ) protonsinside the shock, ǫE , where 0 ≤ ǫ ≤
1. We fix ρ ICM ( r ), T , and B ( r ) from observations. Onthe other hand, we regard E and ǫ as fitting parameters, because there are no observationaldata for them.We assume that T = 3 . r &
70 kpc. On the other hand, the observationsof Faraday rotation showed that the typical magnetic field strength in clusters for r .
500 kpc is 5–10 µ G (Clarke, Kronberg, & B¨ohringer 2001). Therefore, we take B ( r ) =7 µ G ( ρ ICM [ r ] /ρ ICM [150 kpc]) / assuming that the magnetic field is adiabatically compressed.We note that the spectra of particles (equations [9] and [10]) and synchrotron emission fromhigh-energy electrons depend on B . Thus, the results shown below is fairly sensitive to theassumption on B .In the following, the energy of an AGN explosion is E = 1 . × erg, which is threetimes larger than the one observed for MS 0735.6+7421 (McNamara et al. 2005). We usethis value to match R s with the size of the radio minihalo in the Perseus cluster. We takethe acceleration efficiency of ǫ = 0 .
05 to match radio observations (see below). The ratioof high-energy electrons to high-energy protons is taken to be r e − p = 1 / ∼ × < t < × yr). Performing simulations taking account of the back-reactionof accelerated particles on hydrodynamics, Ryu et al. (2003) estimated that the cosmic-rayacceleration efficiency is ∼ . > m p c must be smaller than 0.2. 6 –Although it is not certain whether equation (4) can be extrapolated down to the injectionenergy, the adopted value of ǫ = 0 .
05 is consistent with that of Ryu et al. (2003) because itis smaller than 0.2.Fig. 1 shows the spectrum of nonthermal emission from accelerated particles at t =2 × yr. The distance to the model cluster is 78.4 Mpc (the distance to the Perseus cluster ).Synchrotron emission from primary electrons is dominant upto ∼
100 keV. The maximumenergies for protons and electrons are E max , p = 6 . × eV and E max , e = 2 . × eV,respectively. The radius of the shock at this time is R s = 97 kpc, the shock velocity is V s = 2650 km s − , and the Mach number is 2.7.Fig. 2 shows the spectrum at t = 4 × yr. At this time, E max , p = 4 . × eV, E max , e = 2 . × eV, and R s = 143 kpc, which is close to the size of the minihalo inthe Perseus cluster. The shock velocity is V s = 1950 km s − and the Mach number is 2.0.In Figs. 1 and 2, we plot the observed radio fluxes of the minihalo in the Perseus cluster(Sijbring 1993; Gitti et al. 2002). As can be seen, the predicted radio synchrotron emission(long-dashed line) is too bright to be consistent with the observations. If we take smaller E ,the radio luminosity becomes smaller. However, the size of the minihalo is too small to beconsistent with the observed one. Moreover, if we consider a much smaller electron-protonratio (e.g. r e − p ∼ − ), the radio spectral index is inconsistent with the observations.One possibility is that the age is much larger than 4 × yr and is t & yr. Atthat time, the shock is not prominent because it is almost in pressure equilibrium with thesurrounding ICM. In fact, for the Perseus cluster, a shock of R s ∼ t = 2 × yr)to 2.0 (at t = 4 × yr). Accordingly, the compression ratio ( r b ) decreases, which affectsthe energy spectrum of particles and the emission from them (eq. [4]). Ryu et al. (2003)indicated that particles are no longer accelerated if the Mach number is .
2. Thus, for t & × yr, particle acceleration at the shock is not effective.At t ∼ yr, the emission from primary electrons may have died out, because electronswith a Lorentz factor of γ & , which are responsible for the radio emission, lose theirenergy through synchrotron emission and inverse Compton emission on a time-scale of . × (e.g. Sarazin 1999). On the other hand, the lifetime of protons is much larger than 10 yr(eq. [7]), and the diffusion time of protons having the maximum energy of ∼ eV fromthe central region of the cluster ( ∼
200 kpc) is 2 × yr (V¨olk, Aharonian, & Breitschwerdt1996). Since particles are no longer accelerated at t & × yr, the overall spectrum The redshift of the Perseus cluster is 0.0183. We assumed that the cosmological parameters are Ω = 0 . λ = 0 .
7, and H = 70 km s − Mpc − × . t . × yr.In the radio band, only synchrotron emission from secondary electrons (dot-dashed line inFig. 2) will be observed at t ∼ yr. In this case, the predicted spectrum (thick-solid linein Fig. 2) well fits the radio observations. Since the secondary radio emission is producedby protons having energies of ∼
100 GeV and since the diffusion time of these protons is > Gyr, the radio emission could persist that time. We emphasize that the assumption on theelectron-proton ratio ( r e − p ) is not required to estimate the emission originated from protoncollisions.
4. Discussion
Although our model is basically an one-zone model and cannot quantitatively predictthe spatial change of the spectrum, we can qualitatively predict that. Compared with theone at t = 2 × yr (Fig. 1), the spectrum of synchrotron emission from secondary electronsat t = 4 × yr is softer in the radio band ( ∼ . t = 2 × yr, R s = 97 kpc) to 1.88 ( t = 4 × yr, R s = 142 kpc). Since some of the protons accelerated at an earlier time should remain inthe inner region of a cluster, the spectrum should be less steep in the inner region. Thistendency is consistent with observations (Sijbring 1993; Gitti et al. 2002).As we mentioned above, the radio emission from secondary electrons could persist fora long time ( > Gyr). Our model will be tested for the frequency (or the event rate) oflarge outbursts. Gitti et al. (2007) indicated that large outbursts are likely occurring ∼ < erg(Rafferty et al. 2006), which is smaller than our finding (1 . × erg). Thus, the rarenessmay indicate that strong AGN outbursts with energies of > erg are rare phenomenaor minor cluster mergers often perturb cluster cores. Another possibility is that particleacceleration at low-Mach number shocks occurs only in some specific IGM environmentsdepending on the density of the surrounding matter, magnetic field configurations, and soon. In the future, statistical studies about AGN outbursts of ∼ erg are highly desired.The morphology of the radio surface brightness would also be important to check the validityof the model. If the particle acceleration is triggered by the expanding shock, one wouldexpect a torus-like shape instead of the spherical shape observed for minihalos (Gitti et al.2002). However, for clusters observed so far, the central region behind the shock is notempty; the ICM is still filling (e.g. Fig. 3 of McNamara et al. 2005). Thermal protons there 8 –may work as target protons for the proton-proton interaction and thus the radio emissionmay not be a torus-like shape. A spatially resolved model must be constructed to addressthis issue.In Figs. 1 and 2, we also plot the observational upper limits of gamma-ray emissionfrom the Perseus cluster (Perkins et al. 2006). At t = 2 × yr, the gamma-ray emissionis brighter than the observations. At t ∼ yr, there is no longer emission from primaryelectrons, and only gamma-ray emission of proton origin (thick-solid line in Fig. 2) willbe observed in the gamma-ray band. The predicted gamma-ray flux at E ∼ eV is ∼ × − erg cm − s − , which could be detected with GLAST with a sensitivity of ∼ × − erg cm − s − . The gamma-ray emission would persist for ∼ t pp . If the gamma-rayis detected, it directly indicates that protons as well as electrons are accelerated in clusters.Moreover, the luminosity reflects the total energy of the protons.On the other hand, it would be difficult to detect the emission with imaging atmosphericCherenkov telescopes. For example, H.E.S.S. has a sensitivity of ∼ × − erg cm − s − at ∼ eV). The predicted flux is smaller than the detection limit (Fig. 2).The authors wish to thank the referee for useful comments. We are also grateful toT. Mizuno and Y. Ohira for fruitful discussions. Y. F. and R. Y. were each supportedin part by Grants-in-Aid from the Ministry of Education, Science, Sports, and Culture ofJapan (Y. F.: 17740162, R. Y.: 18740153). K. K. was also supported in part by NASAgrant NNG04GL38G, PPARC grant, PP/D000394/1, EU grant MRTN-CT-2006-035863,the European Union through the Marie Curie Research and Training Network ”UniverseNet”(MRTN-CT-2006-035863) REFERENCES
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11 –Fig. 1.— The spectrum of a shock at t = 2 × yr. Emissions from primary electronsare synchrotron (long-dashed), bremsstrahlung (short-dashed) and inverse Compton (thindotted). Emissions related to protons are π -decay gamma-ray (thin-solid), synchrotron(dot-dashed), bremsstrahlung (short-and-long dashed), and inverse Compton (thick-dotted)emissions from secondary electrons. The thick-solid line shows the total nonthermal flux.Radio observations are shown by dots (Sijbring 1993; Gitti et al. 2002), and gamma-rayupper limits are shown by arrows (Perkins et al. 2006). 12 –Fig. 2.— Same as Fig. 1, but for t = 4 ×7