Nonthermal Radiation from Merging Clusters of Galaxies

1. Nonthermal Radiation from Merging Clusters of Galaxies Robert C. Berrington (NRL) Chuck Dermer (NRL) Penn State U., May 27th, 2003 (ApJ, in press, 2003, astro/ph 0209436)

2. Outline • Shocks are formed during structure formation in merging clusters of galaxies • Nonthermal particle and photon production: • radio, UV, X-ray, g-ray emission • Contributions to unidentified EGRET g-ray sources and diffuse background radiations • UHECR acceleration • Nonthermal probe of CDM distribution

3. Structure Formation • Density fluctuations cause region to collapse. • Magnitude of the density fluctuation determines the formation time • Larger structures form by accreting smaller clumps--hierarchical merging • Lumpy, continuous accretion • Mergers (virialized clumps) Major mergers (disrupts internal dynamics of dominant cluster; >~ 60% relative masses) Minor mergers (~10-60%) Accretion processes (<10%) (Fujita and Sarazin 2001) B. Moore, www.nbody.net

4. Rich Clusters Contain thousands of Galaxies Masses ~1015 Msun Poor Clusters Contain hundreds of Galaxies Masses ~1014 MSun Physical Properties of Galaxy Clusters Coma MKW4

5. Regular and Irregular Clusters Berrington, Lugger, and Cohn 2002 • Measure velocity distributions • Subcluster structure in Abell 2256

6. Galaxy Clusters at X-ray Energies • Hot gas ~5-15% of total mass of cluster • Hot ICM emits in X-ray via thermal bremsstrahlung (free-free) • Rich clusters: ~ 5-10 keV • Poor clusters: ~1-5 keV • Lx ~ 1043-1045 ergs s-1 • Tx ~ 2-10 keV

7. b-model density distributions • Inferred from surface brightness density profile • Profile of bulge/elliptical galaxy and large-scale galaxy cluster structure • Spherically symmetric, isothermal beta-model profile:

8. Model Cluster (Bode et al. 1994) • N-body simulation • CDM cluster and individual galaxy halo King-model distributions • 80000 particles per cluster; 40000 in DM halo; 40000 in galaxies of which 10% in normal matter

9. The Physics of Cluster Mergers • Total gravitational energy available:

10. Cluster Merger Simulation • Zero impact parameter • Cluster galaxies evolutionary • History: morphology of disturbed system (e.g., cD galaxies ) • Merger rate of supermassive black holes • Merger trees

11. Semi-Analytic Cluster Dynamics • Cluster infall velocity • Assume matter follows an isothermal  or NFW model • Calculate merging cluster infall velocity and center-of-mass position by solving: M(r) is the mass interior to radius r, m is subcluster mass. For b-model:

12. Merging Speeds

13. Shocks in Merging Clusters • Shocks form in ICM at boundary • if vs exceeds sound speed of ICM • Thermal particles swept up in shock • Accelerated via first-order Fermi • Sizes: ~1 Mpc are possible • May also reaccelerate particles • Head-tail radio galaxies nearby

14. Hydrodynamical Simulations • Show development of shocks both before and after center-of-mass passage. Ricker and Sarazin (ApJ, 561, 621, 2001)

15. Cluster Radio Emission • Nonthermal Synchrotron radiation • Luminosity: ~1040-1042 ergs s-1 • Steep spectra • Radio galaxies • Sources of extended radio emission • Radio Halos • No optical counterpart; mimic X-ray morphology • Typically with sizes ~1 Mpc • Occur in most massive and X-ray luminous rich clusters • Unpolarized • Radio Relics  Peripheral Halos • Irregularly shaped; cluster periphery • Linearly polarized from shock compression • Found in clusters with evidence of a recent or ongoing merger Coma A2256

16. Nonthermal Cluster Emissions • Nonthermal X-ray Emission • B-SAX, RXTE obs. of A1656 (Coma), A2256, A3667 (~1043-1044 ergs s-1) • Compton-scattered CMB • Nonthermal UV Emission • EUVE observations (~60-250 eV) of Virgo, Coma, Fornax, A2199, … • Either Compton-scattered CMB or thermal tail emission • > 100 MeV g-ray Emission • Association with unidentified EGRET sources Coma (Fusco-Femiano et al. 1999)

17. Shock Dynamics • Solve shock jump conditions • Density follows Isothermal  model for both clusters • Dominant cluster rc = 250 kpc, R1=1.5 Mpc,  = 0.75, n0 = 10-3 cm-3 • Merging cluster rc = 150 kpc, R2=0.75 Mpc,  = 0.75, n0 = 10-3 cm-3 • Energy density equal in forward and reverse shock fluid Shocked fluid velocities

18. Shock Speeds • Forward and reverse Mach numbers: • Compression ratio: •  = 5/3 is the ratio of specific heats for an ideal gas

19. Fermi Acceleration at Shocks • First-order (shock) more important than second-order (stochastic) in nonrelativistic shocks • Produces power law distribution • Index determined from compression ratio

20. Evolution of Compression Ratio, Spectral Index Reverse Shock Forward Shock

21. Nonthermal Particle Evolution • Fokker-Plank equation Coulomb diffusion term Energy loss rate Energy gain rate from stochastic acceleration Source term Catastrophic loss from p-p, p-, and diffusion out of the system

22. Electrons Synchrotron: Bremsstrahlung: Compton: First-order Coulomb: Protons Coulomb: Physical Processes/Energy Loss Rates • Coulomb diffusion coefficient:

23. Particle Injection • Power law distribution with exponential cutoff • Occurs only if M  1.0 • Occurs only during lifetime of shock • Normalization • Where e,p is an efficiency factor, and is set to 5%. • Typical values are Etot1063-64 ergs

24. Maximum Particle Energies • Acceleration time constraint • Energy loss constraint • for electrons • for protons • Size-scale limitation

25. Maximum Particle Energies B = 0.1 mG

26. Nuclear Losses • Pion-production event results in a proton loosing 1/3 of its energy. Treat as a loss with time scale • Secondary electrons produced by proton-proton interactions

27. Photopion Losses • p- interaction result in a proton losing ~1/2 to ~1/5 of its energy. • Treated with a loss timescale • Adopted cross sections are • p (Ep) = 380 mb for 200 MeV < Ep < 500 MeV (K = 0.2) • p (Ep) = 120 mb for Ep > 500 MeV (K = 0.5) (Atoyan and Dermer 2003)

28. Escape • Particles diffuse away from the host cluster on a time scale • Clusters are storage volumes for < 1018 eV cosmic rays Rcl is the radius of the cluster, and Bohm is Bohm diffusion coefficient Larmor radius: (Berezinsky, Blasi,Ptuskin 1997)

29. Particle Energy Spectra zi=0.3; B=1.0 mG

30. with metric Redshift Evolution and Energy Loss • (0, R, ) (mass, curvature, and dark energy) • We adopt (0.3, 0.0, 0.7) • Redshift of cluster: • Total Energy Dependence • Thermal Bremsstrahlung redshift dependence • Cosmic Microwave Background (CMBR) dependence • UCMBR(z) = UCMBR(z=0) (1 + z)4 • UCMBR(z=0) = 2.5 x 10-7 MeV cm-3 • Particle energy loss processes

31. Particle Energy-Loss Timescale n=10-3 cm-3; B=1.0 mG n=10-6 cm-3; B=0.1 mG

32. Nonthermal Photon Spectra zi=0.3, z=0.22 z=0

33. Nonthermal Photon Spectra B = 1.0G

34. Nonthermal Photon Spectra B = 0.1G

35. Nonthermal Particle Luminosity Evolution B= 1 mG zi=0.3 B= 0.1 mG Expect to detect tens to hundreds of galaxy clusters with LOFAR

36. Minimum Spectral Index

37. Unidentified EGRET sources? • Statistical test associating Abell clusters with unidentified EGRET sources. (Colafrancesco 2001; Kitayama and Totani 2002) • Previous studies have assumed an unusually hard particle distribution • If we assume softer spectra—power law slopes ~2.4 • Need luminosities >>1043 ergs s-1 for >100 MeV at a distance of ~100 Mpc

38. Detection with GLAST • Expect several to tens of clusters of galaxies to be observed with GLAST

39. Diffuse Extragalactic -ray Background • Structure formation shocks could produce 50% of g-ray background (Loeb and Waxman 2000) • > 10 MeV power-law with slope: 2.100.03 • Central cusps in dark matter profiles will harden spectral indices • Supported by numerical simulations, and gravitational lensing • Observational evidence questionable Sreekumar et al. 1998

40. Photon Spectra when Nonthermal Particles are Hadronically Dominated

41. NFW Profile • Cuspy central density profile

42. Effect of NFW profile • If CDM distribution is traced by normal matter distribution, clusters of galaxies are • weak and soft -ray sources • make small (~1%) contribution to diffuse extragalactic -ray background • do not accelerate particles to ultra-high (> 1019 eV) energies • If CDM distribution is described by NFW profile, clusters of galaxies are • Slightly harder -ray sources • Could make stronger contribution to diffuse extragalactic -ray background

43. Nonthermal Particle Pressure • Each cluster merger event will contribute a population of nonthermal cosmic rays • Most clusters experience several mergers • Proton distribution is cumulative • Applies pressure in addition to the thermal gas of the system • Nonthermal proton Coulomb processes provide additional heating source

44. Nonthermal Emission from Cluster Merger Shocks: Summary • Unidentified EGRET sources • Diffuse Extragalactic -ray Background • Nonthermal Particle Pressure • Detectability with GLAST and LOFAR • Should be able to detect these features with the next generation of -ray observatories • Possible indicator of the dark matter profiles • Not a dominant contributor to the Diffuse Extragalactic -ray Background • Will significantly alter thermal X-ray emission

45. Backup Slides

46. Structure Formation • Density fluctuations cause region to collapse. • Magnitude of the density fluctuation determines the formation time • Larger structures form by accreting smaller clumps--hierarchical merging • Lumpy, continuous accretion

47. Press-Schecter Formalism • Gives mass distribution of galaxy clusters assuming linear perturbation theory • Structure is built up by hierarchical merging • Fits computer models of structure formation

48. Structure Formation • Lacey-Cole (LC) function • Gives rate of mergers versus redshift and accreting body mass • Similar to PS formalism

49. Lacey-Cole Formalism • Probability of Mergers of Structures with different masses with cosmic time

50. External Pressure Accretion shock Nonthermal Particle Pressure • Accretion vs. Cluster merger shocks • Accretion acts as an external pressure Infalling matter