Turbulent Heating in the X-ray Brightest Galaxy Clusters

Transcription

1 Turbulent Heating in the X-ray Brightest Galaxy Clusters Irina Zhuravleva KIPAC, Stanford University E. Churazov, A. Schekochihin, S. Allen, P. Arevalo, A. Fabian, W. Forman, M. Gaspari, E. Lau, D. Nagai, S. Nelson, I. Parrish, J. Sanders, A. Simionescu, R. Sunyaev, A. Vikhlinin, N. Werner SnowCluster, Snowbird, Utah, March 15-20, 2015

2 Turbulent dissipation in AGN feedback energy release => bubbles =>? => heating Possible channeling mechanisms: shocks, sound waves (Randall et al. 11; Fabian et al. 06) turbulent dissipation (Churazov et al. 02; Fukita et al. 04; Banerjee et al 14) turbulent mixing (Kim & Narayan 03) cosmic rays (Chandran & Dennis 06; Pfrommer et al. 13) radiative heating (Ciotti & Ostriker 01; Nulsen & Fabian 00) etc.

3 Definitions and assumptions Kinetic energy k -5/3 kr -3 stratified turbulence k -5/3 isotropic turbulence unmagnetized magnetized Magnetic energy assumptions: no magnetic fields no plasma effects 1 L l O l diss mfp 1 i k

4 Turbulent dissipation in AGN feedback Kolmogorov constant Q turb = K 0 V 3 l l gas mass density velocity amplitude on scale l Kolmogorov 41 Sreenivasan et al. 95 Kaneda et al. 03 Dennis & Chandran 05

5 Is there any way to probe gas dynamics using currently-available data? cluster in HE: V=0 disturbed cluster: V 0 δρ > V?

6 homogeneous box How do density perturbations scale with the velocity field? δρ M 2 from Bernoulli's equation (solenoidal motions) stratified atmosphere?

7 g-modes in stratified atmosphere stratification in clusters: gradient of S, ρ high-entropy gas small and slow perturbations => g-modes (internal or gravity waves) ~g NBV low-entropy gas surface gravity waves

8 g-modes in stratified atmosphere Dispersion relation:! 2 = N 2 k2? k 2 Brunt-Väisälä frequency: N = r g H s Entropy scale height: H s =(d ln S/dr) 1 Wavenumber: k 2 = k 2? + k 2 r? ~r g-modes are confined inside the cluster core => interact => non-linear => turbulent motions > Balbus & Soker, 1990

9 g-modes in stratified atmosphere! 2 = N 2 k2?? k 2 ~r if ω << N (stratification is important) => k << kr in direction in r direction on large scales V is dominated by V pancake turbulence Waite & Bartello 2006

10 Buoyancy-dominated regime of motions stir the gas slowly with ω<<nbv Turbulent eddy at injection scale L : L Δr gravity Vr << V ~ V Δr L ω N BV V? = L! V V = N BV r gravity provides V - Δr relation

11 Gas displacement and density contrast S(r) gas in pressure equilibrium Pb=P P=(Sb+δS)ρᵞ Sb Pb=Sbρbᵞ Δr Sb slow displacement Sb=const density contrast after (slow) gas displacement: = 1 S S 1 r H entropy gradient gives δρ - Δr relation r entropy scale height

12 Buoyancy-dominated regime of motions entropy gradient: = 1 gravity: r H s V = N BV r N BV = c p s Hs H p = V c s = r Hp H s 1 valid on large, buoyancydominated scales the system adjusts so that η ~ 1

13 Turbulent small-scale regime: teddy << tn Obukhov-Corrsin approach: the spectrum of the passive scalar follows the spectrum of the velocity field in the inertial range Obukhov 1949; Corrsin 1951 any perturbation in ICM hot gas gas entropy (density) k = V k c s η~1 is set on large, buoyancy-dominated scales

14 Verifying the coefficient η AMR cosmological simulations, NR runs, relaxed clusters Kravtsov et al. 99;03; Nagai et al. 07a; Nelson et al. 14 V ρ sample averaged =1± 0.3 Zhuravleva et al. 2014a hydro simulations: η ~1 w/o conduction Gaspari et al. 2014

15 Nature of fluctuations in Perseus 1) sound waves (Fabian et al. 03; 06; Sanders et al. 07) 2) stratified turbulence (Zhuravleva et al. 14; 15)

16 Nature of fluctuations in Perseus: stratified turbulence? Linné FLOW Centre Eugene s GIMP simulations Δr ~HV/cs talk by E. Churazov cross-spectra analysis of SB fluctuations in different energy bands: isobaric fluctuations (gas sloshing, turbulence, g-modes)

17 Amplitude of density fluctuations in Perseus I X / Z kev 3 Z n 2 e (T )dl / n 2 edl

18 Amplitude of density fluctuations in Perseus A 2 3D(k) =4 P 3D (k)k 3 Units are the same of the variable in real space outside central 30 kpc: k 7 15% on scales 6-30 kpc

19 Velocity Power Spectrum in Perseus V k = c s V higher towards the center > power injection from the center larger V on smaller k > consistent with cascade turbulence 70 km/s < V1,k < 200 km/s on scales 6-30 kpc (within central 200 kpc) Zhuravleva et al., 2015, MNRAS, submitted

20 Turbulent dissipation in AGN feedback Kolmogorov constant Q turb = K 0 V 3 l l gas mass density velocity amplitude on scale l Kolmogorov 41 Sreenivasan et al. 95 Kaneda et al. 03 Dennis & Chandran 05 we measure Vl and each scale l => can obtain Qturb

21 Turbulent dissipation in AGN feedback cooling rate: C = n e n i n (T ) heating rate: H(k) =C H V 3 1,kk locally: cooling ~ heating Perseus cluster Virgo cluster AGN > Bubbles > Turbulent dissipation > Heat Zhuravleva et al. 2014b

22 Turbulent dissipation in AGN feedback If we assume Cooling~Heating, then: M k 0.15 n 1/3 e 10 2 cm 3 c s 1000 km/s 1 l 10 kpc 1/3 Dissipation of turbulence with M~0.15 is sufficient to balance cooling of the gas in cores

23 What happens outside cool cores? t our expectations: tcool thubble theat cooling ~ heating R

24 What happens outside cool cores? XMM-Newton, Perseus Hubble time Chandra Work in progress dissipation of gas motions on timescales ~ cluster age

25 Uncertainties (incomplete list) 1. Bias in the normalization of the amplitude of density fluctuations from the Δ-variance method: ~1.3 (Perseus) and 1.2 (Virgo); 2. Division of cluster into perturbed and unperturbed components: small-scale power is robust; 3. Conversion between 2D to 3D power spectrum: < 20%; 4. Accuracy of the Poisson noise subtraction, PSF correction, unresolved point sources correction - robust regions; 5. Stochasticity of density fluctuations - broad annuli; 6. Weighting scheme used to calculate the amplitude of fluctuations: <20%; 7. We cannot prove that we see turbulence; 8. η scatter is ~ 30%, not sure that it is the same in the range of scales - Ozmidov scale is within the range of scales we are probing; etc. M A N Y final uncertainty in the heating rate is ~ a factor of 3 Astro-H is needed to calibrate density/velocity relation

26 Summary k = V 1,k c s relaxed clusters subsonic motions simplest approach V measurements on different scales: Perseus: 70 km/s < V1,k < 200 km/s on 6-30 kpc (within ~ 200 kpc) Virgo: 40 km/s < V1,k < 90 km/s on 2-10 kpc (within ~40 kpc) AGN-feedback: turbulence dissipation is sufficient to offset cooling locally at each r AGN > Bubbles > Turbulent dissipation > Heat Nature of fluctuations in Perseus: dominated by isobaric fluctuations (gas turbulence, sloshing, g-modes) Astro-H (end 2015), Athena (2028), Smart-X (?): verification of the linear relation, importance of microphysics nature of fluctuations

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31 Velocity Power Spectrum in Virgo typical values: 40 km/s < V1,k < 90 km/s on scales 2-10 kpc Zhuravleva et al. 2014b, Arevalo et al. in prep.

32 Known unknowns in ICM (incomplete list) velocity field (turbulence, gas sloshing) transport processes (viscosity, diffusion, convection, conduction) heating of ICM cosmology: non-thermal pressure particle acceleration amplification of mag. fields origin of radio halos crucially important for gastrophysics, plasma physics, cosmology

33 P2D of SB > P3D of density fluctuations projection l=1/k L A 3D / A 2D p N / r 1 N = L l A 2 2D =2 P 2D k 2 A 2 3D =4 P 3D k 3 P 2D / P 3D 1 L simulated cluster central 200 kpc Churazov et al. 12; Zhuravleva et al. 12

34 Measured velocities (so far): Perseus: 70 km/s < V1,k < 200 km/s on scales 6-30 kpc M87: 40 km/s < V1,k < 90 km/s on scales 2-10 kpc NGC4636: V<100 km/s (RS) (Werner, IZ et al. 2009) NGC 5044: 300 (RS) < V < 950 (width) km/s (de Plaa, IZ et al. 2012) NGC 5813: 100 (RS) < V < 670 (width) km/s (de Plaa, IZ et al. 2012) A1835: V< 274 km/s (width) (Sanders et al. 09) 62 cores of clusters: V < 700/500 km/s (width) (Sanders et al. 11) 44 cores of clusters: V< 500 km/s (width) (Pinto et al. 2015)

35 Nature of fluctuations in Perseus Adiabatic fluctuations (sound waves, shocks):, T P Isobaric fluctuations (gas sloshing, turbulence, g-modes):, T P ~const

36 Nature of fluctuations in Perseus adiabatic amplitude is larger in hard band ( kev) F / n 2 (T ) independent of T increases with T isothermal amplitude is larger in soft band ( kev) isobaric T range in Perseus soft band: density hard band: T-dependent need to compare the PS of SB fluctuations in both bands Work in progress

37 Do we see Kolmogorov slope of the spectrum? E (k ) E (kr) kr -3 k -5/3 kr -5/3 ko k,kr V1,k, km/s Ozmidov scale: ko=n -3/2 ε 1/2 Ozmidov 1992

38 Do we probe turbulence within the inertial range? dissipation scale (for unmagnetized plasma) < scales we are probing

39 Power spectrum V ~ power spectrum ρ P(k) dominated by buoyancy buoyancy not important k = V k c s 1 kinj inertial range kdis k, k Zhuravleva, Churazov, Schekochihin et al. 2014a

40 Gas dynamics in simulations E(k) Kolmogorov spectrum energy cascade k -5/3 inertial range of scales 1 Mpc kinj kdiss k Vmax=2020 km/s Bryan et al Vmax=520 km/s 100 kpc ICM turbulence within r500: driven by mergers and central AGN typical V ~ few 100s km/s, sound speed ~ km/s mostly subsonic (in relaxed clusters), M<0.5 nearly incompressible ~Kolmogorov slope -5/3 of E(k) up to 30 % non-thermal pressure contribution

41 Amplitude of density fluctuations in Perseus PSF PS initial PS PS calculations using modified Δ-variance method (Arevalo et al. 2012) Poisson noise Next step: P2D of SB -> P3D of density

42 Amplitude of density fluctuations in Perseus statistical approach to probe fluctuations: power spectrum of SB fluctuations

43 Nature of fluctuations in Perseus soft band: kev hard band: kev Let s compare the amplitudes of fluctuations by calculating their auto- and cross-spectra Work in progress

44 Gas fluctuations in Perseus (based on Chandra 1.4 Ms observations) modest amplitude of density fluctuations: 7-15% on scales 6-30 kpc predominantly isobaric fluctuations (preliminary) velocity: 70 km/s < V1,k < 200 km/s on scales 6-30 kpc

45 Turbulent dissipation in AGN feedback Hubble time t cool = 3 2 nkt n 2 (T ) Lea 76; Cowie & Binney 77; Fabian 77 Basic concept of AGN feedback: radiative cooling of gas => accretion rate onto SMBH => energy release (bubbles) =>? => dissipation of released energy Churazov et al. 00, Omma & Binney 04, McNamara et al. 07, Fabian et al. 12; Birzan et al. 12

46 What s next? Astro-H (Jan 2016) soft X-ray spectrometer (SXS) X-ray microcalorimeter array of 6x6 pixels: ~ 5 ev spectral resolution, ~ 1.7 spatial resolutions, 3 x3 field of view in the kev band T rise upon each incident X-ray photon, achieving ~5eV energy resolution

47 small-scale motions: σ large-scale motions: V At a given R an interval Leff ~ R contributes to the line flux (and width) Observed σ(r) structure function (Leff) Zhuravleva et al. 2012a

48 Nature of fluctuations in Perseus: sound waves? rough concentric rings ripples Fabian et al. 2003, Fabian et al isothermal sound waves Δr ~ time variability of AGN P jumps, no T jumps

49 Astro-H SXS observations of the Perseus Cluster O1 M1 C1 O2 M2 C2 C0 C4 M4 C3 M3

50 Two major problems: perturbed and unperturbed components I I mod, = I mod, = I mod, = I mod = I S [I x /I ]

51 Two major problems: perturbed and unperturbed components k supp. [1/ 00 ]=0.8/ [ 00 ] ksupp.=0.01 arcsec -1 ksupp.=0.03 arcsec -1 ksupp.=0.04 arcsec -1 ksupp.=0.08 arcsec -1 removal of large-scale asymmetry does not change the result amplitude of fluctuations on intermediate scales due to the presence of fluctuations on these scales (not a leakage of power from the larger scales)

52 Characteristic scales in Perseus Ozmidov scale: lo=nbv -3/2 (Qturb/ρ) 1/2 Kolmogorov scale: lk=νkin 3/4 (Qturb/ρ) -1/4

53 Coherence and regression Work in progress adiabatic Soft band Hard band isothermal isobaric C = P 12 p P1 P 2 Regression: y = R x see talk by E. Churazov R = P 12 P 1 / f 2 f 1 isobaric fluctuations (gas sloshing, turbulence, g-modes) are dominating the signal