X-ray surface brightness fluctuations and turbulence in galaxy clusters Jeremy Sanders Andy Fabian Sanders & Fabian 2011, MNRAS, submitted Simulations predict that in galaxy clusters turbulent energy could be a significant fraction of the intracluster medium (ICM) thermal energy... Vazza et al 2010: several Mpc slice of temperature across cluster major merger (ENZO Adaptive Mesh Refinement code) Simulations of cluster-wide motions Lau et al 2009 Vazza et al 2010 ͻ How can we test turbulence in numerical models of galaxy clusters? ͻ ZĞĂůŐĂůĂdžLJĐůƵƐƚĞƌƐŚĂǀĞǀŝƐĐŽƐŝƚLJ͕ŵĂŐŶĞƚŝĐĨŝĞůĚƐ͕ĐŽƐŵŝĐƌĂLJƐ͙ Why is measuring turbulence important? ͻ Important for X-ray mass measurements assuming hydrostatic equilibrium ͻ Measure strength of AGN feedback ͻ Compare to simulations to measure viscosity and other plasma properties ͻ Turbulence may drive heating, preventing cooling in clusters (e.g. Kunz et al 2010) ͻ Study growth of massive galaxies from hot gas Coma galaxy cluster (ROSAT) Hot (107-108 K) intracluster medium (ICM) X-ray surface brightness is primarily proportional to density-squared integrated along LoS Coma: turbulent pressure fluctuations ͻ Schuecker et al 2004: Examined spectrum of pressure variations in Coma using XMM- Newton X-ray data ͻ For turbulence, the energy spectrum of velocity fluctuations, E(k) v k-5/3, depending on some assumptions (Kolmogorov 1941) ͻ Pressure should also follow a similar law (Oboukhov 1949; Batchelor 1951), of -7/3 EP(k) v k Coma: pressure map Schuecker et al 2004 ͻ X-ray-derived pressure map from XMM-Newton ͻ Spectral fitting of data measures temperature and density ͻ Pressure is v density × temperature Coma: pressure power spectrum ͻ Projected pressure spectrum is Kolmogorov type from 40 to 90 kpc scales ͻ Turbulent energy density is a minimum of 10% of thermal energy density ͻ Coma is an unrelaxed cluster, however Abell 1835: a relaxed galaxy cluster Another way to look for velocity structure is directly observing line widths Abell 1835 z = 0.2523 45 -1 LX~ 2×10 erg s Relaxed, very luminous galaxy cluster Sanders et al (2010) Abell 1835: measuring line widths 254 ks XMM- Newton observation Sanders et al (2010) ͻ 90% limit on broadening is 274 km/s ͻ Maximum of 13% of thermal energy density in turbulence AWM 7 ͻ AWM 7 is a poor cluster of galaxies (kT = 3.5 keV) at z=0.0176 ͻ Bright (9×1011 erg cm-2 s-1) ͻ Peaked surface brightness profile and short central cooling time (0.4 Gyr) ͻ Little evidence of AGN activity ͻ However, elongation along E-W direction ʹ Likely due to infall of material (Neumann et al 1995), not tidal ʹ Offset of central galaxy and X-ray peak from outer part of cluster Located in the Perseus-Pisces chain of galaxies ͻ No evidence for galaxy (Image: ROSAT) velocity substructure Chandra XMM-Newton (point sources removed) Analysis method ͻ Characterise the fluctuations in surface brightness ʹ Wide band image sensitive to density fluctuations ͻ Concentrate on these results here ͻ Note: Kolmogorov density fluctuations seen in ISM over five orders of magnitude (e.g. Armstrong+ 95) ʹ Hard band image sensitive to pressure fluctuations ͻ Compare observed surface brightness to a smooth model ͻ Compare to models with turbulent fluctuations Making a simulated cluster image ͻ Take X-ray image of cluster ͻ Remove point sources ͻ Smooth Making a simulated cluster image ͻ Take X-ray image of cluster ͻ Remove point sources ͻ Smooth ͻ Contour (log) Making a simulated cluster image ͻ Take X-ray image of cluster ͻ Remove point sources ͻ Smooth ͻ Contour (log) ͻ Fit ellipses to contours Making a simulated cluster image ͻ Take X-ray image of cluster ͻ Remove point sources ͻ Smooth ͻ Contour (log) ͻ Fit ellipses to contours ͻ Make model by interpolating between ellipses ͻ We try other cluster models ʹ see paper, or ask me at end AWM 7: surface brightness Smoothed X-ray surface brightness Poisson realisation of smooth model Ellipses ʹ fits to surface brightness contours AWM 7: surface brightness residuals Fractional difference between data (or simulated data) and smooth model Histograms confirm that observed distribution is wider than a simulated smooth model Same deviations seen in XMM data How do we characterise the fluctuations? ͻ Use the ȴ-variance method (Stutzki et al 1998) to characterise the strength of signal as a function of scale ͻ Easy to implement method previously used for molecular cloud data ͻ Can use weight map to account for point sources and edges of detectors ͻ Can be related to power spectrum [ 2 [ 2 P(| k |) v| k | V ' v L , if 0 d [ 6 ȴ-variance method See Stutzki et al 1998 and Ossenkopf et al 2008 ͻ Filter input image on a particular length scale ͻ Convolve image by, for example, a Mexican Hat function with a characteristic length Image simulated using a power spectrum ȴ-variance method ͻ Calculate the variance of the filtered map as a function of length scale ͻ Can filter a weight map in the same way to account for excluded regions Filtered using a length scale of 20 pixels Spectrum of whole cluster core 21 to 141 kpc radius region Spectrum of data and several realisations of smooth model (subtracting the smooth model from the image) Noise Note that we refit the smooth model to the simulations before subtraction. -2 -1 2 Units of ʍȴ are (photon cm s ) Spectrum of whole cluster core Subtract smooth model spectrum from data Spectrum of whole cluster core Projected Gaussian fluctuations (2% fluctuations on scales of 5.5 kpc) Simulating realistic turbulent field ͻ Take power spectrum and convert to 3D random field (using inverse FFT) ͻ Normalise field to have required standard deviation (in per cent) ͻ Integrate field along LoS, as fluctuation applied to cluster emissivity profile Spectrum of whole cluster core 3D Kolmogorov spectrum (-5/3) spectra of emissivity variations. Projected onto 2D sky using deprojected emissivity profile of cluster. Normalised by the standard deviation Flat spectrum of the 3D On long scales fluctuation field This is density- Peaks on scales around 15 kpc squared so density fluctuations are ½ of magnitude North vs south North vs south North vs south Conclusions ͻ ^ĞǀĞƌĂůůŽǁƐƵƌĨĂĐĞďƌŝŐŚƚŶĞƐƐ͞channels͟ŝŶƐŽƵƚŚ leading from the core of the cluster ͻ Spectrum of fluctuations is flat (index of -1.9 vs -3.7), with a peak on scales of around 15 kpc ͻ No simple Kolmogorov or powerlaw scaling ͻ Magnitude of density variations is around 4% ͻ Magnitude of pressure variations is 2-4% ͻ No evidence for large-scale cosmological turbulence ͻ Caution! Conversion from surface brightness to density or pressure assumes that dominant pressure component is thermal. Future work ͻ Larger sample of clusters, with different dynamical indicators ͻ Create mock observations from simulations of cluster formation ʹ unfortunately spatial resolution of Vazza et al simulations is not good enough to compare to AWM7 yet ͻ Upcoming launch of ASTRO-H in 2014 ʹ few eV resolution X-ray spectra will let us directly measure velocities as a function of position Coma cluster core XMM unsharp-masked X-ray image Digitised sky survey hƉĐŽŵŝŶŐϱϬϬŬƐŚĂŶĚƌĂŽďƐĞƌǀĂƚŝŽŶŽĨƚŚĞĐŽƌĞŽĨƚŚĞŽŵĂĐůƵƐƚĞƌ͙ Veusz scientific plotting package GUI, scripting, Python interface Available for Unix/Linux, Mac OS X, Windows ZĞĂĚƚĞdžƚ͕^s͕&/d^͕͙ ZƵŶ͚ǀĞƵƐnj͛ŽŶ/Ž>ŝŶƵdžƐLJƐƚĞŵƐ tƌŝƚĞW^͕W&͕^s'͕:W'͕WE'͙ See http://home.gna.org/veusz/ for tutorial video .