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Kinetic SZ effect from galaxy cluster rotation & Another relativistic correction to the SZE JC, Gert Hütsi and Rashid Sunyaev accepted by A&A, 2005, astro-ph/0409058 Max-Planck-Institut für Astrophysik Jens Chluba and Karl Mannheim A&A 396, 419-428 (2002) Universitäts-Sternwarte Göttingen

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Kinetic SZ effect from galaxy cluster rotation

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Large & smalle scale motion of the ICM SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching Mergers in the cosmological context should excite large & small scale motion of the ICM ! (off-axis mergers) Coma Cluster (XMM) (Schuecker et al., 2004) turbulent motions on scales ~20-145 kpc (core radius 420 kpc) turbulence on larger scales is possible! Turbulent cascades from large small scales viscosity plasma instabilities magnetic fields transition between k-SZ & th-SZ Schuecker et al., 2004

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Large & smalle scale motion of the ICM (2) Hydrodynamic simulations by Norman & Bryan 1999 turbulent velocities ~ 25-60% of virial velocity minor mergers maintain the level of turbulence also found „ordered“ circulation, which is likely due to a off-axis merger X-ray spectral lines for Centaurus cluster (Dupke & Bregman 2001) bulk velocities of the order of ~1000 km/s likely due to a previous off-axis merger Several recent hydrodynamic simulations (Nagai et al. 2003; Torman, Moscardini & Yoshida 2004; Diaferio, Borgani, Moscardini et al. 2005) bulk velocities v ~ few 100 km/s SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching

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Toy-model for large scale motion of the ICM Initial stage after (major) merger one large scale eddie simple assumption: solid body rotation line of sight velocity constant Gas follows isothermal -model line of sight integral analytical spectral dependence like k-SZ dipolar signature (inclination) extrema at y ~ few r c core ~ 10 -5 to few 10 -4 T ~ 0.1 - few 10 µK =0.75, =90°, R max = 10 r c SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching

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Multi-frequency observations of the SZE Main signals th-SZ and k-SZ RJ part of the CMB spectrum th-SZ dominant close to cross-over frequency k-SZ + rk-SZ shift of the maximum: y ~ fraction of the core radius optimistic: y ~ few arcsec even more optimistic: y up to arcmin (no k-SZ) Comparison of SZ image at different frequencies This probably also happens for two merging lumps linear polarization many orders smaller (few nK or a fraction of µK level) sensitive to the transverse velocity optimistic: on the level of a few % relative to the k-SZ polarization k-SZ + rk-SZ tilt of the planes of polarization by a few degree frequency-independent (in principle separable from e.g. multiple scattering for rich clusters...) SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching

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Another relativistic correction to the SZE....

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SZ effect from clusters of galaxies Relativistic temperatures & peculiar motions (Rephaeli, 1995; Challinor & Lasenby 1998; Sazonov & Sunyaev, 1998; Itoh et al., 1998) corrections to the lowest order signals especially important at high frequencies 10-20% deviations possiblility to measure the electron temperature only with the CMB (strong frequency dependence) non-thermal SZ Motion of the Solar System ! (Chluba, Hütsi & Sunyaev, 2004) has been neglected so far SZ effect: imprint in the CMB rest frame Doppler boosting & aberration Lorentz boosted y-distortion correction similar to the first order temperature correction to the k-SZ easy to take into account! SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching

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Motion-induced Change of SZ Brightness Example kT e = 5.1 keV, c = 10 -3 and o = 1.241 10 -3 strong frequency and spatial dependence can reach the level of 10% of the k-SZ at high frequencies (e.g.14% at 400 GHz) RJ- limits: motion-induced correction to th-SZ: T/T=-2 y o SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching

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simple analytic model for k-SZ from cluster rotation dipolar signature on few 10 arcsec angular scales close to center T ~ 0.1 - few 10 µK comparing multi-fequency morphology may be useful combined with polarization very useful to constraint motions of ICM turbulent motions interesting contribution to th-SZ (transition) motion-induced correction to the th-SZ similar to the first order temperature correction to the k-SZ strong spectral & spacial dependence reaches the 10% level of the k-SZ easy to take into account !!! Dipolar asymmetry of the cluster number counts (1% level) Conclusions

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Large & smalle scale motion of the ICM SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching Mergers in the cosmological context should excite large & small scale motion of the ICM ! (off-axis mergers) Coma Cluster (XMM) (Schuecker et al., 2004) turbulent motions on scales ~20-145 kpc (core radius 420 kpc) turbulence on larger scales is possible! Turbulent cascades from large small scales viscosity plasma instabilities magnetic fields transition between k-SZ & th-SZ Schuecker et al., 2004

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Large & smalle scale motion of the ICM (2) Details of the processes complex Hydrodynamic simulations by Norman & Bryan 1999 turbulent velocities ~ 25-60% of virial velocity minor mergers maintain the level of turbulence also found „ordered“ circulation, which is likely due to a off-axis merger X-ray spectral lines for Centaurus cluster (Dupke & Bregman 2001) bulk velocities of the order of ~1000 km/s likely due to a previous off-axis merger DM simulations by Bullock et al. 2001 „universal“ angular momentum profile which is consistent with solid body rotation rotational velocity ~ few percent of circular velocity Several recent hydrodynamic simulations (Nagai et al. 2003; Torman, Moscardini & Yoshida 2004; Diaferio, Borgani, Moscardini et al. 2005) bulk velocities v ~ few 100 km/s SZ effect and Alma workshop - Orsay - April 2005 - Jens Chluba - MPA-Garching

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