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/ Max-Planck-Institut für Astrophysik Jens Chluba and Karl Mannheim A&A 396, (2002) Universitäts-Sternwarte Göttingen

Kinetic SZ effect from galaxy cluster rotation

Large & smalle scale motion of the ICM SZ effect and Alma workshop - Orsay - April 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 ~ 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

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 Jens Chluba - MPA-Garching

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 ~ to few    T ~ few  10 µK  =0.75,  =90°, R max = 10 r c SZ effect and Alma workshop - Orsay - April Jens Chluba - MPA-Garching

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 Jens Chluba - MPA-Garching

Another relativistic correction to the SZE....

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 Jens Chluba - MPA-Garching

Motion-induced Change of SZ Brightness Example kT e = 5.1 keV,  c = and  o =  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 Jens Chluba - MPA-Garching

simple analytic model for k-SZ from cluster rotation dipolar signature on few  10 arcsec angular scales close to center  T ~ 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

Large & smalle scale motion of the ICM SZ effect and Alma workshop - Orsay - April 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 ~ 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

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  „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 Jens Chluba - MPA-Garching