Kinetic SZ effect from galaxy cluster rotation

1
Kinetic SZ effect from galaxy cluster
rotationAnother relativistic correction to the
SZE
Jens Chluba and Karl Mannheim AA 396, 419-428
(2002) Universitäts-Sternwarte Göttingen

• JC, Gert Hütsi and Rashid Sunyaev
• accepted by AA, 2005, astro-ph/0409058
• Max-Planck-Institut für Astrophysik

2
Kinetic SZ effect from galaxy cluster rotation
3
Large smalle scale motion of the ICM

• 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
4
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

5
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 b-model
• ? line of sight integral analytical
• spectral dependence like k-SZ
• dipolar signature (inclination)
• extrema at y few ? rc
• bcore 10-5 to few ? 10-4
• ? DT 0.1 - few ? 10 µK

b0.75, i90, Rmax 10 rc
6
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 Dy fraction of the core
  radius
• ? optimistic Dy few arcsec
• ? even more optimistic Dy 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

7
Another relativistic correction to the SZE....
8
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!

9
Motion-induced Change of SZ Brightness

• Example kTe 5.1 keV, bc 10-3 and bo 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
  DT/T-2 y bo m

10
Conclusions

• simple analytic model for k-SZ from cluster
  rotation
• dipolar signature on few ? 10 arcsec angular
  scales close to center
• DT 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)

11
Large smalle scale motion of the ICM

• 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
12
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