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The estimation of the SZ effects with unbiased multifilters

The estimation of the SZ effects with unbiased multifilters. Diego Herranz, J.L. Sanz, R.B. Barreiro & M. López-Caniego Instituto de Física de Cantabria Workshop on the SZ effect & ALMA – Orsay – April 8th 2005. 1. Overview.

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The estimation of the SZ effects with unbiased multifilters

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  1. The estimation of the SZ effects with unbiased multifilters Diego Herranz, J.L. Sanz, R.B. Barreiro & M. López-Caniego Instituto de Física de Cantabria Workshop on the SZ effect & ALMA – Orsay – April 8th 2005

  2. 1 Overview • Linear multifilters for the detection of the SZ effects: motivation & review • Joint study of two signals with the same spatial profile and different frequency dependence: bias. • The unbiased matched multifilter. • Conclusions.

  3. 2 1. Linear multifilters The matched multifilter (Herranz et al, 2002, MNRAS, 336, 1057) is a useful tool to enhance the SZE signal  Blind surveys with low angular resolution (Planck)

  4. 3 1. Linear multifilters (II): • How do the clusters look like? • How do they appear at different wavelengths? • How does the background behave at the different wavelengths?

  5. Data (N maps at different frequencies) Frequency dependence X Source profile (beam included) “Noise” (CMB + foregrounds + instrumental noise) 4 Linear multifilters (III): data model

  6. MATCHED MULTIFILTER 5 Linear multifilters (IV): matched multifilter • Make Qso that w(0)=A (unbiased estimator of the amplitude) • Make Q so that sw is as small as possible (efficient estimator)

  7. 6 Linear multifilters (V): two sources of bias

  8. 7 2.Joint study of the thermal and the kinematic SZ effects

  9. MMF: Bias in the determination of the thermal SZ effect in presence of the kinematic SZ effect 8

  10. MMF: Bias in the determination of the kinematic SZ effect in presence of the thermal SZ effect 9

  11. 10 3. Canceling the bias • Make Qso that w1(0)=A • Make Q so that w2(0)=0 • Make Q so that s1+2 is as small as possible (efficient estimator)

  12. 11 3. Canceling the bias of the thermal effect: UMMFt

  13. 12 3. Canceling the bias of the kinematic effect: UMMFk

  14. 13 3. Filter comparison: thermal effect

  15. 14 3. Filter comparison: kinematic effect

  16. 15 3. Filter comparison: kinematic effect (II)

  17. 16 4. Conclusions: • SZ thermal effect can introduce dramatic systematic effects in the estimation of the kinematic effect • It is possible to cancel this systematic effect introducing a new constraint in the formulation of the filters: • It is not necessary to know a priori the thermal effect • The variance of the estimator increases a little bit • The errors in the determination of the peculiar velocities of individual clusters remain very large. • However, once the estimator is unbiased it can be used for statistical analysis of large numbers of clusters (bulk flows, etc)

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