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. 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. 1

3. 1. Linear multifilters 2 PROSCONS Easy to understand and to implement Adequate for compact sources Robust Fast Not as powerful as more sophisticated techniques (higher order statistics, etc) Not yet optimised for extended/irregular objects 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. 1. Linear multifilters (II): 3 How do the clusters look like? How do they appear at different wavelengths? How does the background behave at the different wavelengths?

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

6. 1.Linear multifilters (IV): matched multifilter 5 a)Make   so that w(0)=A (unbiased estimator of the amplitude) b)Make  so that  w is as small as possible (efficient estimator) MATCHED MULTIFILTER

7. 1.Linear multifilters (V): two sources of bias 6 Identical shape Identical spectral behaviour  THE SAME THING Different shape Identical spectral behaviour  BIAS Identical shape Different spectral behaviour  BIAS Different shape Different spectral behaviour  IDEAL SEPARATION

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

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

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

11. 3. Canceling the bias 10 a)Make   so that w 1 (0)=A b)Make  so that w 2 (0)=0 c)Make  so that  1+2 is as small as possible (efficient estimator)

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

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

14. 3. Filter comparison: thermal effect 13

15. 3. Filter comparison: kinematic effect 14

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

17. 4. Conclusions: 16 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: o It is not necessary to know a priori the thermal effect o 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)