1. Extracting clusters and determining the selection function for SZ surveys
Jean-Baptiste Melin
U.C. Davis
J. Bartlett
J. Delabrouille
APC – College de France

2. Contents I. Theoretical selection function of SZ cluster surveys
II. Fast SZ extraction algorithm
III. Selection function results

3. Contents I. Theoretical selection function of SZ cluster surveys
II. Fast SZ extraction algorithm
III. Selection function results

4. The selection function ?
Contamination
Completeness
(c,Y)=
Number of false detections
Total number of detections
(recovered clusters + false detections)
(c,Y)=
Number of recovered clusters
True number of clusters
If you don’t know  and y,
don’t expect to do science !

5. Matched filters (1/2) AMPLITUDE ? c NORMALIZED TEMPLATE NOISE
Haehnelt & Tegmark 96
Herranz et al. 2002a,
2002b
AMPLITUDE ? c
c=2 arcmin
CMB
CMB+beam
Instrumental noise
NORMALIZED TEMPLATE
NOISE

6. Matched filters (2/2)  in Fourier space  in real space Aest
linear estimator
unbiased <Aest-A>=0
minimize the variance =<(Aest-A)2>
 in Fourier space
 in real space
[arbitrary unit]
[arbitrary unit]
Aest
(S/N)est= Aest/
single-frequency & multi-frequency

7. Y = Aest Tc > 5 .  . Tc
AMI-like : =15GHz, beam=2arcmin inst. noise=5µK/beam, pt. sources : S<100Jy
Aest/>5
Y = Aest Tc > 5 .  . Tc

8. Contents I. Theoretical selection function of SZ cluster surveys
II. Fast SZ extraction algorithm
III. Selection function results

9. Cluster extraction in 3 steps Simulations3º 3º
15 GHz
30 GHz
90 GHz
pix=30’’
Primary CMB anisotropies
Instrumental beam (fwhm=2 arcmin)
Insrumental white noise (DT=20 K/pix)
Radio sources (S<0.1mJy at 15 GHZ)
Multifrequency (n=15, 30, 90 GHz)
Cosmology : LCDM

10. Cluster extraction Filtered map sample
Step 1 … …
c(filter)=3.0 arcmin
c(filter)=0.1 arcmin
c(filter)=1.6 arcmin

11. Cluster extraction Cluster candidates
Step 2
S/Nthreshold = 3, 5, …
S/Ncarte> S/Nthreshold … …
c(filter)=3.0 arcmin
c(filter)=0.1 arcmin
c(filter)=1.6 arcmin

12. Cluster extraction c and Y recovery
Step 3
c given by the node having the highest S/N in a given branch
Y derived from the filtered map at scale c
c=3.0 arcmin .
c=0.3 arcmin
c=0.2 arcmin
c=0.1 arcmin

13. Contents I. Theoretical selection function of SZ cluster surveys
II. Fast SZ extraction algorithm
III. Selection function results

14. Single frequency – 15 GHz 50 simulations (3 deg × 3 deg each)
Cl perfectly known
simulations
detection
theoretical selection fit
CBI excess
simulations
detection
theoretical selection fit

15. Single frequency – 15 GHz Cluster counts
Clusters with Y>5.10-5arcmin2

16. Single frequency – 15 GHz Cosmological parameters
BIAS !

17. Conclusions Multi-frequency/Single-frequency
Selection function non-trivial
depends on instrument, observation strategy, confusion, cluster physics
& data pipeline
Bias
Additional source of error
‘Survey calibration’
&

19. The method A Monte Carlo triangle Fast SZ simulation tool Fast SZ
detection tool
Input catalog
Output catalog
Comparison
Selection function

20. Single frequency – 15 GHz A non-trivial selection function
Clusters with Y>5.10-5arcmin2
Y>10-4arcmin2
Y>3.10-4arcmin2

21. Single frequency – 15 GHz Theoretical selection curves
détecté
detected
non détecté
not detected