1. EBEx foregrounds and band optimization Carlo Baccigalupi, Radek Stompor

2. Contents Band optimization People Foreground polarization templates, existing data and techniques to get them Foreground uncertainties Current and forthcoming results

3. Band optimization Given your input about: Foreground emission, Foreground uncertainties, Microwave frequency interval, Total number of detectors, Noise per detector, Instrumental bandwidth, More instrumental systematics, … You aim at getting the best number, location and bandwidth of frequency bands in order to maximize the quality of background power reconstruction, focusing in the angular domain and on the degree angular scale

4. Band optimization Generalization of Stompor et al. 2002, Jaffe et al. 2004 Model foreground uncertainties With those build the foreground correlation matrix and plug it into the maximum likelihood map-making procedure Optimize the CMB recovery as a function of the band configuration

5. People Carlo, Radek, In case, we may activate students and post-docs at Berkeley and SISSA People involved in CMB activities: S. Ricciardi (PhD student, Rome La Sapienza and Berkeley), F. Stivoli, (PhD student, SISSA), S. Donzelli (pre-doc student, SISSA), S. Leach (post-doc, SISSA) SISSA astrophysics has support for 10 PhD students per year, plus 2 post-docs, about 30% of these resources were dedicated to the CMB in the past years

6. Foreground templates in the area covered by EBEx Total intensity: template by Finkbeiner et al. (1999), BOOMERanG 98 Polarization: ATCA data in the radio band, analyzed by Carretti et al., far extrapolation, affected by Faraday depolarization EBEx frequencies: data by BOOMERanG 2000 Planck foreground models built on radio and infrared frequencies, highly idealized in the polarization part Bottom line: we need to collect existing data to build a reference foreground template in the EBEx area

7. Independent component analysis nominal performance CMB recovery from a mixture of synchrotron and CMB at 50, 80 GHz, few arcminutes resolution, all sky The excellent performance is due to the high level of statistical independence between foreground and background, high level of detail and number of pixels in the dataset

8. Independent component analysis in the EBEx area 40 GHz90 GHz 150 GHz350 GHz Stivoli et al., astro-ph/0505381

9. Independent component analysis in the EBEx area Stivoli et al., astro-ph/0505381

10. Independent component analysis in the EBEx area Stivoli et al., astro-ph/0505381

11. Independent component analysis in the EBEx area Results stable against: variation of the noise amplitude, foreground amplitude, area covered

12. Independent component analysis general requirements Multi-frequency mixture of statistical independent signals, all non-Gaussian but at most one Comparable background and foreground emission amplitude Foregrounds scaling rigidly in frequency Number of frequency channels equal or larger than the number of independent signals Same resolution on all frequency channels Large datasets, preliminary results indicate few thousands of independent samples are enough Low systematics

13. Foreground residuals Take into account measurements errors affecting your reference template Perform the frequency scaling as a function of a certain set of parameters and templates, taking those into account, too Feed the band optimization problem with those errors and uncertainties, adding them to the instrumental ones

14. Foreground residuals in total intensity Keep track of the errors at the reference frequency Keep track of the errors on the parameters affecting the scaling in frequency

15. Foreground residuals in polarization Introduce the polarization fraction Keep track of the errors affecting the polarization intensity

16. Foreground residuals in polarization Introduce the polarization angle pattern and its error

17. Foreground residuals in the harmonic space

18. Foreground residual statistics Once the uncertainty statistics is given, one can build up a Monte Carlo series on the above formulas, to get the mean residual uncertainty after foreground subtraction Simplified expression may be got assuming homogeneity and isotropy for the foreground reference template (Tucci et al. 2004), although the foreground statistics is strongly non-Gaussian and unknown We simplify those assuming limiting cases for the uncertainty statistics

19. Mean foreground residuals from Gaussian, uniform uncertainty Suppose that the uncertainty is Gaussian distributed, uncorrelated, with uniform variance across the sky This may represent a lack of information at a given scale, as in the case of having a reference foreground template which is known up to a certain angular scale

20. Mean foreground residuals from large scale bias Suppose that the uncertainty possesses the monopole only, obeying a Gaussian statistics This may represent an offset error, as in the case of using a wrong spectral index to scale the foreground template in frequency

21. Rediduals in the literature Zero error on the measurements of the reference foreground template Zero error on the polarization fraction Zero error on the polarization angle Zero spatial fluctuations of parameters affecting the frequency scalings 10% error on spectral indices

22. Synchrotron residuals 10% error in the large scale frequency scalings from the radio band data 10% error on the large scale polarized intensity Few percents error on the fine structure of the synchrotron spectral index on the degree scale or less Polarization angle fluctuations on ten arcmin. scales taken from the data in the radio band

23. Dust residuals 10% error in the large scale value of the dust temperature 10% error on the large scale polarized intensity Polarization angle fluctuations on ten arcmin. scales taken from the data in the radio band

24. lightICA ongoing activities Testing and coding (F. Stivoli, PhD student at SISSA) Real foreground templates (S. Ricciardi, PhD student at Berkeley) Stability against systematics (S. Donzelli, pre-doc student at SISSA) CMB lensing (S. Leach, F. Stivoli, Post- Doc and PhD at SISSA)

25. Band optimization: forthcoming milestones Reference foreground template and errors Point source residuals Maximum likelihood implementation in Berkeley in July First indications on how to optimize bands within the end of summer