1. Deciphering the CIB Banyuls 09/10/2012 RESOLVING THE CIB: II) STATISTICAL PROPERTIES OF SOURCES RESPONSIBLE FOR CIB FROM OBSERVATIONAL AND MODELING POINT OF VIEW Matthieu Béthermin CEA Saclay

2. WHAT MAKES THE CIB? Origins of the infrared output of the galaxies (e.g. star formation vs accretion, which star formation mode?) ---> physics of galaxies Global evolution of the statistical properties of the infrared galaxies ---> cosmology

3. SUMMARY Observational point of view Modeling point of view Properties of resolved sources Origin of the CIB SED What information can you extract from the number counts Principle of backward evolution models Properties of the sources responsible for CIB as predicted by empirical models

4. OBSERVATIONAL POINT OF VIEW

5. REDSHIFT DISTRIBUTION OF RESOLVED SOURCES Redshift distribution of resolved 24 microns sources in COSMOS (Le Floc’h+09)

6. REDSHIFT DISTRIBUTION OF RESOLVED SOURCES Redshift distrbution of the sources detected by PACS at 100 (top) and 160 (bottom) microns (Berta+11) Redshift distrbution of the sources detected by SPIRE at 250 (blue), 350 (green) and 500 (red) microns (Béthermin+12b)

7. BUILD-UP OF THE CIB AT 24 MICRONS Contribution of the various redshift to the 24 microns counts (Le Floc’h+09) CIB build-up as a function of redshift at 24 microns(Le Floc’h+09)

8. REDSHIFT DISTRIBUTION OF THE CIB (LOWER LIMITS) Left: redshift distribution of the CIB from 24 microns and lower limits from Spitzer stacking and PACS (Jauzac+11). Right: lower limits from SPIRE stacking (Béthermin+12b).

9. COUNTS PER Z SLICE BY STACKING AND CIB BUILD-UP IN THE SUB-MM DOMAIN Resolved SPIRE number counts (Béthermin+12b)

10. COUNTING SOURCES BELOW THE CONFUSION LIMIT BY STACKING ANALYSIS Measured color per S24 and z slices. The scatter is estimated with a bootstrap method: From the mean color and scatter (assumed to be log-normal), we convert the 24 microns flux into SPIRE flux. Several realizations are used to estimate the uncertainties. Correction of completeness taking into account the flux cut at 24 microns. Incompleteness due to the 24 microns flux cut cut for different scatter (Béthermin+12b).

11. COUNTS PER Z SLICE BY STACKING AND CIB BUILD-UP IN THE SUB-MM DOMAIN Number counts built by stacking (Béthermin+12b) Cumulative contribution to the CIB as a function of the flux cut (Béthermin+12b)

12. COUNTS PER Z SLICE BY STACKING AND CIB BUILD-UP IN THE SUB-MM DOMAIN Number counts per redshift slice built by stacking (Béthermin+12b) CIB build-up from counts per redshift slice(Béthermin+12b)

13. SPECTRAL ENERGY DISTRIBUTION OF THE CIB Empirical spectral energy distribution of the CIB (Béthermin+12b)

14. MODELING POINT OF VIEW

15. WHAT CAN WE LEARN FROM NUMBER COUNTS? The case of the bright-end where Euclidian approximation is valid The volume where you can detect A source with a luminosity density L nu is The number of sources per luminosity density bin and brighter than a flux cut S nu is thus: So, the total number of sources brighter tha S nu in the sky is If you prefer differential number counts, just compute the derivative:

16. WHAT CAN WE LEARN FROM NUMBER COUNTS? The case of the bright-end (Euclidian part) Euclidian level of the bright counts as a function of wavelength/frequency (Planck collaboration 2012)

17. WHAT CAN WE LEARN FROM NUMBER COUNTS? Counts at 160 and 500 microns for various evolutions Number counts at 160 et 500 microns in various cases ΛCDM, without evolution, realistic spectra ΛCDM, with evolution, flat spectrum Evolution of luminosity in (1+z)^2.5 Evolution of luminosity in (1+z)^3.5 Complex evolution in luminosity and density Euclidian without evolution

18. MODELING THE EVOLUTION OF INFRARED GALAXIES Start from our local knowledge on the IR galaxies (Luminosity Function, SEDs...) Use an evolution of the luminosity function to reproduce the observations (and sometimes an evolution of the luminosity- temperature relation with z) Reproduce nicely the observations. BUT, give not physical interpretation. Based on halo model evolving from primordial fluctuations Use semi-analytical recipes to describe how the galaxies formed in the dark halos. Need Top-Heavy IMF to reproduce the sub-mm observations. Give a physical interpretation of the galaxy evolution. 2 approaches: Backwards evolution: Semi-analytical:

19. PRINCIPLE OF THE BACKWARD EVOLUTION MODELS Evolution of the luminosity function used by the model of Franceschini+10 Type I AGN Type II AGN Starbursts Spiral

20. PRINCIPLE OF THE BACKWARD EVOLUTION MODELS SED templates used in the model of Franceschini+10 Type I AGN Type II AGN Starbursts Spiral

21. MANY PRE-HERSCHEL EMPIRICAL MODELS Model name Number of populations Presence of AGN Strongly lensed galaxies Scatter in L-T relation Fitting method Lagache et al. (2003,2004) 2No Tuned manually Negrello et al. (2007) 3NoYesNo Tuned manually Le Borgne et al. (2009) 1No Non- parametric inversion of the counts Valiante et al. (2009) Large library based on observed SEDs YesNoYes Tuned manually Franceschini et al. (2010) 4YesNo Tuned manually

22. … WHICH FAIL TO REPODUCE THE SOME NEW OBSERVATIONS Number counts at 500 microns (Oliver et al. 2010) => No model reproduce the counts at both Herschel wavelengths.

23. A NEW GENERATION OF MCMC MODELS (BETHERMIN+11, MARSDEN+11) Building a «as simple as possible» model which reproduce the new infrared observations → no AGN (low contribution), simple parametrization of IR galaxy evolution. MCMC minimisation to obtain the better parameters (for a given parametrization) and study the degeneracies.

24. THE LUMINOSITY FUNCTION Infrared bolometric infrared luminosity function used by the model (Béthermin+11). The transition between normal and starburst templates is driven by We use the following parametrization of the IR LF:

25. EVOLUTION OF THE LUMINOSITY FUNCTION Evolution in density and in luminosity in: rL and rphi can change at 2 specific redshift zbreak1 (free parameter) and zbreak2 (fixed at z=2). We use the Lagache+04 templates to compute the flux observed by the different instruements. Evolution in density Evolution in luminosity

26. THE LAGACHE ET AL. INFRARED GALAXY TEMPLATES 2 populations: normal and starbursts. The normal templates do not evolve with LIR. The starburst tempapltes evolves with LIR. Spectral energy distribution of starburst galaxy templates for different infrared luminosity.

27. INGREDIENT OF THE MODEL Cosmological context SED libraries Local luminosity function (LF) Evolution of the LF Observables to fit 13 free parameters

28. MCMC FIT OF THE OBSERVED COUNTS AND LFS Extragalactic number counts at 250, 350 and 500 microns (Béthermin+11) Chi2 = 177 for 113 degrees of freedom We fit number counts at 24, 70, 160, 250, 350, 500 and 1100 microns +LFs+FIRAS CIB This fit is performed with a MCMC algorithm.

29. RÉSULTAT: AJUSTEMENT DES COMPTAGES Comptages extragalactique à 24, 160, 350, et 1100 microns (adapté de Béthermin et al. 2011) χ 2 = 177 pour 113 degrés de liberté Confidence region of the various parameters of the model(Béthermin+11) Evolution in density and luminosity at intermediate redshift α α σ σ L* Φ*Φ* Φ*Φ* r L,lz r Φ,lz r L,lz r L,mz r L,hz r L,mz r Φ,mz r Φ,hz r Φ,mz r Φ,lz z b,1 L pop σ pop L pop Ajustement des comptages à 24, 70, 160, 250, 350, 500, et 1100 microns + qq LFs+ CIB FIRAS Ajustement réalisé par méthode MCMC. 1, 2 et 3 sigma r Φ,lz r Φ,mz r L,mz 456 -5 -6 -7 -8

30. EVOLUTION OF THE CHARACTERISTIC LUMINOSITY AND DENSITY Evolution of the characteristic densities and luminosities (Béthermin+11)

31. EVOLUTION OF THE STAR FORMATION RATE Evolution of the infrared luminosity density (and the star formation rate) and contribution of the different luminoisty classes (Béthermin+11) Strong increase of the infrared output from z=0 to z=1. z<0.5: dominated by normal galaxies. 0.5<z<1.5: dominated by LIRGs z>1.5: dominated by ULIRG.

32. COMPARISON WITH MARSDEN+11 MODEL Evolution in density and luminosity of the IR LF (Marsden+11) Evolution of the star formation rate density as a function of redshift (Marsden+11)

33. LINKS BETWEEN NUMBER COUNTS, CIB INTENSITY AND SMALL SCALE FLUCTUATIONS The intensity of the background can be computed with: The level of the Poisson fluctuation (in Jy^2/sr or an equivalent unit) can computed from: The Poisson level of the cross-power-spectrum between a band A and B is:

34. LINKS BETWEEN NUMBER COUNTS, CIB INTENSITY AND SMALL SCALE FLUCTUATIONS The intensity of the background can be computed with: The level of the Poisson fluctuation (in Jy^2/sr or an equivalent unit) can computed from: The Poisson level of the cross-power-spectrum between a band A and B is:

35. ORIGINS OF THE CIB SED of the CIB and contribution per redshift slice (up) and luminosity slice (down) (Béthermin+11)

36. POISSON LEVEL OF THE FLUCTUATIONS: OBSERVATIONS VERSUS MODELS Level of Poisson fluctuations of the CIB as a function of the flux cut (Viero+12)

37. COMPUTE EMISSIVITIES FOR MODELS OF CIB ANISOTROPIES Emissivity of IR galaxies as a function of redshift at various wavelength predicted from Béthermin+11 model (Pénin+12a)

38. CONCLUSION There are more and more constraints on the redshift distribution of the source responsible for the CIB. These constraints come from resolved sources below 160 microns and stacking at larger wavelength. The number counts also provide strong constraints on the evolution of the IR galaxies. The various possible evolution can be explore through MCMC analyses. The results shows that high redshift CIB is dominated by ULIRGs. The mean redshift of the CIB increase with wavelength.