1. Deciphering the CIB Banyuls 08/10/2012 RESOLVING THE CIB: I) METHODS TO IDENTIFY THE SOURCES RESPONSIBLE FOR THE CIB Matthieu Béthermin CEA Saclay

2. THE EXTRAGALACTIC BACKGROUND LIGHT (EBL) SED of the extragalactic background light (from Dole & Béthermin, in prep.)

3. MEASUREMENTS OF THE COSMIC INFRARED BACKGROUND (CIB) LEVEL Absolute measurements: need an absolute photometry and an accurate removing of the foregrounds. Upper limits: derived from the absorptions of TeV photons from the blazars by the COB/CIB. Lower limits: from the number counts and statistical analyses (stacking, P(D)). Measurements of the cosmic infrared background (from Béthermin+11, CRF proceeding) Direct countsStacking Total extrapolated contribution

4. SUMMARY ABSOLUTE MESUREMENTS OF THE CIB UPPER LIMITS FROM OPACITY OF THE UNIVERSE TO TEV PHOTONS LOWER LIMITS FROM DEEP SURVEY (AND SOME TECHNICAL STUFFS ABOUT SOURCE EXTRACTION AND COUNTS) MORE STRINGENT LOWER LIMITS BY STACKING ANALYSIS GO DEEPER WITH P(D) ANALYSIS

5. ABSOLUTE MEASUREMENTS

6. ABSOLUTE MEASUREMENTS OF THE CIB: THE CHALLENGE OF FOREGROUND SUBTRACTION

7. Spectral energy distribution of the background light (Matsuura+11).

8. MODELS OF ZODIACAL EMISSION Earth Model of zodiacal emission in the solar system (Kelsall+98)

9. MODELS OF ZODIACAL EMISSION Model of zodiacal emission in the solar system (Kelsall+98)

10. ABSOLUTE MEASUREMENTS OF THE CIB: THE CHALLENGE OF FOREGROUND SUBTRACTION

11. SUBTRACTION OF THE GALACTIC CIRRUS EMISSIONS Correlation between HI column density and intensity at 100 microns in IRAS data (Lagache+00)

12. SUBTRACTION OF THE GALACTIC CIRRUS EMISSIONS Decomposition of the HI emissivity into 3 components (Penin+12b, see also Miville-Deschênes+05)

13. SUBTRACTION OF THE GALACTIC CIRRUS EMISSIONS Local Intermediate velocity cloud High velocity cloud Spatial distribution of HI clouds in ELAIS-N1 field (Pénin+12) From Miville-Deschênes+05

14. SUBTRACTION OF THE GALACTIC CIRRUS EMISSIONS 100 microns IRAS map around ELAIS-N1: all component (left), model of cirrus (center), cirrus removed (right) (Pénin+12)

15. UPPER LIMITS FROM HIGH ENERGY PHOTONS

16. PHOTON-PHOTON SCATTERING TeV photon from blazar IR EBL photon e- e+ Cross section of the photon-photon interaction: Minimal energy of the IR photon for interaction: 2 (m e c 2 ) 2 /E Υ = 0.5 MeV 2 /E Υ or λ IR (microns) ≈ 0.6 E Υ (TeV) Details and references in e.g. Béthermin+11

17. ABSORPTION OF BLAZAR TEV PHOTONS BY THE EBL Spectral energy distribution of the extragalactic background light (Dole+06) 100 TeV 10 TeV 1 TeV 100 GeV

18. ABSORPTION OF TEV PHOTONS ALONG A LINE OF SIGHT From Hess collaboration

19. EFFECT ON BLAZAR SPECTRUMS Observed and intrinsic TeV spectrum of a distant blazar (Aharaonian+06) Intrinsic Observed Compilation of blazar spectra (Kneise&Dole 10)

20. UPPER LIMITS ON EBL SED From Meyer+12

21. LOWER LIMITS FROM DEEP SURVEYS

22. RESOLVING THE CIB Spitzer 24 microns

23. RESOLVING THE CIB Spitzer 24 microns Galaxy number counts at 24 microns (Béthermin+10a)

24. RESOLVING THE CIB Spitzer 24 microns Cumulative contribution of the IR galaxies to the CIB as a function of the flux cut (Béthermin+10a)

25. SOURCE EXTRACTION: IN A VERY SIMPLIFIED CASE Let’s discuss this (over-?)simplified case: The PSF is a Dirac (i.e. the flux of a source lies only in one pixel). The source density is small (i.e. less than one source per pixel). Constant Gaussian instrumental noise. The PDF of the signal (Smes) in pixel hosting a source with a flux Si is: The probability to detect a source for a threshold Sd is: The mean flux of the detected sources with an initial flux Si is:

26. SOURCE EXTRACTION IN A VERY SIMPLIFIED CASE Completeness for a 5sigma threshold Flux boosting (5 sigma threshold) The probability to detect a source for a threshold Sd is: The mean flux of the detected sources with an initial flux Si is: Smes ≈ Sd Smes ≈ Si

27. EMPIRICAL ESTIMATION OF COMPLETENESS AND FLUX BOOSTING IN A COMPLEXE CASE Principle of source injection (from Morgan Cousin) Step 1: inject few artificial sources in the real map Step 2: Rerun the extraction tool Step 3: compute the completeness from the fraction of recovered sources (and the flux boosting from their mean flux).

28. RESOLVING THE CIB: THE PROBLEM OF THE CONFUSION Spitzer 24 microns CIB 80% résolved (Béthermin+10a)

29. Spitzer 160 microns CIB 15% résolved (Béthermin+10a) RESOLVING THE CIB: THE PROBLEM OF THE CONFUSION

30. Herschel 160 microns CIB 70% résolved (Berta+10) RESOLVING THE CIB: THE PROBLEM OF THE CONFUSION

31. Herschel 500 microns CIB 6% résolved (Oliver+10) RESOLVING THE CIB: THE PROBLEM OF THE CONFUSION

32. CONFUSION LIMIT 2 regimes Source density limited Fluctuation limited In general, when source density reaches 20 beams/sources Fluctuation due to faint sources:

33. CONFUSION NOISE AND CONFUSION LIMIT 1-σ confusion noise (top) and confusion limit (bottom) as a function of wavelength for various diameters of telescopes (Béthermin+11)

34. USING THE 24 MICRON OBSERVATIONS AS A PRIOR 24 microns Spitzer250 microns Herschel

35. 24 microns Spitzer250 microns Herschel USING THE 24 MICRON OBSERVATIONS AS A PRIOR

36. 24 microns Spitzer250 microns Herschel USING THE 24 MICRON OBSERVATIONS AS A PRIOR

37. 24 microns Spitzer250 microns Herschel Principle of the PSF-fitting photometry using a prior on positions. Model fitted to the data USING THE 24 MICRON OBSERVATIONS AS A PRIOR This task can be performed with several codes: DAOPHOT, Starfinder, GALFIT, FASTPHOT…

38. MORE STRINGENT LOWER LIMIT BY STACKING

39. 24 microns Spitzer250 microns Herschel USING THE 24 MICRON OBSERVATIONS AS A PRIOR

40. 24 microns Spitzer250 microns Herschel USING THE 24 MICRON OBSERVATIONS AS A PRIOR

41. 24 microns Spitzer250 microns Herschel

42. STACKING: THE MOVIE Directed by Hervé Dole

43. LOWER LIMIT OF THE CIB BY STACKING Spectral energy distribution of the CIB (Dole+06)

44. LOWER LIMIT OF THE CIB BY STACKING Spectral energy distribution of the CIB (Dole+06)

45. Lower limits to the CIB in the sub-mm derived by stacking in the BLAST data (Marsden+09) LOWER LIMIT OF THE CIB BY STACKING

46. COUNTING THE FAINT INFRARED SOURCES BY STACKING Extragalactic number counts at 160 microns measured with Spitzer (Béthermin+10a) COUNTS AT 160 MICRONS

47. stacking Extragalactic number counts at 160 microns measured with Spitzer (Béthermin+10a) COUNTING THE FAINT INFRARED SOURCES BY STACKING

48. Cumulative contribution of the 160 microns sources to the CIB (Béthermin+10a) CONTRIBUTION OF THE UNRESOLVED SOURCES TO THE CIB

49. BIASES DUE TO THE CLUSTERING The clustering of the 24 microns sources biases the stacking results. This bias can be >20% with Spitzer at 160 microns and with BLAST Effect of the clustering on the stacking (from Bavouzet's thesis) Simulation including the Simulation with clustering

50. CORRELATION FUNCTION AND STACKING - Results of a stacking with IAS method (see Nicolas Bavouzet thesis or the annexe B of Béthermin et al. 2010b) Biases due to clustering Auto-correlation of the stacked population Cross-correlation with other populations Radial profile of the results of a SPIRE stacking (Béthermin+12b)

51. HOW THE CLUSTERING BIASES THE STACKING RESULTS? Estimated on the stacking measurements due to the clustering of the sources (from Bavouzet's thesis) Measured bias caused by clustering with SPIRE (Béthermin+12b)

52. ESTIMATION OF THE CLUSTERING BIAS Method 1: Convolve the 24microns map by the SPIRE beam. Stack the 24 microns catalog and compare with the flux of the individual sources (PROBLEM: do not take into account the dependence of the colors and the clustering with the redshift). Method 2: You make a first stacking to estimate the color (and scatter?) of you populations. You build a simulation using the position of the real sources and the color of them. You compare the input flux and output flux to estimate the bias (PROBLEM: do not take into account the contribution of the sources not seen at 24 microns)

53. ESTIMATION OF THE CLUSTERING BIASES Method 3: You build a simulation from models (PROBLEM: Can we realy trust the clustering in the models?) Method 4: fit directly a clustering and a source component on stacked images.

54. KURCZYNSKI & GAWIWER 2010 METHOD When you do PSF-fitting you fit this model to the map: This method allow to estimate the fluxes (Sk) of the sources. If you assume that the flux of all a population is the same, you can estimate the flux of this population correcting the contamination due to the geometry of the sources. It is the principle of KG method.

55. BIAS DUE TO THE INCOMPLETENESS OF THE INPUT CATALOG Stacking of 2uJy<S3.6<8uJy sources at 24 microns (Nicolas Bavouzet's thesis) Radial profile of the background for a stacking of an incomplete sample of UV sources (Heinis+12)

56. GO DEEPER WITH P(D) ANALYSIS

57. P(D) ANALYSIS Counts Histogram Ilustration of the link between the counts and the pixel histogram of a confusion limited infrared map. The histogram of a map containing only unclustered, point sources depends only on the counts and the instrumental effects (PSF, noise, filtering) Histogram

58. THE P(D) FORMALISM The pixel histogram can be analytically computed from the flux distribution of the sources. It supposes a Poissonian distribution of the sources. It supposes that all the sources are point-like.

59. PDF OF THE SIGNAL IN A PIXEL (SIMPLE CASE: PSF=DIRAC) The mean number of source in a pixel with a flux bin between S(k) and S(k+1) is given by: where dN/dS are the differential number counts, and ΔS = S(k+1) – S(k). The probability distribution of nk is a Poisson's law: The total signal D in a pixel is given by: and,

60. PDF OF THE SIGNAL IN A PIXEL (SIMPLE CASE: PSF = DIRAC) The PDF of the signal in a pixel is given by: It is easier in Fourier space: where: and then: You can pass to the continuous limit: ΔS

61. PDF OF THE SIGNAL IN A PIXEL (SIMPLE CASE: PSF = DIRAC) And finally:

62. TAKING INTO ACCOUNT THE PSF The flux F of a source seen in a given pixel by a sources of a flux S, at a distance θ from the pixel is: The distribution (n(F) = dN/dF) of the seen flux to a pixel is thus: dN/dS is the differential number counts. dN/dF is the distrubution of the seen flux (take into account ). They are linked by: Example of a gaussian PSF n(F) take into account the contribution of the source centered on the considered pixel, but also of ones centered on the other neighboring pixels. You have just to replace S by F, and dN/dS by n(F) into the P(D) formula.

63. ZERO VALUE AND NOISE For a relative photometer, the absolute zero is unknown and the map has a zero mean. In this case you have to shift your PDF. The PDF due to sources distribution must be convolved by the PDF of the instrumental noise.

64. DETERMINATION OF THE NUMBER COUNTS FROM A P(D) ANALYSIS We can fit the parameters of a model of counts comparing the PDF predicted by the counts model and the pixel histogram. The likelihood is thus: where pi is the PDF predicted by the P(D) and ni the pixel histogram. Model of counts dN/dS*S^2.5 S Histogram Number of pixels P(D) formula Predicted from the parameters Data

65. DETERMINATION OF THE NUMBER COUNTS USING A BROKEN POWER-LAW MODEL Patanchon et al. used a broken power-law model to fit the counts. The position in x of the knots is fixed. The position in y is fitted. Sub-mm number counts determined in BLAST data by Patanchon et al. (2009).

66. THE LIMIT DUE TO THE PARAMETRIZATION The broken power-law model do not reproduce exactly a smooth galaxy model. This effect can become larger than the statistical errors. Using a spline to link the knots reduces strongly (but not totally) this effect. Solide line: a galaxy model. Dashed line: the power model.

67. BEAM SMOOTHING If the instrumental noise and confusion noise are at comparable levels, convolving the map by the beam helps a lot. Simulation of a Herschel shallow field without (left) and with (right beam smoothing)

68. LIMITATION OF THE BEAM SMOOTHING But, beam smoothing spreads the PSF, and increase the problem of confusion. It should not be used for field when instrumental noise is negligible comparing to the confusion noise. Simulation of a Herschel deep field without (left) and with (right beam smoothing)

69. THE GALACTIC CIRRUS CONTAMINATION A cirrus in the FLS field at 250 micron. Histogram of 2 fields. Top: without filtering. Bottom: with a high pass filtering The galactic cirrus are contaminent for P(D) analysis. They can be removed with an high-pass filtering.

70. THE EFFECTS OF THE CLUSTERING The Poissonian behavior is dominant for scale smaller than 10 arcmin. For scale larger than 10 arcmin, we are dominated by cirrus and clustering. One solution: high-pass filtering. Power spectrum at 160 microns (Lagache+07).

71. P(D) FORMALISM AND LINEAR FILTERING The filtering is taken into account by the P(D) formalism if you use a filtered PSF. An high-pass filtering generate large and faint negative wings. Effect of a high-pass filtering on au gaussian PSF The center of the PSF is normalized at 1. 10'

72. The basic P(D) formula contain an hypothesis of positivity of the PSF. But, it is relatively easy to adapt it to negative case. We separate positive a and negative contribution: The final contribution is the convolution of the two distributions: We classicaly compute: And, finally: P(D) FORMULA FOR A PSF WITH NEGATIVE WINGS

73. P(D) ANALYSIS: HERMES RESULTS Number counts at 250, 350, and 500 microns measured by P(D) analysis (Glenn+10). P(D) HerMES (Conley's code) SPIRE HerMES resolved (Oliver et al. 2010) P(D) HerMES (Bethermin's code) SPIRE ATLAS resolved (Clements el al. 2010) Combining deep and wide fields, Glenn+10 managed to constrain the counts between 2 mJy and 1 Jy. This flux range is responsible of about 2/3 of the CIB.

74. CONCLUSION AND PERSPECTIVES Absolute measurements of the CIB are limited by the foreground subtraction. Future improvement will be due to a better characterization of these foregrounds (or missions outside the zodiacal could e.g. EXZIT). The upper limits from the absorption of TeV photons are more and more stringent, due to data accumulated by Fermi and HESS. The bulk of the CIB is resolved into individual sources below 160 microns, but due to confusion, it is not the case at longer wavelengths. It should be possible with SCUBA 2 at 450 microns and ALMA in the millimeter. The stacking and the P(D) analysis provide information about sources below the confusion limit. These statistical methods are affected by various bias, which have to be carefully corrected.