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Observational Cosmology: 6. Galaxy Number Counts

Observational Cosmology: 6. Galaxy Number Counts. “ It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories instead of theories to suit facts.”    —  Sherlock Holmes.

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Observational Cosmology: 6. Galaxy Number Counts

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  1. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Observational Cosmology: 6. Galaxy Number Counts “It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories instead of theories to suit facts.”   —  Sherlock Holmes.

  2. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.1: Why Study Source Counts Why Study Source Counts - How many galaxies are there in the Universe ? Why Study Galaxy Source Counts ? • To count the numbers of galaxies in the Universe • Numbers of galaxies • Density of galaxies and the Universe • Fainter and fainter galaxies at higher and higher redshift • To determine the Geometry of the Universe • Faint source counts depend on the geometry of the Universe • low density / cosmological constant  faster expansion  larger volumes  more galaxies • To investigate the contribution of different galaxy populations to the Universe • investigate optical mix of morphological types • local infrared - spirals • bright radio - ellipticals • X-rays - AGN • To investigate the evolution of galaxies • Compare galaxies today with galaxies in the past • Quantify and constrain the evolution in the galaxy populations • Discriminate the nature of the evolution

  3. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 R L=0, W=2q Friedmann-Lemaitre (open) W<1 Milne (open) W=0 Einstein de-Sitter (closed) W=1 Sandage 1961, ApJ, 133, 355 ~mJy Friedmann-Lemaitre (closed) W>1 t Unfortunately, Universe not that simple Galaxy Evolution Measuring Numbers of Galaxies to faint fluxes Cosmological Parameters qo or Wo 6.1: Why Study Source Counts Why Study Source Counts - The Geometry of the Universe

  4. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 100,000th Hubble 90億光年QSO HDF (ISO 15mm) Mk241 (VSOP) 3C216 (VSOP 5GHz) GALEX M51 visible UV g-線 microwave Sub-mm 電波 X-線 赤外 波長 1cm 1mm-200mm 100nm 1km-1m 200mm-2mm 700-400nm 1nm 0.1A • 　電波波長 : AGN / Ellipticals • 　Sub-mm : ULIG (Elliptical?) • 　赤外波長 : Spiral 銀河 • 　Optical : 色々な銀河 • 　X線波長 : AGN (QSO) • g線 : AGN HDF (SCUBA 850mm) HDF 6.1: Why Study Source Counts Why Study Source Counts - Population Contributions

  5. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 • LUMINOSITY EVOLUTION　(Galaxies in the past were brighter than today) REDSHIFT • DENSITY EVOLUTION (Galaxies in the past were more numerous than today) 6.1: Why Study Source Counts Why Study Source Counts - Evolution

  6. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Number ; S Flux ; d L 6.2: Source Counts Derivation How many galaxies are there in the Universe Simple Euclidean Case • For flat, non expanding Universe filled with uniformly distributed galaxies of same luminosity • (A Euclidean Universe) • Galaxy number density = n • Galaxy luminosity = L • Number of galaxies to distance ( d ) = N • Nearby Galaxies generally follow this distribution • More complex when we look to greater distances • We have to consider the cosmology & galaxy evolution • Have to consider a range of galaxy types and luminosities

  7. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 LUMINOSITY FUNCTION GALAXY EVOLUTION COSMOLOGY (Ho, Wo, L) K-CORRECTION (Galaxy SED) 累積銀河計数 Integral Galaxy Source Counts 背景放射 Background Contribution 微分銀河計数 Differential Source Counts 銀河の赤方偏移分布 N-z Distribution 6.2: Source Counts Derivation Derivation of Source Counts SOURCE COUNT MODEL

  8. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.2: Source Counts Derivation Number of galaxies, N (seen to sensitivity, S) = number density galaxies x volume (for all luminosities) Cosmology Galaxy number density (all luminosities) - Luminosity Function Volume depends on cosmology (Ho, Wo, L) Wo= 0, 1 easiest The farthest galaxies you can see depends on the sensitivity The Distance also depends on the cosmology (Ho, Wo, L) Wo= 0, 1 are the easiest.

  9. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 f* a - Faint end slope a L* L*- Characteristic luminosity s f*- Number density normalization s- Gaussian width L<L*(power law) L>L*(exponential) 6.2: Source Counts Derivation Luminosity Function LUMINOSITY FUNCTION Galaxy number density as a function of their luminosity Depends on 4(+) parameters

  10. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Power Law + Exponential (Schecter 1976) Log Gaussian (Saunders 1990) Power Law (Lawrence 1986) 6.2: Source Counts Derivation Luminosity Function

  11. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 For volume limited, non evolving sample; Co-moving number density of objects is (where 1 = probability of object being in sample) Suppose sample is incomplete (e.g. flux limited)  Some objects may drop out of the sample. Probability of the ith object being included is Pi and the are no objects with Pi=0. Then the co-moving number density in an OBSERVED sample of Nobsobjects is; Therefore, for a flux limited sample; Assuming the population is non-evolving and the flux is monotomic function of z, The probability Pi is given by 6.2: Source Counts Derivation Calculation of Luminosity Function (1/Vmax method) In 2-D In 3-D Pi= probability of object staying in sample such that if the probability of dropping out is 1/2 then we require 2x the weight This will be an unbiased estimator of the underlying value Vmax,I= volume enclosed at maximum redshift zmax,i at which the ith object can be observed. Vlimit= arbitrary large volume into which the flux limited sample is embedded

  12. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.2: Source Counts Derivation Calculation of Luminosity Function (Maximum Likelihood method)

  13. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Flux at no related to Luminosity at no by z K-CORRECTION K-CORRECTION - Observed SED True SED 6.2: Source Counts Derivation Want compare luminosities at the same wavelengths  K-Correction K-Correction • Due to redshift effect s, the true galaxy SED and that seen from Earth are different • Need to know about emission from sources at one single wavelength but we have ensemble le = lo/ (1+z) • Need a CORRECTION This correction is called the K-CORRECTION • The significance of the correction depends on the shape of the galaxy SED Observed flux at observed frequency, no, (c=nl) Corresponding to the luminosity at ne The K-Correction depends on the assumed Spectral Energy Distribution (SED)

  14. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Evolution: increases z(L,S) 6.2: Source Counts Derivation Evolution • LUMINOSITY EVOLUTION • Galaxies in the past were more luminous • DENSITY EVOLUTION • Galaxies in the past were more numerous Parameterize luminosity evolution ~ f(z) Parameterize density evolution ~ g(z)

  15. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Integral Counts (60mm) Luminosityの進化 L* f(z) L* Luminosity Evolution : f* g(z) f * Density Evolution : Densityの進化 Differential Counts (60mm) f* L* 6.2: Source Counts Derivation Evolution

  16. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 zmax Vmax(zmax) probability of galaxy detected in volume V, is z dP= probability in rangeV -V+dV V(z) galaxies more “numerous” in past Real Surveys galaxies less “numerous” in past 6.2: Source Counts Derivation V/Vmax Test for Evolution For a galaxy with luminosity, L, in a redshift survey there is a maximum volume within which the object can be detected, Vmax(zmax) Compare with volume in which galaxy was actually detected: V(z), 0 < V(z) < Vmax If there was no change in co-moving number density independent ofVV/Vmax uniformly distributed between 0 - 1 <V/Vmax> = 0.5 <V/Vmax>significantly deviates from 0.5 evolution

  17. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 • Integral Source Counts - • Total (cumulative) number of sources detected above flux threshold, S Euclidean • Differential Source Counts - • Number of sources detected at flux threshold, S in range SdS Euclidean • Commonly, Normalize Differential Source Counts to Euclidean Universe 6.3: Source Counts Results Integral and Differential Source Counts

  18. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.3: Source Counts Results Number Redshift Distributions

  19. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.3: Source Counts Results Back Ground Contributions and Confusion

  20. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.4: Multiwavelength Source Counts Optical Source Counts Faint blue galaxies (relatively low luminosity) were more numerous in the past and may dominate the faint source counts

  21. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Total E/S0 Sabc Sd/Irr I=22.5 I=23.5 I=24.5 I=25.5 6.4: Multiwavelength Source Counts Optical Morphological Evolution Redshift Distributions as function of morphological type • Bright Fluxes - More ellipticals , less Irregular • Faint Fluxes - Few Ellipticals, more Irregular • The Butcher Oemler Effect • Low redshift Clusters have more red galaxies than blue galaxies, • Higher redshift Clusters have higher fraction of blue galaxies • The morphology Density Relationship • Denser regions of clusters have higher proportion of red galaxies than less dense regions

  22. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.4: Multiwavelength Source Counts Near-Infrared Source Counts • Near-infrared • Emission from cool stars • Old populations dominate • Bright Fluxes E/S0 ~ 50% • Tracing Stellar Mass

  23. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 M82, 3.3Mpc Reprocessed 6.4: Multiwavelength Source Counts The Dusty Universe Infrared Emission: UV emission from young hot OB stars Absorbed by dust Reprocessed and emitted at IR wavelength Far-Infrared Source Counts

  24. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 IRAS 60mm Differential Counts IRAS 60mm Integral Counts 6.4: Multiwavelength Source Counts • Infra Red Astronomy Satellite • Launched 1983 • All sky survey 12, 25, 60, 100mm Far-Infrared Source Counts • The importance of DUST. • For normal galaxies LIR/Lopt - 30%. • For Starburst LIR/Lopt - 50-90%. • ULIG - A new population LIR/Lopt - 90-99% • IR - Strong Evolution - High Star Formation. • 50%-60% Star Formation in the Universe is in IR.

  25. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 ISO 15mmの累積銀河計数 ISO 15mmの微分銀河計数 IRAS Evolution !! IRAS Evolution !! IRAS Evolution !! IRAS Evolution !! ISO 170mmの累積銀河計数 ISO 90mmの累積銀河計数 6.4: Multiwavelength Source Counts Far-Infrared Source Counts Infrared Space Observatory ISO, 11/1995-5/1998 • The ISO Universe • Source counts 7-200mm • Strong Evolution • Dominant LIG/ULIG pop.

  26. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 ISO 170mm Integral Counts ISO 15mm Integral Counts ISO 15mm Differential Counts HDF P(D) HDF (PRETTI) 10 8 HDF Lockman-Deep 6 lg (Number / ster 4 BURST Evolution !! 2 ELAIS 0 lg (Flux) {Jy} -5 -4 -3 -2 -1 0 1 2 ISO 90mm Integral Counts IRAS 6.4: Multiwavelength Source Counts Far-Infrared Source Counts Infrared Space Observatory ISO, 11/1995-5/1998 • The ISO Universe • Source counts 7-200mm • Strong Evolution • Dominant LIG/ULIG pop.

  27. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 850mm 6.4: Multiwavelength Source Counts Submillimetre Source Counts • 850mm SCUBA JCMT • Re-emission from dust of Starlight at sub-mm wavelengths • Many line emission from rotational transitions of CO • Large negative K-corrections  access high z Universe • LBOL  1012Lo SFR>102-103Mo/yr (Arp220 like ULIG sources) • ~ 50 detected sources • Strong Evolution • Assembly of an Elliptical Galaxy in < 1Gyr • SCUBA beam ~ 15”  I.D.s difficult  few redshifts • Median redshift ~ 2.5

  28. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 Hopkins et al. 1999 6.4: Multiwavelength Source Counts Radio Source Counts • Radio Sources separated into 2 populations • Bright radio fluxes (S1.4GHz> ~ mJy) •  Radio Loud Ellipticals • Black Hole Power Source • power law emission S1.4GHzn-aa ~ 0.3 • Faint radio sources (S1.4GHz< ~ mJy) •  Star Forming Galaxies (STFG) • SNR synchrotron emission •  Star Formation Power Source • S1.4GHzn-aa ~ 0.8 • Bright radio fluxes - Ellipticals Dominate • sub-mJy fluxes - Emergence of new population (Starburst Galaxies) • <z>~0.3  higher redshift counterpart of IRAS STFG • Follow well known Radio-FIR relation (S60mm ~90 S1.4GHz) • Radio fluxes < 35mJy - Spectral slope flattens to a ~ 0.7  STFG dominate over AGN • z<1.5 optically red star forming galaxies

  29. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 McHardy et al 1999 Manners 2003 Pearson et al 1997 6.4: Multiwavelength Source Counts X-Ray Source Counts Bright (0.5-2keV) X-ray Fluxes Dominant Population - Quasars S (0.5-2keV) < 10-14 ergs cm-2 s-1  new faint population of sources NELGs (Starbursts / AGN) Densities ~ 1000-2000/sq.deg.

  30. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.5: The Star Formation History Background Light

  31. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.6: Future Prospects The Future • Spitzer • GALLEX • ASTRO-F • UKIDSS • VISTA • Herschel • SCUBA-2 • WISE • ALMA • JWST • SPICA • SKA

  32. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.7: Summary Summary • Study Galaxy source counts to • investigate the contribution of different galaxy populations to the Universe • compare the evolution of galaxies today with those in the past • constrain Geometry of the Universe • Source counts depend on • Cosmology • Luminosity Function • K-Correction • Evolution • Source counts are a function of observing wavelength • Different wavelengths are dominated by different classes of sources • To understand the star formation and evolutionary history  multiwavelength analysis • Present and next generation surveys • Larger areas to greater depths • increase statistical samples by orders of magnitudes!

  33. Chris Pearson : Observational Cosmology 6: Galaxy Number Counts - ISAS -2004 6.7: Summary Summary 終 Observational Cosmology 6. Galaxy Number Counts Observational Cosmology 7. The Evolving Universe 次：

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