Baryon Acoustic Oscillations               and Dark Energy                  Bruce Bassett (AIMS/SAAO/UCT)Bruce Bassett (SA...
SCP 96                          High-z / SCP 98                                    M(flat)                          (flat)...
THE CMB                COBE 96L(l+1) Cl            2     10      100   1000            l
COBE                QMASKL(l+1) Cl            2     10    100   1000            l
COBE                QMASK                BOOMERanG 00L(l+1) Cl            2     10      100   1000            l
COBE                QMASK                BOOMERanGL(l+1) Cl                MAXIMA            2    10         100   1000   ...
COBE                QMASK                BOOMERanGL(l+1) Cl                MAXIMA                CBI 03            2    10...
Did not show                COBE                 SPT                QMASK                ACT                              ...
Blake et al, 2011All assumes w = -1
Bruce Bassett (SAAO/UCT)   BAO
Bruce Bassett (SAAO/UCT)   BAO   KITPC - March 2009
Overview of this lecture•   Power spectra•   Origins, uses & measurements of BAO•   Statistical Standard Rulers•   Targets...
The power spectrum• P(k) = <| k|2> where k is the Fourier transform  of the density contrast                              ...
Where is the information?• The power spectrum actually contains relatively  little information in our everyday life…• Most...
Random                          SwappedOriginals      Phases                          Phases            M.S. Bartlett, J. ...
Some examples of images and their P(k)   All images from http://www.sci.utah.edu/~cscheid/spr05/imageprocessing/project3/
P(k)
P(k)
On small (nonlinear) scales phase is       important though…                          Coles 2002
We will look for the BAO in P(k)       …but what is the origin of the                 BAO?Bruce Bassett (SAAO/UCT)   BAO
3D Green’s Function for                           Speed of Sound                                       Sound Horizon      ...
Bruce Bassett (SAAO/UCT)   BAO
Real Space Transfer Function                                 Bashinsky and Bertschinger, 2001Bruce Bassett (SAAO/UCT)   BAO
Evolution of a Spherical OverdensityBaryon Density    Photon Density               Mass Profiles                      Whit...
Baryon Density   Photon Density   Mass Profiles
Baryon Density   Photon Density   Mass Profiles
Baryon Density   Photon Density   Mass Profiles
Baryon Density   Photon Density   Mass Profiles
Baryon Density   Photon Density   Mass Profiles
Baryon Acoustic PeakBruce Bassett (SAAO/UCT)     BAO
13 May 2008, STIASMillenium Simulation, Springel et al   Bispectrum from 1 Million LRGs
2-point Correlation function                 (r)So we expect to see an increase    in (r) at r ~ 150Mpc13 May 2008, STIAS ...
Eisenstein et al, 2005Bruce Bassett (AIMS/SAAO/UCT)   BAO   SDSS LRGs
WiggleZ, Blake et al, 2011Bruce Bassett (SAAO/UCT)             BAO
2 minute Exercise:        Compute the size of the BAO               scale today    • i.e. Derive the BAO scale of 150 Mpc ...
Bruce Bassett (SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Bruce Bassett (SAAO/UCT)   BAO
Bruce Bassett (SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Bruce Bassett (SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Statistical Standard RulersBruce Bassett (AIMS/SAAO/UCT)   BAO
Where are the oscillations in BAO?     (r) P(k)Bruce Bassett (AIMS/SAAO/UCT)   BAO
Eisenstein et al.          Tegmark et al.                             BAP vs BAO     (r) P(k)Bruce Bassett (AIMS/SAAO/UCT)...
BAP Detection Is Hard!  • Consider a typical Luminous Red Galaxy (LRG).    How many LRGs do we expect in a BAP shell    ar...
Power Spectrum Errors                                 Cosmic Variance   Shot Noisem = number of Fourier modes measured in ...
Shot Noise                    Fixed Volume            50 pointsBruce Bassett (AIMS/SAAO/UCT)         BAO
Shot Noise                     Fixed Volume         500 pointsBruce Bassett (SAAO/UCT)            BAO
Shot Noise                     Fixed Volume         5000 pointsBruce Bassett (SAAO/UCT)            BAO
Shot Noise                     Fixed Volume         50k pointsBruce Bassett (SAAO/UCT)            BAO
Cosmic Variance                     1 x Volume   Fixed 50k pointsBruce Bassett (SAAO/UCT)          BAO
Cosmic Variance                     25 xVolume   Fixed 50k pointsBruce Bassett (SAAO/UCT)          BAO
Cosmic Variance                     225 xVolume   Fixed 50k pointsBruce Bassett (SAAO/UCT)           BAO
Cosmic Variance                     2200 xVolume   Fixed 50k pointsBruce Bassett (SAAO/UCT)            BAO
Optimal Survey Design    • What is the optimal sampling      of a page of text?    • Depends what information you      wan...
What choice of target should                  one use for BAO?Bruce Bassett (SAAO/UCT)    BAO
Luminous Red Galaxies (LRGs)e.g. SDSS, BOSS,… Bruce Bassett (SAAO/UCT)   BAO
Blue galaxies…e.g. WiggleZ,… Bruce Bassett (SAAO/UCT)          BAO
(Statistical) Standard RulersBruce Bassett (AIMS/SAAO/UCT)   BAO
Beyond spherical averaging  • In the SDSS exercise you computed the    spherical average of (r) to give an average    dist...
The Beauty of Standard VolumesRadial                                           Only works if                              ...
BAO and AP  • If we only know the volume is spherical, then we    constrain the product H(z) dA(z) (the Alcock-    Paczyns...
Bruce Bassett (SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Bruce Bassett (SAAO/UCT)   BAO
“Standard” is a Crucial        Ingredient of Standard RulersBruce Bassett (SAAO/UCT)   BAO
BAO  have provided the first ever low-z   cosmic distance measure based          on linear physicsBruce Bassett (SAAO/UCT)...
J. HuchraBruce Bassett (SAAO/UCT)   BAO
Complications     A man falls from a window and on the way down           someone asks…``how’s it going”?                 ...
BAO and Nonlinearity                                        Linear Prediction                                      Nonline...
Broadening                 Shift to smaller                                             radius        Bruce Bassett (SAAO/...
(r) P(k)Bruce Bassett (AIMS/SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Bruce Bassett (AIMS/SAAO/UCT)   BAO
Calibrating Nonlinearity  • Although it is (weakly) nonlinear, gravity is still    quite clean (compare turbulent MHD in s...
Photometric BAO Surveys              It is tempting to want to just do an               imaging survey instead of taking  ...
Photometric surveys• Do we have to take spectra? This is slow and expensive…• If we don’t need accurate redshifts we can d...
Visualising the underlying physics                                                    z=0                               rF...
Visualising the underlying physics                                                    z = 0.2                             ...
Visualising the underlying physics                                                    z = 0.4                             ...
Visualising the underlying physics                                                    z = 0.6                             ...
Visualising the underlying physics                                                    z = 0.8                             ...
Visualising the underlying physics                                                    z = 1.0                             ...
Visualising the underlying physics                                                    z = 1.2                             ...
Visualising the underlying physics                                                    z = 1.4                             ...
Visualising the underlying physics                                                    z = 1.6                             ...
5 minute exercise: photometric redshifts • Given two non-overlapping, but contiguous top-   hat filters of width   and per...
BAO and photo-z errors                                        UsBruce Bassett (SAAO/UCT)   BAO
Increasing Photo-z ErrorBruce Bassett (AIMS/SAAO/UCT)   BAO
Increasing Photo-z ErrorBruce Bassett (AIMS/SAAO/UCT)   BAO
Increasing Photo-z ErrorBruce Bassett (AIMS/SAAO/UCT)   BAO
Benitez et alBruce Bassett (SAAO/UCT)   BAO
Benitez et alBruce Bassett (AIMS/SAAO/UCT)   BAO
The Future for BAO  •   DES  •   BOSS  •   BigBOSS  •   LSST  •   EUCLID  •   WFIRST  •   SKA and other 21cmBruce Bassett ...
Conclusions  • BAO/BAP measurements are arguably the    cleanest probe of cosmic expansion we have  • They can provide bot...
Fun Exercise• In groups of 2 or alone write pseudo-code to  compute the spherically averaged (r) for the  original SDSS da...
Bao ctics 2012
Upcoming SlideShare
Loading in …5
×

Bao ctics 2012

389 views

Published on

Bruce Bassett's Baryon Acoustic Oscillations Lecture at CTICS

Published in: Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
389
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Bao ctics 2012

  1. 1. Baryon Acoustic Oscillations and Dark Energy Bruce Bassett (AIMS/SAAO/UCT)Bruce Bassett (SAAO/UCT) BAO KITPC - March 2009 ArXiv:0910.5224
  2. 2. SCP 96 High-z / SCP 98 M(flat) (flat) Evolution of the Hubble Diagram 1996-2009ESSENCE+SNLS07 Constitution 09 M (+BAO) M(flat) Filled by the SDSS SN survey
  3. 3. THE CMB COBE 96L(l+1) Cl 2 10 100 1000 l
  4. 4. COBE QMASKL(l+1) Cl 2 10 100 1000 l
  5. 5. COBE QMASK BOOMERanG 00L(l+1) Cl 2 10 100 1000 l
  6. 6. COBE QMASK BOOMERanGL(l+1) Cl MAXIMA 2 10 100 1000 l
  7. 7. COBE QMASK BOOMERanGL(l+1) Cl MAXIMA CBI 03 2 10 100 1000 l
  8. 8. Did not show COBE SPT QMASK ACT BICEP BOOMERanGL(l+1) Cl TOCO MAXIMA ACBAR CBI 03 VSA SASKATOON WMAP-5 ARCHEOPS DASI PYTHON FIRS Tenerife OVRO SUZIE AMI 2 10 100 1000 ATCA l etc…
  9. 9. Blake et al, 2011All assumes w = -1
  10. 10. Bruce Bassett (SAAO/UCT) BAO
  11. 11. Bruce Bassett (SAAO/UCT) BAO KITPC - March 2009
  12. 12. Overview of this lecture• Power spectra• Origins, uses & measurements of BAO• Statistical Standard Rulers• Targets for BAO surveys• Some Complications• Photometric vs spectroscopic BAO surveysBruce Bassett (AIMS/SAAO/UCT) BAO
  13. 13. The power spectrum• P(k) = <| k|2> where k is the Fourier transform of the density contrast i k | k |e k• Note there is no phase information, k in the power spectrum• P(k) contains all information about x,t) if it is Gaussian distributed
  14. 14. Where is the information?• The power spectrum actually contains relatively little information in our everyday life…• Most of the information is in the phases, k• (Except in cosmology where the power spectrum is much more important)
  15. 15. Random SwappedOriginals Phases Phases M.S. Bartlett, J. R. Movellan, T. J. Sejnowski, IEEE 2002
  16. 16. Some examples of images and their P(k) All images from http://www.sci.utah.edu/~cscheid/spr05/imageprocessing/project3/
  17. 17. P(k)
  18. 18. P(k)
  19. 19. On small (nonlinear) scales phase is important though… Coles 2002
  20. 20. We will look for the BAO in P(k) …but what is the origin of the BAO?Bruce Bassett (SAAO/UCT) BAO
  21. 21. 3D Green’s Function for Speed of Sound Sound Horizon Bashinsky and Bertschinger, 2001Bruce Bassett (SAAO/UCT) BAO
  22. 22. Bruce Bassett (SAAO/UCT) BAO
  23. 23. Real Space Transfer Function Bashinsky and Bertschinger, 2001Bruce Bassett (SAAO/UCT) BAO
  24. 24. Evolution of a Spherical OverdensityBaryon Density Photon Density Mass Profiles White, Eisenstein, Seo
  25. 25. Baryon Density Photon Density Mass Profiles
  26. 26. Baryon Density Photon Density Mass Profiles
  27. 27. Baryon Density Photon Density Mass Profiles
  28. 28. Baryon Density Photon Density Mass Profiles
  29. 29. Baryon Density Photon Density Mass Profiles
  30. 30. Baryon Acoustic PeakBruce Bassett (SAAO/UCT) BAO
  31. 31. 13 May 2008, STIASMillenium Simulation, Springel et al Bispectrum from 1 Million LRGs
  32. 32. 2-point Correlation function (r)So we expect to see an increase in (r) at r ~ 150Mpc13 May 2008, STIAS Bispectrum from 1 Million LRGs
  33. 33. Eisenstein et al, 2005Bruce Bassett (AIMS/SAAO/UCT) BAO SDSS LRGs
  34. 34. WiggleZ, Blake et al, 2011Bruce Bassett (SAAO/UCT) BAO
  35. 35. 2 minute Exercise: Compute the size of the BAO scale today • i.e. Derive the BAO scale of 150 Mpc to within a factor of twoBruce Bassett (AIMS/SAAO/UCT) BAO
  36. 36. Bruce Bassett (SAAO/UCT) BAO
  37. 37. Bruce Bassett (AIMS/SAAO/UCT) BAO
  38. 38. Bruce Bassett (SAAO/UCT) BAO
  39. 39. Bruce Bassett (SAAO/UCT) BAO
  40. 40. Bruce Bassett (AIMS/SAAO/UCT) BAO
  41. 41. Bruce Bassett (SAAO/UCT) BAO
  42. 42. Bruce Bassett (AIMS/SAAO/UCT) BAO
  43. 43. Statistical Standard RulersBruce Bassett (AIMS/SAAO/UCT) BAO
  44. 44. Where are the oscillations in BAO? (r) P(k)Bruce Bassett (AIMS/SAAO/UCT) BAO
  45. 45. Eisenstein et al. Tegmark et al. BAP vs BAO (r) P(k)Bruce Bassett (AIMS/SAAO/UCT) BAO
  46. 46. BAP Detection Is Hard! • Consider a typical Luminous Red Galaxy (LRG). How many LRGs do we expect in a BAP shell around it? • n ~10-4h3Mpc-3 • Volume = 20 Mpcx 1002Mpc2x 5 ~ 106h-3Mpc3  100 LRGs from purely uniform distribution • BAP in (r) gives ~1% excess probability • So gives a single extra LRG on average. • Need lots of volume and large numbers of galaxies…so we can see the extra galaxy on average!Bruce Bassett (AIMS/SAAO/UCT) BAO
  47. 47. Power Spectrum Errors Cosmic Variance Shot Noisem = number of Fourier modes measured in the surveyn = mean galaxy number density in the survey Bruce Bassett (AIMS/SAAO/UCT) BAO
  48. 48. Shot Noise Fixed Volume 50 pointsBruce Bassett (AIMS/SAAO/UCT) BAO
  49. 49. Shot Noise Fixed Volume 500 pointsBruce Bassett (SAAO/UCT) BAO
  50. 50. Shot Noise Fixed Volume 5000 pointsBruce Bassett (SAAO/UCT) BAO
  51. 51. Shot Noise Fixed Volume 50k pointsBruce Bassett (SAAO/UCT) BAO
  52. 52. Cosmic Variance 1 x Volume Fixed 50k pointsBruce Bassett (SAAO/UCT) BAO
  53. 53. Cosmic Variance 25 xVolume Fixed 50k pointsBruce Bassett (SAAO/UCT) BAO
  54. 54. Cosmic Variance 225 xVolume Fixed 50k pointsBruce Bassett (SAAO/UCT) BAO
  55. 55. Cosmic Variance 2200 xVolume Fixed 50k pointsBruce Bassett (SAAO/UCT) BAO
  56. 56. Optimal Survey Design • What is the optimal sampling of a page of text? • Depends what information you want. • E.g. what language it is written in… • E.g. what page layout is being used… • Trade-off between the two… • nP ~ 1-5 is typically optimal • See Bob’s talk.Bruce Bassett (SAAO/UCT) BAO
  57. 57. What choice of target should one use for BAO?Bruce Bassett (SAAO/UCT) BAO
  58. 58. Luminous Red Galaxies (LRGs)e.g. SDSS, BOSS,… Bruce Bassett (SAAO/UCT) BAO
  59. 59. Blue galaxies…e.g. WiggleZ,… Bruce Bassett (SAAO/UCT) BAO
  60. 60. (Statistical) Standard RulersBruce Bassett (AIMS/SAAO/UCT) BAO
  61. 61. Beyond spherical averaging • In the SDSS exercise you computed the spherical average of (r) to give an average distance DV. • With enough data we can do much better than that however…Bruce Bassett (SAAO/UCT) BAO
  62. 62. The Beauty of Standard VolumesRadial Only works if the volume is big enough to measure dz Tangential UsBruce Bassett (AIMS/SAAO/UCT) BAO
  63. 63. BAO and AP • If we only know the volume is spherical, then we constrain the product H(z) dA(z) (the Alcock- Paczynski (AP) test) • If we also know the absolute sizes in both radial and tangential directions (like with BAO), we constrain both dA(z) and H(z) separately. • BAO thus provide an absolute AP test.Bruce Bassett (SAAO/UCT) BAO
  64. 64. Bruce Bassett (SAAO/UCT) BAO
  65. 65. Bruce Bassett (AIMS/SAAO/UCT) BAO
  66. 66. Bruce Bassett (SAAO/UCT) BAO
  67. 67. “Standard” is a Crucial Ingredient of Standard RulersBruce Bassett (SAAO/UCT) BAO
  68. 68. BAO have provided the first ever low-z cosmic distance measure based on linear physicsBruce Bassett (SAAO/UCT) BAO
  69. 69. J. HuchraBruce Bassett (SAAO/UCT) BAO
  70. 70. Complications A man falls from a window and on the way down someone asks…``how’s it going”? The man replies: “So far so good!” Cosmological Methods are similar – they have afree-fall zone and a hard, systematic “floor” where things get toughBruce Bassett (AIMS/SAAO/UCT) BAO
  71. 71. BAO and Nonlinearity Linear Prediction Nonlinearity moves the peak to smaller scales and broadens it. Why? Crocce et alBruce Bassett (AIMS/SAAO/UCT) BAO
  72. 72. Broadening Shift to smaller radius Bruce Bassett (SAAO/UCT) BAO KITPC - March 2009Millenium Simulation, Springel et al
  73. 73. (r) P(k)Bruce Bassett (AIMS/SAAO/UCT) BAO
  74. 74. Bruce Bassett (AIMS/SAAO/UCT) BAO
  75. 75. Bruce Bassett (AIMS/SAAO/UCT) BAO
  76. 76. Bruce Bassett (AIMS/SAAO/UCT) BAO
  77. 77. Calibrating Nonlinearity • Although it is (weakly) nonlinear, gravity is still quite clean (compare turbulent MHD in strong gravitational field) • Good reasons to believe the nonlinear effects can be calibrated at the 1% level for BAO/BAP • Still needs more theoretical and numerical studyBruce Bassett (AIMS/SAAO/UCT) BAO
  78. 78. Photometric BAO Surveys It is tempting to want to just do an imaging survey instead of taking spectra Photometric BAO surveys primarily sacrifice H(z) information and need much larger volume to compete.Bruce Bassett (AIMS/SAAO/UCT) BAO
  79. 79. Photometric surveys• Do we have to take spectra? This is slow and expensive…• If we don’t need accurate redshifts we can do multi-band imaging and compute photometric redshifts instead• This works by learning how the colours depend on redshift (as emission/absorption features move through the filters)
  80. 80. Visualising the underlying physics z=0 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  81. 81. Visualising the underlying physics z = 0.2 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  82. 82. Visualising the underlying physics z = 0.4 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  83. 83. Visualising the underlying physics z = 0.6 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  84. 84. Visualising the underlying physics z = 0.8 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  85. 85. Visualising the underlying physics z = 1.0 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  86. 86. Visualising the underlying physics z = 1.2 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  87. 87. Visualising the underlying physics z = 1.4 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  88. 88. Visualising the underlying physics z = 1.6 rFlux(arbitrary units) i gFor an LRGspectrumAnd SDSSFilter uTransmission zcurves Wavelength (measured)
  89. 89. 5 minute exercise: photometric redshifts • Given two non-overlapping, but contiguous top- hat filters of width and perfect transmission, covering the range 5000- 9000Å, work out the ratio of fluxes in the two bands as a function of z, for a crude approximation to an LRG spectrum consisting of two flat continuum regions with flux f1, f2 separated by a step at 4000Å. • How does the width of the filter determine the photo-z accuracy?Bruce Bassett (AIMS/SAAO/UCT) BAO
  90. 90. BAO and photo-z errors UsBruce Bassett (SAAO/UCT) BAO
  91. 91. Increasing Photo-z ErrorBruce Bassett (AIMS/SAAO/UCT) BAO
  92. 92. Increasing Photo-z ErrorBruce Bassett (AIMS/SAAO/UCT) BAO
  93. 93. Increasing Photo-z ErrorBruce Bassett (AIMS/SAAO/UCT) BAO
  94. 94. Benitez et alBruce Bassett (SAAO/UCT) BAO
  95. 95. Benitez et alBruce Bassett (AIMS/SAAO/UCT) BAO
  96. 96. The Future for BAO • DES • BOSS • BigBOSS • LSST • EUCLID • WFIRST • SKA and other 21cmBruce Bassett (SAAO/UCT) BAO KITPC - March 2009
  97. 97. Conclusions • BAO/BAP measurements are arguably the cleanest probe of cosmic expansion we have • They can provide both distance, dA(z) and expansion rate, H(z) • There is a systematic floor beyond which nonlinearities, nonlinear bias, redshift distortions etc… must be carefully included but these also provide exciting opportunities if we can understand them fully…Bruce Bassett (AIMS/SAAO/UCT) BAO
  98. 98. Fun Exercise• In groups of 2 or alone write pseudo-code to compute the spherically averaged (r) for the original SDSS data (available from me)• Data is RA, DEC, z• Use the simple estimator 1 + = DD/RR• The random catalogue is big (~106 points)Thanks to Dan Eisenstein Bruce Bassett (SAAO/UCT) BAO

×