Here are a few potential complications to consider with BAO measurements:- Non-linear structure formation at low redshifts can distort the BAO feature. This needs to be modeled and accounted for. - Redshift space distortions from galaxy peculiar velocities can smear out the BAO in the radial direction. Again, this effect needs to be modeled.- For photometric redshift surveys, redshift uncertainties degrade the BAO signal. Larger volumes are needed to overcome this.- Galaxy bias - the galaxies may not perfectly trace the underlying matter distribution. Bias needs to be modeled and marginalized over. - Relativistic effects like lensing and redshift space distortions become more important at higher redshifts
1. The document discusses a lecture on baryon acoustic oscillations (BAO) and dark energy given by Bruce Bassett.
2. BAO are density fluctuations in the early universe that were imprinted by sound waves propagating in the plasma of photons and baryons before recombination. These fluctuations provide a "standard ruler" that can be used to measure cosmic distances and expansion.
3. Bassett discusses the origin and detection of BAO, optimal survey design for BAO measurements, and complications including non-linear evolution and use of photometric rather than spectroscopic surveys. He emphasizes BAO as a low-redshift cosmic distance measure based on linear physics.
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
Here are a few potential complications to consider with BAO measurements:- Non-linear structure formation at low redshifts can distort the BAO feature. This needs to be modeled and accounted for. - Redshift space distortions from galaxy peculiar velocities can smear out the BAO in the radial direction. Again, this effect needs to be modeled.- For photometric redshift surveys, redshift uncertainties degrade the BAO signal. Larger volumes are needed to overcome this.- Galaxy bias - the galaxies may not perfectly trace the underlying matter distribution. Bias needs to be modeled and marginalized over. - Relativistic effects like lensing and redshift space distortions become more important at higher redshifts
1. Baryon Acoustic Oscillations
and Dark Energy
Bruce Bassett (AIMS/SAAO/UCT)
Bruce Bassett (SAAO/UCT) BAO KITPC - March 2009
ArXiv:0910.5224
2. SCP 96 High-z / SCP 98
M
(flat) (flat)
Evolution of the Hubble Diagram 1996-2009
ESSENCE+SNLS
07
Constitution 09
M (+BAO)
M
(flat)
Filled by the SDSS
SN survey
6. COBE
QMASK
BOOMERanG
L(l+1) Cl
MAXIMA
2 10 100 1000
l
7. COBE
QMASK
BOOMERanG
L(l+1) Cl
MAXIMA
CBI 03
2 10 100 1000
l
8. Did not show
COBE SPT
QMASK ACT
BICEP
BOOMERanG
L(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…
13. Overview of this lecture
• Power spectra
• Origins, uses & measurements of BAO
• Statistical Standard Rulers
• Targets for BAO surveys
• Some Complications
• Photometric vs spectroscopic BAO surveys
Bruce Bassett (AIMS/SAAO/UCT) BAO
14. 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
15. 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)
16. Random Swapped
Originals Phases Phases
M.S. Bartlett, J. R. Movellan, T. J. Sejnowski, IEEE 2002
17. Some examples of images and their P(k)
All images from http://www.sci.utah.edu/~cscheid/spr05/imageprocessing/project3/
36. 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 two
Bruce Bassett (AIMS/SAAO/UCT) BAO
45. Where are the oscillations in BAO?
(r) P(k)
Bruce Bassett (AIMS/SAAO/UCT) BAO
46. Eisenstein et al. Tegmark et al.
BAP vs BAO
(r) P(k)
Bruce Bassett (AIMS/SAAO/UCT) BAO
47. 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
48. Power Spectrum Errors
Cosmic Variance Shot Noise
m = number of Fourier modes measured in the survey
n = mean galaxy number density in the survey
Bruce Bassett (AIMS/SAAO/UCT) BAO
49. Shot Noise
Fixed Volume 50 points
Bruce Bassett (AIMS/SAAO/UCT) BAO
50. Shot Noise
Fixed Volume 500 points
Bruce Bassett (SAAO/UCT) BAO
51. Shot Noise
Fixed Volume 5000 points
Bruce Bassett (SAAO/UCT) BAO
52. Shot Noise
Fixed Volume 50k points
Bruce Bassett (SAAO/UCT) BAO
53. Cosmic Variance
1 x Volume Fixed 50k points
Bruce Bassett (SAAO/UCT) BAO
54. Cosmic Variance
25 xVolume Fixed 50k points
Bruce Bassett (SAAO/UCT) BAO
55. Cosmic Variance
225 xVolume Fixed 50k points
Bruce Bassett (SAAO/UCT) BAO
56. Cosmic Variance
2200 xVolume Fixed 50k points
Bruce Bassett (SAAO/UCT) BAO
57. 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
58. What choice of target should
one use for BAO?
Bruce Bassett (SAAO/UCT) BAO
62. 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
63. The Beauty of Standard Volumes
Radial
Only works if
the volume is big
enough to measure
dz
Tangential Us
Bruce Bassett (AIMS/SAAO/UCT) BAO
64. 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
71. 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 a
free-fall zone and a hard, systematic “floor” where things
get tough
Bruce Bassett (AIMS/SAAO/UCT) BAO
72. BAO and Nonlinearity
Linear Prediction
Nonlinearity
moves the
peak
to smaller
scales and
broadens
it.
Why?
Crocce et al
Bruce Bassett (AIMS/SAAO/UCT) BAO
73. Broadening Shift to smaller
radius
Bruce Bassett (SAAO/UCT) BAO KITPC - March 2009
Millenium Simulation, Springel et al
78. 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 study
Bruce Bassett (AIMS/SAAO/UCT) BAO
79. 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
80. 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)
81. Visualising the underlying physics
z=0
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
82. Visualising the underlying physics
z = 0.2
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
83. Visualising the underlying physics
z = 0.4
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
84. Visualising the underlying physics
z = 0.6
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
85. Visualising the underlying physics
z = 0.8
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
86. Visualising the underlying physics
z = 1.0
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
87. Visualising the underlying physics
z = 1.2
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
88. Visualising the underlying physics
z = 1.4
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
89. Visualising the underlying physics
z = 1.6
r
Flux
(arbitrary units) i
g
For an LRG
spectrum
And SDSS
Filter u
Transmission z
curves
Wavelength (measured)
90. 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
97. The Future for BAO
• DES
• BOSS
• BigBOSS
• LSST
• EUCLID
• WFIRST
• SKA and other 21cm
Bruce Bassett (SAAO/UCT) BAO KITPC - March 2009
98. 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
99. 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