Galaxy formation

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Cosmological simulations and forecasts for future
surveys
Shaun Cole for Carlos S. Frenk Institute for
Computational Cosmology, Durham
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Outline

• Baryonic Acoustic Oscillations
• Origin
• Measurements
• Distortion due to non-linear evolution, peculiar
  velocities and galaxy bias
• Future Surveys and Forecasts
• Spectroscopic and Photometric Surveys
• EUCLID and Pan-STARRS1

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CMB anisotropies and large-scale structure
Meiksin etal 99
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Baryon oscillations in the power spectrum
Comoving sound horizon at trec (depends mostly
on Wmh2 and weakly on Wbh2)
kBAO 2p/s
wavenumber of acoustic oscillations
Comoving distance/redshift (depends on Wmh2 and
w)
Apparent size of standard ruler depends on
cosmology ? dark energy
eqn of state parameter w
(e.g. Eisenstein HU 1998 Blake Glazebrook
2003, 2005 Seo Eisenstein 2003 2005)
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The final 2dFGRS power spectrum
2dFGRS P(k) well fit by LCDM model convolved with
window function
Cole, Percival, Peacock, Baugh, Frenk 2dFGRS 05
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The final 2dFGRS power spectrum
2dFGRS P(k) well fit by LCDM model convolved with
window function
Cole, Percival, Peacock, Baugh, Frenk 2dFGRS 05
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The final 2dFGRS power spectrum
P(k) / Pref(Wbaryon0)
Baryon oscillations conclusively detected in
2dFGRS!!! Demonstrates that structure grew by
gravitational instability in LCDM universe
LCDM model
LCDM convolved with window
Also detected in SDSS LRG sample (Eisenstein etal
05)
Cole, Percival, Peacock, Baugh, Frenk 2dFGRS 05
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SDSS LRG correlation function
Again, CDM models fit the correlation function
adequately well (although peak height is slightly
too large assuming ns1, h0.72) Wbh2 0.024,
Wmh2 0.1330.011, ? Wb/Wm 0.18
x(s)
Eisenstein et al. 05
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Constraints on w from SnIa, WMAP and LSS
Assume wconst (cosmological constant)
w-0.9 ? 0.1
Spergel et al 2006
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Estimate of w from P(k)
Wavenumber of acoustic oscillations is
kBAO 2p/s
s comoving sound horizon at trec Depends on
physical parameters
Measure kA in redshift survey conversion z ?
k in P(k) depends on geometry and
expansion history and so on w

• Consider idealized case
• All cosmological parameters apart from w known

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Estimate of w from P(k)
Wavenumber of acoustic oscillations is
kBAO 2p/s
s comoving sound horizon at trec Depends on
physical parameters
Measure kA in redshift survey conversion z ?
k in P(k) depends on geometry and
expansion history and so on w
Stretch factor

• Consider idealized case
• Angular size of sound horizon at last scattering
  kept fixed

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Surveys The Next Generation
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Springel etal 05
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The mass power spectrum
z0
The non-linear mass power spectrum is accurately
determined by the Millennium simulation over
large range of scales
z1
z3.05
z7
D2 (k)
z14.9
Lbox500Mpc/h
linear theory
k h/Mpc
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Millennium simulation
Baryon wiggles in the galaxy distribution
The effective keq changes as does kSilk, but
does kBAO ?
Power spectrum from MS divided by a baryon-free
LCDM spectrum Galaxy samples matched to
plausible large observational surveys at given z
z3
z7
DM
gals
z0
z1
Springel et al 2005
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N-body simulations of large cosmological volumes
BASICC L1340/h Mpc N3,036,027,392 20 times
the Millennium volume Halo resolution (10
particle limit) 5.5 e11/h Mpc 130,000 cpu
hours on the Cosmology Machine
Angulo, Baugh, Frenk Lacey 07
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The hierarchical growth of structure
200/h Mpc
500/h Mpc
1000/h Mpc
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Non-linear evolution of matter fluctuations
BASICC simulation dark matter real space
P(k) divided by linear theory P(k), scaling out
growth factor
P(k)/Plinear(k)
Angulo, Baugh, Frenk Lacey 07
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Non-linear evolution of matter fluctuations
Log (P(k)/Plinear(k)) at z1
Angulo, Baugh, Frenk Lacey 07
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Redshift space distortions
Peculiar motions distort clustering pattern
Coherent bulk flows boost large scale power
(Kaiser 1987)
Motions of particles inside virialised structures
damp power at high k
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Redshift space distortions
Peculiar motions distort clustering
pattern Boost in power on large scales due to
coherent flows Damping at higher k affects DM
but not the halos In z-space, halo bias is
scale-dependent
Redshift space
Halos Mgt 1012 Mo
Dark matter
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Galaxy bias in real space
Absolute Magnitude limited sample. Galaxy
clustering boosted relative to mass in real
space
Angulo, Baugh, Frenk Lacey 07
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Galaxy bias in real space
Boost in clustering approximates to a constant
bias factor on large scales.
Angulo, Baugh, Frenk Lacey 07
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Galaxy bias in redshift space
Galaxy P(k) cannot be reproduced by multiplying
mass P(k) by constant factor in redshift space.
? In z-space, galaxies have a scale-dependent
bias out to k0.1
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Galaxy bias in redshift space
Comparison of different selections e.g. colour,
emission line strength
Angulo et al 07
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Fit BAO oscillations

• Remove effect of scale dependent bias by fitting
  a smooth spline and then take ratio
  R(k)P(k)/Psmooth(k).
• Fit ratio, R(k), to determine both the stretch
  factor, a, and the damping scale, knl.

(Percival et al 2008)
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Recovered values

• knl treated as a nuisance parameter.
• Small offsets in
• a, but are they significant?

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Sample Variance

• 50 lower resolution L-BASICC simulations
  used to determine the sample variance.
• Particle mass 30 times larger.
• Bias not significant

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Fractional error in P(k)

• (Feldman, Kaiser Peacock 1994)

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Survey Forecasts
Angulo et al (2008) tabulate rms error in a for
different fiducial samples within the BASICC
simulation
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Error on the measured power
BAO method virtually free of systematics (c.f.
lensing, SNIa)

• Sample variance
• Shot noise

P power n mean no density
Scaling error forecasts to different surveys
delta(w) 1/sqrt (V) x 1 1/(n P)
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EUCLID DMD-based NIR spectra
See poster 21 Andrea Cimatti
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EUCLID Spectroscopy
Category Item Requirement
Spectroscopic BAO Survey Redshift Accuracy sz lt 0.001
Spectroscopic BAO Survey Spectral Range 0.9-1.7 micron
Spectroscopic BAO Survey Number of spectra 1.65x108 galaxies Sampling gt 33
Spectroscopic BAO Survey Limiting magnitude and redshift distribution H(AB)22 mag corresponding to 0ltzlt2
Deep spectroscopic sample Photo-z calibration 105 redshifts down to H(AB)24 mag
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Projected BAO data for planned surveys at z1
Projections based on mock catalogues made from
large N-body simulation plus semi-analytic
galaxy formation model
EUCLID
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Main future BAO surveys
Name N(z) / 106 Stretch Dates Status SDSS/2d
FGRS 0.8 3.5 Now Done WiggleZ 0.4 2 2007-2
011 Running FastSound 0.6 2.8 2009-2012 Proposa
l BOSS 1.5 1 2009-2013 Proposal HETDEX 1 1.5
2010-2013 Part funded WFMOS gt2 0.8 2013-2016
Part funded ADEPT gt100 0.2 2012 JDEM EUCLID
gt100 0.15 2017 ESA SKA gt100
0.2 2020 Long term
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Pan-STARRS1 3p Survey
z
i
r
g
y
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3p size and depth
Detected in griz and y
More than galaxies!
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3p size and depth
Detected in griz only
More details will be presented by Stephanie
Phleps later
More than galaxies!
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Photo-z accuracy
Initial estimates indicate that for red/early
type galaxies
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Damping effect on BAO
Yan-chuan Cai et al (2008)
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Future photo-z BAO surveys
Name N(z) / 106 Stretch Dates Status PS1 gt10
0 0.5 2009-2013 Funded DES 50 lt1
2010-2014 Funded PAU(BAO) 14 0.4 2014 plann
ed
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Summary

• BAO have an important future as a cosmic standard
  ruler used to constrain D(z) and hence Dark
  Energy.
• Systematic errors are not yet dominant, but more
  theoretical work is needed to ensure this remains
  true for the forthcoming generation of surveys
• In advance of the long term space projects,
  photo-z surveys promise interesting constraints