Anisotropic Correlation Function of Large-Scale Galaxy Distribution from the SDSS LRG Sample
Robust cosmological constraints from SDSS-III/BOSS galaxy clustering Chia-Hsun Chuang (Albert) IFT-...
-
Upload
grant-jenkins -
Category
Documents
-
view
219 -
download
0
Transcript of Robust cosmological constraints from SDSS-III/BOSS galaxy clustering Chia-Hsun Chuang (Albert) IFT-...
Robust cosmological constraints from
SDSS-III/BOSS galaxy clustering
Chia-Hsun Chuang (Albert)
IFT- CSIC/UAM, Spain
SDSS-III/BOSS
BOSS at a glance• Dark time observations from Fall 2009 - Spring 2014
(Mar 31)
• Final data release (DR12) in Dec. 2014
• 1,000-fiber spectrograph, resolution R~2000
• Wavelength: 360-1000 nm
• 10,200 square degrees (~quarter of sky)
• Redshifts of 1.35 million luminous galaxies to z = 0.7
• Lyman-α forest spectra of 230,000 quasars (160,000
redshifts > 2.15)
Baryon Acoustic Oscillations
Planck
Baryon Acoustic Oscillations
Galaxy sample
• 690,827 galaxies from SDSS-III BOSS
Data Release 11 CMASS (Complete
stellar MASS) sample (z=0.43~0.7)
• 313,780 galaxies from SDSS-III BOSS
Data Release 11 LOWZ (low redshift)
sample (z=0.15~0.43)
Extracting cosmological information from the galaxy clustering
Measure Power spectrum or correlation function from:
number density field of the galaxy
sample
Measure H(z)rs, DA(z)/rs,
and f(z)σ8(z)
Reconstructed number density field of the galaxy sample
Measure DV(z)/rs ( or H(z)rs & DA(z)/rs) with
higher precision
Data: monopole and quadrupole from BOSS DR11 CMASS and LOWZ sample (Chuang et al. 2013)
Dark energy model independent measurements
• Measured parameters: H(z), DA(z),
f(z)σ8(z), Ωmh2, , β
• Without assuming dark energy model or
curvature – one can use our results to
obtain the constraints of the parameters
of given dark energy models.
Covariance matrix
• Constructed by using 600 mock catalogues for CMASS
(2LPT, see Manera et al. 2013) and 1000 mock
catalogues for LOWZ (2LPT, see Manera et al. 2014)
• For DR12, BOSS will switch to PATCHY mocks
(developed by our group, see Kitaura et al. 2013)
and/or QPM mocks (White et al. 2013).
• A new methodology, EZmock, has also been developed
by our group (see Chuang et al. 2014).
Theoretical Model based on CMB and galaxy formation
• The well fitted and simple models
have following properties:
– Adiabatic initial condition
– Cold dark matter (CDM)
– No early-time dark energy
– No clustering of dark energy
MCMC analysis
• Software: CAMB, CosmoMC
• 9 parameters explored:
– H, DA, Ωmh2, β, and b σ8 are well constrained
– Ωbh2 (±10σPlanck), ns (±10σPlanck), f (0.5~1), and
σv(0~300km/s)
• 36 data bins (monopole+quadrupole,
56<s<200 Mpc/h, bin size = 8 Mpc/h)Chuang et al. 2013 (arXiv:1312.4889)
Measured and derived parameters
Chuang et al. 2013
Normalized covariance matrix (15 x 15)
To be Robust: minimize the systematic bias from priors
• No CMB priors or fixing values from
CMB – one can combine our
measurements with CMB or other
data sets using CMB priors.
To be Robust: Use the scale range of which the model is well
understood
• The model is constructed from linear
theoretical model + nonlinear
correction, since we are using quasi-
linear scales (i.e. 56 < s < 200
Mpc/h).
To be Robust: drop the measurements which are easily
effected by observational systematics.
• The overall shape of monopole is sensitive to
many observational systematics (e.g. stars,
seeing, etc.). We do not include Ωmh2 as our
robust measurements since it is sensitive to
the overall shape. Also, we rotate all the
measurements to be independent of Ωmh2.
Data: monopole and quadrupole from BOSS DR11 CMASS and LOWZ sample (Chuang et al. 2013)
Measured and derived parameters
Chuang et al. 2013
Assuming a Dark Energy Modelhttp://members.ift.uam-csic.es/chuang/BOSSDR9singleprobe/
• E.g., ΛCDM (Ωm, H0, σ8)Chuang et al. 2013 (arXiv:1312.4889)
Assume ΛCDM
Assume non-flat ΛCDM
Chuang et al. 2013 (arXiv:1312.4889)
Assume wCDM Chuang et al. 2013 (arXiv:1312.4889)
Assume oΛCDMChuang et al. 2013 (arXiv:1312.4889)
Conclusion
• We obtained the robust measurements of H(z), DA(z),
f(z)σ8(z) from SDSS-III/BOSS DR11 CMASS or LOWZ
(without assuming dark energy model and curvature).
• Our methodology can be applied on the current and
future large-scale galaxy surveys (e.g. eBOSS,
BigBOSS, and Euclid) to obtain single-probe
cosmological constraints, which will provide a robust
and convenient way to perform a joint data analysis
with other data sets.
EZmocks: extending the Zel'dovich approximation to generate mock galaxy
catalogues with accurate clustering statistics (Chuang and Kitaura et al. 2014)
Power spectrum
EZmocks: extending the Zel'dovich approximation to generate mock galaxy
catalogues with accurate clustering statistics (Chuang and Kitaura et al. 2014)
Correlation function
Bispectrum
Backup slides
Observed correlation function
1. Convert the redshifts to comoving distances with a
fiducial model
2. Minimum variance correlation function estimator(Landy
& Szalay 1993):
where DD, DR, and RR represent the normalized data-data,
data- random, and random-random pair counts
respectively in a distance range.
Covariance matrix & χ2
• Using 600 mock catalogs from the second-order
Lagrangian Perturbation Theory (Manera et al.
(2012))
Rescaling theoretical correlation function with DV(z)
rescaling
S1
S2
αS1αS2
Fiducial model New model
Rescaling theoretical correlation function with DV(z)
where
2D correlation function
σ
π
Measure H(z) and DA(z) with 2D correlation function
• Rescaling theoretical correlation
function with H(z) and DA(z) instead
of DV(z)
2D rescaling
σ1
π2
π1
βσ2
γπ1γπ2
σ2
βσ1
Model
• Anisotropic dewiggle model
(Eisenstein, Seo, and White 2007)
Chuang et al. 2013 (arXiv:1312.4889)
Anisotropic dewiggle model(nonlinear correction in z-space at BAO scales)
The model is validated by Samushia et al. (2012) using N-body simulations.
The computation of the model is speeded up by Chuang and Wang (2013) (arXiv:1209.0210)
Model
• Anisotropic dewiggle model
(Eisenstein, Seo, and White 2007)
• Linear redshift distortion (Kaiser
approximation)
Chuang et al. 2013 (arXiv:1312.4889)
Model
• Anisotropic dewiggle model (Eisenstein,
Seo, and White 2007, Crocce &
Scoccimarro 2006, Matsubara 2008)
• Linear redshift distortion (Kaiser
approximation)
• Pairwise velocity dispersionChuang et al. 2013 (arXiv:1312.4889)
Assuming wCDMChuang et al. 2013 (arXiv:1312.4889)
The strong power of anisotropic information on constraining dark
energy (wCDM)
Chuang et al. 2013 (arXiv:1312.4889)