slides

LSS with angular cross-correlations:
Combining Spectro and Photometric Survey
Enrique Gaztañaga
SDSS
Cosmic Web
galaxies
Goals:
!
- Motivate use of Galaxy Surveys to understand DE
!
- Introduce idea of 2D analysis to combine (3D+2D) probes
!
- Introduce DES and PAU Galaxy Surveys (photo vs spec)
!
- Discuss same sky (overlapping surveys)
!
- Present new Forecast
Dark Energy (cosmic acceleration) studies
•
•
•
What is causing the acceleration of the expansion of the universe?
•
Einstein’s cosmological constant Λ?
•
Some new dynamical field (“quintessence,” Higgs-like)?
•
Modifications to General Relativity?
}
“Dark Energy”
Dark energy effects can be studied in two main cosmological observables:
•
The history of the expansion rate of the universe: supernovae, weak lensing,
baryon acoustic oscillations, cluster counting, etc.
•
The history of the rate of the growth of structure (galaxies) in the universe:
weak lensing, large-scale structure, cluster counting, etc.
For all probes other than SNe, large galaxy surveys are needed:
•
Spectroscopic: 3D (redshift), medium depth, low density, selection effects
•
Photometric: “2.5D” (photo-z), deeper, higher density, no selection effects
3
Euclid'
• 
• 
• 
• 
• 
ESA$Cosmic$Vision$satellite$proposal$(600M€,$M9class$mission)$
5$year$mission,$L2$orbit$
1.2m$primary$mirror,$0.5$sq.$deg$FOV$
Ω$=$20,000deg2$imaging$and$spectroscopy$
slitless$spectroscopy:$
– $100,000,000$galaxies$(direct$BAO)$
– $ELGs$(H9alpha$emiPers):$z~0.592.1$$
•  imaging:$
– $deep$broad9band$opScal$+$3$NIR$images$
– $2,900,000,000$galaxies$(for$WL$analysis)$
– $photometric$redshi\s$
• 
• 
• 
• 
Space9base$gives$robustness$to$systemaScs$
Final$down9selecSon$due$$mid$2011$
nominal$2017$launch$date$
See$also:$LSST,$WFIRST$
!
Observing DE: H(z) & D(z) & more
Expansion history:
H2(z) = H20 [ ΩM (1+z)3 + ΩR (1+z)4 + Ω K(1+z)2 + ΩDE (1+z)3(1+w) ]
matter
•
•
•
•
radiation
curvarure
dark energy w=p/ρ
∫
Measurements are usually integrals over H(z)
r(z) = dz/H(z)
Standard Candles (supernova) dL(z) = (1+z) r(z)
Standard Rulers (BAO) da(z) = (1+z)−1 r(z) or H(z)=cdz/r directly
Volume Markers (clusters)
dV/dzdΩ = r2(z)/H(z)
Linear Growth history: !
!
Non-linear Growth history
•
Higher order correlations, Cluster abundance, profiles
Solar & Astro test of gravity
δ = D(z) δ0
Figure of Merit (FoM): Expansion x Growth
w(z) -> Expansion History (background metric)
we will use w0 and wa
γ -> Growth History (metric perturbations)
probably need one more parameter here
Theory: P(k,z) ~D2(z) P(k,0)
! ! Linear
!! •
∇• v D
∇v +
= − δ =≡ −H
δ θ= − mass
≡ −H
θ
conservation
a D
a
θ = − f(Ω) δ
f = Velocity growth factor: tell us if gravity is really
responsible for structure formation!
Could also tell us about cosmological parameters or Modify
Gravity
=
1!
–––––––––––––––––
σ(w0) σ(wa) σ(γ)
Om - ODE - h - sig8 - Ob - w0 - wa -γ- ns - bias(z)
Is this the best
choice for 3 parameters?
Cosmic Maps
!
They are time machines
!
Can measure “time” =
redshift z
!
Need a way to measure
distance to get H(z):
expansion history
!
Need a way to measure
growth of structure:
!
growth history
!
Comparison of expansion
and growth history will tell
us if GR is correct on large
scales and nature of DE
Galaxy Surveys
Photometric: poor radial (redshift) resolution (~300 Mpc/h), more Volume
good for 2D (WL: Weak Gravitational lensing)
DES, VISTA, Pan-STARRS, Subaru/HSC, Skymapper, LSST
!
PAU
!
Spectroscopic:
!
good radial resolution (1-10Mpc/h), but very costly
(hard to go deep, smaller Volume, and smaller density)
good for BAO and RSD
WiggleZ, BOSS, e-BOSS, Subaru/Sumire, BiggBOSS, DESpec,
Main Observables
galaxy counts:
δG (z) = b δ + δvel + 2(s-1) δ𝜿 + δfg + εG
RSD 3D
bias 3D
galaxy shear:
wl: 2D
δ𝛾 (z) = bia δ + b𝜿 δ𝜿 + δfg +
intrinsic
alignments
3D
CMB Temperature:
δT (z=zd) = δ(z=zd) + δISW+SZ + δ𝜿 + δfg +
2D
δF (z) = bF δ + δvel + αF δ𝜿 +
galaxy magnitudes:
ε𝜿
noise
wl: 2D
intrinsic
Ly-alpha Forest:
noise
foregr
wl:2D
εF
δm (z) = bm δ + δvel + αm δ𝜿 +
εm
εT
2D vs 3D clustering: Photo-z vs Spectro-z
!
1) Can measure photometric clustering with 3D!
!
2) Can measure spectroscopic clustering with 2D angular cross-correlations!
!
3) Can use a mix approach 2Dx3D covariance.!
!
!
!
1.
de Putter R., Dore O., Takada M., astro-­‐ph:1308.6070
The'3D'Fisher'Matrix'describes'
clustering'of'spectroscopic'galaxies'
Seo(&(Eisenstein(Fisher(Matrix((kmax(=(0.2(h/Mpc)(
Pg (k, µ ) = bg2 (1+ βµ 2 )2 Pm (k)
Kaiser'effect:'
Geometry)(Alcock7Paczynski,)BAO,..):)
power(spectrum(measured(assuming(a(
reference(cosmology(
Measured'Spectrum:'
k|| = α||−1k||,ref
k⊥ = α ⊥−1k⊥,ref
2
2
#
&
k
−2
−1
2
||
Pg (k||,ref , k⊥,ref ) = α ⊥ α|| bg %1+ β 2 2 ( Pm (k)
k|| + k⊥ '
$
With'dila>on'factors:'
H ref
α|| ≡
H
dA
α⊥ ≡
d A,ref
linear!'
Non]linear'smearing:'FM''
crec=0.5(
Ellis(et(al(1206.0737(
1.
de Putter R., Dore O., Takada M., astro-­‐ph:1308.6070
The'2D'Fisher'matrix'describes'
angular'clustering'(in'redshid'bins)'
Input:'angular'(cross)'power'spectra:'
Assuming'Limber:'
Kernels:'
ignoring(Intrinsic(Alignments(
ignoring(magnificaMon(bias(
(shear)'
(source'galaxy'clustering)'
(spec'galaxy'clustering)'
shear:'lmax=2000,'GC:'lmax(=(kmax(*(D(zi),'kmax(=(0.2(h/Mpc(
BAO as a
standard ruler
Planck 2013
BAO gives us a standard distance with
a co-moving value
rBAO~ 100 Mpc/h (rBAO= 146.8±1.8 Mpc)
can be measured in z and/or in angles. Can be
used as standard ruler to constrain:
!
radial
- distance to ruler H(z) :
- or parameters in ruler (Omega_M)
SDSS 2005!
€
dr(z) =
c
dz
H(z)
cΔzBAO = rBAO H(z)
angular
dA (z) =
cdz
∫ 0 H(z)
z
rBAO
Δθ BAO =
dA (z)
Amplitude depends on baryon fraction but position is fixed by sound horizon
Anna Cabré’s PhD Thesis arXiv:0807.3551 Crocce etal 2011
DR7
Redshi, Space Distor5ons (RSD)
BAO: radial H(z) H(z=0.34) = 83.8 ±3.0± 1.6 EG, Cabre & Hui (2009) ∫
Errors f19
rom MICE sim
Transverse cdz/H(z) θ(z=0.34) = 3.90 ± 0.38 Carnero etal 2011
Strong
and Weak
Gravitational Lenses
Lentes
Gravitatorias
Can be used to measure distances and growth history in the universe
Midiendo los efectos de lente gravitatoria
but is 2D
(creadas por la materia oscura)
!podemos medir distancias y el crecimiento de estructuras en el universo.
Complementarity of Observables
Forecast: Planck+SNII priors
14000 sq.deg. DES depth
WLxG: shear-shear, galaxy-shear, galaxy-galaxy (including MAG)
RSD
+
BAO
F Photometric
DESI+ (i<22.5)
Combine
F+B
FxB: Cross
Correlated
over same Area
RSD+BAO
WLxG
+
(BIAS IS KNOWN)
(eg 3pt)
no shear
2.7
DES (i<24)
B Spectroscopic
WLxG
WLxG
+
RSD
+
BAO
6.9
21
32 (189)
(55)
astro-­‐ph:1109.4852
Dark Energy Survey (DES)
•
•
5000 deg2 galaxy survey in 5 bands. 300M galaxies up to z < 1.4. Also ~4000 SNe.
Involves groups in USA, Spain, UK, Brazil, Germany, Switzerland.
2 deg ∅ FoV
•
•
525 nights in 5 years
Will start in late 2012
3556 mm
Blanco, CTIO, Chile
Camera Scroll
500 Mpixels
Shutter Filter
Optical Lenses17
2.2 deg. FOV
1575 mm
DES Camera Installation
May 2012
July 2012
18
DECam First light image
•
First light in Sep
12th, 2012
•
Survey starts in
Dec, 1st 2012
19
DES Science Summary
Four Probes of Dark Energy
•  Galaxy Clusters
Forecast Constraints on DE
Equation of State
DES
•  ~100,000 clusters to z>1
•  Synergy with SPT, VHS
•  Sensitive to growth of structure and geometry
•  Weak Lensing
•  Shape measurements of 200 million galaxies
•  Sensitive to growth of structure and geometry
•  Baryon Acoustic Oscillations
•  300 million galaxies to z = 1 and beyond
•  Sensitive to geometry
Planck prior assumed
•  Supernovae
•  30 sq deg time-domain survey
•  ~4000 well-sampled SNe Ia to z ~1
•  Sensitive to geometry
4
Factor 3-5 improvement over
Stage II DETF Figure of Merit
Josh Frieman, DOE-NSF Review, May 1-3, 2007
Photometric Redshifts
• Measure relative flux in
multiple filters:
track the 4000 A break
!
• Estimate individual galaxy
redshifts with accuracy
σ(z) < 0.1 (~0.02 for clusters)
!
• Precision is sufficient
for 2D Dark Energy probes,
provided error distributions
well measured.
!
• Good detector response
in z band filter needed to reach
z>1
Elliptical galaxy spectrum
DES Photo-z Precision
DES
DES griz
griZY +
VHS JHKs on VISTA
DES +VHS
10σ Limiting Magnitudes
g
24.6
J 20.3
r
24.1
H 19.4
i
24.0
Ks 18.3
23.9
Zz
23.8
!Y
21.6
+2% photometric calibration
error added in quadrature
!
!
σ(z) ~ 0.05×(1+z)
Josh Frieman, DOE-NSF Review, May 1-3, 2007
Photo-z error and WL
For pure WL shear a 5-10% photo-z error is good
enough because of broad (2D) projection (WL sees
all matter in front of source galaxies): 𝛾1 ~ 𝛾2 Shear for
source galaxy at z1
𝛾1
𝛾2
Observ
er
To avoid intrinsic alignment contamination
to WL signal we want to do <𝛾1 𝛾2> instead of <𝛾1 𝛾1>
Photo-z outliers might are then
more important
The PAU Survey
@ the WHT
24
The PAUcam@WHT Project in a Nutshell
•
New camera for WHT with 18 2k x
4k CCDs covering 1 deg ∅ FoV.
•
48 100Å-wide filters covering
3700-8600 Å in 6 movable filter
trays, which also include standard
ugrizY filters.
•
As a survey camera, it can cover
~2 deg2 per night in all filters.
•
It can provide low-resolution
spectra (Δλ/λ ~ 2%, or R ~ 50)
for >30000 galaxies, 5000 stars,
1000 quasars, 10 galaxy clusters,
per night.
•
Expected galaxy redshift resolution
σ(z) ~ 0.003×(1+z)
Actual measurements in MICE simulations
25
P.Marti,R.Miquel,
F.Castander, M.Eriksen
26
P.Marti,
R.Miquel,
F.Castander
, M.Eriksen
arXiv:1402.3220
2014MNRAS.442...92M
27
The Importance of Redshift Resolution
z-space, Δz = 0.03(1+z)
+ peculiar velocities
(DES)
z-space, Δz = 0.003(1+z)
+ peculiar velocities
(PAU)
z-space, perfect resolution
+ peculiar velocities
Real space
XTalks in Galaxy Clustering
1. Galaxy Clustering 2pt: 3D, all info but degenerate with
biased: can measure linear shape, but not growth 2. Galaxy Clustering 3pt: 3D (break degeneracy) 3. Weak Lensing: 2D (unbiased but degenerate & few 2D modes)
!
4. Redshift Space Distortions (can be used in to measure bias 1D)
=> measure bias:
Combine probes/traces: RSD + WL
Cross-correlate probes: galaxy-lensing
Combine Photometric & Spectroscopic
Surveys: sampling variance, photo-z accuracy
astro-­‐ph:1109.4852
Galaxy Bias
or how Galaxies trace the mass
Search of Cosmological parameters is hinder by BIAS?
What can we do:
!
A) Avoid BIAS: BAO, SNe, Cluster counts, WL !
!
B) Understand Bias <==> Galaxy Formation
!
Xtalk probes: combine different probes to measure bias
together other cosmological parameters
Clustering with photo-z: 2D analysis
!
• Photo-z quality and clustering (P.Marti)
• need (pdf or) spec-z callibration sample
!
!
• need better radial resolution to get full 3D info (FoM): PAU
!
•Linear Algebra to speed prediction (5D) codes (M.Eriksen)
!
•Get 3D P(k) from angular (2D) clustering:
•Measuring RSD (& galaxy bias) in 2D (J.Asorey)
•Combine WL and RSD (M.Eriksen)
•Measuring bias from 3-point correlations (K.Hoffman)
!
!
Radial BAO in 2D
distance bins: photo-­‐z outliers
Martin Eriksen
Actual measurements in MICE simulations
RSD in 2D
Jacobo Asorey & MarZn Crocce arXiv:1305.0934
Adjacent bins (no photo-­‐z outliers)
34
Photometric Sample i ~ 24
2D lensing
Δz = 0.03
100 Mpc/h
10000Km/s
measure bias
recover full 3D info from 2D+3D
Δz = 0.003
10 Mpc/h
Spectroscopic Sample i ~ 23
1000Km/s
RSD+WL: Same or different sky?
Same Sky: factor of 2 less Area but cross-correlations!
!
but note that covariance <WLxRSD> ~ 0 while <FF BB> ≠ 0
Different Sky: no cross-correlations & no Covariance
(smaller sampling variance, but no sampling variance cancelation)
1. Gaztanaga E., Eriksen M., Crocce M., Castander F. J.,Fosalba P., Marti P., Miquel R., Cabre A., astro-­‐ph:
1109.4852
2. Cai Y.-C., Bernstein G., astro-­‐ph:1112.4478
3. Kirk D., Lahav O., Bridle S., Jouvel S., Abdalla F. B., Frieman J. A., astro-­‐ph:1307.8062 4. Font-Ribera A., McDonald P., Mostek N., Reid B. A., Seo H.-J., Slosar A., astro-­‐ph:1308.4164 5. de Putter R., Dore O., Takada M., astro-­‐ph:1308.6070
1
2D+3D Cov ~ 0 <gF
FxB >> F+B
2
2D+3D Cov ~ 0 <gF
radial
FxB > F+B
3
2D
Cov≠0 <gF
FxB >> F+B
4
2D+3D Cov ~ 0 <g
FxB ~ F+B
5
2D+3D Cov ~ 0 <gF
FxB ~ F+B
36
Relative Gain
in Modified
Gravity Figure
of Merit
(growth rate)
from Same Sky
factor ~1.4 in γ
Cai & Bernstein
DES WL
MS DESI RSD
Note WL data
not available in
the north
LSST WL
12
37
1.
Font-Ribera A., McDonald P., Mostek N., Reid B. A., Seo H.-J., Slosar A., astro-­‐ph:1308.4164 The illusion of overlap
Fourier space coverage
Radial k
Lensing
Photo-z density
Angular k
Redshift space density
38
1.
de Putter R., Dore O., Takada M., astro-­‐ph:1308.6070
Forecasts'are'made'by'combining'2D'
and'3D'Fisher'matrices'
has'transverse'modes'(μ≈0)'removed''
p=photo-z
s=spec-z
2D Limber=no radial modes
See,'e.g.,'Cai(&(Bernstein(2012,'
39
Gaztanaga(et(al(2012(
Importance of Covariance
• <FB> ~ 0 can reduce sampling variance by sqrt(2) • <FB> ~ 1 no reduciton if F and B are the same
• <FB> ~ 1 larger reduciton if F and B are different but
have same noise, because of noise cancelation. In
this case number of modes is less important
!
PF / PB ~ (bF +f µ2)/(bB +f µ2)
!
•
• Because of Limber and 3D+2D approximations
previous studies removes the covariance in radial
modes.
40
Forecast WL+RSD
Nuisance parameters: one bias per z-bin & pop , photo-z transitions (rij, can be measured), noise (σ/n)
Cosmological: Om - ODE - h - sig8 - Ob - w0 - wa - γ - ns - bias(z)
shear-shear (2D): 𝛾<𝛾 𝛾>
galaxy-shear (2D need narrow bins)
<g 𝛾> galaxy-galaxy (3D or narrow bins): <g g> including BAO, RSD and WL magnification
F= Faint (Photometric dz~0.05) sample: <𝛾F 𝛾F>, <gF 𝛾F>, <gF gF>
B= Bright (Spectroscopic dz~0.003) sample: <𝛾B 𝛾B>, <gB 𝛾B>, <gB gB>
F+B= No overlap => no cross <FB>=0 & no Covariance : <FF BB>=0
FxB= Overlaping => <FB>≠0 & <FF BB> ≠ 0
41
Our new Exact Calculation Forecast:
14000 sq.deg.
Martin Eriksen
WLxG*+RSD+BAO (cross Cl: l<300 + Planck priors)
F Photometric
(DES i
!
!
2.7 / fix bias 44
no lens 0.04
no lens 4.3
CrossCorrelated over same Area
/no BAO 4.4/no RSD
2.5
21 / fix bias 171
F+B Combine both as Independent
FxB 2.2
6.9/ fix bias 46
B Spectroscopic
(PAU i
/no BAO 2.1/no RSD
no lens 4.7
/no BAO 14/no RSD
9
32 /fix bias 190
no lens 5.9
*WLxG: shear-shear, galaxy-shear, galaxy-galaxy (including MAG)
/no BAO 23/no RSD
15
no cross FB: 28>21
FxB (no cross) > F+B
Goals:
!
- Motivate use of Galaxy Surveys to understand DE
!
- Introduce idea of 2D analysis to combine (3D+2D) probes
!
- Introduce DES and PAU Galaxy Surveys (photo vs spec)
!
- Discuss same sky (overlaping surveys): the covariance is more
important than the Cross, but both contribute.
!
- Present Forecast
THE END
• Additional slides
44