!

Enrique Gaztañaga

LSS with angular cross-correlations: Combining Spectro and Photometric Survey

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

3

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)? “Dark Energy”

• Modifications to General Relativity?

• 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

}

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,$WFIRST$

!Expansion history: H2(z) = H2

0 [ 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

Observing DE: H(z) & D(z) & more

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

Om - ODE - h - sig8 - Ob - w0 - wa -γ- ns - bias(z)

1!= ––––––––––––––––– σ(w0) σ(wa) σ(γ)

θ = − f(Ω) δf = Velocity growth factor: tell us if gravity is really responsible for structure formation! Could also tell us about cosmological parameters or Modify Gravity

Linear Theory: P(k,z) ~D2(z) P(k,0) + mass conservation

€

δ•

=D•

Dδ = −

! ∇ ! v

a≡ −Hθ

€

δ•

=D•

Dδ = −

! ∇ ! v

a≡ −Hθ

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 SurveysPhotometric:

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 Observablesgalaxy counts: δG (z) = b δ + δvel + 2(s-1) δ𝜿    + δfg + εG

bias 3D wl: 2D noise

galaxy shear: δ𝛾 (z) = bia δ + b𝜿 δ𝜿    + δfg    + ε𝜿intrinsic

alignments

3Dwl: 2D noise

CMB Temperature: δT (z=zd) = δ(z=zd) + δISW+SZ + δ𝜿    + δfg  + εT2Dintrinsic wl:2D

RSD 3D

Ly-alpha Forest: δF (z) = bF δ + δvel + αF δ𝜿    + εFgalaxy magnitudes: δm (z) = bm δ + δvel + αm δ𝜿    + εm

foregr

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.!!!!

The'3D'Fisher'Matrix'describes'clustering'of'spectroscopic'galaxies'

Pg(k,µ) = bg2 (1+βµ 2 )2Pm (k)Kaiser'effect:'

Geometry)(Alcock7Paczynski,)BAO,..):)power(spectrum(measured(assuming(a(reference(cosmology(

Seo(&(Eisenstein(Fisher(Matrix((kmax(=(0.2(h/Mpc)(

Pg(k||,ref ,k⊥,ref ) =α⊥−2α||

−1bg2 1+β k||

2

k||2 + k⊥

2

#

$%

&

'(

2

Pm (k)

With'dila>on'factors:'

k|| =α||−1k||,ref k⊥ =α⊥

−1k⊥,ref

α|| ≡H ref

Hα⊥ ≡

dAdA,ref

Measured'Spectrum:'

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:' (shear)'

(source'galaxy'clustering)'(spec'galaxy'clustering)'

ignoring(magnificaMon(bias(

ignoring(Intrinsic(Alignments(

shear:'lmax=2000,'GC:'lmax(=(kmax(*(D(zi),'kmax(=(0.2(h/Mpc(

1. de Putter R., Dore O., Takada M.,  astro-­‐ph:1308.6070

BAO as a standard ruler

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: !- distance to ruler H(z) :

- or parameters in ruler (Omega_M)

radial angular

€

cΔzBAO = rBAOH(z) ΔθBAO =rBAOdA (z)€

dr(z) =c

H(z)dz dA (z) =

cdzH(z)0

z∫

Amplitude depends on baryon fraction but position is fixed by sound horizon

Planck 2013

SDSS 2005!

19

Anna  Cabré’s  PhD  Thesis  arXiv:0807.3551  Crocce  etal  2011

Errors  from  MICE  sim

BAO:    radial    H(z)    H(z=0.34)  =  83.8  ±3.0±  1.6  EG,  Cabre  &  Hui  (2009)    

Transverse    ∫cdz/H(z)  θ(z=0.34)  =  3.90 ±  0.38  Carnero  etal  2011

DR7 Redshi,  Space  Distor5ons  (RSD)

Lentes Gravitatorias

Midiendo los efectos de lente gravitatoria (creadas por la materia oscura) podemos medir distancias y el crecimiento de estructuras en el universo.

Thursday, November 26, 2009

Strong and Weak Gravitational Lenses

Can be used to measure distances and growth history in the universe but is 2D

!

Complementarity of Observables Forecast: Planck+SNII priors

RSD +

BAO WLxG

WLxG +

RSD +

BAO

RSD+BAO WLxG

+ (BIAS IS KNOWN)

(eg 3pt) no shear

F Photometric DES (i<24)

2.7

B Spectroscopic DESI+ (i<22.5)

6.9

Combine

F+B 21

FxB: Cross Correlated

over same Area

32 (189) (55) astro-­‐ph:1109.4852

WLxG: shear-shear, galaxy-shear, galaxy-galaxy (including MAG)

14000 sq.deg. DES depth

Dark Energy Survey (DES)

• 525 nights in 5 years

• Will start in late 2012

17

3556 mm

CameraFilter

Optical Lenses 2.2 deg. FOV

Scroll Shutter

1575 mm

• 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.

Blanco, CTIO, Chile

2 deg ∅ FoV

500 Mpixels

18

DES Camera Installation

May 2012

July 2012

19

DECam First light image

• First light in Sep 12th, 2012

• Survey starts in Dec, 1st 2012

Josh Frieman, DOE-NSF Review, May 1-3, 20074

DES Science Summary

Four Probes of Dark Energy •  Galaxy Clusters

•  ~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

•  Supernovae •  30 sq deg time-domain survey •  ~4000 well-sampled SNe Ia to z ~1 •  Sensitive to geometry

Forecast Constraints on DE Equation of State

Factor 3-5 improvement over Stage II DETF Figure of Merit

Planck prior assumed

DES

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

Josh Frieman, DOE-NSF Review, May 1-3, 2007

DES grizDES

10σ Limiting Magnitudes g 24.6 r 24.1 i 24.0 z 23.9 !+2% photometric calibration error added in quadrature !! σ(z) ~ 0.05×(1+z)

DES Photo-z Precision

+VHS DES griZY + VHS JHKs on VISTA

Z 23.8 Y 21.6

J 20.3 H 19.4 Ks 18.3

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  

Observer

Shear   for source galaxy

at z1

𝛾2

To avoid intrinsic alignment contamination to WL signal we want to do <𝛾1  𝛾2>    

instead of <𝛾1  𝛾1>

𝛾1

Photo-z outliers might are then more important

Photo-z error and WL

24

The PAU Survey @ the WHT

25

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

26

P.Marti,R.Miquel, F.Castander, M.Eriksen

27

P.Marti, R.Miquel,

F.Castander, M.Eriksen

arXiv:1402.3220

2014MNRAS.442...92M

Real space

z-space, perfect resolution + peculiar velocities

z-space, Δz = 0.003(1+z) + peculiar velocities (PAU)

z-space, Δz = 0.03(1+z) + peculiar velocities (DES)

The Importance of Redshift Resolution

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)

astro-­‐ph:1109.4852

!=> measure bias: Combine probes/traces: RSD + WL Cross-correlate probes: galaxy-lensing Combine Photometric & Spectroscopic Surveys: sampling variance, photo-z accuracy

!

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)

!!

Martin EriksenRadial BAO in 2D

distance  bins:    photo-­‐z  outliers

Actual measurements in MICE simulations

RSD  in  2D Jacobo  Asorey  &  MarZn  Crocce    arXiv:1305.0934

34Adjacent  bins  (no  photo-­‐z  outliers)

Photometric Sample i ~ 24 2D lensing

!

Spectroscopic Sample i ~ 23

measure bias recover full 3D info from 2D+3D

Δz = 0.03

100 Mpc/h

10000Km/s

Δz = 0.003

10 Mpc/h

1000Km/s

RSD+WL:  Same  or  different  sky?

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

36

1 2D+3D Cov  ~  0 <gF FxB  >>  F+B

2 2D+3D Cov  ~  0  radial

<gF 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

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)

37

12

Cai & Bernstein

Relative Gain in Modified Gravity Figure of Merit (growth rate) from Same Sky factor ~1.4 in γ Note WL data not available in the north

LSST WL

MS

DE

SI R

SD

DES WL

38

Radial k

Angular k

Redshift space density

Photo-z densityLensing

The illusion of overlapFourier space coverage

Tuesday, March 5, 13

1. Font-Ribera A., McDonald P., Mostek N., Reid B. A., Seo H.-J., Slosar A., astro-­‐ph:1308.4164  

39

Forecasts'are'made'by'combining'2D'and'3D'Fisher'matrices'

has'transverse'modes'(μ≈0)'removed''

See,'e.g.,'Cai(&(Bernstein(2012,'Gaztanaga(et(al(2012(

p=photo-z s=spec-z

2D Limber=no radial modes

1. de Putter R., Dore O., Takada M.,  astro-­‐ph:1308.6070

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 !!

• • Because of Limber and 3D+2D approximations

previous studies removes the covariance in radial modes.

40

PF / PB ~ (bF +f µ2)/(bB +f µ2)

Forecast  WL+RSD

41

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

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)

Our new Exact Calculation Forecast:

WLxG*+RSD+BAO (cross Cl: l<300 + Planck priors)

F Photometric (DES i

!!

2.7 / fix bias 44 no lens 0.04 /no BAO 2.1/no RSD 2.2

B Spectroscopic (PAU i

6.9/ fix bias 46 no lens 4.3 /no BAO 4.4/no RSD 2.5

F+B Combine both as Independent21 / fix bias 171

no lens 4.7 /no BAO 14/no RSD 9

FxB CrossCorrelated over same Area

32 /fix bias 190 no lens 5.9 /no BAO 23/no RSD 15

no cross FB: 28>21*WLxG: shear-shear, galaxy-shear, galaxy-galaxy (including MAG)

14000 sq.deg.

FxB (no cross) > F+B

Martin Eriksen

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 slides44