LSS with angular cross-correlations: Combining Spectro and Photometric Survey. Enrique Gaztañaga SDSS. Cosmic Web galaxies

Transcription

1 LSS with angular cross-correlations: Combining Spectro and Photometric Survey Enrique Gaztañaga SDSS Cosmic Web galaxies

2 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 3

4 Euclid' ESA$Cosmic$Vision$satellite$proposal$(600M,$M9class$mission)$ 5$year$mission,$L2$orbit$ 1.2m$primary$mirror,$0.5$sq.$deg$FOV$ Ω$=$20,000deg 2 $imaging$and$spectroscopy$ slitless$spectroscopy:$ $100,000,000$galaxies$(direct$BAO)$ $ELGs$(H9alpha$emiPers):$z~ $$ imaging:$ $deep$broad9band$opscal$+$3$nir$images$ $2,900,000,000$galaxies$(for$WL$analysis)$ $photometric$redshi\s$ Space9base$gives$robustness$to$systemaScs$ Final$down9selecSon$due$$mid$2011$ nominal$2017$launch$date$ See$also:$LSST,$WFIRST$

5 Observing DE: H(z) & D(z) & more Expansion history: H 2 (z) = H 2 0 [ Ω M (1+z) 3 + Ω R (1+z) 4 + Ω K (1+z) 2 + Ω DE (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) d L (z) = (1+z) r(z) Standard Rulers (BAO) d a (z) = (1+z) 1 r(z) or H(z)=cdz/r directly Volume Markers (clusters) dv/dzdω = r 2 (z)/h(z) Linear Growth history: Non-linear Growth history Higher order correlations, Cluster abundance, profiles Solar & Astro test of gravity δ = D(z) δ 0

6 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 δ = Hθ Linear Theory: P(k,z) ~D 2 (z) P(k,0) + mass conservation 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?

7 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

8 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,

9 Main Observables galaxy counts: galaxy shear: δ G (z) = b δ + δ vel + 2(s-1) δκ + δfg + ε G bias 3D wl: 2D foregr noise δγ (z) = b ia δ + bκ δκ + δfg + εκ intrinsic alignments 3D RSD 3D wl: 2D noise CMB Temperature: δ T (z=zd) = δ ( z=zd) + δ ISW +SZ + δκ + δfg + ε T intrinsic 2D wl:2d Ly-alpha Forest: δ F (z) = b F δ + δ vel + α F δκ + ε F galaxy magnitudes: δ m (z) = b m δ + δ vel + α m δκ + ε m

10 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.

11 The'3D'Fisher'Matrix'describes' clustering'of'spectroscopic'galaxies' Seo(&(Eisenstein(Fisher(Matrix((k max (=(0.2(h/Mpc)( Kaiser'effect:' Geometry)(Alcock7Paczynski,)BAO,..):) power(spectrum(measured(assuming(a( reference(cosmology( Measured'Spectrum:' With'dila>on'factors:' Non]linear'smearing:'FM'' P g (k,µ) = b g 2 (1+ βµ 2 ) 2 P m (k) k = α 1 k,ref k = α 1 k,ref # 2 2 P g (k,ref, k,ref ) = α α 1 b 2 k g 1+ β & % k 2 2 ( $ + k ' α H ref H 1. de Putter R., Dore O., Takada M., astro- ph: α d A d A,ref 2 P m (k) linear' c rec =0.5( Ellis(et(al( (

12 1. de Putter R., Dore O., Takada M., astro- ph: 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:'l max =2000,'GC:'l max (=(k max (*(D(z i ),'k max (=(0.2(h/Mpc(

13 BAO as a standard ruler Planck 2013 BAO gives us a standard distance with a co-moving value r BAO ~ 100 Mpc/h (r BAO = 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) : radial angular - or parameters in ruler (Omega_M) SDSS 2005 dr(z) = c H(z) dz d (z) = z cdz A 0 H(z) cδz BAO = r BAO H(z) Δθ BAO = r BAO d A (z) Amplitude depends on baryon fraction but position is fixed by sound horizon

14 Anna Cabré s PhD Thesis arxiv: Crocce etal 2011 DR7 Redshi, Space Distor5ons (RSD) Errors from MICE sim 19 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

15 Lentes Gravitatorias Strong and Weak Gravitational Lenses 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.

16 Complementarity of Observables Forecast: Planck+SNII priors sq.deg. DES depth WLxG: shear-shear, galaxy-shear, galaxy-galaxy (including MAG) 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:

17 Dark Energy Survey (DES) 5000 deg 2 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 mm Blanco, CTIO, Chile Camera 500 Mpixels Scroll Shutter Filter Optical Lenses 2.2 deg. FOV mm

18 DES Camera Installation May 2012 July

19 DECam First light image First light in Sep 12th, 2012 Survey starts in Dec, 1st

20 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 4 Josh Frieman, DOE-NSF Review, May 1-3, 2007 Forecast Constraints on DE Equation of State DES Planck prior assumed Factor 3-5 improvement over Stage II DETF Figure of Merit

21 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

22 DES Photo-z Precision DES +VHS DES griz grizy + VHS JHKs on VISTA 10σ Limiting Magnitudes g 24.6 r 24.1 J 20.3 i 24.0 H 19.4 Z z Ks 18.3 Y % photometric calibration error added in quadrature σ(z) ~ 0.05 (1+z) Josh Frieman, DOE-NSF Review, May 1-3, 2007

23 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 To avoid intrinsic alignment contamination to WL signal we want to do <γ1 γ2> instead of <γ1 γ1> Observ er Photo-z outliers might are then more important

24 The PAU the WHT 24

25 The Project in a Nutshell New camera for WHT with 18 2k x 4k CCDs covering 1 deg FoV Å-wide filters covering Å in 6 movable filter trays, which also include standard ugrizy filters. As a survey camera, it can cover ~2 deg 2 per night in all filters. Actual measurements in MICE simulations 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) ~ (1+z) 25

26 P.Marti,R.Miquel, F.Castander, M.Eriksen 26

27 P.Marti, R.Miquel, F.Castander, M.Eriksen arxiv: MNRAS M 27

28 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

29 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:

30 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

31 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)

32 Radial BAO in 2D Martin Eriksen distance bins: photo- z outliers

33 Actual measurements in MICE simulations

34 RSD in 2D Jacobo Asorey & MarZn Crocce arxiv: Adjacent bins (no photo- z outliers) 34

35 Photometric Sample i ~ 24 2D lensing Δz = Mpc/h 10000Km/s measure bias recover full 3D info from 2D+3D Δz = Spectroscopic Sample i ~ Mpc/h 1000Km/s

36 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: Cai Y.-C., Bernstein G., astro- ph: Kirk D., Lahav O., Bridle S., Jouvel S., Abdalla F. B., Frieman J. A., astro- ph: Font-Ribera A., McDonald P., Mostek N., Reid B. A., Seo H.-J., Slosar A., astro- ph: de Putter R., Dore O., Takada M., astro- ph: D+3D Cov ~ 0 <g F FxB >> F+B 2 2D+3D Cov ~ 0 radial <g F FxB > F+B 3 2D Cov 0 <g F FxB >> F+B 4 2D+3D Cov ~ 0 <g FxB ~ F+B 5 2D+3D Cov ~ 0 <g F FxB ~ F+B 36

37 Relative Gain in Modified Gravity Figure of Merit (growth rate) from Same Sky factor ~1.4 in γ LSST WL DES WL Note WL data not available in the north Cai & Bernstein MS DESI RSD 12 37

38 1. Font-Ribera A., McDonald P., Mostek N., Reid B. A., Seo H.-J., Slosar A., astro- ph: The illusion of overlap Fourier space coverage Lensing Radial k Photo-z density Angular k Redshift space density 38

39 1. de Putter R., Dore O., Takada M., astro- ph: Forecasts'are'made'by'combining'2D' and'3d'fisher'matrices' has'transverse'modes'(μ 0)'removed'' 2D Limber=no radial modes p=photo-z s=spec-z See,'e.g.,'Cai(&(Bernstein(2012,' Gaztanaga(et(al(2012( 39

40 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 µ 2 )/(bb +f µ 2 ) Because of Limber and 3D+2D approximations previous studies removes the covariance in radial modes. 40

41 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) galaxy-galaxy (3D or narrow bins): <g γ> <g g> including BAO, RSD and WL magnification F= Faint (Photometric dz~0.05) sample: <γ F γ F >, <g F γ F >, <g F g F > B= Bright (Spectroscopic dz~0.003) sample: <γ B γ B >, <g B γ B >, <g B g B > F+B= No overlap => no cross <FB>=0 & no Covariance : <FF BB>=0 FxB= Overlaping => <FB> 0 & <FF BB> 0 41

42 Our new Exact Calculation Forecast: Martin Eriksen sq.deg. 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 F+B Combine both as Independent 6.9/ fix bias 46 no lens 4.3 /no BAO 4.4/no RSD / fix bias 171 no lens 4.7 /no BAO 14/no RSD 9 FxB CrossCorrelated over same Area *WLxG: shear-shear, galaxy-shear, galaxy-galaxy (including MAG) 32 /fix bias 190 no lens 5.9 /no BAO 23/no RSD 15 no cross FB: 28>21 FxB (no cross) > F+B

43 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

44 THE END Additional slides 44