EUCLID Cosmology Probes
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1 EUCLID Cosmology Probes Henk Hoekstra & Will Percival on behalf of the EUCLID The presented document is Proprietary information of the. This document shall be used and disclosed by the receiving Party and its related entities (e.g. contractors and subcontractors) only for the purposes of fulfilling the receiving Party's responsibilities under the Project and that identified and marked technical data shall not be disclosed or retransferred to any other entity without prior written permission of the document preparer. Meeting Bologna 7-8 Sept
2 How can we achieve this? These numbers only have meaning if systematic biases are small. is designed to achieve this! Meeting Bologna 7-8 Sept
3 Survey Optimization The FoM increases with increasing area/volume and galaxy number density. This ignores that any survey is limited by cost: time is finite For galaxy clustering a large survey area provides the best bang for your buck. This is not the case for weak lensing. If intrinsic alignments are ignored indeed increasing the survey area is more efficient compared to increasing the number density. However, as the survey becomes shallower, intrinsic alignments become increasingly important. This changes the trade-off between area and depth. Meeting Bologna 7-8 Sept
4 Area requirements Given the nominal survey time this leads to an optimal survey area of 15,000 deg 2 Req. ID Parameter Requirement Goal WL.1-1 & GC.1-1 Survey area >15,000 deg 2 >20,000 deg 2 WL.1-2 Number density >30 arcmin -2 >40 arcmin -2 WL.1-3 Mean redshift >0.8 Meeting Bologna 7-8 Sept
5 Weak gravitational lensing Density fluctuations in the universe affect the propagation of light rays, leading to correlations in the their observable shapes. The statistics of shape correlations as a function of angular scale and redshift can be used to directly infer the statistics of the density fluctuations and consequently cosmology. Meeting Bologna 7-8 Sept
6 What do we need? For each galaxy we need: - Estimate of its shape (corrected for observational effects) - Estimate of its redshift (knowledge of mean and distribution) We need to establish the correlations between the galaxy shapes in the absence of lensing (intrinsic alignments) We need to relate the resulting signal as a function of scale and redshift to cosmological parameters through numerical simulations of structure formation. Meeting Bologna 7-8 Sept
7 Measuring shapes The observed lensing signal may be biased: g obs = (1+ m) g true +c which leads to biases in the ellipticity correlation function (Massey et al., in prep): C true» éë 1+ 2 m ù û C obs + c 2 l l Meeting Bologna 7-8 Sept
8 Measuring shapes We require that the FoM is dominated by the statistical uncertainty, rather than systematic biases (R-WL.1.-4): m< : 2 s sys» c 2 <10-7 : multiplicative bias additive bias This drives the constraints on the space craft and the algorithms used to measure shapes. Meeting Bologna 7-8 Sept
9 Case for space space ground The multiplicative bias m and additive bias σ sys (or c) scale with the square of the PSF: it is much easier to measure shapes when the PSF is small. Weak lensing with is primarily feasible thanks to its small PSF! Meeting Bologna 7-8 Sept
10 Sources of bias Given the PSF size, the multiplicative and additive bias depend on - How well we know the instrumental distortion (knowledge) - How well we can correct for the instrumental distortion (method) - The effective PSF sizes is constrained by the mirror diameter/optics. - The required depth (m AB <24.5) constrains the distribution of galaxy sizes. Results of tests of shape measurement methods (STEP, GREAT 10, etc.) constrain the allocation to the method budget. The remainder of the budget set by R-WL.1-4 determines how well we need to know the instrumental distortions. Meeting Bologna 7-8 Sept
11 Another case for space We need to know the instrumental distortions extremely well, which can only be achieved thanks to the stability provided in space. (see the talk by Jerome Amiaux for a detailed flowdown) 67% multiplicative bias 33% method knowledge R-WL : the multiplicative bias in shape measurements shall be known to an accuracy of σ[μ]<2x10-3 under all observing conditions and all types of galaxies used for weak lensing. Feasible based on GREAT 10 results. R-WL.2.1-9: the relative uncertainty in our knowledge of the PSF size should be: σ[r 2 ]/R 2 <10-3 This has been verified using end-to-end simulations (see talk by Lance Miller) Meeting Bologna 7-8 Sept
12 Another case for space We need to know the instrumental distortions extremely well, which can only be achieved thanks to the stability provided in space. (see the talk by Jerome Amiaux for a detailed flowdown) 11% * additive bias 72% 17% method knowledge margin R-WL : the additive bias in shape measurements shall be known to an accuracy of σ[c]<5x10-4 Feasible based on GREAT 10 results. * Includes cross-term R-WL.2.1-8: the spatio-temporal variation of the ellipticity induced by the PSF should be such that a model can be constructed with residals per component: σ[e inst ]<2x10-4 This has been verified using end-to-end simulations (see talk by Lance Miller). CTI contribution has been verified by Richard Massey. Meeting Bologna 7-8 Sept
13 Need for redshifts The achieve our science goals we need to measure the matter distribution as a function of redshift: weak lensing tomography requires redshifts for the sources. Meeting Bologna 7-8 Sept
14 Need for redshifts Tomography can be done using fairly broad bins, and the individual redshifts do not need to be very precise. But the mean redshift in a tomographic bin needs be known to high accuracy: R-WL.1-6: The catastrophic failure fraction (f cat ), shall be less than 10%. R-WL.1-7: The mean of the redshift distribution n(z) in each tomographic redshift bin shall be known to a precision of σ(<z>)/(1+z)<0.002 Tomography Kitching et al. (2008) Meeting Bologna 7-8 Sept
15 External data The VIS and NIR data are not sufficient and therefore we require supporting ground based multi-color data: - PanSTARRS2 (10,000 deg 2 ) - Dark Energy Survey (5000 deg 2 ) - additional data could come from LSST and VST These data are also needed to account to correct galaxy shapes with the correct (wavelength-dependent) PSF. To achieve R-WL.1-7 requires a large calibration sample of ~10 5 galaxies with spectroscopic redshifts. spectroscopy will provide a large sample at z>0.8 adding to results from several ongoing redshift surveys. Meeting Bologna 7-8 Sept
16 Need for redshifts The presence of intrinsic alignments changes this simple picture by placing additional requirements on the precision of the photometric redshifts: R-WL.1-5: The statistical scatter (RMS) of the errors in the measured photometric redshifts, in the range 0.2<z<2.0 shall be σ(z)/(1+z)<0.05 (and with a goal of <0.03). Joachimi et al. Meeting Bologna 7-8 Sept
17 Need for redshifts R-WL.1-5 can be met with by complementing VIS+NISP data with imaging from DES and PanSTARRS2 (assuming nominal survey depths). The use of LSST data allow us to reach the goal of σ(z)/(1+z)<0.03 Abdalla et al. (2008) Meeting Bologna 7-8 Sept
18 Interpretation of the data The largest contribution to the weak lensing power spectrum comes from scales that correspond to groups of galaxies, i.e. non-linear structures. To relate the observations to cosmological parameters we need very accurate predictions from numerical simulations (see talk by Romain Teyssier tomorrow). The lensing signal is sensitive to the total matter power spectrum, not just that of dark matter. If baryons trace the dark matter perfectly then simple n-body simulations might be sufficient, but recent work suggests that feedback processes can redistribute a large fraction of the baryons. Hydro-simulations to infer real C(l) expensive Recipe to convert n-body into real C(l) e.g. Semboloni et al. (2011) Requires better modeling of feedback: data will be extremely useful! Meeting Bologna 7-8 Sept
19 Clusters of galaxies Clusters of galaxies trace the peaks in the density distribution and provide additional information to probe the growth of structure. The data themselves will yield a sample of 60,000 clusters with a S/N>3 between 0.2<z<2 using a conservative optical selection. More than 10 4 of these will be at z>1. The number density of high mass, high redshift clusters is extremely sensitive to any primordial non-gaussianity and deviations from standard dark energy models To reach the projected FoM we need to know: - the masses - selection function Meeting Bologna 7-8 Sept
20 Clusters of galaxies M ass proxies Cluster survey Cosmology? Thanks to no more miracles are needed! Meeting Bologna 7-8 Sept
21 Clusters of galaxies will provide the most accurate masses for the large sample of clusters thanks to its built-in weak lensing analysis. In addition it will probe dark matter density profiles on scales >100 kpc, providing direct and important constraints on numerical simulations. The high resolution imaging also will yield a large number of strong lensing features which provide a unique test of CDM by probing the substructure and small scale density profile (see talk by Massimo Meneghetti). Multi-wavelength analysis (synergy with Planck and erosita, etc.) provide improved constraints on feedback processes, thus improving the fidelity of the numerical simulations and the predicted power spectra. Meeting Bologna 7-8 Sept
22 Galaxy clustering Need angular galaxy positions Need galaxy redshifts For lots of galaxies over a large volume Need to understand population angular completeness radial completeness radial/angular fluctuations This is the hard part Then can go from a density field to an overdensity field, and measure statistics Meeting Bologna 7-8 Sept
23 Using the measured clustering What are the constituents of matter? e.g. neutrino mass, primordial P(k) What is the expansion rate of the Universe? e.g. quintessence, Λ Galaxy Redshift Survey Redshift-Space distortions How does structure form within this background? e.g. modified gravity, GR Understanding acceleration Is the Universe homogeneous on large scales? Copernican principle, Non-Gaussianity How do galaxies form and evolve? semi-analytic models, halo model Meeting Bologna 7-8 Sept
24 Modeling the full P(k) shape There have been significant recent advances modeling the full anisotropic matter power spectrum e.g. Taruya, Nishimichi & Saito 2010; Jennings, Baugh, & Pascoli 2011 There have also been advances in modeling the galaxy power spectrum e.g. Reid & White (2011; arxiv: ) halo power spectra well modeled at z=0.5 everything is simply at higher redshifts! For our predictions, we assume can fit P(k), but take a conservative cut for the range of scale fitted for our predictions consider k<0.2 / hmpc -1 z>1 reduced to k<0.15 / hmpc -1 at z=0.7 Marginalise over galaxy bias Use Figure-of-Merit method developed by Seo & Eisenstein (2007: ApJ, 665, 14) described in Wang et al. (2010: MNRAS, 409, 737). Meeting Bologna 7-8 Sept
25 Area requirements Given the nominal survey time this leads to an optimal survey area of 15,000 deg 2 Meeting Bologna 7-8 Sept
26 Galaxy redshift density Req. ID Parameter Requirement Goal GC.1-2 Galaxy sky density 3,500 / deg 2 5,000 / deg 2 GC.1-5 Redshift range 0.7<z<2.05 also gals z<0.7 GC.1-6 Median of redshift distribution >1 >1.1 GC.1-7 Upper quartile of redshifts >1.35 GC Flux limit erg cm -2 s -1 GC Completeness >45% GC Flux limit at all wavelengths <120% of GC Meeting Bologna 7-8 Sept
27 Redshift accuracy Wang et al Req. ID Parameter Requirement Goal GC.1-3 Redshift accuracy σ(z)<0.001(1+z) GC Spectral resolution >250 GC Resolution element sampled by > 2 pixels Meeting Bologna 7-8 Sept
28 Current clustering measurements Percival et al. 2009; arxiv: Meeting Bologna 7-8 Sept
29 clustering measurements 20% of the data, assuming the slitless baseline at z~1 Distance-redshift relation moves P(k) Meeting Bologna 7-8 Sept
30 Slitless spectroscopy from space NIR Slitless spectroscopy would provide a uniform sample of galaxy redshifts based on the H-alpha line emission, with no need to specify a target sample NIR observations are not possible from the ground due to the high background a near-ir survey is much less affected by the dust extinction of our Galaxy H-alpha is less affected by galaxy internal dust extinction than other lines in the blue (e.g. a factor of about 2 less than [OII]3727) the most important emission lines to estimate gas dust extinction, metallicity and ionization properties are in the rest-frame optical (i.e. redshifted in the near-ir for z>0.7) H-alpha is a primary estimator of the star formation rate near-ir spectroscopy provides spectra in the rest-frame optical for z>0.7, hence allowing the best combination with ground-based optical surveys of low redshift galaxies (e.g. SDSS). Meeting Bologna 7-8 Sept
31 1deg 2 of spectroscopy 1 deg2 of the sky simulated and propagated through end-2-end spectroscopic simulation Shows can meet the required n(z), completeness and purity See talk tomorrow by Bianca Garilli Meeting Bologna 7-8 Sept
32 Understanding redshift systematics Slitless spectroscopy leads to redshift failures (purity 1) we need to calibrate the survey Can use a smaller, complete sample to do this The deep-field gives such a sample if rotate dispersion axis (beat confusion) Need wide & deep surveys Req. ID Parameter Requirement Goal GC.1-10 fraction of catastrophic failures f<20% GC.1-11 fraction of catastrophic failures known to 1% GC.1-12 mean redshift in 0.1 redshift bin known to 0.1% GC Subsample of galaxies >140,000 gals, with >99% purity Meeting Bologna 7-8 Sept
33 Using 1 deg 2 sim to test confusion Slitless spectroscopy leads to confusion (density dependent fluctuations in completeness) Isolated galaxies All Confused galaxies Given dispersion in 2 orthogonal directions, we have confusion if another galaxy within cross Meeting Bologna 7-8 Sept
34 100deg 2 sim test of confusion from Durham group Meeting Bologna 7-8 Sept
35 Scientific Synergy between probes Different degeneracies between parameters in standard analyses Direct test of anisotropic stress in the same volume RSD measure time-like metric fluctuations WL measures a combination of time-like and space-like metric fluctuations The deep photo-z catalog will contain many galaxies per halo hosting each spectroscopic galaxy, and we will have WL halo mass estimates providing better weights (Cai et al. 2011) The WL catalog contains many galaxies in the background of the spectroscopic population, which can be used to measure the bias. This breaks galaxy-bias degeneracies in the standard RSD analysis, significantly improving constraints (Bernstein & Cai 2011) Spectroscopic redshift catalog can be used to constrain intrinsic alignment effect for WL measurements Meeting Bologna 7-8 Sept
36 Implementation Synergy The top-level requirements for both GC & WL include large surveys high image quality accessibility to infra-red wavelengths homogeneity of observation, minimum systematics Space mission provides all of this low background stability lack of terrestrial atmospheric effects survey speed Power of is in complementarities at all levels science, analysis, observations, between VIS, NIP, NIS data, and all require space-based observations Meeting Bologna 7-8 Sept
37 Additional cosmological probes (Clusters already covered) Complementing ESA Planck data tightening of parameters given baseline to last scattering surface measurement of Integrated Sachs-Wolfe effect measurement of the lensed CMB sky Type 1a Supernovae in the Deep Field NIR light-curves and colours for 3,000 Type Ia SNe to z~ 1.2 spectroscopy would provide accurate redshifts for many of the host galaxies, although ground-based spectroscopic redshifts would still be required for subset will be the first large- scale NIR search for SNe from space. Meeting Bologna 7-8 Sept
38 Measuring Dark Energy The dark energy equation of state is the ratio of the pressure to density of dark energy p(a) = w(a) ρ(a)c 2. This dependence can be parameterised using a first order Taylor expansion with respect to the scale factor a=1/(1+z), w(a)= w p +(a p a)w a. Detecting w(a)= 1 at any redshift would demonstrate that dark energy is not a cosmological constant, but rather a dynamical field Define a Figure-of-Merit (FoM) FoM = 1/(Δw p Δw a ) Primary probes give a FoM>400, with subdominant systematic uncertainties, matching the DETF definition of a stage-iv mission Meeting Bologna 7-8 Sept
39 Measuring Modified Gravity The growth factor [or its derivative, the growth rate f(z)] quantifies the efficiency with which cosmological structure is built. The growth rate well described by f(z)=ω m (z) γ. A detection of γ= 0.55 would indicate a deviation from General Relativity, and thus a completely different origin of cosmic acceleration, rather than dark energy. can constrain this parameter to 0.01 (where ΛCDM corresponds to γ=0.55). the γ-parameterisation is merely an example. In general, will provide tight constraints on the cosmological growth rate. Meeting Bologna 7-8 Sept
40 Measuring initial conditions Concordance cosmology assumes an initial Gaussian random field of perturbations, with power-law index n s + Planck will provide a factor ~2 improved n s measurement over Planck alone A detection of non-gaussianity would signify a departure from this central assumption of the current standard model. The f NL parameter is a way to quantify the amplitude of this effect. will measure f NL with an accuracy of 2, compared to Planck which measures f NL to an accuracy of 5 with a complementary approach Meeting Bologna 7-8 Sept
41 Measuring Neutrino Masses The total neutrino mass is the sum of the masses of the three known species (electron, muon and tau neutrinos). Massive neutrinos damp structure growth on small scales. The larger the mass, the more damping occurs, leaving a clear signature in the matter power spectrum observed by. particle physics experiments have established that at least two of the three neutrino species have non-zero mass, with the larger mass difference of the order of 0.06 ev will measure Δm ν < 0.03eV, sufficient to determine the neutrino mass hierarchy, if the total mass turns out to be small, m ν <0.1 ev. will show if neutrinos obey a normal (two light neutrinos, one massive neutrino) or inverted (two massive neutrinos, one light neutrino) hierarchy; understanding this will give indications about the mechanism that gave neutrinos their mass. Meeting Bologna 7-8 Sept
42 Summary Major leap forwards in our understanding of the Universe Meeting Bologna 7-8 Sept
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