1. Strategies for studying Dark Energy Steve Allen, KIPAC KIPAC is at the forefront of experimental/observational dark energy studies. Figure 1: lead figure from `Quantum Universe’ Key to dark energy research is to push on several complementary fronts.

2. Probing dark energy with galaxy clusters Cosmological studies of galaxy clusters are best done at X-ray wavelengths where clusters shine brightly and the `false detection’ of clusters is very low. X-ray emitting gas fills the space between galaxies and dominates the overall baryonic mass (M gas ~ 6M stars ). The `downside’ of X-ray studies is that X-rays do not penetrate the Earth’s atmosphere and so we require X-ray satellites to study clusters in this way.

3. Two independent dark energy tests with galaxy clusters: 2) Direct distance measurements: just like supernovae, X-ray studies of galaxy clusters allow us to measure distances independent of redshift. This allows us to measure cosmic acceleration directly. The density of clusters for a variety of dark energy models (Solevi et al. 2005) KIPAC members are leading the exploitation of X-ray cluster surveys and are involved plans for the next generation of X-ray surveys. 1)Growth of structure experiments: the growth of structure in the Universe is (typically) inhibited by dark energy. In particular, this effects the largest objects (which form last) and so the number density, spatial clustering and evolution of clusters are all strong functions of dark energy.

4. Probing Dark Energy with Galaxy Clusters [Allen et al. 2004, MNRAS, 353, 457] II: Direct Distance Measurements

5. The Chandra X-ray Observatory Launched July 1999. One of NASA’s four Great Observatories (HST, CGRO, Spitzer). Instruments: Micro-channel plate detector (HRC) Transmission gratings (LETG/HETG) Advanced CCD Imaging Spectrometer ACIS main features: Charged Coupled Device array (X-ray CCDs). Field of view 16x16 arcmin 2 (ACIS-I). Good spectral resolution ~100eV over 0.5-8 keV range. Exquisite spatial resolution (0.5 arcsec FWHM). Chandra and XMM-Newton have provided first opportunity to carry out detailed spatially-resolved X-ray spectroscopy of galaxy clusters  revolutionized cosmological work.

6. X-ray mass measurements X-ray observations of clusters probe bulk of the baryonic mass content (M gas ~ 6M stars ). Observables: 1) observed X-ray surface brightness (SB) profile. 2) deprojected (spectrally-determined) kT profile. + assumption of hydrostatic equilibrium (spherical symmetry) → M(r) Studies of distant clusters benefit from the application of modified analysis technique: Take simple parameterized mass model + SB profile. Monte-Carlo simulations  predict kT(r)  compare with obs. MACS1423+24 (z=0.54) 120ks

7. Comparison X-ray/weak lensing Abell 2390 (z=0.23) RXJ1347.5-1145 (z=0.451) Excellent agreement between independent X-ray and weak lensing results confirms validity of hydrostatic assumption in X-ray analysis + rules out significant non- thermal pressure support in the X-ray gas on these scales  robust results! ( X-rays) Allen et al. 02 (Lensing) Fischer & Tyson 97 ( X-rays) Allen et al. 01 (Lensing) Squires et al. 96

8. Chandra observations of 37 X-ray luminous, dynamically relaxed clusters: Direct distance measurements: current data 0.06 10 45 h 70 -2 erg/s kT>5keV All have regular X-ray morphology, sharp central X-ray surface brightness peak, minimal X-ray isophote centroid variation. MACS + BCS SURVEYS (Ebeling et al. ‘98, ’01, ‘05): Based on ROSAT All-Sky Survey. 120 clusters at z>0.3 with L X >10 45 erg/s (>30x improvement over previous samples). Chandra snapshot programs lead by H. Ebeling and L. van Speybroeck. So far ~70 MACS clusters observed with Chandra  21/24 clusters at z>0.3 (16 new). MACS1423+24 (z=0.54) 120ks

9. The Chandra gallery

10. Direct distance measurements: method BASIC IDEA: Galaxy clusters are so large that their matter content should provide a fair sample of matter content of Universe. Chandra (+ lensing) data  robust total mass measurements Chandra data  (very) precise X-ray gas mass measurements If we define: Then: Since clusters provide ~ fair sample of Universe f baryon =b Ω b / Ω m

11. 37 regular, relaxed clusters: f gas (r) large scatter at small radius but → approximately universal value at r 2500 Fit constant value at r 2500 f gas (r 2500 )=(0.1175±0.0015)h 70 -1.5 f gas (r 2500 )=(0.0688±0.0088)h -1.5 Chandra results on f gas (r) For Ω b h 2 =0.0214±0.0020 (Kirkman et al. ‘03), h=0.72±0.08 (Freedman et al. ‘01), b=0.83±0.09 (Eke et al. 98; Allen et al. 2004)

12. However, measured f gas (z) values depend upon assumed distances to clusters f gas  d 1.5. This introduces apparent systematic variations in f gas (z) depending on the differences between the reference cosmology and the true cosmology. Apparent variation of f gas with redshift: SCDM ( Ω m =1.0, Ω Λ =0.0 ) ΛCDM ( Ω m =0.3, Ω Λ =0.7 ) Inspection clearly favours Λ CDM over SCDM cosmology.

13. ΛCDM Cosmology: Using standard priors: (Ω b h 2 =0.0214±0.0020, h=0.72±0.08, b=0.83±0.09) Best-fit parameters ( Λ CDM): Ω m =0.26±0.04, Ω Λ =0.68±0.17 (Note also good fit:  2 =28/35) To quantify: fit Λ CDM data with model which accounts for apparent variation in f gas (z) as underlying cosmology is varied ( Ω m,Ω Λ ) → find model that provides best fit to data.

14. Cluster f gas analysis including standard Ω b h 2, h and b priors. Comparison of independent constraints ( Λ CDM)

15. Cluster f gas analysis including standard Ω b h 2, h and b priors. CMB data (WMAP +CBI + ACBAR) weak prior 0.3<h<1.0 Supernovae data from Tonry et al. (2003). Comparison of independent constraints ( Λ CDM)

16. Constraints from the combination of cosmological data sets [Rapetti, Allen & Weller, 2005, MNRAS, 360, 555]

17. Analysis approach: Analyse using enhanced version of CosmoMC code (Lewis & Bridle 2002). Markov Chain Monte Carlo (MCMC) method. Note analysis of CMB data includes treatment of DE perturbations for models crossing w=-1 (Rapetti & Weller 05). Best available data  tight constraints, minimize systematics. Complementary data  minimize priors. General DE models  robust constraints. USE : DATA USED : 1)Chandra f gas (z) (26 clus: Allen et al 2004) 2)CMB: WMAP (TT/TE)+CBI+ACBAR 3)SNIa (Riess et al. 2004 GOLD SAMPLE)

18. Ω m = 0.29 ± 0.03 w 0 = -1.05 ± 0.11  2 ν =1.03 Constraints for data pairs and 3 data sets combined Constant w model: Analysis assumes flat prior. 68.3, 95.4% confidence limits for all three parameter pairs consistent with each other. Marginalized constraints (68%)

19. The Next Big Step [White Papers submitted to Dark Energy Task Force June 2005]

20. X-ray cluster studies: Constellation-X Constellation-X is one of two flagship missions within NASA’s Beyond Einstein program. [Ranked 2 nd only to JWST in most recent AAAS Decadal Survey.] KIPAC members have substantial involvement in Facility Science Team: Kahn (steering committee), Kahn & Rasmussen (grating/CCD team), Cabrera (microcalorimeter team), Craig (hard X-ray telescope), Allen & Bloom (Science).

21. X-ray cluster studies: Constellation-X Constellation-X (in combination with future cluster surveys) will expand the size of f gas (z) samples by an order of magnitude. The data at high-z will have the same quality as the best current data obtained at low-z from Chandra and XMM-Newton. Median redshift z~1 with sample reaching to z~2.

22. Evolving DE model: X-ray cluster studies: Constellation-X The constraints from Constellation-X will have comparable accuracy and be beautifully complementary to the best other constraints from eg LSST, SNAP, Planck (and galaxy cluster growth studies). The best way to try to understand the nature of dark energy is to constrain its evolution (e.g. search for deviations from w=-1 LCDM model).

23. Experimental strategy for studying dark energy Extraordinary claims demand extraordinary proof and the existence of cosmic acceleration is without doubt extraordinary! Galaxy clusters: Con-X + surveys [direct distance+growth of structure] Supernovae: LSST and SNAP [direct distance] Gravitational lensing: LSST and SNAP [growth of structure] There is no single `ideal’ experiment with which to study dark energy. The best approach is to gather tight, robust constraints from several high quality, complementary experiments and combine them. KIPAC is at the forefront of current work and has substantial involvement in future, major experiments. When combined with eg CMB data from WMAP and Planck, these experiments will lead to precise constraints on the evolution of dark energy – the key experimental data – with sufficient independence and redundancy to ensure robustness to systematic uncertainties.

24. Dark Energy is the name given to the unknown causative agent driving the acceleration of the Universe