Cluster Cluster uster Dist uster Dist stanc stanc ance ance e Measurements e Measurements surements surements Ste Ste teve teve ve All ve All llen llen en (Sta en (Sta tanf tanf nford/SLAC) nford/SLAC) ord/SLAC) ord/SLAC) In collaboratio aboration with: MACSJ0025.4-1222 (z=0.59) Adam am Mantz tz (Chica icago) o) David vid Rapet etti (Cope penha nhagen gen) R. Glenn nn Morr rris is (SLAC AC) Robert bert Schmidt midt (Heidelberg idelberg) Harald rald Ebeling ing (Haw awai aii) i) Andy dy Fabian an (Camb mbridg ridge) Doug ug Applega egate e (Bonn) nn) Patric rick k Kelley ey (Berkeley rkeley) Paul l Nulse sen (CfA) Anja von der der Linden en (Stanf nford) ord) Red: X-rays Blue: lensing (+ many ny more re)
Outl Outl tline tline ine of talk ine of talk lk: lk: I will discuss two ways to measure distances with galaxy clusters. These are complementary to the more familiar tests based on cluster counts, i.e. the mass function and clustering. 1) Measurements of the baryonic mass fraction in the largest dynamically relaxed clusters (a.k.a. the fgas test). 2) Combined X-ray and SZ measurements of the Compton y-parameter (a.k.a. the XSZ test). For further info: Allen, Evrard & Mantz, 2011, ARA&A, 49, 409.
Cluster Cluster uster Distance uster Distance tance tance Measurements Measurements surements surements 1. 1. . . Th The fg Th The fgas fg fgas exp exp xperiment xperiment eriment eriment Featured work: Allen et al. 2008, MNRAS, 383, 879 See also e.g. White & Frenk ’91; Fabian ’91; Briel et al. ’92; White et al ’93; David et al. ’95; White & Fabian ’95; Evrard ’97; Mohr et al ’99; Ettori & Fabian ’99; Roussel et al. ’00; Grego et al ’00; Allen et al. ’02, ’04; Ettori et al. ’03, ‘09; Sanderson et al. ’03; Lin et al. ’03; LaRoque et al. ’06 …
Co Co Constr Constr traini traini aining aining g cosmolog g cosmolog ogy ogy y wi y wi with with f gas as measureme measureme urements urements nts nts gas as BASIC IDEA: galaxy clusters are so large that their matter content should provide a ~ fair sample of matter content of Universe. X - ray gas mass stellar mass f gas f star Define: and total cluster mass total cluster mass Then: f f f f (1 s ) baryon star gas gas b b f baryon Since clusters provide ~ fair sample of Universe: m Simul mulatio ations ns b BBNS BBNS/CMB /CMB f b gas (1 s) m Mea easure sure
For relaxed For relaxed d clusters, d clusters, ters, HS ters, HS HSE modeling HSE modeling precise precise e masses e masses Nagai, Vikhlinin & Kravtsov ‘07 For largest, relaxed clusters (selected on X-ray morphology) measured at r 2500 X-ray data + hydrostatic eq. Total mass and fgas to better 10 % accuracy (both bias and scatter). X-ray gas mass to few % accuracy. Note: weak gravitational lensing data can in principle also aid absolute mass calibration for ensembles of clusters. Relaxed clusters (filled circles)
The observati The observati vations vations ons ons 1.6Ms of Chandra data for 42 hot (kT>5keV), dynamically relaxed clusters spanning redshift range 0<z<1.1. Selected on X-ray morphology: sharp central X-ray surface brightness peaks, minimal X-ray isophote centroid variations and high overall symmetry. Restri trict ction on to hot, relaxed d clusters ters minimizes izes all systema ematic tic effects. cts.
Ch Chandra Ch Chandra ra results ra results ts on f gas ts on gas (r) (r) (r) (r) gas gas 6 lowest redshift relaxed clusters (0<z<0.15) : f gas (r) → approximately universal value at r 2500 Fit constant value at r 2500 f gas (r 2500 )=(0.113±0.003)h 70 -1.5 For Ω b h 2 =0.0214±0.0020 (Kirkman et al. ‘03), h=0.72±0.08 (Freedman et al. ‘01), s=0.16±0.05 (Lin & Mohr ‘04) and b=0.83±0.09 (Eke et al. ‘98 +10% systematics) (0.83 0.09)(0.04 37 0.0041)h -0.5 70 0 . 27 0 . 04 m (0.113 0.003)(1 [ 0.16 0.05]h ) 0.5 70
Di Di Distan Distan ances ances ces and dark energy ces and dark energy y wi y wi with with f gas as (z) (z) (z) (z) gas as The measured f gas values depend upon the assumed distances to clusters as f gas d 1.5 , which brings sensitivity to dark energy through the d(z) relation. To use this information, we need to know the expected f gas (z). What do we expect to observe? Simula latio tions: ns: predicted b(z) (0.5r vir ) For large (kT>5keV) clusters, we expect b(z) and therefore f gas (z) to be approximately constant with z. The precise prediction of b(z) is a key task for hydro. simulations. See e.g. Battaglia et al. 2013, Eke et al. 98 Planelles et al. 2013.
Ch Ch Chandra Chandra ra results ra results ts on ts on f gas as (z) (z) at r 2500 (z) (z) at r gas as 2500 00 00 SCDM ( Ω m =1.0, Ω Λ =0.0 ) Λ CDM ( Ω m =0.3 , Ω Λ =0.7 ) Brute-force determination of f gas (z) for two reference cosmologies: Inspection ection clearly ly favours urs Λ CDM over SCDM cosmology. logy.
To quantify: fit data with model which accounts for apparent variation in f gas (z) as underlying cosmology is varied → find best fit cosmology. 1 . 5 KA b ( z ) d ( z ) LCDM b A f (z) gas 1 s ( z ) d ( z ) model m A For details see Allen et al. (2008).
Allowa Allowa wance wance ces ces s for systemat s for systemat ematic ematic c uncertai c uncertai taint taint nties nties Our analysis includes a conservative treatment of potential sources of systematic uncertainty (marginalized over in analysis). 1) The depletion factor (simulation physics, feedback processes etc.) b(z)=b 0 (1+ b z) ± 20% uniform prior on b 0 (simulation physics) ±10% uniform prior on b (simulation physics) 2) Baryonic mass in stars: define s= f star / f gas =0.16h 70 0.5 s(z)=s 0 (1+ s z) ± 30% Gaussian uncertainty in s 0 (observational uncertainty) ± 20% uniform prior on s (observational uncertainty) 3) Non-thermal pressure support in gas: (primarily bulk motions) = M true / M X-ray 10% (standard) or 20% (weak) uniform prior [1< <1.2] 4) Instrument calibration, X-ray modelling K ± 10% Gaussian uncertainty
With With h these (conservat h these (conservat ervative) ervative) ve) allowa ve) allowa wances wances es for system es for system temati temati atics atics cs cs Model: 1 . 5 KA b ( z ) d ( z ) LCDM b A f (z) gas 1 s ( z ) d ( z ) model m A Results ( Λ CDM) Including all systematics + standard priors: (Ω b h 2 =0.0214 ± 0.0020, h=0.72 ± 0.08) Davis et al. ‘07 Best-fit parameters ( Λ CDM): Ω m =0.27 ± 0.06, Ω Λ =0.86 ± 0.19 (Note also good fit: 2 =41.5/40) Result lt limite ted d by Important b(z), ),K K priors
Da Dark energy equation Da Dark energy equation on of state on of state te te Cons nstant tant w model el (flat): ): 68.3, 95.4% confidence limits for all three data sets consistent with each other. Combined constraints (68%) Ω m = 0.253 ± 0.021 w 0 = -0.98 ± 0.07 Results marginalized over all systematic uncertainties. Note: combination with CMB data removes the need for Ω b h 2 and h priors.
f gas gas (z) (z) distance (z) (z) distance nces nces s have low s s have low s w system w system tematic tematic atic scatt atic scatt tter. tter. er. er. gas gas 2 for best fit acceptable. Intrinsic scatter is undetected. 68% upper limit on fgas scatter fgas ~10% (7% in distance). (Consistent with expectations from hydro. simulations) fgas precise tracer of expansion history (individually, better than SNIa?). Mgas excellent mass proxy for hot, massive clusters.
Mantz et al., in preparation. (5 year project, just unblinded.) Expanded sample: 3x more fgas data. Automated target selection applied to archives (20Ms of observations). Optimized X-ray analysis engine. Improved external priors. Blind analysis: fgas(r) measurements unblinded Feb 2013.
Cluster Cluster uster Distance uster Distance tance tance Measurements Measurements surements surements 2. 2. . Th . Th The XSZ The XSZ Z experiment Z experiment eriment eriment See also e.g. Silk & White 1978, Cavaliere et al. 1979, Myers et al. 1997, Mauskopf et al. 2001, Mason et al. 2001, Jones et al. 2001, Carlstrom et al. 2002, Reese et al. 2002, Schmidt et al. 2004, Bonamente et al. ’06 …
Recommend
More recommend
