Astro/Phys 224 Spring 2014 Origin and Evolution of the Universe Week 5 ! Structure Formation Joel Primack University of California, Santa Cruz Physics 224 - Spring 2014 – Tentative Term Project Topics ! ! Adam Coogan – The BICEP2 Result and Its Implications for In=lationary Cosmology ! Devon Hollowood – Some Aspect of the Dark Energy Survey ! Caitlin Johnson – Observing Plan for ACTs to Constrain the Long-Wavelength EBL ! Thomas Kelly – Various Methods of Testing Modi=ied Newtonian Dynamics (MOND) ! Tanmai Sai – Shapes of Simulated Galaxies ! Vivian Tang – Studying Galaxy Evolution by Comparing Simulations and Observations ! Determination of σ8 and ΩM from CMB+ WMAP9+SN+Clusters Planck+WP+HighL+BAO WP = WMAP l<23 Polarization Data ! Cluster Observations HighL= ACT + SPT Planck ● ●WMAP9 WMAP7 WMAP5 ● ● ● BOSS Power Spectrum Normalization Spectrum Power Cosmic Dark Matter Fraction Planck Clusters vs. CMB? Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts - arXiv:1303.5080 Assuming a bias between the X-ray determined mass and the true mass of 20%, motivated by comparison of the Planck cluster masses 3 observed mass scaling relations to those from a set of numerical simulations, we find that ... σ8 = 0.77 ± 0.02 and The systematic uncertainty quoted here expresses the systematic Ωm = 0.29 ± 0.02. The values of the cosmological parameters are degenerate with the massuncertainty bias, on and the weak-lensing it is masses,found i.e. it includesthat all entries in Table 4 of Applegate et al. (2014) with the exception of the scat- the larger values of σ8 and Ωm preferred by the Planck’s measurements of the primary CMBter anisotropies due to triaxiality, which is accountedcan be for here in the statistical uncertainty. Extending the sample to all 38 clusters yields a consis- accommodated by a mass bias of about 45%. Alternatively, consistency with the primary CMBtent result: constraints can be +0.039 βall = 0.698 0.037 (stat) 0.049 (syst) . achieved by inclusion of processes that suppress power on small scales, such as a component of massive− neutrinos.± The weak-lensing masses are expected to yield the true cluster mass on average, and thereby enable a robust calibration of other mass proxies (see discussion in von der Linden et al. 2014; Apple- This has led to papers proposing ∑mν > 0.23 eV such as Hamann & Hasenkampgate etJCAP al. 2014). Therefore,2013 by identifying β = (1 b), these re- − sults suggest that the mass calibration adopted by the Planck team, (1 b) 0.8, underestimates the true cluster masses by between 5 − ⌘ Relative cluster masses can be determined accurately cluster-by-clusterand 25using per cent on average. X-rays as was done by Vikhlinin+09, Mantz+10, and Planck paper XX, but the absolute masses should3.2 Evidence be for a mass-dependentcalibrated calibration problem using gravitational lensing, say Rozo+13,14 and van der Linden+14. The Arnaud+07,10By eye, Fig. X-ray 1 suggests thatcluster the ratio between masses the WtG weak- lensing and Planck mass estimates depends on the cluster mass: at masses . 6 1014 M , the mass estimates roughly agree, whereas ⇥ used in Planck paper XX are the lowest of all. Using gravitational lensing mass calibrationthe discrepancy appears significant raises for more massivethe clusters. To Figure 1. The ratio of cluster masses measured by Planck and by WtG, for quantify the evidence for such a mass-dependent bias, we use the cluster masses and thus predicts fewer expectedthe clusters commonclusters. to both projects. Solid symbolsThis denote clusterslessens which Bayesian the linear regressiontension method developed between by Kelly (2007) to fit were included in the Planck cluster cosmology analysis (22 clusters) and log(MWtG) as function of log(MPlanck) (fitting the masses directly open symbols additional clusters in the Planck cluster catalog (16 clusters). avoids the correlated errors in the mass ratios one would have to the CMB and cluster observations. The red, solid line indicates a ratio of unity (no bias). The dashed red line account for if fitting the data as shown in Fig. 1). While we show indicates (1 b) = 0.8, the default value assumed throughout most of P16. − MPlanck as function of MWtG in Fig. 2 to reflect that the weak-lensing The blue line and shaded regions show our best-fit mass ratio along with masses are our proxy for true cluster masses, we assign the Planck the 1- and 2-σ confidence intervals. Since the weak-lensing masses are mass estimates to be the independent variable to reduce the e↵ects Closing the loop: self-consistent ... scaling relationsexpected to be unbiased foron average clusters, the ratio of Planck masses of to weak- Galaxies - Rozo+14 MNRAS lensing masses is a measure of the bias (1 b) = M /M of the of Malmquist bias: MPlanck scales with the survey observable, and − Planck true Planck cluster masses as used in P20. by choosing it as the independent variable, we provide a mass esti- Robust weak-lensing mass calibration of Planck galaxy cluster massesmate - forvon each datader point Linden+14 which is to first order independent of other Planck cluster masses 3 selection e↵ects (as X-ray selection to first order does not correlate with SZ selection biases, and the lensing data are a subsample of MPlanck/MWtG vs. MPlanck MPlanckan X-ray selectedvs. M catalog).WtG The Kelly (2007) method accounts for The systematic uncertainty quoted here expresses the systematic measurement errors in both variables, as well as for intrinsic scat- uncertainty on the weak-lensing masses, i.e. it includes all entries ter in the dependent variable. Rephrasing the results as a power-law, The ratio of in Table 4 of Applegate et al. (2014) with the exception of the scat- the best-fit relation for the 22 clusters in the cosmology sample is: Noter due Bias to triaxiality, which is accounted for here in the statistical Best Fit cluster 0.76+0.39 uncertainty. Extending the sample to all 38 clusters yields a consis- 0.20 MPlanck +0.077 MWtG − tent result: = 0.697 0.095 , 1015 M − ⇥ 1015 M masses ! ! +0.039 ⇣ ⌘ βall = 0.698 0.037 (stat) 0.049 (syst) . where theThis systematic decreases uncertainty on the weak-lensing the mass cali-# − ± measured by The weak-lensing masses are expected to yield the true cluster bration is accounted for in the uncertainty on the coefficient. In 24 mass on average, and thereby enable a robust calibration of other per centtension of the Monte Carlo samples, between the slope (of log(M #Planck) vs. Planck and by mass proxies (see discussion in von der Linden et al. 2014; Apple- log(MWtG)) is unity or larger; i.e. the evidence for a mass-dependent gate et al. 2014). Therefore, by identifying β = (1 b), these re- bias is at the 1σ level for these 22 clusters. Best Fit − clusters⇠ and CMB # Weighing the sults suggest that the mass calibration adopted by the Planck team, To further test for a mass-dependent bias, it is instructive to # include the additional 16 clusters in common between Planck and (1 b) 0.8, underestimates⦿ the true cluster masses by between 5 − ⌘ Giants (WtG). and 25 per cent on average. WtG thatand are not used the in the Planck motivationcluster cosmology analysis, # as /M these slightly extend the mass range probed. For all 38 clusters, we find a consistentfor and! morem precise" > result: 0.23 eV. 3.2 Evidence for500 a mass-dependent calibration problem . +0.15 0 68 0.11 MPlanck +0.059 MWtG − Planck By eye, Fig. 1 suggestsM that the ratio between the WtG weak- = 0.699 0.060 . 1015 M − ⇥ 1015 M lensing and Planck mass estimates depends MText on500 the/M cluster Text⦿ mass:WtG ! ⇣ ⌘ ! at masses . 6 1014 M , the mass estimates roughly agree, whereas In 4.9 per cent of the Monte Carlo samples, the slope is unity or ⇥ Figure 2. The direct comparison between M500 cluster masses measured by larger; i.e. the confidence level for a slope less than unity is 95 per the discrepancyPlanck appearsand significant by WtG. The for symbols more massive are the same clusters. as in Fig. To 1. The green line cent3. Figure 1. The ratio of cluster masses measured by Planck and by WtG, for quantify the evidenceand shaded for such regions a mass-dependentshow the best-fit linear bias, relation we use between the the logarithmic the clusters common to both projects. Solid symbols denote clusters which Bayesian linear regressionmasses and methodits 1- and developed 2-σ confidence by Kelly intervals (2007) (the to fit fit was performed with were included in the Planck cluster cosmology analysis (22 clusters) and log(MWtG) as functionlog(MWtG of) as log( functionMPlanck of) log( (fittingMPlanck the)). masses directly 3 We note that when using bootstrap realizations of an unweighted simple open symbols additional clusters in the Planck cluster catalog (16 clusters). avoids the correlated errors in the mass ratios one would have to linear regression as a more agnostic fit statistic, we recover the same slope, The red, solid line indicates a ratio of unity (no bias). The dashed red line account for if fitting the data as shown in Fig. 1). While we show indicates (1 b) = 0.8, the default value assumed throughout most of P16. − MPlanck as functionc 2014 of M RAS,WtG in MNRAS Fig. 2 to000 reflect, 1–5 that the weak-lensing The blue line and shaded regions show our best-fit mass ratio along with masses are our proxy for true cluster masses, we assign the Planck the 1- and 2-σ confidence intervals. Since the weak-lensing masses are mass estimates to be the independent variable to reduce the e↵ects expected to be unbiased on average, the ratio of Planck masses to weak- lensing masses is a measure of the bias (1 b) = M /M of the of Malmquist bias: MPlanck scales with the survey observable, and − Planck true Planck cluster masses as used in P20.