Multi-wavelength scaling relations (scaling relations 101)

Transcription

1 Multi-wavelength scaling relations (scaling relations 101) Gabriel W. Pratt (DSM - IRFU - SAp, CEA Saclay, France)

2 Argument Astrophysics put constraints on formation physics effect of non-gravitational processes Cosmology requires a mass scale we ll never measure a mass for every cluster detected in every survey use scaling laws to leverage statistical power of large surveys Cosmological interpretation depends on astrophysical knowledge Great progress in recent years (from X2 to 10%)

3 Perfect cluster population Similar internal structure (dark matter) log Q Power-law relations between observables Q and mass / redshift (gravity is scale-free) log M

4 Theoretical reality Dispersion Dispersion due to differences in: Internal structure log Q Orientation Large-scale environment Projection effects log M These deviations are ~lognormal (Central Limit Theorem)

5 Observational reality Additional sources of dispersion Additional dispersion due to: log Q Non-gravitational astrophysics Evolutionary effects Observational error log M These deviations are not lognormal

6 Observational reality Non-gravitational astrophysics GWP et al 2009

7 Observational reality Non-gravitational astrophysics GWP et al 2009

8 Observational reality Further uncertainty One really measures observable-observable relations (shear, too) log Q1 Additional scatter and uncertainty due to covariance between observables, leading to correlated errors log Q 2 M

9 Observational reality Further uncertainty Covariance may also be mass-dependent (and redshift dependent) log Q1 log Q 2 M

10 Covariance Pre-heating Gravity only Stanek et al 2010

11 Covariance Rykoff et al 2008

12 Observational reality Selection effects Selection will also bias your relation, especially if there is significant dispersion log Q1 log Q 2 M Extrapolation of your relation below your selection limit will likely be false Knowledge of the true dispersion is crucial

13 Evidence for larger scatter in L X -M Newly-discovered SZ-selected clusters cf X-ray selected sample L Gas density X-ray selected Planck Collaboration IV 2012 More morphologically disturbed than X-ray selected clusters Lower X-ray luminosity (on average) for their mass More scatter than for X-ray selected alone

14 Stacking Anderson et al 2014 quo2ng Dai et al 2007, Mantz et al 2010, Maughan et al 2007, Pra< et al 2009, Rozo et al 2008, Stanek et al 2006, Vihklinin et al 2009, Wang et al 2014 Stacked, optically-selected X-ray selected NB In some cases, considerably different mass ranges being probed Underestimate of scatter (Malmquist bias) in X-ray selected samples? Contamination in optically-selected samples?

15 Powerlaw fitting can be biased S. White, R. Angulo

16 And a power law might not even be the best fit Stanek et al 2010; also Le Brun et al in prep. Hartley et al 2009 Mergers preferentially send objects below mean relation at high mass AGN feedback ejects gas at low mass, plus more mergers

17 Some ways forward Tie down the true mass scale Lensing might (should) be able to do this But needs careful calibration on simulations Get better constraints on relations between observables Particularly between optical / lensing and X / SZ Better constrain covariance using observations Observe a representative richness-selected sample in X, SZ Selection effects Dangerous to estimate the mass from the observable used to detect it, especially at low SNR observational scatter especially critical here Use multi-λ observations simultaneously

18 Conclusions A holistic view is needed Scatter and covariance between mass proxies and true mass Needs tighter observational constraints Should be fully modelled in the analysis Selection effects Need to be quantified and modelled very carefully Especially in the presence of significant scatter, and at the detection limit Some frameworks exist already e.g., Allen, Evrard, Mantz, Maughan, Rozo, Rykoff

19 Happy st. Patrick s Day

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21 Strong evidence for NFW- type total mass profiles Typically seen in relaxed cluster samples X- rays lensing mean NFW fit mean NFW fit ~2 kev ~10 kev Pointecouteau et al 2005 (XMM observa2ons assuming HSE); see also Vikhlinin et al 2006 Postman et al 2012 (lensing using Subaru+HST observa2ons); see also Okabe et al 2013 c- M rela2on seems to be ~OK

22 Converging local scaling X- ray rela;ons M T Y sph M Chandra Chandra XMM XMM Vikhlinin et al 2006; Arnaud et al 2005 Sun et al 2011; Arnaud et al 2010 Huge improvement in recent years

23 Converging agreement with simula;ons Y X M HSE M HSE T CSF, HSE Arnaud et al 2007 ; see also Planelles et al 2014 Le Brun et al 2014, observa2onal data from Sun et al 2009, Vikhlinin et al 2009, Pra< et al 2009 Improved modelling of non- gravita2onal processes in simula2ons Use of synthe2c X- ray analyses (e.g., to measure Tspec and MHSE)

24 fgas Sun 2012, compiling data from Sun et al 2009, Vikhlinin et al 2006, Démoclès et al 2010, Rasmussen et al 2009