Bayesian analysis of joint

1. Bayesian analysis of joint strong gravitational lensing and dynamic galactic mass in SLACS: evidence of line-of-sight contamination Antonio C. C. Guimarães Laerte Sodré Jr. Departamento de Astronomia, IAG-USP, Brazil July 2007

2. Introduction • Motivation • mass is one of most basic galaxy properties and can only be found indirectly • mass estimate methods are based on different sets of assumptions • galaxy density profile is of fundamental astrophysical and cosmological interest – reflects dark matter properties and structure formation scenario • Oportunity • SLACS discovered dozens of galaxy-scale strong gravitational lenses among SDSS early-type galaxies • data are of very good quality and public • Means • gravitational lensing and stellar dynamics allow two independent mass estimates • Maximum Likelihood can find best parameter values of a model • Bayesian Evidence can find best model

3. The Data • SDSS: one quarter of the sky, measured spectra of more than 675,000 galaxies • LRG (Large Red Galaxy) sample: over 100,000 high-redshift (0.2 < z < 0.55) luminous galaxies selected by color and magnitude in SDSS • SLACS: Sloan Lens ACS Survey – HST snapshot imaging survey • * lens candidates (targets) selected by presence of composite spectra • * strong lensing of galaxies by massive field early-type galaxies E/S0 • * Einstein radii determined from HST images using strong lensing modeling of lenses and reconstruction of unlensed sources

4. lens source Einstein velocity redshift redshift radius dispersion 27 events compiled from Koopmans et al. 2006 and Gavazzi et al. 2007

5. Galaxy Mass Estimates Mass enclosed within the Einstein radius Strong Lensing Stellar Dynamics

6. Mass estimates comparison

7. Let’s relax the assumption of a Singular Isothermal Sphere (SIS) density profile Assuming a power law density profile SLACS sample = higher likelihood, but lower Bayes Evidence (extra freedom has its price)

8. source zs lens Vls zl A Vol observer

9. Let’s also consider a line-of-sight mass contamination models SIS power law

10. The likelihood of both mass estimate methods to give the same value • From the • likelihood distribution we can find: • the best fitting parameter • (maximum likelihood) • variance of best p • Bayesian Evidence • of the model Likelihood model parameter

11. Comparing Models/Hypotheses 1. Maximum Likelihood 2. Bayesian Information Criteria 3. Bayesian Evidence

12. Bayesian analysis A. Liddle et al. (2006)

13. Best Model: highest maximum likelihood, lowest BIC, highest Bayesian Evidence Likelihood contours

14. model model (SIS with no line-of-sight contamination)

15. Comparison among models and best parameters l.o.s. cont. 0 4% 14% 11% 9% 12% 0 4% 43% 14% 14% 17%

16. Some Conclusions about the hypotheses • to explain the discrepancy between the • “lensing mass” and the “dynamic mass” • (under our assumptions) • statistical and systematic hypotheses are excluded. • evidence indicates that discrepancy is due to lensing projection effects of line-of-sight mass contamination • (contamination seems to be more associated with material in the • lens vicinity – dependence only on lens area, not with distances) • however there is weak evidence in favor of clustering effect (as expected, since the sample is of field galaxies). • line-of-sight mass contamination interfers in the infered density profile obtained from joint lensing and dynamic analysis.

17. Summary Main Assumptions: sphericity and smoothness of lens galaxy mass distribution, power-law profile, no rotational support, constant mass-to-light ratio, concordance cosmology. Method: strong gravitational lensing and galactic dynamics to obtain two independent mass estimates. Likelihood and Bayesian analyses. Conclusion: line-of-sight mass contamination significant, affects profile determination by the joint lensing and dynamic analysis. Lens galaxy density profile flatter than SIS. Perspective: increase statistics of events, relax assumptions to explore more astrophysical and cosmological parameters.