1. Matteo Barnabè Kapteyn Institute – Groningen University Joint Gravitational Lensing and Stellar Dynamics Analysis of Early-Type Galaxies OZ Lens 2008 - Sydney, 29 th September Collaborators: Léon Koopmans (Kapteyn), Oliver Czoske (Kapteyn), Tommaso Treu (UCSB), Adam Bolton (IfA), and the SLACS team

2.  Detailed study of the inner mass density profile of (distant) early-type galaxies  Understand the internal structure of early-type galaxies: shape of dark matter halos and correlation with total mass, orbital state  Investigate the evolution of the density profile and structural properties with time = with redshifts Goal: understand the formation and evolution of early-type galaxies Ellipticals: great regularity in photometric, spectroscopic and kinematic properties

3. Methods to study the mass profile of elliptical galaxies Strong LensingInnerz < 1 Stellar DynamicsInnerz < 0.1 Weak LensingOuterz ~ 0.1 – 1 X-ray HaloesOuterz < 0.1 Discrete tracers:Inner/Outerz < 0.01 GC/PN dynamics METHODREGIONRANGE

4. GRAVITATIONAL LENSING  Most direct probe to measure mass within the Einstein radius  Depends solely on gravity (no gastrophysics)LIMITATIONS:  Diagnostics of total mass: difficult to separate dark and luminous components  Mass-sheet degeneracy STELLAR DYNAMICS  Can allow in principle very detailed analysis of the orbital structure of the galaxy  “dissect” galaxy in 3DLIMITATIONS:  Scarcity of dynamical tracers at large radii  Mass-anisotropy degeneracy  at z > 0.1 the extraction of detailed kinematic information (higher order moments) is more difficult

5. Joint and self-consistent analysis: + GRAVITATIONALLENSINGSTELLARDYNAMICS Determination of the mass inside the effective radius (= inner regions) Accurate and (nearly) model independent determination of mass inside Einstein radius R Einst R eff Breaking the degeneracies...

6. Sloan Lens ACS (SLACS) Survey  ~80 early-type lens galaxies at z <= 0.35  HST images (F435W, F614W)  Integral field spectroscopy for 17 systems Analysis of 15 SLACS galaxies: Lensing + Dynamics as INDEPENDENT PROBLEMS Lensing : SIE model, M Einst imposed as a constraint for the dynamical models Dynamics : power-law density profile,   r – , spherical Jeans equations HIGHLIGHTS:  Total density profile very close to ISOTHERMAL: log. slope  = 2.01 ± 0.03  Power-law: excellent description of density profile inside R eff  No evidence for evolution in range z = 0.1 – 1 (SLACS + LSD) Bolton et al. 2006 Treu et al. 2006 Koopmans et al. 2006 Image credit: Adam Bolton & the SLACS team

7. Motivation to develop a fully self-consistent approach  The data contain a wealth of information: make full use of the abundant information available from the data: lensed image structure, surface brightness profile and kinematic maps of the lens galaxy  Modeling: spherical  axisymmetric  More detailed information about the lens galaxy potential  Information about the dynamical structure

8. image credit: the SLACS team High resolution imaging with HST-ACS or HST-WFPC2; single 420s exposures in B and I bands (F435W and F814W filters) Lens galaxy subtracted LENSED IMAGE HST and NICMOS images of the galaxy surface brightness distribution Maps of of first and second l.o.s. velocity moments (VLT-VIMOS 2-dim integral field spectroscopy and Keck long-slit spectra) LENS GALAXY image data  surface brightness l.o.s. velocity v los l.o.s. velocity dispersion  los

9. CAULDRON: A SELF-CONSISTENT METHOD FOR JOINT LENSING AND DYNAMICS ANALYSIS (axisymmetric) density distribution:  (R,z) Gravitational potential:  (R,z,  k ) Maximize the bayesian evidence allows model comparison automatically embodies Occam’s razor (MacKay 1992) Maximize the bayesian evidence allows model comparison automatically embodies Occam’s razor (MacKay 1992) Best values for the non-linear parameters  k source reconstruction & DF reconstruction LENSED IMAGE REC. DYNAMICAL MODEL non-linear optimization vary  k when converges linear optimization Barnabè & Koopmans 2007

10. linear optimization LENSED IMAGE REC. CAULDRON: A SELF-CONSISTENT METHOD FOR JOINT LENSING AND DYNAMICS ANALYSIS Axisymmetric density distribution:  (R,z) Gravitational potential:  (R,z,  k ) Maximize the bayesian evidence allows model comparison automatically embodies Occam’s razor (MacKay 1992) Best values for the non-linear parameters  k source reconstruction & DF reconstruction DYNAMICAL MODEL non-linear optimization vary  k when converges linear optimization Barnabè & Koopmans 2007 linear optimization LENSED IMAGE REC.

11. L sd Lensed Image Reconstruction s = source d = observed lensed image (data) L = lensing operator (describes how every source pixel is mapped onto the image plane) Pixelized source reconstruction method (Warren & Dye 2003, Koopmans 2005) Includes regularization, PSF blurring, oversampling L s = dExpressed formally as a linear problem: L s = d

12. CAULDRON: A SELF-CONSISTENT METHOD FOR JOINT LENSING AND DYNAMICS ANALYSIS Axisymmetric density distribution:  (R,z) Gravitational potential:  (R,z,  k ) Maximize the bayesian evidence allows model comparison automatically embodies Occam’s razor (MacKay 1992) Best values for the non-linear parameters  k source reconstruction & DF reconstruction non-linear optimization vary  k when converges linear optimization Barnabè & Koopmans 2007 LENSED IMAGE REC.DYNAMICAL MODEL linear optimization DYNAMICAL MODEL linear optimization

13. TIC 2 + + = surf. br.DFv los  los  TWO-INTEGRAL SCHWARZSCHILD METHOD (Verolme & de Zeeuw 2002) extended and sped up through a novel Monte Carlo approach: one full dynamical model in ~ 10 sec. Dynamical Model TIC 1 TIC 3 total  Building blocks for the superposition: not orbits, but TICs: elementary systems (tori) derived from  DF, completely specified by energy E j and angular momentum L z,j  The (unprojected) density and velocity moments of a TIC are analytical and easy to calculate.

14. HST-ACS image z src = 0.5342 z lens = 0.0819  c = 245 km/s R Einst = 1.68’’ R eff,B = 5.50’’ SLACS lens galaxy J2321: a case study for joint lensing & dynamics analysis velocity mapvelocity disp. map (Czoske, Barnabè, Koopmans, Treu & Bolton 2008)  (m) =, 00 mm m 2 = R c 2 + R 2 + z 2 /q 2 POWER-LAW total mass density profile: axisymmetric POWER-LAW model BEST MODEL  inclination angle: 67 o.8 [60.0 – 68.9]  lens strength  0 : 0.468 [0.467 – 0.475]  logarithmic slope  : 2.061 [1.996 – 2.085]  axial ratio q: 0.739 [0.688 – 0.760]  core radius R c ~ 0 Total density profile close to isothermal

15. J2321: combined analysis LENSING image grid = 100 × 100 source grid = 40 × 40 1 pixel = 0.05’’ blurring operator in the lensing matrix accounts for the PSF of the instrument (HST-ACS, F814W)

16. DYNAMICS surf. bright. grid = 50 × 50 (1 pixel = 0.10’’) moments map grid = 9 × 9 (1 pixel = 0.67’’) Only data points with S/N > 8 are considered N TIC = 10 × 5 × 2 = 100 surf. br.v los  los data reconstr. residuals J2321: combined analysis reconstr. weighted DF

17. J2321: dark and luminous mass  “Maximum bulge”: luminous mass rescaled to maximize the contribution of the stellar component M eff ~ 2 × 10 11 M  ; 5.2 (M/L) B  Dark matter fraction: ~15% at 5 kpc, ~30% at 10 kpc  SAURON: dark matter fraction of 30% within one R eff for local ellipticals (assumption: mass follows light, i.e. constant M/L ratio) M(r) total mass luminous mass Jaffe profile Hernquist profile Radial mass profile for the best model

18. SLACS sample: preliminary results Barnabè et al. in preparation J0037 z src = 0.632 z lens = 0.196 best model:  = 1.97 J0216 z src = 0.524 z lens = 0.332 best model:  = 2.13 J0912 z src = 0.324 z lens = 0.164 best model:  = 1.94 J0959 z src = 0.470 z lens = 0.241 best model:  = 1.79

19. A Crash Test for CAULDRON CRASH TEST: the 2-Integral axisymmetric CAULDRON code is applied to a situation which severely violates its hypothesis (a non-symmetric N-body system) Observables cannot be reproduced to the noise level: the single power-law model is an over- simplified description here Barnabè, Nipoti, Koopmans, Vegetti & Ciotti 2008 (submitted) LENSING DYNAMICS RESULTS:  Total density slope recovered (< 10%)  Total mass radial profile: within ~15%  Total ang. momentum, V/  ratio, anisotropy parameter  : within 10-25% (if rotation in the kinematic maps)  Dark matter fraction within R eff reliably recovered (~10% of total mass),  limitations: flattening, lensed source (requires detailed potential corrections, e.g. adaptive lensing code of Vegetti & Koopmans) CAULDRON IS RELIABLE EVEN IN A WORST-CASE SCENARIO true total density profile recovered profile: “face-on” data-set recovered profile: “yz-plane” data-set recovered profile: “zx-plane” data-set

20.  Joint lensing & dynamics: powerful instrument for the study of the density profile of distant E/S0 galaxies  The inclusion of stellar kinematics constraints allows to break degeneracies that would arise if lensing alone was used  Several fundamental structural quantities are robustly recovered even in a worst case scenario  First in-depth analysis of a sample of elliptical galaxies at redshift beyond ~0.1  Power-law total density distribution: simple yet very satisfactory model  Total density profile close to isothermal (slope  ~ 1.8 – 2.1)  dark matter fraction ~ 30-35% within R eff  Future work:  Extend the analysis to the entire sample of SLACS lens galaxies (17 with VLT-VIMOS IFU spectroscopy, 13 with Keck long-slit spectroscopy)  Extend CAULDRON flexibility: 3-integral models Conclusions