Joint Gravitational Lensing and Stellar Dynamics Analysis of

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

Goal: understand the formation and evolution of early-type galaxies Ellipticals: great regularity in photometric, spectroscopic and kinematic properties § Detailed study of the inner mass density profile of (distant) earlytype 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

Methods to study the mass profile of elliptical galaxies METHOD REGION RANGE Strong Lensing Inner z<1 Stellar Dynamics Inner z < 0. 1 Weak Lensing Outer z ~ 0. 1 – 1 X-ray Haloes Discrete tracers: GC/PN dynamics Outer z < 0. 1 Inner/Outer z < 0. 01

GRAVITATIONAL LENSING q Most direct probe to measure mass within the Einstein radius q Depends solely on gravity (no gastrophysics) LIMITATIONS: q Diagnostics of total mass: difficult to separate dark and luminous components q Mass-sheet degeneracy STELLAR DYNAMICS q Can allow in principle very detailed analysis of the orbital structure of the galaxy “dissect” galaxy in 3 D LIMITATIONS: q Scarcity of dynamical tracers at large radii q Mass-anisotropy degeneracy q at z > 0. 1 the extraction of detailed kinematic information (higher order moments) is more difficult

Breaking the degeneracies. . . Joint and self-consistent analysis: GRAVITATIONAL LENSING STELLAR DYNAMICS + REinst Accurate and (nearly) model independent determination of mass inside Einstein radius Reff Determination of the mass inside the effective radius (= inner regions)

Sloan Lens ACS (SLACS) Survey § § § Bolton et al. 2006 Treu et al. 2006 Koopmans et al. 2006 ~80 early-type lens galaxies at z <= 0. 35 HST images (F 435 W, F 614 W) Integral field spectroscopy for 17 systems Analysis of 15 SLACS galaxies: Lensing + Dynamics as INDEPENDENT PROBLEMS Lensing: SIE model, MEinst imposed as a constraint for the dynamical models Dynamics: power-law density profile, r µ r – g, spherical Jeans equations HIGHLIGHTS: Image credit: Adam Bolton & the SLACS team § Total density profile very close to ISOTHERMAL: log. slope g = 2. 01 ± 0. 03 § Power-law: excellent description of density profile inside Reff § No evidence for evolution in range z = 0. 1 – 1 (SLACS + LSD)

Motivation to develop a fully self-consistent approach q 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 q Modeling: spherical axisymmetric q More detailed information about the lens galaxy potential q Information about the dynamical structure

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

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

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

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

Dynamical Model § 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. The (unprojected) density and velocity moments of a TIC are analytical and easy to calculate. TIC 2 TIC 1 DF TIC 3 § Building blocks for the superposition: not orbits, but TICs: elementary systems (tori) derived from d DF, completely specified by energy Ej and angular momentum Lz, j total § surf. br. vlos slos + + =

SLACS lens galaxy J 2321: a case study for joint lensing & dynamics analysis (Czoske, Barnabè, Koopmans, Treu & Bolton 2008) HST-ACS image velocity map velocity disp. map zsrc = 0. 5342 zlens = 0. 0819 sc = 245 km/s REinst = 1. 68’’ Reff, B = 5. 50’’ total mass density profile: axisymmetric POWER-LAW model r(m) = r 0 mg , m 2 = Rc 2 + R 2 + z 2/q 2 BEST MODEL § inclination angle: 67 o. 8 [60. 0 – 68. 9] § lens strength a 0: 0. 468 [0. 467 – 0. 475] § logarithmic slope g: 2. 061 § axial ratio q: 0. 739 § core radius Rc ~ 0 [1. 996 – 2. 085] [0. 688 – 0. 760] Total density profile close to isothermal

J 2321: 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, F 814 W)

J 2321: combined analysis DYNAMICS moments map grid = 9 × 9 (1 pixel = 0. 67’’) Only data points with S/N > 8 are considered surf. br. vlos slos data surf. bright. grid = 50 × 50 (1 pixel = 0. 10’’) residuals reconstr. weighted DF reconstr. NTIC = 10 × 5 × 2 = 100

J 2321: dark and luminous mass M(r) Radial mass profile for the best model total mass luminous mass Jaffe profile Hernquist profile § “Maximum bulge”: luminous mass rescaled to maximize the contribution of the stellar component Meff ~ 2 × 1011 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 Reff for local ellipticals (assumption: mass follows light, i. e. constant M/L ratio)

SLACS sample: preliminary results J 0037 J 0216 zsrc = 0. 632 zsrc = 0. 524 zlens = 0. 196 zlens = 0. 332 best model: J 0912 J 0959 zsrc = 0. 324 zsrc = 0. 470 zlens = 0. 164 zlens = 0. 241 best model: g = 1. 97 g = 1. 94 g = 2. 13 g = 1. 79 Barnabè et al. in preparation

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

Conclusions q Joint lensing & dynamics: powerful instrument for the study of the density profile of distant E/S 0 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 q 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 g ~ 1. 8 – 2. 1) § dark matter fraction ~ 30 -35% within Reff q 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