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Strong Gravitational Lensing & Stellar Dynamics

Probing the mass distributions of ETGs

Léon Koopmans(Kapteyn Astronomical Institute) 

Kingston (CA), June 2009

Stellar Dynamics

(1) Galaxy formation models predict distinct DM density profiles (e.g. NFW97, Moore et al. 98)‏ (2) DM density profiles are modified by collisional and/or gravitational processes of baryons & stars. (3) Hierarchical models predict abundant CDM mass substructure (Moore et al. 1999), not (yet) found. (4) Strong scaling relations (FP/TF) are observed (e.g. Dressler et al. 1987; Djorgovski & Davis 1987).

The baryonic & DM mass distribution and their evolution are a direct measure of the (hierarchical) galaxy formation process,

in particular for early-type galaxies (i.e. merger remnants).

Galaxy Structure Formation & Formation 101

Masses & Mass profiles from Strong Lensing &

Galaxy Dynamics

Strong Lensing

Stellar Dynamics Weak Lensing

Baryonic + Dark Matteraround the Einstein Radius

CDM SubstructureGrid-based methods

Baryonic + Dark Matteraround the effective radius

Phase-space densityGrid-based methods

Environment &Outer DM halo

Grid-based methods

Integrated Approach

Breaking Degeneracies(mass-anisotropy,

mass-sheet, inclination)

LSD Survey• HST V, I, H• Keck ESI

SLACS Survey• HST B/V, I, H• VLT VIMOS-IFU• Keck LRIS• Gemini/Magellan• VLT X-shooter• Chandra

Slac(s)ers: Leon Koopmans Tommaso Treu Adam Bolton Scott Burles Lexi Moustakas Oliver Czoske Matteo Barnabè Simona Vegetti Raphael Gavazzi Matt Auger

The Sloan-Lens ACS Survey

Higher-z emission line HST F814W imageEarly-type galaxy

spectrum

(Warren et al. 1996, 1998, 1999)

Q0047-2808

SDSS spectroscopically selected lens candidates

The Sloan-Lens ACS (SLACS) Survey

Cycle – 13: SNAP-10174 (PI: Koopmans) : Snapshot imaging F435W/F814W – 39/49 Orbits, ACS Cycle – 14: GO-10494 (PI: Koopmans): Single-orbit multi color follow-up – 45 orbits, ACS+NIC SNAP-10587 (PI: Bolton): Snapshot imaging F814W – 55/118 Orbits, ACS Cycle – 15: GO-10798 (PI: Koopmans): Single-orbit multi color follow-up – 60 orbits, ACS/WFPC2+NIC GO-10886 (PI: Bolton): Single-orbit multi color follow-up – 60 orbits, ACS/WFPC2 Cycle – 16: GO-11202 (PI: Koopmans): Single-orbit multi color follow-up – 159 orbits, WFPC2+NIC

HST Follow-up of SDSS-spectroscopically selected lens candidates(talk by Treu)

SLACS: Spectroscopy-selected

- Lens selected- Uniform lens-galaxy criteria: E/S0- Emission-line selection- Blue starforming source provides good lens/source contrast

- State of the art: few x 105 targets- Lensing rate: ~1/2000

- Results: ~100 confirmed lenses

The Sloan Lens ACS (SLACS) Survey

Smooth Mass Profiles

Mass Modeling using Spherical Jeans Equations

Masses inside the Einstein Radius

Slope

Image Symmetry

In case of relatively symmetriclenses, mass can be determined

to a few % accuracy.

!tot ! r!!!

0.51.0

1.5

1.52.0

2.5

0.9

1.0

1.1

Assuming Spherical Symmetry

Mas

s de

viat

ion

(from

SIS

)

Combining with Stellar Dynamics

Constant M/L model versus SIS

R1/4 constant M/Ldensity profile

SIS density profilewith stellar M/L=0

Lensing mass isthe same

The structure of E/S0 galaxies

Koopmans et al. 2006, 2009

Density Slopes from the full HST-ACS sample (58 systems)

It is not well understoodwhy baryonic & DM add

to a combined ~1/r2 densityprofile, despite different

physics and starting conditions.

!!!LD" = 2.085+0.025"0.018 (68% CL)

Isothermal, but with intrinsic spread of <10%

The structure of E/S0 galaxies

Analysis of the SLACS-ACSsample with good lensing &

kinematic data shows nodependence of the slope on

(i) galaxy properties, (ii) redshift or (iii) environment

Koopmans et al. 2009

Correlations with global parameters

The structure of E/S0 galaxies

Log(L)

Log(L)

!!!SC" = 1.959± 0.077 (68% CL)

Koopmans et al. 2009

Density Profile from Scaling Relations (homology)

The structure of E/S0 galaxies

!!!LD" = 2.085+0.025"0.018 (68% CL)

!!!SC" = 1.959± 0.077 (68% CL)

Dependent on Lensing & Dynamics

Dependent on Lensing & Scalings

Constrain radial anisotropy:

Limits on orbital anisotropy

!!r" = 0.45± 0.25 (68% CL)

The structure of E/S0 galaxiesMass Fundamental Plane & Increase in DM fraction

Taking evolution in stellar M/L into account

(e.g. Cappellari et al. 2007,Proctor et al. 2008, Trujillo et al. 2004)

Mass Fundamental Plane= FP with SB ↔ SD

Self-consistent lensing& Stellar Dynamics

Going beyond spherical Jeans modelling

A SELF-CONSISTENT METHOD FOR LENSING AND DYNAMICS ANALYSIS

Axisymmetric density distribution: ρ(R,z)

Gravitational potential: Φ(R,z,ηk)

Maximize the Bayesian evidence allows model comparisonautomatically embodies Occam’s razor (MacKay 1992)

Best values for the non-linear parameters ηk

source reconstruction & DF reconstruction

LENSED IMAGE REC. DYNAMICAL MODEL

non-linearoptimization

vary ηkwhen converges

linear optimization linear optimization

Barnabè & Koopmans 2007

Monte Carlo 2-Integral f(E,Lz) Schwarzschild method

TIC

2TI

C 1

TIC

3to

tal

+

+

=

Σ v σDF

Bar

nabè

& K

oopm

ans

2007

moc

kre

cons

truc

ted

resi

dual

s∝ DF Σ < vz' > < v2

z' >

Dynamical Model = DF reconstruction

VLT Large Program

Spatially-resolved 2D kinematics of SLACS lenses

VLT VIMOS-IFU Large Program -Resolved Stellar Kinematics at z=0.08-0.35

• VLT VIMOS IFU Large program (77.A-0682): 14 lenses, observations spread over two semesters (HR-orange) plus 3 lenses in pilot program (HR-blue); Observing time 128 hrs (PI:Koopmans) -> Analysis: Czoske • Keck LRIS (long-slit/pseudo-IFU): 13 additional targets were scheduled; Observing time 5 nights (PI: Treu)‏

GOAL: Spatially resolved VLT/Keck kinematics data to be combined with HST gravitational-lensing data.

TOOL: Full Bayesian (ultra-fast; few seconds) non-parametric axisym. 2-Integral f(E,Lz) dynamical code to model these data iteratively, self-consistently with lensing data (grid-based).

See Barnabè & Koopmans (2007) for details and Czoske et al. (2008) and Barnabè et al. (2009) for first results.

VLT VIMOS-IFU Large Program

Pilot Targets

VIMOS IFU

Target MR zlens Reff OBs done

SDSS J2321 15.1 0.0819 2.2 5SDSS J0912 16.1 0.1642 3.4 4SDSS J0037 16.7 0.1954 1.2 9SDSS J0216 17.6 0.3317 3.0 14SDSS J0935 17.6 0.3475 3.6 12SDSS J0959 17.6 0.1260 1.2 4SDSS J1204 17.4 0.1644 1.5 5SDSS J1250A 17.3 0.2318 1.8 6SDSS J1250B 15.7 0.0870 3.1 6SDSS J1251 17.6 0.2243 3.6 12SDSS J1330 17.6 0.0808 0.8 3SDSS J1443 17.6 0.1338 1.2 4SDSS J1451 16.8 0.1254 2.5 7SDSS J1627 17.6 0.2076 2.1 11SDSS J2238 16.9 0.1371 2.2 6SDSS J2300 17.8 0.2282 1.8 10SDSS J2303 16.9 0.1553 3.0 11

(PI: Koopmans/Czoske)

VLT VIMOS-IFU Large Program

SLACS lenses covera wide range in redshifts and stellar velocity dispersions:(triangles: SAURON)

Probe high-mass endof the E/S0 mass function

Czoske et al. 2009

SLACS complements local E/S0 samples

Two-dimensional Kinematic Maps

Czoske et al. 2009, in prep.

Example: HST & IFS of J2321-097

HST B/V& I imaging

HST F435W HST F814W

Czoske et al. 2008

VLT VIMOS-IFU luminosity-weighted

spectrum

Example: HST & IFS of J2321-097

VLT VIMOS-IFU : Kinematic Fields

Integral Field Kinematics Major/Minor Axis Kinematics

Example: HST & IFS of J2321-097

The internal kinematic structure:The system is a slow rotator (see Cappellari et al.2007)

Czoske et al. 2008

Two-integral phase-space distributions

Barnabe et al. 2009

From the DFs the internal stellar density & kinematic fields can be reconstructed

Two-integral phase-space distributions

V/σ relation of SLACS lenses (open circles), shows that their ellipticity comes in most cases from anisotropic velocity dispersion tensors, not from rotation. (Binney 1977, 2005).

For comparison: Sauron E/S0s for slow (red) and fast (blue) rotators.

Barnabe et al. 2009

Flatte

ning o

nly du

e to r

otatio

n (iso

tropic

disp

ersion

)

Test of formation/merger histories: angular momentum

Total & Stellar Density Distributions

A 3D modeling procedure also provides a slope for the stellar density profile: difference total - stars -> DM

Barnabe et al. 2009

Dashed line: Einstein radius

Dotted line: effective radius

dot-dashed:outmore kinematic

data

total

stars

Indications of DM?

Total & Stellar Density Distributions

A fully Bayesian MCMC analysis provides formal errors on all parameters.

• Density slopes are close to isothermal• DM mass fraction inside Reff are around 20-30%, as found in other studies as well.

Total & Stellar Density Distributions

Absence of redshift-trends, average slope and scatter are consistent with simpler spherical Jeans analysis of 58 lenses

and with analyses of local E/SO galaxies (e.g. Gerhard et al 2001)

Barnabe et al. 2009

Triaxial & 3I vs Axi-symmetric & 2I

Use numerical simulations of the (dry) merger of twoelliptical galaxies to test our assumptions and code.

Use the end-product of this numerical simulation (stellar+DM; from Nipoti & Ciotti) to create and artificial lens, including obs. effects (seeing, IFU fibers, etc)

Make reconstruction using axi- symmetric + 2I code

Compare global quantities

Barnabè et al. 2009

***

Triaxial & 3I vs Axi-symmetric & 2I

Barnabè et al. 2009

Best reconstructions do reasonably well,despite some differences (more than in any real galaxy!)

Visual residuals

Also somedifference

in kinematics

Triaxial & 3I vs Axi-symmetric & 2I

However, thedensity slope is well

reconstructed in relevant range of radii

Density difference can be recovered via grid-based method

(Vegetti & Koopmans 2009)

No residuals left!

Softening in sim.

Slope well-reconstructed

Mass Substructure

More than meets the eye!

Grid-based LensingObserved Massive GalaxySimulated Massive Galaxy

Clumpy Dark Matter

Smooth Dark Matter

Stars

Modeling must be more sophisticated than simply parameterized!

Lensed Images Non-parametric model

Lensed Object

Galaxy + Lensed Images

Smooth mass model: Lensed images correlate strongly Clumpy mass model: Lensed images correlate less.

Exploit this to detect mass substructure

(e.g. Warren & Dye 2003, Koopmans 2005, Brewer & Lewis 2005; Suyu & Blandford 2006a&b, Vegetti & Koopmans 2009)

Grid-based Lensing

Detecting small-scale mass structure?

Note that near “critical curves”, the determinant of the inverse

magnification matrix go to zero.

We can use this matrix (assume κ=γ) and add a perturbation

We note that near the critical curves, a small perturbationcan cause large tangential changes in the images.

!"# =!

$! !%! !&1 !!&2

!!&2 1 ! !% + !&1

"!"'

d!"

d!#=

!1! $! %1 !%2

!%2 1! $ + %1

"

Lensing near critical curves is sensitive to mass substructure

Mathematical relations between image fluxes (fold/cusp relations break down due to perturbations -> indication of substructure

Xu et al. 2009

Lensing near critical curves is sensitive to mass substructure

The level of substructure affects by how much the cusp/fold relations are broken and can thus be used to measure the mass substructure mass fraction

Bradac et al. 2004

Lensing near critical curves is sensitive to mass substructure

Dalal & Kochanek (2002) set limitson fCDM based a half a dozen radiolenses with anomalous cusp/foldrelations

However: (1) The mass fraction seems too high(2) There are clear problems with some systems, indicating some systematic effects (scattering, microlensing, etc).

The jury is still out on this!

Direct Imaging of Mass Substructure

Going beyond flux-ratio anomalies

A Differential-Lens Equation

Koopmans (2005, 2009 in prep), Vegetti & Koopmans (2009)

S ! ! !x" S " ! !y ," ! !x""

To solve for (i) the source brightness distribution and (ii) the potential, using

with

! = !! !"" ( !! )

Conservation of sourcesurface brightness

The usual lens equation

Assume that the “best lens model” still givesimage residuals compared with the data:

Since:

one finds the relation :

Between source SB, potential and image residuals

Koopmans 2005

Linearized Differential Equation

Linearized Differential Equation

In algebraic form this reads:

This linear algebraic equation can be solved usinga Bayesian penalty function for the residuals

and standard Cholesky/gradient methods

(Koopmans et al 2005; Suyu et al. 2006/8; Vegetti & Koopmans 2009)

Example: CDM Substructure

Koopmans 2005

Simulation of lenssystem: SIE + SIS

SIS substructureof 108 solar mass

SIE: 1011 solar mass

Strong image distortion

Potential Correction

Reconstruction:SIS substructure

of ~108 solar mass

Best Smooth Model Residuals

Koopmans 2005

Example: CDM Substructure

Source Plane

!

Image Plane

Potential grid

Lensed Image grid

Delaunay tesselation

Higher resolution in higher magnification regions

Allows for faster and more accurate reconstruction

Adaptive Grid Method

(Vegetti & Koopmans 2009)

Example: CDM SubstructureAdaptive grids do remarkably well in reconstructing the mass substructure

Vegetti et al.

General Conclusions

The SLACS survey has yielded nearly 100 well-defined ETGs that have direct mass measurements, stellar kinematic data and deep HST mult-color imaging.

Analyses of this sample has yielded direct measurements of their density profiles in the inner regions, where interactions with baryons are important. They are close to isothermal (1/r2) but have intrinsic scatter.

Strong gravitational lensing can also detect and quantify mass substructure in ETGs at high redshifts (evolution!), which are visually undetectable (large M/L). Analyses of SLACS systems are underway.

• Much more ....