Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
Gravitationallensing
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 ....