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Keck NGAO Science: Strong Gravitational Lensing. Phil Marshall and Tommaso Treu September 2007. Outline. Examples of strong lensing science: The dark and stellar mass of elliptical galaxies out to, and beyond z = 1 CDM substructure: imaging the mass

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Keck ngao science strong gravitational lensing l.jpg
Keck NGAO Science:Strong Gravitational Lensing

Phil Marshall and Tommaso Treu

September 2007


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Outline

  • Examples of strong lensing science:

  • The dark and stellar mass of elliptical galaxies out to, and beyond z = 1

  • CDM substructure: imaging the mass

  • Super-resolving high redshift galaxies – and their velocity fields

  • “Kinematic lensing” - what a well-resolved multiply-imaged velocity field can do for you

  • Why can we not do this now?

  • Why will we need NGAO in the future?

  • What will we need NGAO to provide?


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The masses of elliptical galaxies

  • SEDs – and K-band photometry in particular – gives stellar mass

  • Gravitational lensing measures total mass, independent of dynamical assumptions

  • Combining the two gives the dark matter fraction, and a way of calibrating the masses of larger samples of non-lens galaxies

    Measuring mass (profiles) with

    strong lensing requires high resolution

    imaging

    The combination of gravitational

    lensing with stellar dynamics is

    extremely powerful


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CDM substructure: imaging the mass

  • Extended sources give giant arcs and Einstein rings

  • The multiple nature of the images allows source structure to be separated from lensing effect

  • Small scale perturbing masses can be imaged via this effect (eg Koopmans et al 2005)

108 Mo dark perturber is detectable – with HST ACS resolution imaging

K-band imaging gives:

  • smoother lens and source surface brightness

  • stellar mass of CDM satellites


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Super-resolving high-redshift velocity fields

  • Gravitational lenses typically provide an order of magnitude magnification – independent of the lens mass

  • Fainter, smaller, lower mass galaxies are made much more visible – observe with an IFU

    eg Swinbank et al 2006:

Galaxy-scale lenses are more easily modelled (as the source size is large compared to the lens mass fluctuations – and they are

MUCH more numerous. Select your own cosmic telescope!


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Outline

  • Strong lensing science:

  • The dark and stellar mass of elliptical galaxies out to, and beyond z = 1

  • CDM substructure: imaging the mass

  • Super-resolving high redshift galaxies – and their velocity fields

  • “Kinematic lensing” - what a well-resolved multiply-imaged velocity field can do for you

  • Why can we not do this now?

  • Why will we need NGAO in the future?

  • What will we need NGAO to provide?


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Kinematic-lensing

  • Traditional lensing exploits preservation of surface brightness to construct a model of the potential of the lens and the surface brightness of the source (e.g. yesterday’s talk)

  • Kinematic lensing exploits lensing achromaticity to:

    • Improve the model of the lens potential

    • Reconstruct and super-resolve the velocity field of a magnified source

    • It can be done with the emission lines of background source - and therefore simplifies lens subtraction

    • Lens galaxy dynamics come for free – but ignore this for now...


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'Simplest' Example:

SIE lens mass: , b/a, PA, x, y

Source surface brightness: M, r_e i, PA, x, y,

Source velocity profile: Vmax, r_0, i

Predict OSIRIS data cube,

optimise misfit between this and real data

13 parameters

Lens System Modeling

Use parametric forms:

Lens mass

Source surface brightness

Source line of sight velocity


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Model source plane Model image plane


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Model image plane Simulated data


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Can we do it now, at Keck? Simulated data Sample: SLACS


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Example. I: velocity field Simulated data

Test KLens on a SLACS lens:

  • Using the ACS image, model the lens using surface brightness only.

  • Add 'reasonable' velocity field parameters and generate synthetic OSIRIS image and velocity data.

  • Reconstruct the source and estimate error on parameters.

    • Unlensed

    • Unlensed w/ LGSAO

    • Lensed

    • Lensed w/ LGSAO

  • Assuming: 9500s exptime; line flux 5e-16 cgs; Z-band; Strehl 0.2


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OSIRIS+LGSAO Simulated data

OSIRIS

OSIRIS+lensing

OSIRIS+LGSAO+lensing


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OSIRIS Simulated data

OSIRIS+LGSAO

OSIRIS+lensing

OSIRIS+LGSAO+lensing

160

140

Source rotation velocity: 130-170 km/s

0.04

0.08

Velocity scale radius: 0.04 - 0.08 arcsec


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Example. II: lens model Simulated data

Simulated lens from SLACS:

  • Using the ACS image, model the lens using surface brightness only.

  • Add 'reasonable' velocity field parameters and generate synthetic OSIRIS image and velocity data.

  • Reconstruct the lens parameters for

    • LGSAO+OSIRIS emission line imaging

    • LGSAO+OSIRIS emission lines imaging + velocity field

  • Assuming: 10800s exptime; line flux 5e-16 cgs; Z-band; Strehl 0.15


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Clean lens subtraction! Simulated data

Vmax


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Does it work in practice? Simulated data We don’t know yet...

  • Half night allocated June 2006:

    • partially cloudy. 1.5 hours in three pointings (effectively 1800s) in Z-band. No detection

  • One night allocated September 2006:

    • completely lost to wavefront sensor failure

  • With current technology is hard!

  • 2007: system more stable, targets improved: Richard (Caltech) has data...


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Improvements wish list: Simulated data

  • Higher redshift targets. In Z, OSIRIS field of view is too small, need mosaicing with loss of time:

    • Much better at longer wavelengths. 3.2”x6.4” or 4.8”x6.4” is larger than lens (typically <3”). Dither on targets. Larger field is more efficient

  • Brighter targets:

    • With full SLACS (88 vs 23 last year) or SL2S we can find even brighter emission lines

  • Higher Strehl ratios:

    reduce exposure times and thus make it practical to collect sizeable samples.

    (Beginning to sound like NGAO)


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KLens: Summary Simulated data

  • AO + integral field spectroscopy + kinematic lensing =

    • Virgo-like resolution at cosmological distances

    • Velocity fields/masses (Tully Fisher..)

    • Improved mass models

      • Source/lens decomposition in emission line image

  • Currently hard with SLACS sample and present capabilities/time allocations. Things will improve with ongoing lens surveys

  • With NGAO this will work very well!


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Outline Simulated data

  • Strong lensing science:

  • The dark and stellar mass of elliptical galaxies out to, and beyond z = 1

  • CDM substructure: imaging the mass

  • Super-resolving high redshift galaxies – and their velocity fields

  • “Kinematic lensing” - what a well-resolved multiply-imaged velocity field can do for you

  • Why can we not do this now?

  • Why will we need NGAO in the future?

  • What will we need NGAO to provide?


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Feeder surveys Simulated data

Current samples (eg based on SDSS) are limited to z~0.2 and contain ~100 systems

In the NGAO era, the lens sample will be an order of magnitude larger, and extend to higher redshift (z>1) – interesting subsamples can be selected and exploited

SL2S (2005-) ongoing imaging survey based on CFHTLS, finding ~100 new lenses at z~0.5-1.0

DES (2009-2014) will find a few hundred lenses

PanSTARRS-1 (2008-2012) will find ~few 1000 lenses

SDSS-III (2010?) ~ SLACS x 10 at higher z?

LSST (2014-2024?) would find ~10,000 lenses

SNAP (2019-2021?) would find ~20,000 lenses

Dune (2019-2021?) would find ~few 100,000 lenses


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Ground vs. Space – what can JWST do? Simulated data

NGAO out-performs HST:

We expect JWST

to have resolution

no better than HST

bluer than 2 microns

- but background is lower

Detailed simulations will

show up the differences.

NGAO has planned

multi-object capability...


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Multiplexing over a 3' field of regard Simulated data

Lenses are rare – but a Multiplex IFU:

  • would speed up observation (simultaneous background monitoring)

  • and allow piggy-backing on the high-z program (their targets are more common)

  • and enable cluster lensing science (larger collecting area cosmic telescopes – but that's a whole other talk!)


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Summary: NGAO requirements Simulated data

As for the high-z galaxy program,

(eg high strehl imaging, sufficient spectral resolution to measure velocities to 20km/s, low background, large fraction of sky accessible etc etc)

but with a few additions:

  • > 4” IFU field of view (lenses magnify galaxies, such that ~all systems are 2-3” in diameter)

  • bluer filters broaden the range of accessible redshifts, and help in SED analysis of lensed sources

  • z, Y bands also enable lens galaxy absorption line dynamical mass estimates at z~1


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Extra slides Simulated data


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Strong Lensing Basics. I: Simulated data

  • Strong lensing can be seen as a mapping from the source plane (what would be seen without a lens) to the image plane (what is actually seen)

  • The transformation is the so called lens-equation:

  • =+()

For azimuthal symmetry


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Strong Lensing Basics. II: Simulated data

  • Deflection angle  is gradient of gravitational potential: lensing measures mass.

  • Lensing preserves surface brightness: magnification is given by the Jacobian of the transformation

For azimuthal symmetry


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Strong Lensing Basics. III: Simulated data

caustics

critical lines

0047-281

Koopmans & Treu 2003

Curves where the transformation is singular are called caustics and critical lines. They correspond to infinite magnification. Sources get multiply-imaged when they are inside caustics. They are typically highly magnified.


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SL2S Simulated data

  • Ground based selected candidates (from CFHT-LS)

  • AO-NIRC2 to confirm and exploit scientifically (hopefully in 2007B)

  • Lens redshift z~0.7

  • Source redshift z~1.4 (Ha in H band!)


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Generating 'Ideal' Image Plane Simulated data

Pixellate image plane: {i}

For each , use lens equation to calculate .

Map conserved quantities:

Lens Equation ->

i)

i

SB, vz <-Source model <-


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Recall lens equation: Simulated data

Constructing2

Need to compare:

observed image plane with model source plane

“Forward”:

Given true position, , find observed position(s), .

*Difficult!

“Backward”:

Given observed position, , find true position, .

*Easy!

... but it is not straightforward to map pixellated data onto source plane.


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Creating 'Model' Image Plane Simulated data

Convolve surface brightness with instrumental PSF.

Using exposure time, zero point, convert SB to counts.

Perform weighted convolution for line of sight velocity.

Ignore points for which no velocity measurement is possible.


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Broyden-Fletcher-Goldfarb-Shanno Simulated data method is efficient:

Gives set of best parameters:

Also gives approximate covariance matrix at minimum.

Finding Best Parameters

Finally, compute 2 for given parameters:

Minimize 2 over all free parameters.

This can be challenging since minimizing over many parameters. (Recall, simple example has 13 parameters!)


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MCMC Basics Simulated data

Markov Chain Monte Carlo (MCMC) allows us to sample points from an arbitrary probability distribution, P.

Given a probability distribution P(a) that we can evaluate for any a, create a 'chain' of points using the following rules:

1. From ai draw a new poisition a'from a proposal distribution, Q(a',a).

2. If P' > Pi : ai+1=a'

If P' < Pi: ai+1=a'with probability P'/Pi, otherwise ai+1=ai.

Results in {ai} sampled from true probability distribution, P.

Independent of starting point, a0, and proposal distribution, Q.

Need multiple chains to test for convergence:

variation within each chain = variation between chains


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Efficient MCMC Simulated data

MCMC is useful when dealing with parameter spaces with many dimensions.

Likely that some parameters are degenerate.

(e.g. Vmax and r_0)

Sampling with fixed step sizes along parameter axes is inefficient.

Instead, can use steps given by diagonalizing covariance matrix.


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Tommaso Treu, Phil Marshall and Laura Melling (UCSB) Simulated data

The kinematics of Einstein Rings


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Properties of lens mapping: Simulated data

  • Non-linear

  • Preserves surface brightness

  • Independent of frequency (ACHROMATIC)

  • Magnifies sources


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SLACS: examples Simulated data

See www.slacs.org and Bolton et al. 2006, 2007


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Why do we care? Simulated data

  • Lensing measure masses:

    • Exploiting lensing achromaticity improves knowledge of gravitational potential of deflector

  • Lensing magnifies, hence “gravitational telescopes”:

    • The internal structure of distant galaxies can be study with a typical factor of 10 improvement in sensitivity and spatial resolution