gravitational lensing, dark matter and...

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GRAVITATIONAL LENSING,DARK MATTER AND

COSMOLOGY

Lensing as a cosmological andastro-particle-physics tool.

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Not so hidden agenda…

-- Why is this interesting astrophysics?

-- How does GL test cosmology?

-- How does this link to particle physics?

(Increasing interlinking between astro andparticle physics)

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PLAN• Gravity’s role in cosmology• Gravitational lensing—very

basic theory• Strong gravitational lensing –

dark matter clustering?• Microlensing and the halos of

galaxies—small dark matterlumps?

• Weak gravitationallensing—dark matter and darkenergy?

• Clusters and largerstructures—lensing as acosmological tool.

• Towards , and ww- wherewe are headed.

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Classical Cosmology1920s: Observations by Hubble, theory by Friedmann, Robertson,

Walker, etc.Central to this idea is that the Universe is (on large scales) is

homogeneous and isotropic. It’s described by the Robertson-Walker metric

ds2 = dt2 – a2(t)/c2 (dr2/(1-kr2) + r2 (d 2 – sin2 d 2))

The evolution of the Universe (again on scales much bigger thangalaxy clusters) is described by the evolution of a(t).

This evolution is determined by gravity. On intermediate scales(clusters of galaxies down to galaxy scales), gravity also dominatesthe growth of perturbations.

It all boils down to gravity! The evolution depends on GR and thecomposition of the Universe.

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Dark Matter…• First evidence

in clusters ofgalaxies : FritzZwicky 1933–velocity ofgalaxies in theComa clustertoo high for themass ingalaxies.

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We also now knowabout dark matterin Coma throughthe temperature ofthe loose gasbetween thegalaxies—it’s aBremsstrahlung-emitting plasma atT~107 K

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Additional evidence from the dynamics ofgalaxies throughout the 1960s by VeraRubin and her collaborators.

Spiral galaxy disks are rotationallysupported (no evidence for disksshrinking or expanding in last ~10billionyears). But Vrot too large for observedstellar (and gas) mass.

Original evidence for DM wasall dynamical.

Deviations from V=HD

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… and Dark EnergyIn 1998, two research groups

“independently” found that theUniverse’s expansion wasaccelerating– Dark Energy!

Note: Supernovaemeasure thedeceleration of theUniverse: roughly Dm-2

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What does Dark Energy do?Dark matter has an effect

on the expansion of theUniverse much likenormal matter.Whether it’s cold (non-relativistic atdecoupling, P=0) or Hot(relativistic, P= /3), its

presence slows theexpansion:

0/

3/)3(4/

<

+=

aa

PGaa

&&

&&

To get acceleration, need

P < - /3. In cosmologists’ jargon, w = P/ < -1/3.

Can such a thing exist?

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Dark Energy

Yes. One example:

The Cosmological constant —the infamous

“greatest blunder” of Einstein:

w = -1!

Other possibilities– Vacuum energy (just like acosmological constant).

More generally, any scalar field will give

wf -1 as the kinetic term and spatial gradientsvanish (this is how inflation works, after all).

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Dark Energy—alternate models

Not all have w=-1: a popular alternative

(Quintessence) has w>-1 (but <-1/3 in thematter dominated era).

Different Dark Energy models

predict different w(z) behavior!

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Why the composition matters

The Content affects the growth of thescale factor (via the Friedmann &acceleration equations):

3/)3(4/ PGaa +=&&

The content affects the growth ofstructure via the Jeans equation (andmore complicated effects such asneutrino free streaming).

Also, we’d like to know what the Universe is made of!

kG

a

aH ==

3

8

2

2

2&

GH 42 =+ &&&

Equations for a(z) (or a(t)) Measure (z), where =d /

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Why dark matter and dark energymatter…

The effect on the cosmological equations can be describedby the evolution of the Hubble “constant” H(z) (sinceredshift depends on time).

The effect on the growth of structure can be describedanalytically in the linear perturbation regime; after that,simulations are needed.

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Numerical simulationsNumerical simulations

We can simulate the formation ofdark matter structures quite well.(only gravity)

Simulating the formation ofgalaxies is a very complexproblem.

Best to use something thatmeasures gravity!

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Movie from theZurichcomputationalastrophysicsgroup—inphysical units(note the earlyexpansion).

The areasimulated willbecome a richcluster

(but gravity isnearly scale-free,so this could beany patch largerthan the Jeanslength)

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Best to use something thatmeasures gravity!

8/16/07 NEPPSR 17GIF simulations, Colberg et al.


Example of the galaxydistribution based onsemi-analytic models.

Star formation SNe feedback Chemical enrichment Gas infall Merger history

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Simulations vs. reality

We can compare these semi-analyticmodels with the galaxy clusters we see inthe sky.

But the comparison

is sensitive to the

star formation

details!

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Best to use something thatmeasures gravity! Find the Dark

matter

8/16/07 NEPPSR 20Mathis et al. (2003)


low density (void) high density (cluster)

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Dark Matter on multiple scales

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Dark Matter

For example, the orbital speed of stars ingalaxies depends on the Mass: a constantrotation speed implies that the enclosed massgrows with radius!

constant mass

distribution

edge of visible galaxy

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Other indications of DM• X-ray emission from clusters—thermal emission

in a deep gravitational potential well.

• Infall velocities of galaxies into clusters andfilaments.

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Gravitational Lensing

One way is by using thefact that mattercurves space-time.The more mass, themore space iswarped.

The curved space altersthe path of light,causing it to bend.This is gravitationallensing.

The deflection of light

predicted by Einstein

was the first test of

GR (in 1919)!

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Back to Einstein….The first Lensing calculation made in 1912

(never published)

note lensing diagram!

A short paper in 1936 (prompted by Rudi Mandl)

But even he didn’t get everythingright…

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Simplifying conditions

1) Deflection is small (not near Rs)

2) Deflection localized along line of sight(“thin lens approximation”)

These make the path of the light rays fromthe distant sources much easier tocalculate!

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Back to gravitational lensing.

the lensed backgroundobject is often atCosmologically significantdistances:

For example HE0435– agalaxy at z=0.42, with thesource at z=1.69.

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• Lens Equation:

• Deflection Potential:

where

Notation and Basic Lens Relationships

convergence

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If the source is right behind thelens…

Einstein rings!

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Strong Lensing

• occurs whenmultiple valuesof solve thelens equation.

MULTIPLEIMAGING—canreconstruct and solve for ( ) (and M( ))directly

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Strong lensing isspectacular– butless usefulcosmologically fortwo reasons:

1) It only tells us aboutthe highest densityregions

2) The arcs arestrongly affected bysubstructure.

It Does, however, allowus to determine themass distributionvery precisely.

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Example: CL0024+1654

Measure the clumpiness of Dark Matter—constrainthe self-interaction rates.

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Soucail et al. 1987 (A370)

Fort et al. 1988 (A370)

Lynds & Petrosian 1989 (A2218; Cl 2244-02)

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Microlensing…DM inside galaxies

• Gravitational lensing does not require hugemasses– any point mass will generate a splittingif along the line of sight. However, d ~M1/2, sothe splitting gets small as the masses get small.

Easy to remember:

A galaxy has M~1012 Msun ~1”.

A galaxy cluster has M~1015 Msun ~30”

A star has M ~ 1 Msun ~10-6”

Microlensing!

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The images cannot be resolved—but theamount of light we receive is increased.

We detect microlensing by the flux change.

Lensing probability ~ 10-7–monitor millions of stars!

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Why is this important

Microlensing is a good way to detect“machos”—Massive Compact Halo Objects.These could be dark matter.

The results– after 15 years of surveys:

There aren’t enough events for Machos to be thedark matter in galaxies.

(<8% of the halo – EROS2 collaboration (2006)

(This is good for Dark Matter searches)

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Weak Lensing• If there is only one

image, there is noway to find theunlensed position,so the deflectioncannot be measureddirectly.

• However, if thelensed object isextended, we canuse the shape!

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Object appears in a different location

Object is stretchedtangentially

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If galaxies were dots…

Galaxies have manyshapes—many areflattened disks—theirshape depends onthe orientation!

So the shape you see ismostly influenced by theshape/orientation.

Need to measure manygalaxies and measurethe statistical properties

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We approximate each source as an ellipse

with position angle and (scalar)

ellipticity:

where a and b are the semi-major and

semiminor axes.

We can also define a tensor ellipticity

or equivalently a complex ellipticity(also called polarization).

What can we understand fromobservational data?

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Notation and Basic Lens Relationships

}shear

magnitude of shear

orientation

The convergence , magnifiesthe image isotropically.

We also define , the shear, thetraceless part of the Hessian ofthe deflection potential.

The shear deforms a circularsource to an ellipse.

circular sourceConvergence alone

Shear and convergence

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What can we understand fromobservational data?

Gravitational Lensing is a surface brightness conserving map.

It can be shown that the ellipticity of an object transforms as:

Assuming ,

By making the

approximation that

(weak lensing limit ):

In other words the galaxies don’t have apreferred orientation!

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Notation and Basic Lens RelationshipsKnowing

and

We get:

where

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So can be rewritten as:

where:

Using , and ignoring the random intrinsic ellipticity:

since ,

Direct Methods of Reconstruction:Mapping

Introduced by Kaiser and Squires in 1993.

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The solution is:

where .

(minus) tangential alignment of ellipticity of

galaxy at position relative to :


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Where However,

the random intrinsic ellipticities introduce a white spectrum noise and

consequently the noise diverges at large x. Further, the denominator

blows up x=xg. The problem can be cured by introducing a

filter.

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We can map the mass distribution from the background galaxy ellipticities

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Appendix I: Shape MeasurementGravitational Lensing is a surface brightness conserving map:

or

If we identify galaxies and measure their quadrupole moment:

the moments transform as:

So, we define the intrinsic ellipticity parameters as:

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How to apply this to data:

To measure the shear field (andhence ), need to sample theellipticity of extended objectsbehind the mass. Luckily,galaxies are big and bright, andubiquitous (~50 billion withinobservable Universe).

Many galaxies need to be sampledat each location to remove theeffect of the random individualgalaxy orientation with respectto us.

Distance estimates to the galaxiesallow deprojection of intoactual mass density.

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Weak Lensing needs

• Deep imaging: need to detect objectsbehind the masses!

• Good “seeing”: need to be able tomeasure the shapes of the distantgalaxies

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1.6% of survey

Genericproblem—screen resolution istoo low!

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0.5% of 1.6%...

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WEAK LENSINGTyson 1990 (A1689, CL1409+52)

Kaiser & Squires 1993

convergence map derived from

Hubble volume simulation; e.g.

Evrard et al. (2002) (8.6 x 8.6 deg)

convergence maps; Hamana 2001

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Cosmological Signals

Note that WL measures growth as well as distance, so it givestwo windows into to dark energy!

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N(M,z)

The growth of mass clustering is a directcomparison with cosmological simulations.

N(M,z) is a sensitive probe of w at z>0.4.

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Why N(M,z)

From Hennawi et al.2001

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Shear Correlation and PowerSpectrum

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Two basic techniques

• Shear correlation power spectrum

• Tomography—redshift cross-correlationmethod.

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Power Spectrum of LensingTaken from Bernstein,2005

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Powerspectrum

Note the power atl=100-1000(beyond thatnonlinear effectsare really messy)

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Cross-correlation Method

Ratio of De ection Angles:

No knowledge of foreground mass is required!

Needs very goodredshift resolutionand extremelysensitive to bias inphoto-zs!

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Beyond the DLS: upcoming surveysSurvey Sq. Degrees Filters Depth Dates Status

CTIO 75 1 shallow published

VIRMOS 9 1 moderate published

COSMOS 1 (space) 1 moderate complete

DLS (NOAO) 36 4 deep complete

Subaru 10 2 deep 2005 completeCFH Legacy 170 5 moderate 2004-2008 observingRCS2 (CFH) 830 3 shallow 2005-2007 approved

VST/KIDS 1700 5 moderate 2006-2008? proposedDES (NOAO) 5000 4 moderate 2008-2012 proposed

Pan-STARRS ~10,000? 5? moderate 2006-2012? ~funded

LSST 15,000? 5? deep 2010-2020? proposed

JDEM/SNAP1000+(space)

9 (NIR) deep 2012-2015? proposed

Courtesy of Bernstein, 2005

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What’s needed?

Two approaches– Maximize the numerator (from the Ground)

Minimize the denominator (from Space)

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From the Ground: LSST

• 8.4m telescope

• 10 sq. degree FOV

• 10 Gigapixel Camera

• <5 second readout

• In central Chile

Image the sky every

two weeks to R=24

Build up deep images!

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LSST is a huge project

• Partners and Sponsors– Brookhaven National Laboratory (BNL)– Google Corporation– Harvard-Smithsonian Center for Astrophysics– Johns Hopkins University– Lawrence Livermore National Laboratory (LLNL)– Lucent Technologies– Microsoft Corporation– National Center for Supercomputing Applications (NCSA)– National Optical Astronomy Observatory* (NOAO)– National Science Foundation (NSF)– Stanford Linear Accelerator Center (SLAC)– Stanford University– The Research Corporation*– University of Arizona*– University of California, Davis (UCD)– University of Illinois at Urbana-Champaign– University of Washington*– US Department of Energy, Office of Science

Private-Public fundingmodel. Has ~$30M inprivate funding already.

Was granted $15M inNSF funds on 9/1/05applied for MRSECfunds in December 06

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The devil is in thecamera—

And the dataanalysis!

10 Gigapixel, 2times/minute:

58 Tb of data pernight!

Not quite colliderdata rates…

…but galaxies,unlike electrons,are not all thesame!

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Why the ground?

• Cheaper.

• Can build bigger telescopes—go fainter inthe optical

• Larger grasp—all sky surveys are feasible.

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Why Space?

• Betterresolution—measureshapes better.

• Stability! Instrumentaleffects easy tocalibrate.

• Low Background—canobserve into IR and tohigher redshifts

The goal—Dark Energy JDEM

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Destiny Mission Concept

1.65m telescope at L2

A possible JDEM implementation:

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Weak Lensing Measurement

Destiny will conduct aWeak Lensing surveyas an independent,complementarytechnique for increasedaccuracy and precisionon the determination ofthe dark energyequation of state.

Destiny

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Predicted Survey Results

Assuming a Flat Universew=wo +wa(1+zpivot)

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ConstraintsFrom 2001 publicity!

2010 should read 2017 orlater!

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Timeline

LSST will likely not be completed until 2012at the earliest– first science results by2014.

JDEM, like all of NASA, is in limbo based onthe space priority. NASA/DOE are fundingdevelopment work for a few M$/yr.

Incremental progress on w,w’ until then.

(CFHTLS will double depth of DLS by 2009)

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Lensing constraints on DM;1E0657-558 (Clowe et al. 2006)

This cluster was first discovered in 1994; it’sremarkable because it’s one of the hottest

Imaging revealsthat it is twoclumps, and thespectroscopyshows that thetwo clumps are atthe same redshift

(z=0.296)—

For a standardcosmology, theseparation is0.72 Mpc.

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X-rays reveal what’s going on.

A shock! The lower mass cluster (right) has just rammed through thehigher mass one.

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Why this is useful

The subcluster velocity is estimated from the shock at 4500km/s!

(about 100 million years since the collision)

The galaxies, however, are made from stars—which behave like acollisionless gas—the two galaxy subclumps passed through eachother. The gas, on the other is slowed by ram pressure.

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Separate out the gas from thegalaxies (and DM)

We can estimate the stellar mass and the gas mass—the stellar massfrom the NIR luminosity (these are elliptical galaxies and so their NIRlight measures the integrated amount of star formation– Mstar L_I(with a M/L ratio of ~2)

The gas mass is measured by using the fact that the emission is(mostly) thin thermal Bremsstrahlung, so that I_x ne

2

Making some assumptions about the triaxiality of the gas, can derive the

Mass from the density and the size. (with ~10% uncertainty).

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The baryonic mass is in the gas,not the stars (primarily)

In alternative gravity theories, the mass and thus the gravitational lensingeffect is expected to be where the mass is. In the absence of DM, the gashas ~5x the mass of the stars, so the lensing effect should trace the gasand not the galaxies.

CDM, however, is collisionless, so if dark matter exists (and is thedominant contributor to the mass), then the lensing effect should match thestars.

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Punchline

The lensing signal follows the galaxy peaks—however, offset slightly towardsthe x-ray gas positions (why? Because the gas has mass, too!)

Inconsistent with X-ray positions at the 8sigma (for each peak) level.

The shift corresponds to 15+-10% of the mass being in the gas, consistent withan CDM/to baryon ratio of 6-7 as in the standard cosmology.

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Results from maximum likelihoodanalysis: direct comparison withresults from numerical simulations.

M200=(8.8±0.7) x 1011 h-1 M

Good agreement withCDM prediction!

Halo mass and extentHalo mass and extent

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Flattening of dark matter halosFlattening of dark matter halos

ehalo= f elens

Halos are aligned with the light Spherical halos excluded with 99.5% confidence Good agreement with CDM predictions

We use a simple model:

and determine f

gravitational lensing, dark matter and...

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