# Weak Lensing Workshop Schedule

Work is the operative syllable in this workshop so we have scheduled only six hours of talks during this two day meeting. The rest of the time will be taken up by group or private discussions. Whether or not you are giving a scheduled talk please bring with you any provocative or informative ideas or results, on transparencies if you like. There is also plenty of blackboard space.

All talks will be held in Curia II of Wilson Hall (WH2W)

Thursday, December 12

Chair: Chris Metzler
11:00	Albert Stebbins
Organizational Details
11:10	Gordon Squires
Update on cluster scale observations
12:00	Eelco van Kampen
Testing weak lensing methods using a catalogue of cluster models
12:30	Donn MacMinn
Weak lensing statistics and techniques with the Sloan Digital Sky Survey
13:00
Lunch
Chair: Istvan Szapudi
14:30	Andrew Jaffe
Lensing by gravity waves
14:40	Sergei Kopeikin
Propagation of light in the stationary field of multipole gravitational lens
15:00   Roger Blandford
Galaxy-galaxy lensing in the Hubble Deep Field
15:30
Break
16:00
Private Discussions

Friday, December 13

Chair: Albert Stebbins
09:30	Bhuvnesh Jain
Weak lensing by large-scale structure:  Linear and non-linear regimes
10:15	Francis Bernardeau
Weak lensing statistics in the quasi-linear regime
11:00
Break
11:30	Daniel Holz
A new method to get amplification/shear statistics in inhomogeneous cosmologies
12:00	Nick Kaiser
Sampling strategy for LSS weak lensing surveys
12:30
Group Discussion - A weak lensing telescope
13:00
Lunch
14:00
Private Discussions or Tour
15:30
Chair: Francis Bernardeau
16:00	Alexandre Refregier
Weak lensing by large-scale structures with the FIRST radio catalog
16:20   Ben Metcalf
Lensing of the cosmic microwave background
16:40
Group Discussion



## Organizational Details

• Some participants may wish to schedule discussion groups on topics of particular interest during the "private discussion" periods. Please let the organizers know so that they may be announced.
• Please try to arrange any rides to the restaurant and/or hotel before the end of the day.
• If your are going to any of the organized dinners on Thursday evening you must sign up for them before the end of the day.
• If you are interested in taking the Fermilab tour on Friday afternoon you must sign up for it at the registration desk.

## Group Discussions

We have scheduled some time in Curia II for discussions of specific, but as yet unspecified topics. Some topics which have been proposed are

• A weak lensing (?/SNe search?) telescope: Strategy and scientific goals. Existing/proposed large cameras: what can you do with the time they will get?
• What are the important issues regarding the structure of galaxy clusters which can be addressed by weak lensing? How accurate a surface mass profile can one obtain? A lensing defined cluster sample?
• Lensing of the Microwave Background. What can be measured from MAP and COBRAS/SAMBA? from VSA and VCA? What do we learn that we don't know better from the C_l's? Lensing of other diffuse emission.

We would would welcome your suggestions for topics, e-mail us.

## Private Discussions

You may take this time to discuss privately with other individuals, or groups of attendees on topics of particular interest to you. Curia II, the tables in the 2nd floor cross-over, and some offices in 3 West are available for this purpose. If enough people would instead prefer to take a tour of Fermilab on Friday afternoon (2-4 PM) we will organize such a tour. Please e-mail us soon if you are interested in this tour.

## Update on cluster scale observations

### Gordon Squires University of California, Berkeley

I update the current status of cluster scale weak lensing observations. In particular, I consider the comparison among mass determination methods (lensing, X-ray and virial) to probe the dynamical state of individual clusters. The implication for $H_0$ determinations in SZ clusters is also discussed. Finally, I consider observational evidence for dark clusters'' -- fields where the weak lensing effect is observed but a very weak or non-existent optical counterpart is present.

## Testing weak lensing methods using a catalogue of cluster models

### Eelco van Kampen Theoretical Astrophysics Center, Copenhagen

We test weak lensing mass reconstruction methods using a catalogue of cluster models. This allows us to consider a realistic range of lens models (i.e. the various cluster models from the catalogue), and assess the dependence of the mass estimation on the range of lens parameters that is expected for a specific cosmological scenario. The practical purpose of this is to obtain correction factors with respect to simple analytical lens models, and an estimate of the noise in the mass estimate due to uncertainties in the lens model.

## Weak Lensing Statistics and Techniques with the Sloan Digital Sky Survey

### Donn MacMinn University of Chicago

I will discuss the possibility of measuring a weak lensing signal from large scale structure and nearby, large area clusters with the SDSS, including a description of the likely systematic errors and methods for correcting them.

## Lensing by Gravitational Waves

### Andrew Jaffe University of California, Berkeley

We describe the statistical properties of light rays propagating though a random sea of gravity waves and compare with the case for scalar metric perturbations from density inhomogeneities. For scalar fluctuations the deflection angle grows as the square-root of the path length $D$ in the manner of a random walk, and the rms displacement of a ray from the unperturbed trajectory grows as D^3/2. For gravity waves the situation is very different. The mean square deflection angle remains finite and is dominated by the effect of the metric fluctuations at the ends of the ray, and the mean square displacement grows only as the logarithm of the path length. In terms of power spectra, the displacement for scalar perturbations has P(k)\propto 1/k^4 while for gravity waves the trajectories of photons have P(k)\propto 1/k which is a scale-invariant or `flicker-noise' process, and departures from rectilinear motion are suppressed, relative to the scalar case, by a factor ~(\lambda/D)^3/2 where \lambda is the characteristic scale of the metric fluctuations and D is the path length. This result casts doubt on the viability of some recent proposals for detecting or constraining the gravity wave background by astronomical measurements.

## Propagation of light in the stationary field of multipole gravitational lens

### Sergei Kopeikin National Astronomical Observatory of Japan

A rigorous mathematical formalism for calculating the propagation of light rays in the stationary post-Newtonian field of an isolated celestial body (or system of bodies) considered as a gravitational lens having a complex multipole structure is developed. Symmetric trace-free tensors are used in the definition of gravitational multipoles instead of the less convenient in general situations scalar and vector spherical harmonics. Two types of perturbations of light rays caused correspondingly by the mass and spin multipoles are analyzed in full detail. A new simple method of integration for the equations of light propagation is proposed. This method enables us for the first time to obtain complete expressions both for the relativistic time delay and for the angle of the total deflection of light in any order of multipole perturbations without restriction. The results thus obtained can be applied to the interpretation of the secondary weak gravitational lens effects produced by the Solar system bodies, stars, binary pulsars, and galaxies where the influence of higher-order multipoles on the propagation of null rays may be important and measurable. The methods developed in the paper can be also applied to physical optics of multipole electromagnetic lenses and for calculation of propagation of gravitational waves through the curved space-time. As a particular application of the method the generalized equation for a multipole gravitational lens is derived using Cartesian coordinates and symmetric transverse-traceless tensors.

## Galaxy-galaxy lensing in the Hubble Deep Field

### Roger Blandford Caltech

Results of a search for galaxy-galaxy lensing using the images of faint galaxies by bright galaxies in the HUBBLE DEEP FIELD will be presented. Prospects for the future will also be discussed.

## Weak lensing by large scale structure: linear and nonlinear regimes

### Bhuvnesh Jain Max-Planck-Institute for Astrophysics

Weak lensing by large scale structure induces correlated ellipticities in the images of distant galaxies. The correlation is determined by the matter power spectrum along the line of sight, and by the cosmological parameters $\Omega$ and $\Lambda$. We use the fully nonlinear evolution of the power spectrum to compute the predicted ellipticity correlation. Nonlinear effects in the evolution of the power spectrum significantly enhance the rms shear for $\theta < 10'$ --- for $\theta\simeq 1'$ the shear is $\sim 5\%$, which is nearly twice as large as the linear prediction. The scaling with cosmological parameters also changes due to nonlinear effects. Thus by measuring the correlations on small (nonlinear) and large (linear) angular scales, the different parameters can be independently constrained.

## Weak lensing statistics in the quasi-linear regime

### Francis Bernardeau CE de Saclay

I present a systematic study of the expected dependence of the low order moments of the filtered gravitational local convergence on the power spectrum of the density fluctuations and on the cosmological parameters $\Omega_0$ and $\Lambda$. The results show a significant dependence on all these parameters. The third moment reveals particularly promising since it is expected, in the quasi-linear regime and for Gaussian initial conditions, to be only $\Omega_0$ dependent (with a slight degeneracy with $\Lambda$), when it is correctly expressed in terms of the second moment. More precisely I will show that the skewness is approximately given by $S_3=40 \Omega_0^{-0.8} \ z_s^{-1.35}$, where $z_s$ is the redshift of the sources.

## A new method to get amplification/shear statistics in inhomogeneous cosmologies

### Daniel Holz University of Chicago

In work with R.M. Wald, the geodesic deviation equation is numerically solved for photons on our past light-cone. Using a new Monte-Carlo procedure, we utilize uncorrelated photon runs to generate statistics for amplification and shear for lensing of point sources in inhomogeneous cosmologies. We investigate the lensing effects of various distributions of inhomogeneous matter (such as point masses, isothermal spheres, and cylinders). We apply our results to recent data on Quasar-Absorption Cloud correlations (Vanden Berk et al.), as well as to attempts to determine q_0 from Supernovae.

## Weak Lensing by Large-Scale Structures with the FIRST radio catalog

### Alexandre Refregier Columbia University

The FIRST radio catalog, which contains more than 10^5 sources in over 1550 square degree, provides a unique resource for measuring the effect of lensing by large-scale structures on large angular scales. I will discuss our approach for measuring the ellipticity-ellipticity correlation function and for accounting for both statistical and systematic effects which can induce spurious ellipticity correlations.

## Lensing of the Cosmic Microwave Background

### Ben Metcalf University of California, Berkeley

Weak lensing by large scale structure may have a significant effect on the CMB radiation. We find that the damping tail the CMB power spectrum will fall less rapidly with increasing l. This can result in an increase in the power spectrum of 20-30% at l of 3000. It will be necessary to take lensing into consideration when interpreting future small angle CMB observations.