Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Sjur Refsdal

1979 Quasar microlensing

1970 Numerical ray-tracing in cosmology

1966 Galactic microlensing

1964 Time delays ∝ H−10

1964 Wavefront picture of lensing

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Sjur Refsdal

1979 Quasar microlensing

1970 Numerical ray-tracing in cosmology

1966 Galactic microlensing

1964 Time delays ∝ H−10

1964 Wavefront picture of lensing

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Sjur Refsdal

1979 Quasar microlensing

1970 Numerical ray-tracing in cosmology

1966 Galactic microlensing

1964 Time delays ∝ H−10

1964 Wavefront picture of lensing

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Sjur Refsdal

1979 Quasar microlensing

1970 Numerical ray-tracing in cosmology

1966 Galactic microlensing

1964 Time delays ∝ H−10

1964 Wavefront picture of lensing

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

The Wavefront

The wavefront picture of lensingseems unique to Refsdal. . .

. . . and his students, includingChang and Kayser.

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

The Wavefront

The wavefront picture of lensingseems unique to Refsdal. . .

. . . and his students, includingChang and Kayser.

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefront and Time Delays

From the wavefront Refsdalshowed

∆t ∝ H−10

Soon after, he realized ∆t alsodepends on the cosmologicalmodel.

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefront and Time Delays

From the wavefront Refsdalshowed

∆t ∝ H−10

Soon after, he realized ∆t alsodepends on the cosmologicalmodel.

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefront and Time Delays

From the wavefront Refsdalshowed

∆t ∝ H−10

Soon after, he realized ∆t alsodepends on the cosmologicalmodel.

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefront and Time Delays

From the wavefront Refsdalshowed

∆t ∝ H−10

Soon after, he realized ∆t alsodepends on the cosmologicalmodel.

In 1964–66 Sjur Refsdal

1 Independently derived theShapiro time delay

2 and connected it to the ageof the Universe

3 and the cosmological model.

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefronts and Moving Sources

Then Refsdal considered theGalactic microlensing regime.

. . . if the lens can be observedfrom the Earth and from at leastone distant space observatory.(Refsdal 1966)

MACHO parallaxes from a singlesatellite (Gould 1995)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefronts and Moving Sources

Then Refsdal considered theGalactic microlensing regime.

. . . if the lens can be observedfrom the Earth and from at leastone distant space observatory.(Refsdal 1966)

MACHO parallaxes from a singlesatellite (Gould 1995)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Wavefronts and Moving Sources

Then Refsdal considered theGalactic microlensing regime.

. . . if the lens can be observedfrom the Earth and from at leastone distant space observatory.(Refsdal 1966)

MACHO parallaxes from a singlesatellite (Gould 1995)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Fermat’s Principle

=4πG

c2

H0

c DL

× surf dens

=H0

(1 + zL) DL

× arrival time

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Fermat’s Principle

=4πG

c2

H0

c DL

× surf dens

=H0

(1 + zL) DL

× arrival time

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Fermat’s Principle

∇2 =

=DS

DLS

× −

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

The Earliest Lens Models

P.J. Young et al. (1980)

Nine-parameter (galaxy+cluster)model for Q0957+561.

. . . We settled upon the followingrepresentative case; it must notbe looked upon as a unique orwell-determined solution at thistime, but merely an example. . .

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

The Earliest Lens Models

P.J. Young et al. (1980)

Nine-parameter (galaxy+cluster)model for Q0957+561.

. . . We settled upon the followingrepresentative case; it must notbe looked upon as a unique orwell-determined solution at thistime, but merely an example. . .

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Some Recent Lens-Model Topics

1 Use stellar velocity field as a mass constraint.

Talks by Koopmans, Czoske

2 Compare with stellar population to map dark matter.

Poster by Leier

3 Explore the model-space satisfying (i) data and (ii) minimalassumptions about mass distribution.

Liesenborgs et al. arXiv:0904.2382PixeLens

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Model Ensembles

∇2 =

=DS

DLS

× −

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Model Ensembles

∇2 =

=DS

DLS

× −

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Model Ensembles

∇2 =

=DS

DLS

× −

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Model Ensembles

∇2 =

=DS

DLS

× −

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

ACO 1703

Inner profile like N-body CDM

(thanks to DS/DLS contrast)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

ACO 1703

Inner profile weakly constrained

(without DS/DLS contrast)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Time-delay lenses and H−10

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Time-delay lenses and H−10

10

20

30

10 20

50100

Hubble time (Gyr)

Hubble constant (legacy units)

num

ber o

f mod

els

H−10 = 15.3+1.8

−1.7 Gyr

13.6± 0.6 (WMAP)

13.6± 1.5 (HST key proj)

15.7± 0.3± 1.2 (SN Ia)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Time-delay lenses and H−10

10

20

30

10 20

50100

Hubble time (Gyr)

Hubble constant (legacy units)

num

ber o

f mod

els

H−10 = 15.3+1.8

−1.7 Gyr

13.6± 0.6 (WMAP)

13.6± 1.5 (HST key proj)

15.7± 0.3± 1.2 (SN Ia)

Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays

Time-delay lenses and H−10

10

20

30

10 20

50100

Hubble time (Gyr)

Hubble constant (legacy units)

num

ber o

f mod

els

H−10 = 15.3+1.8

−1.7 Gyr

13.6± 0.6 (WMAP)

13.6± 1.5 (HST key proj)

15.7± 0.3± 1.2 (SN Ia)