![Page 1: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/1.jpg)
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
![Page 2: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/2.jpg)
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
![Page 3: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/3.jpg)
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
![Page 4: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/4.jpg)
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
![Page 5: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/5.jpg)
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.
![Page 6: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/6.jpg)
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.
![Page 7: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/7.jpg)
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.
![Page 8: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/8.jpg)
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.
![Page 9: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/9.jpg)
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.
![Page 10: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/10.jpg)
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.
![Page 11: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/11.jpg)
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)
![Page 12: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/12.jpg)
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)
![Page 13: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/13.jpg)
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)
![Page 14: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/14.jpg)
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
![Page 15: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/15.jpg)
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
![Page 16: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/16.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
Fermat’s Principle
∇2 =
=DS
DLS
× −
![Page 17: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/17.jpg)
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. . .
![Page 18: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/18.jpg)
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. . .
![Page 19: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/19.jpg)
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
![Page 20: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/20.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
Model Ensembles
∇2 =
=DS
DLS
× −
![Page 21: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/21.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
Model Ensembles
∇2 =
=DS
DLS
× −
![Page 22: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/22.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
Model Ensembles
∇2 =
=DS
DLS
× −
![Page 23: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/23.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
Model Ensembles
∇2 =
=DS
DLS
× −
![Page 24: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/24.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
ACO 1703
Inner profile like N-body CDM
(thanks to DS/DLS contrast)
![Page 25: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/25.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
ACO 1703
Inner profile weakly constrained
(without DS/DLS contrast)
![Page 26: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/26.jpg)
Sjur Refsdal Wavefronts Fermat’s Principle Lens modelling Clusters Time Delays
Time-delay lenses and H−10
![Page 27: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/27.jpg)
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)
![Page 28: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/28.jpg)
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)
![Page 29: Fermat's Principle and Gravitational Lensingstar.herts.ac.uk/ewass/talks/sym6/saha.pdf · 1979 Quasar microlensing 1970 Numerical ray-tracing in cosmology 1966 Galactic microlensing](https://reader034.vdocuments.us/reader034/viewer/2022042412/5f2b3d530c942219fe142d72/html5/thumbnails/29.jpg)
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)