ast308-part5 · Title: Microsoft PowerPoint - ast308-part5.ppt Author: baldwin Created Date:...
7
HERE Effect of Lensing on Flux F = F N Max amplification when β = 0 ~ θ E /α S Max amplification when β = 0 ~ θ E /α S β /θ E F /F N β = θ E F 1 /F N F T /F N F 2 /F N Source Lens Earth
Transcript of ast308-part5 · Title: Microsoft PowerPoint - ast308-part5.ppt Author: baldwin Created Date:...
1
HERE
Effect of
Lensingon
Flux
F = FN
Max amplification when β = 0~ θE/αS
Max amplification when β = 0~ θE/αS
β /θE
F/F
N
β = θE
F1 /FN
FT /FN
F2 /FN
Source
Lens
Earth
2
Caustics & Catastrophes
Lensing by a Transparent Mass Distribution
Caustic Surfaces:Number of images changes by 2 each time a caustic is crossed
always an odd number(if lens is transparent).
Rays:
Wave fronts:
Caustic
−= 2
21rcGMc
dtdrWavefront retarded by
gravitational field:
( ) ( ) ( )2222
22
22 /21/21)( dzdydxccdtcds ++Φ−−Φ+≈For a transparent mass distribution:
3
Lensing by a Transparent Mass Distribution
Caustic Surfaces:Number of images changes by 2 each time a caustic is crossed
always an odd number(if lens is transparent).
Rays:
Wave fronts:
Caustic
Location of source
relative to conjugate caustics
from Blandford & Narayan
Conjugate Caustic SurfacesBuilding blocks are
“elementary catastrophes” If source object is on one of these surfaces, observer is on a caustic.
Resulting images
Transparent elliptical lens
4
Location of source
relative to conjugate caustics
from Blandford & Narayan
Conjugate Caustic SurfacesPointy nodes are
“elementary catastrophes” If source object is on one of these surfaces, observer is on a caustic.
Resulting images
θ >> θE
θ < θE1938+666
HST
radio
The “Einstein Cross”
5
Weak (and not-so-weak) LensingAbell 2218
• Foreground cluster distorts images of numerous background galaxies.• Use to determine total mass of foreground cluster.• Shows that 85% of mass is Dark Matter.
Using caustics to search for high-redshift background galaxies
6
The Milky Way’s Dark Matter “Halo”
10 kpc
Milky Way
M31
770 kpc
Ballpark guesstimate based on weak-lensingsurveys of field galaxies
The Remarkable Case of CL0024+1654
• Single distant blue galaxy • z ~ 1.2 – 1.8
• Lensed by foreground cluster • z = 0.39
• 8 different grav. images of blue galaxy.• Allows detailed analysis of mass distribution in cluster.• 83% of mass is non-luminous Dark Matter.• M/L = 270h (390h after allowing for stellar evolution to z = 0)
7
The Remarkable Case of CL0024+1654
• Single distant blue galaxy • z ~ 1.2 – 1.8
• Lensed by foreground cluster • z = 0.39
• 8 different grav. images of blue galaxy.• Allows detailed analysis of mass distribution in cluster.• 83% of mass is non-luminous Dark Matter.• M/L = 270h (390h after allowing for stellar evolution to z = 0)
The Remarkable Case of CL0024+1654
• Single distant blue galaxy • z ~ 1.2 – 1.8
• Lensed by foreground cluster • z = 0.39
• 8 different grav. images of blue galaxy.• Allows detailed analysis of mass distribution in cluster.• 83% of mass is non-luminous Dark Matter.• M/L = 270h (390h after allowing for stellar evolution to z = 0)
Orange = D.M. “mascons”:1 or more for each of 118 galaxies25 for diffuse matter
Blue = stars58 smooth disks of light.
512 free parameters
