Download Analysis of a New Gravitational Lens FLS 1718+59

Analysis of a New Gravitational
Lens FLS 1718+59
Yoon Chan Taak
Feb 14 2013
Survey Science Group Workshop 2013
1
What is Gravitational Lensing?

Deflection of light by body of mass
◦ Deflection angle greater for GR (factor of 2)

vs
(r: source-lens distance)
◦ e.g. Solar eclipse of May 1919

Causes distortion of images
2
Images of GL
Abell 1689 cluster
3
Images of GL
Einstein Ring –
SDSS J073728.45+321618.5
Einstein Cross –
QSO 2237+030
4
Images of GL
5
Types of GL

Strong GL
◦ Big distortions, e.g. rings, arcs, multiple img
◦ Lens is galaxy or cluster

Weak GL
◦ Shear distortion
◦ Lens is galaxy or cluster, but further away from
source

Microlensing
◦ Brightness variations
◦ Lens has stellar masses (e.g. planets)
6
Why GL?

Requires only mass
 Allows detection of dark matter

Acts as “cosmic telescope”
 Lets us see more distant objects

Determines cosmological parameters
◦ Deflection depends on redshift-distance
formula
◦ Time delay related to Hubble constant
 Constrains geometry of universe
7
Gravitational Lensing Theory
Point-mass lens
 Finite lens

8
Point Mass (Schwarzschild) Lens

Lens (Ray-trace) equation
◦
DS
θ11
b − 𝛼DLS
S DS =
DL
◦ θ11,2
1
=
θ ±
2 S
2𝐺𝑀
𝛼= 2
𝑐 𝑏
4α20 + θS 2
(DS/DL)b
αDLS
θSDS
θS : lens-source angular distance
α : deflection angle of light ray
θ1,2: lens-img angular distances
b : lens-deflection pt angular dist.
α0 : Einstein rad. [(4GM/c2) (DLS/DLDS)]1/2
9
Finite Lens

Ray-trace eqn is for 2-D plane
◦ Change scalars to vectors for 3-D

Integrate deflection angle for all
infinitesimal masses
◦I

Calculate numerical solution
10
gravlens: Software for G-Lensing
Developed by C. Keeton (Rutgers)
 Useful for various g-lens images

◦ Able to find best set of lens parameters for
multiple images (lensmodel)

Contains 20+ lens models
◦ Can be superposed, diverse potentials
possible
11
FLS 1718+59
G-lensing image in
Spitzer First Look
Survey Field
 zlens = 0.08
 zsource = 0.245

◦ Closest source so far(?)
RA = 17h 18m 17.6s
 Dec = 59d 31m 46s

FLS 1718+59
Procedures

Simulated lensing images with several
sets of input variables
◦
◦
◦
◦

Mass scale of lens
X coord. of source
Ellipticity (angle) of source
Ellipticity (angle) of lens*
Assumed no external shear
* Obtained from original HST image
Softened Power Law Ellipsoid

κ ξ
1
b2−α
=
2 s2 +ξ2 1−α/2
2
2
1/2
=
1
b
2 s2 + ξ2 0.5
α=1
ξ = x + y /q
 s : size of flat core

◦ s = 0 : singular isothermal ellipsoid
◦ s ≠ 0 : nonsingular isothermal ellipsoid
Results
Discussion
 Mgal ~ 1010.75Mʘ, σ ~ 150km/s
 Possibly an edge-on spiral
Many sets of variables may yield similar
images
 A more careful approach is necessary for
constraining errors
 requires analysis with more sets of variables
