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Analysis of a New Gravita-tional Lens FLS 1718+59

Yoon Chan Taak

Feb 14 2013Survey Science Group Workshop 2013

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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 1919Causes distortion of images

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Images of GL

Abell 1689 cluster

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Images of GLEinstein Ring – SDSS J073728.45+321618.5

Einstein Cross –QSO 2237+030

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Images of GL

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Types of GLStrong 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

sourceMicrolensing◦Brightness variations◦Lens has stellar masses (e.g. planets)

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Why GL?Requires only mass

Allows detection of dark matterActs as “cosmic telescope”

Lets us see more distant objectsDetermines cosmological parameters◦Deflection depends on redshift-distance

formula◦Time delay related to Hubble constant Constrains geometry of universe

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Gravitational Lensing TheoryPoint-mass lensFinite lens

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Point Mass (Schwarzschild) LensLens (Ray-trace) equation◦11

◦1

θS : lens-source angular distanceα : deflection angle of light rayθ1,2: lens-img angular distancesb : lens-deflection pt angular dist.α0 : Einstein rad. [(4GM/c2) (DLS/DLDS)]1/2

θSD S=( D S

DL)b−𝛼DLS(𝛼=2𝐺𝑀

𝑐2𝑏 )θ1,2=

12 (θS±√4 α 02+θS2 )

αDLS

θSDS

(DS/DL)b

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Finite LensRay-trace eqn is for 2-D plane◦Change scalars to vectors for 3-D

Integrate deflection angle for all infini-tesimal masses◦I

Calculate numerical solution

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gravlens: Software for G-LensingDeveloped 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

FLS 1718+59G-lensing image in

Spitzer First Look Survey Field

zlens = 0.08zsource = 0.245◦Closest source so far(?)

RA = 17h 18m 17.6s

Dec = 59d 31m 46s

FLS 1718+59

ProceduresSimulated 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

s : size of flat core◦s = 0 : singular isothermal ellipsoid◦s ≠ 0 : nonsingular isothermal ellipsoid

Results

Discussion

Many sets of variables may yield similar imagesA more careful approach is necessary for con-

straining errors requires analysis with more sets of variables

Mgal ~ 1010.75Mʘ, σ ~ 150km/s

Possibly an edge-on spiral