reu final presentation - k-state physics · saroj adhikari (mentor: dr. weaver) reu final...

HistoryIntroduction

Lensing systemsFinal words

REU Final Presentation

Saroj Adhikari (mentor: Dr. Weaver)

July 28, 2009

Saroj Adhikari (mentor: Dr. Weaver) REU Final Presentation

HistoryIntroduction


Outline

1 HistoryHistorical Background


HistoryIntroduction


Outline


2 IntroductionIntroduction to the projectTheory: Deflection angle, lensing diagram, and equations


HistoryIntroduction


Outline



3 Lensing systemsSchwarzschild lensTwo-point-mass lensesRay-shooting method


HistoryIntroduction


Outline



3 Lensing systemsSchwarzschild lensTwo-point-mass lensesRay-shooting method

4 Final wordsConcluding remarks


HistoryIntroduction


Historical Background


1919: Verification of Einstein’sprediction of 1.74” deviation of grazinglight rays by the sun.


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1936: Einstein publishes a paper:Lens-like action of a star by the

deviation of light in the gravitational

field


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field

Theoretical studies and observationalideas


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field


1979: Walsh, Carswell, and Weymannobserve the fist case of gravitationallensing - a quasar source lensed by agalaxy


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field


1979: Walsh, Carswell, and Weymannobserve the fist case of gravitationallensing - a quasar source lensed by agalaxy

Figure: First multiply imagedquasar Q0957+561 identified asa gravitationally lensed system.


HistoryIntroduction


Introduction to the projectTheory: Deflection angle, lensing diagram, and equations

Project Goals

Some of the project goals:

Understand gravitational lensing


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Project Goals



write tools for calculating and visualizing some gravitational lensingsystems

images of point and extended sourcescritical curves and caustics

lightcurves


HistoryIntroduction



Project Goals



write tools for calculating and visualizing some gravitational lensingsystems

images of point and extended sourcescritical curves and caustics

lightcurves

write tools for the ray-shooting method


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Lensing Diagram

~θI~θS

~α

b

O

b

L

b

L′

bS

bS ′

bI

LensPla

ne

Sourc

ePla

ne

The Len’s equation

~θ = ~θS +DLS

DOS

~α(~θ)


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Definitions and Approximations

~θI~θS

~α

b

O

b

L

b

L′

bS

bS ′

bI

LensPla

ne

Sourc

ePla

ne

The Len’s equation

~θ = ~θS +DLS

DOS

~α(~θ)

Thin lensapproximation

Small angleapproximation

Works for most practicalpurposes

Distances are angulardiameter distances


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The deflection angle

For point mass M , light ray grazing at a distance R from the mass,

Newtonian Calculation

α =2GM

c2

1

R

General Relativity

α =4GM

c2

1

R


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Schwarzschild lensTwo-point-mass lensesRay-shooting method

The simplest case

Point-mass lens of mass M


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The simplest case


Lens equation:

θ = θS +DLS

DOS

4GM

DOLθ


HistoryIntroduction



The simplest case


Lens equation:

θ = θS +DLS

DOS

4GM

DOLθ

Two images:

θ± =1

2

(

θS ±

√

θ2S

+ 4θ2E

)


HistoryIntroduction



The simplest case


Lens equation:

θ = θS +DLS

DOS

4GM

DOLθ

Two images:

θ± =1

2

(

θS ±

√

θ2S

+ 4θ2E

)

θS = 0 =⇒ the image is a ring

Magnification

−1 −0.5 0 0.5 1

−1

−0.5

0

0.5

1

x (in units of DOS

θE)

y (in

uni

ts o

f DO

Sθ E

)Einstein ring

Source disc

Distorted images(arcs)


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Magnification

Images are distorted andhence project differentsolid angle to ourtelescopes


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Magnification


Unresolved images(Microlensing)


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Magnification


Unresolved images(Microlensing)

Total magnification as afunction of time gives atypical lightcurve


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Star-planet type systems

A small mass (planet) near alarger mass (star)


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Expressions for ~α, lensequation, magnification get abit more complicated.


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Expressions for ~α, lensequation, magnification get abit more complicated.

Lightcurves are no moresymmetric but show planetaryperturbations

The region where mag is ∞

(theoretically) is no more apoint in the source plane =⇒more interesting causticformations (next slide)

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

xs ( in units of D

OLθ

E)

Tot

al m

agni

ficat

ion(

µ)

0.2

47

10

0 0.2−0.04

0

0.04

Planetary perturbation(magnified above)


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Image formation and caustics in planet-star type lensing

0 0.1 0.2 0.3−0.2

−0.1

0

0.1

0.2

x (in units of DOS

θE)

y (in

uni

ts o

f DO

Sθ E

)

Caustic and source positions

x (in units of DOL

θE)

Critical curve and image positions

y (in

uni

ts o

f DO

Lθ E)

−1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1Point source insidecaustic (5 images)

Caustic

Point source outsidecaustic (3 images)

Critical curve


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Example of planets detection

OGLE-2006BLG-109Lb,c

A system similarto Jupiter /Saturn orbitingSun

about 5000 lysaway


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Ray-shooting

Standard method in use to generate magnification map for a lensingsystem


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Ray-shooting


Method:

Populate a region of the image plane with large amount of photons(i.e. create a grid)


HistoryIntroduction



Ray-shooting


Method:

Populate a region of the image plane with large amount of photons(i.e. create a grid)calculate the mapping from the image plane to the source plane~θS = ~θ −

DOL

DOS~α(~θ)


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Ray-shooting


Method:


DOL

DOS~α(~θ)

the density of mapping is proportional to the magnification


HistoryIntroduction



Ray-shooting


Method:


DOL

DOS~α(~θ)

the density of mapping is proportional to the magnification

Wrote a C code to implement this basic idea


HistoryIntroduction



Ray-shooting example

x (in units of DOS

θE)

y (in

uni

ts o

f DO

Sθ E

)

−0.1 0 0.1 0.2 0.3

−0.2

−0.1

0

0.1

0.2


HistoryIntroduction



Other models

The ones already discussed are point mass models. There are otherlensing models listed below, the ones that were studied during the projectand codes written to calculate and visualize the models are in bold face.

Singular isothermal sphere (SIS)

Non-singular isothermal sphere (NSIS)

Uniform sheet

Elliptical potential (both singular/non-singular)

Isothermal ellipsoids


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Concluding remarks

Finally..

My basic references:

Gravitational Lensing : Schneider et.al.Singularity theory and gravitational lensing: Petters et al.Many papers on (arxiv, A&A, Phys Rev et.al)

Acknowledgements

KSU REU ProgramDr. Weaver: I learned a lot during the summerEveryone!

Questions??


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