# mccart gravitational lensing

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ARON MCCART

861 S. Rogers, Springfield, MO 65804 (417) 838-9686 [email protected]

March 1, 2009

Mrs. Tracy DaltonMissouri State University

901 S. National Ave.Springfield MO, 65897

Dear Mrs. Tracy Dalton:

I am writing you to express what I experienced while writing my major project. The major

project has been quite the journey. It is not only the longest paper I have ever written, but also I

have never had to research any subject so thoroughly only because I had very little priorknowledge about my subject. In the beginning, I set out to explore gravitational lensing as a

graduate school topic, and I firmly believe that I accomplished my goal.

During the initial prewriting and outlining process, I felt rather confident about how this paper

would turn out; however, I did not realize the depth of my own ignorance regarding gravitationallensing at the time. As a consequence, I had to read an entire book — that I later used significantly

throughout my paper —on Einstein’s theory of general relativity only to begin to comprehendgravitational lensing. I did not stop there either. I was forced to look up many acronyms and

various technical terms in order to comprehend the peer-reviewed research I used. Acronyms can

be quite needlessly misleading in my opinion. For example, a “QSO” is a “quasi-stellar-object”or more simply a quasar, and I already knew what a quasar was.

Because I had to do so much research, I had a lot of subject to cover. I intended from the

beginning to explore gravitational lensing, so in order to solidify my understanding of thescience behind gravitational lensing, I wrote a significant section dedicated to just the science

that came before gravitational lensing. This not only helped me understand gravitational lensing,but it will also help the audience understand the subject as well because the paper took on a tone

for the lay. I do not distress over this though; besides that fact that proofreading a 12,000 wordpaper is not easy, I enjoyed covering a topic without feeling like I had to omit important sections.

In short, this paper has been an enjoyable, albeit time consuming, experience. Without writing apaper of this magnitude, I do not believe I could have ever understood gravitational lensing the

way I do without taking a class on it.

Sincerely,

Aron McCart

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Gravitational Lensing i

An Exploration of Gravitational Lensing

Astronomers Have a Brand New Set of Glasses

By Aron McCart

(Cover art source: www.nasaimages.org)

ENG 321: Writing II: Beginning Technical Writing

Instructor: Tracy Dalton

April 20, 2009

Missouri State University

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Gravitational Lensing ii

TABLE OF CONTENTS

List of Figures ............................................................................................................................... iii Abstract ......................................................................................................................................... iv Introduction ................................................................................................................................... 1

The Problem ................................................................................................................................ 1 What is Gravitational lensing ...................................................................................................... 2

Background Science ...................................................................................................................... 2 Special Relativity ........................................................................................................................ 3

Relativity and the constant speed of light ................................................................................ 3 Time dilation............................................................................................................................ 4 Loss of simultaneity................................................................................................................. 6 Four-dimensional dimensional spacetime ............................................................................... 6

General Relativity ....................................................................................................................... 7 The Equivalence Principle ....................................................................................................... 7 The effects of time on acceleration and gravity ...................................................................... 8 The bending of light ................................................................................................................ 9 Curved Space ......................................................................................................................... 10

Theoretical Background ............................................................................................................. 13 Strong Lensing .......................................................................................................................... 14 Weak Lensing ............................................................................................................................ 15 Microlensing.............................................................................................................................. 15 The Bayesian Method of Analysis ............................................................................................ 15

The Process .................................................................................................................................. 16 Obtaining the Data .................................................................................................................... 16 Computer Modeling .................................................................................................................. 17

Applications ................................................................................................................................. 18 Exoplanet Detection .................................................................................................................. 18 Accretion Disk Theory .............................................................................................................. 19 Dark Matter Detection ............................................................................................................... 20 Big Bang Cosmology ................................................................................................................ 20

Conclusion ................................................................................................................................... 21 References .................................................................................................................................... 22

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Gravitational Lensing iii

LIST OF FIGURES

Figure 1 ............................................................................................................................................1

Figure 2 ............................................................................................................................................1Figure 3 ............................................................................................................................................2

Figure 4 ............................................................................................................................................2Figure 5 ............................................................................................................................................4Figure 6 ............................................................................................................................................6

Figure 7 ............................................................................................................................................6

Figure 8 ............................................................................................................................................8Figure 9 ............................................................................................................................................8

Figure 10 ..........................................................................................................................................8

Figure 11 ........................................................................................................................................10

Figure 12 ........................................................................................................................................10

Figure 13 ........................................................................................................................................11Figure 14 ........................................................................................................................................11

Figure 15 ........................................................................................................................................11Figure 16 ........................................................................................................................................12Figure 17 ........................................................................................................................................13

Figure 18 ........................................................................................................................................14

Figure 19 ........................................................................................................................................14Figure 20 ........................................................................................................................................15

Figure 21 ........................................................................................................................................17

Figure 22 ........................................................................................................................................17Figure 23 ........................................................................................................................................20

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Gravitational Lensing iv

ABSTRACT

With advances in computer science and image analysis, it is now possible to use Einstein’sgeneral relativity to analyze the light that has been distorted by gravity; this allows for

astronomers to examine astronomical phenomena with an entire new set of glasses. Einstein’s

theories of special and general relativity lay the foundation for gravitational lensing. With thisdescription of gravity, astronomers are able to interpret and analyze the light that is affected by

a gravitational lens. Consequently, this allows for much advancement in astronomy not limited

to exoplanet detection, accretion disk theory, dark matter detection, and big bang cosmology.

Keywords: astronomy, gravitational lensing, relativity, science, physics, exoplanet, accretiondisk theory, dark matter, dark energy, cosmology, big bang.

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Gravitational Lensing 1

INTRODUCTION

Astronomy is the oldest science known to man. Before most people lived in cities, there were no

bright city lights to wash out the beauty of the night sky. It was during this time that people usedthe only set of glasses they had — their eyes. Over thousands of years, with great advancements in

technology, astronomers gained access to telescopes. These telescopes showed that patches of sky that were black to the unaided eye were not black at all. In fact, as telescopes got bigger andbetter, it was apparent that there were no empty patches of sky. Modern astronomy is the

scientific inquiry of the cosmos, and Galileo, with his radical idea that Earth was not the center

of universe, marked the beginning of modern astronomy. His quest to find out why certain stars

wandered led to the discovery that the Earth was not the center of the universe and to thediscovery of planetary motion. As astronomers answered more and more questions, an even

greater number of questions emerged. When NASA began launching space telescopes at the

dawn of the space age, the view of the cosmos changed dramatically (see figures 1 and 2).

Astronomers were no longer held back by the distortion of the Earth’s atmosphere; whatastronomers began to see gave rise to new mysteries — mysteries that astronomers set out to

solve. This is where the motivation for methods like gravitational lensing comes from. It is the

ultimate goal of astronomers to answer the big questions about the cosmos, and as astronomers

solve tiny pieces of the puzzle, it gets much harder.

THE PROBLEM

Astronomy is a very interesting science. All other science is almost exclusively done on Earthwhere scientists have plenty of material to test in their labs. However, in astronomy, astronomers

are not granted this luxury. In turn, astronomers almost always rely on light for observationalevidence. This is not discouraging because astronomers can learn a lot just by looking.

Some of the classical techniques of astronomy are spectroscopy, photometry, polarimetry, and

astrometry. These have been keeping astronomers busy for hundreds of years and are still doingso. Astronomers use these techniques to study various physical properties about things that emit

or reflect light. For example, spectroscopy can determine the composition of things reliably.

Figure 1 (Before): This is the center of the galaxy from the 10 meter

Keck telescope. Source: keckobservatory.org

Figure 2 (After): This is the center of the galaxy from the 0.85 meter Spitzer space telescope.

Note that Keck’s image is greatly magnified. Source: nasaimages.org

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Gravitational Lensing 2

Spectroscopy does this by examining the specific frequencies of light an object reflects or emits.

Scientists (chemists) examine the light frequencies of materials here on Earth, in controlledenvironments, and determine what materials look like with a spectrometer. Astronomers then

take this and look at the stars with it. This is just an example of how astronomers can determine

physical properties using only light.

The classical methods of astronomy work great when we have complete observational data;however, this is certainly not the case when light is extremely distorted and other data is missing.

Massive objects, like galaxies or stars, bend light due to their gravity. General relativity tells us

this light arrives at us demagnified and even at different times. This presents an enormouschallenge to astronomers because without information from light we are essentially helpless.

Gravitational lensing is what astronomers believe will be part of the answer to this problem.

WHAT IS GRAVITATIONAL LENSING

Gravitational lensing is the method astronomers use to interpret light that has been distorted bygravity. Gravitational lensing is the first method to involve Einstein’s general relativity

extensively. With general relativity physicists know that light is bent by super massive objects,as can be seen in figures 3 and 4. Gravitational lensing allows for an independent method of

estimating an objects mass. Einstein’s relativity introduces the idea that spacetime is molded intodifferent forms by matter.

Gravitational lensing accounts for the effects that general relativity predicts. It takes those effects

into account in order to interpret the source’s light or object causing the spacetime distortions.

Astronomers accomplish this by precise measurements of the source object’s brightness andincredibly advanced computer simulations.

BACKGROUND SCIENCE

When examining scientific concepts, it is always crucial to understand the science that the

science at hand is built upon. Without an understanding of basic scientific concepts, the

Figure 3: Behind the golden sphere is an overlaid picture of what a

lensing event looks like. The golden sphere is a representation of a

very massive object, which is usually a galaxy. The gray lines

represent the actual path of the light while the orange lines represent

the apparent path of the light. The orange arcs that the orange arrows

are from are the resultant image. Source: centauri-dreams.org

Figure 4: This is an actual image from the Hubble Space Telescope with lensing events. Notice

the long arcs that make a rough circle around the largest white object just to the right of the

picture’s center. Those arcs were originally a complete image of a quasar before the white

object’s gravity distorted it. Source: nasaimgages.org

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foundation new theories are built upon (or are derived from) are nearly impossible to understand.

Here is a summary of the concepts relevant to gravitational lensing contained within Einstein’stheories of special and general relativity.

SPECIAL RELATIVITY

Special relativity is how physicists measure things like motion with regards to a frame of reference. For example, measuring the motion of a ball that is sitting at rest on the floor is notalways very simple. It is, in fact, not at rest: The Earth is moving around the sun at all times, and

the sun is orbiting the center of the galaxy, and even our galaxy is moving. This is the main idea

that caused Albert Einstein to propose special relativity in 1905. Keep in mind that specialrelativity always deals with inertial frames only. An inertial frame is a reference frame tied to the

constant motion of a specific object. Within this reference frame, all the laws of physics apply

with predictable behavior.

Special relativity proposes several counter-intuitive concepts relative to gravitational lensingsome of which are as follows:

Relativity and the constant speed of lightTime dilation

Loss of simultaneity

4 dimensional spacetime

Relativity and the constant speed of light

Imagine riding in a low flying (less than a few hundred meters so it is apparent the Earth is flying

by underneath) jet airplane flying at a constant speed. Without looking out the window or beingpresent during the take off it would be impossible to tell if anyone or anything was moving at all.

If a person looked out the window and saw the trees or buildings flying by at incredible speeds, it

would not be possible to tell if the airplane or the Earth was moving. Without special equipment,

it is not possible to tell who *or what is moving. In fact, as already stated, the Earth is movingaround the sun, the sun is moving around the galaxy, and the entire galaxy is moving relative to

our local cluster. In the jet airplane example, it would be much more difficult to measure what is

moving taking into account all of these variables. In order to deal with this problem, physicistssay all motion is relative; in other words, the plane is moving 200 miles per hour relative to the

Earth’s surface. This is known as the principle of relativity (Stannard, 2008).

Taking into account this principle of relativity, imagine a battleship moving at a constant 45

miles per hour through the ocean. When the battleship fires a training round directly ahead of it,the training round leaves the barrel traveling at 750 miles per hour relative to the motion of the

boat. If one remembers the boat was moving before the training round was fired, it becomes clear

that training round is actually traveling at 795 miles per hour relative to the ocean. This is how

physicists added velocities before Einstein’s general relativity. However, this fails to be accurateat speeds that are a significant fraction of the speed of light (Stannard, 2008).

It may not be intuitive that light has a speed, but it most certainly does. Using Maxwell’s laws of electromagnetism and extremely sensitive equipment, physicists have been able to show that

light speeds through a vacuum at 299,792,458 kilometers per second or about 186,000,000 milesper second. In order to see if light behaved as the training round did when fired from the

battleship, European Organization for Nuclear Research (CERN) physicists set out to do this in a

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Gravitational Lensing 4

Figure 5: This is a diagram of how time dilation works.

Each red square represents the lasers position at aparticular instant in time. The vertical laser pulse is the

laser seen from the astronaut’s perspective while the

diagonal laser is the one seen from the perspective of

the ground observer.

particle accelerator in 1964. They accelerated tiny subatomic particles, or neutral pions, to

99.975 percent the speed of light. When these particles decayed, two pulses of light were sent off in different directions moving at the usual speed of light (measured with a 1 percent margin of

error). This has been found to be true in all cases (e.g. the speed of light is the same from any one

perspective), but this is a clear contradiction with the battleship example. If the way physicists

added the speeds in the battleship example do not hold here, then something is clearly wrong.This was one of the many things Einstein took note of before publishing his paper on general

(not special) relativity — something is wrong about the way physicists are relating objects moving

through space (Stannard, 2008).

Time dilation

The best way to illustrate time dilation is to imagine anastronaut in a transparent spacecraft orbiting the Earth at about

25 percent the speed of light (no one can actually accelerate

spacecraft to this speed). The astronaut is instructed to place a

laser at the bottom of the spacecraft’s cabin and point it

directly up at a target on the spacecraft’s ceiling, which is 4meters away (see figure 5). The astronaut is then instructed by

the ground controller to measure the time it takes for the laserto travel from the bottom of the cabin to the target. The

astronaut finds that the time it took was as follows:

Recall from college algebra that distance equals rate times time or the familiar .Therefore,

And in our case,

So,

Keep in mind that there are one billion nanoseconds for every one normal second. When the

ground controller measures how long the laser took from his perspective something odd happens.To the controller, it appears that the light traveled a diagonal path of 5 meters because the

spacecraft has moved since laser was emitted (see figure 5) . So for the controller the time it took

for the laser to travel its apparent distance is as follows:

There is a disagreement between the astronaut and the controller here; a disagreement of over 3

nanoseconds, but both are correct from their perspectives. The only way for this disagreement tobe reconciled is to conclude that time for the astronaut is moving slower than it is for the ground

controller. This makes absolutely no sense. If the astronaut were to measure the time it took for

other things to happen on the spacecraft to verify this, the astronaut would be very confused to

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find that everything appears completely normal, which means that to the astronaut, time is not

moving slower. It becomes clear to both the astronaut and the controller that time is not passingby at the same rate. This is called time dilation (Stannard, 2008).

This has some interesting consequences. It means that when an object is moving, time slows

down from the outside observer’s perspective. When a different astronaut in a different

spacecraft travels away from Earth, time is moving slower for the astronaut from the perspectiveof the ground controller on Earth; however, looking at things from the perspective of the

astronaut is pertinent before making any conclusions. Assuming that both the astronaut and the

ground controller are holding miniature atomic clocks, what should these two clocks read whencompared to each other? It has already been established in the previous astronaut/controller

example that time is moving slower on the spacecraft from the controller’s perspective, so it is

reasonable to assume that the new astronaut’s time will move slower from the perspective of theground controller. One way to examine this is to compare the clocks. To do this the controller

and astronaut constantly monitor each other’s clocks by sending signals back and forth. Taking

into account the time it takes for the signal to move, the astronaut clock does indeed appear

slower to the controller. However, what is bizarre is that the controller’s clock appears slow from

the astronaut’s perspective using the exact same method. It seems that both clocks are movingslower than each other, so whose clock is really going slower? This is an absolutely meaningless

question because there is no answer. Both assessments are correct because there is no absolute

rate that time passes by; it is relative (Stannard, 2008).

Remembering that time is relative, examining the famous twin paradox will illustrate the next

point well. Take two twins, leave one on Earth, and put the other on a spacecraft that is destined

to travel to a distant place and back. Keeping the idea that from either twin’s perspective the

other’s time appears slower, it is apparent that both people are aging slower than the other. Thisis utter nonsense and a complete impossibility. The only way to reconcile this is to realize that

this example requires the act of calculating the apparent rate at which time passes. Because there

is no universal clock, the only way to see whose time is really moving slower is to compare theclocks side by side. In this example, the spacecraft must accelerate to a speed, decelerate, turn

around, and accelerate back to Earth. Upon the astronaut twin’s arrival, it is apparent that the

astronaut twin came back younger than his terrestrial twin. It is important to note that this

example has not violated the principle of relativity by revealing whose time is really movingslower, because the astronaut twin did not maintain an inertial frame during the whole trip. The

astronaut had to turn around and accelerate in the opposite direction. The principle of relativity

only applies to inertial frame observers (Stannard, 2008).

The realization that there is no universal clock may be disorientating to some people. However,

this effect is so infinitesimally small that we can and do ignore it. A real astronaut orbiting in the

space shuttle actual speed around 17,000 miles per hour (less than 1% the speed of light) will age

only a few milliseconds slower than the rest of us over the course of astronaut’s career (Stannard,2008).

This is an interesting theory after all, but does it hold up under experimentation? The answer is

overwhelmingly yes. In 1977, CERN physicists set out to prove time dilation by experimenting

with muons, which are subatomic particles that usually decay in about 2200 nanoseconds. Whenphysicists accelerated these muons to over 99 percent the speed of light they found that the

muons decayed 29.3 times slower than the muons that were not moving. Experiments involving

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two atomic clocks (the most accurate clocks known to man), one on a fast moving airplane and

the other on the ground, also confirmed the validity of time dilation. Not forgetting the twinparadox, muons that were accelerated to one position and returned to the starting position came

back younger than muons that were stationary during the experiment (Stannard, 2008).

Loss of simultaneity

Generally, it is taught that things either happen before or after one another or at the same time,

but time, in fact, is affected by speed. The speed of something can, and does, affect the perceived

simultaneity of events. Imagine a long rocket ship orbiting the Earth at a significant fraction of the speed of light. There is a double-sided laser pointer placed in the center of the rocket ship’scabin pointing both ends at the front and back of the cabin (see figures 6 and 7). As one would

expect, the laser hits the front and back of the rocket ship at the exact same time, but only to the

astronaut on the rocket ship. An observer on the ground would see the laser hit the front of the

spacecraft before hitting the back of the spacecraft because the spacecraft is moving relative to

the observer and of a concept that goes beyond the scope of this paper, length contraction. This

allows for light to appear to arrive at different times from different perspectives (Stannard,2008).

Four-dimensional dimensional spacetime

All the concepts of special relativity lead to the idea that space and time are intrinsically related,hence, the term spacetime. Instead of moving through space with time passing by, time is

effected by ones position in space in spacetime. In other words, every one lives in a four-

dimensional reality with time being the fourth dimension. This is quite interesting to think aboutsince people view reality through three dimensions. Some may say that people are aware of time,

but without clocks or the familiar night and day cycle, all people would be helplessly unaware of

the passage of time; people are not born with a way to sense the passage of time (Stannard,

2008).

Living in a four-dimensional reality can be a disconcerting epiphany. This particular idea wasnot actually thought by Einstein himself. His teacher, Hermann Minkowski, suggested this idea

to Einstein in 1908 a few years after Einstein published his paper on special relativity.

Minkowski suggested that special relativity was telling Einstein that time is much more likespace than previously realized. Time is simply the fourth spatial dimension instead of the

Figure 6: This diagram is from the astronaut’s perspective. In these figures each

red square represents the lasers position at a particular instant in time. Notice that

the laser hits both sides of the rocket ship at the exact same time.

Figure 7: This diagram is from the perspective of an observer on the ground. Notice

that the laser arrives at the front of the spacecraft because the spacecraft is moving

relative to the ground observer’s inertial frame.

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When dealing with motion, it

is nearly impossible to tell thedifference between

gravitational acceleration and

acceleration due to an external

force. For example, if anastronaut were in a spacecraft

traveling at a constant speed

far from any noticeablegravitational force, he would

feel a sense of weightlessness

because the spacecraft is notaccelerating in any way.

However, if the astronaut wereto fall asleep, only to wake up

to find that himself and objects

in his cabin were movingtoward the back of the

spacecraft, he would be unable

to determine what is causing

this motion withoutinstrumentation. In fact, it

could be either the spacecraft’s

thrusters are causing this acceleration or the spacecraft came close enough to a planet to bewithin its gravitational influence. It is important to note that this is not entirely true. Under the

right circumstances, it would be feasible to tell the difference between acceleration due to gravity

and normal acceleration. If an observer were far enough away from two objects to notice their

trajectories, one could notice that the two objects are either moving parallel or moving towards acommon point. Because gravity always accelerates objects towards a center of gravity, all

objects accelerating due to gravity converge to that center of gravity, like in figure 9. However, if

an external force is causing acceleration, two objects wouldsimply move parallel to each other and would have no

physical motivation to converge to a center of gravity. This is

known strictly as the weak equivalence principal or simplyas the equivalence principal. All of this goes to show that for

a single object, acceleration due to gravity can be treated

exactly the same as any normal acceleration would for

simplicity (Stannard, 2008).

The effects of time on acceleration and gravity

In special relativity, the examples were always dealing with

inertial frames where motion was constant; acceleration was

never a factor. However, when talking about gravity,

acceleration is always a factor and must be accounted for. Inorder to do this, it is easiest to explore the effects of time on

gravity by revisiting the laser in a spacecraft example. If the

Figure 8: This is a diagram of the famous feather

and hammer example. The column on the left

represents normal air and the right column

represents a vacuum. Each separate hammer or

feather represents in location at an instant of time.

On the left column it is clear that the molecules in the

air (represented by blue dots) slow the feather down

considerably, which is known formally as drag.

Because the hammer’s weight-to-surface-area ratio is

low, it is not slowed down like the feather is. In the

vacuum example, no such air molecules slow down

the feather, so the hammer and feather fall at the

exact same rate.

Figure 9: This is a diagram of a parallel set of lines and

a converging set of lines. On the left is the path of two

converging lines and the sphere represents a large

gravitating body. On the right is an example of a parallel

path. The green spheres are objects of small mass, such

as tennis balls. The gravitating body attracts the tennis

balls towards its center of mass; while on the other hand,

the parallel paths of the right represent what would

happen during acceleration by an external force, such as

the rockets boosters.

Figure 10: The white sphere in the center represents any

object moving at a significant fraction of the speed of light

and the lighter colored circles represent a uniform wave of

light that was emitted from the object. The direction of motion

is up. Notice that waves of light in front of the moving object

are closer together and the waves behind the direction of

motion appear stretched out. Source: www.ifa.hawaii.edu

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conditions for an inertial frame were broken by firing the spacecraft’s thrusters, it would be

apparent that the laser hit the back of the spacecraft first. This is because the entire inertial frame,the spacecraft, accelerated relative to when the laser was emitted, as shown in figure 10 on the

previous page. This is known as Doppler shift . Using the equivalence principal, this effect is

identical in a gravitational field, but in a gravitational field, acceleration due to gravity increases

as an object approaches the center of gravity (in relevant cases). This is a different predictionthan the one that would have made using only time dilation from special relativity because we

are no longer dealing with two separate inertial frames. With gravitational fields, it is definitely

agreed upon where one is it at in a gravitational field, so in essence time, really moves slower thefurther down an observer is in a gravitational field (Stannard, 2008).

This is verified by many different sources in astronomy. Astronomers use spectra to measure

Doppler shift, and when measuring the Doppler shift — astronomers call it redshift when thefrequencies of light increase thus moving away from the observer and blueshift for the opposite

case — they consider the following two things: what should the original spectra look like

(determined experimentally on Earth) and what does the apparent spectra look like? Astronomers

can, and do, do this with the sun, but neutron stars provide the most dramatic example. Neutron

stars have a mass 1.4 times the mass of our sun, but they only have a radius of 10 kilometers,which is literally 100 million times smaller than the radius of the sun. While their gravity is not

much greater when directly compared with the sun, an observer can get much deeper into the

gravitational field of a neutron stars center of gravity than an observer can with the sun becausethat observer would run into the surface of the sun before getting deeper into the sun’sgravitational field. When astronomers measure Doppler shift, there can be as much as 35 percent

difference between the experimentally determined and original frequencies (Stannard, 2008).

The bending of light

Through the equivalence principal, it is apparent that acceleration and acceleration due to gravity

produce similar effects on objects like feathers and hammers, but when examining the effect of both accelerations on light, the light can be dramatically affected. Historically, it has beenassumed that light travels in straight lines. Imagining yet another spacecraft example, this

assumption will be challenged. In this example, the spacecraft is far from any gravitating bodies

and moving at a constant speed, thus constituting an inertial frame. A laser at the bottom of the

spacecraft fires pulses at a target at the top of the spacecraft. As expected, the astronaut and adistant observer see the laser travel in a straight line towards the target. If the spacecraft were to

fire its rockets, the distant observer would see the light travel in a straight line, but the light

would miss the target on the ceiling because the spacecraft has moved since the laser wasemitted. The astronaut, however, would see the light miss the target like the distant observer, but

would observe the light travelling a curved and thus bent path. Moreover, this example can be

used to conclude that acceleration bends light. Take this into account and use the equivalence

principal and replace the acceleration due to the spacecraft’s rockets with the acceleration due toa gravitational field.

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From these observations it is natural to expect that gravitational fields bend light. This is

definitely the case as Einstein predicted in 1915. His prediction was not confirmed until

Eddington’s famous 1919 solar eclipse measurements, as shown on the next page in figures 11

and 12. In this experiment, he noted theposition of the stars at night and wanted to

note their positions in the sky while close to

the sun. Because it is not possible to see the

stars during the day, Eddington had to do this during a total solar eclipse. Despite the difficultiesand

inaccuracies of these measurements, he was able to confirm Einstein’s predictions. Moreover,

much later the European Space Agency’s Hipparchos space satellite was able to confirmpredictions made by general relativity to an accuracy of less than 1 percent. This allows for a

phenomenon called gravitational lens, which is the scientific concept crucial to the topic of thispaper. When taking into account the gravitational field of an entire galaxy, it becomes apparent

that light can be severely demagnified, distorted and bent (Stannard, 2008).

Curved Space

As mentioned before, Einstein’s goal with general relativity was to understand why gravityaccelerated objects of different masses at the exact same rate. This has always interested Einsteinbecause Newtonian physics states that it takes more energy to move objects with a greater mass,

and despite what Newtonian physics says about energy and mass, gravity pulls exactly the same

on objects within its influence. In order to model this reality Einstein came up with the idea of curved space (Stannard, 2008).

Einstein argued that it is not the natural for objects to remain at rest or travel in straight lines, but

instead it is natural for objects to follow the contour of bent space. Einstein believed that

Figure 11 (above): This diagram represents the effect of gravity on light. As

shown later in this paper, light follows natural geodesics. The geodesics near amassive body, such as the sun, are curved by influence of the sun’s large mass.

Source: plus.maths.org Figure 12 (right): These are two actual photos of the most recent total solar

eclipse. The top picture is the view from the ground and the bottom picture is

the view from space. Eddington measured the positions of background stars

before and after a total solar eclipse similar to this one, confirming Einstein’s

predictions.

Source: earthobservatory.nasa.gov

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Gravitational Lensing 11

Figure 13: In these two actual bobsledding pictures, try to see how the bobsled tracks are the natural path for the

bobsleds to travel, assuming a high speed. In the right picture, a bobsled would travel in a straight line as expected

intuitively. In the picture on the left, the banked track forces the bobsled to travel in a way that would be impossible

under normal circumstances. Geodesics (explained below) are the natural path an object travels in spacetime, just as the

bobsled track is the natural path the bobsled would take. Source: www.areavoices.com (left); www.waymarking.com

(right)

gravitational fields were the product of space itself being bent by the influence of a massive

body, and the more massive the body the more curved space became. In essence, an astronaut inorbit around the Earth is merely following the curve laid out in space by the Earth (Stannard,

2008).

To visualize this, imagine

a bobsled on a flat track (see figure 13). Assuming

the bobsled has a fast

initial and constant speed,it is natural to expect the

bobsled to go in a straight

line; however, when theracetrack banks and

curves the bobsled will

follow the path of

racetrack quite easily. In

this example, it is nolonger natural for the

bobsled to go in a straight

path when the track isbanked and curved.

Einstein believed that

gravity did to space itself what the curved track did

for the bobsled. These predictions would answer how gravity “knew” to pull on all objects at theexact same rate regardless of their mass. Gravity is no longer seen as pulling on objects, but as

bending space itself so that objects are naturally affected by gravity (Stannard, 2008).

While interesting, this is very difficult to imagine bending space itself. Traditionally, one thinksof space as nothing, so it is only natural to ask how nothing can be bent. In modern physics,

quantum mechanics tells physicists that the subatomic level of space is literally full of particles,

but this goes beyond the scope of this paper. It was essential to introduce quantum mechanics torealize that space is something, and not to be thought of as nothing (Stannard, 2008).

Realizing that space is something rather than nothing is

interesting, but visualizing what bent three dimensional

space looks like is very difficult. In fact, it isimpossible from within the third dimension because it

is impossible to put an observer outside of the third

dimension to observe this phenomenon; however, thisis mostly meaningless because an observer can tell theshape of bent three dimensions from within it.

Physicists can do this by measuring the angles of

Euclidean geometry — Euclidean geometry is thetraditional approach mathematics takes when looking at

circles and triangles i.e. all angles of a triangle adds up to 180 degrees —

with triangles over areas of space. This is a difficult concept within itself; the only way to

Figure 14: This is a normal

Euclidean triangle. This triangle is

normally called a \right triangle.

The angles here add up to 180

degrees. Source:

www.aprweather.com

Figure 15: This is a non-

Euclidean triangle drawn on a

sphere. Note all of the triangle’s

lines are straight. Here the

angles add up to 270 degrees.

Source: www.math.cornell.edu

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Gravitational Lensing 12

imagine when a triangle’s angles would not add up to 180 degrees is to examine a sphere with a

triangle drawn on it, as shown on the previous page in figures 14 and 15. The three 90 degreeangles of the triangle on the sphere add up to 270 degrees. Also, because of gravitational

redshift, gravity should be thought of as bending not only space but spacetime.

In inertial frames and Euclidean geometry, physicists use straight lines as the foundation of their

thinking. As mentioned earlier, objects naturally follow a curved path in curved spacetime;instead of lines in spacetime physicists use geodesics, as illustrated in figure 16. In Euclidean

geometry a line is the shortest path between two points. In spacetime, a geodesic is the path that

has the maximum proper time,which replaces straight lines.

Recalling the twin paradox from

special relativity, it becameapparent that the twin astronaut

would be younger than his

terrestrial brother. It is also

apparent that once the twins are

reunited, they occupy the sameposition in space or same event in

spacetime. When the astronaut twin

left Earth and came back, the pathhe followed did not have the

maximum proper time, but his

terrestrial twin did. Because theterrestrial twin remained in an

inertial frame the entire time, his time was only affected by the natural curvature of spacetime,

thus having the maximum proper time between events. The astronaut twin on the other handaccelerated , thus violating the conditions for an inertial frame and arriving at the same event in

less proper time than his terrestrial brother (Stannard, 2008).

Verification of this prediction has been shown in two main ways: the precession of Mercury’sorbit and the unaccounted for discrepancies in NASA’s deep space communications . It has been

known since 1845 that Newtonian gravity failed to explain a small deviation in Mercury’s orbit.It was a very small deviation, but the fact that it was completely unaccounted for indicated that

Newtonian gravity was incomplete. General relativity was used to calculate Mercury’s orbit

precisely, and in 1974, general relativity successfully predicted the precession of a binary starsystem. In 1964, a radar astronomer proposed to test relativity by measuring the time delay of

reflected radar pulses emitted from the radar observatories on the Earth. The radar astronomers

did this by bouncing radar pulses off the planets as they orbited the sun. As the sun’s edge got in

between the Earth and the planet, the radar pulses were found to be delayed by about 0.00025seconds, which was exactly what relativity predicted. It is important to note that discrepancies

between what Newtonian gravity predicts and what general relativity predicts are very small, but

moreover, not only does general relativity account for these discrepancies, it also explains whythe planets orbit in the first place (Stannard, 2008).

Figure 16: This is a diagram for how four-dimensional spacetime is curved. Since it is impossible to

visualize four dimensions directly, the plane of this diagram represents the three dimensions of space, so

that way an observer can see the curvature in of three-dimensional space. The white lines represent

geodesics. From this perspective, the geodesics appear curved near the Earth in order to account for

Earth’s gravity; however, realize an observer within the plane would not immediately realize that the

three dimensions it inhabits are being bent. Source: www.math.cornell.edu

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THEORETICAL BACKGROUND

There are three different types of gravitational lensing. Strong lensing is where the gravitational

lens has affected the source light to the point the image is split into multiple highly distortedimages. Weak lensing is where the gravitational lens only distorts without splitting the image;

however, the effect is still resolvable by telescopes like the Hubble. Microlensing is where thedistortion caused by the gravitational lens is only detectable through the source’s brightnessvariation. Microlensing cannot be resolved directly by any telescope because if it could, it would

be weak lensing instead.

Before diving into the details, gravitational lensing requires a considerable math and physics

background to be fully understood. Here, a brief introduction to the mathematics will be given.

From general relativity, it is apparent that light is bent by gravity’s influence. When actuallymeasuring the angle it is bent, astronomers use the following equation:

Where is the angle between the apparent path of light and the source, is the universal

gravitational constant, is the mass of the object, is the speed of light, and is theperpendicular distance between the light ray and the object. However, this is only for a point

mass. In reality, point masses do not exist. The actual deflection of alight ray can be given here as a function of density using vector sums:

Where the density of the lens is , is the distance vector between the light ray and the object,

is the derivative of the vector, and is the line of sight coordinate. This equation is the

foundation for approximations of how the light is bent. This is shown above by figure 17.

Figure 17: This diagram formally

demonstrates how gravitational lensing is

calculated. Pay close attention to the

difference between and . Notice that

goes through the lens object, but

because the light rays have been

gravitationally lensed, they can go around

the lens object and arrive to the observer.

Also pay close attention to difference

between the apparent image and where

the source actually is. Note that is inthis diagram. Also, in this particular

diagram can be substituted for , but in

almost all cases the vector will not be

perpendicular to the lens.

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Gravitational Lensing 14

The surface brightness of an image is not altered by gravitational lensing, but the magnification

of objects by a gravitational lens can be greatly demagnified or greatly magnified. Thismagnification is directly proportional to the area of the source and the area of the image, which is

given by:

Where is the factor of magnification, is the angle between the source and apparent image,

and is angle between the source and the lens.

These two mathematical concepts are essential to seeing how gravitational microlensing works,

realizing that all the variables will not be accounted for, and why it is so difficult to apply. Thefirst two equations described only apply to a single theoretical light ray. In order to approximate

an entire image, it takes an enormous amount of computing power as will be shown later. The

third equation is essential to realizing that magnification can be beneficial in the case of the

image being magnified or detrimental when the image is demagnified.

STRONG LENSING

Strong lensing almost always involves a super massive galaxy as the lens, and the source is

usually another galaxy. When dealing with the mass of an entire galaxy, the gravitational

influence becomes astronomically huge, literally. For example, there are an estimated half trillion stars in the galaxy. Just accounting for those half trillion stars, ignoring the dark matter in

our galaxy, and assuming that each star is the same mass as the sun, the combined mass is

grossly 500 billion solar masses or kilograms — for reference is a billion sois forty-billion-billion-billion-

billion kilograms. Even though

this is grossly inaccurate of thegalaxy’s actual estimated mass,

the point is crystal clear;galaxies are super massive.This allows the light from a

source galaxy to be split into

different images by the lensinggalaxy (see figures 18 and 19).

This is what happens to the

source light after the light

follows geodesics that arecreated by a gravitational lens.

Remembering that geodesics

are what replace straight lines in non-Euclidean geometry,it not only strikingly confirms Einstein’s relativity, but gives astronomers a lot of information.As goes for all types of gravitational lensing, astronomers can say something about the mass of

the lens object by determining how much mass would be needed to create the apparent image.

Remembering loss of simultaneity, and that geodesics have the maximum proper time, itbecomes clear that these images can arrive to us at different times. The difference in time can be

determined by a shift in the frequency of the light. The shift in the frequency can be corrected if

Figure 18: Here is an example of a strong lensing event.

Notice the four white spheres surrounding the slightly

larger sphere in the center. The four spheres on the outside

all came from one source. The sphere in the center is the

lensing galaxy. Source: www.astro.cf.ac.uk

Figure 19: This is an actual image from the

Hubble space telescope demonstrating strong

lensing. The blue arcs are the source galaxy in this

image, while the galaxy cluster in the center is the

gravitational lens. Source: www.lsst.org

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Gravitational Lensing 15

enough data is present by matching the correct light curves together (e.g. like putting together the

pieces to a puzzle) (Vegetti & Koopmans, 2009).

WEAK LENSING

Weak lensing is an uncommon type of gravitational lensing. It occurs when the source light has

not been split into different images. This makes it much more difficult to account for the effectsof the gravitational lens since there are not two images to directly compare to each other. As aconsequence, there has to be other methods used to estimate the lens mass in order to properly

calculate the effects of weak lensing (Camera, Bertacca, Diaferio, Bartolo, & Matarrese, 2009).

MICROLENSING

Microlensing is the most common type of gravitationallensing, and therefore, shows the most promise in

science. Unfortunately, it is the most difficult type of

gravitational lensing to interpret. Because a micro lens is

by definition irresolvable by large telescopes, the data

must be interpreted using advanced image analysis withsupercomputers. The conclusions that can be drawn from

microlensing are heavily statistical but can at least giveupper bounds on things like the mass of the source object

or lens object. When dealing with galaxies, computers

must take into account the motion of the stars within the

galaxy. Because of this, magnification patterns arecreated and matched to fit the data (see figure 20)

(Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006).

THE BAYESIAN METHOD OF ANALYSIS

The Bayesian method is a statistical approach to compare hypothesis. When the data isincomplete, the Bayesian method seeks to assign probabilities based on incomplete data. As data

is gathered and collected it is updated into the Bayesian probability equations. When comparing

two hypotheses, the Bayesian method can only say that one hypothesis is more likely than theother. It is important to note that this method is subject to bias because the data gathered could be

intentionally selected to support one conclusion. However, when all available data is taken into

account, the Bayesian method can be used to effectively rule out certain hypotheses when theirprobability is very low (Loredo, 1992).

The Bayesian method of analysis is the most effective method for gravitational lensing. This

means that all conclusions drawn solely on gravitational lensing are statistical arguments, but this

does not mean that these conclusions are meaningless statistical arguments when otherindependent methods verify what the Bayesian probability agrees with. As a consequence,gravitational lensing can only be used to rule out possibilities instead of drawing concrete

conclusions independently (Loredo, 1992).

Figure 20: This is a typical magnification pattern for a lensing

galaxy. The dark areas indicate higher magnification and the light

areas indicate lower magnification. The magnification varies by a

factor of 10 from the highest to lowest magnification. Source:

(Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006)

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THE PROCESS

In astronomy, there is a significant process that must occur in order for astronomers to formulate

hypothesis. Astronomers must first gather the data, which is the “picture taking” of the desiredastronomical object. Second, astronomers must analyze the image with computers, refining

certain factors that are relevant to our hypothesis. Lastly, astronomers must take the data andapply it to theory in order to formulate a hypothesis or determine where further experimentationor observations are necessary.

OBTAINING THE DATA

Obtaining data for gravitational lensing requires three things: one, a larger telescope with good

resolution; two, a couple hours of observing every night; and three, space telescopes for certain

wavelengths of light (Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006). However,

astronomical data is generally collected by charged-coupled devices (CCDs for short) that areattached to telescopes. These CCDs take the analog light signals and turn them into electrical

signals that can be digitally interpreted by a computer. The actual mechanics of this process are

quite complex and beyond the scope of this paper, but it is important to note that modernastronomy uses only digital photographic technology in order to take advantage of digital image

analysis techniques. This is important because digital methods of image analysis are far superior

to the “by hand” methods of pre-digital astronomy, and digital methods allow computers to

analyze the data — computers cannot analyze analog data.

The size of a telescope mirror is a significant factor of the effectiveness of a telescope. In

general, when the radius of a telescope mirror doubles, the surface area of the mirror is roughly

multiplied by 4pi or about twelve times. This means that about twelve times more light will be

received by a telescope that has only twice the radius than a different telescope. This effect addsup quickly when combined with the technical capabilities of the telescopes CCD. Because

computers are digital and images are stored in rows and columns of pixels (also known asresolution), the resolution of a CCD is also very important. For observing lensing events, thetelescopes must be at least one or two meters in diameter, which is rather large. Also, their

resolution must be no less accurate than 1 arc second — an arc second is 1/3600th of a degree

(Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006).

Observing a lensing event for one or two hours seems like a trivial task; however, the waytelescope time is divided currently makes this a near impossibility. Telescope time is typically

divided up into segments of time measured in days. During these allocated time periods,

astronomers are allowed to use the telescopes as they intended because most other methods of observation require long exposure times or numerous short exposures. This is a sociological

issue and is difficult to change, but increased cooperation within the observing community could

easily allow for the one or two hour requirements of lensing observations and would greatly

advance the science of astronomy (Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006).

Astronomers assume that the bending of light is not uniform among all wavelengths of light, andin order to measure this effect, astronomers must observe in multiple wavelengths of light.

Because the Earth’s atmosphere easily lets only radar, visible, and infrared wavelengths through,

astronomers must turn to space telescopes to observe the ultraviolet, gamma, and mostimportantly x-ray wavelengths. Space telescopes are not hindered by the distortion of the Earth’s

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atmosphere, and therefore are capable of many things that are otherwise impossible with

terrestrial telescopes. Astronomy is very fortunate to have enough public support to enable thefunding needed for many space telescopes, but space telescopes are very expensive, which

makes them scarce. Since there are so few of them, there are very few astronomers that get to use

them; therefore, it becomes difficult to overcome the sociological issues with observing lensing

events (Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006).In short, the difficulties of observing lensing events means that it will be about a decade before

the use of gravitational microlensing will be common. However, these same difficulties also

demonstrate that observing lensing events only require a greater cooperation among astronomersinstead of a more costly alternative.

COMPUTER MODELING

Science has become increasingly reliant on computers to make advancements. This is truemainly because the mathematics of the real world rarely allow for analytical, or exact, solutions.

This means that the solution must be found numerically. Before computers, scientists were oftenunable to do these complex computations by hand with useable results. For instance, a crudeexample — albeit possible to solve analytically — of this is approximating the slope of a curve at

any given point. This example will use a standard parabola. In order to guess the slope of point

(x, y), draw a line between two dots that are close to point (x, y) (which are illustrated in figures21 and 22). Realizing that this straight line is not the exact slope of the curve at point (x, y),

imagine drawing the dots as

close as possible to point (x, y)

to get a much closerapproximation. Before the

invention of calculus this was

how Newton approximated theslope of curves, but the

important point here is to realize

that it is needed to get closer and

closer to point (x, y) to

approximate with any realaccuracy. In science, this becomes incredibly difficult to do by

hand with any useable results. For instance, the first approximation of the above parabola is so

far away from the real slope of the curve that it would be unwise to use it for any tangible ortheoretical purposes. It becomes apparent that computers are needed to calculate approximations

that are accurate enough for any real use, and when approximations are made by computers, the

accuracy of numerical approximations are literally trillions of times faster and more accuratethan numerical approximations done by hand.

The equations of gravitational lensing require an enormous amount of computing power. This ismainly for the following two reasons: one, it is required to approximate very small sections of

the light curve in order to obtain results that are accurate enough; two, when the gravitational

lens is another galaxy, we must take into account there are billions of stars in these galaxies thatall have their own magnification patterns and — to severely complicate the simulation — these

Figure 22: This is an example of Newton’s method.

Two points are drawn close to point (x, y) in order to

approximate the exact slope of (x, y)

Figure 21: This is a standard parabola with point

(x, y) represented.

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Gravitational Lensing 18

stars are all moving. Each of these factors on their own is relatively easy for modern personal

computers to handle. For example, approximating a single light curve takes only a couple dozenmegabytes of random access memory (RAM) and a few seconds. However, it becomes apparent

when approximating all the light curves, creating a random star field, and animating that same

star field that the RAM requirements skyrocket into hundreds of gigabytes and require days to

run on supercomputers. Fortunately, supercomputer time is relatively easy to obtain forscientists, but the time factor still limits the amount of data that can be processed for

gravitational lensing (Kochanek, Dai, Morgan, Poindexter, & Chartas, 2006).

APPLICATIONS

There are numerous applications of gravitational microlensing for astronomers. Gravitational

microlensing is uniquely capable of determining the mass of objects. This is only one of the

unique characteristics of gravitational microlensing. Gravitational microlensing will be able to

help astronomers detect extra-solar planets, probe the nature of black holes, determine the natureof dark matter, and even help astronomers figure out how this universe formed.

EXOPLANET DETECTION

It has been assumed, since the dawn of modern astronomy, that other solar systems should haveplanets. This assumption stemmed from the fact that our own solar system has eight planets.

However, for many years astronomers searched and found nothing. In fact, in 1972, Peter Van

De Kamp spent over 30 years — from 1938 to 1963 — using the astrometric method to find extra-

solar planets. Because the light from a star makes it nearly impossible to photograph exoplanetsdirectly, the astrometric method was the first method astronomers used to discover extra-solar

planets. Since planets have gravitational influence on the stars they orbit, they cause tiny

wobbles in their stars’ orbit. This is a well known fact confirmed by Jupiter within the own solarsystem, which pulls the sun a small distance towards itself. However, the resulting distance is so

small it would be nearly impossible to detect the wobble of a star from trillions of miles of way.

With this in mind, Van De Kamp searched for a nearby low mass star known as Barnard’s Star.

After years of observing the same star, he published the results in The Astronomical Journal, butanother study by George Gatewood and Heinrich Eichhorn has failed to replicate his results (Van

De Kamp, 1969) (Gatewood & Eichhorn, 1973).

The first widely accepted exoplanet was not detected until 1995 by the spectroscopic method(Mayor & Queloz, 1995). The spectroscopic method has the same basic idea as the astrometric

method; however, instead of detecting the wobble of a star directly, the spectroscopic method

detects the wobble through tiny Doppler shifts. This method has become the dominant method

for detecting exoplanets and has detected over 200 exoplanets so far. This method does have

some limitation — mainly because the planet must be rather massive to cause a measurablewobble in star. It can only detect planets with similar masses to Neptune because spectrometers

are not sensitive enough (Erskine, Edelstein, Harbeck, & Lloyd, 2005).

Gravitational microlensing overcomes many of the problems with the spectroscopic method, butthe general limitations of gravitational microlensing hinder it from being the most successful

method for detecting extra-solar planets. The main advantage of gravitational microlensing as a

method for detecting extra-solar planets is that it can independently verify the mass of an extra-

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solar planet, and detect planets that are currently beyond the sensitivity of other methods. In

August of 2005, there was a tiny deviation in the light curve of a star during a lensing event. Thisplanet was found to have a mass around 5.5 times the mass of the Earth making it the least

massive exoplanet found to date. At the same time, it was found orbiting a star in the galactic

bulge at a distance of about 21,500 light years, making it by far the most distant exoplanet found

(Beaulieu, Bennett, & Fouque, 2006).This has tremendous potential for exoplanet astronomy. The models for planetary formation are

far from being complete. One of the main problems with creating an accurate and reliable model

for planetary formation is a lack of planets to look at. Before 1995, exoplanets had yet to bedetected, and now new technologies continue to push the limits of sensitivity further.

Gravitational microlensing will greatly benefit the exoplanet research community by acting as an

independent method of verifying the claims of other methods. If claims about exoplanets can beverified by gravitational microlensing and other methods of exoplanet detection, astronomers

will be “one-giant-leap” closer to having enough data to create a complete model of planetary

formation. Also, it appears that gravitational microlensing will be the only method capable of

detecting extremely distant exoplanets for quite some time.

ACCRETION DISK THEORY

Since the dawn of modern physics with Einstein's general relativity, physicists have been

searching for ways to unite the forces of physics into one grand unifying theory. Unfortunately,

when physicists attempt to combine the most complete theory of gravity, general relativity,with the most complete theory of the other three forces, quantum mechanics, by studying black

holes, they get absolutely nowhere. These two models are incompatible with each other. While

both theories can predict what each force of physics will do to a high degree of accuracy, one orboth are wrong to a certain extent. As biologists have the grand theory evolution — which fully

explains the diversity of life — physicists hope to create a grand unification theory. With a theory

that successfully unites and explains all the forces of physics, the genre of science fiction will nolonger be a proper name. Perhaps futuristic fantasy would be more appropriate. Any imaginablemanipulation of matter, space, and time will be known and possible. Cold fusion will be

commonplace, and even the vast distances between stars will no longer be an obstacle. Accretion

disk theory is one of the many ways physicists are trying to unite the forces of physics. Becauseblack holes are unobservable using light, accretion disk theory is an attempt to study the

observable properties of a black hole and even probe the properties of the actual black holes.

Accretion disk theory deals with what happens when matter that is not gravitationally bound

somehow contracts and becomes gravitationally bound to form a star, a quasar, or even a planet.Since astronomers first started modeling accretion disks, it became abundantly clear that there

are large disagreements between observation and theory. Over the last 40 years, astronomers

have begun accounting for the many variables of accretion disks. The current theory built upafter all these years, which deals with magnetic instabilities, is actually being discredited byrecent evidence. This has forced astronomers to rethink the fundamentals of the accretion disk

theory (Hubbard & E, 2008).

Most current research focuses on the X-ray emission of quasars — quasars are supposed to be

super massive black holes with an accretion disk. X-rays are of particular interest because over90% of X-rays are emitted from quasars. Some astronomers believe that understanding why this

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Gravitational Lensing 20

is the case will help refine accretion disk theory. Gravitational microlensing is attempting to

refine the X-ray data with strong lensing. This will help determine the reliability of the data andallow astronomers to focus more on refining the theory (Jovanovic & Popovic, 2009).

DARK MATTER DETECTION

When astronomers first began to estimate the masses of galaxies, they discovered a hugeproblem. Astronomers calculated these estimates by looking at all of the light a galaxy emits andusing the standard photometric method of estimating mass. Another way to estimate the mass of

objects is to measure the speed of the two objects in question. This is done quite often with

binary star systems. Using this idea proves that the stronger the gravity, the faster an objectwithin its influence needs to go in order to stay in orbit. For example, when taking two identical

planets and placing them in the exact same orbit around two different stars, it would become

apparent that the planet around the more massive star would be moving faster, so if the speed and

orbits of two stars in a binary system are known, the mass of both objects can be calculated. Thiswas the first way astronomers measured the mass of astronomical objects.

Using these two methods of measuring mass, astronomers found that the mass estimated this waywas far less than the mass that would be required to account for the speed of the stars rotating

within any given galaxy. In fact, it is estimated that only 4% of the mass in the entire universe isbaryonic (normal), matter. To compensate for these effects, astronomers speculated that invisible

dark matter existed to account for all of the missing mass. For some time, dark matter was purely

speculative. Astronomers believed that it would be possible to indirectly detect dark matterthrough its gravitational effects. With advances in gravitational lensing, it became immediately

apparent that gravitational lensing would play a huge role in dark matter research. While the true

nature of dark matter is still wildly speculative, gravitational lensing is being used to map itstheoretical location in the universe. Determining what and where dark matter is has been the goal

of modern astronomy ever since dark matter’s existence was first proposed.

BIG BANG COSMOLOGY

Since its proposal by the scientist and Roman Catholic priestGeorges Lemaître in 1931 (pictured in figure 22), the big

bang theory has been through a rather interesting scientific

journey (Midbon, 2000). It was scoffed at by scientists for

many years and was not the dominant cosmological theoryfor over 30 years. In 1965, the cosmic microwave

background was discovered, which the big bang theory

directly predicted, marking the beginning of the big bang

theory’s dominance in science. Despite some amazing

successes, the big bang theory still fails to explain the originof our universe with any reasonable sense of authority.

One of the problems with the big bang theory is that it doesnot predict the observed distribution of matter within the

universe. As stated earlier, it is believed that baryonic

(normal) matter makes up only 4% of the matter in theuniverse. Dark matter is believed to account for another 22%

Figure 23: This is a picture of Lemaitre next to Einstein.

Lemaitre was the first scientist to apply Einstein’s general

relativity to cosmology.

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Gravitational Lensing 21

of the matter despite that it has never been directly observed, and dark energy — the most exotic

and unconfirmed astrophysical theory proposed yet — is supposed to account for the rest. Thecurrent understanding of physics can only attempt to explain 4% of the universe. Dark matter and

dark energy need to be understood to make a more serious attempt at understanding the origin of

universe, which is perhaps the grandest question astronomy can answer.

Gravitational lensing is contributing to the solution by indirectly mapping dark matter. The mostbeneficial contribution it may make is preparing astronomy for the advent of super radio

telescopes. These radio telescopes will be capable of resolving the influence of dark matter much

better than gravitational lensing will (Metcalf & White, 2008).

CONCLUSION

Gravitational lensing shows immense promise for astronomers. Since man has looked into the

sky, there has been an indescribable urge to understand. Besides discovering that the Earth

circled the sun and not the other way around, Galileo laid the foundation for modern science by

showing that careful observation and experimentation will lead to a greater understanding of thenatural world. Later, Einstein laid the foundations for gravitational lensing by proposing special

and general relativity. Finally, after amazing advancements in computers and telescopes,

gravitational lensing has become a reality. Astronomers are now free to use gravitational lensingas a method for probing the cosmos.

Astronomers have only had space telescopes for a very short period of time. During this time,

some people have claimed that astronomy has entered a golden age of discovery; however, thesepeople were not aware that methods like gravitational lensing will become viable and useful.

This fact, combined with other new observational methods, like speckle imaging,

interferometers, and astroseismology, will propel astronomy into the real golden age of

astronomy. Astronomers are only beginning to have enough data to answer the big questions, and

hopefully, with enough time astronomers will do just that.

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Gravitational Lensing 22

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