Examining the Accuracy in Weak Gravitational Lensing Department of Physics, Bridgewater State College: Bridgewater MA, 02325 Christopher Cepero Mentor:

Slides:



Advertisements
Similar presentations
General Relativity Physics Honours 2009 Prof. Geraint F. Lewis Rm 560, A29 Lecture Notes 4.
Advertisements

Dark Matter Mike Brotherton Professor of Astronomy, University of Wyoming Author of Star Dragon and Spider Star.
General Relativity is a surprisingly good fit for grade-9 Astronomy. It explains and gives depth to many standard topics like.... What causes orbits?
CS 282.  Any question about… ◦ SVN  Permissions?  General Usage? ◦ Doxygen  Remember that Project 1 will require it  However, Assignment 2 is good.
Analysis of a New Gravitational Lens FLS Yoon Chan Taak Feb Survey Science Group Workshop
Surface Flattening in Garment Design Zhao Hongyan Sep. 13, 2006.
Astrophysical applications of gravitational microlensing By Shude Mao Ziang Yan Department of Physics,Tsinghua.
Extragalactic Astronomy & Cosmology First-Half Review [4246] Physics 316.
Session: Computational Wave Propagation: Basic Theory Igel H., Fichtner A., Käser M., Virieux J., Seriani G., Capdeville Y., Moczo P.  The finite-difference.
Gravitational Faraday Effect Produced by a Ring Laser James G. O’Brien IARD Bi-Annual Conference University Of Connecticut June 13 th, 2006.
Optical Scalar Approach to Weak Gravitational Lensing by Thick Lenses Louis Bianchini Mentor: Dr. Thomas Kling Department of Physics, Bridgewater State.
Scott Johnson, John Rossman, Charles Harnden, Rob Schweitzer, Scott Schlef Department of Physics, Bridgewater State College // Bridgewater MA, Mentor:
PRESENTATION TOPIC  DARK MATTER &DARK ENERGY.  We know about only normal matter which is only 5% of the composition of universe and the rest is  DARK.
How do we transform between accelerated frames? Consider Newton’s first and second laws: m i is the measure of the inertia of an object – its resistance.
Radiative Transfer with Predictor-Corrector Methods ABSTRACT TITLE : Radiative Transfer with Predictor-Corrector Methods OBJECTIVE: To increase efficiency,
General Relativity Physics Honours 2006 A/Prof. Geraint F. Lewis Rm 557, A29 Lecture Notes 6.
Physics 133: Extragalactic Astronomy and Cosmology Lecture 12; February
General Relativity Physics Honours 2006 A/Prof. Geraint F. Lewis Rm 557, A29 Lecture Notes 5.
Physics 133: Extragalactic Astronomy and Cosmology Lecture 13; February
What’s new here? The accuracy of the thin lens approximation has been assessed through convergence of statistics by increasing the number of lens planes.
Computer Vision - A Modern Approach
Einstein’s Lens Presented by: Kevin McLin, SSU NASA E/PO 2008 EA Training, SSU Einstein’s Lens.
Bianchi Identities and Weak Gravitational Lensing Brian Keith, Mentor: Thomas Kling, Department of Physics, Bridgewater State College, Bridgewater, MA.
CHAPTER 3 Describing Relationships
Calculus and Analytic Geometry II Cloud County Community College Spring, 2011 Instructor: Timothy L. Warkentin.
In the previous two sections, we focused on finding solutions to differential equations. However, most differential equations cannot be solved explicitly.
Bouncing Liquid Jets James Bomber, Nick Brewer, and Dr. Thomas Lockhart Department of Physics and Astronomy, University of Wisconsin - Eau Claire
1 Gravitational lensing and neutrinos Why not look where natural lenses exist? Proposal of an additional candidate list in point source search: 1. Motivation.
Dark Matter begin. Definition Dark Matter is matter that we cannot see. It neither emits nor reflects any light. If we can’t see it, how do we know it.
Chapter 26 Relativity. General Physics Relativity II Sections 5–7.
Gravitational lensing of the CMB Richard Lieu Jonathan Mittaz University of Alabama in Huntsville Tom Kibble Blackett Laboratory, Imperial College London.
Computer Science 101 Modeling and Simulation. Scientific Method Observe behavior of a system and formulate an hypothesis to explain it Design and carry.
Chris Pardi, University of Surrey ECT* Trento, Advances in time-dependent methods for quantum many-body systems.
GRAVITATIONAL LENSING
Methods in Gravitational Shear Measurements Michael Stefferson Mentor: Elliott Cheu Arizona Space Grant Consortium Statewide Symposium Tucson, Arizona.
Chapter 25 Galaxies and Dark Matter Dark Matter in the Universe We use the rotation speeds of galaxies to measure their mass:
North America at night from space. Light can be: broken up into component colors broken up into component colors absorbed absorbed reflected reflected.
A Short Talk on… Gravitational Lensing Presented by: Anthony L, James J, and Vince V.
1 Gravitational Model of the Three Elements Theory : Mathematical Details.
Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Numerical Differentiation and Integration ~ Integration.
< BackNext >PreviewMain Chapter 2 Data in Science Preview Section 1 Tools and Models in ScienceTools and Models in Science Section 2 Organizing Your DataOrganizing.
General Relativity Physics Honours 2005 Dr Geraint F. Lewis Rm 557, A29
ORBITAL DECAY OF HIGH VELOCITY CLOUDS LUMA FOHTUNG UW-Madison Astrophysics REU 2004 What is the fate of the gas clouds orbiting the MilkyWay Galaxy?
Abstract It was not realized until 1992 that light could possess angular momentum – plane wave light twisted in a corkscrew. Due to resemblance with a.
The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 3 Describing Relationships 3.2 Least-Squares.
Environmental and Exploration Geophysics II t.h. wilson Department of Geology and Geography West Virginia University Morgantown, WV.
Space Warps. Light is believed to travel the shortest distance between two points But…… the path of light is curved in the presence of a gravitational.
Influence of dark energy on gravitational lensing Kabita Sarkar 1, Arunava Bhadra 2 1 Salesian College, Siliguri Campus, India High Energy Cosmic.
Chapter 2 Examining Relationships.  Response variable measures outcome of a study (dependent variable)  Explanatory variable explains or influences.
Dark Matter Facts Only 20% of all known matter is the matter we can see, or “normal matter.” The other 80% is Dark Matter, which is also around us just.
CHAPTER 3 Describing Relationships
Motions of Self-Gravitating bodies to the Second Post- Newtonian Order of General Relativity.
Section 2.1 Part 2: Transforming Data, Density Curves.
General Relativity and Cosmology The End of Absolute Space Cosmological Principle Black Holes CBMR and Big Bang.
Project Background My project goal was to accurately model a dipole in the presence of the lossy Earth. I used exact image theory developed previously.
Lecture 39 Numerical Analysis. Chapter 7 Ordinary Differential Equations.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Part 6 - Chapters 22 and 23.
VISIBLE PROPERTIES OF COSMIC ANTI-STRING Kotvytskiy A.T., Shulga V.M. Institute of Radio Astronomy of Nat. Ac. Sci. of Ukraine Karazin Kharkov National.
Chapter 9: Gravity & Planetary Motion
Probing Extra Dimensions with images of Distant Galaxies Shaun Thomas, Department of Physics and Astronomy Supervisor: Dr, Jochen Weller Results and Conclusions.
Astronomy 1020 Stellar Astronomy Spring_2016 Day-34.
Measuring Cosmic Shear Sarah Bridle Dept of Physics & Astronomy, UCL What is cosmic shear? Why is it hard to measure? The international competition Overview.
Week 2 Normal Distributions, Scatter Plots, Regression and Random.
CHAPTER 3 Describing Relationships
Regression and Residual Plots
David Berman Queen Mary College University of London
12/1/2018 Normal Distributions
THE UNIVERSE Essential Questions
Project P06441: See Through Fog Imaging
CHAPTER 3 Describing Relationships
Presentation transcript:

Examining the Accuracy in Weak Gravitational Lensing Department of Physics, Bridgewater State College: Bridgewater MA, Christopher Cepero Mentor: Dr. Thomas Kling Abstract: Weak gravitational lensing is a relativistic idea that involves image distortion, or the stretching and shearing of a perceived image. This research project examines the thin-lens approximation for weak gravitational lensing by computing an exact treatment of weak gravitational lensing based on general relativity. We write a c++ program to integrate weak gravitational lensing equations, while accounting for elongation and shear in light rays. By utilizing the Runge-Kutta adaptive step method, we are able to create a computer program to integrate the Euler-Lagrange equations that describe the path of light to yield the geodesics. We then integrate the geodesic deviation equations to determine the distortion patterns. Our goal is to write a program that will numerically integrate the Euler Lagrange equations to model weak gravitational lensing. We anticipate that this method will yield values more accurately than by the use of thin lens approximation. What is Gravitational Lensing: Gravitational Lensing is a phenomenon that effects images we see of a source of light. The types of effects vary, from stretching the image out to duplicating it. This is a result of light traveling in curved space, which is caused by a massive object in space. Gravitational lensing can be divided into two classes: strong lensing and weak lensing. Strong Gravitational Lensing: Causes multiple images. Needs an extremely massive lensing object. Weak Gravitational Lensing: Causes the image to stretch and rotate. Why we care: Gravitational Lensing is a valuable tool in astrophysics. It is used to predict the distribution of matter in the universe, and is also used to calculate the mass density of lensing objects. Furthermore, gravitational lensing is used in studies of black holes. How gravitational Lensing is studied: Gravitational Lensing can be studied by observation, and by modeling it with computer code. While observational study is possible, it is much more useful to model lensing. Currently, there are two ways to model gravitational lensing. The first is to us the thin lens approximation. The second is to model it by calculating the path light travels in it’s entirety. Our Model vs. Thin Lens Model: The difference begins with the fact that our model considers how light is affected in the entirety of it’s journey. Our model also makes use of the geodesic deviation equations to account for the stretching of light. Thin Lens Approximation Computer Code: Overview: Our original code modeled the continuous bending/integration of the light bundle, which means there is no approximation. We modified the previous code for paths and have added new code to calculate the change in shape of the light. In addition, we have expanded the existing adaptive step-size algorithm for all differential equations. Equations for the path: New Lagrangian and Euler-Lagrange equations Three copies of things looking like Equations for the Shape: General geodesic deviation equation Wrote four versions of this segment of code. Light Path: The original RFK-model we began with was written by Dr. Kling and his collaborators. Originally it ran the calculation from the observer to the source, so we altered it to perform the more appropriate calculation from the source to the observer. We also made three new function of the form as follows. double eta_int(double z, double r, double rs, double tau, double delta_c){ double al, x, om, Hsq, M0, term, pot, eta_return; al = 1.0/(1.0+z); x = al*r/rs; om = 0.3; Hsq = H*H*(om/al/al/al +(1.0-om)); M0 = 1.5*delta_c*Hsq*rs*rs*rs; term = atan(x/tau)*(1.0/tau-tau-2.0*tau/x); term = term + log((1.0+x*x/tau/tau)/(1.0+x)/(1.0+x))*((tau*tau- 1.0)/2.0/x - 1.0); term = term + PI*(tau*tau-1.0)/2.0/tau - 2.0*log(tau); pot = M0*tau*tau/rs/(1.0+tau*tau)/(1.0*tau*tau)*(term); eta_return = ( *pot); return eta_return; }//close function Geodesic Deviation: The geodesic deviation is completely new code we wrote over the summer. It required four of the functions shown below, each with 5 subfunctions. double yoy(double ell[], double Y[], double p[]){ double t, x, y, z; t = p[0]; x = p[1]; y = p[2]; z = p[3]; double r = sqrt(x*x + y*y + z*z); double p_xx, p_xy, p_xz;.. (~20 lines of code removed). double yoy_return; yoy_return = p_yy*ell[0]*ell[2]*Y[0] - p_yy*ell[0]*ell[0]*Y[2]; yoy_return = yoy_return + p_yx*ell[0]*ell[1]*Y[0] - p_yx*ell[0]*ell[0]*Y[1]; yoy_return = yoy_return + p_yz*ell[0]*ell[3]*Y[0] - p_yz*ell[0]*ell[0]*Y[3]; yoy_return = yoy_return + (p_yy + p_xx)*ell[1]*ell[2]*Y[1] - (p_yy + p_xx)*ell[1]*ell[1]*Y[2]; yoy_return = yoy_return + (p_yy + p_zz)*ell[3]*ell[2]*Y[3] - (p_yy + p_zz)*ell[3]*ell[3]*Y[2]; yoy_return = yoy_return + p_xz*ell[1]*ell[2]*Y[3] - p_xz*ell[1]*ell[3]*Y[2]; yoy_return = yoy_return + p_zx*ell[3]*ell[2]*Y[1] - p_zx*ell[3]*ell[1]*Y[2]; yoy_return = yoy_return - p_yz*ell[1]*ell[1]*Y[3] + p_yz*ell[1]*ell[3]*Y[1]; yoy_return = yoy_return - p_yx*ell[3]*ell[3]*Y[1] + p_yx*ell[3]*ell[1]*Y[3]; return yoy_return; }//close function Other code work / modifications: Adaptive step-size code was modified to include integrating geodesic deviations equations. Total new functions written: 12 Total new lines of code: 1200 Total lines of code: 2000 Current Project Status: We have a complete code that should integrate the shape parameters. The code runs if the adaptive step-size is turned off for the shape, but the shapes look wrong. In addition, the size of the error in the shape integration looks too large. Question remaining: Is the problem a programming bug or conceptual error? Acknowledgements: Joachim Wambsganss, "Gravitational Lensing in Astronomy", Living Rev. Relativity 1, (1998), 12. URL (cited on ): Dr Kling and Collaborators HubbleSite. HubbleSite Aug