1. Karen Zhu UC Davis COSMOS 2015 Cluster 4 - Astrophysics Finding the Hubble Constant: Gravitational Lensing with B1608

2. What is Gravitational Lensing? http://www.bigbangcentral.com/galaxy_page.html

3. https://commons.wikimedia.org/wiki/File:Diagram_on_%22Gravitational_Lensing%22.jpg

4. https://commons.wikimedia.org/wiki/File:Abell.lensing.arp.750pix.jpg

5. Fermat’s Principle  Light naturally travels along the shortest path  With gravitational lensing, multiple images are likely to come up because there are so many possible paths light can take through space

6. Why is there a time delay between different lensed images? (time delay) = (geometric delay) + (gravitational delay)

7. Using Gravitational Lensing to find the Hubble Constant  The Hubble Constant measures the current rate of expansion of the universe in units of km/s/Mpc  Why is this constant significant?

8. v = H 0 × d  v refers to the redshift of the galaxy  H 0 refers to Hubble’s constant  d refers to the distance from Earth

9.  H 0 refers to Hubble’s constant  S h r efers to the error (in km/s/Mpc)

10. How do you determine the time delay of a gravitational lens?

11. # day ffa ffb ffc ffd fferra fferrb fferrc fferrd#1350.70 20.55246 10.39392 10.78356 3.13611 0.16738 0.12923 0.13037 0.114741352.61 20.92821 9.82246 10.27032 3.24680 0.18470 0.14771 0.14881 0.136841354.86 20.51223 10.78938 10.44631 3.40239 0.17407 0.13908 0.13814 0.124781357.87 20.78028 10.55789 10.55589 3.23687 0.18465 0.15022 0.15021 0.137581358.68 20.27433 10.98596 10.45266 3.23767 0.21267 0.18648 0.18537 0.175521359.59 20.72292 11.33636 10.93333 3.30347 0.18696 0.15531 0.15427 0.141021360.90 20.70605 11.10219 10.49844 3.25444 0.16221 0.12376 0.12185 0.106111362.84 20.95053 11.29777 10.30059 3.36829 0.25439 0.23132 0.22963 0.222081363.43 20.11075 11.11660 10.13437 3.34607 0.26549 0.24571 0.24417 0.237331364.86 21.18397 11.15694 10.62627 3.26848 0.18553 0.15082 0.14944 0.136571367.85 20.95791 10.90968 10.13628 3.46280 0.17948 0.14383 0.14177 0.129741368.60 20.96511 10.80949 10.68382 3.36066 0.18273 0.14756 0.14723 0.134071371.83 21.18596 10.99171 11.01694 3.40179 0.15743 0.11390 0.11399 0.095081372.57 20.95057 11.06180 10.65814 3.41716 0.19106 0.15845 0.15745 0.145331374.83 20.87706 10.79152 10.66900 3.39632 0.19056 0.15753 0.15723 0.145041375.56 20.95630 10.75747 10.79202 3.42691 0.16808 0.12886 0.12897 0.113411378.64 20.98717 11.58318 10.52670 3.47445 0.17011 0.13384 0.13066 0.116261380.71 20.61238 10.12828 10.71931 3.51131 0.21954 0.19130 0.19246 0.182621382.52 21.54874 10.97069 10.74661 3.50045 0.18566 0.14861 0.14802 0.134881384.66 21.26822 10.90501 11.01397 3.37177 0.19538 0.16177 0.16203 0.149321385.73 21.43822 10.70098 11.46433 3.40586 0.18643 0.14944 0.15147 0.136481386.54 22.07854 11.35479 11.07187 3.50235 0.21914 0.18739 0.18678 0.175831389.58 21.53403 10.97782 10.85393 3.46079 0.18534 0.14831 0.14798 0.134491393.73 21.64479 11.13052 10.65909 3.47779 0.27175 0.24788 0.24713 0.239621394.49 21.38868 10.78376 11.01028 3.45450 0.19442 0.15974 0.16029 0.147511396.63 22.34755 10.91366 10.97996 3.59878 0.20040 0.16269 0.16285 0.150491398.73 21.21580 11.40376 11.02463 3.39405 0.18079 0.14548 0.14442 0.129991399.70 21.25489 11.33928 10.48027 3.45204 0.23319 0.20674 0.20511 0.196321402.69 21.71340 11.37170 11.17667 3.53696 0.26928 0.24534 0.24502 0.236621403.72 21.64405 11.36504 10.97688 3.46623 0.19227 0.15733 0.15634 0.143301405.74 22.03692 11.06950 11.07354 3.48872 0.19292 0.15539 0.15540 0.142031408.66 21.77219 11.21370 11.12038 3.45060 0.17630 0.13618 0.13590 0.120191412.61 21.49652 10.34458 11.32424 3.57608 0.17495 0.13351 0.13634 0.120131414.74 21.87198 11.25899 11.25395 3.42446 0.19343 0.15734 0.15733 0.143581417.49 21.24802 11.17616 10.81568 3.62376 0.18718 0.15257 0.15163 0.138761419.71 21.59140 10.99037 11.03929 3.48271 0.16235 0.11799 0.11816 0.100051421.69 21.69540 10.99384 11.05532 3.53359 0.18115 0.14221 0.14238 0.127761422.42 21.86052 10.90429 11.00018 3.50392 0.27151 0.24656 0.24672 0.238651427.65 21.64536 11.09280 11.11699 3.63847 0.18164 0.14338 0.14345 0.128861431.67 21.86189 10.90990 11.48526 3.70479 0.16388 0.11805 0.11999 0.100721433.46 21.31243 10.71395 10.79093 3.55586 0.17768 0.13911 0.13932 0.125201438.48 21.80591 11.21807 11.31572 3.67962 0.20287 0.16902 0.16925 0.156601441.36 21.42814 10.37854 11.21223 3.49739 0.20425 0.17048 0.17237 0.160091443.45 22.36122 11.36537 11.35840 3.76588 0.16889 0.12318 0.12316 0.105051450.34 22.18104 11.17204 11.26607 3.83204 0.20778 0.17307 0.17329 0.161211452.61 21.25431 11.73331 11.46945 3.70814 0.17060 0.13341 0.13258 0.115481453.50 21.56032 11.99737 10.85247 3.65867 0.23589 0.20998 0.20772 0.198471456.49 22.00881 12.06980 11.20243 3.62292 0.15387 0.10715 0.10370 0.081911459.24 21.90676 11.67490 10.97132 3.53287 0.17158 0.13065 0.12844 0.112311464.49 21.27184 11.93421 11.12045 3.72799 0.16757 0.13006 0.12744 0.110861466.54 21.81146 12.38726 11.29719 3.60346 0.15238 0.10778 0.10338 0.081001470.26 22.46718 12.50802 11.29566 3.65009 0.18166 0.14304 0.13936 0.123721473.28 22.00276 11.98821 11.34702 3.59967 0.15972 0.11513 0.11277 0.092451476.35 22.65241 12.13558 11.26294 3.73356 0.16143 0.11353 0.11024 0.089941481.17 21.97071 11.82735 11.29717 3.73293 0.17498 0.13519 0.13354 0.117221484.50 23.11026 12.12099 11.67507 3.55613 0.28053 0.25447 0.25372 0.244791488.48 23.69145 12.49722 12.04472 3.97788 0.17561 0.12750 0.12592 0.105841491.47 24.09164 12.30441 11.89515 3.78417 0.16722 0.11188 0.11028 0.087081494.30 23.38438 12.09691 12.04119 3.85063 0.16543 0.11379 0.11357 0.090631496.34 24.83961 12.22859 12.47130 3.69377 0.17906 0.12342 0.12429 0.101691500.49 24.40040 12.94995 12.40645 3.76052 0.17879 0.12872 0.12678 0.105081503.42 23.60778 12.62858 12.42467 3.73574 0.16171 0.10875 0.10790 0.081161506.53 24.37895 12.63371 12.65951 3.95842 0.15882 0.09785 0.09797 0.066281509.45 24.49354 12.28448 12.52191 3.73782 0.20245 0.15754 0.15821 0.141031511.42 24.23527 12.39073 12.74600 3.80900 0.38108 0.36001 0.36045 0.352991516.51 24.25333 12.13844 11.79848 3.90552 0.16730 0.11008 0.10874 0.085801523.39 26.70486 12.93824 13.30118 4.05928 0.17827 0.11015 0.11169 0.081851526.22 25.12142 12.02701 13.19062 3.79971 0.16523 0.09894 0.10415 0.071431533.46 25.78873 12.81471 12.48472 4.08296 0.19457 0.14080 0.13973 0.120471537.34 25.69142 12.69259 13.22136 4.08217 0.19873 0.14674 0.14841 0.127801540.49 25.78650 12.30748 13.11187 4.23848 0.19411 0.13854 0.14117 0.119951541.33 25.35184 11.97338 13.26401 4.33993 0.18860 0.13264 0.13699 0.114501544.32 25.70946 12.51009 12.73110 4.22553 0.17823 0.11664 0.11750 0.092811548.31 24.88612 12.68278 13.97787 4.35761 0.19983 0.15306 0.15706 0.135351550.30 25.06065 12.61645 12.95590 4.21731 0.18091 0.12590 0.12714 0.103741553.27 25.16708 12.70455 12.02990 4.07518 0.17439 0.11585 0.11323 0.090601555.30 25.53553 12.90120 12.65767 4.17660 0.16921 0.10559 0.10453 0.076061558.40 25.73952 12.67823 12.86461 4.26315 0.17778 0.11637 0.11710 0.091701561.28 25.25141 12.41625 12.81296 4.07414 0.19644 0.14554 0.14677 0.127401564.29 25.79640 12.83083 13.49329 4.17078 0.17920 0.11867 0.12128 0.093711568.26 26.09152 12.71122 13.60433 4.27306 0.18969 0.13149 0.13467 0.110141569.25 24.36635 12.09709 13.19475 4.18960 0.19377 0.14643 0.14980 0.129631574.25 25.42768 12.59846 12.96079 4.31453 0.18000 0.12180 0.12316 0.098951576.24 25.74014 11.82898 12.92061 4.23814 0.20785 0.15616 0.15925 0.141411579.23 25.87534 12.23826 13.44060 4.32783 0.17751 0.11313 0.11794 0.089901585.22 25.67570 12.33133 13.53931 4.49964 0.21153 0.16275 0.16617 0.147451587.21 26.39902 12.39105 12.94346 4.42941 0.18081 0.11459 0.11677 0.091161589.21 25.38212 12.29858 13.80124 4.53449 0.20106 0.15059 0.15521 0.13407 Provided by Lord Fassnacht

14. figure (2) errorbar(nday-25.0,navg2,yerr=err1,fmt='o') #A ** errorbar(nday,navg3,yerr=err2,fmt='o') #B ** errorbar(nday-32.0,navg4,yerr=err3,fmt='o') #C ** errorbar(nday-53.0,navg5,yerr=err4,fmt='o') #D **

15. Model Time Delays: B1608 Provided by Lord Fassnacht

16. Solving for h

22. WORKS CITED Benitez, N., T. Broadhurst, H. Ford, M. Clampin, G. Hartig, and G. Illingworth. 1 Dec. 2003. Web. 29 July 2015.. Fassnacht, C. D., E. Xanthopoulos, L. V. E. Koopmans, and D. Rusin. "A Determination of H 0 with the CLASS Gravitational Lens B1608 656. III. A Significant Improvement in the Precision of the Time Delay Measurements." ApJ The Astrophysical Journal (2002): 823-35. Print. Howell, Elizabeth. "What Is The Hubble Constant? | Space.com." What Is He Hubble Constant? Purch, 21 Mar. 2014. Web. 29 July 2015.. Myers, Steven. "Scaling the Universe: Gravitational Lenses and the Hubble Constant." Proceedings of the National Academy of Sciences of the United States of America. The National Academy of Sciences, 1999. Web. 29 July 2015.. Peeples, Molly. "Gravitational Lensing." Gravitational Lensing. 30 July 2003. Web. 29 July 2015..