I am a freshman at Barrington High School in Barrington, Illinois. My conversations with Fermilab physicists, which highlighted the role of quasar lensing in understanding the nature of dark matter, served as the impetus for my research project.
Since looking up at the night sky at age four, I have been fascinated by astronomy. At age six, watching a video of a 15-pound wrecking ball swing within centimeters of MIT professor Walter Lewin’s face and hearing him exclaim “physics works” crystallized my interest in physics. These initial sparks have burgeoned into a full-fledged career aspiration in astrophysics.
My involvement in scientific endeavors has taught me many lessons, both in understanding the principles of nature and in application of the scientific method to other aspects of life. I learned to persevere through difficulties and think out of the box while still validating my results against established research.
Astrophysicist Subrahmanyan Chandrasekhar is the scientist I admire the most. He was a leader who was not afraid to propose revolutionary ideas in the face of opposition from the establishment and pursued these ideas with great intensity. I am inspired by Chandrasekhar’s work ethic, adherence to principles, and humility.
Winning a prize in the Google Science Fair would motivate and inspire me to pursue research to learn more about the universe we live in. As a Hitchhiker’s Guide to the Galaxy fan, I am thrilled that research in this field could provide the “Answer to the Great Question of Life, the Universe, and Everything.”
Question / Proposal
Purpose and Hypothesis
A novel method was developed to identify gravitationally lensed quasars from the Sloan Digital Sky Survey (SDSS). Understanding gravitational lensing can help decipher the properties of dark matter and dark energy. It is hypothesized that if multiple objects in an SDSS image meet both photometric and spectral criteria, then these objects are gravitationally lensed quasar candidates. The first phase of this project used data from the SDSS Data Release 9. In the follow-up study, the method was improved upon and extended using the SDSS Data Release 10, which included data for over 300,000 quasars. The SDSS data was retrieved and processed using Structured Query Language (SQL) queries. Using this information, the algorithm compared the quasars to their neighbors to determine if the neighbors were images of the same quasar. The results were validated against a control group of lensed quasars reported in the literature. Statistical analyses were also performed to ensure that the comparison parameters were consistent across the data set. A comparison of the project’s results with established data sets of lensed quasars led to the conclusion that the hypothesis was well supported. In addition to identifying a majority of the quasars in the control group, the algorithm also identified additional high-probability lens candidates not reported in the literature.
Review of Literature
Due to its importance and the availability of large data sets, quasar lensing is an active area of research and a number of papers on the subject have been published over the last 25 years.
Turner, Ostriker, and Gott (1984) first explored quasar lensing probabilities due to galaxies and the resulting image separation distributions. This work laid the foundation for the study of quasar lensing. Since this original research, many scientists have developed efficient and reliable ways to identify lensed quasars.
The Hubble Space Telescope (HST) Snapshot Survey was the first large lensed quasar survey, covering a set of 498 quasars from established astronomical catalogs. The analysis of the survey results by Maoz et al. (1993) showed that about 1% of luminous quasars at z > 1 (z = redshift) are gravitationally lensed into multiple images with separations in a 0.1 to 7 arcsecond range.
Oguri et al. (2006) presented an algorithm to identify gravitationally lensed quasar candidates which eventually led to the creation of the SDSS Quasar Lens Search (SQLS). The algorithm used photometric and color selection criteria to identify small- and large-separation lenses, respectively. A statistically valid set of 11 lensed quasars was created by Inada et al. (2008) based on the SQLS catalog.
Oguri et al. (2012) report the results of applying the statistical sampling of lensed quasars to study the limits on the value of the cosmological constant and dark energy distribution. By comparing the observed lensing probability with theoretical predictions, Oguri’s results support the accelerated cosmic expansion theory.
Since quasars were first detected through radio telescopes, there exists a large body of research related to quasar lensing using radio astronomy. The Cosmic-Lens All Sky Survey (CLASS), described in Browne et al. (2003), discovered 22 gravitational lenses from about 16,000 radio sources.
The FIRST radio survey is one of the best complementary QSO data sources to the SDSS, as it covered the same part of the sky. Schechter, Gregg, Becker, Helfand, and White (1998) reported the first lensed quasar identified by the FIRST survey (FBQ 0951+26351.1) by comparing the separation, magnitude and radio signatures of its two images.
Prior to this project, quasar lensing research in optical bands focused solely on either photometric or spectral characteristics of quasars. The selection algorithm developed in this research project combines both types of data to identify potential lensing candidates, thus improving the accuracy and reliability of the candidates identified for follow-up observations.
The results of this research help answer the eternal questions of “where did we come from”, “who are we”, and “where are we going”. I believe this research has a positive impact on society because it can help confirm the expansion of the universe, telling us what our eventual fate will be. It helps us understand many of the fundamental questions in cosmology and astrophysics.
Method / Testing and Redesign
Methods and Procedure
This research project uses a morphological approach for finding candidate lists of lensed quasars in the SDSS DR10. The candidate list from this project is validated against the Master Lens Database, described in Moustakas et al. (2012). The SDSS Data Release 10 provides a robust and uniform selection of over 300,000 quasars with high-quality photometric and spectral data. The histograms below show the number of quasars in the DR9 and DR10 data sets for each redshift range. While the quasar redshifts plotted in the histograms range from 0 to 7, most redshifts lie between 1 and 3. One can discern from these redshift values that quasars existed during very early periods of the Universe. The sky coverage plot below is a location-based plot of all 300,000+ quasars included in the SDSS DR10 data set.
The candidate selection algorithm begins with a list of all objects classified as QSOs by the SDSS pipeline. The pipeline sometimes misses objects spread over a large area. In order to fill this gap, a query using the unique color characteristics of quasars was developed. This query utilized the guidelines for color cuts from Richards et al. (2001). The two data sets were combined and duplicates were removed, resulting in a baseline data set of 532,704 quasar candidates.
The overall candidate selection algorithm is outlined in the figure below. For each quasar in the baseline data set, all the neighbors within a separation threshold were identified. Based on analysis of published research literature, a separation value of 16” was selected. If the neighbor’s spectral data was available, the algorithm compared the redshifts of the neighbor and the reference quasar; it rejected neighbors with a redshift difference of greater than 0.1. The g-r color difference of each valid neighboring object was compared with the color of the reference quasar. If a neighboring object had a similar redshift and color composition, there is a high probability that the two images correspond to the same lensed quasar. If the neighbor did not have spectral data, only the color comparison was performed, and those neighbors that met the criterion were added to a low-probability candidate list.
The first steps of data analysis in this project were data extraction and synthesis, criterion matching, and data validation. Structured Query Language (SQL) was used extensively to target, filter, and manipulate the DR10 data. Python and related Python modules such as SciPy, PyFits, and Matplotlib were used to visualize the results.
In the second step, the neighbors within a 16” separation window of the quasars were extracted and compared against the quasar characteristics. The number of neighbors identified for different values of spatial separation between the target quasar and the neighbor are shown in the figure below.
The figure to the right shows the distribution of quasars with at least one neighbor within 16" of separation. The pattern of the distribution shown in the figure is consistent with the sky coverage of the SDSS and the histogram of quasar redshifts.
Discussion of Results
The candidates generated from the morphological algorithm matched the control group of lensed quasars from the literature. The table below lists the data coverage, selection criteria, and number of preliminary candidates identified. After identifying the potential candidates (table in blue), as a final validation step, the spectra of the 279 high-probability candidates in Type 1 were compared against their neighbors’ spectra. If a neighbor is truly a lensed image of the target quasar, the spectrum of the neighbor should be very similar to the spectrum of the target quasar. The resulting set of 42 high-probability candidates is also shown below.
A set of statistical analyses was performed on the data across different dimensions such as redshift, spatial separation, and candidate groupings. The first analysis compared the spatial separation of all quasars in the candidate lists against their redshifts. As can be seen from below, the differences in the mean values are not statistically significant, as the mean diamonds and Student’s t-test indicate. The analysis of means confirms that the spatial separation limit is consistent across the entire redshift range. An outlier analysis was performed to determine how well the parameters of each high-probability candidate were grouped together.
The gravitationally lensed quasars identified by the morphological approach were compared to the control group of lensed quasars reported in the literature. In order to use the most complete data set for comparison, the Master Lens Database, developed by Moustakas et al. (2012), was used as the control group in this research project. The revised algorithm in this project was able to match about nine-tenths of the candidates in the control group. The table and figure below show the comparison between the results of this project and the control group.
One of the last steps of the algorithm compared the SDSS images to FIRST images. The figure below shows two lens candidates and their corresponding FIRST images. It also shows two lens candidates with ROSAT and WISE images. Just as in the SDSS image, the quasar and its possible lens are visible in the other two images. The objects do not look identical in the SDSS, ROSAT, and WISE images because quasars emit differently in different bands of the electromagnetic spectrum.
The figure below shows a panel of representative lens candidates identified by the algorithm that have not been reported in the literature. A comparison of the spectrum of the target quasar with that of the lens candidate in the third column shows that the spectra have identical characteristics.
Conclusion / Report
A comparison of the lensed quasar candidates identified by the present research and the lensed quasars reported in the literature leads to the conclusion that the original hypothesis of this project is well supported. In addition to matching the control group of lensed quasars, the method also found new candidates from the DR9 and DR10 data sets. The current research project, with the revised morphological algorithm and a modified data extraction strategy, overcame many shortcomings of the algorithm presented in Sivakumar (2013).
Despite the success of this approach in finding high-probability lens candidates, there are some areas where this approach could be improved. One possible source of error was that the selection criteria were too strict or loose, thus generating false negatives or positives. The classification of Type 3 candidates may also have been premature because the match was based solely on color. Errors could also have been introduced due to the procedure’s dependence on the SDSS pipeline for classification of objects as QSOs, stars or galaxies. This last source of error is less likely, however, since classifications from the SDSS pipeline are generally reliable.
Based on the research work performed in this project, it can be concluded that the morphological approach is effective in identifying lensed quasar candidates. Follow-up observations of these high-probability candidates using large telescopes are necessary to confirm the lensing effects. These detailed observations will also eliminate binary quasars, which can easily be mistaken for lensed quasars based solely on SDSS data.
A future extension of this project currently under development is the use of PSF (point spread function)-based criteria to deblend lens images identified as single objects by the SDSS PHOTO pipeline. This extension will almost double the number of lensed quasars that can be identified by the morphological algorithm.
Further research to improve the accuracy of the algorithm is being pursued in follow-up projects. In particular, the accuracy could be improved using a complete set of spectral data, more detailed statistical analyses to refine the threshold values, and implementation of additional validation steps in the algorithm. Opportunities to apply the results of this work to constrain cosmological parameters through lensing statistics (distribution of redshifts and separations) are also being explored.
Bibliography, References and Acknowledgements
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Ahn, C. P., Alexandroff, R., Allende P. C., Anders, F., Anderson, S. F., Anderton, T., . . . Zhu, G. (2013). The Tenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Apache Point Observatory Galactic Evolution Experiment. The Astrophysical Journal Supplement, submitted.
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Browne, I. W. A., Wilkinson, P. N., Jackson, N. J. F., Myers, S. T., Fassnacht, C. D., Koopmans, L. V. E., . . . York, T. (2003). The Cosmic Lens All-Sky Survey - II. Gravitational lens candidate selection and follow-up. Monthly Notice of the Royal Astronomical Society, 341, 13-32. doi:10.1046/j.1365-8711.2003.06257.x
Inada, N., Oguri, M., Becker, R.H., Shin, M., Richards, G.T., Hennawi, J. F., White, R. L., . . . Fukugita, M. (2008). The Sloan Digital Sky Survey Quasar Lens Search. II. Statistical Lens Sample from the Third Data Release. The Astronomical Journal, 135, 496-511. doi: 10.1088/0004-6256/135/2/496
Inada, N., Oguri, M, Shin, M., Kayo, I., Strauss, M.A., Morokuma, T., . . . White, R. L. (2012). The Sloan Digital Sky Survey Quasar Lens Search. V. Final Catalog from the Seventh Data Release. The Astronomical Journal, 143, 119. doi: 10.1088/0004-6256/143/5/119
Kochanek, C. S., Falco, E. E., Impey, C. D., Lehár, J., McLeod, B. A., & Rix, H.W. (1999). Results from the CASTLES survey of gravitational lenses. AIP Conference Proceedings, 470, 163-175.
Moustakas, L. A., Brownstein, J. R., Fadely, R., Fassnacht, C. D., Gavazzi, R., Goodsall, T., . . . True, T. (2012). The Orphan Lenses Project. American Astronomical Society, AAS Meeting, 219, 146.01.
Maoz, D., Bahcall, J. N., Schneider, D. P., Bahcall, N. A., Djorgovski, S., Doxsey, R., . . . Yanny, B. (1993). The Hubble Space Telescope Snapshot Survey. IV - A summary of the search for gravitationally lensed quasars. The Astrophysical Journal, 409, 28-41. doi: 10.1086/172639
The Master Lens Database [Computer Database]. Salt Lake City, UT: The University of Utah.
Oguri, M., Inada, N., Pindor, B., Strauss, M.A., Richards, G.T., Hennawi, J. F., Turner, E. L., . . . Brinkmann, J. (2006). The Sloan Digital Sky Survey Quasar Lens Search. I. Candidate Selection Algorithm. The Astronomical Journal, 132, 999-1013. doi:10.1086/506019
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Richards, G. T., Fan, X., Schneider, D. P., Vanden Berk, D. E., Strauss, M. A., York, D. G., . . . Zheng, W. (2001). Colors of 2625 Quasars at 0 < z < 5 Measured in the Sloan Digital Sky Survey Photometric System. The Astronomical Journal, 121, 2308-2330. doi:10.1086/320392
Schechter, P. L., Gregg, M. D., Becker, R. H., Helfand, D. J., & White, R. L. (1998). The First FIRST Gravitationally Lensed Quasar: FBQ 0951+2635. The Astronomical Journal, 115, 1371-1376. doi:10.1086/300294
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Sivakumar, P. (2013). Identification of Gravitationally Lensed Quasars: A Morphological Approach. Illinois Junior Academy of Science, IJAS State Conference.
Turner, E.L., Ostriker, J. P., & Gott III J. R. (1984). The statistics of gravitational lenses: the distributions of image angular separations and lens redshifts. The Astrophysical Journal, 284, 1-22. doi:10.1086/162379
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I wish to thank Dr. Brian Nord at the Fermilab Center for Particle Astrophysics (FCPA) for giving me a deep understanding of the SDSS camera operation and data pipeline. I would also like to acknowledge Dr. Chris Stoughton, also of the FCPA, for introducing me to the power of the Python and SciPy programming environments. I would also like to thank Dr. Leonidas Moustakas of the Jet Propulsion Laboratory for providing me early access to the Master Lens Database. Many thanks to my father for mentoring me and teaching me effective ways to use SQL to extract and manipulate data. Finally, I wish to thank the faculty of the Saturday Morning Physics program at Fermilab for inspiring me to pursue research in astrophysics.
Official SDSS-III Acknowledgement Statement: Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.