Measuring Exoplanetary Radii Using Transit Photometry


The goal of my study was to analyze the possible changes in planetary characteristics over time through measuring the radii and constraining the orbital periods of three Hot Jupiter exoplanets: HAT-P-25b, HAT-P-9b, and HAT-P-30b. To determine whether or not the radii and mid-transit times of the planets changed since their dates of discovery, each around 10 years ago, I compared my measurements to the previously obtained literature values. 

Raw images of the host stars were acquired using the ARCSAT telescope and Flare-Cam Imaging Instrument in Sunspot, New Mexico. A data processing pipeline utilizing the Python programming language was used to convert the raw data images into calibrated pixels and normalized transit light curve graphs. The graphs of HAT-P-25b and HAT-P-30b were fit with multiple light curve models, which varied based on a given range of radius and time of mid-transit parameters within the Python code. The data of HAT-P-9b were not further analyzed due to a non-detection in the data.

Chi-squared goodness of fit tests were performed on all light curve models to estimate the 1σ error bar ranges, or 68% confidence intervals, for all of my light curve calculations. A significant shift in mid-transit time was detected for HAT-P-25, and a significant difference from the literature value for the normalized radius (Rp/R★) was calculated for HAT-P-30b.

These findings stress the importance of updating exoplanetary measurements in order to obtain more accurate knowledge regarding general planetary population characteristics and the evolution of planets.


Question / Proposal

​​​​​     Hot Jupiter exoplanets are defined as gas giants with orbital periods of less than ten days (Wang et al., 2009). In 2011, roughly 20% of all exoplanets detected were Hot Jupiters, raising the question of whether the commonality of detected Hot Jupiters is due to detection biases or true exoplanet population proportions (Wright et al., 2011). The commonality of Hot Jupiters in other solar systems, and the lack of Hot Jupiters in our solar system also raises the question of whether or not our solar system is common or not. The study of Hot Jupiter exoplanetary characteristics provides us with information regarding planetary populations; it is necessary that we study planetary populations in order to accurately compare our solar system to other solar systems. 

     The goal of my study was to measure the radii and constrain the orbital periods of three Hot Jupiter exoplanets: HAT-P-25b, HAT-P-9b, and HAT-P-30b, in order to study if and how these Hot Jupiter exoplanets change over time. I was also aiming to study Hot Jupiter exoplanet characteristics in general. Due to the relatively short time frames (of around 10 years) between the dates the planets were discovered and the dates I studied the planets, I predicted that my measured radii and times of mid-transit parameters would not have a statistically significant difference from the measurements taken when the exoplanets were discovered, concluding that the radius and time of mid-transit for each planet have remained robust and consistent since their dates of discovery.


The recent development of new technologies and equipments have allowed for further exploration and discovery of exoplanets specifically using the transit detection method. A clear example of this advancement was the Kepler Mission, launched in 2009 by the National Aeronautics and Space Administration (NASA). The Kepler mission had the goal to detect exoplanets specifically using the transit method. By 2015, Kepler had detected 1030 exoplanets (Soutter et al., 2015). More recently, the Transiting Exoplanet Survey Satellite (TESS) was launched by NASA to expand on the work of the Kepler mission by analyzing larger regions of space (Ricker et al., 2014).

In the Kepler and TESS missions, a data processing pipeline was used to convert raw photos taken from a telescope and camera, into calibrated pixels and transit light curve graphs. The Kepler and TESS pipeline stages include data acquisition, calibration, photometric analysis (light measurement), presearch data conditioning, transiting planet search, and data validation (Tenenbaum et al., 2012). In my study, I used a data processing pipeline modeled off of the Kepler and TESS pipeline; my pipeline stages include data acquisition, calibration, photometric analysis, light curve modeling, and light curve analysis.

The three Hot Jupiter exoplanets I studied have been previously detected and classified: HAT-P-25b was detected in 2010 (Quinn et al., 2010), HAT-P-9b was detected in 2008 (Shporer et al., 2009), and HAT-P-30b was detected in 2011 (Johnson et al., 2011). I am basing the parameters of my light curve models off of these previously obtained literature measurements in order to determine whether or not the radii and times of mid-transit parameters have changed since the dates the planets were discovered. 

This previous research validates my project because I am following the general steps that have been used previously in exoplanet missions to observe and characterize my given planets. In other words, I am modeling my pipeline off of the successful Kepler and TESS pipelines for consistency and accurate comparison purposes. I also used the chi-squared goodness of fit test and 1σ error bar ranges in my study to determine whether or not my measured values were statistically different from the literature values, which also utilized 1σ error bar ranges. In using the same 1σ error bar range in my study, I ensured that I was accurately comparing my measured values to the literature values.

The real world benefits from my research because my results provide futher understandings regarding planetary populations, the evolution of planets, and Hot Jupiter exoplanets. Research about these Hot Jupiters could not only provide information regarding how our solar system - sans Hot Jupiters - differs from solar systems that contain Hot Jupiters, but could also tell us why our solar system does not contain these large gas giants. My research could also aid in the process of identifying why Hot Jupiter exoplanets are so commonly detected. 

Through my research, more accurate characteristics of each observed planet may be obtained, giving scientists a more accurate vantage point on Hot Jupiters and planetary populations in general.

Method / Testing and Redesign

This is my data processing pipeline that is based off of the pipeline used in the Kepler and TESS missions:

Data Acquisition

I used the 0.5-meter Astrophysical Research Consortium Small Aperture Telescope (ARCSAT) and Flare-Cam imaging instrument in Sunspot, New Mexico, during the nights of January 16, 17, and 18 of 2018 to collect my data. I used these instruments through remote observing on a computer (with supervision from my mentor). The three Hot Jupiter exoplanets I observed were HAT-P-25b, HAT-P-9b, and HAT-P-30b.


Using the ARCSAT telescope and Flare-Cam imaging instrument, I acquired 4 types of images: raw (uncalibrated star field), bias (short exposures taken with no light exposure), dark (bias images with shorter frame times), and domeflat (60 second light exposures).

Using these bias, dark, and domeflat images, I created the Masterbias, Masterdark, and Masterflat images. To create these Masterimages, all images of that specified image type were stacked and averaged. Equation 1 was used to obtain the final calibrated images:

                                               (Raw - MasterDark) / (Masterflat - Masterbias)                              (1)

These calculations were completed using the Python programming language.

The purpose of calibration is to increase the signal-to-noise ratio, reduce instrumental errors, and account for pixel sensitivity variations within the Charge-Coupled Device (CCD).

Photometric Analysis:

I used a program titled AstroImageJ to perform aperture photometry (light measurement within a fixed size) on the target star and three neighboring comparison stars (Collins et al., 2017). The light measurements of the comparison stars were used to account for atmospheric disturbances, such as clouds. The target star's light flux value for each image was then stored in a text file along with the corresponding 1σ error bar values (generated by AstroImageJ) and barycentric Julian date.

Light Curve Modeling:

The Python programming language was used to create normalized transit light curve graphs for the planets of HAT-P-25b, HAT-P-9b, and HAT-P-30b. For each graph, I normalized the baseline stellar flux value to 1.0, in order to study the transit light curves in terms of relative light flux and transit depth.

The BATMAN Python package was used to fit multiple light curve models to the data sets (Kreidberg, 2015). These models were varying based on a given range of values for the radius and time of mid-transit parameters within the code. Chi-squared maps were created for each data set to determine the 1σ error bar ranges, or 68% confidence intervals for all of my light curve calculations.

Light Curve Analysis:

Utilizing the best-fit transit light curve model, I was able to determine the planet's time of mid-transit and aIso calculate the normalized radii of the planets using the following transit depth equation:

                                                                          ΔF/F=Rp2/R★2                                                                 (2)

where ΔF is the change in stellar flux, F is the baseline stellar flux, Rp is the planet's radius, and R★ is the host star's radius.

Finally, my calculated normalized radius and time of mid-transit values were compared to the corresponding literature values for each given planet to determine whether or not my calculations were statistically different from the literature values.


The Python programming language was used to create normalized transit light curve graphs for the planets of HAT-P-25b(1A), HAT-P-9b(1B), and HAT-P-30(1C). The data collected of HAT-P-9b were not further analyzed because there is a non-detection in the data, which could be due to instrumentation errors.

Chi-squared goodness of fit tests (equation 3) were performed on each light curve model through the Python code to find the chi-squared value closest to 1.0, which would signify a strong data to model fitting.


I found the reduced chi-squared values for the data sets of HAT-P-25b and HAT-P-30b to be 1.1 and 2.9, respectively. Figures 2A and 2B are the chi-squared maps used to determine the 1σ error bar ranges for all of my light curve calculations; the 1σ error bar range ends when the color shifts to yellow.

Tables 1 and 2 show my calculated values and the literature values for the normalized planetary radius and mid-transit time parameters. Circled values show a significant statistical difference from the literature values.



For HAT-P-25b, I found the normalized radius to be 0.13±0.03, which is consistent with the literature value because the 1σ error bars overlap. However, the mid-transit time I found for HAT-P-25b was -0.41±0.31 hours from the expected value. This calculated mid-transit time significantly differs from the expected mid-transit time of 0 by more than the 1σ error bar value. This detected shift indicates that the orbital period of this planet can be constrained further with future analysis.

The shift I detected in the time of mid-transit of HAT-P-25b will be helpful to more accurately predict the transit times for this planet in the future. HAT-P-25b was discovered in 2010, and since my plots are modeled off of the parameters found at that time, my study signifies that the time of mid-transit is occured 0.41 hours, or approximately 24 minutes, earlier than expected. In 20 years, HAT-P-25b will transit more than one hour earlier than the expected time. This is a significant amount of time when it comes to observing planets. It is important to update planetary periods in order to actively study and track these planets.

For HAT-P-30b, the normalized planetary radius was calculated to be 0.15±0.020. This value significantly differs from the literature result by 0.04±0.0020. This signifies that the radius of this planet can be constrained further. As for the mid-transit time, I measured a value of 0.11±0.200 hours from the expected time, and since the expected mid-transit time of 0 falls within the 1σ error bar values of my results, I can conclude that the period of this planet is robust and consistent.

My prediction was not consistent with my data because statistically significant differences were found for the time of mid-transit of HAT-P-25b and the radius of HAT-P-30b, despite the short time frames (around 10 years) between the dates these exoplanets were discovered to the dates I observed the planets. I can therefore conclude that these characteristics can be constrained with further analysis.


I predicted that my observed radii and times of mid-transit parameters would not have a statistically significant difference from the measurements taken when the exoplanets were discovered, due to the relatively short time frames (of around 10 years) between the dates the planets were discovered and the dates I studied the planets. By detecting no significant statistical difference between my results and the literature values, I would be able to conclude that the radius and time of mid-transit for each planet have remained robust and consistent since their dates of discovery.

My prediction was not supported by the data, and statistically significant differences were found for the time of mid-transit of HAT-P-25b and the radius of HAT-P-30b. I can conclude that these characteristics can be constrained with further analysis; these results also stress the importance of updating exoplanetary characteristic measurements so that we can accurately study planetary populations and solar systems as a whole. These findings will encourage and allow scientists to obtain more accurate knowledge about these exoplanets and their characteristics.

To tie my findings into the bigger picture of overarching planetary populations, I created three plots (Figures 3A, 3B, and 3C) where each point represents an exoplanet detected by either the radial velocity method or the transit detection method. I created these plots not only to study possible transit method detection biases towards Hot Jupiter exoplanets, but also to show the differences between planets within our solar system and the exoplanets I observed. 

Notice how in all three graphs, there are two distinct populations that are shown. This could be the result of either detection biases from the radial velocity and transit detection methods or the result of truly unique populations of planet types. However, the latter cannot be supported until more data regarding planetary populations are collected.

In a 2007 study published by Stephen Kane, a possible transit method detection bias towards Hot Jupiter exoplanets was analyzed (Kane, 2007). This finding is consistent with my plots because one of the populations in each figure is shown with a bias towards planets with larger radii, smaller orbits, and shorter distances to the host star, which are all key characteristics of Hot Jupiters exoplanets. The creation of these graphs relates to my project because the results of my project emphasize the importance of updating exoplanetary characteristics in order to accurately interpret planetary populations figures, such as these graphs I have created. 

If I had more observation time on the ARCSAT telescope, I would have liked to gather more data on HAT-P-25b, HAT-P-9b, and HAT-P-30b in order to increase the accuracy of my light curve measurements and further ensure that I am making precise comparisons between my measurements and the literature values.

Overall, I believe that my project was successful because it exposes the commonality of possible inconsistencies in our exoplanetary measurements and observations; my project also stresses the importance of updating exoplanet characteristics in order to obtain accurate data for analysis on planetary populations as a whole.

About me

The unknown of what is beyond our solar system captivates - and slightly bewilders - me. I love all things astronomy, namely exoplanets, and I also enjoy hiking, playing piano, and dabbling in photography. I decided to pursue a project in astronomy because it is an area that I love learning and talking about.

My passion for astronomy has influenced my life in drastic ways; through competing in global science fairs, attending local astronomy meetings, and giving talks around Boulder to inform the public about exoplanets, I have gotten the chance to meet incredible people with the same passions as me. These experiences have showed me that I would like to pursue astronomy in the future. 

I admire Dorothy Vaughan and Stephen Hawking because they displayed a love for what they did, and they both rose above adversities to become pioneers in the field of astronomy.

Winning the Google Science Fair would provide me with a larger platform to share my knowledge and further inform the public about the expanding area of exoplanetary studies. Winning would also enable me to form new connections that could help me positively impact and educate individuals on a larger scale. I would like to use the monetary winnings to build more local programs/communities around the US for astronomy education because astronomy is often an area that is overshadowed, and if I win, I would like to make a difference in other people's lives as well as my own.

Health & Safety

I used the Astrophysical Research Consortium Small Aperture Telescope (ARCSAT) and Flare-Cam imaging instrument located in Sunspot, New Mexico to collect my data (Hawley et al., 2014). I used these instruments through remote observing on a computer. 

This is our ARCSAT observing proposal for the week of January 15:

The remote observing was supervised by my mentor, William Waalkes:


All planning and data analysis were done at home.

Bibliography, references, and acknowledgements

Works Cited

Carson, Joseph, Low, Kat, Jordan, Starr, Stevens, Laura, Rawadi, David II, Schneider, Glenn, Perrino, Kara. (2013). Why Study Exoplanets? College of Charleston.

Charbonneau, David, Brown, Timothy M., Latham, David W., Mayor, Michel. (1999). Detection of Planetary Transits Across a Sun-like Star. The Astrophysical Journal Letters. 529, No. 1.

Collins, Karen A., Kielkopf, John F., Stassun, Keivan G., Hessman, Frederic V.. “AstroImageJ: Image     Processing and Photometric Extraction for Ultra-Precise Astronomical Light Curves (Expanded Edition).” Astronomical Journal. 2017; 153, No. 2.

Gould, Andrew. (2003). 𝜒2 and Linear Fits. Astro-ph.

Hawley, Suzanne, Ketzeback, Bill, Huehnerhoff, Joe, Owen, Russell, Sayres, Conor, Bizyaev, Dmitry. (2014). ARCSAT. New Mexico State University.

Jenkins, Jon M., Caldwell, Douglas A., Chandrasekaran, Hema, Twicken, Joseph D., Bryson, Stephen T., Quintana, Elisa V., Clarke, Bruce D., Li, Jie, Allen, Christopher, Tenenbaum, Peter, Wu, Hayley, Klaus, Todd C., Middour, Christopher K., Cote, Miles T., McCauliff, Sean, Girouard, Forrest R., Gunter, Jay P., Wohler, Bill, Sommers, Jeneen, Hall, Jennifer R., Uddin, AKM K., Wu, Michael S., Bhavsar, Paresh A., Van Cleve, Jeffrey, Pletcher, David L., Dotson, Jessie A., Haas, Michael R., Gilliland, Ronald L., Koch, David G., Borucki, William J.. (2010). Overview of the Kepler Science Processing Pipeline. The Astrophysical Journal Letters. 713, L87-L91.

Johnson, John Asher. How do you find an Exoplanet? 2015. Print.

Johnson, John Asher, Winn, J.N., Hartman, J.D., Bakos, G.A., Morton, T.D., Torres, G., Kovacs, Geza, Latham, D.W., Noyes, R.W., Sato, B., Esquerdo, G.A., Fischer, D.A., Marcy, G.W., Howard, A.W., Quinn, S.N., Beky, B., Sasselov, D.D., Stefanik, R.P., Lazar, J., Papp, I., Sari, P., Buchhave, L.A., Furesz, G.. “HAT-P-30b: A transiting hot Jupiter on a highly oblique orbit.” ApJ. 2011.

Kane, Stephen R.. “Detectability of Exoplanetary Transits from Radial Velocity Surveys.” Astro-ph. 2007

Kreidberg, Laura. "batman: BAsic Transit Model cAlculatioN in Python." Astro-ph. 2015.

Martinez, Patrick, Klotz, Alain, Demers, Andri, Lena, Pierre. A Practical Guide to CCD Astronomy. Edition 1. 2007. Print.

Quinn, S.N., Bakos, G.A., Hartman, J., Torres, G., Kovacs, G., Latham, D.W., Noyes, R.W., Fischer, D.A., Johnson, J.A., Marcy, G.W., Howard, A.W., Szentgyorgyi, A., Furesz, G., Buchhave, L.A., Beky, B., Sasselov, D.D., Stefanik, R.P., Perumpilly, G., Everett, M., Lazar, J., Papp, I., Sari, P.. “HAT-P-25b: a Hot-Jupiter Transiting a Moderately Faint G Star.” ApJ. 2010.

Ricker, George R., Winn, Joshua N., Vanderspek, Roland, Latham, David W., Bakos, Gaspar A., Bean, Jacob L., Berta-Thompson, Zachory K., Brown, Timothy M., Buchhave, Lars, Butler, Nathaniel R., Butler, Paul, Chaplin, William J., Charbonneau, David, Christensen-Dalsgaard, Jorgen, Clampin, Mark, Deming, Drake, Doty, John, Lee, Nathan De, Dressing, Courtney, Dunham, E.W.,Endl, Michael, Fressin, Francois, Ge, Jian, Henning, Thomas, Holman, Matthew J., Howard, Andrew W., Ida, Shigeru, Jenkins, Jon, Jernigan, Garrett, Johnson, John Asher, Kaltenegger, Lisa, Kawai, Nobuyuki, Kjeldsen, Hans, Laughlin, Gregory, Levine, Alan M., Lin, Douglas, Lissauer, Jack J., MacQueen, Phillip, Marcy, Geoffrey, McCullough, P.R., Morton, Timothy D., Narita, Norio, Paegert, Martin, Palle, Enric, Pepe, Francesco, Pepper, Joshua, Quirrenbach, Andreas, Rinehart, S.A., Sasselov, Dimitar, Sato, Bun’ei, Seager, Sara, Sozzetti, Alessandro, Stassun, Keivan G., Sullivan, Peter, Szentgyorgyi, Andrew, Torres, Guillermo, Udry, Stephane, Villasenor, Joel. “The Transiting Exoplanet Survey Satellite.” Journal of Astronomical Telescopes, Instruments, and Systems. 2014.

Shporer, Avi, Bakos, Gaspar A., Bouchy, Francois, Pont, Frederic, Kovacs, Geza, Latham, Dave W., Sipocz, Brigitta, Torres, Guillermo, Mazeh, Tsevi, Esquerdo, Gilbert A., Pal, Andras, Noyes, Robert W., Sasselov, Dimitar D., Lazar, Jozsef, Papp, Istvan, Sari, Pal, Kovacs, Gabor. “HAT-P-9b: A Low Density Planet Transiting a Moderately Faint F star.” ApJ. 2009; 690:1393-1400

Soutter, Jack, Horner, Jonti, Pepper, Joshua, Kelt Science Team. “The Kilodegree Extremely Little Telescope: Searching for Transiting Exoplanets in the Northern and Southern Sky.” Australian Space Research Conference. 2015.

Tenenbaum, Peter, Burke, Chris, Christiansen, Jessie, Jenkins, Jon, McAuliffe, Sean, Seader, Shawn, PT, Twicken, Joe. “Detection of Transiting Planet Candidates in Kepler Mission Data.” National Aeronautics and Space Administration. 2012.


Wright, J. T., Fakhouri, O., Marcy, G.W., Han, E., Feng, Y., Johnson, John Asher, Howard A.W., Fischer, D.A., Valenti, J.A., Anderson, J., Piskunov, N. “The Exoplanet Orbit Database.” Astronomical Society of the Pacific. 2011.


I would like to thank William Waalkes (Department of Astrophysical & Planetary Sciences, University of Colorado, Boulder) for guiding me through this project, providing me with the necessary resources for remote observing, and teaching me about the wonders of exoplanets.

I would also like to thank Dr. Paul Strode (Department of Biology, Fairview High School) for providing guidance and support, and fueling my love for science.

Lastly, I would like to thank my friends and family for supporting me.

Facilities I had Access To

ARCSAT Telescope and Flare-Cam Imaging Instrument, Apache Point Observatory (New Mexico) - 

Hawley, Suzanne, Ketzeback, Bill, Huehnerhoff, Joe, Owen, Russell, Sayres, Conor, Bizyaev, Dmitry. (2014). ARCSAT. New Mexico State University.

University of Colorado, Boulder: