Sunday, October 16, 2016

NSF: A proposition for you.

Just like the personal statement, I am sharing my research proposal for the sake of the many undergrads that have been asking me for advice and essays as they prepare to apply for the NSF Graduate Research Fellowship.

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For exoplanets with a radius 1 to 5 times the radius of Earth, the physical properties evaluated for most of these planets either have high uncertainties or cannot be ascertained at all.  This problem is exacerbated by the faintness of the host star, which makes detailed follow up analysis difficult and expensive.  However, the rate at which Earth-like exoplanets around bright stars are detected and characterized with satisfactory precision can be substantially increased with an observatory that specializes in searching for such exoplanets.  This is why I propose to observe and analyze bright stars via an observatory recently constructed specifically for finding and characterizing rocky planets around the nearest stars.
Background
Within the past two decades, the search for exoplanets and the characterization of their physical properties have given planetary astronomers a vast amount of new knowledge.  The Kepler Mission is responsible for finding more than 900 of these exoplanets [1].  This is confirmed by radial velocity (RV) surveys, where the stellar spectra revealed Doppler shifts that are induced by a star’s companion exoplanet(s). These discoveries revealed that there are many exoplanets within the Galaxy and that they have a large range of masses and radii [2].  There are more planets with a radius less than 4 times the radius of Earth than there are planets larger than this size within the Galaxy [3].  For most of these small-radius exoplanets found by Kepler, their physical properties currently cannot be found because of their excessively faint host stars.  However, this information can be determined for small-radius exoplanets that orbit bright stars. 
Among the planets we find around bright stars via RVs, we expect that only a few of them will transit their host star, as a result of the random orientations that an exoplanet’s orbit can have on the sky.  These few transiting exoplanets are extraordinarily valuable because they offer numerous advantages to study the host star, such as revealing the mean density of the star and the orbital inclination of the exoplanet.  However, finding these valuable transiting exoplanets requires precise photometry of very bright stars.  The orbital inclination along with many other parameters derived from the photometry can be coupled with spectroscopic measurements of the star to ascertain the physical properties (such as the mass and radius) of the exoplanet [4].  For most transiting exoplanets with a radius similar to the Earth’s radius, such physical properties of the exoplanet cannot be determined with satisfactory precision.  This is usually due to the RV signals being dominated by noise from stellar jitter, which is an effect from convective cells of gas rising to the photosphere and thus jostling the surface enough for such jostling to be detected in the RV measurements.  Consequently, there is a need for an observatory that is capable of resolving this stellar jitter in order to obtain high precision RV measurements.  Fortunately, the MINiature Exoplanet Radial Velocity Array (MINERVA) can do this as well as achieve high precision photometry for Earth-like exoplanets transiting bright stars. 
Research Plan
During my graduate career, I propose to conduct a survey of bright stars with MINERVA while using the defocusing technique to obtain high precision photometry in order to characterize Earth-like exoplanets.  By observing bright stars, high precision for the RV becomes feasible to obtain from the spectra.  However, achieving high precision for the photometry of bright stars is difficult for two reasons:
1) Relative photometry must be done to achieve the required precision.  This method entails the observation of satisfactory comparison stars, i.e. stars that are not variable and are similar in brightness and color to the nearby primary target.  Unfortunately, it is typically difficult to find such comparison stars within one telescope’s field of view when the primary star is bright. 
2) Bright stars saturate quickly. 
Resolving these two issues has captivated me much more than the complexities of the RVs.  Therefore, the photometry will be the primary focus of this proposed research.  I can achieve high photometric precision by using MINERVA’s four telescopes and the defocusing technique.  I will conduct this research at Harvard University, which has access to the MINERVA telescopes located on Mt. Hopkins in Arizona.  Each telescope is a PlaneWave CDK-700 with a diameter of 0.7m, a 20.8’ x 20.8’ field of view and an Andor iKON-L camera.
The issues regarding bright star photometry will be resolved by the following methods:
1. To find bright comparison stars, I will use one MINERVA telescope to observe the primary star with the transiting exoplanet while the other three telescopes observe nearby bright comparison stars.  2. The defocusing technique will be used to avoid saturating the CCD quickly.  This method entails the dispersion of stellar photons across more CCD pixels, in comparison to a star in focus.  This allows for a significantly longer exposure time than otherwise capable with a bright star in focus.  Such an increase in the exposure time substantially reduces flat fielding errors, decreases the fractional overheads, and thus results in high precision photometry [5].
Research Outcomes
MINERVA was built to consistently achieve a photometric precision of less than 1 millimagnitude.  While observing with only one telescope, this feat has already been demonstrated [6].  I expect to achieve this precision also, while one telescope observes the primary star and the other three measure the flux of comparison stars.  Due to the volume of data—at two light curves per telescope per week, we estimate 1,248 light curves over the 3-year lifetime of the project—we require the photometry to be highly automated.
My second internship at the Harvard-Smithsonian Center for Astrophysics (CfA) has equipped me with the knowledge to perform this exoplanet research.  I have already written Python code that can perform a variety of tasks including, create schedules which can be read by the MINERVA telescopes and query SIMBAD for a list of potential comparison stars most closely matching the target stars in magnitude, color and proximity. After observations, my code performs relative photometry and produces a light curve of the primary star.
Broader Impacts
After my first REU at the CfA, I gave talks at the Adler Planetarium about my research and continued to update astronomers there via our “Astro-Hangout” YouTube videos (linked to on my blog).  During the proposed research, I will continue to give talks and teach Adler visitors how bright stars enlighten those who seek to learn more about Earth-like exoplanets.  I will also mentor younger students of underrepresented groups so that they may benefit from my resources as a Harvard graduate student, NSF GRFP Fellow and Adler volunteer astronomer.  The excellent guidance I received from the Banneker Institute (BI) at the CfA is my inspiration for becoming a graduate student mentor for the BI.  I will lead my mentees toward opportunities that can jumpstart their careers early, just as the BI mentors have been doing for minority students like myself.  This institute has proven that minority students can be just as brilliant as the stars I am proposing to observe, and I look forward to mentoring and inspiring future BI undergraduates by first earning this NSF GRFP Fellowship and enrolling in Harvard University. 
References
[1] Han, E. et al., 2014, PASP, 126, 827                   [4] Winn, J., 2010, ArXiv:1001.2010 
[2] Johnson, J. A. et al., 2010, PASP, 122, 905         [5] Southworth, J. et al., 2009, MNRAS, 396, 1023 
[3] Fressin, F. et al., 2013, ApJ, 766, 81                   [6] Swift et al., 2015, JATIS, 1, 2

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