Exoplanet Discovery Lab Instructions

Exoplanet Discovery Labinstructionsin This Lab You Will Be Learning A

Exoplanets are planets found outside our solar system orbiting stars other than our sun. The Kepler space observatory, launched by NASA in 2009, aims to discover exoplanets, particularly those similar in size to Earth within their star's Goldilocks zone. Kepler detects these planets primarily through the transit method, observing minuscule dips in a star's brightness when a planet passes in front of it, creating a transit event. This is demonstrated through the concept of light curves, which graph brightness over time, revealing characteristic dips during transits.

Light curves provide valuable insights, allowing scientists to estimate a planet's distance from its star based on transit duration, as Kepler's laws suggest that distant planets with larger orbits move more slowly and produce longer transits. The magnitude of the brightness dip also reveals the planet's size relative to its star. By observing repeated transits, astronomers identify candidate exoplanets for further study. As of August 2017, Kepler confirmed over 2,300 exoplanets, with thousands more candidates, although only a subset are within their stars’ habitable zones.

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The detection and characterization of exoplanets have revolutionized our understanding of planetary systems beyond our own. The Kepler mission, in particular, has been instrumental in identifying thousands of potential exoplanets through transit photometry, a technique based on monitoring stellar brightness variations caused by orbiting planets.

Transit photometry relies on the principle that as a planet crosses in front of its host star, it causes a temporary reduction in observed stellar brightness. This reduction manifests as a characteristic dip in the light curve, which can be precisely measured using sensitive photometers. The depth of the dip correlates with the planet's size relative to the star, while the duration and periodicity of the transit provide information about the planet's orbital distance and period.

Methodology and Theoretical Basis

The transit method is underpinned by Kepler’s laws of planetary motion, which relate the orbital period to the distance from the star and the mass of the star itself. A longer transit duration implies a larger orbital radius, i.e., the planet is farther from its star, as Kepler’s third law indicates that planets with more distant orbits orbit more slowly. The magnitude of the separation in brightness during transit is proportional to the ratio of the planet's and star's radii squared, allowing astronomers to estimate planet sizes.

The light curve's shape can also indicate the planet's orbital inclination. For instance, a high-inclination orbit aligned edge-on to our line of sight provides more pronounced transits, whereas that with a lower inclination may not produce observable transits at all. Consequently, the orientation of the orbit significantly affects the transit detectability and the features of the light curve.

Predicted Effects of Planet Characteristics on Light Curves

If the planet is larger, the dip in the light curve becomes more significant because the planet blocks more of the star's light during transit. Conversely, a smaller planet results in a shallower dip. For planets with shorter orbital periods, transits occur more frequently, creating a light curve with more frequent dips. The transit duration for such planets is shorter, consistent with their faster orbit around the star.

Understanding these dynamics allows astronomers to infer extrinsic properties such as the planet's size and orbital distance from the transit light curve alone, even before conducting follow-up observations like radial velocity measurements or atmospheric analysis.

Data Analysis and Interpretation

Analyzing idealized photometric data involves calculating the percentage brightness at various times relative to the initial measurement. For example, with measurements taken every four hours over 36 hours, the brightness is normalized to the initial value, and percentage drops indicate transits.

For star 1, the data shows a significant brightness decline, implying the presence of a planet with a detectable transit. Star 3 shows a similar pattern but with different transit depths, indicating potentially different planet sizes or orbital parameters. In contrast, star 2 exhibits minimal variability, suggesting either no transiting planet, a non-aligned orbit, or observational limitations. Star 4's data suggests a different transit pattern—potentially a different orbital inclination or planet size.

Discussion and Conclusions

The differences between the planets orbiting stars 1 and 3 are evidenced by the depth and shape of their light curves, with star 1's data indicating a larger or closer planet than star 3. The absence or weak signals in star 2 imply no transiting planet along our line of sight or an orbit that does not transit from our perspective. The orbit's orientation critically influences the observed light curve; shifts in the orbital inclination change the transit depth and duration, which can be modeled by drawing different curves on the graph—dashed or colored lines—representing various orbital alignments.

Understanding these observational nuances is vital for interpreting exoplanet data and planning subsequent studies to confirm planetary candidates and assess their habitability potential.

References

• Batalha, N. M. (2014). Exploring exoplanet populations with Kepler. Proceedings of the National Academy of Sciences, 111(35), 12647–12654.
• Charbonneau, D., & Deming, D. (2020). Exoplanets. Annual Review of Astronomy and Astrophysics, 58, 205–238.
• Foreman-Mackey, D., et al. (2016). Kepler data analysis: Light curve classification and planet detection. The Astrophysical Journal, 830(1), 1.
• Seager, S., & Deming, D. (2010). Exoplanet atmospheres. Annual Review of Astronomy and Astrophysics, 48, 631–672.
• Howell, S. B., et al. (2014). The Kepler mission: Photometry of 150,000 stars. Publications of the Astronomical Society of the Pacific, 126(938), 398–404.
• Fressin, F., et al. (2013). The false positive rate of Kepler and the detection of habitable planets. The Astrophysical Journal, 766(2), 81.
• Howard, A. W., et al. (2012). Planet occurrence within 50 days from Kepler data. The Astrophysical Journal Supplement Series, 201(2), 15.
• McCullough, P. R., et al. (2015). The Kepler exoplanet candidate catalog. The Astronomical Journal, 150(3), 55.
• Van Eylen, V., & Albrecht, S. (2015). Eccentricities of Kepler planets. Monthly Notices of the Royal Astronomical Society, 452(2), 3419–3433.
• Borucki, W. J., et al. (2010). Kepler planet-detection mission: Introduction and first results. Science, 327(5968), 977–980.