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| # Introduction | ||
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| ## Historical overview | ||
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| Transit light curves are an essential tool used for the detection of | ||
| [exoplanets](https://en.wikipedia.org/wiki/Exoplanet). To date, there have been over 4,300 | ||
| confirmed planets discovered in over 3,400 different star systems, with an additional | ||
| 2,400 candidates currently awaiting follow-up analysis and validation[^1]. Since the first | ||
| confirmed discovery of an exoplanet -- as part of a multi-planetary system in 1992[^2], | ||
| and the first exoplanet discovered around a Sun-like star shortly after in 1995[^3] -- | ||
| there has been an explosion in new discoveries, thanks in large part to the successful | ||
| [Kepler/K2](https://www.nasa.gov/mission_pages/kepler/main/index.html) and | ||
| [TESS](https://tess.mit.edu/) space missions. The large majority of these planets have | ||
| been detected via the [transit | ||
| method](https://exoplanets.nasa.gov/faq/31/whats-a-transit/): | ||
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|  | ||
| https://exoplanetarchive.ipac.caltech.edu | ||
|
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| ## Transit method | ||
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| This method works by observing the dimming in apparent brightness of a star as a planet | ||
| passes in front of it from our point of view. The plot of the star's brightness as a | ||
| function of time defines the *white light curve* as seen in the schematic below: | ||
|
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| <br> | ||
| [*How Do You Find an Exoplanet?* by John Asher Johnson](https://www.google.com/books/edition/How_Do_You_Find_an_Exoplanet/-DNJCgAAQBAJ?hl=en) | ||
|
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| Even just starting with a simple single planet system in a circular orbit, there is | ||
| already a wealth of information encoded in this diagram. These observations give us | ||
| insight not only into the bulk properties of the planet, but into the architecture of its | ||
| orbital system and characteristics of its host star as well. For example, *direct | ||
| observables* from the light curve like the *transit duration* $(T)$ and *ingress/egress* | ||
| time $(\tau)$ give us information about how tilted its orbit is and how fast the planet is | ||
| traveling, while the *transit depth* $(\delta)$ gives us a direct measure of the size of | ||
| the planet relative to its star. For circular orbits, these are nicely summarized by: | ||
|
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||
| ```math | ||
| \begin{align} | ||
| \frac{R_\text{p}}{R_*} &= \delta^{1/2} \\ | ||
| b^2 &= 1 - \delta^{1/2}\frac{T}{t} \\ | ||
| \frac{a}{R_*} &= \frac{P\delta^{1/4}}{2\pi} | ||
| \left(\frac{4}{T\tau}\right)^{1/2} | ||
| \rho_* &= \frac{3P}{G\pi^2}\left(\frac{\delta^{1/4}}{\sqrt{T\tau}}\right)^3 \quad, | ||
| \end{align} | ||
| ``` | ||
|
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||
| where $P$ is the period of the planet's orbit and $a$ its semi-major axis, $b$ is the | ||
| impact parameter, $R_*$ is the radius of its star, and $\rho_*$ is the stellar | ||
| density. | ||
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| ### Limb darkening | ||
| Not shown above is an added dimension that `Transits.jl` excels in, [limb | ||
| darkening](https://en.wikipedia.org/wiki/Limb_darkening#:~:text=Limb%20darkening%20is%20an%20optical,construct%20models%20with%20such%20gradients), demonstrated in the schematic below: | ||
|
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||
| <br> | ||
| http://www.astro.utoronto.ca/~astrolab/files/AST326_LimbDarkening_2017.pdf | ||
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| This effect is intimately related to the shape of the light curve, and allows us to | ||
| constrain the brightness profile of the star itself. As we will see next, the method of | ||
| transit light curves is not just useful for the detection of exoplanets, but also for | ||
| taking it to the next step of characterizing its atmosphere. | ||
|
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| ## Transmission spectroscopy | ||
| If we perform the technique of transit light curve modeling on a wavelength-by-wavelength | ||
| basis, we can further probe the properties of the host star and begin to make predictions | ||
| about the properties of the planet's atmosphere, such as its chemical composition and | ||
| whether clouds/hazes are likely to be present at higher altitudes. This analysis begins in | ||
| the same way as with the white light curve seen above, only now a *wavelength binned light | ||
| curve* is measured at a range of different wavelengths: | ||
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|  | ||
| Adapted from Weaver et al. (2021, *submitted*) | ||
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| Plotting these wavelength dependent transit depths then builds a *transmission | ||
| spectrum*, which is filled with information about the planet's atmosphere and its star, | ||
| summarized below: | ||
|
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||
|  | ||
| [Benneke & Seager (2012)](https://ui.adsabs.harvard.edu/abs/2012ApJ...753..100B/abstract) | ||
|
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|  | ||
| [Rackham, Apai, & Giampapa (2018)](https://ui.adsabs.harvard.edu/abs/2018ApJ...853..122R/abstract) | ||
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| Performing forward | ||
| modeling (see, e.g., [Kempton et al. 2016](https://ui.adsabs.harvard.edu/abs/2017PASP..129d4402K/abstract), [Goyal et al. 2017](https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.5158G/abstract)) and | ||
| retrievals (see, e.g., [Barstow et al. 2020](https://ui.adsabs.harvard.edu/abs/2020MNRAS.493.4884B/abstract) and references therein) using these | ||
| frameworks then allows us to explore exoplanetary atmospheres in never before seen detail. | ||
|
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| ## Summary | ||
| The detection and characterization of exoplanets through their transit light curves is a relatively new technique | ||
| in the field of astronomy, with recent advances only being made possible through novel | ||
| uses of large, ground-based telescopes and soon in the future with planned [ELTs](https://en.wikipedia.org/wiki/Extremely_large_telescope) and space based | ||
| missions like [JWST](https://www.jwst.nasa.gov/). Studies using these observing facilities | ||
| will require the fast and precise computation of transit light curves, which [`Transits.jl`](https://github.com/JuliaAstro/Transits.jl) | ||
| aims to provide. | ||
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| [^1]: https://exoplanetarchive.ipac.caltech.edu/ | ||
| [^2]: https://ui.adsabs.harvard.edu/abs/1992Natur.355..145W/abstract | ||
| [^3]: https://ui.adsabs.harvard.edu/abs/1995Natur.378..355M/abstract |