### Question --- What is meant by the “obliquity” of an exoplanet orbit about its host star? How can obliquity be measured, and what are typical values? ### Answer --- ##### What is meant by the “obliquity” of an exoplanet orbit about its host star? ![[obliquity_star_planet.png|align:center|700]] The **obliquity** of a exoplanet is the angular offset between spin axis of star and normal of the exoplanet's orbital plane. *(In the solar system, we use obliquity to describe the angle between the planet's spin axis and the ecliptic plane (orbital plane of planets around star))*. ##### How can obliquity be measured? spectroscopic phenomenon observed when an object moves across the face of a rotating star. The star is seen to undergo a redshift anomaly caused by the obscuration of different parts of its disk. We can measure obliquity by the **Rossiter-Mclaughlin effect** as the planet transits across the face of a rotating star. During the transit (for which we have spectra of), we will see the star is seen to undergo a redshift anomaly as the planet will first block red-shifted or blue-shifted light, and then block the other, causing a rise and fall in the measured radial velocity of the star. ![[RossiterMcLaughlin_effect.png|align:center|550]] ![[RossiterMcLaughlin_lines.png|align:center|550]] This can also be used to infer an obliquity based on how the inferred radial velocity varies over a transit. If the shape of the velocity anomaly (i.e. the radial velocity relative to "mean") is asymmetric, the planet covers the approaching side more or less than the receding side, meaning the orbit is oblique. ![[RossiterMcLaughlin_spin.png|align:center|550]] > [!note]- Historical Development of this Method > - Originally, this method was developed for eclipsing binaries (1924) > - First use of this method for planets *(Queloz et al. 2000)* > - Transit of a planet over star spots *(e.g. Deming+11, Dēsert+11)* > - Gravity darkening from rapid stellar rotation *(e.g Barnes+09,11)* > - Asteroseismology *(e.g. Chaplin+13)* ##### What are typical values? The measured obliquities can have a large diversity: low obliquity (like in solar system), high obliquities, retrograde orbits. > [!sun] In the solar system... > > The obliquity is variable between the different planets, but often small. With respect to the Earth's orbital plane ("Elliptical Plane"), the "orbital inclination" of the planets is... > > ![[solar_system_obliquity.png|align:center|400]] > > For the planetary obliquity in the solar system, it is defined differently. Using the solar system's definition, the obliquity of the planets is... > > ![[obliquity_solarSystem.jpg|align:center|600]]