Transits and Starspots Jeremy Tregloan-Reed Ph.D. Research Student Supervisor: John Southworth

High Precision Photometry Orbital Based Photometry Ground Based Defocused Photometry Credit: NASA Credit: ESO

WASP-50 An Example of Ground Based Defocused Photometry Collected from the ESO NTT La Silla, Chile. Highest achieved ground based photometric precision to date. (Tregloan-Reed et al. In Preparation)

High Precision Transit Photometry Around Active Stars A Transit of WASP-19 modelled using JKTEBOP. The transit parameters were fixed to the values found by Hellier et al. (2011). The transit data points suggest that the planet/star radii ratio is greater than what the model predicts. This change in transit depth is caused by the change in overall flux from the star, caused by the starspot.

High Precision Transit Photometry Around Active Stars Kepler data of HATP-11. The red data points indicate potential star spot transit events. (Sanchis-Ojeda et al. 2011)

PRISM PRISM (Planetary Retrospective Integrated Starspot Model) uses a pixellation approach to create the modelled star on a 2D Cartesian array. Allows us to model the transit, limb darkening and starspots on the stellar disc simultaneously. PRISM is set to use the standard quadratic limb darkening law and uses the stellar and planetary radii scaled by the semi major axis r s,p = R s,p /a.

PRISM PRISM requires 10 parameters to model a planetary transit with a single starspot. Output model of a transit coupled with a starspot using PRISM. The transit cord is represented by the two horizontal black lines. The dark disk to the left is the planet. A starspot has been placed on the curved stellar surface to show how PRISM projects a elliptical shape onto the stellar disc for a circular spot.

Fitting PRISM to the WASP-19 Data We used GEMC (Genetic Evolution Markov Chain) to fit PRISM to the WASP-19 data sets. The best fitted models are shown to the left together with the transit data. Using the best fitting parameters and literature spectroscopic values we find:- Stellar Mass = / M Sun Planet Mass = / M Jup Separation = / AU Stellar Radius = / R Sun Planet Radius = / R Jup Planet Equ Temperature = /- 24 K This agrees with both Hebb et al. (2010) and Hellier et al. (2011)

Modelled Starspots Surface plot of the function used to test GEMC. N=9 to generate 81 local maxima. Output models of the starspots on the stellar disc for the two data sets containing spot anomalies.

Stellar Rotation Period With the two sets of positions for the spot known it was possible to calculate the latitudinal rotation period. The latitudinal rotation period was found to be (10.4 ± 0.1) days. Hebb et al. (2010) found the rotation period to be (10.5 ± 0.2) days. When coupled with the star’s radius we can calculate the surface velocity to be:- v = (4.82 ± 0.15) km s -1

Sky-Projected Spin-Orbit Alignment The position of the spot at two different time periods allows us to determine the alignment between the star’s rotation axis and the planet's orbit in the plane of the sky λ. We calculate that λ = (1.0 ± 1.5)°. While Hellier et al. (2011) found λ = (4.6 ± 5.2)°. This agrees with previous results but is more precise.

WASP-19 Planetary System Evolution Winn et al. (2010) showed that a low obliquity would follow the idea that the planet formed many AU away from the host star and through tidal interactions with the interplanetary disc the orbit of the planet decayed. While a large obliquity would seem to suggest that the orbital decay was by gravitational interactions from other bodies in the system (Schlaufman 2010).

Future Work When a precise value for v sin(I) has been determined it would be possible to find the inclination of the stellar spin axis towards the observer I. If enough observations of the planet crossing the starspot are made, it would be possible to make a direct measurement of the spin-orbit alignment of the system ψ. If λ is large it can be possible to map out rotation periods at different latitudes across the star and hence measure the differential rotation function of the star.

Summary PRISM can simultaneously model the planetary transit, limb darkening and starspots. To allow us to correctly measure the system parameters. High precision photometry can allow us to drive down the uncertainties of the parameters of the transiting planetary system. If the host star is active, then with enough transit data sets it is possible to measure the rotation period and sky-projected spin- orbit alignment of the system, without the need to rely on spectrographs. Because of this high precision photometry can help us better understand the planetary system’s evolution.