Polarimetry of transiting planets: Differences between plane-parallel and spherical host star atmosphere models

Abstract

Context. To properly interpret photometric and polarimetric observations of exoplanetary transits, accurate calculations of centerto-limb variations of intensity and linear polarization of the host star are needed. These variations, in turn, depend on the choice of geometry of stellar atmosphere. Aims. We want to understand the dependence of the flux and the polarization curves during a transit on the choice of the applied approximation for the stellar atmosphere: spherical and plane-parallel. We examine whether simpler plane-parallel models of stellar atmospheres are good enough to interpret the flux and the polarization light curves during planetary transits, or whether more complicated spherical models should be used. Methods. Linear polarization during a transit appears because a planet eclipses a stellar disk and thus breaks left-right symmetry. We calculate the flux and the polarization variations during a transit with given center-to-limb variations of intensity and polarization. Results. We calculate the flux and the polarization variations during transit for a sample of 405 extrasolar systems. Most of them show higher transit polarization for the spherical stellar atmosphere. Our calculations reveal a group of exoplanetary systems that demonstrates lower maximum polarization during the transits with spherical model atmospheres of host stars with effective temperatures of T eff = 4400−5400 K and surface gravity of log g = 4.45−4.65 than that obtained with plane-parallel atmospheres. Moreover, we have found two trends of the transit polarization. The first trend is a decrease in the polarization calculated with spherical model atmosphere of host stars with effective temperatures T eff = 3500−5100 K, and the second shows an increase in the polarization for host stars with T eff = 5100−7000 K. These trends can be explained by the relative variation of temperature and pressure dependences in the plane-parallel and spherical model atmospheres. Conclusions. For most cases of known transiting systems the plane-parallel approximation of stellar model atmospheres may be safely used for calculation of the flux and the polarization curves because the difference between two models is tiny. However, there are some examples where the spherical model atmospheres are necessary to get proper results, such as the systems with grazing transits, with Earth-size planets, or for the hot host stars with effective temperatures higher than 6000 K.

Scattering linear polarization of late-type active stars

“…This is explained by the noticeable temperature differences between atmospheric layers in the input plane-parallel and spherical models, which affect the calculated center-to-limb intensity and polarization profiles. Specifically, spherical models are systematically cooler than the planeparallel models by up to 500 K at T eff = 5000 K (see Fig.4 in Kostogryz et al 2017), and this temperature difference diminishes rapidly toward higher T eff , similarly to what is observed in Figure 1.…”

“…Specifically, spherical models are systematically cooler than the planeparallel models by up to 500 K at T eff = 5000 K (see Fig. 4 in Kostogryz et al 2017), and this temperature difference diminishes rapidly toward higher T eff , similarly to what is observed in Figure 1.…”

“…In general, the curves for the plane-parallel models appear to be less sensitive to the temperature, especially for lower logg, while the spherical models show a noticeable depression in between 4500 and 5500 KK that grows at lower wavelengths. This feature is discussed in detail in Kostogryz et al (2017), who considered the differences between plane-parallel and spherical models of a host star atmosphere for exoplanet transit polarimetry. Similarly, the transit polarization for spherical atmospheres in this temperature range was also found to be lower than for plane-parallel atmospheres.…”

Spatially resolved spectroscopy across stellar surfaces

“…The differences are small, however, and largely masked by the great amount of absorption lines, whose different and complex center-to-limb behavior largely masks the underlying temperature structure (Hayek et al 2012). If extremely good photometric precision could be achieved, polarimetric observations during transit could offer further constraints on atmospheric structure, as simulated by Kostogryz et al (2017).…”

Detecting Magnetic Fields in Exoplanets with Spectropolarimetry of the Helium Line at 1083 nm

“…For a sphericallysymmetric star, the signals integrated over the entire stellar disk cancel out; however, a transiting exoplanet breaks the symmetry of the star as seen by the observer, which results in net polarization. The expected linear polarization signal is on the order of a few ×10 −6 at short wavelengths around 450 nm (Kostogryz et al 2015(Kostogryz et al , 2017. Due to the strong wavelength-dependence of Rayleigh scattering, the amplitude of the polarization signal drops significantly at longer wavelengths and is expected to be negligible at 1083 nm.…”