Refraction of Starlight by Exoplanet Atmospheres

When a planet transits its host star, some of the star’s light passes through the planet’s atmosphere and generates a transmission spectrum which carries information about the planet’s atmosphere. This technique of transmission spectroscopy has been used to characterise the atmospheres of exoplanets ranging from hot-Jupiters to super-Earths. The upcoming James Webb Space Telescope (JWST) and the development of larger ground-based telescopes might make it possible for transmission spectroscopy to characterise the atmospheres of smaller, Earth-size exoplanets.

Light refracts or bends when it passes through a planets’ atmosphere due to the atmosphere’s index of refraction gradient. This is because the index of refraction is altitude-dependent. In the rarefied upper atmosphere of a planet, the index of refraction is lower compared to the dense lower atmosphere. During the events associated with the transit of a planet in front of its host star, the main effect of refraction is that some of the star’s light passing through the planet’s atmosphere can be refracted towards a distant observer prior to a transit and refracted away from a distant observer during a transit.

Taking into account the effect of refraction, Amit Misra et al. (2014) modelled the transmission spectrum of an Earth-analogue (i.e. a planet that is identical to Earth in all respects) prior to and during a transit event. The two cases highlighted in the study are: an Earth-analogue orbiting a Sun-like star and an Earth-analogue orbiting an M5V star (i.e. a red dwarf star). Because of refraction, there is a maximum tangent pressure level that can be probed with transmission spectroscopy during a transit event. In the study, the maximum tangent pressure is defined as the pressure level in the planet’s atmosphere at which 50 percent of the stellar flux is transmitted.

Figure 1: Artist’s impression of a somewhat Earth-like planet in orbit around a red dwarf star. Because a red dwarf star is much cooler and less luminous than the Sun, a planet would need to be much closer-in to receive enough warmth for it to be habitable. At such a close-in distance, the planet would be tidally-locked with one hemisphere permanently pointed towards its host star, likely resulting in an unusual climate system.

Figure 2: Artist’s impression of an Earth-like planet.

The results from the study show that for an Earth-analogue orbiting an M5V star, transmission spectroscopy during a transit event can probe the planet’s atmosphere to pressures of up to ~0.9 bar. This pressure is the maximum tangent pressure level and it corresponds to an altitude of roughly 1 km, indicating that almost the entire atmosphere can be probed. For an Earth-analogue orbiting a Sun-like star, the maximum tangent pressure level during a transit event is ~0.3 bar, corresponding to an altitude of roughly 14 km. This means that transmission spectroscopy is ineffective in probing the lower layers of the planet’s atmosphere.

Different gases in the atmosphere generate the different spectral features that can be identified in the transmission spectrum of a planet’s atmosphere from a transit event. The effect of refraction decreases the signal to noise ratio (SNR) of these spectral features. For an Earth-analogue orbiting an M5V star, the decrease in the SNR is ~10 percent for all spectral features and ~15 percent for H2O features. For an Earth-analogue orbiting a Sun-like star, the decrease in the SNR is much greater, ~60 percent for all spectral features and ~75 percent for H2O features.

As a transit progresses, refraction produces temporal variations in the transmission spectrum of the planet’s atmosphere. The differences in the transmission spectra between each stage of the transit progression can reveal the altitude-dependent abundances of gases, thereby allowing vertical profiling of the planet’s atmosphere. On Earth, the abundance of gases such as oxygen and carbon dioxide are uniform throughout the atmosphere. However, gases such as H2O, ozone and methane have altitude-dependent abundances. For example, H2O is abundant at lower altitudes but becomes rarefied at altitudes above ~10 km.

Figure 3: A model of Earth’s atmospheric temperature profile and gas volume mixing ratios. Amit Misra et al. (2014).

 Figure 4: Maximum amount of transmitted stellar flux at each altitude for an Earth-analogue orbiting a Sun-like star and an Earth-analogue orbiting an M5V star. Amit Misra et al. (2014).

For an Earth-analogue orbiting a Sun-like star, it is possible, prior to ingress, to probe the planet’s atmosphere down to pressures greater than the maximum tangent pressure. This is because the denser lower atmosphere of the planet has a larger index of refraction which allows light to be deflected at large enough angles to a distant observer even though the planet is still some distance away from transiting its host star. However, the transmitted stellar flux prior to ingress is small since most of the planet’s atmosphere is opaque. During the main transit event, particularly during mid-transit, the same large deflection angles corresponding to the denser lower atmosphere of the planet, deflects the stellar flux away from a distant observer. This defines the maximum tangent pressure and prevents the denser lower atmosphere from being probed by transmission spectroscopy during the main transit event.

The upcoming JWST is expected to be able to detect the transmission spectrum of an Earth-analogue orbiting an M5V star. Assuming all transits of the Earth-analogue over a 5 year baseline are observed and co-added, many of the spectral features of the transmission spectrum would have a high enough SNR for the planet’s atmosphere to be characterised. Spectral features associated with H2O and carbon dioxide would have SNRs greater than ~7. Furthermore, spectral features associated with gases such as oxygen and methane, which together constitutes a strong biosignature, would have SNRs of ~3. Nevertheless, the transmission spectrum of an Earth-analogue orbiting a Sun-like star would be beyond the detection capabilities of JWST. Vertical profiling of an Earth-analogue’s atmosphere by observing temporal variations in the transmission spectra of its atmosphere is also beyond JWST’s capabilities regardless of whether the planet’s host star is a Sun-like star or an M5V star.

Figure 5: Diagram showing which altitudes can be probed at different times during a transit for an Earth-analogue orbiting a Sun-like star. The coloured regions correspond to regions of the atmosphere where stellar flux is transmitted and the white regions are portions of the atmosphere that are opaque to a distant observer. During the earliest stage (purple), the transmission of stellar flux occurs at ~2 to 15 km. Subsequently, stellar flux is transmitted through higher portions of the atmosphere: ~5 to 17 km (cyan), ~5 to 30 km (yellow), above ~7 km (blue). As the planet reaches centre of transit (green, then red), most of the stellar flux is transmitted at altitudes above ~14 km. Amit Misra et al. (2014).

Figure 6: Altitude-dependent transmitted flux from pre-transit to centre of transit as deviations from the dotted line. The six stages correspond to the colours in Figure 5. Amit Misra et al. (2014).

Reference:

Amit Misra et al. (2014), “The Effects of Refraction on Transit Transmission Spectroscopy: Application to Earth-like Exoplanets”, arXiv:1407.3265 [astro-ph.EP]