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Retrieving Earth’s phase curve

Presentation #1119 in the session “Open Engagement Session B”.

Published onMar 17, 2021
Retrieving Earth’s phase curve

The EPOXI extended mission phase for the Deep Impact spacecraft observed the Earth in 2008 and 2009 as an analog for a habitable terrestrial exoplanet. The EPOXI data ranges over visible and near-infrared wavelengths and consits of five observations. They are at five different phase angles and three are equatorial observations and two polar (one North and one South) over a 24 hour period. This data is used to create the phase curve and it is compared to a Lambertian scattering disk as can be seen in Figure 1.

The model lines are made using Equation 1 where Ag is the geometric albedo, pi F is the incoming flux and the final term is the Lambert phase function [Madhusudhan and Burrows, 2012].

The geometric albedo to create the lines is 0.2 [Mallama, 2009]. This value is greatly smaller than the classic value for geometric albedo of 0.4341, showing that there is research to be done. Besides this, it can be seen that the difference between model and empirical data is dependent on wavelength. Furthermore, the polar observations have clearly a higher signal than the model for all wavelengths. Since the geometric albedo is the only variable, one can solve for the required geometric albedo to match the model with the data. These values can be seen in Table 1.

From these values, it can be seen that the shorter wavelengths require higher values than longer wavelengths. Furthermore, it shows that the polar observations are distinct from the equatorial ones and it shows that results can be misleading if only equatorial observations would be used. Additionally, it can be seen that despite the different phase angle, the equatorial observations have a similar geometric albedo for each wavelength. The same can be said for the polar observations, even though they are opposite poles. In general, all these numbers are much lower than the geometric albedo of 0.434. Now the values for geometric albedo from EarthObs1 are used to plot the model lines, the result can be seen in Figure 2. This figure visualises what is said before, that the equatorial observations are similar but the polar observations are clearly different.

The analysis still needs to be extended to the infrared region but the visible already shows potential for research. The same potential is expected from the infrared, due to the high signal-to-noise ratio compared to what would be available for a real exoplanet observation. The next step of the research will also involve adapting and improving an exoplanet model made by Dr. D. M. Stam (TU Delft) as the goal is to be able to predict the signal for a certain phase angle.


  • Nikku Madhusudhan and Adam Burrows. ANALYTIC MODELS FOR ALBEDOS, PHASECURVES, AND POLARIZATION OF REFLECTED LIGHT FROM EXOPLANETS. The Astrophysical Journal, 747(1):25, feb 2012. doi: 10.1088/0004-637x/747/1/25. URL

  • Anthony Mallama. Characterization of terrestrial exoplanets based on the phase curvesand albedos of mercury, venus and mars. Icarus, 204(1):11–14, 2009. ISSN 0019-1035.doi: URL


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