We looked at how carefully monitoring the secondary eclipse of a transiting planet can reveal deviations from a uniformly bright disc here. We considered the system to be a “perfect” transiting planet system, with a perfectly spherical planet on a perfectly circular orbit with a perfectly tidally locked rotation, but nature need not be so conveniently arranged and there is room for many different complex scenarios. A paper submitted to Astronomy & Astrophysics takes a look at some of the astrophysical phenomena that can affect the interpretations of a planet’s brightness distribution in the context of deriving a map of the planet.
Lest we forget, the eclipse scanning method for deriving a two-dimensional map of an extrasolar planet involves careful, high-precision monitoring of the secondary eclipse ingress and egress of the planet. Differences in the brightness distribution of the day-side observable surface of the planet will produce an asymmetric ingress/egress light curve.
Above is the section of the light curve showing the ingress (left) and egress (right) of HD 189733 b’s secondary eclipse behind it’s host star. The red line is what would be expected if the planet’s day-side surface were of uniform brightness. The fact that there are significant residuals to this fit indicate that the planet is not adequately described as a uniformly bright disc.
One contribution to an anomalous ingress/egress light curve could of coruse be the shape of the planet. An oblate planet will, for all orientations that are not pole-on, have ingress/egress light curve shape that differs from that of a spherical planet in a way that is different from a localised bright spot on the planet.
The eccentricity of the planet will also have an effect. Circular orbits have an equal time between transits and eclipses, with the eclipse occurring at half-phase. Eccentric orbits for most orientations (longitudes of periapsis of ) will have the secondary eclipse away from half-phase. Obvious eccentricities may reveal themselves through their radial velocity -derived orbit fits, but very tiny ones may not, yet may still add complications to secondary eclipse scanning. If, due to the eccentricity of the planet, the planet’s position is slightly offset from its expected position by an amount that is rather small, on the order of the size of surface features on the planet, then this can cause some ambiguity in the surface brightness distribution map. This is especially a problem if the brightest feature on the planet is shifted away from the substellar point, as indeed is the case for HD 189733 b, however phase curve observations of reflected light from the planet can be used to constrain the true position of the brightest spot.
Because of this so-called “brightness distribution-eccentricity degeneracy” effect, it can be difficult to find a unique solution to the surface brightness distribution of the planet. Assumptions of the underlying brightness distribution can permit estimates of the eccentricity of the orbit (see this paper by de Wit et al).
Using the simplest model (below) to explain both the observed ingress/egress curves and the phase curve, shown below and to the left, is well supported by the amplitude as derived from the secondary eclipse depth (effectively the total brightness of the planet), and in longitudal resolution as derived from the phase curve. The standard deviation from the model (right) is easily seen to be small, much more so than other, more complex models of the underlying brightness distribution.
A more complex underlying brightness distribution model (below), and a much poorer fit to the observed data, allows for the resolution of structures that are less constrained by the secondary eclipse depth and in longitudinal resolution as derived from the phase curve. However, this model is well-constrained by the secondary eclipse scanning.
Increasingly complex models for the underlying brightness distribution produce worse global fits to the data, however a consistent theme of a longitudinally displaced hot spot remains. To illustrate how the day-side mapping of the planet can constrain the parameters of the system, if we assume this brightness model (below) to be a true representation of the underlying brightness distribution of the planet’s dayside surface, then it requires a larger planetary orbital eccentricity. Because of an increased eccentricity, the orbital velocity will be different despite the constant (measured) eclipse duration. Thus, the radius of the star will need to be slightly adjusted to fit this model (in this case made smaller), and accordingly the impact parameter of the planet’s secondary eclipse will be affected (in this case increased), while changing the density of the planet (recall that the planet’s radius is known only as a ratio of the star’s).
Another source of complexity in the analysis of eclipse scanning can come from limb-darkening of the planet, in much the same way a star is limb-darkened. As with stars, the severity of this limb-darkening will be wavelength dependent, and in the 8 µm wavelength that these Spitzer results are derived from, the limb-darkening of a hot Jupiter is expected to be negligible.
The detailed mapping of extrasolar planets, even now, cannot be said to even be in its infancy yet. It is still being born. Small astrophysical effects beyond our current ability to measure can cause profound changes to the derived map of a planet, requiring extreme caution. As of the time of this writing, only two planets – HD 189733 b and υ And Ab – have had surface brightness distributions modelled with Spitzer phase curve photometry, and for both of them, unique models have been put forward to explain the observations. Direct imaging will, in the future, provide more definitive means of mapping extrasolar planets, but until then, we are forced to use tricks requiring very high quality data to tease out such information from planets we can’t even see.