Tag Archives: HAT-P-7

Mapping Extrasolar Planets III. Visible Light Surface Features from Kepler



In our previous looks at mapping extrasolar planets, we have focused on spatial variations in infrared brightness, and thus temperature, on the visible surface of extrasolar gas giant planets. The reason for this bias toward longer wavelengths is two-fold: 1) At the time, Spitzer phase curve photometry has been the dominant means of deriving crude longitudinal maps of extrasolar planets. 2) The ratio between the flux from the star and the planet is an order of magnitude less in infrared than it is in visible light – also the reason that the successes from direct imaging of extrasolar planets have been almost exclusively in infrared (the nature of the object imaged at Fomalhaut by HST in visible is unknown). Short-period extrasolar planets are thus prime candidates for secondary eclipse observations in the infrared. The following table lists several prominent planets and the eclipse depths as measured in four infrared channels by Spitzer, known as the IRAC channels (Infrared Array Camera) which have been a cornerstone of the building up of the foundation of our understanding about extrasolar planets in the past decade.

Spitzer IRAC Eclipse Depths
Planet 3.6µm 4.5µm 5.8µm 8.0µm
HAT-P-7 Ab 0.098% 0.159% 0.245% 0.225%
Kepler-5 b 0.103% 0.107%
Kepler-6 b 0.069% 0.151%
HD 189733 b 0.256% 0.214% 0.310% 0.391%
HD 209458 b 0.094% 0.213% 0.301% 0.240%

Of course the eclipse depth of a planet depends on its intrinsic brightness at the observed wavelength, the brightness of the star itself, and the radius ratio between the two, and given the comparitive brightness and size of a star, it is not hard to see why the drop in flux from the system during the planet’s eclipse behind the star would be so miniscule, < 1%.

The difficulty involved is exaggerated in visible wavelengths, where the flux is dominated less by thermal emission of the two bodies and more by intrinsic processes within the star and how reflective the planet is of the star’s light. Here are some secondary eclipse depth measurements from Kepler, which observes in a filter that is approximately visible light (0.400 – 0.865µm).

Kepler Eclipse Depths
Planet ΔF
HAT-P-7 Ab 0.0069%
Kepler-5 b 0.0021%
Kepler-6 b 0.0022%
Kepler-7 b 0.0042%
Kepler-12 b 0.0031%

Notice that the eclipse depths in visible light are much lower than the eclipse measurements in infrared. For planets with both Spitzer (infrared) and Kepler (visible light) eclipse depth measurements, the contrast is clear: the star-planet brightness ratio is less in infrared than it is in visible light and therefore hot Jupiters are essentially relatively brighter in infrared than in visible.

This does not exclude extrasolar planets from visible light mapping using the phase curve analysis and eclipse scanning techniques described before, it only makes it harder. Optical phase curves are weaker than infrared phase curves, so either a bigger telescope is needed to observe with enough photometric precision to resolve the phase curve in one orbit, or several orbits must be observed with existing instrumentation and allow the data to build up until a phase curve can be resolved.

Fortunately, Kepler has offered quasi-continuous coverage of the transits of many hot Jupiters over the course of four years, and in some cases, it is enough to confidently detect a phase curve. One such planet is Kepler-7 b.

Kepler-7b Phase_Curve

Kepler-7b Phase_Curve

In this image, the green curve corresponds to the expected phase curve if the planet reflected light in a geometrically symmetric way. The red and blue curves are fitted to the data and incorporate a longitudinal offset (see Demory et al for details). The primary transit is on the left side, and the planet passes behind the star on the left side (the secondary eclipse). The depth of the primary transit is so deep on this scale that it is off the image. Notice that the phase curve is not perfectly phased to the orbit of the planet – the secondary eclipse does not occur at the peak apparent brightness. This would be comparable to the Moon being brightest not when it is full, but rather at a gibbous phase. Keep in mind that this is an optical phase curve, the brightness variations on the planet’s dayside hemisphere suggested by the phase curve corresponds to actual features you would be able to see with the human eye (and maybe a welding helmet).

The Kepler-7 b phase curve shows us that the brightest part of the planet’s dayside atmosphere is on the westward side of the dayside hemisphere. Because this phase curve is an accumulation of 14 quarters of Kepler data, it is best thought of as an “average” phase curve over the course of 3.5 years, and therefore the longitudinally resolved visible light map of the planet is an average of the planet’s surface brightness over 3.5 years. Since the planet does not contribute to the phase curve of the system during secondary eclipse, the scatter of the data during that secondary eclipse is a good representative of the overall data scatter. It may come from instrumental noise or stellar noise, but whatever its origin, the fact that it is not obviously different from the scatter in the phase curve when the planet’s brightness is contributing implies that the surface features resolved here are both stable and long-lived.

Kepler-7b Visible Map

Kepler-7b longitudinal brightness distribution

What could be the cause of this bright area on the planet? Demory et al explain:

Kepler-7b may be relatively more likely to show the effects of cloud opacity than other hot Jupiters. The planet’s incident flux level is such that model profiles cross silicate condensation curves in the upper, observable atmosphere, making these clouds a possible explanation. The same would not be true for warmer planets (where temperatures would be too hot for dayside clouds) or for cooler planets (where silicates would only be present in the deep, unobservable atmosphere). Furthermore, the planet’s very low surface gravity may play an important role in hampering sedimentation of particles out of the atmosphere.

Now how do we know that this bright spot is not simply due to thermal emission? Some hot Jupiters are sufficiently hot that the glow from their heat in visible light can affect, or even dominate their eclipse depths. The obvious answer would be to check Kepler-7 b’s eclipse depths in the infrared, and this is a job for Spitzer. Spitzer observed the secondary eclipse of Kepler-7 b in both 3.6 µm and 4.5 µm, and in both wavelengths, the eclipse of the planet behind the star was not confidently detected. This means that the planet isn’t just not hot enough to produce the brightness asymmetry in the Kepler phase curve, but it’s eclipse couldn’t even be confidently detected in infrared. This firmly rules out thermal emission as the source of the optical phase curve asymmetry.

This represents the first time that visible light “surface” features have been identified on an extrasolar planet. This is but a baby-step forward in our ability to map extrasolar planets, but it is a milestone nonetheless. Kepler data may be able to detect phase curve asymmetries in other hot Jupiter systems (or if we are lucky, smaller worlds!), and this can significantly contribute to our understanding of the atmospheres of these planets.

The Phases of an Extrasolar Planet

The transit of a planet across the disc of its star (see here) produces a characteristic dip in the observed brightness of the system. This can be understood simply as a light source being occulted by another object. Extending this to a slightly more extreme case, we can see that a similar event occurs when the star occults the planet, at least as far as the appearance of the light curve is concerned. Planets don’t typically emit much light on their own but they do of course reflect light from their parent stars. So in this sense, they are light sources. When a planet passes behind a star, the star blocks the light reflected off the planet from reaching the telescope on Earth.

While the shape of the effect in the light curve will be about the same, there are notable changes, one being the obvious — the effect is far more diluted. The other notable difference is that the “floor” of the light curve shape is flat instead of curved. This is of course because the total brightness of the system does not change depending on where behind the star the planet is, all else held constant, whereas in a primary transit, the apparent stellar disc is unevenly illuminated due to limb darkening. Below is the example of the light curve of the transiting planet HAT-P-7 b as obtained by the Kepler spacecraft.

The Light Curve of HAT-P-7 b

In this graph, all the data is folded to the period of the planet, and so therefore repeats each orbit. That little dip half way between the two transits corresponds to the secondary eclipse (it might help to click on the light curve to enlarge it). That is when the planet HAT-P-7 b passed behind the star HAT-P-7, which blocked its light from reaching the telescope. The extreme difference in the depths of the transit and eclipse speak to the difference in brightness of the planet and the star. Such detections require photometers of much more precision than is needed to simply detect the planet transit itself.

The secondary eclipse depth can be expressed as

\displaystyle a = \left( \frac{R_p}{R_*} \right)^2 \left( \frac{T_p}{T_*} \right)

where T_p is the effective temperature of the planet, and T_* is the effective temperature of the star.

If we vertically stretch this data to make the secondary eclipse more visible, another phenomena reveals itself.

Light Curve of HAT-P-7 b

After the transit, we see the system brightening all the way up toward the secondary eclipse, and then after the eclipse, we see the system dimming back down. This effect can be understood when considering the appearance of the system throughout this light curve and considering the phases of Venus. As Venus orbits its star as seen from Earth, it shows to us varying amounts of its illuminated hemisphere. The exact same effect explains the apparent changes in brightness of the HAT-P-7 system (for the telescope cannot resolve which light comes from the planet and which comes from the star). During the transit of HAT-P-7 b, only its unilluminated hemisphere is facing us. After the transit, we see the planet as a crescent, then half phase, then a gibbous phase. The “full” phase of the planet occurs when the planet is behind the star so we do not expect to detect light from the planet during this time. Of course the phases of Venus are a bit different because we are close enough to Venus to see it grow in apparent size toward its crescent phase. For the changing brightness of a planet due to its phases, it’s perhaps best to think of the Moon, which is always brighter near full phase than at a crescent.

A light curve that is folded over the period of the planet which reveals its phases may be called a “phase curve.” It’s best to think of a phase curve as a special type of light curves.

The phases of Venus approximate the phases of an exoplanet

Consider observations of this type in the infrared. If we assume the planet and star radiate as blackbodies (which is more reasonable for longer wavelengths), you can estimate the day side equilibrium temperature of the planet with

\displaystyle T_{eq} = T_* \left( \frac{R_*}{2a} \right) ^{1/2} [\alpha (1 - A_B)]^{1/4}

Where \alpha is a constant that describes the heat recirculation efficiency of the atmosphere and A_B is the Bond albedo of the planet. If \alpha = 1, then the circulation of the planet is maximally efficient, redistributing heat to the night side of the planet enough to even the day and night side temperatures (you might consider Venus a good example of a planet with a value of \alpha very near to unity). The Bond Albedo quantifies the fraction of radiation that reaches the planet which is reflected back off into space. A value of \alpha = 2 implies that only the day side is emitting radiation. For a Bond Albedo of 1, the planet reflects all energy back into space and stays at absolute zero. While this situation is unphysical of course, high albedos are achievable. Snow and water clouds have a high albedo, while coal and asphalt has a low albedo.

Notice for the HAT-P-7 b phase curve above, the secondary eclipse depth is actually deeper than the brightness of the system just before and just after primary transit, which are the next best proxies for the brightness of the star without the planet. This subtle effect betrays the night-side brightness of the planet. The only time that the star is the only (known) contribution to the light curve is when the planet is hidden behind it. Right before transit and right after, though, only the night side of the planet is facing the observer. So we must conclude that the extra source of light is from the night side of the planet. This can be understood by the physical process of heat redistribution due to atmospheric winds (again, think Venus). For gas giant planets, the process is typically not as efficient, however.

However this observation of HAT-P-7 b with the Kepler telescope is in optical light. This phase curve therefore reveals to us that the heat redistribution to the planet is at least efficient enough to cause the night side of the planet to visibly glow red hot.

Let us turn our attention away from HAT-P-7 b for now to a hot Jupiter with less extreme irradiation, HD 189733 b. The Spitzer spacecraft observed the planet over an entire orbit to construct an infrared phase curve. An anomaly was noted in that the peak excess infrared brightness did not occur immediately before and after the secondary eclipse as would be expected if the sub-stellar point on the planet were the hottest. Instead, it was shifted over slightly.

8 µm Phase Curve of HD 189733 b

Note that not only does the transit not occur at the point of the least infrared excess, but the secondary eclipse does not occur exactly at the peak infrared excess. It turns out that you can construct a crude infrared map of an extrasolar planet by making the reasonable assumption that the planet is tidally locked to its star, such that the same longitude always faces the star. If this is the case, then it’s easy to figure out what longitude of the planet is facing the telescope, as it is a simple function of the observed orbital phase. Subtracting out the brightness of the star from the phase curve gives you just the observed brightness of the the planet. The brightness of the planet versus its longitude can therefore be represented graphically.

HD 189733 b longitudinal 8 µm brightness

This is, of course, only longitudinally resolved, and tells us nothing about where the warm spots are on the planet in latitude. Nevertheless, making various assumptions and simplifications, you can work up a crude 8 µm map of the planet.

8 µm map of HD 189733 b

We see, therefore, that the hot spot of the planet is pushed away from the substellar point at 0° longitude by 16 ± 6 degrees east. It seems reasonable to invoke upper atmospheric winds to explain this.

A more extreme case of this kind of anomaly can be seen for the innermost planet of the Upsilon Andromedae system, where the hottest spot has been pushed over Eastward a remarkable 80°(!). As of the time of this writing, it is not clear if winds alone can produce this extreme a discrepancy. This planet does not transit, as observed from Earth, however the detection methodology is similar. A phase curve can be clearly detected, only the transit and secondary eclipse are absent (here is a decent video that shows the dynamics of what goes into measuring this infrared offset).

In summary, the detection of the secondary eclipse of a planet can shed light on its reflectivity and, if measured in the infrared, temperature and heat redistribution properties of the atmosphere (and by extension a rough idea of its upper atmospheric wind behaviour).