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## The Venus Transit: an analog to exo-climate detection

There has been a large interest during the last couple of days in the Venus transit, where the second planet in our solar system passed directly between Earth and the sun, which was seen by many people and shown in the video above. For us, this phenomenon will not happen again until 2117. However, a viewer on a planet orbiting a distant star might see a Venus transit every Venusian year (~225 Earth days) if they resided in the same plane of orbit. Likewise, it would be possible for that observer (or for example, an observer on Mars) to see an Earth transit.

This leads to the subject of the post, which may be a bit more descriptive than others. Unknown to many yesterday, the world had a front row seat to a common method that is used to detect exoplanets (distant planets that orbit around stars other than our own, often tens of light-years away). The Venus transit will be used a test of the quality of the technique. The detection of such exoplanets is the goal of the Kepler satellite, one of the greatest scientific missions of our time. Kepler is NASA’s first mission capable of detecting Earth-size planets in orbit around other solar-like stars. So far, well over 1200 candidate planets have been discovered since 2009, with sizes ranging from less than Earth to twice as large as Jupiter (and with orbital periods shorter than a day to more than a year). It is a photometric space-based mission with the intent of finding bodies that orbit in the so-called habitable zone of their host star. This is the region where liquid water water is capable of being sustained on the surface of a planet (the factors that govern these limits will be discussed in later posts). From an observational and climate perspective, it is also possible to retrieve information about the atmospheres of such planets based on spectroscopy techniques of selected transiting planets.

As we’ll see, transiting planets offer the possibility to detect and characterize atmospheres of giant planets like Jupiter, and should also provide an access to detecting biomarkers (atmospheric constituents indicating the presence of life) in the atmospheres of Earth-like exoplanets. This science is in its infancy but is growing rapidly, and offers the most promising way to detect life outside our solar system. But how does it all work?

When a planet passes in front of its host star, it blocks a very small amount of starlight and there is a slight reduction in brightness when viewed from Earth. The transit reduces the stellar brightness in an amount equal to the ratio of planet-to-star area. Assuming the flux from the planet is negligible compared to that of the star, then:

$\displaystyle \frac{\Delta F}{F} = (\frac{r_{planet}}{r_{star}})^2$

The left hand side is the fractional brightness change, and r represents the radius of the planet or star.

Idealized brightness curve as the planet transits in front of the star. Brightness is reduced when the planet passes in front of the star. From Murray, 2012, Science

For those interested, when the radiation passes through the atmosphere and absorbed, the emerging radiation has of course been attenuated by a certain factor. The intensity of the resulting radiation at wavelength $\displaystyle \lambda$ is:

$I_{\lambda} = I_{o}exp(-\tau (\lambda) / \mu)$

where $\tau$ is the slant optical depth integrated through the planet’s atmosphere along the observer’s line of sight (a measure of the atmospheric absorption efficiency, neglecting additional scattering), $\mu$ is the cosine of the viewing angle, and $I_{o}$ is the initial intensity.

The reduction in brightness is on the order of ~1% for a Jupiter-sized planet orbiting our sun and ~0.01% for an Earth-sized planet. This makes it a challenging problem but still accessible with current technology. The timing between subsequent “dips” in the brightness curve is related to the orbital period, and in principle the size and duration of those brightness “dips” will be constant.

Thus, detections of repeated reductions in stellar brightness (of similar magnitude) indicate the presence of a transiting body around the star. It also turns out that the probability of observing a transit from Earth is related to the distance of the planet to its host star. That probability increases for planets closer in. Fortunately, it is now known that there is a large population of planets orbiting very close to their host stars. These are so-called hot-Jupiters, hot-Neptunes, or even hot super-Earths, and they reside in the neighborhood of just 5% the distance between Earth and Sun! Temperatures of these bodies can exceed 1000-2000 K, and the close proximity of the planet to the star forces such planets into a tidally-locked state in which one side is in perpetual daytime and one side in darkness. The distribution of stellar radiation and resulting atmospheric circulation is therefore unlike any in our solar system, but may be a common occurrence in general.

Figure 2) From Seager (2010), Exoplanet Atmospheres

Figure 3) Schematic of starlight passing through a planet’s atmosphere and emerging to be viewable from an observer on Earth. From Deming, Nature, 2010

Absorption of starlight passing through the planet’s atmosphere during transit can give information concerning the composition and scale height of the exoplanet atmosphere. The passage of the starlight that has passed through the atmosphere carries with it a signature of the atmospheric composition, as the planet’s absorption features become superimposed on the observed stellar flux. As seen in Figure 2 (directly above), when the planet occults a portion of the stellar disk, a fraction of light from the star is seen that has traversed a part of the atmosphere around the planet’s limb (the smaller white area surrounding the black circle that represents the planet). Figure 3 shows the same thing in a different way. Light that penetrates to the lower atmosphere will not likely emerge “from the other side” and will be invisible to an Earth-based observer, though light that “skims” the atmosphere will make it through and be viewable from an Earth observer. This depends on the nature of the atmosphere itself (e.g., its height) and how well it interacts with radiation. The spectral signature of the starlight that passes through the upper, optically thin region can be compared with observations of the planet-star system when not in transit, and the planet’s transmission spectrum measured from the difference.

Of course, planets in circular orbits that pass in front of the star must also disappear behind the star (Figure 2). When this happens, only starlight can be observed from Earth, and not the light from the planet+star combined (planets emit energy in the infrared wavelengths, and these “hot” planets emit generous amounts, within detection limits). On Earth, the received light from the planet+star can be contrasted with observations of the star only after the planet disappears in the secondary eclipse. The difference is an estimate of the planetary emission alone. Of course, the secondary eclipse will correspond to a smaller reduction in brightness than in the primary eclipse (since the star is being blocked in the primary case, and the planet being blocked in the secondary case) (see figure below).

The flux of the planet+star system viewed from an observer. When the planet passes in front of the star, that portion of the starlight is blocked (first dip). When the planet is hidden by the star in the secondary eclipse, the planetary light is hidden, corresponding to the smaller dip. From Seager (2010, Exoplanet Atmospheres)

It actually turns out the size of the smaller dip (at second eclipse) can be related to the brightness temperature of the planet, although this is not a full estimate of surface temperature, since other things like the presence of a greenhouse effect may come into play.

As some examples, Charbonneau et al., detected sodium absorption in the atmosphere of planet HD 209458b (Charbonneau et al. 2002), and methane in the atmosphere of planet HD189733b (Swain et al., 2008, see figure below). This was the first detection of any carbon-bearing molecule on a planet outside our Solar System, all possible because that planet can be seen to transit its star from Earth!

Measurements of the difference in spectra during the secondary eclipse was done, for example, in 2005 by Deming et al. on the extra-solar planet HD 209458b (Deming et al. 2005). Water vapor, carbon dioxide, and methane have all been detected in exoplanetary atmospheres (e.g., Swain et al., 2009; Tinetti et al., 2010). Moreover, thermal inversions have been detected on a number of exoplanets indicating a solar absorber in the upper atmosphere (see Seager (2010) for a review).

CO2 features have been found in the HD 189733 thermal emission spectrum, which is somewhat surprising since at very high temperatures atmospheres which are dominated by molecular hydrogen are expected to have carbon primarily in the form of CO or CH4.

These examples are all “large” planets; characterizing the atmospheres of Earth-mass planets with transmission spectroscopy is extremely challenging because of the small extent of their gaseous envelopes. One can imagine from the second and third figure that obtaining good enough light signatures (that have passed through an exoplanet atmosphere) is very difficult if those atmospheres are more compact.

The measured spectrum (black triangles), and two theoretical spectra of the predominantly H2 atmosphere, showing the effects of small amounts of water (blue) and methane in combination with water (orange). The measured spectrum contains significant differences at 1.7–1.8 micron and at 2.15–2.4 micron from what is expected due to water vapour alone. We interpret these departures as additional absorption features due to the presence of one or more other species in addition to water. When considering only water and methane, the theoretical spectrum best fitting the data was determined by binning the model (shown as white crosses) to the spectral resolution of the observations. Different model predictions based on changing abundances and molecules were compared to the observations using the reduced chi2; the best fitting model has a water abundance of 5 times 10-4 and a methane abundance of 5 times 10-5. The model spectrum can be improved slightly with the addition of small (approx 1 times 10-5) amounts of either ammonia or carbon monoxide (shown in green and purple crosses, respectively). From Swain et al (2008)

Venus as an Exoplanet

Testing the above methods will be useful for the planetary science community since we know the atmosphere of Venus rather well through independent methods, such as visits from monitors like the Venus express mission. It is a hellish place. The temperature of the Venusian surface is roughly 735 K (860 Fahrenheit), hot enough to melt lead. Its primary atmospheric constituent is carbon dioxide, though with trace amounts of water vapor and sulfur dioxide. The greenhouse effect generated by CO2 is largely responsible for this high temperature, and is a far-away extreme case of anything humans are capable of doing on Earth, though the physics is precisely the same. Venus has multiple cloud decks composed of sulfuric acid particles, and exerts an atmospheric pressure of roughly 90 Earth atmospheres (equivalent to about half a mile of ocean water above you).

A theoretical transmission spectrum of the atmosphere of Venus that will be tested with spectroscopic observations during yesterday’s transit was provided by Ehrenreich et al (2012) (a solar transit of Venus in the 1700’s was actually the first time it was discovered that Venus had an atmosphere). Shown below are typical temperature profile and profiles of constituents in the atmosphere, provided by the Venus Express mission.

Left: Atmospheric pressure-temperature profile . Right: Gas mixing ratios (thin lines) and haze densities for mode-1 (thick violet line) and mode-2 (thick blue line). From Ehrenreich et al.

The transmission spectrum covers a range of 0.1–5 μm and probes the limb between 70 and 150 km in altitude. This is caused by droplets of sulfuric acid composing an upper haze layer above the main deck of clouds, so someone on Earth cannot “see” radiation passing through Venus at altitudes lower than this. The lowest altitude reached by transmission spectroscopy is determined by the dominant scattering regime (Rayleigh scattering on Earth caused by the dominant atmospheric constituent N2, which preferentially scatters blue light and explains the color of the sky; in contrast, Venus is primarily in a Mie scattering regime, caused by cloud cover, and less so by the main constituent, CO2). The difference is caused by the relative size of the particles doing the scattering compared to the wavelength of light.

(a) Absorption cross sections of the considered atmospheric gases, Rayleigh scattering cross section of CO2 (dashed red line), and Mie extinction cross sections for mode-1 (thick blue line) and mode-2 (thick violet line) haze particles. (b) Transit spectrum of Venus transiting in front of the Sun, as seen
from Earth, in relative absorption and (c) effective height of absorption. The different transit spectra shown are models with no upper haze (black), mode-1 upper haze (red), and modes- 1+2 upper haze (green). The top of the main cloud deck is set at 70 km. The transit spectrum of the Earth calculated by Kaltenegger & Traub (2009) is overplotted (blue) and shifted by +100 km for clarity.

Earth as an Exoplanet

A holy grail of exoplanet detection, and arguably of science itself, is the detection of a life-bearing world. Transmission spectroscopy has also been applied to Earth as well from satellites looking back (e.g., Kaltenegger and Traub, 2009). Ozone and diatomic oxygen are present in these measurements as expected, even though the lower part of the troposphere is not accessible for detection using this method for reasons mentioned earlier.

On Earth, oxygen is very reactive and could not exist in substantial amounts unless it was constantly produced. That source is photosynthesis. Oxygen and ozone together are Earth’s two most robust biosignatures. There are other ways to have high oxygen loadings in the atmosphere, however, which would not indicate life. Such a condition could arise if the planet’s ocean were vaporized into the atmosphere. This is the classical “runaway greenhouse” phenomenon thought to have occurred on ancient Venus. A byproduct of this is large quantities of water at high altitudes in the atmosphere, where high-energy radiation can break apart the water molecule and the light hydrogen species can escape into outer space while the heavier oxygen molecule is left behind (and O2 builds up in the atmosphere for a short period of time before reacting with the crust). The relative ratios of oxygen and methane in our atmosphere are not compatible with an abiotic world either, although it may be difficult to establish both spectral features for a far away exoplanet. It may therefore be challenging to find robust biosignatures.