Category Archives: Characterisation

Super-Earths and Mini-Neptunes


Low-Mass Habitable Zone Planets (artist images)

Our Solar System did not prepare us for what we would discover orbiting other stars. Instead, it told us that planets fall into neat categories: Gas giants made mostly of hydrogen and helium (of which Jupiter and Saturn are the archetypes), ice giants made mostly of water (for which Uranus and Neptune are representatives), and solid terrestrial planets with comparatively thin atmospheres — that would be the planets of the inner solar system and the one right under your feet). Since the discovery of thousands of planets orbiting other stars, and the measurement of their masses and densities, it has become clear that not all planets fit into this paradigm. Significantly, unless rocky worlds have an optimistically high abundance, what may be the most abundant type of planet in the Galaxy is a sort of mix between low-density, volatile-rich Neptune-like planets and rocky terrestrial planets. The Solar System features no such planet — after Earth, the next most massive planet is Uranus at ~14.5 times as massive. A casual look at the entirety of discovered transiting planet candidates discovered by Kepler reveals the magnitude of this problem.


While Kepler is no longer observing its original field, the massive amount of data can still be combed through to reveal new planet candidates. Here, previously discovered planet candidates are blue dots, and newly announced planet candidates are yellow. A few things are noteworthy. Firstly, the overwhelming majority of the newly discovered planet candidates have reasonably long orbital periods. This can be expected as shorter period planets have been detectable in the existing data for longer, and have had time to be spotted already. Secondly, and not really the point of this post… they’re still finding warm Jupiters in the data? Wow! What’s up with that? I would have thought those would have been found long ago.

With the obvious caveat that lower regions of that diagram feature harder to detect planets leading to that part being less populated than would be the case if all planets were detected, it would appear that there is a continuous abundance of planets from Earth-sized to Neptune-sized. While radius and mass may only be loosely related, it may also be that there is a continuous abundance of planets from Earth-mass to Neptune-mass, as well. Not having an example of such an intermediate planet in the Solar System, we really don’t know what to expect for what these planets are composed of. As such we began to call them (sometimes interchangeably) super-Earths or Mini-Neptunes. Are they enormous balls of rock with Earth-like composition extending up toward maybe 10 Me? Are they dominated by mass by a rocky core with a thick but comparatively low-mass hydrogen envelope? Do they have some fraction of rock, water and gas? Are they mostly entirely water with a minimal gas envelope? Answering this question would require some constraints on the masses of these planets, as it would allow one to know their density.

The first data point was CoRoT-7 b, the first transiting super-Earth — discovered before Kepler. The host star is very active, leading to a lot of disagreement in the literature about its mass, but further work seems to have settled on a rocky composition for the planet with ~5 Me. Great! Next data point was the transiting super-Earth orbiting GJ 1214, a ~6.5 Me planet with a much lower density, which is too low to be explained by even a pure water composition. This is decidedly not Earth-like. Additional measurements by highly precise spectrometers (namely HARPS and SOPHIE) of Kepler discovered planets have allowed for more data to be filled in, and an interesting trend can be seen.


Mass-Radius Diagram of Extrasolar Planets with RV-Measured Masses

Interestingly, planets less than ~1.6 Earth-radii seem to have not only solid, but Earth-like compositions. It’s worth noting that only planets where the mass measurement is acquired through Doppler spectroscopy are shown here. Planets like the Kepler-11 family where the masses have been derived by transit timing variations are not shown. If these planets are added, the adherence to the Earth-like composition is much less strict. This may imply that planets which have masses measurable by detectable transit timing variations have had a different formation history and therefore a much lower density. Further data will be very useful in addressing this issue.

On a somewhat unrelated topic, several new habitable planet candidates have been validated by ruling out astrophysical false positives. Among them is Kepler-442 b, which appears to me to be a more promising habitable planet candidate than even Kepler-186 f. Some newly discovered but not yet validated habitable planet candidates have been found as well, including one that appears to be a near Earth-twin.


New Kepler habitable planet candidates

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.

Transits Across g-Darkened Stars


Titan transiting its oblate fluid planet (Credit: HST)

We have previously looked at modelling the transit of an extrasolar planet incorporating limb darkening. How can we build upon this? For starters, it would be nice to actually take into consideration more physical phenomena – nature is not always simple. Take for example the case of a non-spherical star. Consider the case of Saturn, whose rapid rotation distorts the planet away from a spherical shape and more into an oblate shape. Stars, being fluid bodies like gas giant planets, are subject to similar physics, and have measurable effects on the transit light curve.

How does this affect a system? A rotating fluid body like a gas giant planet or a star is subject to centrifugal force which causes the equatorial radius to be larger than the polar radius. This effect, called oblateness, can be measured with

\displaystyle \text{oblateness} = \frac{a-b}{a}

Where a is the equatorial radius and b is the polar radius. In the case of Saturn, the oblateness is about 0.1. Despite a higher rotational velocity, Jupiter’s higher density and surface gravity are able to keep it’s oblateness lower, but still noticeable, at about 0.06. All of the other planets have very different, non-gas-dominated compositions, and have much a lower oblateness (in all cases, less than 0.025). The sun, however, with it’s high surface gravity (28 times that of Earth) and long rotation period (about a month), is almost perfectly spherical, with an oblateness of 0.000009.

In the case of a self-luminous body like a star, oblateness will cause the surface gravity and therefore surface temperature of the star to be a function of latitude. Parts of the surface closer to the poles will be hotter than those near the equator which are pushed further from the stellar centre due to the centrifugal force imposed by the stellar rotation. The temperature of the surface at a given latitude, θ, is given by

\displaystyle T_{eff}(\theta)=T_p\left(\frac{g(\theta)}{g_p}\right)^\beta

Where Tg and Tp are the surface gravity and temperature at the pole, respectively, and β is the gravity darkening coefficient, which much like limb-darkening coefficients, are dependent on the properties of the star and will have to be tinkered with to get a good fit.

An example of this comes from the nearby and well-known rapidly rotating, A-type star Altair, which has been spatially resolved using interferometry, allowing for the construction of a low-resolution temperature map.


Altair (Source)

Notice the oblateness of Altair is greater than even that of Saturn. This has a strong effect on the surface temperature of the star, with the equator being over 1,000 K cooler than the poles!

Much like in the case of limb-darkening, gravity-darkening will cause the luminosity profile of the stellar disc to be concentrated in one particular area. Unlike the case of limb-darkening, however, this area need not be the centre of the disc, but could instead be anywhere on the disc. This allows for transit light curves to actually be asymmetric in the case of a misaligned planetary orbit. A transiting planet in a polar orbit of a gravity-darkened star with, for example, a 45 degree rotation axis inclination, will have its planet occulting the bright polar region before moving over the more equatorial regions, causing the minima of the transit light curve to be displaced from the transit centre over toward the ingress.

Consider for example the case of KOI-13, a rapdily rotating A-type star, much like Altair, which was discovered to have a transiting hot Jupiter by the Kepler mission.

KOI-13 Light Curve

KOI-13 Light Curve (Source)

KOI-13 Light Curve Residuals

KOI-13 Light Curve Residuals

You may need to click on the light curve to expand it to full size to see the slight difference between the gravity-darkened and non-gravity-darkened model. If nothing else, the residuals to the non-gravity-darkened model are clear that the star is not uniformly luminous.

The stars where gravity darkening will be most pronounced will of course be the stars which have high absolute rotation rates. While a high v sin Istar implies a rapid rotation, the converse is not necessarily true since the stellar inclination angle is not known a priori. However, because a gravity-darkened star appears rotationally symmetric when viewed pole-on, the effects it has on the transit light curve are greatly diminished for low values for v sin Istar. This conspires to mean that the stars for which gravity-darkening effects on the light curves of transiting planets will be those stars where Doppler spectroscopy is less effective. Thus, while the Rossiter-McLaughlin effect may not be measurable due to the stellar spectral line broadening and corresponding lack of radial velocity precision, one can still in some cases use gravity-darkening to determine the projected stellar obliquity (or misalignment between the planetary orbit axis and stellar spin axis, however one chooses to interpret the system). Your typical system for which this is applicable is a bloated hot Jupiter transiting a rapidly rotating A-type star, and at present, only a couple such such systems are known.

From the perspective of modelling, gravity darkening is essentially asymmetric limb-darkening. This post was designed to give you the idea behind gravity darkening of stars and how it can affect the light curve for a transiting planet. In a future post, we will look at modelling transiting planets orbiting gravity-darkened stars.

Probability of Transit

Transiting Planets. Credit: NASA

Transiting Planets. Credit: NASA

Transiting planets are valuable items to explore the properties of planetary atmospheres. Planet searches like Kepler that focous on fields of sky tend to reap rewards amongst dimmer stars simply because there are many more dim stars in a given patch of the sky than bright ones. Transiting planets around bright stars are of particular value, though, as the increased brightness makes the system easier to study.

Radial velocity surveys tend to monitor brighter stars since spectroscopy is even more severely limited by stellar brightness than photometry, but it is not limited to observing patches of sky – telescopes performing Doppler spectroscopy tend to observe a single object at a time due to technical and physical limitations. Radial velocity surveys are also much less sensitive to the inclination angle of a planet orbit with respect to the plane of the sky. The planet doesn’t have to transit to be spectroscopically detectable. As such, radial velocity surveys tend to generate discoveries of planet candidates with unknown inclinations and true masses, but around much brighter stars than those planets discovered by the transit method.

As such, planet candidates discovered by radial velocity, especially planet candidates in short orbital periods are excellent targets for follow-up observations to attempt to detect transits. Transiting planets that have been discovered first through radial velocity have been of great scientific interest due to their host stellar brightness and thus ease of study. If more such systems are found, it would be of great benefit to understanding extrasolar planet atmosphere. While only a hand-full of transiting planets have been discovered first through radial velocity, they all orbit bright stars and are some of the best-characterised planets outside our solar system.

The probability that a planet will transit is, as has been discussed previously, given by
\displaystyle P_{tr} = \frac{R_*}{a}
where a is the semi-major axis of the planet orbit. This is the distance between the centre of the star and the centre of the planet. However, due to the inclination degeneracy – the reoccurring evil villain constantly plaguing radial velocity science – the star-planet separation is unknown. Remember that the period of the RV curve gives only the orbital period of the planet. If the orbital period is held constant, increasing the mass of the planet increases the star-planet separation. An increase in the total system mass requires greater separation between the two bodies to preserve the same orbital period.

For example, if radial velocity observations of a star reveal the presence of a mp sin i = 1 ME planet candidate, but the inclination is actually extremely low such that the true mass of the companion is in the stellar regime, then because the mutual gravitational attraction between the two stars will be much greater than the mutual gravitational attraction between the star and an Earth-mass planet at the same period, the two stars must have a wider separation, otherwise their orbital period would be smaller.

Mathematically, the true semi-major axis is given by
\displaystyle a = \left(\frac{G[M_*+M_{\text{pl}}(i)]}{4\pi^2}\right)^{1/3}T^{2/3}
Where G is the gravitational constant, and Mpl(i) is the mass of the planet at a given inclination i, and T is the period of the system. It is worth noting that the true semi-major axis is not significantly different from the minimum semi-major axis as long as the mass of the star is much greater than the mass of the planet – which is typically the case.

The fact that the true semi-major axis is a function of the unknown inclination makes for an interesting clarification: The probability that a planet of unknown inclination will transit is not simply given by Rstar/a, but is only approximated by it. If we assume that the distribution of planet masses is uniform (and extending through into the brown dwarf mass regime), then you would expect a planet with a minimum mass equal to Earth to have a much greater chance of being a bona-fide planet than a planet with a minimum-mass of 10 MJ, simply because there is a greater range of inclinations the former planet can be while still remaining in the planetary mass regime. Taking this a step further, even if both the Earth-mass planet candidate and the 10 Jupiter-mass planet candidate have the same orbital period, the probability that the latter planet transits ends up being less than the Earth-mass planet simply because of its high mass. Since its inclination is unknown, the probability that its mass is so high that the true semi-major axis is noticeably larger than the minimum semi-major axis is much higher, resulting in a likely lower transit probability.

Except it turns out that the mass distribution of planets and brown dwarfs isn’t constant. Earth-sized planets are significantly more common than Jupiter-sized planets, and super-Jupiters appear rare. It isn’t clear yet what the mass distribution planets actually is, with significant uncertainty in the sub-Neptune regime, but it is clear that for a highly accurate estimate of the transit probability, the inclination distribution cannot be thought of as completely random as it is fundamentally tied to the planet mass distribution.

Planet Mass Distribution

Planet Mass Distribution given by Ida & Lin (Left) and Mordasini (Right)

Consider the case of a super-Jovian planet candidate, perhaps with a minimum mass of 7 or 8 Jupiter-masses. Because a significant fraction of physically allowable inclinations would place the true mass planet into a mass regime that is in reality sparsely populated, it is less likely that the planet candidate’s orbit is in those inclinations. It is thus more likely that the planet candidate’s orbit is edge-on than would be expected from the probability function of randomly oriented orbits. As such, the transit probability of a super-Jovian planet is actually boosted by ~20 – 50% over what you would expect from Ptr = Rstar/a. If this is the case, then we would expect to find an excess in the fraction of transiting planets in this mass regime then would be expected purely from the standard transit probability function. Indeed this is what we see.

Candidate planets with masses in the terrestrial planet regime are similarly affected, with broadened transit probabilies owing to the fact that terrestrial planets are more common than higher mass planets, arguing in favour of a higher inclination than the random inclination distribution function.

On the other hand, planet or brown dwarf candidates of minimum masses in the most sparsely populated region of the mass distribution are unlikely to truly have that mass. They are quite likely in orbits with low inclinations and with much higher true masses. The transit probability for companion candidates with minimum masses in this mass regime are actually reduced from the standard transit probability function.

Geometric and a posteriori transit probabilities

Geometric and a posteriori transit probabilities

In the table above, taken from this preprint, we see that the geometric transit probability, Ptr,0, can be much less than the a posteriori transit probability, Ptr. The transit probability for 55 Cnc e, for example, jumps up from 28% to 36%. With these higher a posteriori transit probabilities, these short-period low-mass planets should be followed-up for transits. If transits are found, it would be of significant benefit to the extrasolar planet field.

In summary, there are various additional effects that can cause the a posteriori transit probability to be significantly different from the geometric transit probability. Planets with only minimum masses known can be more accurately assigned a transit probability when taking into account the uneven planetary mass distribution. Low-mass planets and super-Jupiters are more likely to transit than their geometric transit probability because a significant range of the inclination space is consumed by planets of masses that are simply rare. These planet candidates are more promising targets for transit follow-up than, for example, Jupiter-mass planets or intermediate-mass brown dwarfs.

The Rossiter-McLaughlin Effect

A retrograde hot Jupiter (Credit: ESO)

A retrograde hot Jupiter (Credit: ESO)

It is a convenient fact that stars spin in space – a result of angular momentum imparted upon them from the collapse of the progenitor clouds from which they form. This fact, while easily taken for granted, can permit a great deal of information to be gained about surrounding planets whose orbits are fortuitously oriented to cause them to transit.

For the case of a rotating star, one hemisphere of the star will be approaching the observer, and the opposite hemisphere will be receding. The approaching hemisphere is therefore blueshifted, and the receding hemisphere is redshifted. Because the stellar spectrum will accordingly be blueshifted and redshifted, the spectral lines of a rotating star appear widened or broadened. This spectral line broadening is directly proportional to the star’s rotational velocity, and the angle between the line of sight and the stellar rotation axis. Much like with Doppler spectroscopic detection of planets, the constraints you can set to the rotational velocity of a star are only a lower limit because the rotation axis is unknown. Indeed, a rapidly rotating star viewed pole on (i = 0o), there will be no observed spectral line broadening because all of the surface rotation is perpendicular to the line of sight. Because of this inclination degeneracy, the rotational velocity of the star is represented in terms of v sin i.

The redshifting of the receding hemisphere is typically balanced by the blueshifting of the approaching hemisphere, and so there is no net change in the colour of the star. However the transit of a planet will cause an imbalance in this hemispheric Doppler shifting. For a planet in an equatorial, prograde transiting orbit the planet will first cover part of the approaching hemisphere. The Doppler shifting of the rotating stellar surface is no longer balanced and the stellar spectrum has a net redshift. This anomaly disappears as the planet moves to the centre of the stellar disc, as the redshifted and blueshifted hemispheres are both equally apparent again. Then as the planet moves over the receding hemisphere, there is a net blueshift in the spectrum as some of the redshifted light is occulted.

This radial velocity anomaly is known as the Rossiter-McLaughlin effect. It can be used to measure the projected stellar spin-orbit alignment angle (the angle between the spin axis of the star, and the orbital axis of the star+planet orbit). It can be thought of as the projected obliquity of the star relative to the planet orbit, or the inclination of the planetary orbit relative to the stellar equator. For an equatorial orbit (spin-orbit alignment), λ = 0°, and for a polar orbit (spin-orbit misalignment), λ = 90°.

The Rossiter-McLaughlin Effect

The Rossiter-McLaughlin Effect

As we can see in the diagram above, the RM effect will have a different RV shape depending on the orientation of the planet’s orbit axis relative to the spin axis of the star. If the orbit is nearly polar and the planet transits across only one of the approaching or receding hemispheres, then the RM effect will be entirely blueshifted (if the planet crosses the receding hemisphere as is shown in the third example above) or redshifted (if the planet crosses the approaching hemisphere).

The amplitude of the RM effect, KR, relative to the amplitude of the star’s reflex velocity due to the influence of the planet over the course of the orbit, KO, can be estimated by
\displaystyle  \frac{K_R}{K_O} \approx 0.3\left(\frac{M}{M_J}\right)^{-1/3}\left(\frac{P}{3\text{ days}}\right)^{1/3}\left(\frac{v \sin i}{5\text{ km s}^{-1}}\right)

Very few stars have their spin axes perfectly perpendicular to our line of sight. If the star is viewed pole-on, the RM effect amplitude will be zero. It’s worth remembering that it isn’t the absolute stellar rotation velocity that determines the Doppler shifting (and thus the RM effect amplitude), but the apparent rotational velocity, v sin i.

Another degeneracy affecting the RM effect is that impact parameters close to zero have the planet occupying both hemispheres more equally in time. This causes the RM effect to be much more symmetric than an off-centre transit with a high impact parameter. For the case of b = 0, the RM effect will be symmetric regardless of the value for λ, and only the RM effect amplitude will have changed. Since the RM effect amplitude is also a function of v sin i, some ambiguity is present in low- impact parameter systems over the value of λ.

The overwhelming majority of planets which have had RM effects measured are hot Jupiters, whose short orbital periods and high mass cause high orbital RV amplitudes, leaving the RM effect amplitude to be small in comparison. Interestingly, however, the magnitude of the RM effect amplitude is not dependent on the planet’s mass or semi-major axis, but on only the stellar v sin i and Rp. A planet of a given radius will have the same RM effect amplitude whether it is close to the star, producing a high orbital RV amplitude, or far from the star, with a much smaller orbital RV amplitude.

Accordingly, transiting planets in long-period orbits may have RM effect amplitudes several times their orbital RV amplitude. The advantages of this become quite apparent when one takes into consideration the timescales involved. Without the Rossiter-McLaughlin effect, a Doppler spectroscopic detection of an Earth-analogue around a solar-type star (with v sin i = 5 km s-1) would require at least a year to secure a full orbit, and furthermore, would require a Doppler precision on the order of 10 cm s-1. With noise issues in the RV data, it may require several orbits to build up enough data to confirm the planet. However, the Rossiter-McLaughlin effect for the same planet would be on the order of ~30 cm s-1 and would last less than a day. The far shorter time needed to observe the RM effect and the far greater amplitude make this a promising tool to validate extrasolar planet candidates whose existence are known from transits alone, but whose mass may take a considerable amount of effort to determine. Instead of wasting months trying to validate a planet candidate and run the risk that the candidate is a false-positive, a single night can conclusively demonstrate that the object is an orbiting planet.


Rossiter-McLaughlin Effect for a transiting Earth analogue

Because the rotational velocity of a star is correlated with its age and mass, which itself is correlated to the spectral type of the star, the true rotational velocity of a star is loosely correlated to the spectral type. Comparing a measured v sin i to the expected rotational velocity can give you a loose estimate for the inclination of the stellar rotation axis to the line of sight. This, combined with λ, can permit you to estimate the true spin-orbit alignment angle, typically denoted with φ (though variations on this definitely exist).

Constraining the spin-orbit alignment angle of extrasolar planetary systems provides clues to their dynamical histories. It is still not clear how hot Jupiter systems form. Giant planets may tidally interact with the planet-forming disk to migrate inward toward the star, or they may be gravitationally scattered inward by close encounters with other planets. Either scenario has testable predictions in the context of the observed spin-orbit alignment of a planetary system.

Peaceful migration through disk-interaction is expected to result in well-aligned planetary systems. Like in our Solar System, planets that form in a protoplanetary disk coplanar with the stellar equator will maintain that orientation, and you’ll end up with planets orbiting close to the stellar equatorial plane. However if hot Jupiters are the result of the scattering of planets through close encounters with each other, then the migration behaviour of hot Jupiters will have been much more chaotic in the early history of the planetary system and the spin-orbit alignment angle may have a wide range of values.

The first few hot Jupiters to have their RM effects measured were all fairly well aligned, consistent with calm migration as was generally believed to be the most likely explanation of their origin. Later work with planets from the SuperWASP survey uncovered several misaligned planets, including even retrograde hot Jupiters. Further work since has found planets across a wide range of values for λ.

Correlation between stellar temperature and hot Jupiter alignment.

Hot Jupiter Alignments

As spin-orbit alignment angles came in over the years it became apparent that misaligned planets are preferentially around hotter stars. Specifically above stellar effective temperatures of Teff > 6250 K, the distribution of λ seems to be much more random. This is clearly a clue to understanding the dynamical histories of hot Jupiters, but it’s not currently clear what it means.

Not only will measuring λ for extrasolar planet systems help us understand their formation histories, but it can also prove to be a powerful tool for confirming small, long-period planets with relatively little effort. It can require fairly high quality RV data, but it is well worth the effort to obtain these values, especially for smaller planets to see how the dynamical histories of low-mass, short-period planets compare to those of hot Jupiters. Do these multi-planet systems of low-mass planets form in a similar way to hot Jupiters? So far the evidence appears to point to “no,” but more data is needed to understand this question.

Meeting the Neighbours

One of six mirrors for the Giant Magellan Telescope

One of six mirrors for the Giant Magellan Telescope

The proximity of a planet to our own solar system will be critically important in the near-future when we begin to characterise the atmospheres and assess the potential habitability of extrasolar planets through direct imaging spectroscopy. Additionally, the nearest extrasolar planets will likely be the first targets of interstellar probes launched by humanity to investigate these worlds up close. To this end, there is considerable interest in discovering planetary companions to nearby sun-like stars. I’ve compiled a brief table below to show the nearest sun-like (FGK) stars to us. I’ve omitted the sea of red dwarfs (as well as a couple A-type stars: Sirius and Altair) interspersed between them in the interests of brievity.

Nearest Sun-like (FGK) Star Systems
D (pc) Spectral Type(s)
Sol 0.0 G2V
Alpha Centauri 1.3 G2V + K1V + M5V
Epsilon Eridani 3.2 K2V
Procyon 3.5 F5IV + DQZ
61 Cygni 3.5 K5V + K7V
Epsilon Indi 3.6 K5V + T1V + T6V
Tau Ceti 3.6 G8V
Groombridge 1618 4.9 K7V
40 Eridani 4.9 K1V + DA + M4V

This interest in our sun’s nearest neighbors can hardly be said to be confined to the scientific community. How many of these star names do you recognise, even if simply from works of fiction?

Until this year, there has been evidence for a giant planet around ε Eri (though the existence of this planet has been questioned recently). But over the last couple of months, we have seen extraordinary announcements of planetary companions around both α Cen and τ Cet.

Firstly, and perhaps most importantly, the discovery of a planet around α Cen is an important milestone in our attempts to understand our place in the Universe. The nearest star system to our own has been found to have a planet – only twenty years after it was not known for sure that extrasolar planets existed at all. But for the details (which are likely not news to the reader): The planet orbits the secondary star in the system in a 3 day orbit, exposing the planet to temperatures that completely throw the question of habitability out the window. But we now know that the system was conductive to planet formation billions of years ago, and we have learned that planets often come in groups. There may yet be more planets around α Cen B, and perhaps even planets around α Cen A as well.

But from the perspective of technological progress, the planetary companion reported around \alphaCen B has a minimum mass that is roughly equal to that of Earth. This planet isn’t some super-Earth or a mini-Neptune: It’s almost certainly a terrestrial planet, and it is the lowest-mass planet detected thusfar from Doppler spectroscopy.

With an increasing number of planet candidates in their star’s habitable zones, and an increasing number of planets discovered nearby, we are approaching a time where there will be a known sample of small planets in the habitable zones of the nearest stars. These planets will likely be our best targets for a search for biosignatures in their atmospheres. Large ground-based telescopes with aperture sizes on the order of 25 – 30 metres, such as the Thirty Metre Telescope and the Giant Magellan Telescope will likely be the key to characterising the atmospheres of these planets.

Thirty Metre Telescope (Concept image)

Thirty Metre Telescope (Concept image)

There are about 125 main sequence stars within 8 pc. Depending on what the abundance and properties of planets in general are in the solar neighbourhood, there may well be a hundred or so small planets that will be available to characterisation by the next generation of ground-based telescopes. You can estimate the underlying distribution of planets (with help from the Kepler mission results) and calculate their angular separation from their stars and their brightness contrast. This can give you an idea of what planets exist in our celestial backyard that are available to us for direct study. Looking in the infrared will make this all easier as the contrast is greater between the two (still extreme, but not as difficult as visible light). A study was recently posted to arXiv about this specifically.

It is notable that the recentlty discovered low-mass planet candidate α Cen Bb presents a contrast of 10-7 and is eminently observable in this baseline scenario (assuming a radius of 1.1 RE) … Despite the worse contrast achieved on this fainter star, the massive planets GJ 876 b and c can be directly characterised if Ag (Rp / RE)2 > ~19 and ~6, respectively (Ag > ~0.02) … The currently known planets GJ 139 c and d can also be characterised of Ag(Rp / RE)2 > ~0.9 and ~1.8 respectively (i.e. Ag > ~0.4), and the planet candidates τ Cet b, c, and d could be characterised for Ag (Rp / RE)2 > ~0.08, ~0.4, and ~1.2 respectively (Ag > ~0.04, ~0.14, and ~0.35). Theoretical efforts to model all these planet’ near-infrared reflectance are clearly warranted.

With nearby planets at α Cen, GJ 876, τ Cet and 82 Eri (GJ 139) being potentially available to direct atmospheric characterisation in the next decade, we are approaching an exciting time where we will have some idea of what these planets are like. This understanding will transcend the basic understanding we have been able to gather from transit light curves and radial velocity.

Still, it will be some time until these planets are known as well as the planets of the Solar System. Our understanding of them will likely be comparable to our current understanding of Pluto. We know there are surface features, we know there are ices of various compositions, but beyond that, Pluto is very much a mystery. Unlike Pluto, a world where in three years time we will have close-up images of thanks to the New Horizons spacecraft, we are not likely to see close-up images of extrasolar planets for the foreseeable future, at least certainly not within our lifetime. Our generation, and likely the next several, will be forced to be content with getting only hints of the nature of the surface conditions on planets outside our solar system. But those hints may be very revealing. They can imply the presence of interesting chemistry and perhaps even biological activity. The limited nature of the understanding of these worlds that we will see unfold in our lifetime is therefore no reason to be pessimistic or to despair. There is much to learn even in the near future, and we should be thankful to be alive in an exciting time where we are beginning to discover the nearest planetary systems to our own and, in the near future, characterise their atmospheres.

Great Mysteries Revealed

Giant squid finally caught on video

Giant squid finally caught on video

It was recently announced that Japanese scientists have managed to finally capture video footage of a giant squid. We’ve known for some time that they exist, but until now, they have never been seen like this in their native environment.

Previously discussed detection methods for extrasolar planets leave much to be desired. Doppler spectroscopy tells you only a minimum mass for the planet and its orbital period. Transit photometry tells you the size and orbital period of the planet, and is typically not capable of confirming the detected object as a planet (since the mass is unknown, a brown dwarf or low-mass star could masquerade as a planet). Gravitational microlensing tells you the planet’s mass but only a projected distance from the star, and usually nothing about the orbit. Astrometry tells you the planet’s true mass and orbit in three dimensions, but otherwise permits you no more information about the planet than Doppler spectroscopy. Combining these techniques will allow one to tease out more information, but it’s still awfully indirect. We know the planets are out there, but it would be nice to actually see them.

The ultimate detection method of the future that will provide the most information is direct imaging. It’s very straightforward, all it involves is a large telescope with a decent imaging contrast ratio. It sounds easy but there are daunting challenges involved due to the proximity of planets to their stars and the brightness of their host stars.

The first directly imaged exoplanet

The first directly imaged exoplanet

As of the time of this writing, only a couple dozen or so planets have been imaged with 8 – 10 metre class telescopes as well as HST. For the most part, they were all imaged in the infrared, they are all very massive as far as planets go, and they are all widely separated from their stars – typically hundreds of AU.

The greatest problem is that stars are very bright, and planets are comparatively very dim. In visible light, there’s a brightness contrast between the Sun and Jupiter of a factor of a billion, but depending on the wavelength and system age and planet mass, the brightness contrast can be as low as ten thousand. This problem is made worse by the diffraction of the starlight across the focal plane of the telescope produces a large amount of “noise,” with the star’s light spread out over a greater area of the image. A method of removing this excess light from a star is a requirement for directly imaging its planets.

One method of doing so is to use a coronograph. This is effectively an object in the telescope to block the light from the star, allowing one to see “around” the star. While you might therefore expect there to be dark “hole” in the image where the star is, the diffraction of light around the coronograph still produces a brighter, noisy area where the star would be. Imperfections in the coronograph will result in extra noise, and it is not clear that perfect coronographs are achievable. Since coronographs (even perfect ones) only attenuate the coherent part of the light’s wavefront (the shape of the waves of light). Imperfections in the wavefront (called aberrations) can leak through the coronograph to produce a residual noise in the form of a speckled halo around the star. Methods exist to correct this, such as wavefront correction with deformable mirrors or to calibrate images for speckles. It’s not perfect, but it certainly removes a lot of the excess starlight.

Four planets at HR 8799

Four planets at HR 8799

Some caution is necessary when discovering planets through direct imaging. A supposed planet next to a star could turn out to be a background star. Monitoring of the planet candidate over some time will be needed to determine if it is bound to the star. Since stars and their associated planets move through space together, there is a certain motion in the sky that the planet and the star will follow if they are bound, whereas the two will have vastly divergent motions in the sky if they are not.

The advantages of directly imaging extrasolar planets is beyond having pictures – it permits direct spectroscopy of the planet’s light. Now while it is possible to gather information about the atmosphere of a transiting planet at a great distance from the star, the fraction of planets at large distances from their star that will transit are quite low. Direct imaging opens up access to all planets with a sufficient brightness and angular separation from the star.

I suspect in the future that this will be the most prevalent way of truly characterizing the planets in the solar neighborhood. Statistically speaking, few nearby Earths will transit, so we will require direct imaging to test their atmospheres for the presence of bio-markers that may be indicative of life.