Planetary transits: how can one measure the mass, size, density, and atmospheric composition of a planet one cannot even see?

Finding transiting planets

Our Solar System is shaped like a rather flat disk: all the major components are very close (to within a few degrees) to some imaginary “average” plane. Indeed, most (but not all) planetary systems are flat, so we can imagine other planetary systems as roughly disk-shaped. Relative to our own Solar system some of these flat systems will be seen “face on”, some will be “edge on”, and most will be somewhere in between.

One result of this randomness is that only a small minority of these systems will be oriented in such a way that their orbital plane is close to our line of sight (i.e. “edge-on”)—but this serendipity has multiple wonderful results indeed! Planets in such a system will seem to pass, or transit, in front of their host star once every orbit—as seen from earth—blocking a small fraction of the host star’s light for a short while in a “mini Solar eclipse”. This, as we will see below, allow us to both detect new exoplanets and learn a great deal about them.

Now, since stars appear like (very small) luminous disks, to a good approximation if half of the stellar disk is blocked by something opaque then we will see that star’s light diminish by half—this is what exoplanetary transits are all about. Firstly, we may ask: how small or large will this “mini eclipse” be? It is useful to have some examples: a Jupiter-like planet is about 10% the diameter of the Sun, so it can block about 1% of the Sun’s light (since the area of a circle is proportional to its diameter squared). Reversing this relation, if an astronomer finds a 1% deep transit-like dimming of a far-away star, he/she will conclude that the transiting object is approximately 10% the diameter of the host star—without ever measuring the size of the planet by an image that actually resolves the planet (obtaining such an image will require an unrealistically large telescope with a primary mirror about a kilometer in diameter).

Now, a 1% dimming of a star is something one can measure from the ground—so ~15 years ago multiple surveys started looking for such large planets (scale of Jupiter in size)—monitoring millions of stars every few minutes for months, and even years, on end. Why millions? Because not all stars are bright enough or stable enough to allow the detection of a 1% transit, and only a fraction of them actually host a large planet close-in to its host star (a so-called “Hot Jupiter”), and only a fraction of those are aligned close to our line of sight… so one has to start with millions of stars to find a handful of transiting planets. Processing this large amount of data requires sophisticated algorithms and a large degree of automation, and so quite some time passed before astronomers found out how to do this the right way. Today, a few hundreds of these ground-based detected transiting planets are known.

Top: As planets revolve around their star they exhibit phases akin to the phases of the Moon, since we see variable parts of their day or night sides throughout their orbit. This picture, however, is not what one can see with a telescope. Bottom: the observed flux (=brightness) of a star hosting a transiting planet. We will see different amount of flux depending on the part of the planetary orbit: when the planet goes behind the star we will see just the star alone. At all other phases we will see a both the star and the planet , and the the latter will also block some of the star's light during transit.
Top: As planets revolve around their star they exhibit phases akin to the phases of the Moon, since we see variable parts of their day or night sides throughout their orbit. This picture, however, is not what one can see with a telescope. Bottom: the observed flux (=brightness) of a star hosting a transiting planet. We will see a different amount of flux depending on the part of the planetary orbit: when the planet goes behind the star we will see just the star alone. At all other phases we will see both the star and the planet, and the latter will also block some of the star’s light during transit.

The space revolution

Unfortunately, detecting transiting planets much smaller than Jupiter is very difficult from the ground, if not impossible: an Earth-sized planet is a about tenth the diameter of Jupiter, or 1/100 the diameter of the Sun, so if can only impart a transit which is about 0.01% deep, much too small to be detected from ground-based observatories, which have to combat things like day/night cycles, weather, atmosphere, variable temperatures, etc.—all of which make precise measurements difficult. Fortunately, space-based observatories simply avoid all of these disturbances, so even by simply placing the exact same equipment in space one immediately gets much more precise measurements due to the very stable environment available in space—with no day/night cycles, no weather, no atmosphere etc. Indeed, NASA’s Kepler mission did more than that: the instrument aboard the Kepler spacecraft was highly optimized to the precise measurement of stellar brightness that does allow the detection of small Earth-like planets despite their small transit depth and long period. This, in turn completely revolutionized the exoplanets field.

Before Kepler about 300 exoplanets were known from all transit and radial velocity surveys combined, while Kepler alone found (as of today) over 1,000 confirmed planets, with >3,000 more candidates still waiting confirmation. Importantly, the kinds of planets Kepler found were very different from the giant planets usually found by other transit and radial velocity surveys; it found that most planets are small, with the most common type of planet only 2-3 times the diameter of the Earth. In fact, so many planets were found that it is now understood that most stars have at least one planet, and likely multiple planets, around them.

More than just detecting planets

Indeed, finding lots of planets is a lot of fun, but there is more—much more—to transiting planets than that. For starters, by combining the mass (from instruments like HARPS that measure precise radial velocity) and radius (from transits), one can easily calculate the planet’s mean density, which in turn can tell us something about the bulk composition of the planet. It was found that planets are indeed far more diverse than anyone had ever suspected before—with planets having densities spanning about two orders of magnitude; some planets are almost all high-density iron while others are less dense than Styrofoam, virtually devoid of solid material and probably all made of light elements like hydrogen and helium.

One of the early successes of the transit method stemmed from the understanding that the top layers of the planetary atmosphere are rarefied enough so they are not completely opaque. This means that as the planet transits the host star, some of the stellar light that passes through these layers is not completely absorbed and actually makes it through to us, and now it carries some information about the conditions that exist in these upper layers of the planetary atmosphere in its spectrum. By subtracting the on- and off- transit spectra one can isolate this faint planetary contribution to the overall light coming from the star, and this indeed allowed the detection of multiple interesting molecules on these far-off worlds, for example: carbon monoxide, carbon dioxide, water, hydrogen, methane and more. In the future the detection of “biomarkers”—evidence of extraterrestrial life—will be attempted using this technique.

The observed global temperature map of exoplanet HD 189733 b, the first of its kind, as inferred from the different phases of this remarkable hot Jupiter. Temperatures range from about 650 degrees Celsius on the coldest part, to 930 degrees Celsius on the hottest. Note that this hottest spot on the planet is not directly in the middle, i.e. it is not just
The observed global temperature map of exoplanet HD 189733 b, the first of its kind, as inferred from the different phases of this remarkable hot Jupiter. Temperatures range from about 650 degrees Celsius on the coldest part, to 930 degrees Celsius on the hottest. Note that this hottest spot on the planet is not directly in the middle, i.e. it is not just “below” the star or at “high noon”—but rather shifted to the East.

Moreover, by observing these planets at longer wavelengths, in the infrared, one can observe light emitted from the planet (vs. just reflected from—or refracted by—it) and thus permit us to measure the planet’s temperature on the day side. Some planets also allow the creation of rudimentary temperature maps (!) for them, finding that the hottest point on the day-side of the planet is not exactly facing the star—but shifted from it by strong, persistent jet streams. At that point one can start talking about the planet’s energy budget and global weather patterns, cloud formation and circulation,… characterizing the planet, and not just detecting it.

In some other cases “transit timing variations” were identified: the transits of some pairs of planets are not quite periodic but they appear to transit slightly earlier or later than they “should”, and in sync; when one was late, the other was early. These perturbations are cause by the gravitational interaction between different planets in the systems: both are pulling on each other, disturbing their regular rhythms. This allows us to reverse the problem and ask: “if I do see these irregularities, what kind of masses can cause them?”, the answer effectively finds the mass of the planet(s) in the system without ever using the expensive resources like HARPS—but for free—just by carefully analyzing the times of transit.

By studying yet finer details of the transit light curve—some of which have been detected and some are still too difficult to find even with current space-based data—many more things can be inferred about the planet: from planetary rings, from planetary oblateness to a measure of its rigidity, to planetary rotation rate and mean wind speed—all are derivable (in principle) from transit light curves.

We are thus able to sometimes measure the size, density, composition, dynamical interaction and much more for transiting planets, and I remind you: all that for a planet we can’t resolve or even directly see, and only because by some pure chance they happen to cross the face of their host star as seen from Earth.

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About the author. Aviv Ofir is a Dean’s Postdoctoral Fellow at the Weizmann Institute of Science’s Planetary Sciences department. Prior to arriving at Weizmann, he was a Minerva Postdoctoral Fellow at Göttingen University in Germany. He has been a member of the science team of the HATNet ground-based transit survey, as well as the space-based CoRoT and Kepler transit surveys and the Cool Tiny Beats radial velocity collaboration. Dr. Ofir has extensive experience analyzing large photometric datasets, and invented a number of techniques for the efficient detection of faint signals in these data.