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You Can’t Always Tell an Exoplanet by its Size

The views expressed are those of the author and are not necessarily those of Scientific American.

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Warning: Exoplanets may appear less massive than they really are (images used: Eysteinn Guðni Guðnason and NASA/Kepler)

Exoplanets can be confusing things. Recently we’ve seem the announcement of a milestone for NASA’s Kepler mission with the confirmation of a planet in the habitable zone of its Sun-like star. The planet, Kepler 22-b, has a diameter 2.4 times that of the Earth, which in exoplanet parlance puts it somewhere roughly in the “super-Earth” category. Hence the excited headlines about an “Earth-like” planet.

The truth is though, a planet of this size is almost without a doubt significantly more massive than the Earth, a fact pointed out by numerous pundits. So why don’t we know its mass for sure? The problem is that the technique used by Kepler to find planets simply measures the amount of light that a planet blocks when (by chance geometry) it passes between its parent star and our viewpoint. This yields the radius, or diameter, of a planet – not its mass. To estimate a planet’s mass the best bet is to try and measure the “wobble” induced on the star due to the gravitational pull of the planet. Alternatively, one can look for the variations in when the transit of other planets in the system occur (if they’re detected) – which also betrays information about these planetary masses tugging at each other. It’s also possible, again if there are multiple planets detected in a system, to try to deduce what the planetary masses really are by simulating the orbital dynamics to find what’s necessary for the whole system to be stable.

But for a single detection of a distant world like that of Kepler 22-b, for the time being we’re left with trying to guess what mass it might actually be. These guesses are however are based on some pretty sophisticated reasoning, and the key terminology here is “planetary mass-radius relationship”. In the simplest terms, suppose we knew what compounds a planet was made of – for the sake of argument let’s say it was made entirely of carbon. We could then apply our knowledge of the physics of carbon (in solid forms) to calculate how the gravity of all that carbon squeezes itself into a planetary ball, and what the radius of that ball might be for different masses of carbon. We know that carbon is somewhat compressible, especially if you stick a planet’s worth of mass on top of it, so we have to take that compressibility into account. We do this through what’s called an equation-of-state, precisely the same type of formula that tells you how much air you have to put into a tire to reach a certain pressure, depending on how hot or cold things are.

Doing this for real planets is, not surprisingly, a wee bit more complicated. Matter under pressure behaves in a variety of ways, the phases of compounds can change (e.g. like liquid turning to solid and vice-versa), and planets are likely to be multi-layered. We also don’t actually know what the composition of exoplanets really is, although we can make some pretty good educated guesses to get us started. Bearing all of these things in mind, astronomers and planetary scientists have invested a lot of effort into computing how it might all play out, and so we can begin to make some educated guesses at what the possible masses are for planets like Kepler 22-b.

And here’s an example of how planetary mass varies with planetary radius, in this case drawing on work by Fortney, Marley, and Barnes in 2007, also Gillion et al. in 2007. It’s not definitive, because of the inherent uncertainties in the physics, and other excellent studies such as those by Seager et al. will give slightly different answers. But it’s enough to get an idea of where Kepler 22-b lands.

The radius of planets versus their mass, for a range of possible compositions - from iron, to "rock", to ice, to large atmospheres of hydrogen and helium. The red dotted line shows Kepler 22-b's 2.4 Earth radius (Image adapted from C. Scharf, Extrasolar Planets and Astrobiology, University Science Books, with sources given in post).













…and it’s not entirely pretty. In fact, even if Kepler 22-b were made entirely of pure water ice, it would weigh in at about 5 times the mass of the Earth. Allowing for a more probable mix of ice and rock, and we’re up into over 10 Earth mass territory. If it had a similar composition to the Earth, then we’re looking at a world in excess of about 40 Earth masses – at which point all the “Earth-like” newspaper headlines should be consumed by fire.

Kepler 22-b is still a terrific result for Kepler, but the next time you look in your wing mirror just remember, objects may really be more massive than they appear.



Caleb A. Scharf About the Author: Caleb Scharf is the director of Columbia University's multidisciplinary Astrobiology Center. He has worked in the fields of observational cosmology, X-ray astronomy, and more recently exoplanetary science. His books include Gravity's Engines (2012) and The Copernicus Complex (2014) (both from Scientific American / Farrar, Straus and Giroux.) Follow on Twitter @caleb_scharf.

The views expressed are those of the author and are not necessarily those of Scientific American.

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  1. 1. Abelard Lindsey 7:33 pm 12/9/2011

    The graph that shows the radii vs. mass for planets of various compositions, if you draw a line that starts with where Earth and Venus are, go through the ice giants, then on to the gas giants, that line is somewhat of a curved arc. Make that line wider such that it is like a band. I will bet you donuts to dollars that almost all planets in the galaxy fit within that band. If so, kepler 22-b is likely to be a “pure ice” planet, with a density between that of the Earth/Venus and Uranus/Neptune. Kepler 22-b is going to be a lot more Neptune-like than Earth-like.

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  2. 2. Caleb A. Scharf in reply to Caleb A. Scharf 6:58 pm 12/10/2011

    I’d definitely agree that the odds are high that Kepler 22-b is more Neptune-like than Earth-like. The caveat is that the curves on this diagram are simply ‘what if’ curves, in other words we don’t really know yet what the real ranges are for planetary compositions – for all we know there are NO pure iron planets above (or below) a certain mass, or NO pure ice planets below or above a certain mass…and so on. But certainly on the basis of the range of objects in our solar system (which may or may not be statistically representative of planets anywhere) your point is a good one!

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  3. 3. Scribe747SP 4:20 pm 12/29/2011

    In the context of interstellar comparison by “beings” from another solar system perhaps looking at our Sun, would it not be said that Venus, Mars, and Earth fall within the habitability zone from our star?

    The Tycho-2 catalog, the most complete and most accurate obtained at present for nearby stars, was released in 2000 from observations of the Hipparcos satellite. This catalog contains 2,539,913 stars exactly located within 500 light years from the Sun, whose luminosity is equal to or greater than a magnitude of 11.

    Of course, there are many among the fainter stars, which has a distance of 500 light-years or less that went undetected by Hipparcos. Also, research of life is not interested in the number of stars, but the number of star systems. Indeed, most stars form systems with 2, 3, 4 or even 5 stars (these are called multiple systems).

    To estimate the average number of stars within 600 light years, one could extrapolate the data from the Research Consortium On Nearby Stars that posts the closest stars to our solar system. The main advantage is that even the less luminous objects as brown dwarfs are detectable in the nearby suburb of our Sun system in which the Research Consortium On Nearby Stars compiles its data.

    One might argue that the density of stars is changing, but I do not think that this density is changed significantly up to 1000 light years. Indeed, the solar system is in a particular structure of our Galaxy, in which the density of stars varies little, called the Orion Arm or Gould Belt. Its size is estimated at 3000 light years thick for 10,000 light years long. So in a bubble of 600 or 1000 light years, the density of stars is not expected to vary significantly.

    On the site of Research Consortium On Nearby Stars reads:

    Research Consortium On Nearby Stars made the first Accurate distance measurements for 12 of the 100 nearest systems, and 32 of the 259 total systems within 10 parsecs.

    One parsec is 3.26 light-years ~ The distance between the star system is about 5.1 L.Y. Within 600 light years, there are about 1.6 million star systems. Within 1000 light years ago 7.5 million star systems around.

    I think the estimates of 1.6 and 7.5 million stars within 600 and 1000 L.-Y. respectively, are slightly overestimated, as are the objects in that wing mirror :) simply because it takes into account the fact that brown dwarfs, which are not really stars, and because these bodies are very faint, can not contain habitable zone (which is the area where a planet would be destroyed by the tidal gravitational forces).

    Caleb, there are far more challenges to one’s scientific mind than merely the assessment of the mass of K-22.

    As a matter of fact, has it been produced a sort of 3D overview representation of stars known at the 600 light years / 1000 light years distance around? Do we know what is the the typical interstellar distance. Which solar systems are closest to ours? And what about now, given what is known about the frequency of planets in the system? We do not know precisely the position and number of stars within 600 light years around the sun. Yet, Voyager 1 and Voyager 2 are joyously parting out of our solar system by when? By a time no scientist really knows.

    While VOY-1 is OUT of the solar wind region and now is feeling interstellar pressure, How long before it truly reaches the true interstellar region? Anytime now! or in 5 years! We know not, yet the estimate is real as VOY-1 is traveling at ~ one AU per year away from the sun.

    Notwithstanding our estimate of Keppler22 mass (what!), when we will be OUT of sun’s sphere, which are all based on the highest level of “educated guess”, Voyager exploring Interstellar space in the galaxy is ultimately the greatest scientific achievement of manking in understanding what’s out there.

    …while no other country on Earth is even close to US
    gotta luv it!

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