Crunching the Numbers on Earth-Size Planets

by Paul Gilster on October 28, 2010

Finding Earth-size planets around other stars is a long-cherished goal, and new results from Geoffrey Marcy and Andrew Howard (UC Berkeley) give us reason to think they’re out there in some abundance. As reported in Science, the astronomers have used the 10-meter Keck telescopes in Hawaii to make radial velocity measurements of 166 G and K-class stars within 80 light years of Earth. The resulting five years of data suggest that about one in every four stars like the Sun could have Earth-size planets, although none has thus far been detected.

“Of about 100 typical Sun-like stars, one or two have planets the size of Jupiter, roughly six have a planet the size of Neptune, and about 12 have super-Earths between three and 10 Earth masses,” said Howard, a research astronomer in UC Berkeley’s Department of Astronomy and at the Space Sciences Laboratory. “If we extrapolate down to Earth-size planets — between one-half and two times the mass of Earth — we predict that you’d find about 23 for every 100 stars.”

Howard and Marcy were homing in on close-in planets, but their findings support the possibility of finding more Earth-sized planets at greater distances, and that includes worlds in the habitable zone. But the findings seem at variance with some models of planet migration, which suggest that interactions in the gas disk around the star would cause many planets to spiral inward. That would create what the researchers call a ‘planet desert’ in the inner region of solar systems, one that these two researchers do not see in their findings. Says Marcy:

“Just where we see the most planets, models predict we would find no cacti at all. These results will transform astronomers’ views of how planets form.”

And let me quote the abstract on this:

Theoretical models of planet formation predict a deficit of planets in the domain from 5 to 30 Earth masses and with orbital periods less than 50 days. This region of parameter space is in fact well populated, implying that such models need substantial revision.

Image: The data, depicted here in this illustrated bar chart, show a clear trend. Small planets outnumber larger ones. Astronomers extrapolated from these data to estimate the frequency of the Earth-size planets — nearly one in four sun-like stars, or 23 percent, are thought to host Earth-size planets orbiting close in. Each bar on this chart represents a different group of planets, divided according to their masses. In each of the three highest-mass groups, with masses comparable to Saturn and Jupiter, the frequency of planets around sun-like stars was found to be 1.6 percent. For intermediate-mass planets, with 10 to 30 times the mass of Earth, or roughly the size of Neptune and Uranus, the frequency is 6.5 percent. And the super-Earths, weighing in at only three to 10 times the mass of Earth, had a frequency of 11.8 percent. NASA/JPL-Caltech/UC Berkeley

Out of the 166 stars surveyed, 22 had detectable planets, with 33 planets being found in all (twelve planet candidates are still in the process of confirmation, which could raise the total as high as 45 planets around 32 stars). We’ll get another read on this from Kepler, for plugging these conclusions into its survey of 156,000 stars should yield 120 to 260 ‘plausibly terrestrial worlds’ with orbital periods of less than 50 days around G and K stars. Adds Howard: “One of astronomy’s goals is to find eta-Earth, the fraction of Sun-like stars that have an Earth. This is a first estimate, and the real number could be one in eight instead of one in four. But it’s not one in 100, which is glorious news.”

Needless to say, Earth-sized planets orbiting a Sun-like star at roughly one quarter of an AU do not make for habitable places, but these are statistical calculations that give us a rough read on what to expect. If we follow up with the assumption that thus far undetected Earth-sized planets should also form in the habitable zone, then G and K stars should yield numerous targets for future terrestrial planet hunter missions. We’re still looking for a ‘second Earth’ in the habitable zone of a Sun-like star, but these calculations suggest the prospects are promising.

The paper is Marcy and Howard, “The Occurrence and Mass Distribution of Close-in Super-Earths, Neptunes, and Jupiters,” Science Vol. 330, No. 6004 (29 October, 2010), pp. 653 – 655 (abstract).

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{ 30 comments }

spaceman October 28, 2010 at 14:55

Hi,

It is exciting to know that we may be on the verge of knowing how many potential abodes for life exist in our cosmic neighborhood–what a fine accomplishment! These are promising numbers especially when one would have expected, based on much of the existing theory, not to find many planets this close to their stars: the inner regions around a non-negligible number of solar type stars appear to have planets.

BUT I thought recent estimates, including one made by Marcy’s team, are that 10-20% of solar type stars have a gas giant more mass than Saturn out to several A.U.; this is certainly at odds with the 1-2 stars out of a 100 having a Jupiter statistic mentioned in this article, no? I thought it is that roughly 1 out of 100 solar type stars has a hot-Jupiter, not a Jupiter period.

Another question : Is this estimate of 1 in 4 stars having an earth-sized planet an extrapolation out to several A.U., or, is it limited to, say, periods of less than 50-100 days, as solar systems more like ours would be flat-out undetectable by even the most state-of-the-art radial velocity surveys)?

Importantly, I cannot help but notice the glaring inconsistency between the numbers listed in this article and the numbers claimed by the Swiss planet hunting team in recent years. As many Centauri Dreams frequenters know, the Swiss team announced in the autumn of 2009 that at least 1/3 of solar type stars have super-earths (planets 3-30 Earth-masses)–and I believe when this was reported in October 2009 the Swiss researchers said that the actual number is likely to be between 30 and 60%! The situation is made even murkier by the fact that the Swiss numbers are not part of any published per-reviewed paper. How are we to reconcile these clearly conflicting statistics regarding small planet prevalence?

Istvan October 28, 2010 at 15:35

“50-day periods” around G-type stars…? Unless I’m gravely mistaken, that’s going to mean an orbital radius putting the planet closer in than Mercury to our sun. I haven’t access to a good source of data on expected surface temperature by orbital distance, based on a star’s energy output, but I’m thinking that nothing with a 50-day period around even the coolest K-stars is remotely habitable.

Paul Gilster October 28, 2010 at 15:40

Istvan, I make this point in the last paragraph:

Needless to say, Earth-sized planets orbiting a Sun-like star at roughly one quarter of an AU do not make for habitable places, but these are statistical calculations that give us a rough read on what to expect. If we follow up with the assumption that thus far undetected Earth-sized planets should also form in the habitable zone, then G and K stars should yield numerous targets for future terrestrial planet hunter missions.

The researchers haven’t found Earth-size planets, but they’re extrapolating from what they have found (in tight orbits much less than 1 AU out) to the number of Earth-size planets that should exist, and going from there to make assumptions about similar planets further out — i.e., in the habitable zone.

Paul Gilster October 28, 2010 at 15:45

spaceman writes:

Is this estimate of 1 in 4 stars having an earth-sized planet an extrapolation out to several A.U., or, is it limited to, say, periods of less than 50-100 days, as solar systems more like ours would be flat-out undetectable by even the most state-of-the-art radial velocity surveys)?

I have yet to see the original and am going off a news release. And I’m with you, it’s a bit unclear. But from what I can see, the estimate of 23 percent refers to planets of Earth-size anywhere in the system. That estimate is based on what they found within the tight margins studied in this sample — in other words, well less than 1 AU. I’m on the run today and can’t check this, but maybe one of the other readers has read the paper and can comment further on this important question.

andy October 28, 2010 at 15:59

@spaceman: the problem is all these surveys seem to have different inclusion criteria. I think the HARPS results included periods out to 100 days, versus this survey which goes out to only 50 days. The paper abstract states the value is for close-in Earths (up to 50 days). And it is difficult to make claims of “glaring inconsistency” without considering the error bars on the measurements, or the properties of the samples or the extrapolations being made.

Same goes for the case of hot Jupiters, a case of “out to several AU” means you are going to be sampling the far more common giant planets population which extends outwards from periods of 100 days or so – there is an observed lack of Jupiter-mass planets between about 10 and 100 day orbital periods. Putting the cutoff of the survey at 50 days essentially excludes the main giant planet population, so it is not so surprising the value is more consistent with the hot Jupiter frequency than the overall giant planets frequency.

Paul Gilster October 28, 2010 at 16:04

It looks like I was wrong in my comment above. This just in from yet another news release, a quote from Marcy (italics mine):

“The data tell us that our galaxy, with its roughly 200 billion stars, has at least 46 billion Earth-size planets, and that’s not counting Earth-size planets that orbit farther away from their stars in the habitable zone.

I’ve just added a graphic to the original post that clarifies the situation. Marcy is saying these are the Earth-size planets within the 50-day orbits (and shorter) the survey studied. The Earth-size planets in the habitable zone would be a separate population, not part of the 23 percent.

bigdan201 October 28, 2010 at 16:31

In general, this is a time for great optimism in exoplanet research. It seems that the more we look, the more we find. Given the great variety of planets we’ve already identified, I say it is only a matter of time before we find exoplanets around 1 earth mass and even smaller. That would fit with the general trend of discovery.

While there’s nothing wrong with reasonable extrapolation and speculation, we will need to do much more observation to get more precise figures. Until then, we shouldn’t debate too heavily on the specifics of what are only educated guesses.

kurt9 October 28, 2010 at 18:28

Reading the paper carefully, its a statistical analysis for planets within 50-100 day orbital period. Our own solar system nearly flunks this standard as Mercury, which is not anywhere near Earth-sized, has an 88 day orbital period and the other three terrestrial planets (including the two Earth-sized ones) lie outside this parameter. This means that Earth-sized planets are probably more common than suggested by this analysis.

Venus reminds us that Earth-sized does not mean Earth-like.

Mike October 28, 2010 at 18:59

What an interesting paper. It will also be interesting to compare these numbers with Kepler’s upcoming results to see how well they match.

David October 29, 2010 at 1:57

Mike,

I would be very surprised if they did match for the radial velocity method is less sensitive towards detecting less massive and longer period planets than the Kepler three year data.

kzb October 29, 2010 at 7:34

The key point for me was that existing models are shown to be lacking. I’ve always thought this was very likely.

Mike October 29, 2010 at 9:48

To David, I think Kepler can provide a good test of the predictions of Marcy and Howard’s extrapolations on the number of Earth-size planets with close-in (50 days or less) orbits. Precisely because Kepler is capable of detecting Earth-size planets. Kepler can detect short period planets as well as long period planets. Possibly some of the short period Earth-size worlds in Kepler’s FOV have already been detected and identified or are in the process of being identified and confirmed, or at least their mass constrained.
What I’m saying is if the close-in Earth size worlds predicted by this paper are actually there then Kepler has the ability to find them. It is great to have the ability to test theory.

Tarmen October 29, 2010 at 12:54

Lots of them will be Venus ‘earth-like’ , or Mars types. On the other hand there are likely to be many additional ‘earth-like’ moons of gas giant planets too. And plenty of giant oceanic moons would have thick atmospheres and water for shielding mollusks etc against radiation belts or flares. Of course many moons will be even bigger , far bigger, than this planet Earth.
So there’s another 46 billion or so ‘earthlikes’ .

bigdan201 October 29, 2010 at 19:12

Tarmen, that’s why I was careful to say earth-mass rather than earth-like. I believe that as we find more terrestrial exoplanets, they will be greatly varied. We may find more like the (unconfirmed) gliese 581 g, tidally locked with a temperate zone in the twilight of the terminator. Perhaps as you suggested we will find earth-mass moons of gas giants. There could be ocean worlds, carbon planets, snowballs, and more. We might even find a world very similar to earth, but with an important difference, such as strong winds across the surface or much longer/shorter days or seasons. When we colonize another planet in future centuries, we may end up going to a world consisting of an ocean with archipelagos, or a world in an ice age where we’d rely on solar, nuclear, and geothermal energy.

If nothing else, the universe has variety.

Eniac October 29, 2010 at 21:00

It may be worth reflecting on the increasing solar output over time and what it means for habitability. As I understand, solar output now is 30% higher than it was when the Earth was young. Venus would have been more Earth-like then, at least in terms of insolation. Conversely, the Earth probably was more Venus like, with lots of carbon dioxide and a strong greenhouse effect. Which is probably what allowed life to begin, keeping temperatures pleasant despite lack of solar warmth. Since then, the planets have taken very different paths: Venus became warmer and warmer, but Earth remained cool, because life took all the carbon out of the atmosphere.

andy October 30, 2010 at 6:31

Tarmen: I’m not so sure such large moons are particularly likely, the problem seems to be that gas giant moon systems are far more susceptible to migration. Larger moons migrate faster and end up falling into the planet.

One thing that will be very interesting to see once space-based microlensing missions come on line is how the planetary distributions change from the region very close to the star (where transit and radial velocity surveys are most sensitive) and close to the ice-line (where microlensing missions are most sensitive). There are already indications that gas giants are much more frequent in the outer parts of solar systems.

kurt9 October 30, 2010 at 17:38
spaceman October 31, 2010 at 1:39

Andy, I agree with you that it is generally a good idea to withhold judgement when it comes to claiming any inconsistency between scientific data sets. However, here is a paragraph quoted from the Nature article on the Marcy et al paper in which a professional astronomer, Greg Laughlin of UC Santa Cruz, weighs in on the apparent factor of two discrepancy between the two teams’ results on the abundance of small exoplanets:

“The occurrence of close-in, Earth-like planets is roughly half that of a previous estimate from the Geneva Observatory in Switzerland, says Greg Laughlin of the University of California, Santa Cruz, who was not involved with the work. This discrepancy will be solved when data from Kepler, a space-based telescope that can detect exoplanet with high precision, becomes available early next year, he says. “I think this is an advance clue to what the Kepler results will be,” he says, since it is consistent with the small amount of Kepler data already released.”

Anyways, Paul, yes, I just read that the 23% figure only applies to planets close to their stars; indeed, the actual percentage of stars with Earth-sized planets in ANY-sized orbit is likely to be much higher than 23%. Here is a quote that led me to believe that this statistic is merely a lower limit:

“This is the statistical fruit of years of planet-hunting work,” said Marcy. “The data tell us that our galaxy, with its roughly 200 billion stars, has at least 46 billion Earth-size planets, and that’s not counting Earth-size planets that orbit farther away from their stars in the habitable zone.”

spaceman November 1, 2010 at 10:32

So, we have existing theory that predicted that we would find very few planets in the parameter space where Marcy et al are finding quite a few. What I am wondering is if because we are finding so many planets this close to their stars, then perhaps many of the planets that were predicted by existing theory to populate the region around the so-called “ice-line” will turn out not to be there; in other words, the planets that were predicted to exist in abundance further out actually will not be found further out because migration to inner extrasolar systems is so efficient and we are already detecting this population. I thought about this further and realized that the above line of thought conflicts with microlensing searches planet which are finding many planets near the ice-line.

The Marcy et al results will be tested very soon by Kepler. Here’s one possible projection: 20-25% of solar type stars have planets down to Earth size within 0.25 A.U. If all of the “0.25 A.U. bins” out to 1 A.U. are as populated with planets as the inner 0.25 A.U. as Marcy et al predict, then the fraction of solar type stars hosting planets down to Earth-size out to 1 A.U. will turn out to be ( 0.25 x 4)=1 or 100%–that is, if the current pattern holds out to one A.U, then the total fraction of solar type stars with small planets will be approximately 100%. Of course, there could be a drop off in frequency as the searches look further out, which is where each additional year of the Kepler mission will really weigh in.

Question: I noticed that the focus of the Marcy et al paper was on solar-type stars. What about the ubiquitous M-dwarfs? Kepler and some of the precision radial velocity searches are looking for planets around these small red stars, right?

Daniel November 1, 2010 at 13:02

spaceman ask this question:

Question: I noticed that the focus of the Marcy et al paper was on solar-type stars. What about the ubiquitous M-dwarfs? Kepler and some of the precision radial velocity searches are looking for planets around these small red stars, right?

“This set of 176 stars has yielded 60 high priority stars that show evidence of terrestrial mass planets.”

http://online.kitp.ucsb.edu/online/exoplanets_c10/mayor/pdf/Mayor_ExoPlanetsConf_KITP.pdf

super-Earth are common around the red dwarf (>30%)

andy November 1, 2010 at 17:24

Here’s yet another estimate of terrestrial planet frequency, this time from white dwarfs. This is probing another region of stellar mass space, as most of the observed white dwarfs in the galactic disc are remnants of stars of spectral types A and F.

From the abstract:

From the number of stars surveyed in various studies, the fraction of white dwarfs that host terrestrial planetary system remnants is at least a few percent, but likely to be in the range 20−30%. Therefore, A- and F-type stars form terrestrial planets efficiently, with a frequency at least as high as the remnants detected at their white dwarf descendants.

Daniel November 3, 2010 at 9:06

this is a interest paper about M-Dwarf stars planets:
http://www.noao.edu/perl/abstract?2009A-0338

Abstract: M dwarfs comprise 70% of all nearby stars. They are by the principle targets of future interferometry (VLTI, SIM) and direct imaging missions. Due to the lower flux and mass of M dwarfs, Doppler programs that achieve 1 to 3 m/s precision are able to probe the habitable zone of these stars for planets as small as 2 earth-masses. Over the past 7 years we have received on average two nights per semester of NASA Keck time to survey the nearest 176 M dwarfs, resulting in most of the known M dwarf planets, the first neptune-mass planet, and the first terrestrial mass planet. This set of 176 stars has yielded 60 high priority stars that show evidence of terrestrial mass planets. These stars require higher observing cadence to confirm the existence of planets, and to break orbital aliases. Two NOAO nights per semester would allow us to triple the observing cadence on this set of sieved stars, from 1 to 3 nights per semester. This program will yield terrestrial mass planets around the nearest stars.

Tulse November 3, 2010 at 14:08

Paul, I don’t know if you’ve seen this paper yet, but a group has announced a Neptune-sized planet in the habitable zone of Gl 785:

http://exoplanet.hanno-rein.de/system.php?hash=eedebd59f17d13b739aba9e396481918

It looks like this is an excellent candidate for a Pandora-style habitable exo-moon.

andy November 3, 2010 at 14:20

Tulse: the equivalent distance of the planet of Gliese 785 in our solar system which would receive the same stellar flux is about 0.6 AU. Venus receives less stellar flux than Gliese 785b. Would be interesting to know what the source for the limits of the habitable zone depiction on that website are…

Tulse November 3, 2010 at 15:49

andy, what are the standard stellar flux figures for the limits of a habitable zone? In my brief search I haven’t found any clear numbers for how to determine a habitable zone for any arbitrary star.

I also wonder if a moon in an orbit around a gas giant might not be cooler somewhat because of shadowing (as long as the orbit is in the ecliptic), and thus the possible habitable zone for an exo-moon might be different than for a planet.

andy November 4, 2010 at 2:58

Tulse: eclipses would only be a small fraction of the orbit: for a perfectly coplanar system and assuming circular orbits, for Io the value is roughly 5% of the orbit, for Ganymede roughly 2%. Most real systems will be inclined, thus the eclipse would take place along a shorter chord of the planet’s disc. These values are far too small to compensate for putting the planet at the equivalent of 0.6 AU.

spaceman November 8, 2010 at 8:48

Daniel,

Thanks for bringing that abstract to our attention, nice find. I had not heard about this particular observational campaign, but it looks like, based on the initial results, a sizeable fraction of nearby M dwarfs have planets down to 2-Earth masses. This is especially interesting in light of the fact that most models of planet formation predict the inner solar systems of M dwarfs to be populated by smaller Mars and Mercury-sized dry rocky planets (Raymond et al 2007).

Ronald November 11, 2010 at 19:22

A few (late) observations to this thead:

- Marcy’s statement that “our galaxy, with its roughly 200 billion stars, has at least 46 billion Earth-size planets” seems to be erroneous, since this research is about sun-like stars only, which constitute only a small fraction of the total stellar population, say some 7% (also depending on definition and criteria), so one has to take 23% of that 7%.

- If not a “‘planet desert’ in the inner region of solar systems”, then at least a semi-desert: a frequency of 1.6% for each of the mentioned giant planet categories and 6.5% for the sub-giant (Uranus/Neptune) category does not seem like a lot, for instance if compared with the frequency of giant planets out to several AU, or the total estimate for sub-giants and super-earths.

It would be really fascinating to be able to not only extrapolate/relate the frequency of various size planets, but to add distance/orbital period as an extra dimension, in other words to extrapolate the frequency of a particular size class planet at various distances from the star from known frequency at a particular distance. But I suppose it is still too early for that, too few data at greater AU distance.

Torbjörn Larsson, OM November 28, 2010 at 15:33

“one has to take 23% of that 7%.”

Not if the criteria is “Earth-size”, other stars have been sen to have planets such as the numerous M-stars.

Martin J Sallberg June 14, 2011 at 9:35

Habitability is not confined to Earth-size planets. Super-Earths, with their stronger gravity and probably more active geology, are good candidates for keeping warm enough for liquid water outside the habitable zone by virtue of greenhouse gases, as are moons of Jupiter-sized planets due to tidal heating causing more active geology. This is not to say that all geologically inactive worlds must be lifeless, absolutely not, they can be habitable if they are at just the right distance from the star. Gaia-geology and goldilock zone are in fact two separate ways of making worlds habitable, and should be treated as two distinct classes of habitable worlds. Earth would be frozen without greenhouse gases, so it is in the Gaian class, but it is (in geologically modern times) close to the border of the Goldilockian zone, and has some quasi-Goldilockian features due to its relatively high insolation and low concentration of greenhouse gases. Venus could have been habitable in the Goldilockian class if it had not that CO2-belching geology.

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