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PLoS One. 2010; 5(10): e13061.
Published online 2010 October 4. doi:  10.1371/journal.pone.0013061
PMCID: PMC2949384

A Scientometric Prediction of the Discovery of the First Potentially Habitable Planet with a Mass Similar to Earth

Enrico Scalas, Editor

Abstract

Background

The search for a habitable extrasolar planet has long interested scientists, but only recently have the tools become available to search for such planets. In the past decades, the number of known extrasolar planets has ballooned into the hundreds, and with it, the expectation that the discovery of the first Earth-like extrasolar planet is not far off.

Methodology/Principal Findings

Here, we develop a novel metric of habitability for discovered planets and use this to arrive at a prediction for when the first habitable planet will be discovered. Using a bootstrap analysis of currently discovered exoplanets, we predict the discovery of the first Earth-like planet to be announced in the first half of 2011, with the likeliest date being early May 2011.

Conclusions/Significance

Our predictions, using only the properties of previously discovered exoplanets, accord well with external estimates for the discovery of the first potentially habitable extrasolar planet and highlight the the usefulness of predictive scientometric techniques to understand the pace of scientific discovery in many fields.

Introduction

The search for a habitable extrasolar planet has long interested scientists, but only recently have the observational tools become available to search for such planets [1]. Beginning in 1995 with the discovery of an extrasolar planet around Pegasi 51, a star much like our own [2], the number of confirmed extrasolar planets has expanded into the hundreds. We now have a panoply of physical and orbital data on planets outside the solar system, and with it an increase in understanding of the formation of planetary systems. However, the holy grail of extrasolar planetary research – an Earth-like planet – has yet to be discovered. This search has more recently become even more intense with such large-scale surveys as NASA's Kepler mission [3].

While many, astronomers included, have speculated about when the first habitable planet might be discovered [4], no quantitative scientometric analysis has been performed. In order to do this, we develop a metric of habitability for all discovered planets, and use this to arrive at a prediction for when the first habitable planet is expected to be discovered.

Of course, predicting future scientific and technological progress is a slippery and difficult process. While there have been many such successes, such as Moore's Law [5], history is littered with predictions that are far off the mark [6].

Here too there are many difficulties. Estimating the habitability of planets is itself a complicated process with many parameters [7], but most research dwells on the combination of two properties of a planet: surface temperature necessary for liquid water, and planetary mass [8]. Using these guidelines, we constructed a simple habitability metric. Using the habitability time series of previously discovered exoplanets, we created a bootstrap method to predict when the first Earth-like planet would be discovered. We predict the announcement of its discovery with a high probability by mid-year 2011.

Materials and Methods

Habitability Metric

Using the calculated mass and temperature of a planet, we constructed a simple habitability metric, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e001.jpg, for a given planet An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e002.jpg, where An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e003.jpg is uninhabitable, and An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e004.jpg is an Earth-like planet. An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e005.jpg is defined as the following:

equation image
(1)

where An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e007.jpg is the product of three sub-measures, each themselves on a scale of 0 to 1:

equation image
(2)
equation image
(3)
equation image
(4)

The formulas for the submeasures that makes up An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e011.jpg are below, where An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e012.jpg is one Earth mass, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e013.jpg is the approximate width of half the acceptable temperature range (here we used An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e014.jpg), An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e015.jpg is the midpoint of the range (An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e016.jpg), An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e017.jpg (for An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e018.jpg, and An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e019.jpg can either be An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e020.jpg (semi-major axis) or An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e021.jpg (semi-minor axis) of planet An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e022.jpg):

equation image
(5)
equation image
(6)

Each sub-measure is simply the product of two opposing modified logistic curves with some rescaling, which yield functions of the forms seen in Fig. 1. Note that while there is a positive probability assigned to negative masses, this is simply a byproduct of the symmetric nature of the function, and does not affect the calculations, as there are no such planets with negative mass. For An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e025.jpg to be 1, all sub-measures must themselves be 1. Due to the “step-function-like” nature of these sub-measures, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e026.jpg is likely to be either very low near 0 or very close to 1. Additional separate conditions (such as presence or absence of atmosphere) would make the model more restrictive and necessarily lower An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e027.jpg, so our model is erring optimistically on habitability, is an upper bound on An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e028.jpg.

Figure 1
Habitability metric curves.

Note that while a nominal temperature, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e031.jpg exceeds the boiling point of water, this value is representative only of the simple blackbody equilibrium temperature at the substellar point. Actual surface temperatures for potentially habitable planets will be controlled by a host of effects, some well-understood, some entirely speculative: The stellar flux is intercepted by an area An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e032.jpg, but must warm a planet of surface area An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e033.jpg. Our assigned limits on potential habitability represent correspond to a habitable zone whose outer radius is a factor of 2.6 times larger than its inner radius. Given the uncertainties on what constitutes the range of potentially habitable environments, this ratio is intended to be somewhat optimistic. Estimates by Mischna et al. (2000) [9], for example, advocate a ratio of 2.1, whereas the influential study of Kasting et al. (1993) [10] found a ratio of bounding distances equal to 1.76. The atmosphere may provide a significant greenhouse warming effect. The planet may have endogenous sources of energy, and cloud cover can provide a significant reflective albedo. For a recent detailed discussion of the geophysical and atmospheric factors relevant to potentially habitable planets, see, e.g. Lammer et al. (2010) [11].

Calculations of planetary surface temperature involve assumptions of stars on the Main Sequence and black body radiation models, and were as follows [11]:

equation image
(7)

Using these metrics, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e035.jpg was calculated from readily available data [12] for all 370 planets in the dataset.

Discovery Date Prediction

In order to create a robust estimate of the date of discovery of the first Earth-like planet, the following factors were considered:

  1. The extrasolar planets considered were detected by two methods: radial velocity (RV) and transit. The radial velocity method detects a planet using the Doppler effect to determine the motion of the planet's star, and the transit method detects a planet using changes in brightness of the star due to the planet's transit in front of it. While the transit method provides accurate estimates of the mass, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e036.jpg of a planet, the radial velocity method yields an estimate for An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e037.jpg, where An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e038.jpg is an unknown inclination for the planetary system, thereby only giving a lower bound for An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e039.jpg.
  2. Any estimate of the detection of the first Earth-like planet will necessarily be dependent on the vagaries of those planets which were previously discovered. If other stars were examined, a different set of of planets, and therefore An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e040.jpg values, would have been found.

A bootstrap analysis was conducted, which accounts for the An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e041.jpg estimates for planets discovered by the radial velocity method, and provides a robust estimate of the date of discovery. Each realization consisted first of calculating An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e042.jpg for each RV-detected planet in the dataset by drawing an inclination randomly chosen from the surface of the sphere. We then sampled 370 planets, each with its year of discovery, from the complete planetary data set with replacement, in order to create a bootstrapped time series of An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e043.jpg values of exoplanet discovery. The date of discovery chosen for each extrasolar planet was the mid-point of the year of discovery (including for 2010), due to the lack of more precise data.

To predict when the first habitable planet (An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e044.jpg) will be discovered, we examined the upper envelope of each realization's An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e045.jpg values by year (the points described by the highest habitability metric for each year). Since the upper and lower bound of An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e046.jpg are known to be An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e047.jpg and An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e048.jpg, respectively, fitting a logistic equation is appropriate, and is similar to many other discovery curves, such as the number of mammalian species or number of chemical elements [13], [14]. A logistic best fit of of the upper envelope of An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e049.jpg over time, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e050.jpg, where the parameters An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e051.jpg and An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e052.jpg were allowed to vary, is as follows:

equation image
(8)

The logistic curves of best-fit were performed using non-linear least squares fits on the sampled An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e054.jpg values. Due to the step-like function of An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e055.jpg, the best fit curves were extremely sensitive to initial conditions. While parameters close to the final fits were chosen for precision, variation in the results can be introduced by choosing different initial conditions. To determine the date as a fraction of the year, the value at which the logistic function first reached An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e056.jpg was calculated. To test the robustness of using this assumption, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e057.jpg was used, which predicted early April 2011, and An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e058.jpg which predicted early June 2011.

Other robustness checks were performed as well. For either a bounds of An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e059.jpg or An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e060.jpg for the habitability equation, a prediction of discovery in early May 2010 was found. It is likely then that the precision of the fit, along with the data available, are what drive the prediction. Assuming an error of a month in either direction is therefore reasonable. In order to convert this to days and months of a year, non-leap years were assumed.

Results and Discussion

We examined 370 exoplanets, all of which have well-characterized properties. Doing so, yields An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e061.jpg for the majority of exoplanets. Notably, Gliese 581 d, thought to be in the habitable zone, yields the highest value, with about An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e062.jpg, and is still quite low. While some authors (e.g. Wordsworth et al. 2010 [15]) actually argue that Gliese 581 d is potentially habitable, we are of the opinion that its measured An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e063.jpg leads to an expected mass close to 10 Earth masses, and a possibly water-dominated composition more akin to an ice giant planet such as Uranus or Neptune than to a terrestrial planet like the Earth.

We conducted 10,000 realizations of the bootstrap method, where the data could successfully be fit to a curve, in order to arrive at a distribution of dates of discovery of the first habitable planet. This distribution is heavy-tailed, as seen in Fig. 2, with a median date of discovery of early May 2011 (2011.34). Additionally, detecting an Earth-like planet by the end of 2013 has a An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e064.jpg probability, we reach 75% in 2020, and don't achieve 95% likelihood until 2264.

Figure 2
Distribution of 10,000 realizations of bootstrap analysis by year.

An example realization is shown in Fig. 3, where the best-fit logistic curve arrives at An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e065.jpg (the upper border), in the first half of the year 2011. More precisely, it reaches An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e066.jpg at about one-third (An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e067.jpg) through the year, which is early May 2011.

Figure 3
A single realization of the habitability of extrasolar planets over time.

Additionally, we conducted the same bootstrap analysis for subsets of the planetary dataset up to the end of the years 2001–2010 (prior to this, there is not enough data to yield robust estimates). This allows us to determine what the likeliest date of the discovery of an Earth-like planet would have been predicted to be, if the analysis were conducted throughout the previous decade. The median dates of discovery are shown in Fig. 4.

Figure 4
Median date of discovery using planetary data up to the end of a given year.

The creation of a single metric of habitability, An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e073.jpg, allows for quantitative prediction of when the first Earth-like planet is expected to be discovered – in this case, a date of early May 2011. Of course, this prediction of when the discovery of the first Earth-like planet will be announced has ignored technological advancement entirely, as well as many other factors. However, technological progress can often be well-described by a functional form independent of the processes underlying its advancement [16]. Similarly, it is likely that the multiple methods of extrasolar planet discovery (such as radial velocity and transit methods) combine to yield relatively smooth curves on the march towards further discovery. The testable prediction given here is likely found to be accurate in the coming months, given the recent launch and ongoing results of many projects.

A great deal of current interest is focused on NASA's ongoing Kepler mission [17]. The Kepler spacecraft employs the photometric transit method to detect planet candidates, and it is an open question as to whether this method can achieve the first detection of a planet with An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e074.jpg. While the initial results of Kepler were released on June 15, 2010, the Kepler team has delayed publication of 400 of the most promising extrasolar planetary candidates until February 2011. Within this large pool of withheld candidates, it is virtually certain that some have radii that are observationally indistinguishable from Earth's radius. It is likely, however, that because of the limited time base line of the mission to date, the Kepler planet candidates to published in February 2011 may be too hot to support significant values for An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e075.jpg.

In order to determine how useful Kepler will be in the search for a habitable planet, we reran our prediction analysis using only those planets discovered using the transit method. And it turns out that the method is unable to converge on a likely date of discovery, due to the paucity of the data (62 planets) and the low An external file that holds a picture, illustration, etc.
Object name is pone.0013061.e076.jpg values for these planets. No doubt Kepler will increase this number of planets, but this provides a counter-balance to the assumption that the Kepler team will discover the first habitable planet.

It must be noted that by publicizing our prediction, there is a concern that it will become accurate, simply due to the well-studied Hawthorne Effect [18]. However, due to the large number of observations and long periods of time required to confirm an extrasolar planet discovery, it is unlikely that our prediction at this time will appreciably affect the announcement of the discovery of an Earth-like planet.

Therefore, it is reasonable to use the habitability metric curve as a rough prediction for when the first potentially habitable planet will be discovered, in this case, as early as May 2011, and likely by the end of 2013.

Acknowledgments

We would like to thank Jukka-Pekka Onnela for reading drafts of this manuscript and David Charbonneau for the initial conversation which prompted this investigation.

Footnotes

Competing Interests: The authors have declared that no competing interests exist.

Funding: The authors have no support or funding to report.

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