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"Goldilocks" Gleise 581g: A Fairytale?

by John G. Cramer

Alternate View Column AV-157
Keywords: extrasolar, planets, habitable, zone, Goldilocks, just, right, radial, Doppler, shift, tide, locked
Published in the May-2011 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 12/08/2010 and is copyrighted ©2010 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


In October-2010 the headlines of the science press were dominated by the announcement of the discovery of a “Goldilocks Planet”, Gleise 581g, which has a mass not too different from that of the Earth and has an orbit squarely in the middle of the habitable zone of its parent star.  It was supposed to be not too hot, not too cold, but just right for the evolution of life.  Steven Vogt of UC Santa Cruz, the lead author of the paper, was quoted (out of context) as saying, “The chances of life on the planet are 100%.”  Now that some of the dust has settled concerning this reported discovery, I’d like to have a look at the work behind the announcement and consider its present status.

First, I want to review how such extrasolar planets are now being discovered.  The principle technique is to observe a star repeatedly over a long period of time, measuring its radial velocity (i.e., its speed along the line of sight towards the observer), based on spectral-line wavelength variations due to the Doppler shift.  When a planet orbits a star, its gravitational pull on the star causes small shifts in the position of the star’s center of mass that show up as time-dependent changes in radial velocity.  Astronomers have developed very sensitive multiple-grating spectrograph instruments that can measure such radial velocity variations of a star down to about 1 meter per second.

This is the technique that was used at the Keck Observatory by the Vogt group to study Gleise 581, a class M3V red dwarf star with a mass about 1/3 that of our sun.  Gleise 581 is a distance of about 20 light years from the Earth.  The Vogt group combined 122 precision measurements of their own of the radial velocity of Gleise 581 taken at the Keck Observatory over a period of 11 years with 119 similar measurements with somewhat better resolution from a Swiss group taken over a period of 4.3 years.

Previous work by other groups of astronomers using the radial velocity technique had already identified four planets of the Gleise 581 system: Planet-b, a “hot Neptune ”, with 17 Earth-masses and a 5.37 day orbit, Planet-c with 5.06 Earth-masses and a 12.931 day orbit, and Planet-d with 8.3 Earth-masses and a 66.8 day orbit.  (The letters start with “b” because “a” is the star itself.)  There was also some indication of “Mercury-like” Planet-e with 1.7 Earth-masses and a 3.15 day orbit.  Planet-c lies at the Venus-like inner edge of the habitable zone of Gleise 581, and Planet-d is at the Mars-like outer edge of the star.  Several studies have already suggested that, given the presence of an atmosphere that produced a strong greenhouse effect for extra heating, the “super-Earth” Planet-d might represent a good opportunity for finding evidence of life on an extrasolar planet.

The Vogt group analyzed their combined 241-measurement data set using Fourier analysis, which is a way of converting time-sequence data to a “power spectrum” of frequencies corresponding to the orbital frequencies of hypothetical planets.  They modeled masses and orbits of possible planets, adding one planet at a time and observing the effect of each planet on the frequency power spectrum, then removing its effects.  They chose to restrict the parameter set by assuming that all orbits were circular and had 90 degree inclinations, i.e., all planets orbited in the same plane that was being viewed edge-on from the Earth.  They started with the previous work and added planets until they obtained a satisfactory fit to the Fourier frequencies.  This involved reducing the so-called “False-alarm Probability” to a value on the order of 1 in 100,000.   They found that they needed to assume a 6-planet system in order to do this.

In particular, the analysis produced indications of two new planets, Gleise 581f, an outer planet with a mass of 7.0 earth-masses and a 433 day orbit, and Gleise 581g, orbiting between planets c and d with a mass of 3.1 earth-masses and a 36.6 day orbit.   The orbit of planet Gleise 581g would be in the middle of the star’s habitable zone.  If it had the same average mass per unit volume as the Earth, its mass would give Gleise 581g a surface gravity of about 1.5 g.

Not all combinations of planetary orbits are stable, because orbiting planets interact gravitationally with each other, often leading to collision and ejection events.  The Vogt group has analyzed the orbital stability of the system of Gleise 581 planets produced by their fit.  They concluded that the 6-planet system was stable at least to a 50 million year time scale.  This stability tends to support the model system they deduced, but that may be related to their assumption of a coplanar planetary system with circular orbits, since many instabilities are associated with orbit eccentricities and differences in orbit inclinations.

Within a few weeks after the media circus caused by the announcement of “Goldilocks” Gleise 581g, the Swiss group that had produced some of the data analyzed made their own announcement.  Their group, analyzing additional data, had been able to find no sign of the Vogt group’s two new planets.

Their original data set of 119 measurements of radial velocity taken over 4.3 years had been expanded to 180 measurements that had been taken over 6.5 years, with improved accuracy in the radial velocity measurements.  At a conference in Turin , Italy , the group announced that analysis of this enlarged data set showed no evidence of the two new planets claimed by the Vogt group.

That result is disturbing, but perhaps not surprising.  The Vogt group had separately analyzed the Keck and Swiss data and had not found evidence for the two planets in the data sets, taken individually.  In any case, the results of the Vogt group remain unconfirmed, and the Swiss analysis casts some doubt on the validity of its predecessor.

Since I have some experience in data analysis, I can also complain a bit about how the Vogt group did their analysis.  The procedure of putting in one planet at a time and re-analyzing the residuals after its effects are subtracted is not optimal and can lead to serious systematic errors.  The proper procedure is to do a simultaneous non-linear least-squares or maximum likelihood search, varying all the parameters of the model together or in groups and obtaining a fit from this minimization.  Further, the assumptions of 90 degree inclination and zero eccentricity circular orbits seem questionable.  It is still possible that the Vogt group has found a Goldilocks planet, but I would not take it seriously until there is an independent confirmation.

As a start, a new analysis should be performed that combines the new Swiss data with that of the Vogt group, and a more optimal fitting procedure should be used.  If Gleise 581g still appears, I would take this as a sign of encouragement, but I would still like an independent confirmation.

However, this is a science fiction magazine, and the discovery of a new planet is an exciting prospect for contemplation and for story writing.  Assuming that Gleise 581g actually exists, would the planet really be Earth-like?  Almost certainly not.  There are several potential problems, all arising from the fact that Gleise 581 is a relatively small and dim class M3V red dwarf star.  First, small stars tend to be relatively unstable and may go through fluctuation events producing large stellar flares that could periodically clean its planets of life.   Fortunately, Gleise 581 appears to be more stable than many stars of its stellar class, so that might not be a problem.   Second, from astronomical observation of spectral lines in the starlight from Gleise 581, we know that it is relatively poor in metals as compared to our Sun.  The chain of processes leading to the development of life could encounter some show-stopper in a metal poor environment because some key element or chemical compound is not sufficiently abundant.

A third problem comes from the tidal forces (see my AV-63 “The Force of the Tide”) that the primary star exerts on its planets.  Because Gleise 581 is such a small, dim star, the habitable zone of orbits is much closer to the primary star than is the case in our Solar System.  In fact, the mean distance of Mercury from our Sun is about 2.5 times greater than the orbital distance from its primary calculated for Gleise 581g.  The star itself, at about 1/3 of a solar mass, would still have a radius about 70% of that of our Sun, but the planet’s orbital distance would only be about 15% that of the Earth from the Sun.  Therefore, the sky of Gleise 581g would be dominated by the primary star, which would appear 4.6 times larger across in the sky than our Sun appears in our sky.  The tidal force that a primary star exerts on its planets depends on the third power of the linear angle in the sky of the planet that the star subtends.  This leads to the conclusion that the tidal force of its primary on Gleise 581g would be about 100 times stronger than the tidal force that the Sun exerts on the Earth.

This means that the planet would be tide-locked and probably somewhat pear shaped.  It would always present the same side to the star as it orbited.  It would have a hot side toward the star, a cold side away from the star, and perhaps a more habitable band somewhere around the equator.  If it had water, most of it would be frozen on the dark side of the planet and there would be no oceans.  The same might apply to the atmosphere, if the dark-side temperatures dipped low enough to liquefy nitrogen, oxygen, and other gases.  Goldilocks or not, Gleise 581g would not be very Earth-like.

However, life tends to exist by exploiting an energy flow, as with the Sun illuminating the Earth or superheated water flowing out of volcanic vents in the ocean floor.  The temperature gradient across the equator of Gleise 581g should represent an energy flow that could be a basis for some form of life.

Are there Goldilocks planets out there, more Earthlike than Gleise 581g?  Very likely there are, and we can expect to find some of them in the years to come.  Astronomers are getting better at measuring variations in radial velocity, and better techniques involving interferometry and star shades are in the pipeline.  NASA’a Kepler Mission, launched in March 2009, is presently surveying a list of 145,000 stars for signs of light emission variations caused by planets momentarily eclipsing a part of the parent star as they orbit.  The mission is working and data is coming in.  As of December, 2010, Kepler has discovered eight new extra-solar planets, but none so far falls in the Goldilocks planet category.  The Earth-like planets are out there, and we will find them.  However, I don’t think that we have found any yet, except the Earth itself.

AV Columns Online: Electronic reprints of about 150 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at:


Extrasolar Planets:

“The Lick-Carnegie Exoplanet Survey: A 3.1 Mo Planet on a Habitable Zone of the Nearby MeV Star Gleise 581”,  Steven S. Vogt, R. Paul Butler, E. J. Rivera, N. Haghighipour, Gregory W. Henry, and Michael H. Williamson, accepted fro publication in Astrophysics Journal, preprint ArXiv: 1009.5733v1 [astro-ph.EP].  

SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : .

AV Columns Online: Electronic reprints of about 177 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at:

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 This page was created by John G. Cramer on 07/08/2011.