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## A Habitable Earth

June 17th, 2007

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There remain three blockbuster, front-page discoveries in exoplanetary science. The first is the identification of a potentially habitable Earth-mass planet around another star. The second is the detection of a life-bearing planet. The third is contact with extraterrestrial intelligence.

It’s hard to predict when (and in which order) discoveries #2 and #3 will take place. Discovery #1, on the other hand, is imminent. We’re currently 2Â±1 years away from the detection of the first habitable Earth-mass planet (which implies ~15% chance that the announcement will come within one year).

The breakthrough detection of a habitable Earth will almost certainly stem from high-precision Doppler monitoring of a nearby red dwarf star, and already, both the Swiss team and the California-Carnegie team are coming tantalizingly close. The following table of notable planet detections around red dwarfs gives an interesting indication of how the situation is progressing:

Planet

M star

M sin(i)

date K #obs sig Âµ
Gl 876 b 0.32 615 1998 210 13 6.0 247
Gl 876 c 0.32 178 2001 90 50 5.0 127
Gl 436 b 0.44 22.6 2004 18.1 42 4.5 26
Gl 581 b 0.31 15.7 2005 13.2 20 2.5 23
Gl 876 d 0.32 5.7 2005 6.5 155 4.0 20
Gl 674 b 0.35 11.8 2007 8.7 32 0.82 60
Gl 581 d 0.31 7.5 2007 2.7 50 1.23 16
Gl 581 c 0.31 5.0 2007 2.4 50 1.23 14

The masses of the stars and planets are given in Solar and Earth masses respectively. The year of discovery for each planet is listed, along with the half-amplitude, K, of the stellar reflex velocity (in m/s), the number of RV observations on which the detection was based, the average reported instrumental error (sigma) associated with the discovery observations, and a statistic, “Âµ”, which is K/sigma multiplied by the square root of the number of observations at the time of announcement. The Âµ-statistic is related to the power in the periodogram, and gives an indication of the strength of the detection signal at the time of discovery. In essence, the lower the Âµ, the riskier (gutsier) the announcement.

What will it take to get a habitable Earth? Let’s assume that a 0.3 solar mass red dwarf has an Earth-mass planet in a habitable, circular, 14-day orbit. The radial velocity half-amplitude of such a planet would be K=0.62 m/s. Let’s say that you can operate at 1.5 m/s precision and are willing to announce at Âµ=20. The detection would require N=2,341 radial velocities. This could be accomplished with an all-out effort on a proprietary telescope, but would require a lot of confidence in your parent star. To put things in perspective, the detection would cost ~10 million dollars and would take ~2 years once the telescope was built.

Alternately, if the star and the instrument cooperate to give a HARPS-like precision of 1 m/s, and one is willing to call CNN at Âµ=14, then the detection comes after 500 radial velocities. The Swiss can do this within 2 years on a small number of favorable stars using HARPS, and California-Carnegie could do it on a handful of the very best candidate stars once APF comes on line. Another strategy would be to talk VLT or Keck into giving several weeks of dedicated time to survey a few top candidates. Keck time is worth ~$100K per night, meaning that we’re talking a several-million dollar gamble. Any retail investor focused hedge funds out there want to make a dramatic marketing impact? Or for that matter, with oil at$68 a barrel, a Texas Oil Man could write a check to commandeer HET for a full season and build another one in return. “A lone star for the Lone Star.”

If I had to bet on one specific headline for one specific star, though, here’s what I’d assign the single highest probability:

The Swiss Find a habitable Earth orbiting Proxima Centauri. Frequent visitors to oklo.org know about our preoccupation with the Alpha-Proxima Centauri triple system. We’ve looked in great detail at the prospects for detecting a habitable planet around Alpha Centauri B, and Debra Fischer and I are working to build a special-purpose telescope in South America to carry out this campaign (stay tuned for more on this fairly soon). Proxima b, on the other hand, might be ready to announce right now on the basis of a HARPS data set, and the case is alarmingly compelling.

Due to its proximity, Proxima is bright enough (V=11) for HARPS to achieve its best radial precision. For comparison, Gl 581 is just slightly brighter at V=10.6. Proxima is effortlessly old, adequately quiet, and metal-rich. If our understanding of planet formation is first-order correct, it has several significant terrestrial-mass planets. The only real questions in my mind are, the inclination of the system plane, the exact values of the orbital periods, and whether N_p = 2, 3, 4 or 5.

The habitable zone around Proxima is close-in. With an effective temperature of 2670K, and a radius 15% that of the Sun, one needs to be located at 0.03 AU from the star to receive the same amount of energy that the Earth receives from the Sun. (Feel free to post comments on tidal locking, x-ray flares, photosynthesis under red light conditions, etc. Like it or not, if the likes of Gl 581 c is able to generate habitability headlines and over-the-top artist’s impressions, just think what a 1 Earth-Mass, T=300 K Proxima Centauri b will do…) A best guess for Proxima’s mass is 12% that of the Sun. An Earth in the habitable zone thus produces a respectable K=1.5 m/s radial velocity half-amplitude. It’s likely that HARPS gets 1.2 m/s precision on Proxima. A Âµ=15 detection thus requires only 144 RV observations. Given that Proxima is observable for 10 months of the year at -30 South Latitude, there are presumably already more than 100 observations in the bag. We could thus get an announcement of Proxima Cen b as early as tomorrow.

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1. June 17th, 2007 at 23:13 | #1

Hi Greg!
There are around 470 VLT/UVES
Spectras of Proxima Centauri at:
http://archive.eso.org/eso/eso_archive_main.html
NIKKI

2. June 17th, 2007 at 23:39 | #2

Where did Gl 849 go from the list of notable red dwarf planets? After all, it does seem to be the only known system apart from Gl 876 to have a jovian-mass planet around a red dwarf, and also seems to be the greatest orbital radius, though granted it seems to be less studied than some of the other systems.

3. June 17th, 2007 at 23:48 | #3

Hi Andy, NIKKI,

That’s an interesting point regarding the availability of the spectra…

Gl 849 is indeed a notable red dwarf planet, but I left it out because I was more interested in discussing the progression to lower and lower mass red-dwarf companions.

Gl 849 is interesting because it bucks the trend toward an apparent paucity of true Jovian-mass companions to red dwarf stars (as do Gl 876 b and c).

best,
Greg

4. June 19th, 2007 at 13:59 | #4

Hi Greg,

Given the cost that you mentioned above of surveying for several weeks a red dwarf in search of a potential habitable Earth using VLT or Keck, I can see why you would have to be very prudent in your choice of candidates and pretty darn sure that it’s worth the gamble. Thanks for enlightening us.

best,
Eric

5. June 23rd, 2007 at 14:28 | #5

In case anyone was wondering what the mass of Earth would be if it were expressed in terms of Jupiter’s mass, 1.0 Earth mass is equal to 0.003144 of Jupiter’s mass.

Just thought you’d like to know in the event that you’re searching for one of those “habitable Earths” around one of those red dwarfs.

Eric

6. June 25th, 2007 at 00:04 | #6

Greg:

Interesting stuff. You say that weâ€™re currently 2Â±1 years away from the detection of the first habitable Earth-mass plane. How do you go about calculating that? Also, what is the certainty that we will find one with 3 years? (85%?)

7. June 25th, 2007 at 05:56 | #7

Hey Pieter,

The estimate is based on the (more-or-less) known rate at which the radial velocity observations are being accumulated by the various teams, and on the (theoretically completely reasonable) expectation that 1-Earth mass planets will be just as common as the 5-Earth mass planets that are already turning up around the nearby red dwarf stars. Assigning a one-sigma error bar pins down my sense of the uncertainty, but it was also slightly tongue-in-cheek for the benefit of the blogosphere.

I do think there’s an 85% chance that we’ll have a habitable Earth within three years. The real question is who’s going to get there first…

Greg