Crunching the Numbers

The doppler effect
Earth as seen by the departing Voyager spacecraft: a tiny, pale blue dot.
Credit: NASA

Maggie Turnbull, an astronomer with the Carnegie Institution, has spent many years thinking about what kind of stars could harbor Earth-like planets. Her database of potentially habitable star systems could be used as a target list for NASA’s upcoming Terrestrial Planet Finder (TPF) mission.

Turnbull presented a talk, “Remote Sensing of Life and Habitable Worlds: Habstars, Earthshine and TPF,” at a NASA Forum for Astrobiology Research on March 14, 2005.

This edited transcript of the lecture is part two of a four-part series
(Part 1 * 2 * 3 * 4).

There are 400 billion stars in the galaxy, and obviously we’re not going to point the Terrestrial Planet Finder at all of them. The TPF science working group has defined a successful mission as a search for planets around 35 stars — these stars will be our best targets. Then, once that is completed, we’ll look at 130 more stars. So we’ll have 165 stars to work with during the TPF mission lifetime.

It’s going to take a lot of observing time to discover a planet in the first place, and it’s going to take even longer to do spectroscopy on a planet once it’s been discovered. So 165 stars is a large task, even though it doesn’t sound like much. But it’s not many stars compared to the number of possible targets in the Galaxy, so we want to choose very wisely, especially considering the amount of money this mission is going to cost.

The number of HabCat stars, as a function of distance for M-type stars (solid red histogram), K stars (dark-hatched green histogram), G stars (light-hatched violet histogram), F stars (horizontal-lined yellow histogram), and all stars (open blue histogram). Click image for larger view. Inset, Allen Telescope Array. Credit: Turnbull, Tarter

I hesitate to mention money, because I want everybody to focus on how TPF is this fantastic mission. But we’re going to be spending somewhere between 12 and 30 million dollars per star that we look at. I personally think it’s worth it, even if we only find an Earth-like planet around just one of those stars. But given the sheer price tag of each target in this mission, we owe it to the taxpayers and to ourselves to think very carefully about which stars we look at.

We should design the core target list of 35 stars so that, when the TPF-C mission is done, in case we haven’t found anything, we can still make a meaningful scientific statement. We don’t want to just look at a smattering of every different kind of star that’s out there, because there really are a lot of different kinds of stars.

Instead, we should design a core target list to hone in on a particular kind of star, or at least a small range of stars, that are similar to our own star. Places where, if there were a planet in the habitable zone, we could live. So, in the case of not finding anything, we can make a statement that, “X percent of G2-V stars of solar metallicity that are thin disk members don’t have planets,” or “No more than X percent has an Earth-like planet around it.”

But on the other hand, we may not be able to be that picky. We’re going to be up against engineering constraints. But if I put on my scientist hat and say, “Engineers, you’re just going to have to build what I want for this mission,” then as a scientist I would want to look at Habstars.

My definition of a Habstar is a star that has a habitable zone, first of all. That habitable zone is dynamically stable, meaning that it’s not perturbed by giant planets on eccentric orbits swooping in and out of the habitable zone.

We know now that many stars have giant planet companions. In many of these systems, the giant planets do not enter the habitable zone. There are a few giant planet systems where the known planet is in the habitable zone throughout its entire orbit, and those actually should be top TPF targets. Not because we’ll be able to image any habitable moons those planets might have, but because the planet itself should be a “can’t-miss-it” target. For something like TPF that’s designed to see Earths, we should certainly be able to see giant planets.

Click here for larger image. The Sun, a typical G2V dwarf. G stars are characterized by the presence of metallic lines and weak hydrogen.
Credit: Harvard University

A dynamically stable habitable zone is also not perturbed by any other stellar companions. Most stars are not single like the sun. Instead, they exist in binary, triple, or quadruple stellar systems. Could the orbits of those stars interfere with planets orbiting within the habitable zone?

To figure this out, we have to look at the mass ratio of the various components, the location of the habitable zone, and the orbit of the second star. I’ve mapped all that out for about 15,000 binaries. It turns out that the vast majority of binaries are perfectly safe places to live for habitable planets.

A Habstar will need to be dynamically stable on a timescale that’s comparable to the timescale of global biosignature production. The Earth didn’t have continents covered with plants and a strong oxygen signature from day one; it took at least a couple billion years to build up. It wasn’t until about 2 billion years ago that a strong and detectable oxygen signature would have existed on this planet.

If we use a minimum age of 2 billion years, that means we can eliminate some of the stars in the solar neighborhood from our TPF target list.

A star should have a habitable zone that is spatially static on that same 2 billion year time scale. All stars are variable to some extent, and as they evolve over time, their luminosity changes. Main sequence stars burn hydrogen, and as they evolve they get brighter and cooler, and eventually end up as red giants. The speed at which stars evolve depends on their mass. Very massive stars evolve quickly into red giants, whereas less massive stars will remain a main sequence star for a long time, not changing much in brightness.

Blue stars in the Pleiades. These stars produce more UV radiation than red stars.
Credit: DSS and LTImage

To see how this long term evolution of a star affects habitability, let’s look at the sun. When the sun was young, it was fainter, so the habitable zone was closer to the sun. As the sun has aged, up to today at almost 5 billion years, the habitable zone has slowly moved outwards. At somewhere between 6 and 7 billion years in age, Earth will no longer be in the habitable zone. We will be interior to the habitable zone, because the sun will have increased in luminosity. At that point, the oceans will evaporate into space and we won’t want to live here anymore.

In between 7 and 8 billion years, however, Mars will enter the outer habitable zone. This doesn’t mean that we can just move from Earth to Mars, because there’s a 1 billion year gap where nothing is habitable.

Mars will be in the habitable zone for about 2 billion years, until the sun becomes a red giant. At that point, nowhere in the solar system is habitable. The sun spends only another 1 billion years as a red giant before it starts to lose its outer envelope and become a planetary nebula.

Since higher mass stars evolve more quickly then lower mass stars, then if we want our targets to have been habitable for 2 billion years or longer, we don’t want stars that are so massive that they evolve all the way to red giants in less then 2 billion years. So stars that are more massive than about a solar mass and a half are not good TPF targets. That really limits the mass range for this mission.

The Terestrial Planet Finder will search for Earth-like planets orbiting 250 of the closest stars.
Credit: NASA

Related to this is the concept of short-term variability. The sun is variable over days, decades and millennia, in addition to this longer term trend over billions of years. Those shorter period variability cycles don’t seem to impact biology much. The sun is exceptionally stable, but for other stars with levels of variability 10 or even 30 times as much as the sun, I don’t think that’s really going to make too much of a difference for biology.

Metallicity is a concern. We have seen that, at least for giant planets in very short period orbits, the likelihood of a planet being present is related to the metallicity of the star — the heavy metal content of the star itself. Since stars and planets form out of the same original material, that makes sense. The Earth is made out of heavy elements — for example, iron — so a star that has zero metallicity is probably not a good target.

So after we apply all of these cuts, we end up with about 500 scientifically interesting stars within 30 parsecs. You could go further out in distance if you wanted to find more stars, but I think 500 is plenty.

Related Web Pages

Speeding Up in the Zone
Star Light, Star Bright… Any Oxygen Tonight?
How To Find An Extrasolar Planet
Extrasolar Planets Encyclopedia
Planet Quest (JPL)
Kepler Mission
Darwin Mission
Space Interferometry Mission
Voyager: Beyond the Great Beyond
Fire and Ice
Beyond Pluto: Ice Planet