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Tuning Up RV: A Test Case at Tau Ceti

The new work on Tau Ceti, which analyzes radial velocity data showing four planets there, looks to be a step forward in this workhouse method for planetary detection. With radial velocity, we’re analyzing tiny variations in the movement of a star as it is affected by the planets around it. These are tiny signals, and the new Tau Ceti paper discusses working with variations as low as 30 centimeters per second. It’s a good number, but we’ll want better — to detect a true Earth analog around a Sun-like star, we need to get this number into the 10 cm/s range.

The planets detected in this work all come in at less than four Earth masses, and two of them are getting attention because they are located near the inner and outer edges of the habitable zone respectively. Tau Ceti has always drawn our attention, being relatively close (12 light years) and a solitary G-class Sun-like star. No wonder it and Epsilon Eridani were the two targets Frank Drake chose for Project Ozma when he launched observational SETI in 1960.

Image: This illustration compares the somewhat larger and hotter Sun (left) to the relatively inactive star Tau Ceti. Credit: R.J. Hall / Wikimedia Commons.

The idea that there are planets around Tau Ceti is not new, but the current study, led by Fabo Feng (University of Hertfordshire, UK) re-examines the star and actually eliminates two of the candidate planets identified four years ago. Radial velocity depends on picking out the faint signature of planets against ‘noise’ such as activity on the surface of the star, the rotation of the star, and uneven sampling times from observations. This is why validating some RV planet candidates can be tricky. Feng and team, however, have applied a new method.

This is the same team that did the 2013 paper on Tau Ceti, using the nearby star as a test case for its methods. The idea was to examine how activity on Tau Ceti itself differed when observed in a range of wavelengths. The thinking here is that the ‘jitter’ in variations of the radial velocity signal is dependent on wavelength, which needs to be accounted for in the analysis.

To do this, the authors introduce what they call “differential RVs.” The radial velocity signals of planets do not depend on wavelength, so differential RVs are those that contain only the noise that needs to be screened. Working with 9000 measurements of the star from the HARPS spectroscope, including new measurements, the team found four strong planet candidates.

The signals are consistent with orbits of 20.0, 49.3, 160 and 642 days. This is an interesting mix given the earlier work, as it identifies two new RV signals (20 and 49.3 days), while tightening up the precision on the previously identified candidates at 160 and 600 days, and at the same time ruling out two of the candidates identified in 2013. “But no matter how we look at the star,” says Mikko Tuomi (University of Hertfordshire), “there seems to be at least four rocky planets orbiting it.”

We’re learning something crucial here about how radial velocity methods work. Remember that we thought for a time that we had identified a planet around Alpha Centauri B, a detection that was later acknowledged to be a mistake in the analysis. When we’re dealing with planets of roughly Earth’s size, the radial velocity signals we can expect even from nearby stars are well below 1 meter per second. The complexity of the problem in relation to Tau Ceti is evident:

The planetary candidates we have identified partially overlap with the ones found by MT13 [the authors’ 2013 paper on Tau Ceti RV analysis]. We find two new planetary candidates with periods around 20 and 49 d, but fail to confirm the signals around 14 and 35 d. Although there is evidence for the existence of the signal at around 92 d, we cannot confirm it as a Keplerian candidate because it cannot be consistently identified in all data sets and solutions. The signal around 14 d becomes weak when we subtract the 20 d signal from the data. But the opposite is not true, suggesting a non-Keplerian origin of the 14 d signal. Nevertheless, the 14 d signal does exist in some Keplerian and circular solutions after accounting for the 20 d signal. In addition, by evenly dividing the data into 3 chunks, we find that the 14 d is significant in the first chunk while the 20 d is significant in the second and third chunks…

And so on. The lesson is clear enough: We have to be extremely careful when interpreting signals below 1 meter per second, the range in which we’ll need to identify Earth-class planets.

But the value of radial velocity is unquestioned. Unlike the transit technique, we don’t have to rely on a fortuitous line-up between a distant planetary system and the Earth — we can therefore extend it to all bright stars of interest. Feng and colleagues think we will be able to use new high precision spectrometers along with these emerging statistical and noise models to find a true Earth analog in the coming decade. Thus this work on Tau Ceti, modeling wavelength-dependent noise, becomes a test case of a new noise model framework that can help us filter background noise out of RV observations.

Image: The four planet candidates at Tau Ceti in comparison with our Solar System. Credit: University of Hertfordshire.

And while two of these planets (e and f) have been cited as being close to the boundaries of the habitable zone, the massive debris disk around Tau Ceti is going to be a factor in habitability in this system, leading to presumed cometary bombardment. We’ll want to learn more about the inner boundaries of the debris disk, and also whether the disk and planetary system orbit in the same plane, which would have a strong effect on the masses of these planet candidates. A co-planar disk brings the mass estimates of these four planets up sharply.

The paper is Feng et al., “Color difference makes a difference: four planet candidates around tau Ceti,” accepted at the Astronomical Journal (preprint).


Comments on this entry are closed.

  • andy August 16, 2017, 13:45

    There seems to be quite a bit of evidence that systems of low-mass planets tend to be coplanar so assuming they share the inclination of the debris disc seems quite reasonable. This would result in the true masses being approximately twice the minimum masses, which takes planets e and f into the range where they are likely to be volatile-rich mini-Neptunes. This doesn’t bode well for the probability of habitable worlds in the system, particularly given Kepler’s results on the (non-)occurrence of large moons and co-orbital planets. As for cometary bombardment, it’s not clear how much material is ending up on planet-crossing orbits. ALMA puts the inner edge of the disc at 6.2 (+9.8/-4.6) AU, the error bars are large enough that it is not clear whether planet f is setting the location of the inner edge or whether undiscovered outer planets are responsible.

    Incidentally there is also recent news of a detection of at least three low-mass planets around Tau Ceti’s close neighbour YZ Ceti. These seem unlikely to be habitable: they are too close to the star to be located in the water zone, plus YZ Ceti is a flare star.

    • Ronald August 16, 2017, 14:17

      “This doesn’t bode well for the probability of habitable worlds in the system”.
      Well, I think that also depends wether there is another small terrestrial planet between e and f, or even two. There is plenty of space there, and the fact that no larger planets have been detected there yet may actually be a hopeful sign.

      • james stilwell August 16, 2017, 17:40

        I hope the Webb people are getting this…

      • andy August 16, 2017, 18:42

        The authors state that the four planet system is dynamically packed (section 6.3 of the paper), so I’m not sure that planets between e and f are a realistic prospect. Figure 17 appears to show a stable zone, though it’s not clear whether you can put a planet (as opposed to a test particle) in there without destabilising the system.

      • Brett August 17, 2017, 1:40

        Wouldn’t another planet between e and f show up in its gravitational influence on the two? Maybe if it was Mars mass instead . . . .

  • Astronist August 16, 2017, 13:52

    “this workhouse method” – I believe the expression is: this workhorse method.

    “we don’t have to rely on a fortuitous line-up between a distant planetary system and the Earth” – true. But some indication of the orbital inclination is still needed before we can really pin down the masses.

  • Geir Lanesskog August 16, 2017, 13:54

    The thing with Tau Ceti is that based on ALMA readings of the dust disk ( https://arxiv.org/abs/1607.02513) there’s a good chance these planets are nearly head-on. In that case, their mass could be considerably larger than the minimum computed by radial velocity, as in 3 or 10 or more times greater.
    On the positive side, there seems to be plenty of room between planets e and f, and a head-on earth-sized planet could easily exist smack dab in the middle of the habitable zone and escape detection.

    • Ashley Baldwin August 16, 2017, 18:22

      Absolutely. Titus-Bode eat your heart out. Looking at the packing of “b” through “e” then there could be a terrestrial planet in the hab zone “sweet spot ” of this 0.52 Sun Luminosity star betwen 0.7 AU and 0.9 AU . Too small to detect with even the improved 30cms/sec RV precision used here but well within the bounds of Debra Fischer’s hundred Earth study coming up later this year using the high res EXPRES spectrograph on the Discovery 4.3m telescope. On a system just 12 light years away with a highly quiescent Doppler spectroscopy friendly star too.

      Be interesting to see if some of these planets at least can be directly imaged by WFIRST . It is meant to target Jupiter down to Neptune mass planets but given the somewhat reduced contrast difference of this dimmer than Sun star and it’s close proximity then hab zone and outwards Super Earth terrestrials might just be within its reach as has been posited in data on the telescope and its coronagraphy so far . Just maybe . All things being equal.

      • Ronald August 17, 2017, 10:57

        How about ESPRESSO on the VLT? With a RV sensitivity of 10 cm/s or even less, it should be able to detect an Earth mass planet in the HZ of Tau Ceti.

        • Ashley Baldwin August 23, 2017, 6:23

          It may indeed. What sets EXPRES apart from ESPRESSO is that the former has been optimised for RV searches incorporating algorithms designed to accommodate spurious signals arising from stellar photospheric activity . This should work best for M dwarfs with their higher intrinsic levels of activity . However, despite being quiescent by most standards even Tau Ceti demonstrates sufficient activity to impact on RV changes and most especially when the instrument sensitivity is down at a quite frankly ,incredibly sensitive , 10cm/sec. ESPRESSO is an “all round ” spectrograph and its development began without the benefit of the practical experience of exoplanet searches that Debra Fischer had had with previous high res spectrographs such as CARMENES. In many respects if it lives up to expectations , EXPRES and the related “100 Earths” project should match or even out do the TESS and PLATO transit searches given its potential to discover habitable zone terrestrial planets within reach of future direct imaging telescopes. ( and more important providing a potent scientific rationale to build them ). What price Tau Ceti “I” at 0.9 AU?

  • Ronald August 16, 2017, 14:33

    With regard to planetary habitability, there may be some more bad news: many more planets may be tidally locked than we thought based on orbital distance alone, because the initial rotation may have been much slower than assumed:
    Rory Barnes. Tidal Locking of Habitable Exoplanets. Celestial Mechanics and Dynamical Astronomy, August 2017.

    • Ashley Baldwin August 16, 2017, 18:07

      “What is now known was once only imagined . ” And has been so since Kasting’s seminal work in the early 90s, heavily cited here . ( and updated by Kopparapu and Kasting several years back . )

      I don’t think there is anything particularly new about this study. It’s thrust is that tidal locking isn’t just limited to the Hab zones of M dwarfs but K and G too given certain conditions and the age of the system. It’s central tenet is that starting planetary rotation rates can govern time to and likelihood of tidal locking , positing that if Earth’s starting rotation rate had been 3 days instead of nearer ten hours , then it would now be tidally locked . Equations to estimating time to tidal locking are well established and also include many other variables such as semi major axis and planetary mass ( with bigger planets more likely to “lock”) . Venus’ slow rotation implies it is showing signs of tidal locking but it’s significantly 30 % nearer to the Sun than Earth and if Earth isn’t tidally locked due to its rapid starting rotation why should it be assumed that other similar such hab zone planets are any different ? The study involves a more multidimensional simulation but as with all such simations it easily possible to change the endpoint by inputting differing starting data . So just a sophisticated revamp of older work . ” What is now known can now been re- imagined “.

      • Ronald August 17, 2017, 11:12

        Yes, very essential in this study is initial planetary rotation period, and the assumption that Earth’s fast initial rotation may have been the result of the moon-creating impact (i.e. not original spin). That assumption will be crucial.

    • RAS August 17, 2017, 11:24

      As regards habitability need I remind you of this as quoted from a article reporting this paper.

      “For a tidally-locked planets that orbit close to their stars, it was believed this situation would be even worse. However, astronomers have since come to speculate that the presence of an atmosphere around these planets could redistribute temperature across their surfaces. Unlike Mercury, which has no atmosphere and experiences no wind, these planets could maintain temperatures that would be supportive to life.”


  • Dave Moore August 17, 2017, 0:08

    Tau Ceti appears to be what I call an anti-Jovian system that is the type of system that you get when a Jovian planet doesn’t form. Given that the debris disk imaged by ALMA is almost face on, I would say that you have four Mini-Neptunes here.

    This type of system forms a series of similar sized planets closely packed around the parent body with the average size roughly proportion to the mass of the star. (The Trappist system being an ideal example.) Unfortunately, to get Earth mass planets in this type of system, you have to go down to a small red dwarf.

    Epsilon Eridani is a much closer analog to our system with its Jovian planet and a debris disk that cuts off at an inner radius of 2.5 au and no sign of massive planets inside that.

    A point about trying to squeeze on smaller planet between Tau Ceti e & f. You can pack similar-sized planets quite close together (Earth & Venus for example), but if the planets have much different masses, the larger one ejects the smaller. A small planet between TC e & f would be unstable.

    • Ronald August 18, 2017, 9:58

      What you write is very interesting in more than one way;

      One part of it is well-known by now: that this kind of compact planetary system, consisting of medium-sized planets (gas dwarfs, ice giants) is very common.

      “an anti-Jovian system that is the type of system that you get when a Jovian planet doesn’t form”.
      Is this already well-established? That this system forms in the absence of a gas giant? I suspect that you are right: the idea is then, that a gas giant (or two) eats up most of the planetary material, leaving only a little bit in the inner system, just enough to form small terrestrial planets.

      “This type of system forms a series of similar sized planets closely packed around the parent body with the average size roughly proportional to the mass of the star”.
      Ok, I already got the idea, that this kind of system indeed forms a series of medium-sized planets. But is the average size mainly proportional to the mass of the parent star? Or also, as I suspect, in proportion with stellar metallicity? Compare for instance: Tau Ceti, 82 Eridani, 61 Virginis, Nu2 Lupi, as a few very nice examples. Tau Ceti and partic. 82 Eri have very low metallicities and smaller planets than 61 Vir. Nu2 Lupi is in between.

      The main questions remaining then are:
      – If a planetary system like ours is determined by the presence of a gas giant, what determines the presence of the gas giant? Probably stellar metallicity.
      – Is our kind of system the only type that can produce small terrestrial planets? Or could these also be produced in such a ‘compact’ (anti-Jovian as you nicely put it) systems, with (very) low metallicity? Or even in between the gas dwarfs and Neptunes?

      With ref. to my last question: you state that such a small planet could not exist in between the larger ones (e.g. between TC e and f). Also not if the gap is large enough? Or on the outside, where primordial dust disk was ‘thin’ enough? E.g. beyond 61 Virginis d, or beyond 82 Eridani d, or beyond Nu2 Lupi d.

  • J. Jason Wentworth August 17, 2017, 5:53

    The planetary systems of orange K dwarf stars like Tau Ceti (if not Tau Ceti itself, although its lack of a suitable habitable zone planet has yet to be established) seem, all factors considered, to be possibly the best abodes for indigenous life–or of human colonization, even if it means “settling” them in O’Neill-type colonies built (perhaps 3D printed?) out of local materials. K dwarf’s’ longevity, relative paucity of ultraviolet light, and still-abundant visible and infrared light, make them more attractive than yellow G dwarfs like our Sun. (I feel sorry for any inhabitants of yellow-white F dwarf systems, who must soon seek new homes before their suns age off the Main Sequence and become red giant stars, which they do more quickly than G dwarfs.)

    • Ronald August 18, 2017, 9:32

      Well, strictly speaking Tau Ceti is a late G (slightly smaller and dimmer solar type G8-G9) star, more like 82 Eridani. But your general idea is clear: quiet long-term stable stars.

      • J. Jason Wentworth August 20, 2017, 5:07

        I’d read that Tau Ceti is a K dwarf, but the books *were* pretty old (a few decades), and I’ve since read about other stars (mostly more distant ones) being reassigned different classifications after new observations were made with more refined equipment.

  • andy August 17, 2017, 17:24

    On the subject of whether planets between the orbits of e and f would be stable, figure 17 in the Feng et al. paper asks the question of whether the planets would be stable with respect to each other, so it doesn’t deal with what would happen if an additional planet were added to the system. I set up a quick program to plot whether inequality 2 from Barnes & Greenberg (2006) (which was used for figure 17 in the Feng et al. paper) indicated stability when I added an additional planet. Note that if the inequality is not satisfied, this means that the Hill stability of the system is unknown, i.e. systems in this region could still be Hill-stable.

    For the case of an Earth-mass planet and the planets having their nominal eccentricities, the guaranteed Hill-stable zone vanishes for inclinations less than 70°. For an inclination of 30° (to match the debris disc), the eccentricities of planets e and f need to be less than about 0.13 for the guaranteed Hill-stable region to reappear for Earth-mass planets. This may not be entirely unreasonable given that Feng et al. state that there are good reasons to believe the eccentricity values are dominated by artifacts. Mars-mass planets appear to have a smaller guaranteed Hill-stable zone (not sure if this is to do with the approximation being only to first order), in this case the condition for the zone to appear at 30° inclination is for the eccentricities of e and f to be less than about 0.045.

    While this is not conclusive regarding whether or not the Hill stability condition is met, it is interesting to note that Barnes & Greenberg (2006) find that the criterion is a reasonable approximation to the stricter criterion of Lagrange-stability (one notable difference being that the outermost planet is not allowed to escape to infinity, unlike in the Hill-stability criterion). Nevertheless, for now it seems that answering the question of whether this region can contain an additional planet depends on getting better constraints on the orbital eccentricities of the known planets and on more detailed computational analyses.

    • Ronald August 22, 2017, 5:12

      do I understand correctly that, assuming a 30° inclination, an earth-sized planet between e and f has a greater likelihood of surviving (also permitting a greater eccentricity) than a Mars-sized planet?

      • andy August 23, 2017, 13:07

        It’s not quite so simple. What I’m saying is that, considered as a three body system Tau Ceti + known planet + additional planet, the region where Tau Ceti + Tau Ceti e + additional planet is analytically Hill-stable and the region where Tau Ceti + additional planet + Tau Ceti f is analytically Hill stable have a smaller overlap in the region between the orbits of e and f when the additional planet is Mars mass than if the additional planet is Earth mass. (In fact the region for Mars-mass planets is nonexistent at 30°, while there is a very small possible region for Earth-mass planets at this inclination).

        The actual system we want to consider is a 6-body system (Tau Ceti+g+h+e+additional planet+f), we are usually more interested in Lagrange stability than Hill stability (where we don’t allow the outermost planet to escape to infinity, but there is unfortunately no analytic criterion although the Hill stability criterion appears to be a relatively good approximation), plus we care about whether the system is actually stable rather than just the region where the equations guarantee that it is stable.

        My point is that we can’t just assert (as people have done in this comment thread) that the gap between e and f is large enough to fit an additional planet: the situation is not clear-cut. The system diagram is somewhat misleading as it does not depict the orbital eccentricities. Admittedly there are good reasons to believe that the values in the latest orbital solution are too high, so the possibility that there is a stable region is not entirely ruled out. Detecting an Earth-mass planet at 30° is equivalent to detecting a 0.5 Earth-mass planet at 90° (without the benefit of transits) and would therefore be very tricky, so getting better constraints on the orbital eccentricities of the known planets is probably the best way to go.

  • Andrew LePage August 18, 2017, 9:38

    For those readers who may be interested, here is my latest installment of “Habitable Planet Reality Check” where I address the potential habitability of the exoplanet candidates of Tau Ceti:


    • Ronald August 22, 2017, 5:09

      Very nice and clear analysis again! And I fully agree with your conservative HZ approach.
      And now I keep hoping for an additional earth-sized planet between e and f ….

  • hiro August 18, 2017, 16:27

    The last bet is quasi-Europa orbiting around planet f, if it exists.