systemic

This post follows up post #14, The Next Big Thing.

In 1916, in circular #30 of South Africa’s Union Observatory , Robert T. A. Innes reported the discovery of a faint red star in Centaurus. This otherwise unremarkable star, more than 100 times too faint to be seen with the naked eye, attracted his attention because it was rapidly moving with respect to other stars in the same part of the sky. This large proper motion indicated that the star was almost certainly a close neighbor of the Sun, and in 1917, this suggestion was verified. The distance to the star was measured to be only 4.22 light years, closer to the Sun than any other known star. Its extremely faint appearance, in spite of its close proximity, made it the intrinsically least luminous star known to astronomy at that time.

Proxima Centauri, as the star was later named, is now known to be merely the nearest (and most famous) of the roughly 50 billion red dwarfs (also called M-dwarfs) which inhabit our galaxy.

What about planets? Is it possible to have a terrestrial planet in orbit around Proxima? Do red dwarfs have a shot at harboring life-bearing worlds? If such worlds exist can we detect them?

Yes.

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The black cloud post describes how the formation of a star and a planetary system can be traced back to the moment when a dense core within a giant molecular cloud begins to suffer an inside-out collapse. The gas at the center of the cloud collapses first, and congregates into the beginnings of a hydrostatically supported protostar. The overlying regions thus lose their support and begin to career inward as well. A wave of collapse radiates outward from the center of the cloud, triggering a downward avalanche of gas and dust. Computer simulations show how gas that has fallen from large distances comes together to form a protostellar disk in orbit around the nascent central protostar. In the image shown below, a simulation of the earliest phases of our own solar system show a region (viewed edge-on) that is several hundred astronomical units across, and plotted 40,000 years after the collapse has started. At this stage of the simulation, roughly half of a solar mass of material has collected in the central protostar, and another half a solar mass or so is orbiting in a very massive protostellar disk.

As the disk grows in mass, it begins to feel its own self-gravity, and some regions begin to collapse under their own weight. At the same time, the pressure of the gas in the disk resists the tendancy to collapse, and the differential rotation of the disk acts to sheer out fragments as they grow. This process can also be simulated, and the result is spiral waves (viewed here from above):

The presence of the spiral waves causes angular momentum to be transferred outward through the disk, while allowing the majority of the mass to flow inward to eventually join with the central protostar. Even after the spiral waves have dissipated, there must exist continuing source(s) of angular momentum transfer through the disk. The identification of these mechanisms is still an active area of research. Possible mechanisms that might operate after the disk is no longer massive enough to support self-gravitating spiral waves include the magneto-rotational instability, as well as convection-driven turbulence in the disk. One way or another, angular momentum transport was extremely effective. The initial cloud that formed our solar system was rotating more or less uniformly, wheras at the present day, there is nearly a complete separation between mass and angular momentum in the solar system. The Sun contains more than 99.8% of the mass, and the planets carry more than 98% of the system angular momentum.

When I give public talks on planet formation, I like to show the above image (taken by HST, and released in 1995) of a protostellar disk, or proplyd, in the Orion star-forming region. We see the cold proplyd from an edge-on vantage, against a diffuse background of hot glowing gas. This disk is at a somewhat later phase of evolution than the ones pictured in the above simulations. It’s roughly 1400 AU across, which is more than 15 times the diameter of Neptune’s orbit, and considerably larger even than the orbits of the newly discovered Kuiper belt objects 2003 UB313, and Sedna. To give an idea of scale, I’ve integrated both Sedna and 2003 UB313 for one Sedna orbit (12,050 years) and plotted their positions relative to the plane of our solar system and superimposed (to scale) on the proplyd. Sedna, is currently in the portion of its orbit where it is speeding (in its rather lazy, loosely bound fashion) through perihelion, and hence the dots plotted at 120.5 year intervals in that region are spaced widely apart. Seen from above, Sedna’s eccentric (e=0.855) orbit would have a aphelion point considerably beyond the radial edge of the proplyd.

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Nine extrasolar planets are known to transit their parent stars, but all of these planets have periods shorter than 5 days. They are frying beneath the brilliance of their parent stars. It would be nice to find a transiting planet with a longer period. Preferably, this would be a giant planet with towering thunderstorms and warm, drenching rains, and orbited by a habitable Earth-sized moon that we could detect with HST photometry.

Advanced observers can make the discovery of a transiting room-temperature Jupiter a reality by participating in the systemic team‘s distributed observing project: Transitsearch.org. A brief blurb on the transitsearch.org home page describes the basic strategy:

Transitsearch.org is a cooperative observational effort designed to allow experienced amateur astronomers and small college observatories to discover transiting extrasolar planets. In order to utilize the advantages of a network of small telescopes most effectively, our strategy is to observe known planet-bearing stars at the dates and times when transits are expected to occur.

At present, the majority of confirmed extrasolar planets have been discovered using the Doppler radial velocity technique (see the tutorials at www.oklo.org). The Doppler method, however, cannot determine the inclination of a planetary orbit to the line of sight from Earth. Therefore, each planet discovered by the Doppler method has an a-priori probability of transiting, which depends mainly on the orbital period of the planet. Short-period planets have relatively high transit probabilities, whereas long-period planets have low transit probabilities.

Transitsearch.org hasn’t found a new transiting planet. But if we can maintain the enthusiasm of the collaboration, then eventually it will. Every planet that is detected by the radial velocity technique has a finite a-priori probability of transiting. Hence we need to work systematically down through the list. Chances of success (among planets that have not yet been fully checked) range from a sporty 12.9% for HD 118203 “b” down to a depressingly low 0.1% for 55 Cancri “d” (for which our best-guess next opportunity to observe a transit center occurs, curiously enough, a week after the start of the next long count).

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Users familiar with console tutorial #3 will have noticed that the self-consistent 2-planet fit to the remarkable multi-planet system orbiting GJ 876 is presented as a fait accompli. We are currently implementing an “epoch” slider for the console which will greatly smooth the transition from Keplerian to Newtonian fits for interacting systems, but amazingly, it turns out to be possible to obtain a competitive 3-planet fit to the Rivera et al (2005) GJ 876 data set using only the current version of the systemic console. This post gives the details, and gets a bit technical, so if you are interested in following it closely, we suggest that you first work through tutorials 1, 2, and 3.

Also, a cautionary remark. The 3-planet integrated fit requires patience. I was able to get the fit described below in about 2 hours on a machine with two 3.4 GHz Intel Xeon CPU’s (with hyperthreading turned on). Thus, I was able to use the other CPU’s to do other work. On single-core, single-processor machines, the systemic console will hog the CPU (unless it’s niced and put in the background).

In any case, here’s the 411:

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