Extra-Solar Planet Data Trends

Data Trends

Although a few of the known exoplanets circle pulsars, exoplanet searches focus on sun-like stars for several reasons. One is that habitable planets are more likely to be found around a star that has a long lifetime to give any possible life on the planet time to evolve. Second, sun-like stars are less prone to massive outbursts, and the intense ultraviolet radiation that is emitted from larger stars is not as severe. Third, it is easier to detect planets around stars that aren't as bright, so fainter stars like our sun are preferable.

The 193 known planets circle around 165 different stars, and there are 18 multiple planet systems, where 13 are double, 4 are triple, and 1 is a quadruple system. Because of the large number of planets, this site will no longer maintain a database of them. Rather, the data used in the information below is based upon The Extrasolar Planets Encyclopedia, which maintains an active database.

No one really knows for sure what the planets look like, but there is no shortage of theories. First of all, we know that almost all of the known exoplanets are "hot Jupiters." This name comes from the fact that they are very close to their parent stars (many are much closer than Mercury to the sun), and most are many times the size of Jupiter.

Why so close and so big? This comes out of the biases inherent to the detection methods: The closer to the star, and the bigger the planet, the larger the movement of the star will be due to the effects of the planet. So these "hot Jupiters" are the easiest to detect, and therefore they make up the bulk of those discovered thus far. It was also, until recently, unknown whether these planets were jovian (gaseous) or terrestrial (rocky). Then, a planet was seen eclipsing its star, and the resulting image showed that it had a very gaseous atmosphere. It is assumed that most - if not all - of those known are like this.

Only in the past few years have planets as small as Saturn (approx. 30% the mass of Jupiter) been found, and this detection is due to the more sensitive equipment that is constantly being developed. Most of the planets found thus far also have very short (some a matter of a few days) orbits around their stars. This is both due to the detection techniques, and it is a statistical anomaly: Since the discoveries have been so recent, there are not enough data to find planets that have longer years.

Nevertheless, these discoveries have forced many changes upon the theories of solar system development, which had, until recently, only our solar system as a model. According to the old model, large, gaseous bodies should not have been able to form that close to their parent stars; the gas should have either accreted to the star, or been "blown away" to a much farther distance by the young star's solar wind. So, the main change that has been made to the theories of solar system formation and evolution is that the planets migrated: After they formed farther out, they moved into much closer orbits.

Mass Mass Histogram

The easiest planets to find are the giant planets that orbit close to their parent stars. Because of this, the first few exoplanets found were the "hot Jupiters," and these massive planets remain the easiest to find and so they are still the most numerous.

As time goes on and detection techniques and instrumentation increase in sensitivity, lower-mass planets are found more easily. In 2004, planets that were the mass of Jupiter or less accounted for less than 30% of the ones that had been detected. At the end of 2005, this went up to 36%, and by mid-2006, it was up to 38%.

As shown here, 73 planets (38% of the total found) have a minimum mass as small or smaller than Jupiter's. Only 28 (15%) are smaller than Saturn, and about 10 (5%) have a minimum mass smaller than or equal to Neptune's. None have been found that are even close to Earth's mass.

The blue line on the histogram above is an exponential decay fit. The amplitude is 41.3±1.1 and the decay constant is 0.580±0.028. This means that for every increase in mass by about two Jupiter masses, the number of known extra-solar planets decreases by a factor of e (≈2.72). This exponential decay law is probably an accurate representation for the actual number of exoplanets that exist.

Period Mass Histogram

Going with the theme of this section, the closer a planet is to its parent star, the more easily it is detected. If it is closer to its host star, then it will (a) orbit more quickly, and (b) it will have less distance to travel in one orbit, so its period will be much shorter than if it were more distant.

From a practical standpoint, it's easier to detect planets with short periods because it requires less telescope time. If a planet has a period of about 4 days, then you could catch over 7 of the planet's years in one month of observing. But, if the planet had a period the same as Earth's, then all you would observe of the star is a very slight velocity change (if using the Doppler method), or nothing at all (because it would be highly unlikely to observe it during the few hours it would spend transiting the star out of its entire year).

For these reasons, the planets that have been found so far mostly have very short periods. This is easily visible in the histogram displayed on the right by the first bin of 0-50 day period having about 1/3 of the planets discovered so far. This bin has been expanded in the inset graph, which, even though it is expanded so that each bin covers 2.5 days, still the 2.5-5 day period bin has about 15% of the known exoplanets.

As more large-scale surveys are carried out, it is likely that more planets with longer years will be discovered because of the longer time spans of the available data.

Semi-Major Axis Semi-Major Axis Histogram

The semi-major axes follow the same general pattern as the period chart above. This is because the semi-major axes are not an observed value (except in the one case of a directly imaged exoplanet), but they are derived from the period using Kepler's Third Law:

As with most applications of Kepler's Third Law to planetary systems, the second mass, M₂, is much less than the primary mass. For this reason, it can be effectively neglected. Stellar models have been able to predict the mass of stars for about 50 years, so based upon the spectrum of a star, its mass can be accurately determined. So with the mass and period, the semi-major axis (r) can be calculated.

The variations between this histogram and the one for period are introduced due to the differences in the masses of parent stars. But, the differences are not as extreme as one might expect because most of the stars that have been surveyed are sun-like for the reasons discussed above.

Eccentricity Eccentricity Histogram

The eccentricity of an orbit is how much it varies from a perfect circle. A stable orbit can have an eccentricity anywhere from a perfect circle with an eccentricity of 0, up to a highly elliptical orbit with an eccentricity up to (but not including) 1. If an orbit had an eccentricity of 1, it would be parabolic and escape from the system. If it were larger than 1, it would be hyperbolic and also escape from the system.

Earth's eccentricity is 0.017, while Jupiter's is 0.094. In our solar system, the planet with the largest eccentricity is Pluto at 0.244, and Mercury with 0.205. The planet with the lowest eccentricity is Venus with 0.007. Unless there is some gravitational tugging (such as with the Galilean Satellites) that keeps an orbit eccentric, orbits will usually circularize with time.

About 10% of the planets found so far have an eccentricity of nearly 0. About 15% have an eccentricity smaller than Earth's, and over 25% have an eccentricity smaller than Jupiter's. 45% are smaller than Mercury's eccentricity, and 50% are lower than Pluto's. The other half have very eccentric orbits; this means that, throughout their years, they come very close to and very far from their parent star. This will create wide temperature swings, and for any life like Earth's, this would make survival quite difficult, if not impossible.

Comparisons Chart of Known Exoplanets (Mass vs. Semi-Major Axis)

The graph on the right is a dramatic display of what current technology can detect in terms of the minimum mass of an exoplanet and the distance from its parent star that the planet can get before it can no longer be detected with current technology. A Jupiter-like planet is just within the realm of detection today, while Earth-like planets are well below detection limits with current techniques available.

One of the main goals of extra-solar planet detection today is to find the elusive Earth-like planets circling other stars. The goal of the Kepler mission, which should be launched in 2008, is to find hundreds of Earth-like exoplanets, and it is expected that it will also discover hundreds of planets that are much like those that have already been discovered. Kepler will work by aiming a space-based telescope at one field of stars in the Cygnus-Lyra region of space, and it will take images of that area for a nominal period of 4 years. This will allow a long enough baseline to detect planets with Earth-like years, and the detectors are being designed so they are sensitive enough to detect the tiny changes in light that will be caused by Earth-like planets transiting their parent stars.