Exoplanet Statistics and Demographics Update

Exoplanet statistics and demographics update for July 2014: In 2014, not only did the number of confirmed exoplanets discovered exceed 1000, a batch of over 700 planets observed by Kepler was added to the list of confirmed exoplanets. It is time once again to see how the basic numbers pertaining to exoplanet observations have changed. Previously, approximately two years ago (6 July 2012), according to the Extrasolar Planets Encyclopedia, the total confirmed planet count was nearly 800 (777), breaking down into 623 unique planetary systems, 101 of which harbored more than 1 planet. Those results were shown as updated versions of those shown in Exoplanets and Alien Solar Systems which included data only up to 8 October 2011. We now look at the state of exoplanet demographics (of strictly confirmed planets only), as it was on 5 July 2014, when (according to the Extrasolar Planets Encyclopedia), there were 1800 confirmed exoplanets, in 1118 unique planetary systems, 462 of which harbored more than 1 planet.

The first graph shows the number of exoplanets discovered per year, and the cumulative number discovered by the end of each year (or by 5 July 2014 in final year).

Prior to the batch addition of hundreds of Kepler-discovered exoplanets in 2014, typically, more than 98&#37 of the confirmed exoplanets had mass estimates (or lower/upper limits on the mass). However, Kepler-discovered explanets generally do not have mass estimates or limits (since they are discovered by the transit method, which does not yield sufficient information by itself to constrain the mass). Consequently, the percentage of confirmed exoplanets that have mass estimates or limits is now much lower than it used to be. For the sample of 1800 confirmed exoplanets as of 5 July 2014, only 57.6&#37 have mass estimates or limits (either lower or upper bounds). A histogram of the mass distribution of this subset of confirmed exoplanets is shown below.

Our solar system planets are shown for direct comparison. The histogram for the July 2014 sub-sample (solid, black) is essentially unchanged compared to the July 2012 sample (dotted, red), when there were 766 confirmed exoplanets with mass estimates or limits. In fact the basic form of the mass distribution has not changed since the October 2011 sample (at which time only 686 exoplanets had mass estimates or limits — see Exoplanets and Alien Solar Systems). The mass distribution still has two broad peaks, one around a Jupiter mass, and the other around Uranus/Neptune mass. The origin of this distribution is not understood and it cannot be due to observational biases alone (see Exoplanets and Alien Solar Systems for details). There is still a painful deficit below a couple of Earth masses. The planet (KOI-1843b) with the lowest mass (that does not orbit a pulsar) has a mass lower limit of about a third of Earth’s mass and has a radius about two-thirds of that of Earth. The orbital period of KOI-1843b is very short (about 17&#37 of an Earth day). I will not give the so-called equilibrium temperatures here since they are misleading because without knowledge of details of the surfaces and atmospheres of the planets, their “equilibrium temperatures” may be completely different from their actual temperatures (as is the case for Venus).

Of the 1800 confirmed exoplanets in the July 2014 sample, 1744 have measured periods (96.89&#37), and a histogram of the orbital periods is shown below.

The distribution is still double-peaked but the detailed shape of the distribution has changed compared to that for the July 2012 sample (dotted, red). The peak at lower periods is now much broader than before, stretching between about 2 Earth days to several tens of Earth days. The broad peak at larger periods (hundreds to several thousand Earth days) is relatively weaker now compared to the lower period peak.

Over half of the July 2014 sample confirmed exoplanets (981 out of 1800) have both orbital period measurements and mass estimates (mostly lower or upper limits). Below, an updated orbital period versus mass diagram is shown.

The results are essentially unchanged compared to earlier results. The three “patches” that are heavily populated in the diagram persist with the addition of the new data. The interpretations of the period versus mass diagram have been discussed at length in Exoplanets and Alien Solar Systems, including observational biases. Those discussions are still relevant. In particular, the pile-up of hot-Jupiters seen in the lower right-hand-side patch remains unexplained: no convincing explanation has yet been offered in the literature. Another thing that remains fascinating is that all of our solar-system planets are still way offset from the populated regions of the extrasolar planet period versus mass diagram.

Since, by Kepler’s law, the square of the orbital period is proportional to the cube of the semi-major axis of the orbit, the distribution of the semi-major axis of the orbits of confirmed exoplanets also shows the same double-peaked structure of the period distribution, as shown below.

In the 6 July 2012 sample, 252 out of 777 exoplanets had radius (i.e., size) estimates, corresponding to about 32&#37. In the 5 July 2014 sample, 1152 confirmed exoplanets have radius estimates, which corresponds to 64&#37 of the sample of 1800. The histogram of the exoplanet radius distribution is shown below.

It can be seen that there is a significant change in the shape of the exoplanet size distribution. Previously (dotted, red histogram), the distribution was double-peaked, but now (black, solid histogram), a strong peak between about 1 to 4 Earth radii dominates the distribution. The second peak in the former distribution, which stretched from about 10 to 20 Earth radii is now heavily suppressed. The change in the distribution is obviously affected by the characteristics of the large batch of Kepler-discovered exoplanets added to the list of confirmed exoplanets in early 2014.

Clearly, the physical properties of confirmed exoplanets that have both size and mass estimates can be constrained much better than those for which only a radius estimate or a mass estimate exists. In the July 2014 sample, 389 out of 1800 confirmed exoplanets have both radius and mass estimates (or lower or upper limits). This constitutes about 21.6&#37 of the sample. Compared to the October 2011 sample discussed in Exoplanets and Alien Solar Systems, this represents a slight decrease in the percentage of confirmed exoplanets that have both size and mass information (for the October 2011 sample the corresponding percentage was 26.9&#37, or 186 out of a sample of 692 exoplanets). Below is the latest radius versus mass diagram for the July 2014 sample, showing the positions of our solar-system planets for direct comparison.

Compared to the corresponding plot for the October 2011 sample shown in Exoplanets and Alien Solar Systems, the region between about 1 to 4000 Earth masses and 1 to 10 Earth radii is more populated. Nevertheless, the concentration of exoplanets in the region between approximately 100 to 1000 Earth masses and 10 to 20 Earth radii persists. This region corresponds to roughly a third to three times Jupiter’s mass, and about 1 to 2 times Jupiter’s radius. The region below about 2 Earth radii (regardless of mass) is still only sparsely populated, as is the region below about 2 Earth masses (regardless of size).

Two extremely important quantities that can be estimated when there is both size and mass information for a confirmed exoplanet are the density and the surface gravity. In both cases, since the exoplanet mass estimates are usually lower limits, the densities and surface gravities are in most cases also lower limits. We first show the density distribution below:

It can be seen that the distribution has not changed significantly compared to that for the July 2012 sample (red, dotted). The dominance of density lower limits in the range of about 0.1 to 0.3 times the density of Earth persists in the distribution with the addition of the new data (which more than doubles the number of exoplanets with both size and mass information). Below, the density lower limit versus semi-major orbital axis diagram is shown, and it can be seen that the addition of the new data again does not significantly change the occupied regions in the diagram. There is still a heavy concentration of exoplanets with the orbit semi-major axis less than 0.1 astronomical units (AU) and with density lower limits less than about 0.3 times the density of Earth. The region with exoplanet density lower than 0.3 times the density of Earth and with orbital semi-major axis greater than 1 AU is conspicuously barely occupied. Moreover, Neptune, Uranus, Saturn and Jupiter lie in this sparsely populated region.

Below we show the surface gravity distribution of the sub-sample of confirmed exoplanets in the July 2014 sample that have both size and mass information (black, solid histogram). The surface gravity is expressed as a ratio to the surface gravity of Earth. Also shown is the corresponding histogram from the July 2012 sample (red, dotted), which shows that the distribution has not changed significantly despite the new data increasing the number of exoplanets in the sub-sample by more than a factor of two.

The surface gravity distribution is broad, with most exoplanets having a value between about 0.6 and 6 times that of the surface gravity of Earth, and peaking between about 1 to 2 times the surface gravity of Earth. One should bear in mind that the surface gravity values of most exoplanets are lower limits only.

Below we show the distribution of the distances to the 828 exoplanet systems that have measured distances to the host star. The distances lie in a wide range of about 10 light years up to about 30,000 light years. Compared to the sub-sample of July 2012 (red, dotted), the histogram of exoplanet host star distances has not changed significantly for the July 2014 sample (although there are only 151 additional stellar distances contributing, compared to the July 2012 sample).

We show below the distribution of the masses of 1458 host stars from the July 2014 confirmed exoplanets sample. The host-star mass distribution is still strongly peaked around a solar mass and only minor differences in the distribution compared to the July 2012 sample are apparent.