Predicting Planetary Populations for COROT

It was the goal of my PhD Thesis to predict the population of gas giant planets that will be detected by the COROT satellite via Transit Search. So the aim of the theory was to make a prediction for close-in planets with orbital periods less than 50 days. As this is a very difficult task, I first tried to analyze the full set of gas giant structures hoping to gain a more global understanding of giant planet formation.

The basis of my work is a set of equilibrium calculations that contain all hydrostatic solutions for gas giant envelopes according to the equations of stellar structure. The newest calculations 'Corot Survey Mark 2a' make use of the opacities by Alexander & Ferguson 2005 for Grevesse & Sauval 1998 solar composition and the Hydrogen/Helium equation of state by Saumon, Chabrier & van Horn 1995. They confirm the results of the previous survey 'Corot Survey Mark 1.0/1.1' which was calculated with a different opacity table.

Click this link to see a comparison between the equilibrium mass distribution and the observations as of August 3, 2007. The histogram includes all planets found so far with orbital periods less than 10 days. For every detected planet, the corresponding mass spectrum for the planet's parameters (host star, orbital period) is added to the theoretical mass spectrum. In this way, the protoplanetary equilibria are compared to the detected mature planets. I assume that the equilibrium mass distributions compare reasonably well to mature planets up to periods of roughly 40 days. This is caused by the changing role of the critical core mass for close-in planets.

The Corot Surveys

The satellite COROT will search for close-in exoplanets around a few thousand stars using the transit search method. The COROT mission holds the promise of detecting numerous exoplanets. Together with radial velocity follow-up observations, the masses of the detected planets will be known.

We have devised a method for calculating all possibly existing gas giant structures according to the laws of stellar structure. Our method works by looking at all hydrostatic envelopes of giant gas planets that could possibly exist in arbitrary planetary nebulae, i.e. we have tried to find all solutions to the equations of 'planetary' structure for a range of planetary orbits. We have completed the first such surveys of hydrostatic equilibria in an orbital range covering periods of 1 to 50 d. The current survey is called Corot Survey Mark 2a.

Already during surveys Mark 1.0 / 1.1 statistical analysis of the calculated envelopes suggested division into three classes of giant (proto)planets that are distinguished by orbital separation. We term them using classes G (extremely close-in), H (Hot), and J (large separation, Jupiter-like). Each class has distinct properties such as a typical mass range. Furthermore, the division between classes H and J appears to mark important changes in the formation: for close-in planets (classes G and H) the concept of a critical core-mass is meaningless while it is important for class J. This result needs confirmation by future dynamic analysis. These findings have been confirmed by the Mark 2a survey.

Read more:

or go directly to the results browser:

Update: CoRoT Survey Mark 3

Thanks to a collaboration with Andrea Fortier we have discovered a bug in our implementation of the Saumon et al. (1995, henceforth SCVH) Mixing Entropy. We had previously corrected the errors contained in SCVH. However, as it turns out now, we have introduced an error of our own. Because this error is only relevant in a rather extreme Pressure-Temperature regime of the EOS, it remained undetected before. Our comparison calculations with Ikoma et al. (2001), for instance, are exactly the same after correcting the error. The comparison calculations have been published in my PhD thesis (Broeg 2006).

Nevertheless, the changes affect many locations in the CoRoT survey. Especially the close-in planets with large accretion rates can be affected. The new results are currently being published (Broeg 2009). The are referred to as CoRoT survey Mark 3.

To browse the new results and compare them with the old please have a look at the new result browser Mark 3.

The Mark 3 mass spectra are plotted somewhat differently. To avoid binning effects they contain a cumulative distribution function (CDF, dashed line). On the right axis both the total number of planets and the relative fraction are given. The distribution function (DF, black line) is then derived as the derivative of the CDF. Additionally, also a binned version, i.e. histogram, is plotted (blue line). Vertical dashed lines indicate the masses of Saturn, Jupiter, and the WGESP (working group on extrasolar planets, IAU) brown dwarf mass limit of 13 Jupiter masses for easy reference. However, the deuterium burning and thus the deuterium burning limit appears to have no influence on the "planetary nature". The formation method would be a much better criterion to distinguish between Planet and brown dwarf. Nevertheless, looking at the CoRoT Survey Mark 3, almost all planets (by chance) appear to be below this limit (see Broeg 2008).

Differences Mark 3 - Mark 2a

The mass spectra typically exhibit two or three peaks. We call these peaks according to their origin self-gravity peak (SGP), Low nabla peak (LNP) and compact peak (CP). Please refer to the result browser at location A2, 2 day orbit 1e-2 accretion rate: At this location all three peaks are present and are easily identified. With increasing mass, the peaks are the SGP, LNP, and CP. Going from Mark 2a to Mark 3, we have the following changes:

The LNP is caused by very low nabla values in the envelope (see Broeg 2009). Using the corrected mixing entropy term for SCVH, the nabla values are slightly larger. Therefore the originally very sharp LNP becomes wider and moves to higher masses. The CP is also moved to higher masses due to this.

In summary, only the high-mass end of the mass spectra is affected. Furthermore the LNP, if present, is much reduced in height and wider - spread over a larger mass range. For the very hot planets at 1 day orbits this is a dramatic effect. The upper mass limit rises dramatically: From 57 Jupiter masses to 268 Jupiter masses. The shape of the mass spectrum, and the position of the SGP, however, remain unchanged. For the majority of locations, on the other hand, the changes are very small. Check out the result Browser for Mark 2a and 3...

Beyond 128 days orbital period all results are identical (this is not shown here).



Broeg 2009 Broeg C.: The full set of gas giant structures I: On the origin of planetary masses and the planetary initial mass function, Icarus, 204, 15

Broeg 2006 Broeg C.: Gasplanetenentstehung und der COROT-Planetenzensus. Ph. D. thesis, Friedrich-Schiller-Universität Jena, Germany. download

Ferguson et al. 2005 Ferguson, J. W., D. R. Alexander, F. Allard, T. Barman, J. G. Bodnarik, P. H. Hauschildt, A. Heffner-Wong, and A. Tamanai 2005. Low-Temperature Opacities. ApJ 623, 585–596.

Anders and Grevesse, 1989 Anders, E. and Grevesse, N.: Abundances of the elements - Meteoritic and solar. Geochim. Cosmochim. Acta 53(1989) 197–214.

Ikoma et al. 2001 Ikoma, M. ; Emori, H. ; Nakazawa, K.: Formation of Giant Planets in Dense Nebulae: Critical Core Mass Revisited. ApJ 553 (2001) 999–1005

Saumon et al. 1995 Saumon, D. ; Chabrier, G. ; van Horn, H. M.: An Equation of State for Low-Mass Stars and Giant Planets. ApJS 99 (1995) 713–+

Valid XHTML 1.0