Home  Research  Exoplanet Models  Publications  Academic Courses  C.V.  Honors/Awards/Memberships  My Family  Internal Cultivation  Hobbies  Travels 
Exoplanet Models 
★New Interactive Tool to Plot Planets on MassRadius Diagram: Click HERE. (Wolfram CDF Player Required)Download the massradius plot in postscript (eps) format: Click Here.
★The following diagram shows the currently known transiting exoplanets with their measured mass and radius with observation uncertainties. Earth and Venus are shown for comparison. The curves are calculated for planets composed of pure Fe, 50% Fe50% MgSiO3, pure MgSiO3, 50% H2O50% MgSiO3, 75% H2O25% MgSiO3 and pure H2O. These percentages are in mass fractions. The data of these six curves are available in Table 1 of paper 1 in Publications. The red dashed curve is the maximum collisional stripping curve calculated by Marcus et al. (2010). If you use this diagram, please cite the following papers: (1) Li Zeng, and Dimitar Sasselov. "A Detailed Model Grid for Solid Planets from 0.1 through 100 Earth Masses". In the Publications of the Astronomical Society of the Pacific (PASP), Chicago Journals, Volume 125, No. 925, pp. 227239, March 2013. (pdf download)(2) Li Zeng (曾理), and Dimitar Sasselov. "The Effect of Temperature Evolution on the Interior Structure of H2Orich Planets". ApJ, 784, 96, April 2014. (pdf download)
Interactive Tool for ThreeLayer Planet Models
★A dynamic and interactive tool (Version 5, click HERE to access) to characterize and illustrate the interior structure of exoplanets. In order to run this tool in your web browser, you need to download and install the free Wolfram CDF player.A few important things to note about this tool:1. The Wolfram CDF Player is completely free and available for download online. You just need to visit www.wolfram.com/cdfplayer/ and input your institution's name and any email address to download it. 2. If the tool fails to load in any other web browser, try open it in Firefox. 3. You may need to click "Enable Dynamics" at the upper righthand corner when necessary to allow the tool to display properly in your web browser. 4. Please be patient, the tool may take a while (up to ~30 seconds) to initialize and load in your web browser. If it runs too slow, try to relaunch your web browser or restart your computer. 5. When you click the Locator, please wait one second before dragging it around, to allow it enough time to respond. DO NOT release the click during the entire dragging process until the Locator is moved to the desired location in the massradius diagram. 6. This interactive tool is for research & education purpose only, all rights reserved. If you use this tool, please cite the paper below: (1) Li Zeng, and Dimitar Sasselov. "A Detailed Model Grid for Solid Planets from 0.1 through 100 Earth Masses". In the Publications of the Astronomical Society of the Pacific (PASP), Chicago Journals, Volume 125, No. 925, pp. 227239, March 2013. (pdf download)(2) Li Zeng (曾理), and Dimitar Sasselov. "The Effect of Temperature Evolution on the Interior Structure of H2Orich Planets". ApJ, 784, 96, April 2014. (pdf download)7. Any questions or comments are much appreciated, please contact me at lzeng@cfa.harvard.edu
Major updates: (1) New Planet's M and R and uncertainties (δM+/, δR+/) can be plotted as a rectangular uncertainty region with chosen color on the MR diagram . (2) p0 can be input in GPa. (3) 11 values of p0 range for each Locator {Mass,Radius} are available as 11 clickable buttons. Min and Max values correspond to twolayer planets. (4) Two dashed curves enclose the composition uncertainty in the ternary diagram due to (δM+/, δR+/).
Illustration on how to use it (older version):
★The following diagram shows the massradius contours of doublelayer planet. The xaxis is in unit of Earth Masses. The yaxis is in unit of Earth Radii. 1st row: FeMgSiO3 planet. 2nd row: MgSiO3H2O planet. 3rd row: FeH2O planet. 1st column: contour mesh of p1/p0 with p0. 2nd column: contour mesh of CMF with p0. 3rd column: contour mesh of CRF with p0. Given mass and radius input, various sets of massradius contours can be used to quickly determine the characteristic interior structure quantities of a 2layer planet including its p0 (central pressure), p1/p0 (ratio of coremantle boundary pressure over central pressure), CMF (core mass fraction), and CRF (core radius fraction). The 2layer model is uniquely solved and represented as a point on the massradius diagram given any pair of two parameters from the following list: M (mass), R (radius), p0, p1/p0, CMF, CRF, etc. The contours of constant M or R are trivial on the massradius diagram, which are simply vertical or horizontal lines. The contours of constant p0, p1/p0, CMF, or CRF are more useful. Within a pair of parameters, fixing one and continuously varying the other, the point on the massradius diagram moves to form a curve. Multiple values of the fixed parameter give multiple parallel curves forming a set of contours. The other set of contours can be obtained by exchanging the fixed parameter for the varying parameter.
The data for the massradius contours with a finer grid are given as follows. Each xls file contains two sheets, one for mass and one for radius, both in Earth units. The rows of the table correspond to Log10[p0] from 8 to 14.4 with stepsize 0.025. The column of the table correspond to one of the three parameters: p1/p0, CMF, or CRF from 0 to 1 in stepsize of 0.025. This data could be used to transform a probability distribution in massradius phase space, into the probability distribution of the interior structure parameter phase space, such as the probability distribution in p0p1/p0 phase space, p0CMF phase space, or p0CRF phase space, assuming doublelayer model. FeMgSiO3 planet:
MgSiO3H2O planet:
FeH2O planet: If you use the diagram or tables, please cite the following paper: Li Zeng, and Dimitar Sasselov. "A Detailed Model Grid for Solid Planets from 0.1 through 100 Earth Masses". In the Publications of the Astronomical Society of the Pacific (PASP), Chicago Journals, Volume 125, No. 925, pp. 227239, March 2013. (pdf download) Summer 2007: MIT Department of Earth, Atmospheric and Planetary Science Summer UROP with Prof. Sara Seager on MassRadius relation of Earthlike exoplanet. ★We Built Computer Models for the interior structure and the atmosphere of extrasolar planets to understand the MassRadius relation and atmospheric spectral lines of exoplanets. Our basic assumption for the interior of Earthlike exoplanets is that they all have an iron core, a silicate mantle and a water crust. We also assumed that the temperature dependence of the Equation Of State (EOS) is negligiable, which is a very good approximation. Based on these assumptions, we developed two computer codes in matlab to interpret the bulk composition of solid exoplanets based on their mass and radius measurements. For details, please refer to our paper published on Publications of the Astronomical Society of the Pacific (PASP). If you use this tool, please cite the following paper: Li Zeng, and Sara Seager. "A Computational Tool to Interpret the Bulk Composition of Solid Exoplanets based on Mass and Radius Measurements". In the Publications of the Astronomical Society of the Pacific (PASP), Chicago Journals, Volume 120, No. 871, pp. 983991, September 2008. (pdf download)Code download instructions: Frist of all, download the code zip files and decompress them. Please put the decompressed files into your Matlab work directory so that the Matlab can recognize them. Use addpath command if necessary. Based in Matlab if using this computer code please cite Li Zeng & Prof. Sara Seager.
ExoterDE(M, Munc, R, Runc); Take a lot of time, but more accurate. This program can deal with the a case of zero uncertainties in planet mass and radius. It plots 1σ,2σ,3σ contours of given Mass, Radius and the uncertainties associated with them. example: for Mass=10 Earth Mass , Mass uncertainty=0.5 Earth Mass; Radius= 2 Earth Radius, Radius uncertainty= 0.1 Earth Radius: just type ExoterDE(10, 0.5, 2, 0.1); in your Matlab command window. Then hit Enter.
ExoterDB(M, Munc, R, Runc); based upon database interpolation. It plots a colormap showing the possible proportions of iron, silicate and water for continuous range of σ from 0 up to 3.
example: for Mass=10 Earth Mass , Mass uncertainty=0.5 Earth Mass; Radius= 2 Earth Radius, Radius uncertainty= 0.1 Earth Radius: just type ExoterDB(10, 0.5, 2, 0.1); in your Matlab command window. Then hit Enter. The results should look similar to the diagram below:
