Li Zeng

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Exoplanet Models

Tool to Plot Planets on M-R Diagram

Interactive Tool for Tri-Layer Planet Model

Mass-Radius Contours
Old Matlab Code Download

Plot Planets on M-R Diagram

★New Interactive Tool to Plot Planets on Mass-Radius Diagram: Click HERE. (Wolfram CDF Player Required)

Download the mass-radius 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% Fe-50% MgSiO3, pure MgSiO3, 50% H2O-50% MgSiO3, 75% H2O-25% 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. 227-239, March 2013. (pdf download)

(2) Li Zeng (曾理), and Dimitar Sasselov. "The Effect of Temperature Evolution on the Interior Structure of H2O-rich Planets". ApJ, 784, 96, April 2014. (pdf download)

Mass-Radius Curves

 

 

 

 

Interactive Tool for Three-Layer 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/cdf-player/ 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 right-hand 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 mass-radius 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. 227-239, March 2013. (pdf download)

(2) Li Zeng (曾理), and Dimitar Sasselov. "The Effect of Temperature Evolution on the Interior Structure of H2O-rich Planets". ApJ, 784, 96, April 2014. (pdf download)

7. Any questions or comments are much appreciated, please contact me at lzeng@cfa.harvard.edu

 

Version 5:

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 M-R 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 two-layer 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):

 

 

Mass-Radius Contours

★The following diagram shows the mass-radius contours of double-layer planet. The x-axis is in unit of Earth Masses. The y-axis is in unit of Earth Radii. 1st row: Fe-MgSiO3 planet. 2nd row: MgSiO3-H2O planet. 3rd row: Fe-H2O 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 mass-radius contours can be used to quickly determine the characteristic interior structure quantities of a 2-layer planet including its p0 (central pressure), p1/p0 (ratio of core-mantle boundary pressure over central pressure), CMF (core mass fraction), and CRF (core radius fraction).

The 2-layer model is uniquely solved and represented as a point on the mass-radius 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 mass-radius 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 mass-radius 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 two sets of contours crisscross each other to form a mesh, which is a natural coordinate system (see the following figure) of this pair of parameters, superimposed onto the existing Cartesian (M,R) coordinates of the mass-radius diagram. This mesh can be used to determine the two parameters given the mass and radius input or vice versa.

 

M-R Contours

The data for the mass-radius 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 mass-radius phase space, into the probability distribution of the interior structure parameter phase space, such as the probability distribution in p0-p1/p0 phase space, p0-CMF phase space, or p0-CRF phase space, assuming double-layer model.

Fe-MgSiO3 planet:

Fe-MgSiO3 p0-p1/p0 table

Fe-MgSiO3 p0-CMF table

Fe-MgSiO3 p0-CRF table

 

MgSiO3-H2O planet:

MgSiO3-H2O p0-p1/p0 table

MgSiO3-H2O p0-CMF table

MgSiO3-H2O p0-CRF table

 

Fe-H2O planet:

Fe-H2O p0-p1/p0 table

Fe-H2O p0-CMF table

Fe-H2O p0-CRF table

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. 227-239, March 2013. (pdf download)

 

Old Exoplanet Code Download

Summer 2007:

MIT Department of Earth, Atmospheric and Planetary Science

Summer UROP with Prof. Sara Seager on Mass-Radius relation of Earth-like exoplanet.

★We Built Computer Models for the interior structure and the atmosphere of extra-solar planets to understand the Mass-Radius relation and atmospheric spectral lines of exoplanets. Our basic assumption for the interior of Earth-like 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. 983-991, 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 1-σ,2-σ,3-σ 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:

 

 

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