Homework 2 Question 1 (William Matzko)

[Images were embedded into the actual document when I wrote this. Here, they are just included as an attachment]

How big can a planet get?

Title: Evidence of an upper bound on the masses of planets and its implications for giant planet formation

Author: Kevin C. Schlaufman

First Author’s Institution: Department of Physics and Astronomy, Johns Hopkins University.

Status: Published in the Astrophysical Journal, January 20, 2018.

               Just as there is a fine line between dwarf planets and small “real” planets, there is also a fine line between high-mass planets and brown dwarfs. This paper explores the boundary of the latter. Currently, the International Astronomical Union has a limit on the upper mass of a planet; anything above about 13 Jupiter masses should be considered a brown dwarf, because at this mass the body should be able to fuse deuterium in its core. Schlaufman raises an objection to that limit, in part because the mass alone is not sufficient in determining when deuterium fuses. As he points out, the actual mass at which a body fuses deuterium is dependent on its composition. So, a metal-rich body that is about 13 Jupiter masses would be considered a brown dwarf, while if it were not rich in metals it would be a planet. A more fundamental way to distinguish between planets and brown dwarfs is how they formed. Planets are thought to have formed by the core accretion model, while brown dwarfs are thought to have formed similarly to stars—from gravitational instabilities in the original molecular cloud. It is possible to determine how a body formed by observing its host star. High-mass planets are much more likely to orbit metal-rich stars than metal-poor stars, but brown dwarfs show no such bias. Therefore, it is possible to put an upper limit on the mass of planets by determining when the metallicity of host stars ceases to be an important factor in the orbit of high-mass bodies.

               Schlaufman used the NASA Exoplanet Archive to find low-mass planets that have been detected using the Doppler and transit method (this cuts down on false positives and allows us to know the mass of the body to a high accuracy). He searched the literature to find brown dwarfs that have also been detected by both the transit and Doppler methods. In total, he is working with 146 high-mass planets, brown dwarfs and low-mass stars, all of which orbit stars similar to ours. You might be tempted to question his selection techniques, since they are biased towards bodies with a shorter period. However, Schlaufman cites studies that show high-mass bodies orbit metal-rich stars at all periods, and that metal-rich and metal-poor systems occur uniformly regardless of period. So, the short period bias will not propagate into the results. Schlaufman analyses the bodies in two ways. First, he uses an algorithm to plot relationships between the mass of the bodies and the metallicity of the host star, which then sorts them into two groups. The boundary between these groups would represent the mass at which a body no longer prefer to orbit around metal-rich stars. Second, he plots the median metallicity as a function of the orbiting body’s mass. When the moving median metallicity dips below the lowest moving median metallicity of the high-mass bodies, the mass at that point should also correspond to the upper bound on planetary masses.

               The results of the algorithms agree and show that the upper bound of bodies formed by the core accretion method is around 10 times the mass of Jupiter. The following plot shows the distribution of masses and metallicities produced by the algorithm.

Solid points mean that the algorithm classified that body unambiguously as a high-mass planet (circle) or low-mass star (square). Open points mean that the algorithm didn’t unambiguously classify the body but is still reasonably confident in its classification. The gray section is the separation between the two classification areas, and the dashed line is the midpoint of the gray section.

The next plot shows the moving median metallicity as a function of the body’s mass. The black line is the median metallicity. The lighter gray region is the uncertainty in the median. The blue area represents the high-mass body metallicity range, while the green area is where the median metallicity is below that of the high-mass body region. Note that the boundaries in both of these plots should indicate the upper limit on planetary masses. Both boundaries fall around 10 times the mass of Jupiter. This indicates that high-mass bodies cease to care about the metallicity of their host star around that mass. Thus, bodies less than 10 times the mass of Jupiter should be considered planets, while higher mass bodies should not be considered planets.