A Definition for Giant Planets Based on the Mass-Density Relationship
AA Definition for Giant Planets Based on theMass − Density Relationship
Artie P. Hatzes
Th¨uringen Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenburg, Germany [email protected] andHeike Rauer
Institut f¨ur Planetenforschung, Deutsches Zentrum f¨ur Luft- und Raumfahrt,Rutherfordstrasse 2, D-12489, Berlin, GermanyZentrum f¨ur Astronomie und Astrophysik, TU Berlin, Hardenbergstr. 36, D-10623 Berlin,Germany
ABSTRACT
We present the mass-density relationship (log M - log ρ ) for objects withmasses ranging from planets ( M ≈ M Jup ) through stars (
M > M (cid:12) ).This relationship shows three distinct regions separated by a change in slope inlog M – log ρ plane. In particular, objects with masses in the range 0.3 M Jup to 60 M Jup follow a tight linear relationship with no distinguishing feature to separatethe low mass end (giant planets) from the high mass end (brown dwarfs). Thedistinction between giant planets and brown dwarfs thus seems arbitrary. Wepropose a new definition of giant planets based simply on changes in the slope ofthe log M versus log ρ relationship. By this criterion, objects with masses lessthan ≈ M Jup are low mass planets, either icy or rocky. Giant planets coverthe mass range 0.3 M Jup to 60 M Jup . Analogous to the stellar main sequence,objects on the upper end of the giant planet sequence (brown dwarfs) can simplybe referred to as “high mass giant planets”, while planets with masses near thatof Jupiter can be considered to be “low mass giant planets”.
Subject headings: planets and satellites: fundamental parameters — stars: lowmass – stars: brown dwarfs a r X i v : . [ a s t r o - ph . E P ] J un
1. Introduction
The nature of stellar and sub-stellar objects is determined by their mass. Stars aredefined as an object with sufficient mass to ignite hydrogen fusion in the core. Sub-stellarobjects, on the other hand, have masses below that needed to ignite hydrogen burning intheir cores ( M ∼ M Jup ). Like their stellar counterparts, sub-stellar objects encompass awide range of masses from those that are accepted as planets, with masses of a few M Jup , toobjects often considered to be brown dwarfs with masses of a few tens of M Jup . The exactboundary in mass between what one considers a “planet” and what one considers a “browndwarf”” is blurred and is still the subject of debate.One definition of giant planet is that it is a sub-stellar object that has not undergonedeuterium burning anytime during its life. By this criterion the boundary between planetsand brown dwarfs should be about 13 M Jup (Burrows et al. 2001). However, this distinctionseems arbitrary as the mass distribution for companions below 25 M Jup show no characteristicfeatures at this mass limit (Udry 2010). Furthermore, the period of deuterium burning haslittle influence on the future evolution of the brown dwarf. This is contrary to stars wherehydrogen burning under hydrostatic equilibrium significantly alters the further evolution ofthe object. Chabrier et al. (2014) argued that deuterium burning, or lack thereof, plays norole in either giant planet or brown dwarf formation. They also pointed out that these twotypes of objects “might bear some imprints of their formation mechanism, notably in theirmean density and in the physical properties of their atmosphere.”On the other hand, the intersection of the mass distributions of sub-stellar objectsappear to have a distinctive dip around M ≈ M Jup (Udry 2010). Schneider et al.(2011) attributed this dip as the boundary between the mass spectrum of planets, whichis decreasing with increasing mass, and the distribution of sub-stellar and low mass starswhich is increasing beyond this point. The dip is also coincident with a possible break in themass-radius relationship for low mass and sub-stellar objects (Pont et al. 2005; Andersonet al. 2011) which suggests a difference in the physical natures between objects on eitherside of this boundary (Schneider et al. 2011). For these reasons Schneider et al. (2011) arbitrarily (our emphasis) assigned a maximum mass of 25 M Jup as the limit for includingobjects in the
Exoplanet Encyclopaedia M Jup boundary we still do not know its nature, i.e. to which distribution (planets orbrown dwarfs) it actually belongs.The mean density versus mass relationship for planets show a broad minimum arounda mass of 0.3 M Jup (Rauer et al. 2014; Laughlin & Lissauer 2015) which separates the H/Hedominated giant planets from low-mass planets of Neptune-mass or smaller. The differentslopes in the density-mass plane of the two objects highlights the differences in structure 3 –between the two classes of planets. We extend the density-mass relationship through sub-stellar and stellar objects and show that this also shows a change in slope marking thedifferences in structure between giant planets/brown dwarfs and stellar objects. We arguefor a definition of giant planets based on the mass-density diagram.
2. The Density versus Mass Relationship ≈ M Jupiter ,the boundary between core nuclear burning stars and degenerate core brown dwarfs. Thesecond inflection is a minimum in density at M ≈ M Jupiter , roughly the boundary between 4 –H/He dominated planets and low mass planets.Fits were made to the data in these regions in order to define better the boundarybetween lower mass planets, giant planets/brown dwarfs and stars. Although the stars showa roughly linear relationship, in the mass range 0.08 – 1 M (cid:12) the relationship is best fit by asecond order polynomial shown by the curved line. For low mass stars in the range 0.08 – 1 M (cid:12) the log M − log ρ relationship can also be fit by a line resulting in ρ ∝ M − (2 . ± . ).This follows from the mass-radius relationship on the low mass end of the main sequencewhere R ∝ M , thus ρ ∝ M − .The log M – log ρ relationship for giant planets and brown dwarfs show a very tightcorrelation (correlation coefficient, r = 0.976). A linear fit over the mass range 0.35 – 65 M Jup results in: logρ = (1 . ± . logM − (0 . ± . ∼ M Jup ) up to low mass stars all have approximatelythe same radius. Thus an increase in mass is accompanied by proportional increase in density.Note that this curve closely follows the mass-density relationship for H/He dominated giantplanets (Fortney et al. 2007) which is shown as the dashed line. At the low mass end ofthe giant planet range, the linear fit to the giant planets deviates significantly from thedashed line for planets with Jupiter-like composition. The planets below the dashed line arelarger than expected by such models and called “inflated” planets. The linear relationshipintercepts the main sequence for stars at M = 63 ± M Jup .For simplicity we shall refer to all exoplanets with masses less than ≈ M Jup as lowmass exoplanets. These can be either rocky or ones that have a large fraction of volatiles(i.e. Neptune-like). The low mass planets show considerable scatter in their densities. Inspite of this scatter there clearly appears to be a minimum in density around ∼ M Jup .Indeed, a parabolic fit to the valley of this ‘V’-shape results in a minimum of the density atthis value for the mass. For higher mass objects the density increases. We take this as theboundary between the low mass planets and giant planets.Fig. 2 shows the more traditional Mass-Radius relationship with our boundaries shownas the vertical dashed lines. One can also see inflections in this curve at roughly the sameboundaries seen in Fig. 1, although these are not as striking or well defined particularlybetween the low mass and giant planets. 5 – .001 .01 .1 1 10 100 1000 10000.01.11101001000 Mass (Jupiter) D en s i t y ( g m c m − ) Low Mass Planets Giant Planets Stars
Fig. 1.— The density and mass of stars (red squares), giant planets and brown dwarfs, andlow mass planets. Triangles represent Kepler discoveries and dots are CoRoT exoplanets.Ground-based discoveries for high mass giant planets are shown by pentagons. The linerepresents a linear fit to the giant planets and brown dwarfs in the mass range M = 0.35- 60 M Jup . A second order polynomial fit (curved line) was made to the lower end of thestellar main sequence. The boundary between the low mass planets and giant planet occursat M = 0.3 M Jup . The boundary between the giant planets and stars is at M = 60 M Jup (0.060 M (cid:12) ). The dashed red line shows the mass-density relationship for H/He dominatedgiant planets taken from Fortney et al. (2007). 6 – .01 .1 1 10 100 1000 10000.01.11101001000 Mass (M Jupiter ) R ad i u s ( R J up i t e r ) Fig. 2.— The points from Figure 1 shown in the mass-radius plane. 7 –
3. Discussion
The mass density diagram for all objects with masses ranging from planets to stars areseparated by three distinct regions marked by an abrupt change in sign of the slope of thelog M − log ρ relationship. Stars show a negative slope, whereas giant planets and browndwarfs have a positive slope. However, below about 0.3 M Jup objects show considerablescatter in their densities. We shall simply refer to this region of the diagram as the “low massplanets” (LMP). It is beyond the scope of this paper to discuss this region of the diagram,the origin of such scatter, or any relationship between the mass and density. Instead wewill focus on the giant planets and for the sake of discussion we shall refer to these regionsbetween the LMP and stars as the “gaseous planet sequence” (GPS). MS will refer to theclassic main sequence for stars.The beginning of the GPS occurs at M ≈ M Jup , roughly the boundary betweenplanets with a significant amount of volatiles, and those dominated by H/He. The boundarybetween the GPS and the MS occurs at 60 M Jup . Laughlin & Lissauer (2015) noted that thedistribution of planetary densities had a broad minimum at a planet mass of M P ∼ M J (30 M Earth ) which they took as the boundary between giant planets and low mass planets(termed “ungiants” in their paper) We propose that this boundary is actually at a muchhigher mass of M P ∼ M J .We also fit the density-mass data from Laughlin & Lissauer (2015, Fig. 5 of their paper)for planets with in the mass range 0.01 to 0.1 M J . The data are well fit by a linear functionthat intercepts our GPS at M P ∼ M J ( ≈ M Earth ), consistent with our proposedboundary.The striking feature about GPS is that there is no distinguishing characteristic thatseparates the low mass end where objects are clearly planets, and the high mass end whereobjects are generally considered to be brown dwarfs. The 25 M Jup limit (the arrow inFig. 1) taken by Schneider et al. (2009) to be the boundary between planets and browndwarfs shows no obvious differences in the GPS on either side of this limit. If anything, thearrow only seems to mark the boundary where the data are sparce. Clearly, the discoveryof more objects in this mass range is desperately needed. Possibly differences between thegiant planets and the “traditional” brown dwarfs may become more apparent with morediscoveries. For instance, if no objects can be found that fill the gap marked by 25 M Jup (arrow) and the onset of the MS then this “gap” might be taken to separate the planets fromthe brown dwarfs and stars. For now we note that the few brown dwarfs with masses ≈ M Jup all fall on the GPS.In light of Figure 1 making a distinction between objects on the low- and high-mass 8 –end of the GPS seems arbitrary and may only obscure the fact that all objects on this trackare physically the same objects governed by the same underlying physics and with similarstructure, analogous to the MS. Chabrier et al. (2014) also argued that the mass boundarybetween giant planets and brown dwarfs given by the present IAU definition was “incorrectand confusing and should be abandoned”. Figure 1 certainly supports this claim. Thisfigure also shows that the density provides us with no obvious hints regarding a differentformation mechanism between brown dwarfs and giant planets. Possibly the differences inthe physical properties of the atmospheres may show indications of a different formationmechanism (Chabrier et al. 2014).Comparing the properties of the GPS to the MS provides us with additional argumentsto support the claim that all objects along the GPS should be considered the same type ofobjects. Stars have masses that cover over two orders of magnitude. The structure of thestar changes considerably along the main sequence. High mass stars have a convective coreand radiative envelope and as one moves down the main sequence this structure changesto objects with a radiative core and a convective envelope. The lowest mass stars, on theother hand, are fully convective. The stellar atmosphere changes considerably along themain sequence in terms of effective temperatures and the types of spectral features that areobserved.Finally, stars may also have different formation scenarios. Low mass stars are believedto form from the collapse of a proto-cloud and subsequent accretion (Palla & Stahler 1993).The formation mechanism for high mass stars is still open to debate. For massive starsradiation from the core halts the accretion process thus limiting the mass (e.g. Yorke &Kr¨ugel 1977). One hypothesis is that they are formed by the merger of lower mass stars(Bonnell et al. 1998). Regardless of all these substantial differences, all objects along the MSare considered to be the same general class of objects that is governed by the same physics- nuclear burning in the core under hydrostatic equilibrium. We only make sub-distinctionsin the form of “low mass” and “high mass” stars.Objects along the GPS also have masses that differ by over two orders of magnitudes.Like stars, they certainly have a wide range of effective temperatures, atmospheric features,and possibly even different formation mechanisms. Making an arbitrary distinction betweengiant planets and brown dwarfs only confuses the central issue that these objects share asimilar structure. Analogous to stars we can make subtle distinctions between “high massgiant planets” and “low mass giant plants”, but the class should be considered as a whole inorder to gain a more fundamental understanding of their formation, evolution, and nature.Comparing the GPS to the MS also provides a natural explanation to the so-called“Brown Dwarf Desert”. The paucity of brown dwarf companions simply reflect the decrease 9 –in number of high mass much in the same way there is a decrease in the number of highmass stars in the stellar distribution. Compared to low mass main sequence stars O-typestars in our galaxy are extremely rare – it is simply harder for nature to form these highermass stars. To our knowledge, astronomers never refer to the “O-star desert.”We propose a new definition of planets, brown dwarfs, and stars based not on arbitraryseparation of distributions, or whether short-lived deuterium burning has occurred, or justbecause we are biased in thinking that giant planets should all have masses close to that ofour Jupiter. Rather, our definition is based on the observed inflections in the mass-densitydiagram that separate regions governed by different underlying physics. Thus,
M < M Jup ⇒ Low Mass Planets0.3 M Jup < M < M Jup ⇒ Giant Gaseous Planets
M > M Jup ⇒ Stellar ObjectsWe note that by our definition Saturn has a mass near the boundary between low massplanets and gas giant planets. Although we refer to objects with
M > M Jup as “stars”,the exact boundary between objects supported by electron degeneracy pressure and thosewith a hydrogen burning core is not well known and can be as high as 80 M Jup . Possiblyobjects with 60 M Jup < M < M Jup should be considered to be the bona fide brown dwarfs.Another obvious feature of Figure 1 is the relative paucity of objects in the mass range20 < M
Jup < ρ diagram can serve as a powerful tool for understanding planetarystructure. 10 – REFERENCES
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