Fizzy Super-Earths: Impacts of Magma Composition on the Bulk Density and Structure of Lava Worlds

Fizzy Super-Earths: Impacts of Magma Composition on the Bulk Density and Structure
of Lava Worlds
Kiersten M. Boley1,4
, Wendy R. Panero2
, Cayman T. Unterborn3
, Joseph G. Schulze2
, Romy Rodríguez Martínez1
, and
Ji Wang (王吉)1
1
Department of Astronomy, The Ohio State University, Columbus, OH 43210, USA; boley.62@osu.edu
2
School of Earth Sciences, The Ohio State University, Columbus, OH 43210, USA
3
Space Science & Engineering, Southwest Research Institute, San Antonio, TX, USA
Received 2023 February 3; revised 2023 July 21; accepted 2023 July 24; published 2023 September 7
Abstract
Lava worlds are a potential emerging population of Super-Earths that are on close-in orbits around their host stars,
with likely partially molten mantles. To date, few studies have addressed the impact of magma on the observed
properties of a planet. At ambient conditions, magma is less dense than solid rock; however, it is also more
compressible with increasing pressure. Therefore, it is unclear how large-scale magma oceans affect planet
observables, such as bulk density. We update ExoPlex, a thermodynamically self-consistent planet interior
software, to include anhydrous, hydrous (2.2 wt% H2O), and carbonated magmas (5.2 wt% CO2). We find that
Earth-like planets with magma oceans larger than ∼1.5 R⊕ and ∼3.2 M⊕ are modestly denser than an equivalent-
mass solid planet. From our model, three classes of mantle structures emerge for magma ocean planets: (1) a
mantle magma ocean, (2) a surface magma ocean, and (3) one consisting of a surface magma ocean, a solid rock
layer, and a basal magma ocean. The class of planets in which a basal magma ocean is present may sequester
dissolved volatiles on billion-year timescales, in which a 4 M⊕ mass planet can trap more than 130 times the mass
of water than in Earth’s present-day oceans and 1000 times the carbon in the Earth’s surface and crust.
Unified Astronomy Thesaurus concepts: Exoplanet astronomy (486)
1. Introduction
As terrestrial planets evolve, they are thought to transition
through a magma ocean phase directly following formation
(Elkins-Tanton 2012; de Vries et al. 2016; Schaefer & Elkins-
Tanton 2018). During this phase, the temperatures are
sufficiently high for global melting of the silicate mantle
(Elkins-Tanton 2012; Chao et al. 2021). Although global
magma oceans would generally be considered a transient phase
in the lifetime of a terrestrial planet, it is possible for them to be
long-lived. In particular, planets on close-in orbits will
experience longer magma ocean lifetimes, maintaining their
surface temperatures through the radiation of their host star
(Chao et al. 2021). Ultra-short-period (USP) planets orbiting a
host star with a strong magnetic field are also subject to an
additional form of heating due to induction that could produce
magma layers in the upper mantle as well (Kislyakova et al.
2017, 2018; Kislyakova & Noack 2020). These nontransient
magma oceans or lava worlds undergo a distinct evolution that
is unique to their temperatures and orbital distance.
After formation, many of these planets will initially
experience significant atmospheric mass loss due to the high
irradiation of their host stars, making them unlikely to maintain
a substantial atmosphere (Lopez et al. 2012). There are several
works that find USP super-Earths that are consistent with the
absence of such atmospheres (Kreidberg et al. 2019; Keles
et al. 2022). Although these planets would require rare initial
conditions to maintain their primary atmosphere so close to
their star, some planets may still have partial atmospheres due
to the vaporization of silicate rock on their permanent dayside
as a result of tidal locking (Léger et al. 2011; Zieba et al. 2022).
During their evolution, they inevitably become tidally locked
with their host star, resulting in a dayside and a nightside
(Kasting et al. 1993; Barnes 2017). There is evidence that the
dayside may possess an atmosphere at low pressures (P „
10−5
bar, 1.5 Pa), consisting of rock vapor (Léger et al. 2011;
Zieba et al. 2022). The proximity to their host star makes short-
period planets not only more easily detectable but also optimal
for characterization.
The vast majority of likely terrestrial planets with masses
10 M⊕ or radii 1.7 R⊕ discovered are on orbits less than
10 days. These discoveries have naturally prompted the
characterization of these planets in order to understand their
properties. For the majority of terrestrial planets without
atmospheres, the stellar abundances of the host stars are
correlated with the bulk density of the planet (Adibekyan et al.
2021; Schulze et al. 2021). Previous studies have specifically
focused on solid planets while including the low densities with
high equilibrium temperatures of some of the planets in their
samples, e.g., 55 Cnc e and WASP-47 (McArthur et al. 2004;
Becker et al. 2015; Adibekyan et al. 2021; Schulze et al. 2021).
In these works, high-density planets are explained by an excess
of iron. However, the description of low-density planets is
largely unexplored due to their nonunique relationships
between planet composition and density.
There are several reasons for which one might attempt to
explain the low-density of these planets using magma oceans.
The first of which is that the surface temperatures of many of
these planets are above 1350 K, which is approximately the
zero-pressure melting temperature of Earth-like rocks (Katz
et al. 2003). Therefore, their surfaces may exceed the melting
The Astrophysical Journal, 954:202 (11pp), 2023 September 10 https://doi.org/10.3847/1538-4357/acea85
© 2023. The Author(s). Published by the American Astronomical Society.
4
NSF Graduate Research Fellow.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
distribution of this work must maintain attribution to the author(s) and the title
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1

temperature of typical rocks, which range from 900 to 1500 K,
making them unlike any planet in our Solar System (Takahashi
& Kushiro 1983; Hirose & Kushiro 1993; Liu et al. 2010).
Materials also expand when they are heated and melt; however,
magmas are also highly compressible, potentially counteracting
any expansion at depth (Rivalta & Segall 2008; McCormick
et al. 2016). While Earth-like magmas are up to 24% less dense
than their solid at the surface, they experience 20% compres-
sion compared to their zero-pressure volume at a pressure
equivalent to 150 km below the Earth’s surface (5 GPa)
(Dannberg & Heister 2016), compared to a 6% compression of
a solid of the same composition. As a result, it is possible that
planets with deep magma ocean are denser than an equivalent-
mass solid planet. However, it is not well-understood the
degree to which this would impact the bulk density of the
planet, and whether this difference is observable.
This paper will demonstrate that global magma oceans have
little impact on bulk density of likely lava worlds. We will
quantify the degree to which melting can lower the observed
densities. For close-in super-Earths with masses 6 M⊕, such as
55 Cnc e (McArthur et al. 2004) and WASP-47 e (Vanderburg
et al. 2017), there have been many studies that propose several
explanations for their low densities, which range from the
presence of an atmosphere to a core-free planet (Gillon et al. 2012;
Ito et al. 2015; Demory et al. 2016; Dorn et al. 2019; Dorn &
Lichtenberg 2021). However, there has been little investigation on
the impact of magma on planet density, independent of an
atmosphere. This is particularly important for less massive planets
that are too small to maintain a substantial atmosphere, such as
TOI-561 b (Lacedelli et al. 2021).
We will address the impact of magma on the mantle structure
of a lava world. Given that volatile species readily dissolve within
magma, we explore the implications for trapping these volatiles in
the interior over planetary lifetimes with implications for
outgassing. Previous studies have shown evidence for basal
magma oceans to occur in likely lava worlds and during the
phases of Earth’s evolution (Labrosse et al. 2007; Andrault 2019).
H2O and CO2 are volatiles thought to be commonly outgassed
from the mantle during the thermal evolution of a planet to form
the early atmosphere (Lupu et al. 2014; Schaefer & Fegley 2017).
By dissolving H2O or CO2 within magma, we can explore the
amount of volatiles that may be stored on billion-year timescales.
Therefore, we consider the mass–surface temperature relationship,
exploring the mantle structures that arise and whether volatiles
may be sequestered within the mantle.
The outline of our paper is as follows. Section 2 provides a
description of our approach and additions to ExoPlex5
(Unterborn et al. 2018, 2023; Unterborn & Panero 2019). In
Section 3, we discuss the resulting density–radius relationships,
comparing our findings to likely magma ocean planets, and the
impact of magma composition on the bulk density and structure
of a planet. We discuss the limitations of our model in
Section 4, along with comparing our results to previous studies
and known exoplanets. Finally, we provide a summary and
conclude in Section 5.
2. Method
The base of our planet interior model uses ExoPlex, a
thermodynamically self-consistent planet interior software
(Unterborn et al. 2018, 2023; Unterborn & Panero 2019).
ExoPlex solves five coupled differential equations: the mass
within a sphere, hydrostatic equilibrium, adiabatic temperature
profile, Gauss’s law of gravity in one dimension, and the
thermally dependent equation of state for solid planets. We
construct a magma module within this software to include the
liquid phase of the mantle when the temperature exceeds the
melting point. As melting temperatures are compositionally
dependent, we constrain this module to Earth-like mantle
compositions. In this study, we assume a spherically symmetric
planet for simplicity. However, tidal locking would cause lava
worlds to have drastic temperature differences between the
substellar and antistellar point (Léger et al. 2011). Therefore,
this module considers the upper limit that magma may have on
a planet’s observed properties.
2.1. Mantle
We adopt an Earth-like pyrolitic molar composition of
0.5Na2O–2CaO–1.5Al2O3–4FeO–30MgO–24SiO2, which is
within 1 wt% of the bulk silicate composition of the Earth
(McDonough & Sun 1995; Solomatova & Caracas 2021). For a
more realistic model, we incorporate both the solid and melt
phases of pyrolite. To simplify, we neglect chemical fractiona-
tion, assuming the melt phase to have a liquid pyrolite
composition at all temperatures above the melt curve. We also
include the effects of volatiles within the melt phase using three
separate model scenarios: Anhydrous, Hydrous, and Carbo-
nated models.
In the multicomponent systems of planetary mantles, melting
occurs over a range of temperatures. The solidus is the
temperature at which the melting begins with a very small
volume fraction of melt. As the temperature increases, the
volume fraction of melt also increases until all components of
the rock are liquid. The temperature at which the rock becomes
completely liquid is referred to as the liquidus. For most silicate
rocks, the solidus is hundreds of degrees lower than the
liquidus. When a rock undergoes a small degree of melting just
above the solidus, the trapped volatile species tend to enter the
melt phase (Hirschmann 2000). As one of the objectives of this
study is to determine whether a magma ocean is observable via
the bulk density of a planet, use of the solidus as the
temperature at which the planet melts will overestimate the
density effects of melting. However, it is solid layers, forming a
mechanical barrier, that will sequester volatiles deep in the
interior. Therefore, we choose to focus on the solidus
temperature, acknowledging that the effects on density are
lower bounds.
Many previous studies that incorporate the effects of melt in
exoplanets have used single-component melt curves (e.g.,
Stixrude 2014; Dorn et al. 2019; Dorn & Lichtenberg 2021).
However, multicomponent systems are more likely to occur,
given the diversity of rock-forming refractory materials
available within the protoplanetary disk during formation
(Helling et al. 2014). Therefore, we adopt the solidus
temperature at which significant changes in physical properties
occur. Specifically, we model the solidus using a method
similar to that of Boukaré et al. (2022). Boukaré et al. (2022)
rely on solidus and liquidus curves from Zhang & Herzberg
(1994) and Fiquet et al. (2010). Adopting a similar method, we
use a solidus that is lower than Zhang & Herzberg (1994),
using methods that overcome experimental limitations of
detecting small volumes of melts (Nomura et al. 2014).
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https://github.com/CaymanUnterborn/ExoPlex/
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The Astrophysical Journal, 954:202 (11pp), 2023 September 10 Boley et al.

To determine the solid–melt transition within the mantle, we
use a peridotite solidus melt curve from Katz et al. (2003) for
pressures less than 10 GPa for the anhydrous and hydrous
compositions. This gives us the following equation for the
solidus melt within the mantle:
( )
= + +
T a P a P a , 1
Melt,Anhydrous 1
2
2 3
where P is pressure, a1 = −5.1° C GPa−2
, a2 = 132.9° C GPa−1
,
and a3 = 1358.85 K.
For the hydrous melt, we use the Katz et al. (2003) solidus
melt curve for hydrous melts, which has an additional term to
account for H2O within the melt:
( )
= + + - g
T a P a P a KX , 2
Melt,Hydrous 1
2
2 3 H O
2
where K = 43° C wt%−γ
and γ = 0.75. We assume the wt% of
H2O in the melt is =
X 2.2
H O
2
wt%, which corresponds to the
wt% used in Solomatova & Caracas (2021) hydrous magma
equation of state.
To extend each solidus to higher pressures for all melt
compositions, we fit a power law similar to the Simon melting
law (Ross 1969; Stixrude 2014):
( ) ( )
=
T T , 3
P
P
b
Melt ref
ref
where Tref and Pref are the reference temperature and pressure at
higher pressures. We adopt the anhydrous melt temperature and
pressure from Nomura et al. (2014) of Tref = 3570 K at
Pref = 136 GPa. We use these values to provide an upper bound
for the transition between solid and melt at higher pressures.
We then fit for b so that the computed melt curve intersects the
peridotite solidus temperature of Tref = 3570 K at Pref =
136 GPa along with the solidus melt curves at lower pressures.
We find the b for the anhydrous melts to be banhydrous = 0.188
above 10 GPa. For the hydrous melt curve, we similarly use the
Nomura et al. (2014) constraint as an upper bound for the
hydrous melting between 10 and 136 GPa. As melting
temperatures are closely related to density, differences in the
volatile content of the melt for pyrolitic compositions become
less prominent at higher pressures. Therefore, anhydrous,
carbonated, and anhydrous melts converge at higher pressures.
For the hydrous model above 10 GPa, we find bhydrous = 0.201.
For the carbonated melt, we use an approach similar to the
above, fitting 5.2 wt% carbonated peridotite solidus data from 0
to 10 GPa Dasgupta & Hirschmann (2006) and the Nomura
et al. (2014) high-pressure point (i.e., Tref = 3570 K at
Pref = 136) to the Simon melting law in Equation (3) to derive
b for the carbonated melt to be bcarbonated = 0.265.
The consequences of extrapolating these melt curves beyond
Nomura et al. (2014) are minor as the difference in
compression at such high pressures becomes modest, and our
structural model is insensitive to the location of the melt curve
at higher pressures. Our computed melt curves are shown in
Figure 1.
To calculate the EOS of the solid mantle, we use ExoPlex.
ExoPlex relies on a fine-mesh grid approach to calculate the
stable mantle mineral assemblage for a given pressure and
temperature from PerpleX (Connolly 2009) grids. We
construct a grid consistent with the pyrolitic composition used
in Solomatova & Caracas (2021), as we also use their data for
the melt within the mantle. Within ExoPlex, we set the
mantle composition to reproduce the pyrolytic composition as
in Solomatova & Caracas (2021), using the following molar
fractions: Ca/Mg = 0.067, Si/Mg = 0.8, Al/Mg = 0.05, and
Fe/Mg = 0.9. Given that the molar fraction of iron within
ExoPlex includes the core and mantle, we specify a mass
fraction of 0.079 wt% FeO within the mantle, to remain
consistent with Solomatova & Caracas (2021).
For the melt, we use ab initio molecular dynamics data for
pyrolite from Solomatova & Caracas (2021) shown in Table 1.
Within ExoPlex, we recast the Solomatova and Caracas
series of isothermal equations of state between 2000 and
5000 K to a single pressure (P)–density (ρ)–temperature (T)
equation of state model for each composition by fitting their
results as follows:
( ) ( ) ( )
r r
= +
P T P P
, , 2000 K , 4
0 th
where P(2000 K) is calculated by the BM3 equation and the
2000 K ρ0 is as in Table 1. The thermal pressure (Pth) is
expressed by the Mie–Grüneisen relation:
[ ( ) ( )] ( )
g
q q
= -
P
V
E T E
, 2000 K, , 5
th D D
where γ is the Grüneisen parameter, ( )
g g r r
= q
0 0 , and the
Debye temperature [( ) ]
q q g g
= - q
exp
D D,0 0 . The harmonic
Figure 1. Solidus melt curves for the three magma compositions: Anhydrous
(purple), Hydrous (teal), Carbonated (magenta). We include the pressure–
temperature profile of a planet at a surface temperature, Tsurf = 2000 K and 1
Earth mass (orange). These are compared to the melt curves within the work of
Dorn & Lichtenberg (2021), who use a piecewise solidus melt curve (green).
Table 1
ExoPlex Model Parameters Recalculated from Solomatova & Caracas (2021)
for Magma with Earth-like Compositions, and with Added 2.2 wt% H2O and
5.2 wt% CO2
Melt Composition ρ0 (g cm−3
) K0 (GPa) ¢
K0 wt%
Pyrolite 2.49 24 4.7 L
Pyrolite+ 4 H2O 2.32 15 5.5 2.2
Pyrolite+ 4 CO2 2.37 18 5 5.2
Notes. Each value in the table is at a reference temperature of 2000 K fit using
the third-order Birch–Murnaghan EOS. For all compositions, we find a best-fit
thermal equation of state of γ0 = 1.7, q = 0.93, and θD,0 = 1000 K.
3

internal energy E(T, θD) is calculated from the Debye model
(e.g., Fei et al. 1992).
To determine the best-fit thermal parameters, we use a
Markov Chain Monte Carlo (MCMC). For all compositions,
we use the higher-temperature calculations (up to 5000 K) to
constrain γ and q. We assume θD,0 = 1000 K, as fluctuation in
θD,0 accounts for minimal differences in γ and q. Within each
step of the MCMC, a γ and a q are proposed, we then use the
Solomatova & Caracas (2021) 2000 K data to determine the
pressures and densities for the higher temperature (up to
5000 K). The densities at 135 GPa are compared to Solomatova
& Caracas (2021) data at higher temperatures using the two-
sample Anderson–Darling statistic (Anderson & Darling 1952;
Pettitt 1976). We find the best-fit thermal parameters for all
compositions to be: γ0 = 1.7, q = 0.93, and θD = 1000 K.
Using the best-fit thermal parameters, we self-consistently
calculate the interior temperature along an adiabat that
corresponds to the surface temperature of the planet. Therefore,
we fit the suite of pressure (P)–density (ρ)–temperature (T) data
to the BM3 Mie—Grüneisen equation of state at a reference
temperature of 2000 K for dry, hydrous, and carbonated
pyrolite from Solomatova & Caracas (2021) as shown in
Table 1. We then determine the density along the adiabat,
drawing from the melt or solid EOS depending on the relative
position of the adiabatic temperature and the solidus.
2.2. Metallic Core
We explore two core scenarios as an upper and lower bound
on the density variation that may arise from the core instead of
mantle melting. We assume an Earth-like core composition.
Given the surface temperatures required to produce a global
magma ocean, our model assumes a liquid metallic core, as the
core–mantle temperatures will exceed that of the melting
temperature of iron.
As an upper bound on the bulk density, we assume a pure
liquid iron core. For this scenario, we rely on the liquid Fe
pressure and temperature grid within ExoPlex. This grid uses
the temperature-dependent equation of state of Anderson &
Ahrens (1994) and is calculated up to 15 TPa and 10,000 K
(Unterborn et al. 2023).
We include a lower bound on the bulk density with the
addition of lighter elements in the core, which results in a
decrease in the bulk density of a planet. We use FeO within our
models with realistic mass fractions within the core: Fe = 84%
and O = 16%. We choose these values to represent a lower
bound on the density, as the highest estimate for light alloys in
the core of Earth is ∼16% by mass (Hirose et al. 2021).
ExoPlex assumes that, to first order, the presence of light
elements lowers only the molar weight of liquid Fe while not
affecting its compressibility at pressures indicative of exopla-
netary cores. This assumption means that, for an Fe core
containing 16 wt% O, the density of the planet would be ∼7%
lower than a planet with a pure Fe core for a 1 M⊕ solid planet.
2.3. Interior Compositions
To investigate the impacts of volatile compositions on the
mass and radius of a planet, we consider four different model
scenarios in which each scenario assumes a liquid iron core:
1. Solid rocky mantle.
2. Solid rocky mantle and anhydrous melt.
3. Solid rocky mantle and a carbonated melt.
4. Solid rocky mantle and a hydrous melt.
Figure 2 illustrates each model scenario with masses equal to
four Earth masses at a surface temperature of 2000 K,
demonstrating that for low masses generally, the hydrous
magma composition has the largest radius while the solid
planet has the smallest radius.
3. Results
Incorporating melting temperatures into our model, we find
three distinct magma ocean mantle structures when surface
temperatures exceed the solidus. Specifically, we find that the
mantle of a lava world may be completely molten, only molten
at the surface of the planet, or exhibit a layered magma ocean
structure hereafter referred to as a MOSMO structure. Here, we
define a mantle with a MOSMO structure as having a magma
ocean (MO) at the surface, a solid rock layer (S) mid-mantle,
and a basal magma ocean (MO) at the base of the mantle (see
Figure 3). It is this intermediate solid rock layer that has the
potential to serve as a mechanical barrier to volatile transport
from a basal magma ocean to the surface.
In Figure 4, we show the “phase diagram” for the mantle
structure, including several known planets that are likely lava
worlds. The planets are colored by their bulk density ratio,
which is their observed density divided by the expected density
assuming a solid, Earth-like composition with an Earth-like
light-element budget and core-mass fraction. Bulk density
ratios <1 indicate low-density planets, whereas those >1
indicate likely super-Mercuries. We construct this planet
sample using the Exoplanet archive, making the following
cuts. We require all planets within the sample to have mass and
radius measurements. We remove any planets with flagged or
controversial measurements. Using the period-dependent radius
Figure 2. We show an example of the four model scenarios using the results of
our study of 4 M⊕ planet with a surface temperature of 2000 K. Model (1) is a
solid rocky planet, where liquid rock phases are neglected. For Model (2), we
introduce a molten phase within the mantle in addition to the mantle. Model (3)
has additional volatile CO2, making it a carbonated melt. Model (4), the
hydrous melt, generally exhibits the largest increase in radius of the four
scenarios.
4

gap as an upper bound on planet radius, we remove planets
with larger radii (Van Eylen et al. 2018). We then explore the
structure and bulk density of planets with surface temperatures
above 1350 K, assuming no atmosphere and a surface albedo of
zero. We choose 1350 K as it is the lowest temperature that is
predicted by the anhydrous melt curve. Our results suggest that
MOSMO structure and surface magma ocean planets are
slightly more common than planets that are completely molten
(see Figure 4).
We investigate the impact of surface temperature on the
depth of the solid–melt transition. Using the median mass of
our planet sample, 4 M⊕, we vary the surface temperature,
displaying the lower boundary of the surface magma ocean and
the upper boundary of the basal magma ocean (see Figure 5).
As the surface temperature increases, the depth of the surface
magma increases until the mantle no longer contains a solid
layer at depth. We find that the planet becomes completely
molten at a surface temperature (Tsurf) of 2050 K for Models (2)
and (3), whereas Model (4) becomes mantle magma ocean at a
Tsurf = 2100 K. In the interval where a planet’s mantle
transitions from solid to mantle magma ocean, the planet will
form a MOSMO structure.
Figure 5(A) shows that, for a given mass, a planet will have a
surface temperature range in which they exhibit a MOSMO
structure that spans Tsurf ∼ 2000 K for 4 M⊕ planets. The
formation of a basal magma ocean occurs at Tsurf ∼ 1872 K, but
varies minimally depending on the magma volatile content.
Any differences between the models are not significant, given
the assumptions of the melt curve at high pressures. Within this
range, the majority of the melt is located within the basal
magma, with the surface melt only deepening by a few percent
with increasing surface temperature.
The depth of the surface magma ocean on a 4 M⊕ planet is
dependent on the magma composition and the imposed surface
temperature (see Figure 5(A)). Model (2), the anhydrous
magma, has a surface magma ocean that reaches a depth of
68 km (4.8 GPa) given a surface temperature of 1600 K.
Comparing Model (3) and Model (4) to Model (2), we find that
Model (2) has a shallower surface magma for a given surface
temperature, with the most prominent depth difference
occurring at Tsurf = 1600 K. At this surface temperature, the
surface magma oceans of Model (3) and Model (4) respectively
have 10% and 12% greater depth than that of Model (2). The
difference in surface magma depth between the models
becomes less pronounced with increasing surface temperature.
Before the mantle becomes mantle magma ocean for Model
(2), the depth of the surface magma ocean reaches 732 km
(28 GPa) at a Tsurf ∼ 1900 K. At 1900 K, Model (3) and (4)
only reach ∼4% greater depth than Model (2). Overall, we find
that the surface magma oceans for all model scenarios are
shallow, consisting of less than 5% of the radius fraction before
the mantle becomes mantle magma ocean.
The formation of a basal magma ocean on a 4 M⊕ planet is
invariant with respect to the volatile composition of the mantle
(see Figure 5(A)). We find the basal magma ocean forms with a
Tsurf ∼ 1870 K), melting only at the base of the mantle,
570 GPa. As the surface temperature increases, the top of the
basal magma ocean rises to 118 GPa for a Tsurf ∼ 2080 K. At
this point, the MOSMO structure transitions to a mantle magma
ocean as the top and bottom of the solid, mid-mantle region
meet. Therefore, the surface temperature at which the basal
magma ocean first forms relies on a significant extrapolation of
the melting curve, while the existence of the MOSMO structure
only relies on solidus temperatures at pressures not requiring
extrapolation. Uncertainties in the melting curve parameters in
Equations (1)–(3) will shift the top and bottom of the solid mid-
mantle region to higher or lower pressures, but will not
eliminate the layer.
Although we show a 4 M⊕ planet in Figure 5(A), we
investigate the impact that mass has on magma depth as well.
For planets <4 M⊕, we find that the MOSMO structure spans a
smaller range of surface temperatures, which can be seen in
Figure 7. The reduced surface temperature range results in a
reduced mantle melt fraction of the basal magma ocean. For a
4 M⊕ planet at Tsurf1900 K, the basal magma ocean would
account for 19% of the planet radius whereas a basal magma
ocean on a 2.5 M⊕ planet at Tsurf1900 K would only account
for 5.2% of the planet’s radius. The reduction in the basal
magma ocean depth occurs due to the relative location of the
solidus with respect to the geotherm, the temperature–pressure
gradient of the planet. The opposite is true for planets >4 M⊕,
where MOSMO structure exists over a wider surface temper-
ature range and at greater pressures.
We also include an analysis of the impact of surface
temperature on the bulk density of a planet. Generally, we find
that bulk density decreases with increasing surface temperature
(Figure 5(B)). The density decrease for Model (1) within
Figure 5(B) demonstrates the effects of the thermal expansion
of solid rock. The bulk density of a lava world decreases at a
higher rate than that of a solid planet at surface temperatures
that only produce a surface magma ocean, demonstrating the
greater thermal expansion of magmas at low pressures.
However, Model (2) and Model (3) exhibit an increase in the
bulk density within the surface temperature range where the
MOSMO structure is present. This result indicates that the
magma is highly compressed under the basal magma ocean
pressure conditions, resulting in a density greater than solid
rock under equivalent conditions. Therefore, the rapid increase
in the basal magma fraction causes a local maximum in the
bulk density before decreasing once the planet is above the
solidus at all depths. Surface temperature, mass, core
Figure 3. Mantles structures produced by our model. We find that the mantle
may be mantle magma ocean, a surface magma ocean and solid rock layer, or a
MOSMO structure (i.e., Surface Magma Ocean (MO)–Solid Rock Layer (S)–
Basal Magma Ocean (MO)).
5

composition, and magma composition all impact the bulk
density of a planet.
3.1. Impacts of Magma Composition
To quantify the effects of magma and volatile composition
on the density of the planet, we calculate the percent difference
between the magma models and Model (1). We use Model (1)
as the control model to determine the impact that the magma
composition has on the mass and radius of the planet. Each
subsequent model is compared with Model (1), as shown in
Figure 6. We set the mass to 4 M⊕ and surface temperature of
each model to Tsurf = 1600 K and Tsurf = 2000 K, considering
the impact of surface temperature on differences in magma
composition.
Generally, we find that all four models behave similarly at
Tsurf = 1600 K compared to Tsurf = 2000 K, with any features
being more prominent at higher surface temperatures. As planet
mass increases, the density difference between a magma ocean
and an equivalent-mass solid planet decreases, reflecting the
effect of steeper pressure gradients in the planet and greater
magma compressibility. At both surface temperatures of both
1600 and 2000 K, Model (4) results in the greatest decrease in
density whereas Model (2) results in the least. Broadly
speaking, all models find that low-mass planets exhibit the
largest fractional inflation due to magma, compared to higher
mass planets. We will focus on the Tsurf = 2000 K results, as
that is the average surface temperature of the known low-
density planets with surface temperatures above 1350 K.
However, we will briefly address the lower surface temperature
model.
As described above, we find that planets at Tsurf = 1600 K
follow similar bulk density trends as a function of planet mass
as those at Tsurf = 2000 K. Model (4) results in the lowest
density, being 4.3% less dense than an equivalent-mass solid
planet at a mass of 0.7 M⊕. Model (2) results in the least
density decrease at 2.9% at a mass of 0.7 M⊕. As mass
increases, we find that the decrease in the bulk density due to
the presence of magma becomes less pronounced, with the
density difference being approximately 0.2% for 10 M⊕. With
the greatest density decrease for planets with a surface
temperature of 1600 K being <4.3%, the inflation due to
magma would be indistinguishable from a solid planet with
observational uncertainties on mass and radius.
For planets at Tsurf = 2000 K, we find distinct differences
from the Tsurf = 1600 K models. At 2000 K, Model (2) results
in the least difference in density when compared to Model (1).
It exhibits the most significant decrease in density of 9.8% at
lower masses and radii, with the largest decrease at a mass and
radius of 0.7 M⊕ and 0.93 R⊕, respectively. This reflects a
planet with a mantle magma ocean mantle ocean with a core–
mantle boundary pressure of 93.6 GPa. As mass and radius
increase, we find that the anhydrous magma becomes more
compressible. Therefore, the anhydrous magma becomes
denser than that of the solid planet (Model (1)). We find that
this planet density crossover occurs at a mass and radius of
3.14 M⊕ and 1.45 R⊕. For the range of masses that we
consider, we find the highest density increase of 2.4%
compared to Model (1) at a radius of 1.83 R⊕.
The carbonated magma composition or Model (3) at
Tsurf = 2000 K results in a moderate decrease in density of
10.4% at a radius of 0.94 R⊕ and mass of 0.7 M⊕. Similarly to
Model (2), the magma becomes more compressible with
increasing mass. At a radius of 1.51 R⊕ and 3.85 M⊕, Model
(3) becomes denser than Model (1), with a maximum density
Figure 4. Phase diagram for each model, showing the mantle structure for a given mass and surface temperature. We include likely lava worlds selected using criteria
described in Section 3. The planets are colored by their bulk density ratio, which is their observed density divided by the expected density assuming an Earth-like
composition. Planets distinguished with white circles and planet names are discussed in detail in Sections 4.2 and 4.3.
6

increase of 1.3%. Compared to Model (2), the planet density
crossover occurs at a higher mass and radius.
Model (4), the hydrous magma, results in the greatest
decrease in density at 11.1% compared to all other models at a
radius of 0.94 R⊕, mass of 0.7 M⊕, and surface temperature of
2000 K. Given the EOS parameters for this magma composi-
tion (see Table 1), we expect the hydrous magma to start at a
lower density. For the mass range that we consider, it would
not become more compressible than the solid planet. However,
we are limited to a smaller range of masses, due to the hydrous
model becoming dynamically unstable at masses greater than
8.7 M⊕. The solid rock layer within the mantle becomes denser
than the basal magma beneath, requiring dynamical
simulations.
3.2. Light Elements in the Core
We explore the impact of light elements in the core,
assuming an Earth-like composition. In Figure 6, we show the
percent difference between the models with pure iron cores to
the models with light alloys in the core. As the mass increases,
the difference in density of the magma compared to an
equivalent-mass solid planet is reduced as a result of the
converging compressibility of the materials with increasing
pressure (planet depth). When considering Earth-like composi-
tions as described by Fe/Mg, the effect of light elements in the
core is to reduce the planet’s density, due to the reduced mass
of the core. However, the radius of the core increases to
account for the added volume of oxygen when Fe/Mg remains
constant. Assuming a pure iron core, a planet with a mantle
magma ocean results in a bulk density difference of ∼−9% at
1 M⊕, and a MOSMO structure results in a ∼2% density
difference at 10 M⊕. The combined effects of a light alloy core
and a magma ocean are ∼−11% and ∼1.5% at 1 M⊕ and
10 M⊕, respectively (Figure 6(B)). Therefore, the impact on the
bulk density is dominated by the effects of the magma ocean at
constant Fe/Mg. This result suggests that the bulk density of an
Earth-like composition lava planet with an Earth-like core
light-element budget and core-mass fraction is more sensitive
to the presence of magma than light elements in the core. The
effects of the presence of light elements are magnified at greater
core-mass fractions, potentially equivalent to the predicted
density deficits of a surface magma ocean (Unterborn et al.
2023).
4. Discussion
4.1. Basal Magma Oceans
Several studies have proposed the potential for basal magma
oceans to exist as a planet cools (Elkins-Tanton et al. 2005;
Labrosse et al. 2007; Pachhai et al. 2022). Magma oceans may
solidify in various ways: downward from the surface, upward
from the core, or outward from the mid-mantle. The behavior
of the solidification is a function of the mantle composition,
and differences in gradient between the melting temperature
and the local geotherm. When a planet solidifies from the mid-
mantle, the magma ocean beneath the rock layer is a basal
magma ocean. However, the inferred mechanical behavior of
the intermediate rock layer changes depending on the melt
curve that is used.
We use the solidus melt curve to identify the existence of a
solid rock layer separating the basal and surface magma. This
differs from a liquidus melt curve, as the rock layer would be a
potentially porous crystal mush (Marsh 1989). The resulting
solid layer that we find could potentially trap volatiles deep
within the mantle, as there would not be a path for them to
outgas. Lava worlds that are continuously bombarded with
radiation from their host star likely have a dry surface melt
(Léger et al. 2011; Kite et al. 2016). Earth-sized planets have
been shown to be inefficient at outgassing their volatiles
(Miyazaki & Korenaga 2022; Salvador & Samuel 2023) over
the timescales of the cooling Earth shortly after formation.
However, it is unclear if long-lived magma oceans can retain
their volatiles over long timescales. For this reason, the
presence of a MOSMO structure is potentially significant for
maintaining large volatiles within the mantle (Labrosse et al.
2007; Edmonds & Woods 2018; Caracas et al. 2019; Bower
et al. 2022), even if the surface magma ocean eventually
degasses. For a 4 M⊕ mass planet with a volatile concentration
similar to those of Model (4) and (3), the presence of a basal
magma ocean could potentially sequester approximately 130
times the mass of the water in Earth’s present-day oceans and
Figure 5. (top) The depth of the solid–melt transition as a function of surface
temperature for a 4 M⊕ planet over a range of surface temperatures. The
pressure on the y-axis corresponds to the hydrous melt (Model (4)). The core–
mantle boundary pressures for all three scenarios are between 573 and
594 GPa. (bottom) We show the bulk planet density for each model as a
function of surface temperature. The increase and decrease for Models (2) and
(3) reflect the competing effects of thermal expansion and compression for a
planet with a MOSMO structure. Additionally, we include Model (1),
demonstrating the effects of thermal expansion on solid rock.
7

1000 times the carbon in the Earth’s surface and crust,
respectively, for the water and carbon contents of the modeled
magma.
For simplicity, we do not consider a thermal boundary layer
within the solid mid-mantle rock layer of the MOSMO
structure. However, a nonconvective solid rock layer with a
thickness of a few kilometers would be enough to cause a
thermal boundary layer (Monteux et al. 2016; Andrault 2019),
resulting in thinning of the mid-mantle solid layer. However, a
fully convective system, in which material melts and solidifies
as it crosses the solid material depth, will reduce the net thermal
boundary layer resulting from producing and consuming the
heat of fusion.
4.2. Lowest-density Planet Produced
To discuss the impact of magma on reducing the density of a
planet, we consider our planet sample of likely lava worlds in
terms of density and radius illustrated in Figure 7. We include
density–radius curves for each of our models for planets with
surface temperatures of 2000 K. Because magma is highly
compressible, the greatest effects of its thermal expansion are
seen at lower pressures or in Earth-sized planets as opposed to
super-Earths. In particular, when considering larger super-
Earthsʼ masses (7–8 M⊕), our results suggest that magma ocean
worlds without an atmosphere would be denser than their
cooler counterparts.
Within our planet sample, TOI-561 b, CoRoT-7 b, and TOI-
500 b have the lowest bulk densities with densities of
3.00 ± 0.80 g cm−3
, 5 ± 1.5 g cm−3
, and -
+ -
4.9 g cm
0.88
1.03 3
,
respectively (Léger et al. 2011; Lacedelli et al. 2021; Serrano
et al. 2022). However, we find that the lowest bulk density
produced by our models for the same planet mass is only
consistent with the measurements for TOI-500 b. For TOI-561
b and CoRoT-7 b, our model overestimates the bulk density by
79% and 50%. If we instead calculate the density with light
elements within the core discussed in Section 3.2, we find a
bulk density of 5.1 and 4.9 g cm−3
for TOI-561 b and CoRoT-7
b. These densities are still 69% and 50% greater. These results
suggest that magma alone cannot account for the decrease in
Figure 6. The percent difference between the bulk density of each magma ocean planet and the solid planet with the corresponding core (i.e., light alloy core or pure
iron core) at surface temperatures of (A) 1600 K and (B) 2000 K. The top axis shows radius values for Model (2). The dashed lines represent models with light-
element alloys in the core, whereas solid lines show models with pure iron cores. Model (2), the anhydrous magma, is shown in purple. Model (3), the hydrous
magma, is shown in teal and has the greatest decrease in density. Model (4), the carbonated magma, is shown in magenta.
Figure 7. Density–Radius plot for each model that is equivalent to a planet
with a surface temperature of 2000 K. We include likely lava worlds selected
using criteria described in Section 3. The planets are colored by their
equilibrium temperatures. Planets distinguished with white circles and planet
names are discussed in detail in Sections 4.2 and 4.3. Model (4), the hydrous
magma, is limited to a radius of 1.7 R⊕, because the density of the magma
becomes greater than the density of the solid in the surface magma ocean,
making it dynamically unstable.
8

planets’ bulk density, assuming they have Earth-like composi-
tions. The impact of magma on the density of a planet is less
than typical observational uncertainties on mass and radius,
such that planets below the expected density for a rocky planet
cannot be explained by the presence of melt.
Assuming an Earth-like composition for low-density planets
requires the presence of an atmosphere regardless of the
presence of a magma ocean. However, there is little evidence to
suggest that a USP planet could sustain a substantial
atmosphere that would significantly decrease the bulk density
of a planet at such close proximity to its host star. Even
assuming the presence of rock vapor atmosphere can only
increase the radius of a super-Earth planet by approximately
1%. For this reason, it may be more likely that these planets
may have significantly different compositions from Earth, with
potentially lower core-mass fractions (Schulze et al. 2021;
Unterborn et al. 2023).
4.3. Known Lava Worlds
Seventy-five percent of the super-Earths that have been
discovered to date are on orbits of less than 10 days. Given the
presence of an atmosphere, ∼50% of these planets have surface
temperatures large enough to sustain a magma ocean (Dorn &
Lichtenberg 2021). However, without an atmosphere, the
majority of these planets would still be able to maintain a
magma ocean on their dayside.
Of the hundreds of super-Earths discovered, only six
planets6
have been discovered with masses and radii that fall
below the potential planet density crossover of 3.14 M⊕ and
1.45 R⊕ at surface temperatures greater than 1350 K. There-
fore, the majority of the hot, relatively low-density planets exist
in the regime where the presence of magma would cause them
to have a slight increase in bulk density if they possess a
magma ocean. For this reason, we cannot attribute the
extremely low densities of some likely lava worlds primarily
to magma. Instead, models addressing hot, relatively low-
density planets should consider an atmosphere or smaller core-
mass fraction in addition to magma.
To investigate the impact of magma on known planets, we
select planets from our planet sample (Section 3) that have a
high probability of being atmosphere-free or having a thin
atmosphere that could not result in significant changes in the
density of the planet. When available, we select likely lava
worlds from our sample evaluated within Schulze et al. (2021)
that have a high probability that the inferred compositions from
mass and radius alone are statistically indistinguishable from
that of their host star at the >1σ level, assuming no
atmosphere. Therefore, we include K2-265 b and WASP-47e,
which have high probabilities of having no more than a thin
atmosphere and a core-mass fraction comparable to their host
star (94% and 80%, respectively) (Schulze et al. 2021).
We also include three additional planets that are likely to be
atmosphere-free or have thin atmospheres adopting the
nominally rocky planet zone (NRPZ) introduced by Unterborn
et al. (2023). The NRPZ is the likelihood that the planet’s
observed mass and radius alone are consistent with the planet
having a bulk rocky composition, without the addition of
significant surface volatiles (Unterborn et al. 2023). We include
HD 80653 b, Kepler-10 b, and K2-141 b, which have
respective NRPZ probabilities of 66%, 60%, and 55%.
Below, we discuss these five likely atmosphere-free lava
worlds. Due to the current observational uncertainties of planet
mass and radius for this population, we cannot distinguish
between Models (1)–(4). However, we include a discussion on
bulk density, to demonstrate that magma alone cannot cause
extremely low densities in planets. We also discuss the required
observational uncertainties to distinguish between a solid
planet and lava world for each planet. Therefore, we choose
Model (4), as it produces the largest differences from Model
(1), the solid planet. We also assume a pure iron core.
We provide the following discussion primarily to consider
the impacts that high surface temperatures may have on the
structure of a planet. By relying on the underlying physics, we
can gain insight into the potential structures that may arise
assuming an Earth-like composition. We consider the potential
melt fraction and structure of the mantle assuming an Earth-like
composition.
4.3.1. K2-265 b
K2-265 b is a short-period planet discovered in 2018 on an
orbit of 2.37 days with a density of 7.1 ± 1.8 g cm−3
(Lam
et al. 2018). It has a mass and radius of 6.54 ± 0.84 M⊕ and
1.71 ± 0.11 R⊕, respectively (Lam et al. 2018). Given the close
proximity its host star, K2-265 b is exposed to strong stellar
irradiation, likely resulting in the photoevaporation and loss of
its atmosphere (Lopez et al. 2012). Assuming the planet is a
blackbody with a zero albedo, the dayside equilibrium
temperature is calculated to be Teq ∼ 1400 K.
Applying Model (4), we find that 1% of the mantle is molten
at the surface, due the low equilibrium temperature. We find the
bulk density to be 7.94 g cm−3
, 11% greater than the measured
density. The density is consistent with a lava world, due to
observation uncertainties; however, it is also indistinguishable
from a solid planet, as Model (1) also produces a bulk density
of 7.95 g cm−3
. With such a small percentage of melt, there is
minimal impact on the bulk density, and the surface magma
ocean is likely entirely degassed. With the low equilibrium
temperature, the uncertainties on mass and radius required to
differentiate a lava world with 1% melt fraction must be less
than 0.01%.
4.3.2. WASP-47 e
WASP-47 e is a USP planet on an orbit of 0.7895 days
(Bryant & Bayliss 2022). It has an observed bulk density of
6.29 ± 0.60 g cm−3
with a mass and radius of 6.77 ± 0.57 M⊕
and 1.808 ± 0.026 R⊕ (Bryant & Bayliss 2022). Assuming a
zero albedo, the dayside equilibrium temperature of the planet
is 2200 K. As it is a well-characterized super-Earth, previous
studies conjecture that the low density of WASP-47 e may be
due to a Ca- and Al-rich interior or the presence of a magma
ocean and secondary atmosphere (Dorn et al. 2019; Gupta &
Schlichting 2021). However, these studies do not account for
effects due to magma within their models.
Applying Model (4) to WASP-47 e, we find that the mantle
has a MOSMO structure. The total melt within the mantle is
88% by volume. The majority of the melt is within the basal
magma ocean within 80%, whereas only 8% of the melt within
the mantle is in the surface magma ocean. The basal magma
ocean, therefore, has the potential to trap a significant inventory
deep in the interior over extended times. Dynamical models of
transport across a solid intra-mantle would be required in order
6
https://exoplanetarchive.ipac.caltech.edu, retrieved 2023 March 27.
9

to determine if outgassing may still be feeding an atmosphere at
the surface.
Considering the density of WASP-47 e, Model (4) produces
a density of 7.89 g cm−3
. Given the uncertainties on the mass
and radius, Model (4) produces a radius that is above the
uncertainties on the observed density. Model (1) produces
similar results, with the bulk density being 7.95 g cm−3
.
Although Model (4) has a slightly lower density, the presence
of a magma ocean would not increase the radius enough to
account for the observed low density. In order to distinguish
between a solid or lava world for WASP-47 e, the uncertainties
on mass and radius required are 0.14% and 0.05%,
respectively. Therefore, it is necessary to invoke compositional
variables, such as a reduced core-mass fraction, or a thick,
unobserved atmosphere in order to account for the low density.
4.3.3. HD 80653 b
Discovered in 2020, HD 80653 b is a USP planet on an orbit
of 0.719 day. It has a mass and radius 5.60 ± 0.43 M⊕ of
1.613 ± 0.071 R⊕, respectively (Frustagli et al. 2020). The
observed bulk density is 7.4 ± 1.1 g cm−3
. Using a zero albedo,
the dayside equilibrium temperature of the planet is 2300 K.
Using Model (4), we find that the mantle of HD 80653 b is a
mantle magma ocean structure, where the magma ocean
extends from the surface to the core–mantle boundary, and
therefore it is unlikely to be able to trap volatiles in the interior
over the age of the system. The calculated bulk density is
7.4 g cm−3
. With Model (1), we find the bulk density to be
7.7 g cm−3
. Therefore, the density of HD 80653 b is consistent
with either a solid or lava world, due to the uncertainties on the
observed mass and radius. To differentiate between Model (1)
and Model (4), the uncertainties required would be 1.8% on
the mass and 0.6% on the radius of the planet.
4.3.4. Kepler-10 b
As the first rocky planet discovered with Kepler, Kepler-10 b
is a well-known USP planet on an orbit of 0.8374 day with a
mass of -
-
3.57 0.53
0.51
M⊕ and radius of -
-
1.489 0.021
0.023
R⊕ (Batalha
et al. 2011; Dai et al. 2019). With an equilibrium temperature
of Teq = -
2130 60
120
K, it is a low-density lava world that does not
deviate far from a solid planet on the density–radius relation-
ship. The observed bulk density is 6.0 ± 1.1 g cm−3
(Dai et al.
2019).
We apply our models to Kepler-10 b with Model (4); the
mantle consists of a mantle magma ocean structure. Similarly
to HD 80653, a magma ocean structure that extends from the
surface to core–mantle boundary is unlikely to be able to trap
volatiles in the interior over the age of the system. The
calculated bulk density is 6.6 g cm−3
. Applying Model (1), we
find the bulk density to be 6.8 g cm−3
. Therefore, a solid or
lava world would be consistent with the observed density, as
they both produce densities that are well within the observa-
tional uncertainties. The required uncertainties on mass and
radius to distinguish between Model (1) and Model (4) are
1.9% and 0.06%, respectively.
4.3.5. K2-141 b
K2-141 b is another USP planet on an orbit of 0.2803 day
with a density of 8.2 ± 1.1 g cm−3
(Barragán et al. 2018;
Malavolta et al. 2018). It has a mass and radius of 5.08 ±
0.41 M⊕ and 1.51 ± 0.05 R⊕ with an equilibrium temperature of
Teq = -
2161 60
120
K (Malavolta et al. 2018). However, K2-141 is
also an active star with strong magnetic activity (Barragán et al.
2018). Therefore, induction heating could also be a potential heat
source for K2-141 b. There is evidence showing that K2-141 b is
inconsistent with a thick atmosphere (Malavolta et al. 2018;
Zieba et al. 2022). However, it could possess a thin rock vapor
atmosphere, but this would not significantly lower the bulk
density. For this reason, we include this planet assuming that is
atmosphere-free, as a thin rock vapor atmosphere would not
significantly impact the density.
Applying Model (4) to K2-141 b, we find the planet to have
a MOSMO structure. The total melt fraction of the mantle is
82% by volume, with the basal magma ocean containing the
majority of the melt (68% by volume). Therefore, the surface
melt accounts for only 14%. As with WASP-47e, the MOSMO
structure has the potential to trap volatiles in its interior with
the basal magma ocean if the solid mid-mantle layer prevents
mass transport to the surface.
Considering the bulk density of the K2-141 b, we apply
Model (4). We calculate the bulk density to be 7.3 g cm−3
.
Model (1) produces a bulk density of 7.4 g cm−3
. Due to the
uncertainties on the mass and radius, both Model (1) and
Model (4) are consistent with the observed density. To
distinguish between the solid planet and magma ocean model,
the uncertainties on the mass and radius must be 0.2% and
0.06%, respectively. However, K2-141 b is a likely lava
world that is denser than expected for a solid Earth-like planet.
Therefore, Model (4) would be more appropriate, but the
observational uncertainties required to distinguish between the
models are not yet achievable. Given that it is denser than
expected for an equivalent-mass solid planet, K2-141 b may
also have significant iron enrichment indicative of an Fe-rich
super-Mercury, in addition to a magma ocean.
5. Summary and Conclusions
Nearly half of the terrestrial planets discovered to date could
maintain magma on their surfaces, in particular on their
dayside. Therefore, it is important to understand the way in
which magma oceans may impact the structures and observable
properties of these likely lava worlds, in order to better
characterize them. Given that many of the likely lava worlds on
USP have yet to detect substantial atmospheres large enough to
significantly decrease its bulk density (e.g., Léger et al. 2011;
Kreidberg et al. 2019; Keles et al. 2022; Zieba et al. 2022),
compositional factors such as the impact of magma or core-
mass fraction must be considered when characterizing these
planets.
In this paper, we investigated the impact of magma on the
1D structure and bulk density of atmosphere-free magma ocean
planets for the following magma compositions: anhydrous,
hydrous, and carbonated magma. The objectives of this study
were to determine whether a magma ocean is observable via the
bulk density of a planet and to determine if volatiles may be
trapped in the interior. Therefore, we constructed our model
using a solidus melt curve placing an upper limit on the impact
of magma on the bulk density of a lava world and placing a
conservative lower limit on the mantle structure. From this
study, we present our primary conclusions:
1. The presence of a magma ocean alone is not sufficient to
explain low-density magma ocean planets that are
10

expected to be atmosphere-free or have thin atmospheres
(Section 4.2).
2. For a given mass, there exists a range of surface
temperatures in which a planet will have a basal magma
ocean, which may sequester a significant amount of
dissolved volatiles (Section 3).
3. The addition of H2O or CO2 to the magma does not
significantly impact the calculated bulk density of a
planet, only resulting in a maximum density difference of
∼1% (Section 3.1).
4. For magma ocean planets that are atmosphere-free, the
presence of magma can impact the bulk density of the
planet, causing two distinct regimes where magma ocean
planets exhibit a planet density crossover that is
dependent on mass and surface temperature. This leads
to two regions where a magma ocean planet may be more
or less dense than an equivalent-mass solid planet for
anhydrous or carbonated magmas (Section 3.1).
5. For an Earth-like core light-element budget and core-
mass fraction, the addition of magma has a greater impact
on the bulk density than the addition of lighter elements
within the core for planets with masses and radii less than
∼3.14 M⊕ and ∼1.45 R⊕ (Section 3.2).
Acknowledgments
K.M.B. acknowledges support from the NSF Graduate
Research Fellowship Program under grant No. (DGE-
1343012). Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the
National Science Foundation. W.R.P. acknowledges support
from NSF under grant No. (EAR-1724693). C.T.U. acknowl-
edges support under grant NNX15AD53G. The results reported
herein benefited from collaborations and/or information
exchange within NASA’s Nexus for Exoplanet System Science
(NExSS) research coordination network sponsored by NASA’s
Science Mission Directorate. J.W. acknowledges the support
by the National Science Foundation under grant No. 2143400.
Software: ExoPlex (Unterborn et al. 2018, 2023; Unter-
born & Panero 2019).
ORCID iDs
Kiersten M. Boley https:/
/orcid.org/0000-0001-8153-639X
Wendy R. Panero https:/
/orcid.org/0000-0001-5753-2532
Cayman T. Unterborn https:/
/orcid.org/0000-0001-
8991-3110
Joseph G. Schulze https:/
/orcid.org/0000-0003-3570-422X
Romy Rodríguez Martínez https:/
/orcid.org/0000-0003-
1445-9923
Ji Wang (王吉) https:/
/orcid.org/0000-0002-4361-8885
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