# A Comparison of the Composition of Planets in Single- and Multi-Planet
Systems Orbiting M dwarfs

Romy Rodríguez Martínez Department of Astronomy, The Ohio State University,
140 W. 18th Avenue, Columbus OH 43210, USA  David V. Martin NASA Sagan Fellow
Department of Astronomy, The Ohio State University, 140 W. 18th Avenue,
Columbus OH 43210, USA  B. Scott Gaudi Department of Astronomy, The Ohio State
University, 140 W. 18th Avenue, Columbus OH 43210, USA  Joseph G. Schulze
School of Earth Sciences, The Ohio State University, 125 South Oval Mall,
Columbus, OH 43210, USA  Anusha Pai Asnodkar Department of Astronomy, The Ohio
State University, 140 W. 18th Avenue, Columbus OH 43210, USA  Kiersten M.
Boley NSF Graduate Research Fellow  Department of Astronomy, The Ohio State
University, 140 W. 18th Avenue, Columbus OH 43210, USA  Sarah Ballard
University of Florida Department of Astronomy, 1772 Stadium Rd, Gainesville,
FL 32607, USA

###### Abstract

We investigate and compare the composition of M-dwarf planets in systems with
only one known planet (“singles”) to those residing in multi-planet systems
(“multis”) and the fundamental properties of their host stars. We restrict our
analysis to planets with directly measured masses and radii, which comprise a
total of 70 planets: 30 singles and 40 multis in 19 systems. We compare the
bulk densities for the full sample, which includes planets ranging in size
from 0.52$R_{\oplus}$ to 12.8$R_{\oplus}$, and find that single planets have
significantly lower densities on average than multis, which we cannot
attribute to selection biases. We compare the bulk densities normalized by an
Earth model for planets with $R_{p}<6R_{\oplus}$, and find that multis are
also denser with 99% confidence. We calculate and compare the core/water mass
fractions (CMF/WMF) of low-mass planets ($M_{p}<10M_{\oplus}$), and find that
the likely rocky multis (with $R_{p}<1.6R_{\oplus}$) have lower CMFs than
singles. We also compare the [Fe/H] metallicity and rotation period of all
single versus multi-planet host stars with such measurements in the literature
and find that multi-planet hosts are significantly more metal-poor than those
hosting a single planet. Moreover, we find that host star metallicity
decreases with increasing planet multiplicity. In contrast, we find only a
modest difference in the rotation period. The significant differences in
planetary composition and metallicity of the host stars point to different
physical processes governing the formation of single- and multi-planet systems
in M dwarfs.

Exoplanet systems – exoplanet structure – exoplanet formation

##  1 Introduction

The NASA $Kepler$ (Borucki et al., 2010) and TESS missions (Ricker et al.,
2015) have discovered hundreds of systems with multiple planets orbiting stars
of almost every stellar type. At the time of writing, we know of $\sim$800
multi-planet systems111https://exoplanetarchive.ipac.caltech.edu/index.html
displaying a staggering diversity of architectures (Winn & Fabrycky, 2015).
This large sample of multis enables statistically meaningful comparisons
between systems with only one detected planet and those with 2 or more. Such a
comparison can provide crucial insights into planet formation and evolution,
as different formation mechanisms may be observably imprinted in the orbital
and physical properties of the planets in these two different architectures.
In addition, a comparison could help elucidate whether single- and multi-
planet systems belong to the same underlying population (but perhaps have
different dynamical histories), or to completely separate planetary
populations.

Several authors have compared the properties of singles and multis222In this
paper, we use the term ‘single’ interchangeably to mean both 1) a planet in a
system in which there is only one (detected) planet, and 2) a system in which
a single planet is known. and their host stars, although the majority have
focused on FGK stars. Wright et al. (2009) compared the distribution of multis
and singles and found that the multis have lower masses and lower
eccentricities. Morton & Winn (2014) found that singly transiting planets have
higher obliquities than those in multiples. Limbach & Turner (2015) found that
for radial velocity (RV) planets, eccentricity decreases with increasing
planet multiplicity. Similarly, Xie et al. (2016) and Van Eylen et al. (2019)
found that singles have significantly higher eccentricities than multis.
Latham et al. (2011) compared a sample of multis and singles and found that
small, sub-Neptunes are more frequent in multis (present in 86${}^{+2}_{-5}$%
of multis) than in singles (69${}^{+2}_{-3}$%). Latham et al. (2011) suggested
that giant planets may disrupt the orbits of sub-Neptunes in flat systems,
either ejecting them or altogether preventing their formation. All of the
aforementioned lines of evidence seem to point to single planets having hotter
or more ‘violent’ dynamical histories than multis. More recently, Weiss et al.
(2018a) compared the planetary and stellar properties of singles and multis in
FGK stars and found no substantial difference in the stellar mass
($M_{\star}$), metallicity ([Fe/H]), and projected rotation speed ($v\sin i$),
nor in the radii and orbital periods of the planets. Weiss et al. (2018a)
interpreted this lack of correlation as indicative of a common origin for
multis and singles and concluded that host star properties are poor predictors
of planet multiplicity, at least amongst FGK stars.

In this paper, we extend this line of research to planets orbiting M dwarfs.
We examine how the fundamental stellar and planetary properties vary for
planets in systems with only one planet versus those in multi-planet systems.
Ballard & Johnson (2016) was one of the first detailed studies of the $Kepler$
M-dwarf sample. They found an excess of single planetary systems, with roughly
half of M-dwarf systems being singles and half multis. This implies that the
so-called Kepler dichotomy seemingly extends to M dwarfs. The Kepler dichotomy
is the discovery of an unexpectedly abundant population of singly-transiting
systems, more than one would expect from transit geometry biases alone. It was
originally discovered based on FGK stars only. Whilst the majority of planet
discoveries and consequent studies have been for FGK stars, the most common
stars ($\approx 70\%$) in the galaxy are the smallest ones: M dwarfs
($M_{\star}<0.6M_{\odot}$). M dwarfs actually have a higher occurrence rate of
small planets (Howard et al., 2012; Mulders et al., 2015; Dressing &
Charbonneau, 2015; Ment & Charbonneau, 2023). There is also intense community
interest in M dwarfs, owing to a shorter-period habitable zone, in which it is
easier to find and characterize potentially habitable worlds (e.g.,
TRAPPIST-1, Gillon et al. 2017 and TOI-700, Gilbert et al. 2020). It is
therefore crucial to understand both the architectures and compositions of
M-dwarf planetary systems, given how they also relate to formation and
habitability.

Most of the existing comparative studies of exoplanet singles and multis have
focused on the differences between the orbital and architectural properties
–such as eccentricity, orbital period and mutual inclinations. In this paper,
we focus on the compositional differences of exoplanets in singles and multis.
To our knowledge, such a comparison is yet to be made in the literature, at
least for M-dwarf planets. Evidence of a dichotomy in planetary composition
between singles and multis could point to different formation or evolution
mechanisms. We also consider here how the planet’s composition is related to
the star’s chemical composition (specifically, the [Fe/H] metallicity), and
how that might vary between singles and multis. If there are significant
differences between the planetary composition of singles versus multiples,
then it would be reasonable to expect differences in the properties of the
parent stars themselves as well since we assume that they formed from the same
protoplanetary disk and thus that planets will inherit some characteristics of
their parent stars. On the other hand, similar stellar properties among the
hosts of multis and singles would be indicative of a common formation
mechanism or origin for these populations. This is something we test.

This paper is organized as follows. In section 2, we describe our sample
selection. In sections 3 and 4, we present a comparison between the properties
of planets in multis and singles and their host stars. Finally, in section 5,
we discuss the implications of our findings and conclude.

##  2 Sample Selection

We selected our targets from the publicly available NASA Exoplanet Archive
(Akeson et al., 2013) on July 2022. In this study, we focus on planets
orbiting M-dwarf stars, so we began by selecting all the stars with effective
temperatures between 2450 K and 4000 K, following the spectral classifications
by Pecaut & Mamajek (2013). To avoid possible contamination by red giants, we
additionally checked that all the stars in our sample had surface gravity
values of log$g_{*}$ $>$ 3.5. This search resulted in 170 M dwarfs hosting a
single (detected) planet and 75 multi-planet hosts. Specifically, 45 stars
host 2 known planets, 19 host 3, 6 host 4, 4 host 5 planets, and only one
hosts 7 (TRAPPIST-1; Gillon et al. 2017). See Figure 1 for a breakdown of the
systems by number of planets.

Figure 1: Histogram showing the distribution of planet-hosting M dwarfs by the
number of planets per star. There are currently 170 systems hosting a single
(detected) planet and 75 systems with 2 or more planets. There are currently
no known M dwarfs hosting 6 planets.

We applied a series of quality cuts to this sample of M-dwarf planetary
systems. First, we selected planets with directly measured masses, and thus we
excluded any planets with only a minimum mass ($m\sin i$) or with masses
determined with empirical mass-radius relationships. There were 100 exoplanets
with direct masses. Of those, we excluded objects with masses above $\sim$13
$M_{\rm Jup}$, which may potentially be brown dwarfs. From the remaining
sample of 91 planets, we additionally removed any objects with upper/lower
mass limits, and objects with calculated (rather than measured) radii (i.e.,
non-transiting planets that have radii calculated by the NASA Exoplanet
Archive using the mass-radius relationships from Chen & Kipping 2017). We
further discarded planets with unphysical bulk densities, $\rho_{p}$, which we
define as anything that falls below the pure iron theoretical mass-radius
curve333These ultra-dense planets could be Super-Mercuries (see, e.g. Santerne
et al. 2018, Adibekyan et al. 2021, Schulze et al. 2021, Rodríguez Martínez et
al. 2023, and Barros et al. 2022), but they have relatively large mass
uncertainties so more observations are needed to robustly determine their
composition. (using the planet interior models from Zeng et al. 2019). These
planets were: Kepler-54c with $\rho_{p}=$ 58 g cm-3 (Steffen et al., 2013),
Kepler-231b with $\rho_{p}=$ 37 g cm-3 (Rowe et al., 2014), and Kepler-327c
with $\rho_{p}=$ 100 g cm-3 (Rowe et al., 2014). This leaves a total of 65
planets. Because of the relatively small sample, we did not impose a cut in
planetary mass/radius uncertainty.

To this sample we added six more exoplanets with revised masses and radii from
the sample of Luque & Pallé (2022). This brings the total number of planets in
our sample with measured masses and radii to 70. They range in mass from 0.06
to 2002 $M_{\oplus}$ (6.2$M_{Jup}$) and in radius from 0.5 to 14 $R_{\oplus}$.
We did not make a cut based on stellar multiplicity. Several planets have
outer stellar companions, but we do not have any circumbinary planets in our
sample. In addition, K2-18b has another planet candidate in the system
(K2-18c) but it has been flagged as “controversial” by the NASA Exoplanet
Archive and therefore, out of caution, we treat K2-18b as a single.444K2-18c
has been recently validated by Radica et al. (2022), however, we do not
include it in our analysis since it does not have a radius measurement. We
note that for the TOI-1685 system, Bluhm et al. (2021) find tentative evidence
for a second planet, but we also treat this system as a single in our
analysis. The same is true for TOI-1201 and GJ 436. Our final sample is shown
in Figure 2 and their properties are listed in Table 3.

Throughout the paper, there are occasions when we make an additional cut of
$R_{\rm p}<6R_{\oplus}$ in the planet sample, such that we can see how the gas
giants potentially skew any distributions. As with the planet sample, we
sometimes also split the stellar sample up as a function of planet radius,
where we separate the $R_{\rm p}<6R_{\oplus}$ planets.

Figure 2: Orbital architectures of representative planetary systems in our
sample. The x-axis shows the orbital periods. The symbol sizes are
proportional to the planets’ radii and they are color-coded by planet mass.
The circles are planets with masses determined from radial velocity
measurements while the triangles represent planets with masses from transit
timing variations (TTV). All of them are transiting exoplanets. They are
sorted by planet multiplicity from top to bottom, with systems with a higher
number of planets at the top.

##  3 Comparison of Planetary Properties

###  3.1 Bulk Density

Figure 3: Left: Histograms of the bulk densities of planets in single-planet
systems (blue), and multi-planet systems (red) for our entire sample of
planets (top) and for planets with $R_{p}<6R_{\oplus}$ (bottom). The red
dashed line shows the median density of the multis while the blue dashed line
shows the median density of the singles. Right: Bootstrapped empirical
cumulative distribution functions (CDF) for our entire sample of planets (top)
and for planets with $R_{p}<6R_{\oplus}$ (bottom). The Kolmogorov-Smirnov
statistic, or $p$ values, of the original distributions are overplotted.
$f_{\rm threshold}$ is explained in Section 4.3. We note that removal of the
dense outliers at $\sim$12 g cm-3 and $\sim$18 g cm-3 does not considerably
affect the observed differences in the density distributions.

Figure 4: Left: Histograms of the bulk density normalized by the density that
an Earth-like planet (i.e., with $\sim$0.30 core mass fraction) would have at
that mass. Single planets are shown in blue and multis in red; all planets
have $R_{p}<6R_{\oplus}$. Right: bootstrapped cumulative distributions.
$f_{\rm threshold}$ is explained in Section 4.3.

We analyzed the differences in bulk density –which is a first-order
approximation for composition– of planets in singles and in multi-planet
systems. The densities were taken from the NASA Exoplanet Archive and they
range from 0.8 to 18 g cm-3. As shown in the left panel of Figure 3, there
seems to be a clear difference between the distribution of densities of
singles and multis: singles have lower densities on average compared to
planets in multis. The median density of the singles is $\rho_{p}=$ 2.2 g cm-3
while the median density of planets in multis is $\rho_{p}=$ 4.57 g cm-3. For
reference, the density of the Earth is $\rho_{\oplus}=$ 5.5 g cm-3.

To test whether the difference in the bulk densities of planets in these two
architectures is statistically significant, we performed a Kolmogorov-Smirnov
(K-S) and an Anderson-Darling (A-D) test for comparison, which test whether
two data sets belong to the same underlying normal distributions. With a
p-value of $p=0.0002$ from the K-S test and $p=0.001$ from the A-D test, we
find that the densities of singles and multis belong to different populations
with over 99% confidence.

We suspect that this big difference between the densities of multis and
singles, however, is mostly due to the presence of single giant planets, which
can be easily seen in Figure 2. This may be driving the density distributions
because a substantial fraction of single planets are massive and therefore
likely to be gaseous and have low densities. We were therefore interested in
making the same density comparison but focusing on smaller planets, which can
be expected to have similar formation pathways. We restricted the sample to
smaller planets with $R_{\rm p}<6R_{\oplus}$. This radius cut removed 9
planets from our full sample: HATS-71b (Bakos et al., 2020), COCONUTS-2b
(Zhang et al., 2021), TOI-530b (Gan et al., 2022a), TOI-3714b (Cañas et al.,
2022), HATS-6b (Hartman et al., 2015), HATS-74 Ab (Jordán et al., 2022),
HATS-75b (Jordán et al., 2022), Kepler-45b (Johnson et al., 2012), and
TOI-1899b (Cañas et al., 2020). For this subset of planets, we find a less
strong difference in their bulk density, which is to be expected, since we
have now removed larger –and thus generally lower-density– planets. The
planets in multis have a median density of $\rho_{\rm p}=4.57$ g cm-3 and the
singles have a median of $\rho_{\rm p}=3.32$ g cm-3. The A-D and K-S
statistics of this restricted sample yield $p$-values of 0.025 and 0.046,
respectively. These results are significant at the 2$\sigma$ ($>$95%)
confidence. The right panel of Figure 3 shows their cumulative distributions.
We discuss potential selection biases that may affect these differences in
density in singles and multis in Section 4.3. We note that the radius cut at
$R_{\rm p}=6R_{\oplus}$ is rather arbitrary, and we therefore reproduce our
analysis with a radius cut at $R_{\rm p}=4R_{\oplus}$, which is another
commonly used size threshold in the literature. Excluding planets with $R_{\rm
p}\geq 4R_{\oplus}$ (15 planets), we get a K-S and A-D statistic of 0.12 and
0.22, respectively. In other words, the bulk density distributions of singles
and multis smaller than $4R_{\oplus}$ are statistically indistinguishable.

In addition to comparing bulk densities, we also consider another
compositional proxy commonly used in the literature. Namely, we calculate the
bulk density normalized by an Earth model, denoted $\rho/\rho_{\oplus,s}$.
This parameter is defined as the bulk density of the planet divided by the
density that an Earth-like planet (i.e., a rocky planet with $\sim$0.32 CMF)
would have at the mass of the planet under consideration. We compute these
density ratios only for planets in our sample with $R_{p}<6R_{\oplus}$, since
larger planets are unlikely to be terrestrial and therefore a density scaled
by an Earth model is not a useful way to characterize them. For this small-
planet sample, we obtain scaled density ratios ranging from 0.07 to 1.62. When
expressed in these units, the density distributions of multis and singles
differ significantly, with K-S and A-D p-values of 0.01 and 0.005,
respectively, implying that they belong to different underlying populations.
This contrasts with our high p-values when using the original bulk densities.
Figure 4 shows the density distribution histograms and the cumulative
distributions.

Figure 5 shows the mass-radius diagram of this sub-sample of small planets
with $R_{p}\lesssim 6R_{\oplus}$ and $M_{p}\lesssim 100M_{\oplus}$ and the
composition curves from the planet interior models of Zeng et al. (2019). The
circles represent planets in multis and the squares are apparently single
planets. The majority of single planets are clustered near or above the 50%
$\rm H_{2}O$/50% magnesium silicate (rock) composition lines, likely requiring
large fractions of water or substantial H/He envelopes to explain their
observed low-density. This is in agreement with our finding that they are
generally less dense than multis (see Figure 3). In contrast, the majority of
the planets in multis are either terrestrial or water-worlds (falling neatly
on the 50% $\rm H_{2}O$/50% or Earth-like lines as was previously shown by
Luque & Pallé 2022). Thus, multis seem more likely to be rocky whereas giant
planets or sub-Neptunes tend to be single. This picture is compatible with the
phenomenon observed in sunlike stars that hot Jupiters tend to be isolated
(Steffen et al., 2012).

We note that there were two planets in our sample that have unusually high
masses and densities that are not expected for rocky planets from planet
formation theories. These are Kepler-54b ($\rho_{\rm p}=12.8$ g cm-3, Hadden &
Lithwick 2014) and Kepler-231c ($\rho_{\rm p}=18.4$ g cm-3, Hadden & Lithwick
2014). These were both discovered and characterized using transit timing
variations (TTV) and have relatively large mass uncertainties of $\sim$25%
(Kepler-54b) and $\sim$50% (Kepler-231c). Thus, it is likely that these
planets are actually less massive than observations suggest. Despite the
relatively large mass uncertainties, we included these planets in our
analysis, since we did not make any cuts based on mass/radius uncertainty
given the relatively small sample size. However, we note that removing these
two planets from our analysis would not significantly affect our results:
without them, the K-S statistic or $p$-value only changes by 0.0001 for the
full sample, and 0.01 for the sample of small planets.

Figure 5: Mass-radius diagram of the planets in our sample with
$R_{p}<6R_{\oplus}$. The colored lines represent mass-radius composition
curves from Zeng et al. (2019). Earth and Venus are also plotted for
reference. The circles represent planets in multi-planet systems and the
squares are singles. The majority of planets above the 100% water line are
single.

###  3.2 Planetary Core/Water Mass Fractions

Previous studies of multi-planet systems have revealed that planets within the
same system tend to have similar radii, orbital spacings (Weiss et al.,
2018b), and masses (Millholland et al., 2017; Goyal & Wang, 2022), such that
they are like “peas in a pod”. Put another way, planets within the same system
have similar bulk densities. This might seem to imply by extension, that their
compositions ought to be similar as well. However, a planet’s bulk density is
degenerate with respect to composition. This degeneracy is reduced when the
planet can be assumed to be rocky (i.e., density greater than pure silicate).
For such planets, the primary constraint on bulk density is the planet’s mass
and core mass fraction (Unterborn et al., 2016), which is defined as the mass
of the core divided by the total mass of the planet as

$\rm CMF=M_{core}/M_{planet}$ (1)

The CMF plays an important role in the existence and lifetime of a magnetic
field, which is, in turn, important for habitability, as it may shield the
planet from high-energy radiation and reduces atmospheric loss (Driscoll &
Barnes, 2015; Green et al., 2021). Although studies have revealed intrasystem
uniformity in terms of mass and radius, whether or not the interior structure
of planets within the same system are similar, and how it varies among singles
and multis, remains an open question.

Figure 6: Representation of the interior structure and core/water mass
fractions for low-mass planets in our sample with $M_{p}<10M_{\oplus}$. The
gray circles are the liquid iron cores and the blue and orange circles
represent water and rocky layers, respectively. The relative sizes of the
circles are proportional to the planet/core/water masses. The numbers above
each planet are the derived water/core mass fractions. The systems are sorted
by planet multiplicity from low (top) to high (bottom) multiplicity.

We therefore now turn our attention to this property and calculate the CMFs of
all planets in our sample with $M_{\rm p}<10M_{\oplus}$ and densities greater
than pure silicate at their mass. To do this, we used the open-source ExoPlex
package (Unterborn et al., 2018; Unterborn & Panero, 2019; Unterborn et al.,
2023), which self-consistently solves the equations of planetary structure
including the conservation of mass, hydrostatic equilibrium, and the equation
of state. We use the ExoPlex parallel mass-radius script, which solves for the
Fe/Mg distribution from a planet’s observed mass and radius distributions, and
calculate the CMF per Eq. 8 of Unterborn et al. (2023). We model planets with
densities greater than pure silicate with a pure, liquid iron core and an
iron-free magnesium silicate ($\rm MgSiO_{3}$) mantle. Planets with densities
less than pure silicate are modeled as “water worlds”. This approach is
reasonable given the findings of Luque & Pallé (2022), who revised the
properties of a large sample of M-dwarf planets and identified a large
population of water-rich planets. We solve for the water mass fraction (WMF)
of each water world by fixing the rocky interior to have 29% iron core and 71%
silicate mantle by mass. Given the degeneracies of the three-layer (Fe-core,
silicate mantle, water) models, studies generally assume the rocky interiors
of terrestrial planets to either be Earth-like or have relative amounts of Fe,
Mg, and Si that reflect their host star’s photospheric abundances of these
materials (e.g., Unterborn et al. (2023) and references therein). Most of the
stars in our sample do not have abundances beyond [Fe/H] and so we assume
their compositions, and therefore the compositions of their planets, reflect
the galactic stellar composition, for which we use the values calculated in
Unterborn et al. (2023) using the Hypatia Catalog Database (Hinkel et al.,
2014), which yield an average rocky interior that is 29% Fe core and 71% $\rm
MgSiO_{3}$ mantle. To constrain WMFs, Exoplex uses the Seafreeze software,
which calculates the physical properties of water like the phase and
thermoelastic parameters. See section 2.4 of Unterborn et al. (2023) for a
more thorough description. See also Aguichine et al. (2021) for a more
detailed exploration of water-world interior modeling.

We calculate core/water mass fractions for a total of 41 exoplanets in our
sample, of which 24 are consistent with being rocky and 17 water-rich. For the
likely rocky planets, we find that the core mass fractions range from 0.07 to
0.87. Similarly, for the potential water worlds, we find water mass fractions
ranging from 0.13 to 0.92. Our core/water mass fraction values are listed in
Table 3. We note that measuring core mass fractions precisely is difficult,
and it is often more reliable for well-measured exoplanets with mass and
radius fractional uncertainties of $\Delta m/m\leq 20\%$ and $\Delta r/r\leq
10\%$, as noted in Schulze et al. (2021). Since some of the planets in our
sample have relatively large mass and radius uncertainties, their CMF
estimates have correspondingly significant uncertainties. Figure 6 shows the
orbital architectures and core/water mass fractions of the planets in our
sample. The orange and blue circles are rocky and water worlds, respectively.

We make note of the compositionally diverse system Kepler-138. This multi-
planet system consists of three small planets with relatively low densities.
We model the innermost planet, Kepler-138b as a rocky planet and obtain a CMF
of 0.24. We model planets c and d as water worlds and obtain WMFs of 0.42 and
0.92, respectively. Jontof-Hutter et al. (2015) determined the masses and
radii of these planets and inferred that, given its extremely low density,
Kepler-138d must have a deep H/He envelope. Recently, Piaulet et al. (2023)
updated the properties of the system and found that, although Kepler-138d is
small (1.5 $R_{\oplus}$), it must have a substantial amount of water, with at
least $11^{+3}_{-4}$% volatiles/water by mass or $\sim$51% by volume. We find
a much higher WMF for Kepler-138d because we adopted the mass and radius of
Jontof-Hutter et al. (2015) instead. Regardless, this is an interesting system
that shows that small planets can be significantly volatile-rich and that
there can be a wide range of compositions within systems of similarly sized
worlds.

We compare the core mass fractions of the singles and multis for the likely
terrestrial planets in our sample. Excluding planets with orbital periods
longer than 5 days, we find that the error-weighted average of the CMFs of the
singles and multis is 0.51 $\pm$ 0.07 and 0.23 $\pm$ 0.02, respectively. This
appears to be in slight tension with our finding that the multis are denser
than singles on average, given that one would naively expect denser planets to
have higher core mass fractions. However, this is because the sample we used
to compare bulk densities is a different sample than that of planets with CMF
measurements. The former includes planets with $R_{p}<6R_{\oplus}$, while the
latter includes only low-mass planets with $M_{p}<10M_{\oplus}$, which in our
sample corresponds to a radius range of $R_{p}<1.6R_{\oplus}$. We do not
compare the WMFs of singles and multis, since the vast majority of water
worlds reside in multi-planet systems.

Figure 7: Left: Core mass fraction as a function of orbital period for the 24
likely rocky planets in our sample with $M_{p}<10M_{\oplus}$. The blue, and
red horizontal dashed lines are the weighted average CMFs of the singles and
multiples, respectively. We do not find any correlation between CMF and
period. The red and blue bands are $1\sigma$ confidence intervals on the mean.
Right: Core/Water mass fractions as a function of planet mass. The circles are
multis and squares are singles. The Earth, with a CMF of 0.33, is plotted for
reference in both plots.

We also explore the correlation between CMF and semi-major axis, or orbital
period. In Figure 5 of Rodríguez Martínez et al. (2023), we show a trend with
density and equilibrium temperature of known planets with $M_{\rm
p}<10M_{\oplus}$: the densest planets appear to have higher equilibrium
temperatures (or equivalently, smaller semi-major axes) than volatile-rich
planets. This may be a result of photoevaporation: short-period planets become
smaller and denser after their primordial H/He envelopes are evaporated due to
the high irradiation from their host stars (Owen & Wu, 2017). Alternatively,
this may support the theory that the densest planets form in the inner regions
of the protoplanetary disk where there may be a greater supply of iron
compared to other elements (McDonough & Yoshizaki, 2021). One potential
observational signature of this is that the CMF would be inversely
proportional to distance from the host star, since CMF is essentially the
amount of iron in a planet. However, as shown in the left panel of Figure 7,
we do not see any trends between CMF and orbital period, at least by eye, for
either singles or multis. This agrees with the findings of Plotnykov &
Valencia (2020), who measured the core mass fractions of a sample of rocky
planets and did not see any correlation between CMF and insolation (which is
proportional to orbital period), shown in Figure 5 of their paper. One might
also expect to see a gradual decrease (or gradient) in iron, or equivalently,
in CMF, as a function of distance within a given planetary system. In other
words, we might expect the innermost planets in multi-planet systems to be
more iron-rich than their outer siblings. In fact, Barros et al. (2022)
characterized the HD 23472 system, which contains 5 small planets orbiting a
K-dwarf, and they found a clear decrease in the core mass fractions of the
planets with increasing period. Similarly, they found that the water and gas
mass fraction increases as a function of period such that the innermost
planets are dry and dense and the outermost ones have much larger fractions of
water and gas. However, we do not see a trend with CMF and orbital period
within individual planetary systems either, as shown in Figure 6. Regarding
the question of whether there is intra-system uniformity in terms of core mass
fractions, (or whether CMFs are similar for exoplanets in the same system), we
observe a variety of CMF values within multi-planet systems, which possibly
argues against any uniformity (see Figure 6). However, we note that there are
less than ten muli-planet systems in our sample with two or more CMF or WMF
measurements, so it is hard to quantify the uniformity given the small sample
size.

Exploring the connection between CMF and orbital period or insolation may
inform theories of planet formation and evolution and therefore it is worth
investigating this further, perhaps by extending this analysis to multi-
planetary systems orbiting sunlike stars. Such analysis is beyond the scope of
this paper, however. Finally, in the right panel of Figure 7, we plot the
core/water mass fractions as a function of planet mass. Interestingly, we do
not see a strong dependence of CMF/WMF on planet mass for either singles or
multis.

##  4 Comparison of Stellar Properties

Table 1: Statistics of Planetary and Stellar Properties  Property | Kolmogorov-Smirnov | Anderson-Darling | Median | $N_{\rm systems}$
---|---|---|---|---
|  |  | (Multi, Single) |
Planetary Bulk Density (Full sample) | 0.0002 | 0.001 |  (4.57, 2.20 g/$\rm cm^{3}$) | 70
Planetary Bulk Density ($R_{\rm p}<6R_{\oplus}$) | 0.046 | 0.025 |  (4.57, 3.32 g/$\rm cm^{3}$) | 61
Stellar Metallicity (All planet hosts) | 0.0009 | 0.001 |  ([Fe/H] = $-$0.09, 0.0) | 221
Stellar Metallicity (Hosts of $R_{\rm p}<6R_{\oplus}$) | 0.009 | 0.001 |  ([Fe/H] = $-$0.1, $-$0.03) | 192
Stellar Rotation Period (All planet hosts) | 0.066 | 0.051 | (60, 39 days) | 80
Stellar Rotation Period (Hosts of $R_{\rm p}<6R_{\oplus}$) | 0.237 | 0.151 | (56, 42 days) | 72

We compared the stellar rotation periods and [Fe/H] metallicities of all
M-dwarf hosts of multis and singles with those reported properties in the
literature. For each property of interest, we excluded stars for which there
were no reported uncertainties in the NASA Exoplanet Archive. The rotation
period and metallicity values of our samples have a mean uncertainty of 3.5
days and 0.12 dex, respectively.

###  4.1 Stellar Rotation Period

Figure 8: Left: Histograms of the rotation periods of single- (purple) and
multi-planet (pink) host stars for the full sample (top) and for the sub-
sample excluding $R_{p}\geq 6R_{\oplus}$ planet host stars (bottom). The
vertical dashed lines denote the median values of each distribution. Right:
Empirical cumulative distribution functions of the samples, with their
Kolmogorov-Smirnov statistic values overplotted. $f_{\rm threshold}$ is
explained in Section 4.3.

We found 80 M dwarfs with rotation period measurements in the literature: 58
hosting single planets and 22 hosting multiple. The rotation periods range
from 1.4 to 168.3 days. We find that the multis are slightly slower rotators,
with a median rotation period of 60 days, while the singles have a median
rotation of 39 days. With a K-S statistic of 0.06, these distributions are
only marginally statistically different. Since the stellar rotation period is
generally considered a proxy for youth, as stars spin down with age
(Skumanich, 1972), multi-planet hosts may be older on average than single-
planet hosts. However, there is the caveat that young stars/rapid rotators are
also more magnetically active, which in turn can negatively affect the
sensitivity to planet detections. Thus, it is possible that the higher
prevalence of multis around slow rotators (older stars) is at least partly a
consequence of the higher RV sensitivity around those stars compared to faster
rotators (younger stars).

If we remove hosts of Neptune-sized and larger planets ($R_{p}\geq
6R_{\oplus}$), we get 72 stars: 51 singles and 21 multis. The median rotation
of the singles and multis is 42 and 56 days, respectively. The K-S statistic
yields $p=0.23$, indicating that they are likely drawn from the same
distribution and are statistically indistinguishable. The bottom two panels of
Figure 8 show the rotation periods for hosts of singles and multis for the
full sample (top) and for the subset of stars hosting planets with
$R_{p}<6R_{\oplus}$ (bottom).

###  4.2 Stellar Metallicity

We found 221 M dwarfs on the NASA Exoplanet Archive with reported [Fe/H]
metallicities ranging from $-$0.59 to +0.52 dex. Of these, 148 host single
planets, and 73 host multiples. We find that stars hosting multiple planets
are more metal-poor than those hosting only one planet. The multi-planet hosts
have a median metallicity of [Fe/H] $=-0.09$ while the single-planet ones have
a median of [Fe/H] $=0.0$. This difference is highly statistically
significant, with a K-S statistic of 0.0009 and A-D statistic of 0.001. If we
exclude hosts of planets with $R_{p}\geq 6R_{\oplus}$, we get 192 stars: 125
hosting single planets and 67 hosting multiples. The multis have a median
metallicity of [Fe/H] $=-0.1$ and the singles [Fe/H] $=-0.03$. This difference
is less strong than with the full sample, however, with a K-S statistic of
0.009 (see the top two panels of Figure 9 and Table 1 for a summary of both
K-S and A-D statistic values). This difference between the full sample and the
subset without the giant planets possibly suggests that these larger planets
are skewing the observed metallicity distribution in the full sample of
planets. This may be hinting at the existence of a scaled-down population of
Saturn-mass, short-period giant planets around M dwarfs, analogous to the
population of hot Jupiters around sunlike stars, which, as is well known, are
isolated and more frequently found around metal-rich stars (Steffen et al.,
2012; Fischer & Valenti, 2005). In fact, we note that all the planets with
radii larger than $6R_{\oplus}$ in this sample are seemingly isolated and they
have masses and radii between $\sim$ 100-200 $M_{\oplus}$ (except for
HATS-74Ab and COCONUTS-2b, which have significantly larger masses), closer to
the mass of Saturn (95$M_{\oplus}$). They also orbit predominantly metal-rich
(0 $<$ [Fe/H] $<$ 0.5, with a median [Fe/H] of $\sim$0.3), early M dwarfs
(M0-M3). This population may also be seen in the left panel of Figure 10,
which shows planet radius as a function of metallicity for singles and multis
(color-coded in blue and red, respectively). There are significantly more
large, single planets orbiting stars with solar and supersolar metallicities
than subsolar metallicity stars. Likewise, there is an apparent lack of multis
orbiting metal-rich stars. Beyond [Fe/H] $\sim$ 0.1 dex, the majority of
systems are single. The right panel of Figure 10 shows the same sample but we
plot planet radius as a function of orbital period. It is difficult to draw
any robust conclusions yet, however, given the small number of known
transiting giants around M dwarfs. The core-accretion theory of planet
formation predicts giant planets to be rare around M dwarfs and several
studies find low occurrence rates for such planets (Schlecker et al., 2022;
Gan et al., 2023; Bryant et al., 2023). Gan et al. (2022a) explored the
correlation between giant planets and stellar metallicity for M dwarfs and
compared it to the metallicity correlation for sunlike stars. They found that
transiting giants around M dwarfs orbit mostly metal-rich M dwarfs. Overall,
including both RV-only and transiting giants, the median metallicity of an
M-dwarf hosting a giant is higher than the median metallicity ([Fe/H]$\sim
0.13$ dex) of a sunlike star hosting a giant (see their Figure 12). They
conclude that giants orbit predominantly metal-rich stars, indicating that
(transiting) giant planets have a strong host star metallicity dependence, as
predicted by core-accretion theory. This is also consistent with the findings
of Maldonado et al. (2020), who discovered a strong correlation between having
a high metallicity and the probability of hosting a giant planet for M dwarfs.

Figure 9: Left: Histograms of the [Fe/H] of the single- (purple) and multi-
planet (pink) host stars for the full sample (top) and for the sub-sample
excluding $R_{p}\geq 6R_{\oplus}$ planet host stars (bottom). The vertical
dashed lines denote the median values of each distribution. Right: Empirical
cumulative distribution functions of the samples, with their Kolmogorov-
Smirnov statistic values overplotted. $f_{\rm threshold}$ is explained in
Section 4.3.

We further investigated stellar [Fe/H] metallicity as a function of planet
multiplicity for systems with 1, 2, 3, and 4 or more planets. The error-
weighted average [Fe/H] metallicity for 1, 2, 3, and 4+ planet host stars is
$-0.01$, $-0.11$, $-0.13$, $-0.18$, dex, respectively. As illustrated in the
top panel of Figure 11, there is an apparent downward trend of metallicity
with planet multiplicity, such that metallicity appears to decrease with
increasing number of planets. The error bars show the dispersion in the values
of stars with N planets, where N goes from 1 to 4+. We model this relationship
with a straight line and find a significant anti-correlation between these two
parameters, namely

$\rm[Fe/H]=-0.062~{}(\pm 0.016)\times N_{\rm p}-0.047~{}(\pm 0.026),$ (2)

where $N_{\rm p}$ is number of planets.

We repeated this analysis excluding hosts of planets larger than
$6R_{\oplus}$, and we find a similar negative correlation between metallicity
and planet multiplicity (see bottom panel of Figure 11). It should be noted
that this analysis naturally only includes M dwarfs that have metallicity
measurements and therefore these lists are not complete. This fraction of
stars with metallicity measurements may be biased in some unknown way.
Furthermore, we point out that there is some uncertainty associated with the
number of planets itself, as there are several systems in our sample that
contain “controversial” planets in the literature, and whose designation as a
candidate or real planet may affect the trends that we see. This uncertainty
is very difficult to quantify.

A comparison between the metallicity of singles and multis has been previously
explored by several authors. For example, Weiss et al. (2018b) compared the
metallicities of single- and multiply- hosting FGK stars from the California-
Kepler Sample (CKS) and found no significant difference between them (with a
$p=0.29$). Similarly, Munoz Romero & Kempton (2018) compared the metallicities
of single and multiple-planet FGK host stars using values from the CKS survey
and did not find any significant differences. On the other hand, Brewer et al.
(2018) found that compact, multi-planet systems occur more frequently around
(FGK) stars of lower [Fe/H] metallicities. Anderson et al. (2021) also found a
higher prevalence of compact multis around metal-poor M- and late K-dwarfs.
Our results are more in line with Brewer et al. (2018) and Anderson et al.
(2021).

Figure 10: Left: Planet radius as a function of stellar [Fe/H] metallicity for
all planet hosts with measured metallicities. The points are color-coded by
planet multiplicity. Right: Planet radius as a function of orbital period for
the same sample on the left.

Figure 11: Average [Fe/H] metallicity of M dwarfs hosting 1, 2, 3, and 4+
planets for our full sample (top) and for the subset of planets with
$R_{p}<6R_{\oplus}$ (bottom). The error bars show the dispersion in the
metallicity for each multiplicity. The shaded blue region shows the confidence
interval for the slope.

###  4.3 Consideration of Selection Biases

One important caveat of this study is the uncertainty in planet multiplicity;
namely, that a non-negligible fraction of the observed singles may be multis
in which other hidden planets eluded detection555This is not a concern with
multi-planet systems, however, which we consider to be true multis, following
the statistical arguments from Lissauer et al. (2012, 2014); Rowe et al.
(2014).. Ballard (2019) found that roughly one third of TESS M-dwarf single-
planet systems are expected to have one or more additional planets that are
missed by TESS. There are 18 single planets discovered by TESS in our sample
(of 30 singles in total). The rest of the singles were discovered by ground-
based surveys (9 planets) or by Kepler/K2 (3 planets). Here we analyze the
effects that instrument detection completeness may have on our results.
Specifically, we investigate what the bulk density and stellar metallicity
distributions look like if we assume that a third of the singles are actually
multiples. We focused on these properties since those are the ones for which
we find a significant difference between singles and multis.

We performed a bootstrap analysis in which we randomly changed the
multiplicity designation of one third of the TESS singles 1000 times. We then
compute the K-S statistic and cumulative distribution for each of the randomly
generated samples. The right panels of Figure 3 show all the bootstrapped
cumulative distributions for the bulk density of the full sample (top) and the
subset of small planets (bottom). In each plot, $f_{\rm threshold}$ is the
fraction of bootstrapped values that have a K-S statistic below 0.01 (99%
confidence), which is our conservative threshold for statistical significance.
In the case of the bulk density of the full sample, about 83% of the
bootstrapped samples are below 0.01. This fraction is high enough that we
conclude that detection completeness does not significantly affect the
observed difference in density between the singles and multis. For the sample
of small planets, the K-S statistic of the true, observed distributions is
lower (K-S = 0.04), and thus $f_{\rm threshold}$ is lower as well ($f_{\rm
threshold}=4.70\%$) and therefore detection completeness does affect this
difference more strongly.

For the stellar metallicity, we get a lower fraction of values below 0.01 for
both the full sample ($f_{\rm threshold}=54\%$) and for the subset of small-
planet hosts ($f_{\rm threshold}=10.6\%$). See the top two right panels of
Figure 9. Thus, the difference in metallicity between the singles and multis
is less robust than the difference in planet density and should be interpreted
more cautiously.

We also consider the extent to which detection and characterization methods
bias the observed difference in density in multis and singles. Within our
sample of multi-planet systems, roughly half have masses obtained through
transit timing variations and half have masses from radial velocities. Within
the full sample, 14 have masses from TTVs, and 56 have RV masses. All the
single planets are entirely detected through RVs, since TTVs are only
measurable in multi-planet systems.

The signal-to-noise ratio of TTV signals has a strong direct dependence on
planet radius and orbital period (unlike RV data), and therefore TTVs can
measure lower masses than RVs for both larger planets and/or at longer
periods. The strong sensitivity to $R_{p}$ also implies that TTV planets will
generally have lower densities than RV planets of the same mass. This is
visible in the mass-radius distribution of RV and TTV planets in Figure 1 of
Steffen (2016) (made with data from Wolfgang & Lopez 2015) and in Figure 5 of
Jontof-Hutter et al. (2015). However, in this work, we find that planets in
multi-planet systems (most of which have TTV masses) are actually denser than
single (RV) planets, which is the opposite of what we would expect if
detection biases played a role in the observed density distributions of multis
and singles.

On the other hand, although the RV method is more sensitive to more massive
planets, we expect lower mass (denser) planets to have been detected if they
existed, in systems where only one planet was found via RV (at least within
$\sim$30 days, which is the longest period for the planets in our sample). We
have already tested the former assumption with the bootstrap analysis
discussed above, and we find that even if we assumed that there were
additional planets in one third of the TESS singles (all of which have RV
masses and which comprise the majority of the singles in our sample), it would
not significantly affect the observed difference in bulk density between the
singles and multis. In summary, we conclude that the observed differences in
the planetary bulk density and stellar metallicity we find here (at least for
the full samples of planets and stars) cannot be attributed to detection
completeness or to detection/characterization methods.

Finally, we recognize that Figure 2 shows a different orbital period
distribution of singles and multis, which will likely be a combination of the
true distributions in nature and a reflection of our observational biases.
Most of the singles have a period between 1 and 5 days. Only two singles have
periods longer than 10 days. Most of the multis have an innermost planet
between 1 and 5 days, but the majority of multis include at least one planet
beyond 10 days.

A possible “natural” explanation is that the M-dwarf singles contain more gas
giants, which seem to be lonely, as is the case around FGK stars. If their
formation mechanism includes high eccentricity migration, either from planet
scattering or Kozai-Lidov cycles, then this may destabilize any nearby planets
at longer periods. Another natural explanation is that multis are believed to
migrate in resonant chains, which are typically then disrupted but sometimes
preserved (as is the case for TRAPPIST-1). This resonant chain migration would
lead to a short-period inner planet, like the ones seen between 1 and 5 days,
and a string of planets out beyond 10 days. With respect to observing biases,
as previously mentioned, TTVs are generally more sensitive than RVs to planets
at a given mass and period. This would bias the singles to shorter periods.

If there is a bias in the orbital period distribution between the singles and
multis, then it is natural to consider what effect it would have on our
results. According to the ‘peas in a pod” paradigm for multi-planet systems,
there is intra-system radius uniformity. This means that comparing singles,
with periods $\sim$1-5 days, to multis with periods $\sim$1-25 days, may be
reasonable because the long-period planets in multis are similar to the short-
period planets. With the recent advent of spectrographs with redder wavelength
sensitivity, such as KPF (Gibson et al., 2016), HPF (Mahadevan et al., 2012),
NIRPS (Bouchy et al., 2022), MAROON-X (Seifahrt et al., 2018) and SPIRou
(Artigau et al., 2014), that are more suitable for M dwarfs, it is hoped that
the population of longer period single planets around M dwarfs will grow.

##  5 Discussion and Conclusions

In this paper, we have calculated and compared the properties and interior
composition of planets in single- versus multiple-planet systems around M
dwarfs. In addition, we have compared the fundamental properties of M dwarfs
hosting a single versus multiple planets. Our main conclusions are as follows:

1\. The bulk density of planets in multi-planet systems is significantly
higher than that of singly-transiting planets (with a $p$-value of 0.0002). If
we remove larger planets with $R_{\rm p}\geq 6R_{\oplus}$, this difference
remains but is less significant ($p=0.046$). We cannot attribute these
differences in composition to selection biases.

2\. We measured the core mass fractions of the likely rocky, low-mass planets
in our sample ($M_{\rm p}<10M_{\oplus}$, which corresponds to
$R_{p}\lessapprox 1.6R_{\oplus}$ in our sample) and we find that on average,
single planets have considerably higher core mass fractions than the multis
(0.51 $\pm$ 0.07 versus 0.23 $\pm$ 0.02). We do not see correlations between
core/water mass fraction (CMF/WMF) and orbital period nor between CMF/WMF and
distance from the host star within individual planetary systems.

3\. We compare the [Fe/H] metallicity and rotation period of all single- and
multi-planet M-dwarf hosts with such measurements in the literature. We find a
statistically significant difference between the metallicity distributions of
singles and multis; namely, that the hosts of singles are significantly more
metal-rich than those hosting multiple planets ($p=0.0009$). If we remove
larger planets ($R_{\rm p}\geq 6R_{\oplus}$), this difference is less strong
($p=0.009$) and less robust to selection effects and detection completeness.
On the other hand, we find only a moderate difference between the rotation
period distributions, with multis being slightly slower rotators on average
($p=0.06$).

4\. All the transiting planets in our sample larger than $6R_{\oplus}$ are
single and they orbit early type (M0-M3), metal-rich (median of [Fe/H] = 0.3
dex) M dwarfs. This metallicity is higher than the average metallicity of a
sunlike star ([Fe/H] $\sim$ 0.13 dex) hosting a giant, per Gan et al. (2022a).
This possibly indicates that the strong metallicity dependence observed for
sunlike stars (Fischer & Valenti, 2005; Santos et al., 2004; Wang & Fischer,
2015) also holds for M-dwarf giant planets. This agrees with results from
previous authors (Maldonado et al., 2020; Gan et al., 2022a).

Thus, our work reveals two notable features of the M-dwarf planetary
population. First, there appears to be a clear difference in the bulk density
of M-dwarf planets such that single planets are significantly less dense than
those in multi-planet systems. Second, the metallicity of multi-planet host
stars is lower on average than those of singles. Moreover, the number of
observed planets increases with decreasing host star metallicity. These two
observations combined are suggestive of a divergence in the formation
mechanisms of multis and singles.

One possibility we consider is that metal-rich hosts give rise more often to
the formation of giant planets, whereas metal-poor M dwarfs could
predominantly favor the formation of low-mass, rocky planets in flat
(coplanar), compact, and dynamically “quiet” configurations that are stable
over long timescales. This could be because higher metallicity protoplanetary
disks are more massive, and thus there is more available material to form more
massive, giant planets. The idea that multis and singles come from different
underlying populations (at least for sunlike stars) is also supported by
previous authors who have found significant differences in their obliquities
(Morton & Winn, 2014) and eccentricities (Limbach & Turner, 2015; Xie et al.,
2016; Van Eylen et al., 2019; Sagear & Ballard, 2023). In our own sample,
single planets have higher eccentricities on average than those in multiples
($e_{\rm singles}=0.14$ and $e_{\rm multis}=0.08$), in agreement with the
literature. Alternatively, it is possible that multis and singles may have a
common physical origin, or come from the same underlying population, but
evolve in vastly different ways, given their significantly different planetary
architectures and compositions. However, this possibility seems less likely
given that singles and multis have markedly different host star metallicity
distributions, as shown here. The trends and conclusions in this paper could
be better tested with a larger sample of well-characterized M-dwarf planets.
There are currently $\sim$500 TESS planet candidates orbiting M dwarfs, in
agreement with predictions (Barclay et al., 2018; Ballard, 2019). The
validation and characterization of these candidates will enable much stronger
conclusions about the differences between singles and multis. In addition, it
remains to be seen whether the observed trends in M-dwarf planets also hold
for sunlike stars, and the role that stellar metallicity plays in such trends.
It would also be interesting to see whether these correlations in [Fe/H]
metallicity are also seen with other rock-forming, refractory elements, such
as with Si and Mg. We could not make these comparisons because most of the
stars in our sample do not have reported Si and Mg abundances in the
literature. Nevertheless, the trends shown here begin to offer clues about the
formation and evolution of single- and multi-planet systems and motivate
further theoretical work into this area.

RRM and BSG were supported by the Thomas Jefferson Chair for Space Exploration
endowment from The Ohio State University. RRM acknowledges support from the
Presidential Fellowship granted by The Ohio State University. RRM acknowledges
Jack Neustadt for insightful conversations that improved this manuscript.
Support for DVM was provided by NASA through the NASA Hubble Fellowship grant
HF2-51464 awarded by the Space Telescope Science Institute, which is operated
by the Association of Universities for Research in Astronomy, Inc., for NASA,
under contract NAS5-26555. APA acknowledges the support of the NASA NSTGRO
fellowship under contract number 80NSSC22K1197. This research has made use of
the NASA Exoplanet Archive, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space
Administration under the Exoplanet Exploration Program.

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Table 2: Planet Properties

Planet Name | Orbital Period | Mass | Radius | Bulk density |  $\\#$ Planets | CMF or | Reference
---|---|---|---|---|---|---|---
| (days) | ($M_{\oplus}$) | ($R_{\oplus}$) | (g cm-3) |  | WMF |
TRAPPIST-1 b | 1.510826 | 1.374 $\pm$ 0.069 | 1.11${}^{+0.014}_{-0.012}$ | 5.44${}^{+0.26}_{-0.27}$ | 7 | CMF = 0.24 $\pm$ 0.07 | Agol et al. (2021)
TRAPPIST-1c | 2.421937 | 1.308 $\pm$ 0.056 | 1.097${}^{+0.014}_{-0.012}$ | 5.46${}^{+0.22}_{-0.24}$ | 7 | CMF = 0.30 $\pm$ 0.07 | Agol et al. (2021)
TRAPPIST-1 d | 4.049219 | 0.388 $\pm$ 0.012 | 0.788${}^{+0.011}_{-0.010}$ | 4.37${}^{+0.15}_{-0.17}$ | 7 | CMF = 0.16 $\pm$ 0.04 | Agol et al. (2021)
TRAPPIST-1 e | 6.101013 | 0.692 $\pm$ 0.022 | 0.92${}^{+0.013}_{-0.012}$ | 4.90${}^{+0.17}_{-0.18}$ | 7 | CMF = 0.22 $\pm$ 0.07 | Agol et al. (2021)
TRAPPIST-1 f | 9.20754 | 1.039 $\pm$ 0.031 | 1.045${}^{+0.013}_{-0.012}$ | 5.02${}^{+0.14}_{-0.16}$ | 7 | CMF = 0.17 $\pm$ 0.06 | Agol et al. (2021)
TRAPPIST-1 g | 12.352446 | 1.321 $\pm$ 0.038 | 1.129${}^{+0.015}_{-0.013}$ | 5.06${}^{+0.14}_{-0.16}$ | 7 | CMF = 0.15 $\pm$ 0.06 | Agol et al. (2021)
TRAPPIST-1 h | 18.772866 | 0.326 $\pm$ 0.02 | 0.755 $\pm$ 0.014 | 4.16${}^{+0.32}_{-0.30}$ | 7 | CMF = 0.12 $\pm$ 0.06 | Agol et al. (2021)
LHS 1140 b | 24.73694 | 6.38${}^{+0.46}_{-0.44}$ | 1.635 $\pm$ 0.46 | 8.04${}^{+0.84}_{-0.80}$ | 2 | CMF = 0.36 $\pm$ 0.12 | Lillo-Box et al. (2020)
LHS 1140 c | 3.77792 | 1.76${}^{+0.17}_{-0.16}$ | 1.169${}^{+0.037}_{-0.038}$ | 6.07${}^{+0.81}_{-0.74}$ | 2 | CMF = 0.34 $\pm$ 0.15 | Lillo-Box et al. (2020)
K2-25 b | 3.48456408 | 24.5${}^{+5.7}_{-5.2}$ | 3.44 $\pm$ 0.12 | 3.31 $\pm$ 0.20† | 1 |  | Stefansson et al. (2020)
GJ 1214 b | 1.58040433 | 8.17 $\pm$ 0.43 | 2.742${}^{+0.050}_{-0.053}$ | 2.2${}^{+0.17}_{-0.16}$ | 1 |  | Cloutier et al. (2021a)
GJ 1132 b | 1.628931 | 1.66 $\pm$ 0.23 | 1.13 $\pm$ 0.056 | 6.3 $\pm$ 1.3 | 2 | CMF = 0.40 $\pm$ 0.22 | Bonfils et al. (2018)
LTT 3780 b | 0.768448 | 2.62${}^{+0.48}_{-0.46}$ | 1.332${}^{+0.072}_{-0.075}$ | 6.1${}^{+1.8}_{-1.5}$ | 2 | CMF = 0.24 $\pm$ 0.26 | Cloutier et al. (2021a)
LTT 3780 c | 12.2519 | 8.6${}^{+1.6}_{-1.3}$ | 2.3${}^{+0.16}_{-0.15}$ | 3.9${}^{+1.0}_{-0.9}$ | 2 | WMF = 0.90 | Cloutier et al. (2021a)
GJ 486 b | 1.467119 | 2.82${}^{+0.11}_{-0.12}$ | 1.305${}^{+0.063}_{-0.067}$ | 7.0${}^{+1.2}_{-1.0}$ | 1 | CMF = 0.40 $\pm$ 0.17 | Trifonov et al. (2021)
LTT 1445 A b | 5.3587657 | 2.87${}^{+0.26}_{-0.25}$ | 1.305${}^{+0.66}_{-0.61}$ | 7.1${}^{+1.2}_{-1.1}$ | 2 | CMF = 0.41 $\pm$ 0.20 | Winters et al. (2022)
LTT 1445 A c | 3.1239035 | 1.54${}^{+0.20}_{-0.19}$ | 1.147${}^{+0.55}_{-0.54}$ | 5.57${}^{+0.68}_{-0.60}$ | 2 | CMF = 0.26 $\pm$ 0.23 | Winters et al. (2022)
TOI-2136 b | 7.851928 | 6.37${}^{+2.45}_{-2.29}$ | 2.19 $\pm$ 0.17 | 3.34${}^{+2.55}_{-1.63}$ | 1 |  | Gan et al. (2022b)
GJ 3473 b | 1.1980035 | 1.86 $\pm$ 0.30 | 1.264 $\pm$ 0.05 | 5.03${}^{+1.07}_{-0.93}$ | 2 | CMF = 0.07 $\pm$ 0.24 | Kemmer et al. (2020)
GJ 3929 b | 2.6162745 | 1.21${}^{+0.40}_{-0.42}$ | 1.15${}^{+0.040}_{-0.039}$ | 4.4 $\pm$ 1.6 | 2 | WMF = 0.13 | Kemmer et al. (2022)
LHS 1478 b | 1.9495378 | 2.33 $\pm$ 0.20 | 1.242${}^{+0.051}_{-0.049}$ | 6.67${}^{+1.03}_{-0.89}$ | 1 | CMF = 0.39 $\pm$ 0.17 | Soto et al. (2021)
K2-146 b | 2.6446 | 5.77 $\pm$ 0.18 | 2.05 $\pm$ 0.06 | 3.69 $\pm$ 0.21 | 2 | WMF = 0.78 | Hamann et al. (2019)
K2-146 c | 4.00498 | 7.49 $\pm$ 0.24 | 2.19 $\pm$ 0.07 | 3.92 $\pm$ 0.27 | 2 | WMF = 0.80 | Hamann et al. (2019)
HATS-71 b | 3.7955202 | 117.6 $\pm$ 76.3 | 11.478 $\pm$ 0.20 | 0.42 $\pm$ 0.28 | 1 |  | Bakos et al. (2020)
COCONUTS-2 b | 402000000 | 2002.31${}^{+476}_{-603}$ | 12.442 $\pm$ 0.36 | 5.71 $\pm$ 1.48† | 1 |  | Zhang et al. (2021)
L 98-59 b | 2.2531136 | 0.4${}^{+0.16}_{-0.15}$ | 0.85${}^{+0.061}_{-0.047}$ | 3.6${}^{+1.4}_{-1.5}$ | 4 | WMF = 0.16 | Demangeon et al. (2021)
L 98-59 c | 3.6906777 | 2.22${}^{+0.26}_{-0.25}$ | 1.385${}^{+0.095}_{-0.075}$ | 4.57${}^{+0.77}_{-0.85}$ | 4 | WMF = 0.18 | Demangeon et al. (2021)
L 98-59 d | 7.4507245 | 1.94 $\pm$ 0.28 | 1.521${}^{+0.12}_{-0.09}$ | 2.95${}^{+0.79}_{-0.51}$ | 4 | WMF = 0.63 | Demangeon et al. (2021)
TOI-1685 b | 0.6691403 | 3.78 $\pm$ 0.63 | 1.7 $\pm$ 0.07 | 4.21${}^{+0.95}_{-0.82}$ | 1 | WMF = 0.40 | Bluhm et al. (2021)
K2-18 b | 32.939623 | 8.92${}^{+1.7}_{-1.6}$ | 2.37 $\pm$ 0.22 | 4.11${}^{+1.72}_{-1.18}$ | 2 |  | Sarkis et al. (2018)
GJ 1252 b | 0.5182349 | 2.09 $\pm$ 0.56 | 1.193 $\pm$ 0.074 | 6.76 $\pm$ 0.67† | 1 | CMF = 0.45 $\pm$ 0.35 | Shporer et al. (2020)
TOI-1201 b | 2.4919863 | 6.28${}^{+0.84}_{-0.88}$ | 2.415${}^{+0.091}_{-0.09}$ | 2.45${}^{+0.48}_{-0.42}$ | 1 |  | Kossakowski et al. (2021)
GJ 357 b | 3.93072 | 1.84 $\pm$ 0.31 | 1.217${}^{+0.084}_{-0.083}$ | 5.6${}^{+1.7}_{-1.3}$ | 3 | CMF = 0.23 $\pm$ 0.29 | Luque et al. (2019)
TOI-270 b | 3.3601538 | 1.58 $\pm$ 0.26 | 1.206 $\pm$ 0.039 | 4.97 $\pm$ 0.94 | 3 | CMF = 0.09 $\pm$ 0.21 | Van Eylen et al. (2021)
TOI-270 c | 5.6605731 | 6.15 $\pm$ 0.37 | 2.355 $\pm$ 0.064 | 2.6 $\pm$ 0.26 | 3 |  | Van Eylen et al. (2021)
TOI-270 d | 11.379573 | 4.78 $\pm$ 0.43 | 2.133 $\pm$ 0.058 | 2.72 $\pm$ 0.33 | 3 |  | Van Eylen et al. (2021)
TOI-269 b | 3.6977104 | 8.8 $\pm 1.4$ | 2.77 $\pm$ 0.12 | 2.28${}^{+0.48}_{-0.42}$ | 1 |  | Cointepas et al. (2021)
TOI-674 b | 1.977143 | 23.6 $\pm$ 3.3 | 5.25 $\pm$ 0.17 | 0.91 $\pm$ 0.15 | 1 |  | Murgas et al. (2021)
GJ 367 b | 0.321962 | 0.546 $\pm$ 0.078 | 0.718 $\pm$ 0.054 | 8.106 $\pm$ 2.16 | 1 | CMF = 0.87 $\pm$ 0.30 | Lam et al. (2021)
TOI-1634 b | 0.989343 | 4.91${}^{+0.68}_{-0.70}$ | 1.79 $\pm$ 0.08 | 4.7${}^{+1.0}_{-0.90}$ | 1 | WMF = 0.35 | Cloutier et al. (2021b)
TOI-1231 b | 24.245586 | 15.4 $\pm$ 3.3 | 3.65${}^{+0.16}_{-0.15}$ | 1.74${}^{+0.47}_{-0.42}$ | 1 |  | Burt et al. (2021)
GJ 436 b | 2.64388312 | 22.1 $\pm$ 2.3 | 4.17 $\pm$ 0.168 | 1.8 $\pm$ 0.29 | 1 |  | Maciejewski et al. (2014)
GJ 3470 b | 3.3366496 | 13.9 $\pm$ 1.5 | 4.57 $\pm$ 0.18 | 0.8 $\pm$ 0.13 | 1 |  | Demory et al. (2013)
TOI-1266 b | 10.894843 | 13.5${}^{+11}_{-9}$ | 2.37${}^{+0.16}_{-0.12}$ | 5.57$\pm$ 1.14† | 2 |  | Demory et al. (2020)
TOI-1266 c | 18.80151 | 2.2${}^{+2.0}_{-1.5}$ | 1.56${}^{+0.15}_{-0.13}$ | 3.18$\pm$ 0.38† | 2 | WMF = 0.60 | Demory et al. (2020)
TOI-530 b | 6.387597 | 127.13${}^{+28.6}_{-31.8}$ | 9.303 $\pm$ 0.70 | 0.93${}^{+0.49}_{-0.35}$ | 1 |  | Gan et al. (2022c)
TOI-3714 b | 2.15 | 222.48 $\pm$ 10 | 11.321 $\pm$ 0.3 | 0.85 $\pm$ 0.08 | 1 |  | Cañas et al. (2022)

Note. — The density values marked by a ${\dagger}$ have been calculated in
this paper by propagating the errors from the planet’s mass and radius. WMF
values are calculated assuming a rocky core with a fixed Fe:$\rm MgSiO_{3}$
ratio.

Table 3: Planet Properties (Continued)

Planet Name | Orbital Period | Mass | Radius | Bulk density |  $\\#$ Planets | CMF or | Reference
---|---|---|---|---|---|---|---
| (days) | ($M_{\oplus}$) | ($R_{\oplus}$) | (g cm-3) |  | WMF |
AU Mic b | 8.4629991 | 20.12${}^{+1.57}_{-1.72}$ | 4.07 $\pm$ 0.17 | 1.32${}^{+0.19}_{-0.2}$ | 2 |  | Cale et al. (2021)
|  |  |  |  |  |  | Gilbert et al. (2022)
AU Mic c | 18.858991 | 9.6${}^{+2.07}_{-2.10}$ | 3.24 $\pm$ 0.17 | 1.22${}^{+0.26}_{-0.29}$ | 2 |  | Cale et al. (2021)
|  |  |  |  |  |  | Martioli et al. (2021)
Kepler-54 b | 8.0109434 | 21.5${}^{+5.6}_{-4.9}$ | 2.19 $\pm$ 0.07 | 12.8 $\pm$ 2.0† | 3 |  | Hadden & Lithwick (2014)
TOI-776 b | 8.24661 | 4.0 $\pm$ 0.9 | 1.85 $\pm$ 0.13 | 3.4${}^{+1.1}_{-0.9}$ | 2 | WMF = 0.70 | Luque et al. (2021)
TOI-776 c | 15.6653 | 5.3 $\pm$ 1.8 | 2.02 $\pm$ 0.14 | 3.5${}^{+1.4}_{-1.3}$ | 2 | WMF = 0.80 | Luque et al. (2021)
HATS-6 b | 3.3252725 | 101.38 $\pm$ 22.2 | 11.187 $\pm$ 0.213 | 0.399 $\pm$ 0.089 | 1 |  | Hartman et al. (2015)
Kepler-231 c | 19.271566 | 24.1${}^{+13.5}_{-11.2}$ | 1.93 $\pm$ 0.19 | 18.4 $\pm$ 9.01† | 2 |  |  Rowe et al. (2014),
|  |  |  |  |  |  | Hadden & Lithwick (2014)
HATS-74 A b | 1.73185606 | 464.029 $\pm$ 44 | 11.568 $\pm$ 0.24 | 1.64 $\pm$ 0.19 | 1 |  | Jordán et al. (2022)
HATS-75 b | 2.7886556 | 156.053 $\pm$ 12 | 9.91 $\pm$ 0.15 | 0.878 $\pm$ 0.013 | 1 |  | Jordán et al. (2022)
L 168-9 b | 1.4015 | 4.6 $\pm$ 0.56 | 1.39 $\pm$ 0.09 | 9.6${}^{+2.4}_{-1.8}$ | 1 | CMF = 0.63 $\pm$ 0.22 | Astudillo-Defru et al. (2020)
HD 260655 b | 2.76953 | 2.14 $\pm$ 0.34 | 1.24 $\pm$ 0.023 | 6.2 $\pm$ 1.0 | 2 | CMF = 0.32 $\pm$ 0.19 | Luque & Pallé (2022)
HD 260655 c | 5.70588 | 3.09 $\pm$ 0.48 | 1.533${}^{+0.051}_{-0.046}$ | 4.7${}^{+0.8}_{-0.9}$ | 2 | WMF = 0.22 | Luque & Pallé (2022)
Kepler-45 b | 2.455239 | 160.49 $\pm$ 28.6 | 10.76 $\pm$ 1.23 | 0.8 $\pm$ 0.5 | 1 |  | Johnson et al. (2012)
Kepler-138 b | 10.3126 | 0.066${}^{+0.059}_{-0.037}$ | 0.522 $\pm$ 0.032 | 2.6${}^{+2.4}_{-1.5}$ | 3 | WMF = 0.24 | Jontof-Hutter et al. (2015)
Kepler-138 c | 13.7813 | 1.97${}^{+1.91}_{-1.12}$ | 1.197 $\pm$ 0.07 | 6.2${}^{+5.8}_{-3.4}$ | 3 | CMF = 0.42 $\pm$ 0.49 | Jontof-Hutter et al. (2015)
Kepler-138 d | 23.0881 | 0.64${}^{+0.674}_{-0.387}$ | 1.212 $\pm$ 0.075 | 2.1${}^{+2.2}_{-1.2}$ | 3 | WMF = 0.92 | Jontof-Hutter et al. (2015)
TOI-1899 b | 29.02 | 209.76 $\pm$ 22.24 | 12.89 ${}^{+0.448}_{-0.56}$ | 0.54${}^{+0.09}_{-0.1}$ | 1 |  | Cañas et al. (2020)
LP 714-47b | 4.052037 | 30.8 $\pm$ 1.5 | 4.7 $\pm$ 0.3 | 1.7 $\pm$ 0.3 | 1 |  | Dreizler et al. (2020)
|  |  |  |  |  |  | Luque & Pallé (2022)
LHS 1815 b | 3.81433 | 1.58${}^{+0.64}_{-0.60}$ | 1.088 $\pm$ 0.064 | 6.74${}^{+3.12}_{-2.66}$ | 1 | CMF = 0.46 $\pm$ 0.34 | Gan et al. (2020)
|  |  |  |  |  |  | Luque & Pallé (2022)
TOI-1728 b | 3.49151 | 26.8${}^{+5.4}_{-5.1}$ | 5.05${}^{+0.16}_{-0.17}$ | 1.14${}^{+0.26}_{0.24}$ | 1 |  | Kanodia et al. (2020)
|  |  |  |  |  |  | Luque & Pallé (2022)
TOI-1235 b | 3.444717 | 6.69${}^{+0.67}_{-0.69}$ | 1.694${}^{+0.08}_{-0.077}$ | 7.25${}^{+1.3}_{-1.1}$ | 1 | CMF = 0.25 $\pm$ 0.19 | Bluhm et al. (2020)
|  |  |  |  |  |  | Luque & Pallé (2022)
K2-3 b | 10.054626 | 6.48${}^{+0.99}_{-0.93}$ | 2.103 $\pm$ 0.25 | 3.7${}^{+1.67}_{-1.08}$ | 3 | WMF = 0.77 | Crossfield et al. (2015)
|  |  |  |  |  |  | Luque & Pallé (2022)
K2-3 c | 24.646582 | 2.14${}^{+1.08}_{-1.04}$ | 1.584${}^{+0.197}_{-0.195}$ | 2.98${}^{+1.96}_{-1.5}$ | 3 | WMF = 0.69 | Crossfield et al. (2015)
|  |  |  |  |  |  | Luque & Pallé (2022)

Note. — The density values marked by a ${\dagger}$ have been calculated in
this paper by propagating the errors from the planet’s mass and radius. WMF
values are calculated assuming a rocky core with a fixed Fe:$\rm MgSiO_{3}$
ratio.