A Comparison of the Composition of Planets in Single-planet and Multiplanet Systems Orbiting M dwarfs

We analyzed the differences in bulk density–which is a first-order approximation for the composition–of planets in singles and in multiplanet systems. The densities were taken from the NASA Exoplanet Archive and 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 ρ_p = 2.2 g cm⁻³ while the median density of planets in multis is ρ_p = 4.57 g cm⁻³. For reference, the density of the Earth is ρ_⊕ = 5.5 g cm⁻³.

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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 therefore repeated our analysis for smaller planets with R_p < 6 R_⊕, which can be expected to have similar formation pathways. 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, as we have now removed larger –and thus generally lower-density–planets. The planets in multis have a median density of ρ_p = 4.57 g cm⁻³ and the singles have a median of ρ_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 2σ (>95%) confidence level. 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_p = 6 R_⊕ is rather arbitrary, and we therefore reproduce our analysis with a radius cut at R_p = 4 R_⊕, which is another commonly used size threshold in the literature. For planets with R_p < 4 R_⊕, 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 4 R_⊕ 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 ρ/ρ_⊕,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 ∼0.32 core mass fraction (CMF)–would have at the mass of the planet under consideration. We compute these density ratios only for planets with R_p < 6 R_⊕, as 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 their cumulative distributions.

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Figure 5 shows the mass–radius diagram of this subsample of small planets with R_p ≲ 6 R_⊕ and M_p ≲ 100 M_⊕ 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% H₂O/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% H₂O/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).

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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 (ρ_p = 12.8 g cm⁻³, Hadden & Lithwick 2014) and Kepler-231 c (ρ_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 ∼25% (Kepler-54b) and ∼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, as 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.

Previous studies of multiplanet 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

$$\begin{eqnarray}&&\mathrm{CMF}={{\rm{M}}}_{\mathrm{core}}/{{\rm{M}}}_{\mathrm{planet}}.\end{eqnarray} \tag{ 1 }$$

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.

We therefore now turn our attention to this property and calculate the CMFs of all planets in our sample with M_p < 10 M_⊕ 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 Equation (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 (MgSiO₃) 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 the photospheric abundances of these materials of their host stars (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% MgSiO₃ mantle. To constrain the 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 2. We note that measuring core mass fractions precisely is difficult, and it is more reliable for well-measured exoplanets with mass and radius fractional uncertainties of Δm/m ≤ 20% and Δr/r ≤ 10%, as noted in Schulze et al. (2021). As some of the planets in our sample have relatively large mass and radius uncertainties, their CMF estimates have correspondingly significant uncertainties. Figure 6 shows our resulting core/water mass fractions.

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We make note of the compositionally diverse system Kepler-138. This multiplanet system consists of three small planets with relatively low densities. We model the innermost planet, Kepler-138b, as a water world and obtain a WMF of 0.24. We model planet c as rocky and obtain a CMF of 0.42. Finally, planet d is modeled as a water world and we obtain a high WMF of 0.92. 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_⊕), it must have a substantial amount of water, with at least ${11}_{-4}^{+3}$% volatiles/water by mass or ∼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 five days, we find that the error-weighted average of the CMFs of the singles and multis is 0.51 ± 0.07 and 0.23 ± 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 < 6 R_⊕, while the latter includes only low-mass planets with M_p < 10 M_⊕, which in our sample corresponds to a radius range of R_p < 1.6 R_⊕. We do not compare the WMFs of singles and multis, as the vast majority of water worlds reside in multiplanet systems.

We also explore the correlation between the CMF and semimajor axis, or orbital period. In Figure 5 of Rodríguez Martínez et al. (2023), we highlight a trend with the density and equilibrium temperature of known planets with M_p < 10 M_⊕: the densest planets appear to have higher equilibrium temperatures (or equivalently, smaller semimajor 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 the distance from the host star, as the 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 the 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 super Earths and did not see any correlation between the 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 the CMF, as a function of the distance within a given planetary system. In other words, we might expect the innermost planets in multiplanet systems to be more iron-rich than their outer siblings. For instance, 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 the 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 the CMF and orbital period within individual planetary systems either, as shown in Figure 6. Regarding the question of whether there is intrasystem uniformity in terms of core mass fractions, (or whether the CMFs are similar for exoplanets in the same system), we observe a variety of CMF values within multiplanet systems, which possibly argues against any uniformity (see Figure 6). However, we note that there are less than 10 muliplanet 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.

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Exploring the connection between the 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 multiplanet 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 the planet mass. Interestingly, we do not see a strong dependence of the CMF/WMF on planet mass for either singles or multis.

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. As the stellar rotation period is generally considered a proxy for youth as stars spin down with age (Skumanich 1972), multiplanet 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 ≥ 6 R_⊕), 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 < 6 R_⊕ (bottom).

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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 multiplanet 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 ≥ 6 R_⊕, 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 6 R_⊕ in this sample are seemingly isolated and they have masses and radii between ∼100 and 200 M_⊕ (except for HATS-74Ab and COCONUTS-2b, which have significantly larger masses), closer to the mass of Saturn (95M_⊕). They also orbit predominantly metal-rich (0 < [Fe/H] < 0.5, with a median [Fe/H] of ∼0.3), early M dwarfs (M0-M3). This population may also be seen in the left panel of Figure 10, which shows the planet radius as a function of the metallicity for singles and multis (color coded in blue and red, respectively). There are significantly larger 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] ∼0.1 dex, the majority of systems are single. This is consistent with the work by Burn et al. (2021), in which they predict a trend of increasing metallicity with planet mass. The right panel of Figure 10 shows the same sample but we plot planet radius as a function of the orbital period. However, it is difficult to draw any robust conclusions yet, 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] ∼ 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.

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Table 2. Planet Properties

Planet Name	Orbital Period	Mass	Radius	Bulk density	# Planets	CMF or	Reference
	(days)	(M⊕)	( R⊕)	(g cm−3)		WMF
TRAPPIST-1 b	1.510826	1.374 ± 0.069	${1.11}_{-0.012}^{+0.014}$	${5.44}_{-0.27}^{+0.26}$	7	CMF = 0.24 ± 0.07	Agol et al. (2021)
TRAPPIST-1 c	2.421937	1.308 ± 0.056	${1.097}_{-0.012}^{+0.014}$	${5.46}_{-0.24}^{+0.22}$	7	CMF = 0.30 ± 0.07	Agol et al. (2021)
TRAPPIST-1 d	4.049219	0.388 ± 0.012	${0.788}_{-0.010}^{+0.011}$	${4.37}_{-0.17}^{+0.15}$	7	CMF = 0.16 ± 0.04	Agol et al. (2021)
TRAPPIST-1 e	6.101013	0.692 ± 0.022	${0.92}_{-0.012}^{+0.013}$	${4.90}_{-0.18}^{+0.17}$	7	CMF = 0.22 ± 0.07	Agol et al. (2021)
TRAPPIST-1 f	9.20754	1.039 ± 0.031	${1.045}_{-0.012}^{+0.013}$	${5.02}_{-0.16}^{+0.14}$	7	CMF = 0.17 ± 0.06	Agol et al. (2021)
TRAPPIST-1 g	12.352446	1.321 ± 0.038	${1.129}_{-0.013}^{+0.015}$	${5.06}_{-0.16}^{+0.14}$	7	CMF = 0.15 ± 0.06	Agol et al. (2021)
TRAPPIST-1 h	18.772866	0.326 ± 0.02	0.755 ± 0.014	${4.16}_{-0.30}^{+0.32}$	7	CMF = 0.12 ± 0.06	Agol et al. (2021)
LHS 1140 b	24.73694	${6.38}_{-0.44}^{+0.46}$	1.635 ± 0.46	${8.04}_{-0.80}^{+0.84}$	2	CMF = 0.36 ± 0.12	Lillo-Box et al. (2020)
LHS 1140c	3.77792	${1.76}_{-0.16}^{+0.17}$	${1.169}_{-0.038}^{+0.037}$	${6.07}_{-0.74}^{+0.81}$	2	CMF = 0.34 ± 0.15	Lillo-Box et al. (2020)
K2-25 b	3.48456408	${24.5}_{-5.2}^{+5.7}$	3.44 ± 0.12	3.31 ± 0.20†	1		Stefansson et al. (2020)
GJ 1214 b	1.58040433	8.17 ± 0.43	${2.742}_{-0.053}^{+0.050}$	${2.2}_{-0.16}^{+0.17}$	1		Cloutier et al. (2021a)
GJ 1132 b	1.628931	1.66 ± 0.23	1.13 ± 0.056	6.3 ± 1.3	2	CMF = 0.40 ± 0.22	Bonfils et al. (2018)
LTT 3780 b	0.768448	${2.62}_{-0.46}^{+0.48}$	${1.332}_{-0.075}^{+0.072}$	${6.1}_{-1.5}^{+1.8}$	2	CMF = 0.24 ± 0.26	Cloutier et al. (2021a)
LTT 3780c	12.2519	${8.6}_{-1.3}^{+1.6}$	${2.3}_{-0.15}^{+0.16}$	${3.9}_{-0.9}^{+1.0}$	2	WMF = 0.90	Cloutier et al. (2021a)
GJ 486 b	1.467119	${2.82}_{-0.12}^{+0.11}$	${1.305}_{-0.067}^{+0.063}$	${7.0}_{-1.0}^{+1.2}$	1	CMF = 0.40 ± 0.17	Trifonov et al. (2021)
LTT 1445 A b	5.3587657	${2.87}_{-0.25}^{+0.26}$	${1.305}_{-0.61}^{+0.66}$	${7.1}_{-1.1}^{+1.2}$	2	CMF = 0.41 ± 0.20	Winters et al. (2022)
LTT 1445 A c	3.1239035	${1.54}_{-0.19}^{+0.20}$	${1.147}_{-0.54}^{+0.55}$	${5.57}_{-0.60}^{+0.68}$	2	CMF = 0.26 ± 0.23	Winters et al. (2022)
TOI-2136 b	7.851928	${6.37}_{-2.29}^{+2.45}$	2.19 ± 0.17	${3.34}_{-1.63}^{+2.55}$	1		Gan et al. (2022b)
GJ 3473 b	1.1980035	1.86 ± 0.30	1.264 ± 0.05	${5.03}_{-0.93}^{+1.07}$	2	CMF = 0.07 ± 0.24	Kemmer et al. (2020)
GJ 3929 b	2.6162745	${1.21}_{-0.42}^{+0.40}$	${1.15}_{-0.039}^{+0.040}$	4.4 ± 1.6	2	WMF = 0.13	Kemmer et al. (2022)
LHS 1478 b	1.9495378	2.33 ± 0.20	${1.242}_{-0.049}^{+0.051}$	${6.67}_{-0.89}^{+1.03}$	1	CMF = 0.39 ± 0.17	Soto et al. (2021)
K2-146 b	2.6446	5.77 ± 0.18	2.05 ± 0.06	3.69 ± 0.21	2	WMF = 0.78	Hamann et al. (2019)
K2-146 c	4.00498	7.49 ± 0.24	2.19 ± 0.07	3.92 ± 0.27	2	WMF = 0.80	Hamann et al. (2019)
HATS-71 b	3.7955202	117.6 ± 76.3	11.478 ± 0.20	0.42 ± 0.28	1		Bakos et al. (2020)
COCONUTS-2 b	402000000	${2002.31}_{-603}^{+476}$	12.442 ± 0.36	5.71 ± 1.48†	1		Zhang et al. (2021)
L 98-59 b	2.2531136	${0.4}_{-0.15}^{+0.16}$	${0.85}_{-0.047}^{+0.061}$	${3.6}_{-1.5}^{+1.4}$	4	WMF = 0.16	Demangeon et al. (2021)
L 98-59 c	3.6906777	${2.22}_{-0.25}^{+0.26}$	${1.385}_{-0.075}^{+0.095}$	${4.57}_{-0.85}^{+0.77}$	4	WMF = 0.18	Demangeon et al. (2021)
L 98-59 d	7.4507245	1.94 ± 0.28	${1.521}_{-0.09}^{+0.12}$	${2.95}_{-0.51}^{+0.79}$	4	WMF = 0.63	Demangeon et al. (2021)
TOI-1685 b	0.6691403	3.78 ± 0.63	1.7 ± 0.07	${4.21}_{-0.82}^{+0.95}$	1	WMF = 0.40	Bluhm et al. (2021)
K2-18 b	32.939623	${8.92}_{-1.6}^{+1.7}$	2.37 ± 0.22	${4.11}_{-1.18}^{+1.72}$	2		Sarkis et al. (2018)
GJ 1252 b	0.5182349	2.09 ± 0.56	1.193 ± 0.074	6.76 ± 0.67†	1	CMF = 0.45 ± 0.35	Shporer et al. (2020)
TOI-1201 b	2.4919863	${6.28}_{-0.88}^{+0.84}$	${2.415}_{-0.09}^{+0.091}$	${2.45}_{-0.42}^{+0.48}$	1		Kossakowski et al. (2021)
GJ 357 b	3.93072	1.84 ± 0.31	${1.217}_{-0.083}^{+0.084}$	${5.6}_{-1.3}^{+1.7}$	3	CMF = 0.23 ± 0.29	Luque et al. (2019)
TOI-270 b	3.3601538	1.58 ± 0.26	1.206 ± 0.039	4.97 ± 0.94	3	CMF = 0.09 ± 0.21	Van Eylen et al. (2021)
TOI-270 c	5.6605731	6.15 ± 0.37	2.355 ± 0.064	2.6 ± 0.26	3		Van Eylen et al. (2021)
TOI-270 d	11.379573	4.78 ± 0.43	2.133 ± 0.058	2.72 ± 0.33	3		Van Eylen et al. (2021)
TOI-269 b	3.6977104	8.8±1.4	2.77 ± 0.12	${2.28}_{-0.42}^{+0.48}$	1		Cointepas et al. (2021)
TOI-674 b	1.977143	23.6 ± 3.3	5.25 ± 0.17	0.91 ± 0.15	1		Murgas et al. (2021)
GJ 367 b	0.321962	0.546 ± 0.078	0.718 ± 0.054	8.106 ± 2.16	1	CMF = 0.87 ± 0.30	Lam et al. (2021)
TOI-1634 b	0.989343	${4.91}_{-0.70}^{+0.68}$	1.79 ± 0.08	${4.7}_{-0.90}^{+1.0}$	1	WMF = 0.35	Cloutier et al. (2021b)
TOI-1231 b	24.245586	15.4 ± 3.3	${3.65}_{-0.15}^{+0.16}$	${1.74}_{-0.42}^{+0.47}$	1		Burt et al. (2021)
GJ 436 b	2.64388312	22.1 ± 2.3	4.17 ± 0.168	1.8 ± 0.29	1		Maciejewski et al. (2014)
GJ 3470 b	3.3366496	13.9 ± 1.5	4.57 ± 0.18	0.8 ± 0.13	1		Demory et al. (2013)
TOI-1266 b	10.894843	${13.5}_{-9}^{+11}$	${2.37}_{-0.12}^{+0.16}$	5.57 ± 1.14†	2		Demory et al. (2020)
TOI-1266c	18.80151	${2.2}_{-1.5}^{+2.0}$	${1.56}_{-0.13}^{+0.15}$	3.18 ± 0.38†	2	WMF = 0.60	Demory et al. (2020)
TOI-530 b	6.387597	${127.13}_{-31.8}^{+28.6}$	9.303 ± 0.70	${0.93}_{-0.35}^{+0.49}$	1		Gan et al. (2022a)
TOI-3714 b	2.15	222.48 ± 10	11.321 ± 0.3	0.85 ± 0.08	1		Cañas et al. (2022)
AU Mic b	8.4629991	${20.12}_{-1.72}^{+1.57}$	4.07 ± 0.17	${1.32}_{-0.2}^{+0.19}$	2		Cale et al. (2021)
							Gilbert et al. (2022)
AU Mic c	18.858991	${9.6}_{-2.10}^{+2.07}$	3.24 ± 0.17	${1.22}_{-0.29}^{+0.26}$	2		Cale et al. (2021)
							Martioli et al. (2021)
Kepler-54 b	8.0109434	${21.5}_{-4.9}^{+5.6}$	2.19 ± 0.07	12.8 ± 2.0†	3		Hadden & Lithwick (2014)
TOI-776 b	8.24661	4.0 ± 0.9	1.85 ± 0.13	${3.4}_{-0.9}^{+1.1}$	2	WMF = 0.70	Luque et al. (2021)
TOI-776 c	15.6653	5.3 ± 1.8	2.02 ± 0.14	${3.5}_{-1.3}^{+1.4}$	2	WMF = 0.80	Luque et al. (2021)
HATS-6 b	3.3252725	101.38 ± 22.2	11.187 ± 0.213	0.399 ± 0.089	1		Hartman et al. (2015)
Kepler-231 c	19.271566	${24.1}_{-11.2}^{+13.5}$	1.93 ± 0.19	18.4 ± 9.01†	2		Rowe et al. (2014),
							Hadden & Lithwick (2014)
HATS-74 A b	1.73185606	464.029 ± 44	11.568 ± 0.24	1.64 ± 0.19	1		Jordán et al. (2022)
HATS-75 b	2.7886556	156.053 ± 12	9.91 ± 0.15	0.878 ± 0.013	1		Jordán et al. (2022)
L 168-9 b	1.4015	4.6 ± 0.56	1.39 ± 0.09	${9.6}_{-1.8}^{+2.4}$	1	CMF = 0.63 ± 0.22	Astudillo-Defru et al. (2020)
HD 260655 b	2.76953	2.14 ± 0.34	1.24 ± 0.023	6.2 ± 1.0	2	CMF = 0.32 ± 0.19	Luque & Pallé (2022)
HD 260655c	5.70588	3.09 ± 0.48	${1.533}_{-0.046}^{+0.051}$	${4.7}_{-0.9}^{+0.8}$	2	WMF = 0.22	Luque & Pallé (2022)
Kepler-45 b	2.455239	160.49 ± 28.6	10.76 ± 1.23	0.8 ± 0.5	1		Johnson et al. (2012)
Kepler-138 b	10.3126	${0.066}_{-0.037}^{+0.059}$	0.522 ± 0.032	${2.6}_{-1.5}^{+2.4}$	3	WMF = 0.24	Jontof-Hutter et al. (2015)
Kepler-138 c	13.7813	${1.97}_{-1.12}^{+1.91}$	1.197 ± 0.07	${6.2}_{-3.4}^{+5.8}$	3	CMF = 0.42 ± 0.49	Jontof-Hutter et al. (2015)
Kepler-138 d	23.0881	${0.64}_{-0.387}^{+0.674}$	1.212 ± 0.075	${2.1}_{-1.2}^{+2.2}$	3	WMF = 0.92	Jontof-Hutter et al. (2015)
TOI-1899 b	29.02	209.76 ± 22.24	12.89 ${}_{-0.56}^{+0.448}$	${0.54}_{-0.1}^{+0.09}$	1		Cañas et al. (2020)
LP 714-47b	4.052037	30.8 ± 1.5	4.7 ± 0.3	1.7 ± 0.3	1		Dreizler et al. (2020)
							Luque & Pallé (2022)
LHS 1815 b	3.81433	${1.58}_{-0.60}^{+0.64}$	1.088 ± 0.064	${6.74}_{-2.66}^{+3.12}$	1	CMF = 0.46 ± 0.34	Gan et al. (2020)
							Luque & Pallé (2022)
TOI-1728 b	3.49151	${26.8}_{-5.1}^{+5.4}$	${5.05}_{-0.17}^{+0.16}$	${1.14}_{0.24}^{+0.26}$	1		Kanodia et al. (2020)
							Luque & Pallé (2022)
TOI-1235 b	3.444717	${6.69}_{-0.69}^{+0.67}$	${1.694}_{-0.077}^{+0.08}$	${7.25}_{-1.1}^{+1.3}$	1	CMF = 0.25 ± 0.19	Bluhm et al. (2020)
							Luque & Pallé (2022)
K2-3 b	10.054626	${6.48}_{-0.93}^{+0.99}$	2.103 ± 0.25	${3.7}_{-1.08}^{+1.67}$	3	WMF = 0.77	Crossfield et al. (2015)
							Luque & Pallé (2022)
K2-3 c	24.646582	${2.14}_{-1.04}^{+1.08}$	${1.584}_{-0.195}^{+0.197}$	${2.98}_{-1.5}^{+1.96}$	3	WMF = 0.69	Crossfield et al. (2015)
							Luque & Pallé (2022)

Note. The density values marked by a † 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:MgSiO₃ ratio.

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We further investigated stellar [Fe/H] metallicity as a function of the 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 anticorrelation between these two parameters, namely,

$$\begin{eqnarray}&&[\mathrm{Fe}/{\rm{H}}]=-0.062\,(\pm 0.016)\times {{\rm{N}}}_{{\rm{p}}}-0.047\,(\pm 0.026),\end{eqnarray} \tag{ 2 }$$

where N_p is the number of planets.

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We repeated this analysis excluding hosts of planets larger than 6 R_⊕, and we found 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-hosting 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, multiplanet 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 dwarfs and late K dwarfs. Our results are more in line with Brewer et al. (2018) and Anderson et al. (2021).

One important caveat of this study is the uncertainty in planet multiplicity; namely, that a nonnegligible fraction of the observed singles may be multis in which other hidden planets eluded detection. ¹⁰ 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. In particular, 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 only on bulk density and metallicity as these are the properties for which we find significant differences 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_threshold is the fraction of bootstrapped values that have a K-S statistic below 0.01 (99% confidence), which is our threshold for statistical significance. In the case of the bulk density for 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_threshold is lower as well (f_threshold = 4.70%) and therefore detection completeness does affect this difference more strongly. For the case of the bulk densities normalized by the density of an Earth-like planet at that mass, we get a f_threshold of 100%, indicating that this parameter is robust to selection biases (see Figure 4).

For the stellar metallicity, we get a lower fraction of values below 0.01 for both the full sample (f_threshold = 54%) and for the subset of small-planet hosts (f_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 multiplanet 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, as TTVs are only measurable in multiplanet systems.

The signal-to-noise ratio (S/N) 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 multiplanet systems (many 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.

Furthermore, 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 ∼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 multiplanet systems, there is intrasystem radius uniformity. This means that comparing singles, with periods ∼1–5 days, to multis with periods ∼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.