# SWEET-Cat: A view on the planetary mass-radius relation

S. G. Sousa, V. Adibekyan, E. Delgado-Mena, N. C. Santos, B. Rojas-Ayala, S. C. C. Barros, O. D. S. Demangeon, S. Hoyer, G. Israelian, A. Mortier, et al.

► To cite this version:

S. G. Sousa, V. Adibekyan, E. Delgado-Mena, N. C. Santos, B. Rojas-Ayala, et al. SWEET-Cat: A view on the planetary mass-radius relation. Astronomy & Astrophysics - A&A, 2024, 691, 10.1051/0004-6361/202451704. insu-04846490

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Submitted on 18 Dec 2024

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# SWEET-Cat: A view on the planetary mass-radius relation

S. G. Sousa<fnref n="1" />,*, V. Adibekyan<fnref n="1" />, E. Delgado-Mena<fnref n="1" />, N. C. Santos<fnref n="1" />,<fnref n="2" />, B. Rojas-Ayala<fnref n="3" />, S. C. C. Barros<fnref n="1" />, O. D. S. Demangeon<fnref n="1" />,<fnref n="2" />, S. Hoyer<fnref n="4" />, G. Israeliian<fnref n="5" />, A. Mortier<fnref n="6" />, B. M. T. B. Soares<fnref n="1" />,<fnref n="2" />, and M. Tsantaki<fnref n="7" />

Received 29 July 2024 / Accepted 16 September 2024

## ABSTRACT

**Aims.** SWEET-Cat (Stars With ExoplanETs Catalog) was originally introduced in 2013, and since then, the number of confirmed exoplanets has increased significantly. A crucial step for a comprehensive understanding of these new worlds is the precise and homogeneous characterization of their host stars.

**Methods.** We used a large number of high-resolution spectra to continue the addition of new stellar parameters for planet-hosting stars in SWEET-Cat following the new detection of exoplanets listed both in the Extrasolar Planets Encyclopedia and in the NASA exoplanet archive. We obtained high-resolution spectra for a significant number of these planet-hosting stars, either observed by our team or collected through public archives. For FGK stars, the spectroscopic stellar parameters were derived for the spectra following the same homogeneous process using ARES+MOOG as for the previous SWEET-Cat releases. The stellar properties were combined with the planet properties to study possible correlations that could shed more light on the star-planet connection studies.

**Results.** We have increased the number of stars with homogeneous parameters by 232 (~25% – from 959 to 1191). We focus on the exoplanets that have had both mass and radius determined to review the mass-radius relation, and we find results consistent with the ones previously reported in the literature. For the massive planets, we also revisit the radius anomaly, confirming a metallicity correlation for the radius anomaly already hinted at in previous results.

**Key words.** planets and satellites: formation – planets and satellites: fundamental parameters – stars: abundances – stars: fundamental parameters

## 1. Introduction

Planetary system studies have grown immensely in the last couple of decades following the first detections of exoplanets orbiting solar-type stars (e.g., Mayor & Queloz 1995; Marcy & Butler 1996) and the thousands of exoplanets detected since. More interesting than the fantastic increase in the rate of discoveries is the surprisingly vast diversity of exoplanets present in the Galaxy, unraveled mostly by dedicated search surveys using radial velocity (RV) and transit techniques (e.g. Ehrenreich et al. 2020; Lillo-Box et al. 2020; Armstrong et al. 2020). These discoveries provide crucial constraints for the exhaustive understanding of planet formation and evolution, based initially on our knowledge of the Solar System alone.

Because the main techniques to detect and characterize these exoplanets rely on the observation of their host stars, it is crucial to derive precise, accurate, and homogeneous stellar parameters. The homogeneous determination of such parameters is even more important if we want to perform statistical studies on the different populations of exoplanets that have been discovered in recent years (e.g. Adibekyan et al. 2024; Buchhave et al. 2018; Santos et al. 2017; Goda & Matsuo 2019).

The SWEET-Cat database (“Stars With ExoplanETs Catalog”<fnref n="1" />) compiles an updated list of all stars known to host planets. First presented in Santos et al. (2013), SWEET-Cat started with a list of only ~700 planet-hosting stars, with about 65% of these having homogeneous spectroscopic parameters derived by our team using a well-defined spectral analysis procedure. The number of planet-hosting stars has grown to more than 4000 stars (hosting approximately 5000 exoplanets in total) over the past decade given the very productive results of many well-known ground- and space-based projects such as HARPS, ESPRESSO, *Kepler*, and TESS (Mayor et al. 2011; Pepe et al. 2021; Borucki et al. 2010; Ricker et al. 2014, respectively). The high rate of planet-hosting discoveries is hard to follow with the derivation of homogeneous spectroscopic parameters, especially for the many faint stars coming from *Kepler* transit detections for which it is much more difficult to obtain high-quality spectra. Because of this, in recent years the percentage of planet-hosting stars in SWEET-Cat with homogeneous parameters has decreased to only about 20%.

Here, we present a significant update to SWEET-Cat. This work consists of the addition of 232 new stellar atmospheric parameters for planet hosts, in addition to the 31 recent

<footnote n="1">¹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal</footnote>

<footnote n="2">² Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal</footnote>

<footnote n="3">³ Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile</footnote>

<footnote n="4">⁴ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France</footnote>

<footnote n="5">⁵ Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain</footnote>

<footnote n="6">⁶ School of Physics & Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK</footnote>

<footnote n="7">⁷ INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy</footnote>

<footnote>* Corresponding author; sergio.sousa@astro.up.pt</footnote>

<footnote n="1">¹ sweetcat.iastro.pt</footnote>
planet-hosting stars that we also included in SWEET-Cat since
its last update in 2021. These came from different planet
detection and characterization works to which our team has
contributed for the stellar characterization. For all these new
planet-hosting stars, we maintain the link to the NASA exoplanet
archive database<fnref n="2" /> (Akeson et al. 2013), as well as the Extraso-
lar Planets Encyclopedia<fnref n="3" /> (Schneider et al. 2011) to allow for
an easy correlation between stellar and planet properties for the
community.

The following sections describe the work done for the update
of SWEET-Cat as well as a short review of the mass-radius
of exoplanets as an example for the use of SWEET-Cat data.
Section 2 describes the spectroscopic data compilation for the
catalog. Section 3 recalls how the spectroscopic parameters were
homogeneously derived for SWEET-Cat. Section 4 is focused on
the planetary mass and radius relations review. In Sect. 5, we
revisit the radius anomaly observed for giant massive planets and
its observational link with metallicity. In Sect. 6, we conclude
with a summary of this work.

## 2. Spectroscopic data

### 2.1. Selection of host stars for SWEET-Cat

We used the same procedure as before to add new planet-hosting
stars in SWEET-Cat. We started by searching for all confirmed
planets in the Extrasolar Planets Encyclopedia and selecting only
the ones detected by RV, primary transit, and astrometry meth-
ods. We then performed a crossmatch of these with the stars
in SWEET-Cat and included the missing hosts, while at the
same time we removed some of the stars for which the previ-
ous planet detection is controversial at present. The same method
was undertaken with the NASA exoplanet archive to add the con-
firmed host stars missing in the Extrasolar Planets Encyclopedia.
We also kept the few confirmed planet hosts that the exoplanet
databases do not have in common. The source of the planet's
database was also updated in SWEET-Cat with this information.

### 2.2. Spectra compilation

The compilation of the spectra follows the same exact procedure
as the one described in Sect. 2.2 from Sousa et al. (2021). Here,
we briefly summarize the procedure. We used the Spectral Data
Product Form of the ESO Archive<fnref n="4" /> to automatically find and
download the data, using the *astroquery.eso*<fnref n="5" /> sub-module. This
search includes private data from our recent UVES programs for
SWEET-Cat (106.20ZM.001, 109.22VY.001, 110.23TD.001, and
111.24HZ.001) as well as high-quality, publicly available data of
the host stars with declinations of less than ~+30°.

For each FGK star (with an effective temperature above
4500 K and below 7000 K<fnref n="6" /> listed in SWEET-Cat, we searched
for individual exposures of high-resolution spectra and com-
bined these individual exposures for each instrument (and dif-
ferent configurations, in the case of UVES). The combination of
the spectra was done by adding all the individual spectra after
the respective RV shift, which was estimated during this process
using one of the exposures as a reference spectra.

We also searched spectra in other public archives includ-
ing data from the SOPHIE<fnref n="7" /> and HARPS-N<fnref n="8" /> spectrographs<fnref n="9" />. We
combined these data in the same way as for the ESO spec-
tral data. Here, we would also like to emphasize a specific
program (20B.PNP.Hoyer) that was run on SOPHIE to collect
planet-hosting spectra from the northern hemisphere.

For this work, we compiled a total of 333 combined spectra for 251 different FGK stars. The typical signal-to-noise (S/N) is around 150–200, and only 18% of these spectra are below an S/N of ~100.

## 3. Stellar parameters

### 3.1. Spectroscopic parameters

We carried out the spectroscopic analysis with “ARES+MOOG”
for the new spectroscopic data. The spectral analysis relies on
the excitation and ionization balance of the iron abundance. The
ARES code<fnref n="10" /> (Sousa et al. 2007, 2015a) automatically mea-
sured the equivalent widths of the absorption lines. The radiative
transfer code MOOG (version of Nov. 2019; Sneden 1973) was
used for the element abundances assuming a local thermody-
namic equilibrium (LTE) and using a grid of Kurucz ATLAS9
plane-parallel model atmospheres (Kurucz 1993). We applied
this method in our previous spectroscopic studies of planet hosts
(e.g., Sousa et al. 2008, 2011, 2015b, 2018, 2021; Mortier et al.
2013; Andreasen et al. 2017). We use the same line list introduced
in Sousa et al. (2008), except for the stars with an effective tem-
perature below 5200 K, for which we used the line list provided
in Tsantaki et al. (2013).

For a few stars, we were able to collect combined spectra
from two or more instruments or configurations. We recall that
the results derived from spectra from different instruments are
generally very consistent within the errors shown in Sousa et al.
(2018). We include only one set of converged parameters per
star in SWEET-Cat, following the same reasoning as in our last
update (Sousa et al. 2021), which is mostly based on the errors
derived in the spectroscopic analysis.

In Fig. 1, we show the comparison between the parame-
ters derived in this work and the values previously listed in
SWEET-Cat that were compiled previously from literature val-
ues. We derived homogeneous parameters for 232 new stars in
SWEET-Cat. For nineteen stars in our starting sample, conver-
gence was not reached, either because the spectra were of bad
quality or because the star has a relatively high rotation rate.
Both these issues cause difficulties in obtaining good measure-
ments of the lines' equivalent widths. The general consistency
between our values and the literature (mainly gathered from the
discovery paper) is similar to previous comparisons: for effective
temperature and [Fe/H] (top panels of Fig. 1), the mean differ-
ences are 44 ± 133 K and 0.01 ± 0.11 dex, respectively. There
are, however, significant differences between the parameters for
some host stars, in particular for the hotter stars above ~6500 K.
The offset that we see for these hotter stars is mostly related to
the increase in rotational velocity at these temperatures, which
makes it more difficult to derive spectroscopic parameters with
different methodologies. For these fourteen stars for which we

<footnote n="2">² http://exoplanetarchive.ipac.caltech.edu</footnote>

<footnote n="3">³ http://exoplanet.eu/</footnote>

<footnote n="4">⁴ http://archive.eso.org/wdb/wdb/adp/phase3_main/form</footnote>

<footnote n="5">⁵ http://astroquery.readthedocs.io</footnote>

<footnote n="6">⁶ For M stars a different spectroscopic analysis is used and is addressed in Antoniadis-Karnavas et al. (2024)</footnote>

<footnote n="7">⁷ http://atlas OBS-hp.fr/sophie/</footnote>

<footnote n="8">⁸ http://archives.ia2.inaf.it/tng/</footnote>

<footnote n="9">⁹ Other instruments and public archives are planned to be included in future works depending on the automatization to retrieve and treat the data from them.</footnote>

<footnote n="10">¹⁰ The latest version of ARES can be found on github.com/sousasag/ARES.</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** New SWEET-Cat homogeneous parameters ($T_{\text{eff}}$, log g, and [Fe/H]) compared to the literature values previously listed in SWEET-Cat. The bottom right panel shows the difference between [Fe/H] and the derived effective temperature. Here, the dashed black line represents a linear fit.</figcaption></figure>

derived effective temperatures above 6500 K, all have $v \sin i$ values reported in the literature between 10 and 20 km/s. For several of the stars, we can find a large spread in the effective temperature from different methods. One example can be seen in Raynard et al. (2018), which used three different methods to characterize NGTS-2, for which they derived effective temperatures as high as 6604 ± 134 K, but in the end they adopted a lower value of $6478^{+94}_{-89}$ K. Other factors such as the lower quality of spectra data could also contribute to the offset and spread. The bottom line is that caution should be taken when using different estimations from different methods, in particular for these hotter stars.

The metallicity comparison also shows a generally consistent result, with some outliers. Some of these outliers can even be explained by typos in the exoplanet databases<fnref n="11" />. Moreover, when we compare the difference between the derived metallicity and literature values as a function of the effective temperature (bottom right panel of Fig. 1), there is evidence for a small trend (−6.84e−5 ± 1.07e−5, with a Spearman correlation coefficient of −0.43 and a very low p value of 1.79e−10). The observed difference is generally covered by the provided errors, as we also see in the top right panel of the same figure, but it is a different way of showing the importance of using homogeneous spectral analysis in statistical studies.

In the bottom left panel of Fig. 1, the comparison of the spectroscopic surface gravity is generally consistent with a mean difference of 0.00 ± 0.27 dex, although there are a few outliers with significant differences, and a large spread of values is seen for the dwarf stars. This is similar to our previous results and can be corrected to some degree, as is discussed in Mortier et al. (2014).

We also derived the trigonometric surface gravity, following the same procedure as in Sousa et al. (2021) to obtain more accurate values for all the stars. We matched the new stars with homogeneous parameters listed with the Gaia ID in DR3, using their coordinates and the VizieR catalogs (Gaia Collaboration 2016, 2021). We checked the magnitudes and astrometry data to confirm that we selected the correct star. For each target with Gaia ID, we derived the stellar luminosities directly from the precise data in Gaia DR3, following Eq. (8.6) from the Gaia documentation<fnref n="12" /> where $M_G$ is the absolute Gaia magnitude, $T_{\text{eff}}$ is the effective temperature listed in SWEET-Cat, $M_{\text{bol}} = 4.74$ (defined by the IAU resolution 2015 B2), and $BC_G(T_{\text{eff}})$ is a temperature-dependent bolometric correction provided in the Gaia documentation (Eq. (8.9) and Table 8.3, Andrae et al. 2018). Instead of a simple inversion of the Gaia parallax to provide a distance, we preferred to include the geometric distance and an error directly taken from the maximum of the asymmetric uncertainty measures (16th and 84th percentiles) reported in Bailer-Jones et al. (2021).

<footnote n="11">¹¹ As an example, at the time of compilation of these values, for WASP-137 exoplanets.eu listed a metallicity ([Fe/H]) of 0.487 (±0.051), pointing to the work Anderson et al. (2018) where the value listed is 0.08 ± 0.09 dex. The 0.487 value was mistakenly sourced from the line below corresponding to the stellar luminosity.</footnote>

<footnote n="12">¹² https://gea.esac.esa.int/archive/documentation/GDR2/ – in particular chapter 8.3.3 authored by Orlagh Creevey and Christophe Ordenovic.</footnote>
<table><caption>**Table 1.** Updated statistics for SWEET-Cat.</caption><thead><tr><td>Number</td><td>Description</td></tr></thead><tbody><tr><td>4106</td><td>Stars in SWEET-Cat</td></tr><tr><td>1191</td><td>Planet-hosts with homogeneous parameters</td></tr><tr><td>232</td><td>New stars with homogeneous parameters</td></tr><tr><td>312</td><td>Bright FGK stars without<br>homogeneous parameters (<i>G</i> &lt; 12)</td></tr></tbody></table>

To estimate the trigonometric surface gravity, we need the stellar mass. As in previous works, we used the stellar mass calibration in Torres et al. (2010), and for estimates between 0.7 and 1.3 $M_\odot$ we used the recommended Eq. (1) in Santos et al. (2013), which corrects for the offset between the calibrated stellar mass and the ones estimated using isochrones. However, the Torres et al. (2010) calibration requires spectroscopic parameters of the star as inputs, including the surface gravity. Therefore, we performed an iterative process to converge simultaneously on the best estimates of the stellar mass and the trigonometric surface gravity. The procedure only takes a few iterations until it converges and it is described in detail in Sect. 3.4 in Sousa et al. (2021).

## 3.2. SWEET-Cat planet-hosting statistics

Table 1 presents the updated numbers of host stars in SWEET-Cat. The percentage of stars with spectra and homogeneous parameters increases for bright stars listed in SWEET-Cat. With the work presented in this paper, despite the addition of 232 new stars with homogeneous parameters, we continue to have ~86% and ~77% completeness for FGK stars with $G < 9$ and $G < 12$, respectively. The completeness represents the number of host stars with homogeneous spectroscopic parameters relative to the total number of stars listed in SWEET-Cat. The continuous increase in new host stars in the catalog keeps the percentage for bright stars almost the same. In Table 1, we can also see that there is still a subset of bright FGK planet-hosting stars (312 stars, about ~25% of the bright FGK stars) for which we had not (yet) obtained good-quality data at the time of the search for this work. These will be the focus of future SWEET-Cat updates.

## 4. The planetary mass-radius relation

A brief overview of the planetary mass radius relation can be explored with the known exoplanets with both a derived mass and radius. Several works have explored the mass-radius relation of exoplanets (e.g. Bashi et al. 2017; Chen & Kipping 2017; Ulmer-Moll et al. 2019; Otegi et al. 2020; Edmondson et al. 2023). In these works, the mass-radius relation is characterized by fitting into different regimes that correspond to different planet populations. In some cases, there are also suggestions of different correlations with other planetary system properties, which could then be explained by different theoretical arguments. It is out of the scope of this work to discuss theories that could explain the proposed correlations. Instead, our only goal is to give examples and demonstrate how SWEET-Cat can be very useful to update and/or strengthen previously identified observational correlations between different parameters. In particular, we want to explore the planetary mass radius relation dependence with a more homogeneous derivation of the planet

equilibrium temperature that could be estimated using SWEET-Cat's homogeneous effective temperatures derived for their host stars.

We started by crossmatching the updated SWEET-Cat table with the planet properties that one can find in the NASA exoplanet archive as well as the Extrasolar Planets Encyclopedia. This was easily done by following the Python tutorial available on SWEET-Cat's website<fnref n="13" />. Here, we collected first the planet properties listed by default in the NASA exoplanet archive<fnref n="14" />. If for a specific planet no values could be found in the NASA exoplanet archive, then we took the planet's properties from the Extrasolar Planets Encyclopedia. This allowed us to build a more complete set of planet properties.

The next step was to derive the planet's equilibrium temperature, which is useful to compare similar planets orbiting different stars with different periods. To derive the equilibrium temperature for each planet, we used Eq. (3.9) from Seager (2010):

$$T_{\text{eq}} = T_{\text{eff},*} \left(\frac{R_{*}}{a}\right)^{1/2} [f'(1 - A_{B})]^{1/4}, \quad (1)$$

using the effective temperature ($T_{\text{eff},*}$) and stellar radius ($R_*$) listed in SWEET-Cat, and the semi-major axis ($a$) as the proxy for the average distance of the planet. Moreover, we assumed a bond albedo ($A_B$) of zero in the process for all planets for this estimation<fnref n="15" />. $f'$ is the redistribution factor with a value of 1/4, assuming that the stellar radiation is uniformly distributed around the exoplanet.

At this point, we took a subsample of the planets that have relatively precise values for both their mass and radius. We kept only the planets with masses and radii with relative uncertainties below 45% and 15%, respectively. Moreover, we also only considered the planets with a measured velocity semi-amplitude, $k$. The goal is to make sure that we avoid planet masses determined only by transit time variations (see e.g. Adibekyan et al. 2024, and references therein, for a discussion). Using these constraints, we get a total of 765 exoplanets. Of these, when considering only the planet host with homogeneous spectroscopic parameters listed in SWEET-Cat, the sample is reduced to 426 planets.

Figure 2 presents the mass-radius relation for the two subsamples of planets, in which the color of the points represents their equilibrium temperature. In both panels, it is evident that the presence of two clear regimes hints at two distinct populations of planets. Both panels of Fig. 2 show the best-fitting lines minimizing a model composed of two linear regimes separated on a common mass or radius point ($x_c$). To find the best fit for this simple bilinear model, we used the *lmfit* Python package (Newville et al. 2014). In the left panel, the best fit shows a separation of the different populations at $x_c = 150 \pm 29 M_\odot$ with a slope of $m_1 = 0.58 \pm 0.01$ for the low-mass planets, while the slope is zero for the massive planets. An almost equal result was obtained when fitting the points in the right panel of the

<footnote n="13">¹³ https://sweetcat.iastro.pt/catalog/SC-Python-Tutorial.pdf</footnote>

<footnote n="14">¹⁴ Priority was given to the NASA exoplanet archive because it provides a more complete set of planet properties. It also provides a column with the equilibrium temperature for each planet which we could use directly for comparison.</footnote>

<footnote n="15">¹⁵ Although we may be expected to have different bond values for different planets, as we observe in planets in our own Solar System, there are only very few measurements available for known exoplanets. Therefore, since our goal is to compare our results with others in the literature, we followed the same assumption made for this and used a zero value for the albedo of all planets in our sample.</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Planetary mass-radius relation for planets orbiting stars listed in the SWEET-Cat catalog. The left panel includes all the planets with precise values for the planetary mass and radius, while the right panel includes only the planets hosted by stars with homogeneous stellar parameters. The black box represents the position and its respective uncertainty for the transition between the two regimes in the diagram.</figcaption></figure>

<table><caption>**Table 2.** Planetary mass-radius linear regimes.</caption><thead><tr><th>Parameter</th><th>Full set (765)</th><th>Homogeneous (426)</th></tr></thead><tbody><tr><td><i>m</i><sub>1</sub></td><td>0.58 ± 0.01</td><td>0.59 ± 0.01</td></tr><tr><td><i>b</i><sub>1</sub></td><td>-0.13 ± 0.01</td><td>-0.15 ± 0.02</td></tr><tr><td><i>m</i><sub>2</sub></td><td>0.00 ± 0.01</td><td>0.00 ± 0.02</td></tr><tr><td><i>b</i><sub>2</sub></td><td>1.14 ± 0.04</td><td>1.15 ± 0.06</td></tr><tr><td><i>x</i><sub>c</sub> (<i>M</i><sub>J</sub>)</td><td>2.18 ± 0.08</td><td>2.20 ± 0.15</td></tr><tr><td><i>x</i><sub>c</sub> (<i>M</i><sub>⊕</sub>)</td><td>150 ± 29</td><td>159 ± 53</td></tr><tr><td><i>y</i><sub>c</sub> (<i>R</i><sub>⊕</sub>)</td><td>13.8 ± 1.3</td><td>14.1 ± 2.6</td></tr></tbody></table>

**Notes.** *m*₁ and *b*₁ is the slope and intercept of the linear model for the low-mass planets. *m*₂ and *b*₂ is the slope and intercept of the linear model for the high-mass planets. *x*<sub>c</sub> and *y*<sub>c</sub> are the interception mass, and radius, point of the two linear models.

figure, in which we find the separation between the two population of planets at *x*<sub>c</sub> = 159 ± 53 *M*<sub>⊕</sub>. The parameters obtained by this two-regime model are reported in Table 2. These values are also close to the ones reported in the work of Bashi et al. (2017), which used a much smaller sample (238 exoplanets) and presented slopes of *m*₁ = 0.55 for the small planets, *m*₂ = 0.01 for the large planets, and a transition point of *x*<sub>c</sub> = 124 *M*<sub>⊕</sub>.

Other works also present consistent slopes and transition mass between these two populations, although some of these also identify an additional transition at lower masses at around *x*<sub>c2</sub> = 4.37 ± 0.72 *M*<sub>⊕</sub> (e.g. Müller et al. 2024; Otegi et al. 2020; Chen & Kipping 2017). This additional transition of regimes is not clearly seen in our Fig. 2, although there is a hint of this in the lower-mass regime. Looking carefully, one can notice the increase in hotter planets below ~10 *M*<sub>⊕</sub> and below ~2 *R*<sub>⊕</sub>, which even seems to follow a different slope when compared with the rest of the surrounding planets in the figure. This might be connected with the known radius gap that is discussed in many different works (e.g. Fulton et al. 2017; Kubyshkina & Fossati 2022). We note, however, that several planets that would fall into these low-mass regimes, such as the ones from the Trappist system (e.g. Gillon et al. 2017), were excluded because the

semi-amplitude velocity, *k*, was not reported in the databases. This comes from our sample selection to try to avoid masses that were not derived by the RV method<fnref n="16" />. In addition, most of these excluded planets orbit faint host stars and are therefore more difficult to obtain spectroscopic data for, and thus unlikely to have homogeneous parameters in SWEET-Cat. For these reasons, the third population of small planets should be handled with caution, given the generally lower precision of its stellar and planetary properties.

A clearly visible color gradient can be observed for giant planets in Fig. 2, indicating a much stronger positive correlation with the equilibrium temperature rather than with mass. This was already noticed in previous works; for example, in Edmondson et al. (2023), in which the planet radius was fit by a power law both on planet mass and the equilibrium temperature (Eq. 9) of their paper: $\frac{R}{R_{\oplus}} = CT_{\text{eq}}^{\beta_1} (\frac{M}{M_{\oplus}})^{\beta_2}$, where *C*, $\beta_1$, and $\beta_2$ are constants and $T_{\text{eq}}$ is the equilibrium temperature of the planet). Edmondson et al. (2023) derived a temperature index of $\beta_1$ = 0.35 ± 0.02 and a mass index of $\beta_2$ = 0.00 ± 0.01. Doing a similar fit to our data in Fig. 2 for planets with masses above 150 *M*<sub>⊕</sub>, in the left panel, we get a temperature index of $\beta_1$ = 0.31 ± 0.01 and a mass index of $\beta_2$ = -0.06 ± 0.01. Doing the same fit but for the planets with homogeneous spectroscopic stellar parameters, with masses above 159 *M*<sub>⊕</sub>, we get a temperature index of $\beta_1$ = 0.40 ± 0.01 and a mass index of $\beta_2$ = 0.00 ± 0.01. This represents a very substantial difference for the temperature index when comparing both samples. We note that the sampling distributions resulting from this combined fit are close to Gaussian distributions and are quite narrow, as is demonstrated by the adopted parameter errors. We also note a small but noticeable correlation between the parameters, which is more evident between *C* and $\beta_1$. The conclusion here is that the correlation with the temperature is stronger when using the smaller

<footnote n="16">¹⁶ Although this is correctly assumed for most of the planets, there are a few stars listed in the exoplanet databases for which no RV amplitude is reported, even though there are mass values in the literature derived by the RV method (e.g. WASP-43).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 3. Planet radius, and radius anomaly, dependence on planet temperature and metallicity. Left: planet radius and equilibrium temperature for the 159 massive exoplanets ($0.5 M_J < \text{mass} < 10 M_J$) with homogeneous high precision [Fe/H]. Right: radius anomaly vs. equilibrium temperature for the same planets. The line is the best fit of a power law.</figcaption></figure>

sample of planets with the more precise homogeneous spectroscopic parameters, which is relevant for the computation of the equilibrium temperature of the planet.

## 5. Revisiting the radius anomaly of Jupiter-like planets

The radius dependence on equilibrium temperature for massive planets was previously presented in the work of Laughlin et al. (2011), in which they investigated the radius anomaly observed in giant exoplanets. These planets, despite being expected to follow a mass-radius relationship consistent with a core made of heavy elements and a hydrogen-helium envelope, exhibit anomalously large radii. Potential mechanisms for these inflated radii, including tidal heating, enhanced atmospheric opacities, and heat redistribution, were explored. Understanding which mechanism dominates is crucial for explaining the observed deviations. One of the interesting results presented in the work of Laughlin et al. (2011) was the evidence for a significant correlation between the residual radius anomalies and host star metallicities – a correlation that is generally interpreted as evidence that metal-rich protoplanetary disks lead to planets with larger core masses, and thus with larger radii.

In this section, we quickly revisit the relations presented in Laughlin et al. (2011) using the updated SWEET-Cat data with the only goal being to verify the metallicity correlation on the residual radius anomalies. While in Laughlin et al. (2011) the planets were selected to have masses between 0.1 and 10 Jupiter masses, here we have used our mass transition from the previous section by selecting planets with masses above 159 earth masses (0.5 Jupiter masses). Of these, we only considered the planets hosted by stars with homogeneous stellar parameters and with a good precision below or equal to 0.05 dex in [Fe/H]. This left us with only 158 planets, but with very precise and homogeneous metallicity determinations. The left panel of Fig. 3 shows the dependence of the radius on equilibrium temperature for these massive planets. We also computed the radius anomaly, following the same procedure as in Laughlin et al. (2011) by using its Eq. (3), which provides an acceptable approximation to the

Bodenheimer et al. (2003) baseline structural models throughout the mass and temperature ranges in this sample of massive planets:

$$R_{\text{pl}}/R_{\text{Jup}} = 1.08417 + 0.0940857m - 0.242831m^2 \\ + 0.0947349m^3 + 0.0387851t + 0.00243981mt \\ - 0.0244656m^2t + 0.0130659m^3t + 0.0240409t^2 \\ - 0.0419296mt^2 + 0.00693348m^2t^2 \\ + 0.00302157m^3t^2. \qquad (2)$$

The radius anomaly was computed by subtracting the result of this fit to the observed radius values for all the planets. The right panel of Fig. 3 reproduces Fig. 2 of Laughlin et al. (2011) for our sample of massive planets around precisely characterized host stars in SWEET-Cat. In this panel, we also used a power law to fit the distribution points ($R \propto T_{\text{eq}}^{\alpha}$, $R$ being the radius anomaly, and $T_{\text{eq}}$ the equilibrium temperature)$^{17}$ for which we derived $\alpha = 1.35 \pm 0.51$, which is consistent with the value of $\alpha = 1.4 \pm 0.6$ originally presented in their work with only 90 early-detected transiting massive exoplanets.

After correcting for the equilibrium temperature trend and plotting the resulting radius anomaly against the host stellar metallicity, Laughlin et al. (2011) reported evidence for a negative correlation in their Fig. 3, but no slope value was presented. Here, we reproduce this correlation using our sample of planets with a precise and homogeneous metallicity in Fig. 4, for which we find a negative slope of $m = -0.42 \pm 0.04$ (we also derived a Spearman correlation coefficient of $-0.23$ with a low p value of 0.004 for these data points), which confirms the observed trend originally presented.

As a comparison to the use of our homogeneous SWEET-Cat parameters, we performed the same exercise using the parameters that are found directly in the NASA exoplanet archive for

<footnote n="17">17 We note that a linear fit to these points will do basically the same work, nevertheless we keep the fit of the same power law model for a direct comparison with the original work.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Radius anomaly with corrected equilibrium temperature trend vs. the metallicity of the host star [Fe/H].</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Same as Fig. 4 but using parameters directly listed in the NASA exoplanet archive.</figcaption></figure>

the same 158 planets. For these, we directly collected the equi-
librium temperature and the stellar metallicity compiled from
the literature. For 14 of these exoplanets, the stellar metallic-
ity was not available in the NASA database. For the few other
exoplanets that did not had uncertainties for the stellar metal-
licity, we assumed an error of 0.10 dex. For the few exoplanets
with no equilibrium temperature reported in the NASA exoplanet
database, we used Eq. (1) with the effective temperature and
stellar radius reported in the NASA's database to estimate the
missing values. With these data to hand, the power law fit on
the radius anomaly versus equilibrium temperature gave consis-
tent results, with a very similar $\alpha = 1.33 \pm 0.51$, meaning that
the changes in equilibrium temperature do not much affect these
results. However, when we observe the metallicity dependence
on the radius anomaly with the corrected equilibrium temper-
ature trend (Fig. 5), we derived a significant different linear fit,
with a stronger negative slope of $m = -0.88 \pm 0.12$, which is also
less precise (we also derived a Spearman correlation coefficient

of -0.21 with a p value of 0.01 for these data points). More-
over, we derived Spearman correlation coefficient distributions
to take into account the errors included for both Figs. 4 and 5.
The average correlation coefficient obtained was -0.20 with an
average p value of 0.03 for Fig. 4, while for Fig. 5 we obtained a
similar correlation of -0.18 but with a significantly higher aver-
age p value of 0.07. The higher uncertainty of the fit as well as
the higher p values obtained for Fig. 5 are caused by the higher
uncertainties of the metallicities available in the literature.

We also performed a simultaneous 3D fit to the radius
anomaly with a dependence on both the equilibrium temperature
and metallicity. The goal was simply to check if the observed
correlations remained consistent with the step-by-step analysis
done in Laughlin et al. (2011). Therefore, we used a model
to follow the relation $R = kT_{eq}^{\alpha} + m[\text{Fe/H}] + b$, for which we
derived the following coefficients: $k = 2.75e^{-5} \pm 5.46e^{-5}$, $\alpha =
1.40 \pm 0.17$, $m = -0.23 \pm 0.05$, and $b = -0.18 \pm 0.03$. We note
that there is a significant decrease in the uncertainty of $\alpha$ doing
this simultaneous fit. This way we were able to confirm that
both trends on equilibrium temperature and metallicity remain
present, although the metallicity slope seems to have reduced
significantly.

All these exercises done on updated exoplanet data confirm
that the metallicity trend is present. Using homogeneous data
we were able to obtain a more precise correlation, although this
depends on the extraction approach used, which can produce
different slope values. This metallicity dependence may be con-
nected with the presence of larger and more massive cores for the
planets orbiting metal-rich stars, which could compensate for the
inflation of their radius. We recall that the baseline models used
in Laughlin et al. (2011) come from Bodenheimer et al. (2003),
which assumed a near-solar composition. It would be interest-
ing to compare with more updated models, preferably with the
metallicity accounted for, but this is out of the scope of this
paper.

**6. Summary**

We present another large update of SWEET-Cat, for which
we have derived precise and homogeneous spectroscopic stel-
lar parameters for 232 new planet-hosting stars. To achieve this,
we compiled spectra collected from different instruments, by
both exploring public archives and making use of our own
observation programs at different observatories. The spectro-
scopic parameters were complemented with additional data as
in previous works, including estimation of stellar masses, radius,
and trigonometric surface gravities, which are made available
at the SWEET-Cat website. For all new planet hosts added in
SWEET-Cat, we maintain the cross reference columns for an
easy correlation with the planets's properties listed in the NASA
archive exoplanet database as well as the Extrasolar Planets
Encyclopedia.

We have conducted a quick review of the planetary mass
radius relation of exoplanets using homogeneous spectroscopic
data, where we can easily identify the two populations of exo-
planets following two different linear relations for low-mass and
high-mass planets. The relations derived in this work are con-
sistent with several others derived in different works, including
the dependence on equilibrium temperature observed for the
massive planets.

We have also revisited the radius anomaly observed for giant
planets with the goal of quantifying the metallicity correlation
presented as evidence in Laughlin et al. (2011). Using different
larger samples of massive exoplanets, we find that the metallic-
ity correlation persists with the same models. However, these
studies assume that giant planets are perfectly absorbing (black
bodies, which is unrealistic. Early exoplanet models have demon-
strated that the Bond albedo depends on the spectral type of
the host stars and the expected composition of planetary atmo-
spheres, considering their temperatures (e.g. Gelino et al. 1999;
Sudarsky et al. 2000). Recent research has shown that photo-
chemical hazes, rather than cloud condensates, may serve as
the primary aerosols depending on the planets' temperatures
(Steinrueck et al. 2023), thereby altering their expected albedos.
Consequently, more comprehensive and recent models should be
examined to assess the significance of this metallicity correlation
on the radii of these massive planets.

We shall continue to expand SWEET-Cat in the com-
ing years to provide the community with a more complete
dataset relevant for statistical studies of exoplanets. There is
still a significant number (≥300) of relatively bright planet
hosts listed without homogeneous parameters. We shall pro-
vide spectroscopic parameters once good-quality spectra are
available. Furthermore, we have plans to include additional
stellar parameters in SWEET-Cat. These include v sin i, stel-
lar activity indices, homogeneous element abundances for the
stars with the highest-quality spectra, making the spectra avail-
able for download on the website, and including more robust
determinations of stellar masses, radius, and ages from stellar
modeling.

Data availability

A copy of the SWEET-Cat catalog used for this work is available
at the CDS via anonymous ftp to cdsarc.cds.unistra.fr
(130.79.128.5) or via https://cdsarc.cds.unistra.fr/
viz-bin/cat/J/A+A/691/A53.

Acknowledgements. This work was supported by FCT – Fundacção para a Ciência e Tecnologia through national funds and by FEDER through COM-PETE2020 – Programa Operacional Competitividade e Internacionalização by these grants: 2022.06962.PTDC; UIDB/04434/2020; UIDP/04434/2020. S.G.S acknowledges the support from FCT through Investigador FCT contract nr. CEECIND/00826/2018 and POPH/FSE (EC). E.D.M. further acknowledges the support from FCT through the Stimulus FCT contract 2021.01294.CEECIND. Co-funded by the European Union (ERC, FIERCE, 101052347). BMTBS is supported by an FCT fellowship, grant number 2022.11805.BD. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. 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. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation. SH acknowledges CNES funding through the grant 837319. AM acknowledges funding from a UKRI Future Leader Fellowship, grant number MR/X033244/1. B.R-A acknowledges funding support from ANID Basal project FB210003.

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