Stellar spectral-type (mass) dependence of the dearth of close-in planets around fast-rotating stars. Architecture of Kepler confirmed single-exoplanet systems compared to star-planet evolution models

In 2013 a dearth of close-in planets around fast-rotating host stars was found using statistical tests on Kepler data. The addition of more Kepler and Transiting Exoplanet Survey Satellite (TESS) systems in 2022 filled this region of the diagram of stellar rotation period (Prot) versus the planet orbital period (Porb). We revisited the Prot extraction of Kepler planet-host stars, we classify the stars by their spectral type, and we studied their Prot-Porb relations. We only used confirmed exoplanet systems to minimize biases. In order to learn about the physical processes at work, we used the star-planet evolution code ESPEM (French acronym for Evolution of Planetary Systems and Magnetism) to compute a realistic population synthesis of exoplanet systems and compared them with observations. Because ESPEM works with a single planet orbiting around a single main-sequence star, we limit our study to this population of Kepler observed systems filtering out binaries, evolved stars, and multi-planets. We find in both, observations and simulations, the existence of a dearth in close-in planets orbiting around fast-rotating stars, with a dependence on the stellar spectral type (F, G, and K), which is a proxy of the mass in our sample of stars. There is a change in the edge of the dearth as a function of the spectral type (and mass). It moves towards shorter Prot as temperature (and mass) increases, making the dearth look smaller. Realistic formation hypotheses included in the model and the proper treatment of tidal and magnetic migration are enough to qualitatively explain the dearth of hot planets around fast-rotating stars and the uncovered trend with spectral type.


Introduction
The architecture of observed exoplanet systems is tailored by the complex interplay between the stars and planets.It is impacted from the beginning by the structure and evolution of the protoplanetary disks and later by the tidal and magnetic interactions (Mathis 2018;Strugarek 2018) between all the objects in the system.In 2013, by studying 737 main-sequence Kepler Objects of Interest (KOIs, Borucki et al. 2010) that had a measured stellar rotation period (P rot ), McQuillan et al. (2013) uncovered the existence of a dearth of close-in planets around fast-rotating stars, as initially suggested by Pont (2009).Recently, Messias et al. (2022) extended this study to 934 KOIs and 79 TESS Objects of Interest (TOIs, Ricker et al. 2014), and concluded that the previously mentioned dearth could be related to an observational bias.
The engulfment of close-in planets was first proposed as a possible physical origin for such a dearth by Teitler & Königl (2014) based on tidal interactions.In their pioneering work, Zhang & Penev (2014) carried out the first population simulations of star-planet systems, taking into account tidal interaction, which causes the planet to migrate inwards or outwards while making the star spin up or spin down.Based on this seminal work, Ahuir et al. (2021b, hereafter A21b) improved the ES-PEM code (Benbakoura et al. 2019) by including equilibrium tides, dynamical tides in the convective envelope of the host star, as well as magnetic torques from the stellar wind acting on the star and from star-planet magnetic interactions (following Strugarek et al. 2017).A similar approach was recently followed by Lazovik (2023) to estimate the proportion of hot Jupiters that are engulfed by their star during their life on the main sequence.In addition, A21b used their large grid of models to produce a synthetic population of star-planet systems that can be directly compared with the Kepler sample.In that initial work the imprint of the initial population of exoplanets after the disk dissipation was not considered, and it was found that the modelled stars still retained too many close-in planets compared to what was observed with Kepler.McQuillan et al. (2013) and Messias et al. (2022) used statistical tests to asses the existence (or lack thereof) of a dearth of close-in planets, which did not shed light on the physical processes leading to the architecture of observed exoplanet systems.In this work we follow a different approach by comparing the architecture of the observed systems to a synthetic population computed with the star-planet evolution code ESPEM, which takes into account tidal (Benbakoura et al. 2019) and magnetic interactions (A21b) between a star and a single planet, from the disk-dissipation phase up to the end of the main sequence.

Sample selection and stellar P rot extraction
Our study is limited to observed single-planet systems to avoid introducing additional biases in the comparison between theoretical models and observations.Moreover, we use only Kepler observations because the most complete possible P rot distribution of stars with and without detected planets is required to compute the models.To have the same observational biases in both samples, these periods should be assessed following the same method.This cannot be done with TESS data yet because of the difficulties in measuring rotation periods in a large sample of stars (e.g.Claytor et al. 2022;Holcomb et al. 2022;Avallone et al. 2022), in particular for P rot longer than 10-15 days.
To elaborate the list of confirmed single-planet exosystems observed by Kepler, we used the full list of exoplanets available at the NASA Exoplanet Archive1 (NEA; Akeson et al. 2013) in March 2022.A total of 4,935 planets are registered in 3,576 systems, 2,889 of which are single-planet exosystems.Following the methods described in Appendix A, we obtained 1,967 confirmed planet systems observed by Kepler, of which 1,476 are single-planet systems (based on the catalogues used here).
Two sets of light curves (LCs) were used in this work to look for P rot : Pre-search Data Conditioning -Maximum A Posteriori (PDC-MAP, Jenkins et al. 2010;Stumpe et al. 2012;Smith et al. 2012;Thompson et al. 2013) and our custom KEPSEISMIC2 (García et al. 2011).More details on the corrections and the data preparation are given in Appendix B.
The values of P rot were obtained using the automatic selection procedure described in Santos et al. (2021) coupled to the machine learning algorithm ROOSTER (Breton et al. 2021).Moreover, all the stars (with and without a retrieved P rot ) were visually inspected using the three new folded-KEPSEIMIC and the PDC-MAP LCs.In Table 1 we provide the list of 796 stars with P rot after the visual checks.
For the moment, ESPEM is only optimized for systems in which the central star is single and on the main sequence.Hence, it is necessary to remove post-main-sequence stars as well as binary systems.To do so, we used the astrometric and photometric data from releases EDR3 and DR3 of the Gaia mission (Gaia Collaboration et al. 2021, 2023b).This allowed us to remove potentially evolved exoplanet hosts, as well as different categories of binary systems.We give further details of the selection cuts in Appendix A. After applying these cuts, we ended up with 576 confirmed single-planet-host main-sequence solarlike stars (CSPHMSS) with a reliable rotation period.To perform meaningful comparisons, we applied the same selection cuts to the latest Kepler rotation catalogue (Santos et al. 2019(Santos et al. , 2021) ) to remove post-main-sequence stars and binary systems, which yielded our reference Kepler sample (RKS, see Appendix C) for the remainder of the paper.

Observed P orb versus P rot distributions
In this section we investigate the P rot and planet orbital period (P orb ) distributions and their relationship.Figure 1 shows the rotation period as a function of the orbital period for 576 CSPHMSS of all spectral types, similarly to Fig. 2 in McQuillan et al. (2013).While the overall picture is similar in the two analyses, our samples differ (see a detailed comparison with this and other previous works in Appendix D).We note that there are a few more stars below the edge of the dearth of close-in planets region and fewer fast rotators.Although there are more fast rotators in Mc-Quillan et al. (2013), the P rot distributions become similar when the same selection criteria are applied (see Appendix D).
Exoplanet occurrence rates on Kepler fast-rotating mainsequence stars depend on the spectral types (F dwarfs spin faster than G and K dwarfs, Santos et al. 2019Santos et al. , 2021)).Hence, we also separated our exoplanet sample by spectral types (K to F, see blue dots and black lines in Fig. 2).M dwarfs were excluded from this study because there are only five, which is not enough to draw any reliable conclusions.
Because a large fraction of the stars in the Kepler field have near solar metallicity (Dong et al. 2014) and because our planet hosts are all main-sequence stars, the spectral type (defined using T eff ) is a very good proxy of stellar mass.Hence, the ranges of masses (from Berger et al. 2020) corresponding to our cuts in spectral type are for K, G, and F: 0.436 ≲ M ≲ 0.896, 0.769 ≲ M ≲ 1.162, and M ≳ 1.015 M ⊙ , respectively, where the ⊙ quantities refer to solar values.There is some overlap at the edges of the spectral types as the relative mass uncertainties are two to three times larger than those on T eff (from ∼2 to ∼9 %).
Qualitatively speaking, stars in the P rot -P orb diagram follow several trends with T eff and mass (see left panels in Fig. 2).First, there are more fast-rotating F dwarfs than G and K dwarfs at all P orb , a behaviour similar to that in the RKS.Second, there are more slow-rotating K dwarfs with close-in planets than G and F dwarfs.For F dwarfs there is a general lack of close-in planets at all P rot , except for three stars below P orb = 2 days.
There is also a larger number of synchronized systems for G stars: adopting a P rot /P orb tolerance of 5%, we find 23 synchronized systems (9% of the sample) for G stars, and 12 (5%) and 4 (4%) for K and F stars, respectively.Although captivating, their investigation is beyond the scope of this work.
To examine the distribution of CSPHMSS against the RKS, we generated the histogram and the cumulative distribution func-  tion (CDF) by spectral types (Fig. 2 middle and right panels, respectively).For the K dwarfs the two samples follow similar distributions.We performed the Kolmogorov-Smirnov (KS, Kolmogorov 1933;Smirnov 1939) test to quantify their differences.We find a KS statistic of 0.07, with a p-value of 0.29, suggesting that for the K dwarfs CSPHMSS and RKS are both drawn from the same underlying distribution.In the G-dwarf CDF we see a lack of fast rotators in the CSPHMSS below ∼12 days (0.08 KS statistic with a p-value of 0.11 supporting the null hypothesis).Finally, for the F dwarfs we find a clear deficit of CSPHMSS rotating faster than 7 days, while there is an excess of P rot between 7 and 15 days, with a peak at 7-8 days as shown in the histogram.For this sample, the KS statistics increases significantly (0.27), with a p-value of 1.24 × 10 −6 , rejecting the null hypothesis.
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Synthetic population of rotating stars and hot exoplanets with ESPEM
We assessed the plausible physical scenarios behind the distribution of star-planet systems via the ESPEM code.ESPEM solves a budget of momentum between the angular momentum in the circular orbital motion of a planet, the angular momentum in the convective envelope of a solar-like star, and the angular momentum within the radiative interior of the same star.It takes into account coupling between the two zones of the star (MacGregor & Brenner 1991;Gallet & Bouvier 2015), stellar wind torque on the star (Matt et al. 2015), stellar evolution during the premain sequence and the main sequence (Amard et al. 2016) To build a synthetic population, we started by producing three sets of 8,000 ESPEM models.Each set includes 40 different initial semi-major axes between 0.005 and 0.2 AU, five different initial rotation periods between 1 and 10 days, five planetary masses between 0.5 M Earth and 5 M Jupiter , and eight stellar masses between 0.5 and 1.2 M ⊙ .Each set of 8,000 models includes its own physical ingredients: set 1 considers only tidal interaction; set 2 tidal and magnetic interactions with a planetary magnetic field strength of 1 G; and set 3 is like set 2, but with the planetary field of 10 G (see A21b for more details).Within these 8,000 models, we select instantaneous stellar evolution epochs for a given stellar mass to mimic the distribution of the RKS.The main difference between the three sets lies in the population of low-mass planets (A21b), where the magnetic torques dominate their migration and affect their distribution.Nevertheless, these planets hold low angular momentum in their orbit, and therefore their net effect on the population of stars is negligible.In this work we primarily focus on the population of stars with close-in planets, hence in what follows we only consider set 3 and defer a detailed comparison of planetary populations between ESPEM to a future publication.
The comparison between ESPEM and Kepler results from McQuillan et al. (2013) made by A21b showed good qualitative agreement, but the synthetic populations exhibited an excess of close-in planets.Several reasons could be at the origin of this discrepancy: an enhanced magnetic interaction of close-in planets harbour larger surface magnetic fields than 10 G (Yadav & Thorngren 2017;Hori 2021); additional star-planet angular momentum exchanges, for example due to tidal interactions with the radiative core of the star (Ahuir et al. 2021a); a bias due to the selection of the initial semi-major axes used in the ESPEM set that should correspond to a population of planets right after the dissipation of the disk.Here we consider the last hypothesis and remove from the ESPEM population all the planets that were initiated below the inner radius of the dead zone (R dz ) of the stellar disk.We provide an analytical derivation of R dz in Appendix E, as well as a formulation of R dz as a function of M ⋆ .It should be noted that we also consider the transit detection probability when building up our synthetic population of rotating stars with close-in exoplanets (for more details, see Section 5 of A21b).
We show in the left panels of Fig. 2 the ESPEM probability of the occurence of star-planet systems as a function of P rot and P orb in logarithmic scale colour map.The ESPEM population is separated into the three different spectral types we focus on in this work (K, G, and F dwarfs).The predicted P rot ranges from 0.6 to 50 days and the orbital period ranges from 0.3 to 50 days.In ESPEM we do not consider planets beyond a given P rot , as indicated by the dashed grey area that labels the parameter space not covered by the simulations.
The simulated populations also exhibit trends with spectral type, as shown in Fig. 2: a larger fraction of fast-rotating F dwarfs that progressively decreases for G and K dwarfs, and a lower edge of the dearth well aligned with the lower envelope of points deduced by McQuillan et al. (2013) (magenta dotted lines in left panels of Fig. 2).This is particularly striking for K-dwarf systems with P orb between 1 and 40 days.
Compared to the initial work of A21b, we obtain in this work fewer close-in planets, thanks to a refined selection of the initial star-planet population since we do not consider here planets with orbits closer to the inner R dz of the protoplanetary disk.This clearly shows the importance of taking into account planetary formation processes.In addition, we also explored the effect of the chosen mass-loss rates and stellar magnetic-field laws on our population synthesis.Following Ahuir et al. (2020), we considered two extreme sets of mass-loss rate and magnetic field laws, covering the range of possibilities still compatible with all the observational constraints at hand to date.This extended study is shown in Appendix G, and we note that none of the conclusions in this work are strongly affected by choosing one specific set of evolutionary laws.
In all cases the dearth originates from angular momentum exchange between the rotating star and the orbit of the planet by tidal and magnetic interactions, making hot exoplanets around fast-rotating stars migrate efficiently inwards (if P orb is shorter than P rot , i.e. left of the dashed black line) and outwards (if P orb is longer than P rot , i.e. right of the dashed black line).Interestingly, the population of planets on the shortest period orbits around P rot = 30 days in the top left panel stems from the migration of these planets from an initial longer orbital period.We find that this population is shaped by both tidal and magnetic effects, since the ESPEM set 1 only predicts a scarce amount of planets in this region (see Appendix F).Finally, the simulated P rot distribution of planet hosts shifts towards slower P rot compared to the RKS population, confirming the results obtained by Sibony et al. (2022).

Discussion and conclusions
Comparing the CSPHMSS to the ESPEM predictions, we find a general good agreement (see Fig. 2).The high-density regions (red area in the left panels) closely match the locations with the higher number of systems detected by Kepler, particularly for the G-type stars (0.769 ≲ M ≲ 1.162 M ⊙ ).It is important to note that there is a factor of 100 difference between the red and green colours in the density scale.Thus, it is normal that only a few observed systems populate the lower density regions.For cooler K-type stars (top panel, 0.436 ≲ M ≲ 0.896 M ⊙ ), a greater number of slow-rotating stars hosting close-in planets are observed compared to the simulation.Therefore, in its current configuration, planets do not migrate fast enough in ESPEM to repopulate this region of the diagram.A possible solution could be to increase the stellar magnetic field for this spectral type, which would strengthen the magnetic torques (see the comparison with Fig. F.1 made including only tidal interactions), or to take into account the dissipation of tidal waves within the radiative core of stars (Ahuir et al. 2021a).
Article number, page 4 of 13 Since the number of observed F-type stars (M ≳ 1.015 M ⊙ ) is small, it prevents us from properly interpreting how well the simulation behaves close to low-density regions.The comparison of the histograms (middle panels in Fig. 2) shows that the shapes of the three distributions (RKS, ESPEM, and CSPHMSS) are very similar, but there is a progressive reduction in the overall number of stars for each P rot bin.However, there are two noticeable differences at P rot of around 8 and 15-20 days, where there is an excess of CSPHMSS and of simulated systems, respectively.In this last case the discrepancy may be due to an overestimation of the stellar wind-break effect (whose rotation evolution is known to be difficult to capture accurately; see e.g.Amard et al. 2019).This will be investigated in a future study.
Up to P rot ∼ 7 days, the three distributions of the G-type stars show the same slope in the histograms.An excess of CSPHMSS is clearly visible up to P rot ∼ 15 days.For K-type stars the differences are minimal, with just an overall excess of observed systems compared to the simulated systems.
Finally, CDFs are shown in Fig. 2 (right column).In all of them a steep slope is observed, indicating a more concentrated distribution of exoplanets around stars with a longer P rot for all three samples.The ESPEM CDFs (red lines) reflect that the model reproduces relatively well the K-and G-dwarf populations (black lines), and shows a slight overdensity of fast-rotating F stars.
In conclusion, ESPEM models predict a dearth, in agreement with Kepler CSPHMSS, and with a clear dependence on the stellar spectral type.More observations will be necessary to better constrain the dearth and the mechanisms at play to define the architecture of exoplanet systems.

Appendix A: Sample selection
At NEA we select the table containing only confirmed exoplanet systems.Because this table contains TESS Input Catalog identifiers (TIC identifiers, Stassun et al. 2019), we cross-match the TICs with the Kepler Input Catalog identifiers (KIC identifiers, Brown et al. 2011) using the KIC2TIC tool3 to know the systems observed by Kepler.Then we select the systems with the column sy_pnum= 1 to ensure that they are single exoplanet systems.To remove already known binaries, we select those systems with the column sy_snum=1 and cb_flag=0 (to also remove circumbinary planets).
As mentioned in Sections 2 and 3, for both the exoplanet host and RKS samples, our analysis is focused on single mainsequence stars.For this purpose, we removed evolved stars and binary systems taking full advantage of the state-of-the-art Gaia data, using an identical procedure for both samples.Here we provide a summary of these selections, and refer interested readers to Godoy-Rivera et al. (in preparation) for further details.
As some of our cuts depend directly on the position on the colour-magnitude diagram (CMD), we first apply a quality criterion and we flag stars that lack Gaia magnitudes or that have a flux signal-to-noise ratio (S/N) in any of the three Gaia bands (G, BP, or RP) of phot_mean_flux_over_error ≤ 100.We used the distance information from the Gaia EDR3 catalogue by Bailer- Jones et al. (2021).To de-redden the photometry, we used the Gaia DR3 gspphot values when available, and otherwise used the Green et al. (2019) extinction values or the Total Galactic Extinction (TGE; Delchambre et al. 2023) values (queried via the dustmaps package; Green 2018) following the approach of Godoy-Rivera et al. (2021).With these values the stars are placed on the absolute and de-reddened CMD.We illustrate this for the confirmed single-planet-host star sample with measured P rot in Figure A.1, showing the stars with enough data to be placed on the diagram (i.e. with photometric, distance, and extinction information).
In this way evolved stars are identified by applying a cut in the CMD.We define a line that distinguishes between dwarfs and evolved stars based on the whole Kepler sample, and we illustrate it as the black dotted line in Figure A.1.Stars that fall inside this region (i.e.redder colours and more luminous absolute magnitudes than the dotted line) are flagged as evolved.Binary stars are placed in one of six categories: 1) RUWE binaries (Lindegren et al. 2021), meaning stars with high astrometric noise in the Gaia solution, are identified as stars with Renormalized Unit Weighted Error (RUWE) > 1.2 (Berger et al. 2020); 2) photometric binaries are identified on the CMD as dwarf stars above 0.9 mag or below 0.3 mag of the reference population MIST isochrone (Dotter 2016;Choi et al. 2016;Paxton et al. 2011Paxton et al. , 2013Paxton et al. , 2015)), which we take to be a 200 Myr and [Fe/H]=+0.25dex model following Messias et al. (2022) and Gordon et al. (2021); 3) stars that are found in the cross-match by Beck et al. (2023) with the Gaia DR3 NSS TBO (Non-Single-Star Two-Body-Orbit; Gaia Collaboration et al. 2023a) table; 4) radial velocity (RV) variable stars are identified from the Gaia RV measurements following Katz et al. (2023); 5) NEA binaries are identified as multiple systems according to the NEA database (sy_snum>1); and 6) eclipsing binaries are identified from the third revision of the Kepler Eclipsing Binary Catalog. 4or purposes of completeness, we also performed a check to identify potential circumbinary stars.We cross-matched our targets with the list of known circumbinary exoplanet hosts (e.g.Martin 2018), and found seven of them in our KOI sample: KIC 5473556 (Kepler-1647), KIC 6504534 (Kepler-1661), KIC 6762829 (Kepler-38), KIC 8572936 (Kepler-34), KIC 9632895 (Kepler-453), KIC 12351927 (Kepler-413), and KIC 12644769 (Kepler-16).We note that all these targets also correspond to NEA-identified binaries, and hence no further binary category was needed to flag them.
Regarding the sample of confirmed single-planet-host stars with measured P rot , we illustrate the CMD location of the abovementioned categories in   2013), but a few of these targets are located in the dearth.ets are transiting are removed and all the gaps are interpolated using in-painting techniques based on a multi-scale discrete cosine transform (García et al. 2014b;Pires et al. 2015;Benbakoura et al. 2021).To remove the long-period trends (mostly instrumental), the KEPSEISMIC light curves are then filtered at low frequency with three different high-pass triangular filters of 20, 55, and 80 days, as done in previous analyses of the surface rotation using our rotation pipeline (e.g.García et al. 2014a;Ceillier et al. 2016;Santos et al. 2019Santos et al. , 2021)).However, we also produced three additional LCs per star after doing a new correction in KADACS prior to the filtering, in order to minimize the impact of the Kepler annual modulation: P Kepler ∼ 372.5 days.For each star the auto-correlation function (ACF) of the light curve is performed, and we look for the highest peak around ± 30 days of P Kepler .Then, the LC is phase-folded with this periodicity and fitted.The corrected light curve is obtained by subtracting this fitted curve linearly scaled to the data in each segment of length P Kepler .We verified that the new folded LCs are in general flatter and less perturbed when analysing the longer filters (55 and 80 days), helping the inference of longer P rot .Finally, we filter the PDC-MAP LCs at 54 days.However, it is important to mention that, in the original PDC-MAP LCs, each quarter could be intrinsically filtered (or not) independently from the rest of them with a cut-off period between 3 and 20 days.Therefore, in several stars some quarters could be filtered and others not.This could lead to spurious periodic signals in the PDC-MAP LCs.

Appendix C: Defining the reference Kepler sample
To make a fair comparison of the CSPHMSS sample with the broad Kepler sample of stars with known rotation periods, we need to build our reference Kepler sample (RKS) by removing known KOIs and by applying the same selection criteria that was considered for the CSPHMSS (Appendix A).The starting sample is that of Santos et al. (2019Santos et al. ( , 2021)), which contains subgiant stars by design, but this work focuses on main-sequence stars.After removing the confirmed planet hosts and the stars that did not pass the criteria from the Appendix B, the reference sample for this study includes 34,265 dwarfs: 316 M dwarfs (T eff < 3, 700 K); 12,081 K dwarfs (3, 700 ≤ T eff < 5, 200 K); 14,705 G dwarfs (5, 200 ≤ T eff < 6, 000 K); and 7,163 F dwarfs (T eff > 6, 000 K).
As Article number, page 8 of 13

Appendix E: Estimate of the dead-zone radius in disks
In this section we provide the derivation used to estimate the inner radius of the dead zone (R dz ) in a stellar disk.This radius is then used as a lower limit for the initial semi-major axis of planets within ESPEM, which improves the initial conditions considered in the ESPEM population synthesis developed in A21b.For this estimation of R dz , we suppose that the disk is passive (i.e. that it is heated only by the central star).The model derived here is based partially on the work of Chiang & Goldreich (1997).
The first constraint on the radius of the dead zone comes from the criterion for the magneto-rotational instability (MRI).In the dead zone we consider the MRI to be inactive, which translates into where R m is the magnetic Reynolds number, c s is the speed of sound, Ω K the Keplerian rotation rate, and η the Ohmic dissipation coefficient (Stone et al. 2000).The speed of sound is related to the height of the disk H and the local rotation rate (Ω K ), and this gives This can be recast as where α H = H/R is the disk thickness at radius R, R is expressed in astronomical units, and η is given in cm 2 /s.The ohmic dissipation in a disk can be classically estimated as a function of the temperature through the formula η = 4 × 10 6 T −1/2 exp (25188/T ) , (E.4) with T the temperature of the disk in K and η again in cm 2 /s.
In the passive disk model of Chiang & Goldreich (1997), the temperature of the disk can be approximated in the stationary state to T eff , (E.5) with T eff the stellar effective temperature.
Combining Equations E.3, E.4, and E.5 we obtain for the inner dead-zone radius R dz

Fig. 1 .
Fig. 1.P rot as a function of P orb for the CSPHMSS sample.The grey dashed line corresponds to the 1:1 line (synchronization).The magenta dotted line is the fit to the lower envelope of points obtained by McQuillan et al. (2013).

Fig. 2 .
Fig. 2. P rot vs P orb per spectral type (K-, G-, and F-type stars from top to bottom, left panels).The coloured regions depict the distribution of star-planet occurrences computed with ESPEM, while the blue dots are the CSPHMSS.The grey shaded region indicates the parameter space not covered by the simulation.The dotted and dashed lines are the same as in Fig. 1.The middle and right panels correspond to the P rot histograms and CDFs, respectively, for the three distribution of stars: CSPHMSS (black), ESPEM (red), and RKS (grey).
Fig. A.1.Absolute and de-reddened CMD of the sample of confirmed single-planet-host stars with measured P rot .The grey points represent the stars that survived all the selection cuts, i.e. the 576 CSPHMSS.The different categories described in Appendix A are highlighted according to the legend.The MIST isochrone of the reference population is shown as the solid black line.The dotted line represents the separation between dwarf and evolved stars.

Figure A. 2
Figure A.2 shows the stellar rotation period as a function of the planet orbital period, highlighting the stars that were considered to be in multiple systems or evolved according to the criteria above.Most of the removed stars are above the dearth line defined byMcQuillan et al. (2013), but a few of these targets are located in the dearth.

Fig. A. 2 .
Fig. A.2. Same as Fig. 1, but separated by spectral type and highlighting the stars that are not main-sequence and single stars.

Fig
Fig. C.1.Cumulative distribution function for P rot per RKS spectral type, indicated by the thickness and shade of the lines (see legend).

Table 1 .
Article number, page 2 of 13 R. A.García et al.: Stellar spectral-type (mass)dependence of the dearth of close-in planets around fast-rotating stars Stellar and exoplanet properties.
(Strugarek 2016;Strugarek et al. 2017athis 2016 due to tidal(Mathis 2015;Ogilvie 2013;Bolmont & Mathis 2016) and magnetic interactions(Strugarek 2016;Strugarek et al. 2017).The complete description of the model can be found in A21b; in this work a methodology was developed to build a synthetic population of star-planet systems comparable with the Kepler sample ofMc- Quillan et al. (2013).We revisit this work here, and compare such a synthetic population with the CSPHMMS and RKS samples.

Table A .
1. Categories and their respective numbers of evolved and confirmed non-single planet-host stars.
eff is expressed in Kelvin.The solution to this equation can be numerically fitted for solar-like stars (M ⋆ ≤ 1.2M ⊙ ), assuming a canonical value α H = 0.3 to obtain the generic formulation