Examining the radius valley: a machine-learning approach

Close-in planets smaller than Neptune form two distinct populations composed of rocky super-Earths and sub-Neptunes that may host primordial H/He envelopes. The origin of the radius valley separating these two planet populations remains an open question and has been posited to emerge either directly from the planet formation process or via subsequent atmospheric escape. Multitransiting systems that span the radius valley are known to be useful diagnostics of XUV-driven mass loss. Here, we extend this framework to test XUV-driven photoevaporation, core-powered mass loss, and an accretion-limited primordial radius valley model. Focusing on multitransiting systems allows us to eliminate unobservable quantities that are shared within individual systems such as stellar XUV luminosity histories and the properties of the protoplanetary disk. We test each proposed radius valley emergence mechanism on all 221 known multitransiting systems and calculate the minimum masses of the systems’ enveloped planets to be consistent with the models. We compare our model predictions to 75 systems with measured masses and find that the majority of systems can be explained by any of the three proposed mechanisms. We also examine model consistency as a function of stellar mass and stellar metallicity but find no significant trends. More multitransiting systems with mass characterizations are required before multitransiting systems can serve as a viable diagnostic of radius valley emergence models. Our software for the model evaluations presented herein is available on GitHub and may be applied to future multitransiting system discoveries.

We report precise radial velocity (RV) observations of HD 212657 (= K2-167), a star shown by K2 to host a transiting sub-Neptune-sized planet in a 10 d orbit. Using Transiting Exoplanet Survey Satellite (TESS) photometry, we refined the planet parameters, especially the orbital period. We collected 74 precise RVs with the HARPS-N spectrograph between August 2015 and October 2016. Although this planet was first found to transit in 2015 and validated in 2018, excess RV scatter originally limited mass measurements. Here, we measure a mass by taking advantage of reductions in scatter from updates to the HARPS-N Data Reduction System (2.3.5) and our new activity mitigation method called CCF Activity Linear Model (CALM), which uses activity-induced line shape changes in the spectra without requiring timing information. Using the CALM framework, we performed a joint fit with RVs and transits using exofastv2 and find Mp = $6.3_{-1.4}^{+1.4}$ $\, M_{\hbox{$\oplus $}}$ and Rp = $2.33^{+0.17}_{-0.15}$ $\, R_{\hbox{$\oplus $}}$, which places K2-167 b at the upper edge of the radius valley. We also find hints of a secondary companion at a ∼22 d period, but confirmation requires additional RVs. Although characterizing lower mass planets like K2-167 b is often impeded by stellar variability, these systems especially help probe the formation physics (i.e. photoevaporation, core-powered mass-loss) of the radius valley. In the future, CALM or similar techniques could be widely applied to FGK-type stars, help characterize a population of exoplanets surrounding the radius valley, and further our understanding of their formation.

Transit Timing Variations (TTVs) are deviations from the time an observer would expect to see an exoplanet transit its host star. In multiplanetary systems, significant TTVs may indicate the presence of another body in the system gravitationally interacting with the transiting exoplanet. T. Holczer et al. catalog 2599 Kepler Objects of Interest (KOIs) and provide a statistical analysis of their TTVs for candidates that have transited at least seven times. However, this conservative limit on the number of transits neglects long-period KOIs. Therefore, we extend the statistical analysis performed by T. Holczer et al. to the population of KOIs that have between three and six transits. We identify six KOIs, three of which have Kepler names (Kepler–103 c, Kepler–90 g, and Kepler–1662 c), with significant TTV signals that were originally overlooked by T. Holczer et al. Additionally, we search for trends regarding the planetary radius and orbital period of KOIs with significant TTVs. Through a survival analysis, we determine that planets with shorter orbital periods require larger TTV signals to be detected compared to longer period planets, regardless of planetary size. Uncovering trends in TTV statistics such as this one will provide targets for future forward modeling of planetary architectures.

We present the discovery by the TESS mission of one transiting Neptune-sized planet, TOI-6223 b, and two transiting super-Earths, TOI-1743 b and TOI-5799 b. We validate these planets using a statistical validation method, multi-color light curves, and other ancillary observations. We combined TESS and ground-based photometric data to constrain the physical properties of the planets. TOI-6223 b is slightly larger than Neptune Rp = 5.12−0.25+0.24 R⊕) orbiting an early M dwarf in 3.86 days, and it has an equilibrium temperature of Teq = 714 ± 14 K. TOI-1743 b orbits its mid-dwarf star every 4.27 days. It has a radius of Rp = 1.83−0.10+0.11 R⊕ and an equilibrium temperature of Teq = 485−13+14. TOI-5799 b has a radius of Rp = 1.733−0.090+0.096 R⊕ and an equilibrium temperature of Teq = 505 ± 16 K. It orbit around an M2 dwarf in 4.17 days. We also present the discovery of an additional transiting planet, TOI-5799 c, which we identified in the TESS data and validated using the SHERLOCK pipeline. TOI-5799 c is a super-Earth with a radius of Rp = 1.76−0.10+0.11 R⊕. Its orbital period and its equilibrium temperature are 14.01 days and Teq = 337 ± 11 K, respectively, which place it near the inner edge of the habitable zone of its star. We show that these planets are suitable for both radial velocity follow-up and atmospheric characterization. They orbit bright (<11 Kmag) early M dwarfs, making them accessible for precise mass measurements. The combination of the planet sizes and stellar brightness of their host stars also make them suitable targets for atmospheric exploration with the JWST. Such studies may provide insights into planet formation and evolution, as TOI-1743 b, TOI-5799 b, and TOI-5799 c lie within what is known as the radius valley, while TOI-6223 b is located on the Neptunian ridge in the period-radius plane.

Context. The vast majority of exoplanet discoveries to date have occurred around stars in the solar neighbourhood, with chemical compositions comparable to that of the Sun. However, models suggest that planetary systems in different Galactic environments, with varying dynamical histories and chemical abundances, may exhibit distinct characteristics, which can help improve our understanding of planet formation processes. Aims. This study aims to assess the potential of the upcoming PLATO mission to investigate exoplanet populations around stars in diverse Galactic environments, specifically focusing on the Milky Way thin disk, thick disk, and stellar halo. We aim to quantify PLATO’s ability to detect planets in each environment and determine how these observations could constrain planet formation models. Methods. Beginning with the all-sky PLATO Input Catalogue, we kinematically classified the 2.4 million FGK stars into their respective Galactic components. For the sub-sample of stars in the long-observation LOPS2 and LOPN1 PLATO fields, we estimated planet occurrence rates using the New Generation Planet Population Synthesis dataset. Combining these estimates with a PLATO detection efficiency model, we predicted the expected planet yields for each Galactic environment during a nominal 2+2 year mission. Results. Based on our analysis, PLATO is likely to detect at least 400 exoplanets around the α-enriched thick disk stars. The majority of those planets are expected to be super-Earths and sub-Neptunes with radii between 2 and 10 R⊕ and orbital periods between 2 and 50 days, which is ideal for studying the link between the radius valley and stellar chemistry. For the metal-poor halo, PLATO is likely to detect between 1 and 80 planets with periods between 10 and 50 days, depending on the potential existence of a metallicity threshold for planet formation. The PLATO fields contain more than 3400 potential target stars with [Fe/H] < −0.6, which will help improve our understanding of planets around metal-poor stars. We identified a specific target list of 47 (kinematically classified) halo stars in the high-priority, high-signal-to-noise PLATO P1 sample, offering prime opportunities in the search for planets in metal-poor environments. Conclusions. PLATO’s unique capabilities and large field of view position it as a valuable tool for studying planet formation across the diverse Galactic environments of the Milky Way. By probing exoplanet populations around stars with a varying chemical composition, PLATO will provide helpful insights into the connection between stellar chemistry and planet formation.

\n Context. Each transiting planet discovered is characterized by 7\nmeasurable quantities, that may or may not be linked. This\nincludes those relative to the planet (mass, radius, orbital period, and\nequilibrium temperature) and those relative to the star (mass, radius, \neffective temperature, and metallicity). Correlations between planet\nmass and period, surface gravity and period, planet radius and star\ntemperature have been previously observed among the 31 known transiting\ngiant planets. Two classes of planets have been previously identified based on their\nSafronov number.\n Aims. We use the CoRoTlux transit surveys to compare simulated events to\n the sample of discovered planets and test the statistical\nsignificance of these correlations. Using a model proved to be able to\nmatch the yield of OGLE transit survey, we generate a large sample of\nsimulated detections, in which we can statistically test the different\ntrends observed in the small sample of known transiting planets.\n Methods. We first generate a stellar field with planetary companions based on\n radial velocity discoveries, use a planetary evolution model\n assuming a variable fraction of heavy elements to compute the\n characteristics of transit events, then apply a detection\n criterion that includes both statistical and red noise\n sources. We compare the yield of our simulated survey\n with the ensemble of 31 well-characterized giant transiting\n planets, using different statistical tools, including a multivariate\n logistic analysis to assess whether the simulated distribution\n matches the known transiting planets.\n Results. Our results satisfactorily match the distribution of known transiting\n planet characteristics. Our multivariate analysis shows that our simulated \n sample and observations are consistent to 76%. The mass vs. period correlation for giant\n planets first observed with radial velocity holds with transiting\n planets. The correlation between surface gravity and period can be\n explained as the combined effect of the mass vs. period lower limit\n and by the decreasing transit probability and detection efficiency\n for longer periods and higher surface gravity. Our model also\n naturally explains other trends, like the correlation between\n planetary radius and stellar effective temperature. Finally, we are\n also able to reproduce the previously observed apparent bimodal\n distribution of planetary Safronov numbers in 10% of our simulated\n cases, although our model predicts a continuous\n distribution. This shows that the evidence for the existence of two\n groups of planets with different intrinsic properties is not\n statistically significant.\n

Corrigendum to ‘Deep learning improves taphonomic resolution: high accuracy in differentiating tooth marks made by lions and jaguars'

The study of exoplanets provides crucial insights into the nature of planetary atmospheres and orbital dynamics. Transit photometry and secondary eclipse observations have become revolutionary tools in this field. This case study focuses on WASP-32b, a hot Jupiter orbiting an F-type star about 950 light years away in the constellation Pisces. Our objective is to probe the atmospheric and orbital characteristics of WASP-32b through light curve analysis. Data were collected from both ground-based and space-based observatories. SuperWASP-South at the South African Astronomical Observatory first detected WASP-32b using transit photometry. The Swiss Euler Telescope at La Silla Observatory and its CORALIE spectrograph provided radial velocity confirmation, planetary mass, and orbital parameters. Space telescopes contributed complementary data: the Spitzer Space Telescope measured secondary eclipse photometry in the infrared (3.6 µm and 4.5 µm), constraining thermal emission and albedo, while TESS delivered high-precision optical transit data that refined planetary radius and orbital period. Analysis of these datasets reveals signatures of thermal emission, constraints on reflective properties, and preliminary indications of atmospheric circulation. The results underline the importance of multi-wavelength light curves for atmospheric characterization and establish WASP-32b as a significant benchmark for understanding hot Jupiter systems

The purpose of this study was to examine the performance of Naive Bayes, k-nearest neighborhood, neural networks, and logistic regression analysis in terms of sample size and test data rate in classifying students according to their mathematics performance. The target population was 62728 students in the 15-year-old group who were participated in the Programme for International Student Assessment (PISA) in 2012 from The Organisation for Economic Co-operation and Development (OECD) countries. The performance of each algorithm was tested by using 11%, 22%, 33%, 44% and 55% of each dataset for small (500 students), medium (1000 students) and large (5000 students) sample sizes. 100 replications were performed for each analysis. As the evaluation criteria, accuracy rates, RMSE values, and total elapsed time were used. RMSE values for each algorithm were statistically compared by using Friedman and Wilcoxon tests. The results revealed that while the classification performance of the methods increased as the sample size increased, the increase of training data ratio had different effects on the performance of the algorithms. The Naive Bayes showed high performance even in small samples, performed the analyzes very quickly, and was not affected by the change in the training data ratio. Logistic regression analysis was the most effective method in large samples but had a poor performance in small samples. While neural networks showed a similar tendency, its overall performance was lower than Naive Bayes and logistic regression. The lowest performances in all conditions were obtained by the k-nearest neighborhood algorithm.

A few studies have reported a significant dearth of exoplanets with Neptune\nmass and radius with orbital periods below $2$--$4$ d. This cannot be explained\nby observational biases because many Neptunian planets with longer orbital\nperiods have been detected. The existence of this desert is similar to the\nappearance of the so-called brown-dwarf desert that suggests different\nformation mechanisms of planets and stellar companions with short orbital\nperiods. Similarly, the Neptunian desert might indicate different mechanisms of\nformation and evolution for hot Jupiters and short-period super-Earths. We here\nfollow a previous study and examine the location and shape of the desert in\nboth the period-mass and period-radius planes, using the currently available\nlarge samples of planets. The desert in the period-mass plane has a relatively\nsharp upper edge, with a planetary mass that is inversely proportional to the\nplanetary orbital period, while the lower, somewhat blurred, boundary is\nlocated along masses that are apparently linearly proportional to the period.\nThe desert in the period-radius plane of the transiting planets is less clear.\nIt seems as if the radius along the upper boundary is inversely proportional to\nthe period to the power of one-third, while the lower boundary shows a radius\nthat is proportional to the period to the power of two-thirds. The combination\nof the two upper bounds of the desert, in the period-mass and period-radius\nplanes, yields a planetary mass-radius relation of $R_{\\rm p}/R_{\\rm Jup}\\simeq\n(1.2\\pm0.3)(M_{\\rm p}/M_{\\rm Jup})^{0.27\\pm0.11}\\,$ for $ 0.1\\lesssim M_{\\rm\np}/M_{\\rm Jup}\\lesssim 1$. The derived shape of the desert, which might extend\nup to periods of $5$--$10$ d, could shed some light on the formation and\nevolution of close-in planets.\n

We present precise Doppler measurements of four stars obtained during the past decade at Keck Observatory by the California Planet Survey (CPS). These stars, namely, HD 34445, HD 126614, HD 13931, and Gl 179, all show evidence for a single planet in Keplerian motion. We also present Doppler measurements from the Hobby-Eberly Telescope (HET) for two of the stars, HD 34445 and Gl 179, that confirm the Keck detections and significantly refine the orbital parameters. These planets add to the statistical properties of giant planets orbiting near or beyond the ice line, and merit follow-up by astrometry, imaging, and space-borne spectroscopy. Their orbital parameters span wide ranges of planetary minimum mass (M sin i = 0.38-1.9 M_Jup), orbital period (P = 2.87-11.5 yr), semi-major axis (a = 2.1-5.2 AU), and eccentricity (e = 0.02-0.41). HD 34445b (P = 2.87 yr, M sin i = 0.79 M_Jup, e = 0.27) is a massive planet orbiting an old, G-type star. We announce a planet, HD 126614Ab, and an M dwarf, HD 126614B, orbiting the metal-rich star HD 126614 (which we now refer to as HD 126614A). The planet, HD 126614Ab, has minimum mass M sin i = 0.38 M_Jup and orbits the stellar primary with period P = 3.41 yr and orbital separation a = 2.3 AU. The faint M dwarf companion, HD 126614B, is separated from the stellar primary by 489 mas (33 AU) and was discovered with direct observations using adaptive optics and the PHARO camera at Palomar Observatory. The stellar primary in this new system, HD 126614 A, has the highest measured metallicity (\feh = +0.56) of any known planet-bearing star. HD 13931b (P = 11.5 yr, M sin i = 1.88 M_Jup, e = 0.02) is a Jupiter analog orbiting a near solar twin. Gl 179b (P = 6.3 yr, M sin i = 0.82 M_Jup, e = 0.21) is a massive planet orbiting a faint M dwarf. The high metallicity of Gl 179 is consistent with the planet-metallicity correlation among M dwarfs, as documented recently by Johnson and Apps.

In this chapter, we discuss large sample theory that can be applied under conditions that are quite likely to be met in large samples even when the Gauss–Markov conditions are broken. There are two reasons for using large sample theory. First, there may be some problems that corrupt our estimators in small samples but tends to diminish down as the sample gets bigger. Thus, if we cannot get a perfect small sample estimator, we will usually want to choose the one that will be best in large samples. Second, in some circumstances, the theory used to derive the properties of estimators in small samples just does not work, and working out the properties of the estimators can be impossible. This makes it very hard to choose between alternative estimators. In these circumstances we judge different estimators on their “large sample properties” because their “small (or finite) sample properties” are unknown.

Nanosuspensions have been used for enhancing the bioavailability of poorly soluble drugs. This study explores the temperature evolution during their preparation in a wet stirred media mill using a coupled experimental-enthalpy balance approach. Milling was performed at three levels of stirrer speed, bead loading, and bead sizes. Temperatures were recorded over time, then simulated using an enthalpy balance model by fitting the fraction of power converted to heat ξ. Moreover, initial and final power, ξ, and temperature profiles at 5 different test runs were predicted by power-law (PL) and machine learning (ML) approaches. Heat generation was higher at the higher stirrer speed and bead loading/size, which was explained by the higher power consumption. Despite its simplicity with a single fitting parameter ξ, the enthalpy balance model fitted the temperature evolution well with root mean squared error (RMSE) of 0.40-2.34°C. PL and ML approaches provided decent predictions of the temperature profiles in the test runs, with RMSE of 0.93-4.17 and 1.00-2.17°C, respectively. We established the impact of milling parameters on heat generation-power and demonstrated the simulation-prediction capability of an enthalpy balance model when coupled to the PL-ML approaches.

Classification and prediction tasks are common in health research. With the increasing availability of vast health data repositories (e.g. electronic medical record databases) and advances in computing power, traditional statistical approaches are being augmented or replaced with machine learning (ML) approaches to classify and predict health outcomes. ML describes the automated process of identifying ("learning") patterns in data to perform tasks. Developing an ML model includes selecting between many ML models (e.g. decision trees, support vector machines, neural networks); model specifications such as hyperparameter tuning; and evaluation of model performance. This process is conducted repeatedly to find the model and corresponding specifications that optimize some measure of model performance. ML models can make more accurate classifications and predictions than their statistical counterparts and confer greater flexibility when modelling unstructured data or interactions between covariates; however, many ML models require larger sample sizes to achieve good classification or predictive performance and have been criticized as "black box" for their poor transparency and interpretability. ML holds potential in family medicine for risk profiling of patients' disease risk and clinical decision support to present additional information at times of uncertainty or high demand. In the future, ML approaches are positioned to become commonplace in family medicine. As such, it is important to understand the objectives that can be addressed using ML approaches and the associated techniques and limitations. This article provides a brief introduction into the use of ML approaches for classification and prediction tasks in family medicine.

We reanalyse the time-variable light curves of the transiting planetary system PTFO 8-8695, in which a planet of 3 to 4 Jupiter masses orbits a rapidly rotating pre-main-sequence star. Both the planetary orbital period Porb of 0.448 d and the stellar spin period Ps of less than 0.671 d are unusually short, which makes PTFO 8-8695 an ideal system to check the model of gravity darkening and nodal precession. While the previous analysis of PTFO 8-8695 assumed that the stellar spin and planetary orbital periods are the same, we extend the analysis by discarding the spin–orbit synchronous condition, and find three different classes of solutions roughly corresponding to the nodal precession periods of 199 ± 16, 475 ± 21, and 827 ± 53 d that reproduce the transit light curves observed in 2009 and 2010. We compare the predicted light curves of the three solutions against the photometry data of a few percent accuracy obtained at Koyama Astronomical Observatory in 2014 and 2015, and find that the solution with a precession period of 199 ± 16 d is preferred even though it is preliminary. Future prospects and implications for other transiting systems are briefly discussed.