arXiv subjects

Nathan C. Hara

Publications and source records attributed to Nathan C. Hara.

9 recordsLinked to original sources

arXiv2025

A continuous multiple hypothesis testing framework for optimal exoplanet detection

When searching for exoplanets, one wants to count how many planets orbit a given star, and to determine what their characteristics are. If the estimated planet characteristics are too far from those of a planet truly present, this should be considered as a false detection. This setting is a particular instance of a general one: aiming to retrieve parametric components in a dataset corrupted by nuisance signals, with a certain accuracy on their parameters. We exhibit a detection criterion minimizing false and missed detections, either as a function of their relative cost or when the expected number of false detections is bounded. If the components can be separated in a technical sense discussed in detail, the optimal detection criterion is a posterior probability obtained as a by-product of Bayesian evidence calculations. Optimality is guaranteed within a model, and we introduce model criticism methods to ensure that the criterion is robust to model errors. We show on two simulations emulating exoplanet searches that the optimal criterion can significantly outperform other criteria. Finally, we show that our framework offers solutions for the identification of components of mixture models and Bayesian false discovery rate control when hypotheses are not discrete.

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arXiv2023

New Mass and Radius Constraints on the LHS 1140 Planets -- LHS 1140 b is Either a Temperate Mini-Neptune or a Water World

The two-planet transiting system LHS 1140 has been extensively observed since its discovery in 2017, notably with $Spitzer$, HST, TESS, and ESPRESSO, placing strong constraints on the parameters of the M4.5 host star and its small temperate exoplanets, LHS 1140 b and c. Here, we reanalyse the ESPRESSO observations of LHS 1140 with the novel line-by-line framework designed to fully exploit the radial velocity content of a stellar spectrum while being resilient to outlier measurements. The improved radial velocities, combined with updated stellar parameters, consolidate our knowledge on the mass of LHS 1140 b (5.60$\pm$0.19 M$_{\oplus}$) and LHS 1140 c (1.91$\pm$0.06 M$_{\oplus}$) with unprecedented precision of 3%. Transits from $Spitzer$, HST, and TESS are jointly analysed for the first time, allowing us to refine the planetary radii of b (1.730$\pm$0.025 R$_{\oplus}$) and c (1.272$\pm$0.026 R$_{\oplus}$). Stellar abundance measurements of refractory elements (Fe, Mg and Si) obtained with NIRPS are used to constrain the internal structure of LHS 1140 b. This planet is unlikely to be a rocky super-Earth as previously reported, but rather a mini-Neptune with a $\sim$0.1% H/He envelope by mass or a water world with a water-mass fraction between 9 and 19% depending on the atmospheric composition and relative abundance of Fe and Mg. While the mini-Neptune case would not be habitable, a water-abundant LHS 1140 b potentially has habitable surface conditions according to 3D global climate models, suggesting liquid water at the substellar point for atmospheres with relatively low CO$_2$ concentration, from Earth-like to a few bars.

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arXiv2023

Statistical methods for exoplanet detection with radial velocities

Exoplanets can be detected with various observational techniques. Among them, radial velocity (RV) has the key advantages of revealing the architecture of planetary systems and measuring planetary mass and orbital eccentricities. RV observations are poised to play a key role in the detection and characterization of Earth twins. However, the detection of such small planets is not yet possible due to very complex, temporally correlated instrumental and astrophysical stochastic signals. Furthermore, exploring the large parameter space of RV models exhaustively and efficiently presents difficulties. In this review, we frame RV data analysis as a problem of detection and parameter estimation in unevenly sampled, multivariate time series. The objective of this review is two-fold: to introduce the motivation, methodological challenges, and numerical challenges of RV data analysis to nonspecialists, and to unify the existing advanced approaches in order to identify areas for improvement.

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arXiv2023

Radial-velocity discovery of a second planet in the TOI-1338/BEBOP-1 circumbinary system

We report the detection of a gas-giant planet in orbit around both stars of an eclipsing binary star system that also contains the smaller, inner transiting planet TOI-1338b. The new planet, called TOI-1338/BEBOP-1c, was discovered using radial-velocity data collected with the HARPS and ESPRESSO spectrographs. Our analysis reveals it is a $65.2~\rm{M_{\oplus}}$ circumbinary planet with a period of $215.5~$days. This is the first detection of a circumbinary planet using radial-velocity observations alone, and makes TOI-1338/BEBOP-1 only the second confirmed multiplanet circumbinary system to date. We do not detect the smaller inner transiting planet with radial-velocity data, and can place an upper limit on the inner planet's mass at $21.8~\mathrm{M}_\oplus$ with $99\%$ confidence. The inner planet is the first circumbinary planet amenable for atmospheric characterisation, using the James Webb Space Telescope.

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arXiv2023

A statistical model of stellar variability. I. FENRIR: a physics-based model of stellar activity, and its fast Gaussian process approximation

The detection of terrestrial planets by radial velocity and photometry is hindered by the presence of stellar signals. Those are often modeled as stationary Gaussian processes, whose kernels are based on qualitative considerations, which do not fully leverage the existing physical understanding of stars. Our aim is to build a formalism which allows to transfer the knowledge of stellar activity into practical data analysis methods. In particular, we aim at obtaining kernels with physical parameters. This has two purposes: better modelling signals of stellar origin to find smaller exoplanets, and extracting information about the star from the statistical properties of the data. We consider several observational channels such as photometry, radial velocity, activity indicators, and build a model called FENRIR to represent their stochastic variations due to stellar surface inhomogeneities. We compute analytically the covariance of this multi-channel stochastic process, and implement it in the S+LEAF framework to reduce the cost of likelihood evaluations from $O(N^3)$ to $O(N)$. We also compute analytically higher order cumulants of our FENRIR model, which quantify its non-Gaussianity. We obtain a fast Gaussian process framework with physical parameters, which we apply to the HARPS-N and SORCE observations of the Sun, and constrain a solar inclination compatible with the viewing geometry. We then discuss the application of our formalism to granulation. We exhibit non-Gaussianity in solar HARPS radial velocities, and argue that information is lost when stellar activity signals are assumed to be Gaussian. We finally discuss the origin of phase shifts between RVs and indicators, and how to build relevant activity indicators. We provide an open-source implementation of the FENRIR Gaussian process model with a Python interface.

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arXiv2021

BEBOP III. Observations and an independent mass measurement of Kepler-16 (AB) b -- the first circumbinary planet detected with radial velocities

The radial velocity method is amongst the most robust and most established means of detecting exoplanets. Yet, it has so far failed to detect circumbinary planets despite their relatively high occurrence rates. Here, we report velocimetric measurements of Kepler-16A, obtained with the SOPHIE spectrograph, at the Observatoire de Haute-Provence's 193cm telescope, collected during the BEBOP survey for circumbinary planets. Our measurements mark the first radial velocity detection of a circumbinary planet, independently determining the mass of Kepler-16~(AB)~b to be $0.313 \pm 0.039\,{\rm M}_{\rm Jup}$, a value in agreement with eclipse timing variations. Our observations demonstrate the capability to achieve photon-noise precision and accuracy on single-lined binaries, with our final precision reaching $\rm 1.5~m\,s^{-1}$ on the binary and planetary signals. Our analysis paves the way for more circumbinary planet detections using radial velocities which will increase the relatively small sample of currently known systems to statistically relevant numbers, using a method that also provides weaker detection biases. Our data also contain a long-term radial velocity signal, which we associate with the magnetic cycle of the primary star.

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arXiv2021

Testing whether a signal is strictly periodic. Application to disentangling planets and stellar activity in radial velocities

Searches for periodicity in time series are often done with models of periodic signals, whose statistical significance is assessed via false alarm probabilities or Bayes factors. However, a statistically significant periodic model might not originate from a strictly periodic source. In astronomy in particular, one expects transient signals that show periodicity for a certain amount of time before vanishing. This situation is encountered for instance in the search for planets in radial velocity data. While planetary signals are expected to have a stable phase, amplitude and frequency - except when strong planet-planet interactions are present - signals induced by stellar activity will typically not exhibit the same stability. In the present article, we explore the use of periodic functions multiplied by time windows to diagnose whether an apparently periodic signal is truly so. We suggest diagnostics to check whether a signal is consistently present in the time series, and has a stable phase, amplitude and period. The tests are expressed both in a periodogram and Bayesian framework. Our methods are applied to the Solar HARPS-N data as well as HD 215152, HD 69830 and HD 13808. We find that (i) the HARPS-N Solar data exhibits signals at the Solar rotation period and its first harmonic ($\sim$ 13.4 days). The frequency and phase of the 13.4 days signal appear constant within the estimation uncertainties, but its amplitude presents significant variations which can be mapped to activity levels. (ii) as previously reported, we find four, three and two planets orbiting HD 215152, HD 69830 and HD 13808.

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arXiv2021

Improving exoplanet detection capabilities with the false inclusion probability. Comparison with other detection criteria in the context of radial velocities

Context. In exoplanet searches with radial velocity data, the most common statistical significance metrics are the Bayes factor and the false alarm probability (FAP). Both have proved useful, but do not directly address whether an exoplanet detection should be claimed. Furthermore, it is unclear which detection threshold should be taken and how robust the detections are to model misspecification. Aims. The present work aims at defining a detection criterion which conveys as precisely as possible the information needed to claim an exoplanet detection. We compare this new criterion to existing ones in terms of sensitivity and robustness. Methods. We define a significance metric called the false inclusion probability (FIP) based on the posterior probability of presence of a planet. Posterior distributions are computed with the nested sampling package Polychord. We show that for FIP and Bayes factor calculations, defining priors on linear parameters as Gaussian mixture models allows to significantly speed up computations. The performances of the FAP, Bayes factor and FIP are studied with simulations as well as analytical arguments. We compare the methods assuming the model is correct, then evaluate their sensitivity to the prior and likelihood choices. Results. Among other properties, the FIP offers ways to test the reliability of the significance levels, it is particularly efficient to account for aliasing and allows to exclude the presence of planets with a certain confidence. We find that, in our simulations, the FIP outperforms existing detection metrics. We show that planet detections are sensitive to priors on period and semi-amplitude and that letting free the noise parameters offers better performances than fixing a noise model based on a fit to ancillary indicators.

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arXiv2016

Radial Velocity Data Analysis with Compressed Sensing Techniques

We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian processes framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen.

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