arXiv subjects

Roman V. Baluev

Publications and source records attributed to Roman V. Baluev.

At least 19 recordsLinked to original sources

arXiv2025

Cleaning WASP-33 b transits from the host star photometric variability: analysis of TESS data from two sectors

Based on TESS observations of a $δ$ Scuti variable WASP-33 obtained in 2019 and 2022, we thoroughly investigate the power spectrum of this target photometric flux and construct a statistically exhaustive model for its variability. This model contains $30$ robustly justified harmonics detected in the both TESS sectors simultaneously, $13$ less robust harmonics detected in a single TESS sector, a red noise and a quasiperiodic noise terms. This allowed us to greatly improve the accuracy of the exoplanet WASP-33 b transit timings, reducing the TTV residuals r.m.s. drastically, by a factor of $3.5$, from $63$ s to $18$ s. Finally, our analysis does not confirm existence of a detectable orbital phase variation claimed previously based on WASP-33 TESS photometry of 2019.

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arXiv2022

Comparing the frequentist and Bayesian periodic signal detection: rates of statistical mistakes and sensitivity to priors

We perform extensive Monte Carlo simulations to systematically compare the frequentist and Bayesian treatments of the Lomb--Scargle periodogram. The goal is to investigate whether the Bayesian period search is advantageous over the frequentist one in terms of the detection efficiency, how much if yes, and how sensitive it is regarding the choice of the priors, in particular in case of a misspecified prior (whenever the adopted prior does not match the actual distribution of physical objects). We find that the Bayesian and frequentist analyses always offer nearly identical detection efficiency in terms of their tradeoff between type-I and type-II mistakes. Bayesian detection may reveal a formal advantage if the frequency prior is nonuniform, but this results in only $\sim 1$ per cent extra detected signals. In case if the prior was misspecified (adopting nonuniform one over the actual uniform) this may turn into an opposite advantage of the frequentist analysis. Finally, we revealed that Bayes factor of this task appears rather overconservative if used without a calibration against type-I mistakes (false positives), thereby necessitating such a calibration in practice.

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arXiv2021

The impact of photospheric brightness field on exoplanetary transit timings and the TTV excess of HD 189733 b

We consider the issue of excessive TTV noise observed for the exoplanet HD 189733 b. Trying to explain it through the host star photospheric activity, we model the stellar surface brightness as a random field, then characterize statistical properties of the resulting transit signal perturbation and compute individual corrections to transit timings uncertainties. We find that possible effect of the photospheric brightness field can explain only a minor portion ($\sim 10$ s) of the observed ($\sim 70$ s) TTV excess of HD 189733, suggesting that the rest should be attributed to other sources. Regarding the photospheric pattern, we place an upper limit of $\sim 0.01$ on the combination $\varepsilon_{\rm cell} r_{\rm cell}$, where $\varepsilon_{\rm cell}$ is the relative magnitude of brightness variations, and $r_{\rm cell}$ is the geometric cellularity scale (relative to star radius).

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arXiv2018

Fast error-controlling MOID computation for confocal elliptic orbits

We present an algorithm to compute the minimum orbital intersection distance (MOID), or global minimum of the distance between the points lying on two Keplerian ellipses. This is achieved by finding all stationary points of the distance function, based on solving an algebraic polynomial equation of $16$th degree. The algorithm tracks numerical errors appearing on the way, and treats carefully nearly degenerate cases, including practical cases with almost circular and almost coplanar orbits. Benchmarks confirm its high numeric reliability and accuracy, and that regardless of its error--controlling overheads, this algorithm pretends to be one of the fastest MOID computation methods available to date, so it may be useful in processing large catalogs.

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arXiv2018

PlanetPack3: a radial-velocity and transit analysis tool for exoplanets

PlanetPack, initially released in 2013, is a command-line software aimed to facilitate exoplanets detection, characterization, and basic dynamical $N$-body simulations. This paper presents the third major release of PlanetPack that incorporates multiple improvements in comparison to the legacy versions. The major ones include: (i) modelling noise by Gaussian processes that in addition to the classic white noise may optionally include multiple components of the red noise, modulated noise, quasiperiodic noise (to be added soon in minor subversions of the 3.x series); (ii) an improved pipeline for TTV analysis of photometric data that includes quadratic limb-darkening model and automatic red-noise detection; (iii) self-consistent joint fitting of photometric + radial velocity data with full access to all the functionality inherited from the legacy PlanetPack; (iv) modelling of the Rossiter-McLaughlin effect for arbitrary eclipser/star radii ratio, and optionally including corrections that take into account average characteristics of a multiline stellar spectrum; (v) speed improvements through multithreading and CPU-optimized BLAS libraries. PlanetPack was written in pure C++ (standard of 2011), and is expected to be run on a wide range of platforms.

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arXiv2018

Statistical detection of patterns in unidimensional distributions by continuous wavelet transforms

Objective detection of specific patterns in statistical distributions, like groupings or gaps or abrupt transitions between different subsets, is a task with a rich range of applications in astronomy: Milky Way stellar population analysis, investigations of the exoplanets diversity, Solar System minor bodies statistics, extragalactic studies, etc. We adapt the powerful technique of the wavelet transforms to this generalized task, making a strong emphasis on the assessment of the patterns detection significance. Among other things, our method also involves optimal minimum-noise wavelets and minimum-noise reconstruction of the distribution density function. Based on this development, we construct a self-closed algorithmic pipeline aimed to process statistical samples. It is currently applicable to single-dimensional distributions only, but it is flexible enough to undergo further generalizations and development.

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arXiv2016

State of the Field: Extreme Precision Radial Velocities

The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state of the art Doppler precision and identified the critical path challenges for reaching 10 cm/s measurement precision. The presentations and discussion of key issues for instrumentation and data analysis and the workshop recommendations for achieving this precision are summarized here. Beginning with the HARPS spectrograph, technological advances for precision radial velocity measurements have focused on building extremely stable instruments. To reach still higher precision, future spectrometers will need to produce even higher fidelity spectra. This should be possible with improved environmental control, greater stability in the illumination of the spectrometer optics, better detectors, more precise wavelength calibration, and broader bandwidth spectra. Key data analysis challenges for the precision radial velocity community include distinguishing center of mass Keplerian motion from photospheric velocities, and the proper treatment of telluric contamination. Success here is coupled to the instrument design, but also requires the implementation of robust statistical and modeling techniques. Center of mass velocities produce Doppler shifts that affect every line identically, while photospheric velocities produce line profile asymmetries with wavelength and temporal dependencies that are different from Keplerian signals. Exoplanets are an important subfield of astronomy and there has been an impressive rate of discovery over the past two decades. Higher precision radial velocity measurements are required to serve as a discovery technique for potentially habitable worlds and to characterize detections from transit missions. The future of exoplanet science has very different trajectories depending on the precision that can ultimately be achieved with Doppler measurements.

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arXiv2015

Analytic models of the Rossiter-McLaughlin effect for arbitrary eclipser/star size ratios and arbitrary multiline stellar spectra

We present an attempt to improve models of the Rossiter-McLaughlin effect by relaxing several restrictive assumptions. We consider the entire multiline stellar spectrum rather than just a single line, use no assumptions about the shape of the lines profiles, and allow arbitrary size ratio for the star and its eclipser. However, we neglect the effect of macro-turbulence and differential rotation. We construct our model as a power series in the stellar rotation velocity, $V\sin i$, giving a closed set of analytic formulae for up to three terms, and assuming quadratic limb-darkening law. We consider three major approaches of determining the Doppler shift: cross-correlation with a predefined template, cross-correlation with an out-of-transit stellar spectrum, and parametric modelling of the spectrum. A numerical testcase revels that our model preserves good accuracy for the rotation velocity of up to the limit of $2-3$ times the average linewidth in the spectrum. We also apply our approach to the Doppler data of HD 189733, for which we obtain an improved model of the Rossiter-McLaughlin effect with two correction terms, and derive a reduced value for $V\sin i$.

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arXiv2015

Benchmarking the power of amateur observatories for TTV exoplanets detection

We perform an analysis of ~80000 photometric measurements for the following 10 stars hosting transiting planets: WASP-2, -4, -5, -52, Kelt-1, CoRoT-2, XO-2, TrES-1, HD 189733, GJ 436. Our analysis includes mainly transit lightcurves from the Exoplanet Transit Database, public photometry from the literature, and some proprietary photometry privately supplied by other authors. Half of these lightcurves were obtained by amateurs. From this photometry we derive 306 transit timing measurements, as well as improved planetary transit parameters. Additionally, for 6 of these 10 stars we present a set of radial velocity measurements obtained from the spectra stored in the HARPS, HARPS-N, and SOPHIE archives using the HARPS-TERRA pipeline. Our analysis of these TTV and RV data did not reveal significant hints of additional orbiting bodies in almost all of the cases. In the WASP-4 case, we found hints of marginally significant TTV signals having amplitude 10-20 sec, although their parameters are model-dependent and uncertain, while radial velocities did not reveal statistically significant Doppler signals.

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arXiv2014

Keplerian periodogram for Doppler exoplanets detection: optimized computation and analytic significance thresholds

We consider the so-called Keplerian periodogram, in which the putative detectable signal is modelled by a highly non-linear Keplerian radial velocity function, appearing in Doppler exoplanetary surveys. We demonstrate that for planets on high-eccentricity orbits the Keplerian periodogram is far more efficient than the classic Lomb-Scargle periodogram and even the multiharmonic periodograms, in which the periodic signal is approximated by a truncated Fourier series. We provide new numerical algorithm for computation of the Keplerian periodogram. This algorithm adaptively increases the parameteric resolution where necessary, in order to uniformly cover all local optima of the Keplerian fit. Thanks to this improvement, the algorithm provides more smooth and reliable results with minimized computing demands. We also derive a fast analytic approximation to the false alarm probability levels of the Keplerian periodogram. This approximation has the form $(P z^{3/2} + Q z) W \exp(-z)$, where $z$ is the observed periodogram maximum, $W$ is proportional to the settled frequency range, and the coefficients $P$ and $Q$ depend on the maximum eccentricity to scan.

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arXiv2014

Enhanced models for stellar Doppler noise reveal hints of a 13-year activity cycle of 55 Cancri

We consider the impact of Doppler noise models on the statistical robustness of the exoplanetary radial-velocity fits. We show that the traditional model of the Doppler noise with an additive jitter can generate large non-linearity effects, decreasing the reliability of the fit, especially in the cases when a correleated Doppler noise is involved. We introduce a regularization of the additive noise model that can gracefully eliminate its singularities together with the associated non-linearity effects. We apply this approach to Doppler time-series data of several exoplanetary systems. It demonstrates that our new regularized noise model yields orbital fits that have either increased or at least the same statistical robustness, in comparison with the simple additive jitter. Various statistical uncertainties in the parametric estimations are often reduced, while planet detection significance is often increased. Concerning the 55 Cnc five-planet system, we show that its Doppler data contain significant correlated ("red") noise. Its correlation timescale is in the range from days to months, and its magnitude is much larger than the effect of the planetary N-body perturbations in the radial velocity (these perturbations thus appear undetectable). Characteristics of the red noise depend on the spectrograph/observatory, and also show a cyclic time variation in phase with the public Ca II H & K and photometry measurements. We interpret this modulation as a hint of the long-term activity cycle of 55 Cnc, similar to the Solar 11-year cycle. We estimate the 55 Cnc activity period by $12.6\pm^{2.5}_{1.0}$ yrs, with the nearest minimum presumably expected in 2014 or 2015.

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arXiv2014

On the orbital structure of the HD 82943 multi-planet system

HD 82943 hosts a mysterious multi-planet system in the 2:1 mean-motion resonance that puzzles astronomers for more than a decade. We describe our new analysis of all radial velocity data currently available for this star, including both the most recent Keck data and the older but more numerous CORALIE measurements. Here we pay a major attention to the task of optimal scheduling of the future observation of this system. Applying several optimality criteria, we demonstrate that in the forthcoming observational season of HD 82943 (the winter 2014/2015) rather promising time ranges can be found. Observations of the near future may give rather remarkable improvement of the orbital fit, but only if we choose their time carefully.

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arXiv2014

PlanetPack software tool for exoplanets detection: coming new features

We briefly overview the new features of PlanetPack2, the forthcoming update of PlanetPack, which is a software tool for exoplanets detection and characterization from Doppler radial velocity data. Among other things, this major update brings parallelized computing, new advanced models of the Doppler noise, handling of the so-called Keplerian periodogram, and routines for transits fitting and transit timing variation analysis.

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arXiv2014

Possible solution to the riddle of HD 82943 multiplanet system: the three-planet resonance 1:2:5?

We carry out a new analysis of the published radial velocity data for the planet-hosting star HD82943. We include the recent Keck/HIRES measurements as well as the aged but much more numerous CORALIE data. We find that the CORALIE radial velocity measurements are polluted by a systematic annual variation which affected the robustness of many previous results. We show that after purging this variation, the residuals still contain a clear signature of an additional $\sim 1100$ days periodicity. The latter variation leaves significant hints in all three independent radial velocity subsets that we analysed: the CORALIE data, the Keck data acquired prior to a hardware upgrade, and the Keck data taken after the upgrade. We mainly treat this variation as a signature of a third planet in the system, although we cannot rule out other interpretations, such as long-term stellar activity. We find it easy to naturally obtain a stable three-planet radial-velocity fit close to the three-planet mean-motion resonance 1:2:5, with the two main planets (those in the 1:2 resonance) in an aligned apsidal corotation. The dynamical status of the third planet is still uncertain: it may reside in as well as slightly out of the 5:2 resonance. We obtain the value of $\sim 1075$ days for its orbital period and of $\sim 0.3 M_{\rm Jup}$ for its minimum mass, while the eccentric parameters are uncertain.

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arXiv2013

Detecting non-sinusoidal periodicities in observational data: the von Mises periodogram for variable stars and exoplanetary transits

This paper introduces an extension of the linear least-squares (or Lomb-Scargle) periodogram for the case when the model of the signal to be detected is non-sinusoidal and depends on unknown parameters in a non-linear manner. The attention is paid to the problem of estimating the statistical significance of candidate periodicities found using such non-linear periodograms. This problem is related to the task of quantifying the distributions of maximum values of these periodograms. Based on recent results in the mathematical theory of extreme values of random field (the generalized Rice method), we give a general approach to find handy analytic approximation for these distributions. This approximation has the general form $e^{-z} P(\sqrt z)$, where $P$ is an algebraic polynomial and $z$ being the periodogram maximum. The general tools developed in this paper can be used in a wide variety of astronomical applications, for instance in the studies of variable stars and extrasolar planets. For this goal, we develop and consider in details the so-called von Mises periodogram: a specialized non-linear periodogram where the signal is modelled by the von Mises periodic function $\exp(ν\cos ωt)$. This simple function with an additional non-linear parameter $ν$ can model lightcurves of many astronomical objects that show periodic photometric variability of different nature. We prove that our approach can be perfectly applied to this non-linear periodogram. We provide a package of auxiliary C++ programs, attached as the online-only material. They should faciliate the use of the von Mises periodogram in practice.

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arXiv2013

Detecting multiple periodicities in observational data with the multifrequency periodogram - II. Frequency Decomposer, a parallelized time-series analysis algorithm

This is a parallelized algorithm performing a decomposition of a noisy time series into a number of sinusoidal components. The algorithm analyses all suspicious periodicities that can be revealed, including the ones that look like an alias or noise at a glance, but later may prove to be a real variation. After selection of the initial candidates, the algorithm performs a complete pass through all their possible combinations and computes the rigorous multifrequency statistical significance for each such frequency tuple. The largest combinations that still survived this thresholding procedure represent the outcome of the analysis. The parallel computing on a graphics processing unit (GPU) is implemented through CUDA and brings a significant performance increase. It is still possible to run FREDEC solely on CPU in the traditional single-threaded mode, when no suitable GPU device is available. To verify the practical applicability of our algorithm, we apply it to an artificial time series as well as to some real-life exoplanetary radial-velocity data. We demonstrate that FREDEC can successfully reveal several known exoplanets. Moreover, it detected a new $9.8$-day variation in the Lick data for the five-planet system of 55 Cnc. It might indicate the existence of a small sixth planet in the 3:2 commensurability with the planet 55 Cnc b, although this detection is model-dependent and still needs a detailed verification.

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arXiv2013

Detecting multiple periodicities in observational data with the multi-frequency periodogram. I. Analytic assessment of the statistical significance

We consider the "multi-frequency" periodogram, in which the putative signal is modelled as a sum of two or more sinusoidal harmonics with idependent frequencies. It is useful in the cases when the data may contain several periodic components, especially when their interaction with each other and with the data sampling patterns might produce misleading results. Although the multi-frequency statistic itself was already constructed, e.g. by G. Foster in his CLEANest algorithm, its probabilistic properties (the detection significance levels) are still poorly known and much of what is deemed known is unrigourous. These detection levels are nonetheless important for the data analysis. We argue that to prove the simultaneous existence of all $n$ components revealed in a multi-periodic variation, it is mandatory to apply at least $2^n-1$ significance tests, among which the most involves various multi-frequency statistics, and only $n$ tests are single-frequency ones. The main result of the paper is an analytic estimation of the statistical significance of the frequency tuples that the multi-frequency periodogram can reveal. Using the theory of extreme values of random fields (the generalized Rice method), we find a handy approximation to the relevant false alarm probability. For the double-frequency periodogram this approximation is given by an elementary formula $\fracπ{16} W^2 e^{-z} z^2$, where $W$ stands for a normalized width of the settled frequency range, and $z$ is the observed periodogram maximum. We carried out intensive Monte Carlo simulations to show that the practical quality of this approximation is satisfactory. A similar analytic expression for the general multi-frequency periodogram is also given in the paper, though with a smaller amount of numerical verification.

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arXiv2013

PlanetPack: a radial-velocity time-series analysis tool facilitating exoplanets detection, characterization, and dynamical simulations

We present PlanetPack, a new software tool that we developed to facilitate and standardize the advanced analysis of radial velocity (RV) data for the goal of exoplanets detection, characterization, and basic dynamical $N$-body simulations. PlanetPack is a command-line interpreter, that can run either in an interactive mode or in a batch mode of automatic script interpretation. Its major abilities include: (i) Advanced RV curve fitting with the proper maximum-likelihood treatment of unknown RV jitter; (ii) User-friendly multi-Keplerian as well as Newtonian $N$-body RV fits; (iii) Use of more efficient maximum-likelihood periodograms that involve the full multi-planet fitting (sometimes called as ``residual'' or ``recursive'' periodograms); (iv) Easily calculatable parametric 2D likelihood function level contours, reflecting the asymptotic confidence regions; (v) Fitting under some useful functional constraints is user-friendly; (vi) Basic tasks of short- and long-term planetary dynamical simulation using a fast Everhart-type integrator based on Gauss--Legendre spacings; (vii) Fitting the data with red noise (auto-correlated errors); (viii) Various analytical and numerical methods for the tasks of determining the statistical significance. It is planned that further functionality may be added to PlanetPack in the future. During the development of this software, a lot of effort was made to improve the calculational speed, especially for CPU-demanding tasks. PlanetPack was written in pure C++ (standard of 1998/2003), and is expected to be compilable and usable on a wide range of platforms.

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