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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)., Comment: 15 pages, 10 figures, 3 tables, accepted for publication in MNRAS

We homogeneously reanalyse $124$ transit light curves for the WASP-4 b hot Jupiter. This set involved new observations secured in 2019 and nearly all observations mentioned in the literature, including high-accuracy GEMINI/GMOS transmission spectroscopy of 2011-2014 and TESS observations of 2018. The analysis confirmed a nonlinear TTV trend with $P/|\dot P|\sim (17-30)$ Myr (1-sigma range), implying only half of the initial decay rate estimation. The trend significance is at least $3.4$-sigma in the agressively conservative treatment. Possible radial acceleration due to unseen companions is not revealed in Doppler data covering seven years 2007-2014, and radial acceleration of $-15$ m s$^{-1}$yr$^{-1}$ reported in a recent preprint by another team is not confirmed. If present, it is a very nonlinear RV variation. Assuming that the entire TTV is tidal in nature, the tidal quality factor $Q_\star'\sim (4.5-8.5)\cdot 10^4$ does not reveal a convincing disagreement with available theory predictions., Accepted to MNRAS Letters. 5 pages, 1 figure. TTV data files and an online-only PDF supplement are in the download archive

We perform statistical wavelet analysis of the Main Belt asteroids, seeking statistically significant asteroid families. The goal is to test the new wavelet analysis algorithm and to compare its results with more traditional methods like the hierarchic clustering. We first consider several 1D distributions for various physical and orbital parameters of asteroids. Then we consider three bivariate distributions for the three orbital parameters (a,e,i) taken pairwisely. The full 3D analysis of this space is not available here, but based on the 2D results we perform a disentangling of overlapped 2D families and derive total of 44 3D families with confirmed statistical significance., Comment: 24 pages, 11 figures, 3 tables; accepted by Celestial Mechanics & Dynamical Astronomy

We homogeneously analyse $\sim 3.2\times 10^5$ photometric measurements for $\sim 1100$ transit lightcurves belonging to $17$ exoplanet hosts. The photometric data cover $16$ years 2004--2019 and include amateur and professional observations. Old archival lightcurves were reprocessed using up-to-date exoplanetary parameters and empirically debiased limb-darkening models. We also derive self-consistent transit and radial-velocity fits for $13$ targets. We confirm the nonlinear TTV trend in the WASP-12 data at a high significance, and with a consistent magnitude. However, Doppler data reveal hints of a radial acceleration about $(-7.5\pm 2.2)$~m/s/yr, indicating the presence of unseen distant companions, and suggesting that roughly $10$ per cent of the observed TTV was induced via the light-travel (or Roemer) effect. For WASP-4, a similar TTV trend suspected after the recent TESS observations appears controversial and model-dependent. It is not supported by our homogeneus TTV sample, including $10$ ground-based EXPANSION lightcurves obtained in 2018 simultaneously with TESS. Even if the TTV trend itself does exist in WASP-4, its magnitude and tidal nature are uncertain. Doppler data cannot entirely rule out the Roemer effect induced by possible distant companions., Comment: 19 pages, 4 figures, 6 tables; revised manuscript submitted to MNRAS; online-only supplements are in the download archive

We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is expressed explicitly, using only elementary functions of orbital elements, and allows us to significantly increase the speed of processing for large asteroid catalogs. Benchmarks confirm high practical benefits of the lower bound constructed., Comment: 23 pages, 10 figures, 8 tables

We investigate 1D exoplanetary distributions using a novel analysis algorithm based on the continuous wavelet transform. The analysis pipeline includes an estimation of the wavelet transform of the probability density function (p.d.f.) without pre-binning, use of optimized wavelets, a rigorous significance testing of the patterns revealed in the p.d.f., and an optimized minimum-noise reconstruction of the p.d.f. via matching pursuit iterations. In the distribution of orbital periods, $P$, our analysis revealed a narrow subfamily of exoplanets within the broad family of "warm jupiters", or massive giants with $P\gtrsim 300$~d, which are often deemed to be related with the iceline accumulation in a protoplanetary disk. We detected a p.d.f. pattern that represents an upturn followed by an overshooting peak spanning $P\sim 300-600$~d, right beyond the "period valley". It is separated from the other planets by p.d.f. concavities from both sides. It has at least two-sigma significance. In the distribution of planet radii, $R$, and using the California Kepler Survey sample properly cleaned, we confirm the hints of a bimodality with two peaks about $R=1.3 R_\oplus$ and $R=2.4 R_\oplus$, and the "evaporation valley" between them. However, we obtain just a modest significance for this pattern, two-sigma only at the best. Besides, our follow-up application of the Hartigan & Hartigan dip test for unimodality returns $3$ per cent false alarm probability (merely $2.2$-sigma significance), contrary to $0.14$ per cent (or $3.2$-sigma), as claimed by Fulton et al. (2017)., 27 pages, 16 figures, 1 table; submitted to Ap&SS

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 $V\sin i$., Comment: Accepted to MNRAS; 23 pages, 5 figures, 2 tables

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., 18 pages, 5 tables, 18 figures; accepted for publication in MNRAS

We perform a detailed analysis of the latest HARPS and Keck radial velocity data for the planet-hosting red dwarf GJ581, which attracted a lot of attention in recent time. We show that these data contain important correlated noise component ("red noise") with the correlation timescale of the order of 10 days. This red noise imposes a lot of misleading effects while we work in the traditional white-noise model. To eliminate these misleading effects, we propose a maximum-likelihood algorithm equipped by an extended model of the noise structure. We treat the red noise as a Gaussian random process with exponentially decaying correlation function. Using this method we prove that: (i) planets b and c do exist in this system, since they can be independently detected in the HARPS and Keck data, and regardless of the assumed noise models; (ii) planet e can also be confirmed independently by the both datasets, although to reveal it in the Keck data it is mandatory to take the red noise into account; (iii) the recently announced putative planets f and g are likely just illusions of the red noise; (iv) the reality of the planet candidate GJ581 d is questionable, because it cannot be detected from the Keck data, and its statistical significance in the HARPS data (as well as in the combined dataset) drops to a marginal level of $\sim 2\sigma$, when the red noise is taken into account. Therefore, the current data for GJ581 really support existence of no more than four (or maybe even only three) orbiting exoplanets. The planet candidate GJ581 d requests serious observational verification., Comment: 19 pages, 12 figures, 3 tables; accepted to MNRAS

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., Comment: 45 pages, 23 Figures, workshop summary proceedings

We consider the task of distinguishing between two different alternative models that can roughly equally explain observed time series data, mainly focusing on the period ambiguity case (aliasing). We propose a test for checking whether the rival models are observationally equivalent for now or they are already distinguishable. It is the Vuong closeness test, which is based on the Kullback-Leibler Information Criterion. It is asymptotically normal and can work (in certain sense) even in the misspecified case, when the both proposed alternatives are actually wrong. This test is also very simple for practical use. We apply it to several known extrasolar planetary systems and find that our method often helps to resolve various model ambiguities emerging in astronomical practice, but preventing us from hasty conclusions in other cases.

We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original $N$-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet \emph{d}, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by $\sim 0.2$. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets \emph{b} and \emph{c} orbits by $5^\circ-15^\circ$, depending on the angular position of the mutual orbital nodes., 36 pages, 11 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronomy

Applications of the theory of optimal design of experiments to radial velocity planet search surveys are considered. Different optimality criteria are discussed, basing on the Fisher, Shannon, and Kullback-Leibler informations. Algorithms of optimal scheduling of RV observations for two important practical problems are considered. The first problem is finding the time for future observations to yield the maximum improvement of the precision of exoplanetary orbital parameters and masses. The second problem is finding the most favourable time for distinguishing alternative orbital fits (the scheduling of discriminating observations). These methods of optimal planning are demonstrated to be potentially efficient for multi-planet extrasolar systems, in particular for resonant ones. In these cases, the optimal dates of observations are often concentrated in quite narrow time segments., Comment: 8 pages, 2 figures, no tables, Accepted to MNRAS

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. They include an upper limit to the false alarm probability (or a lower limit to the significance). These estimations are tested numerically in order to establish regions of their practical applicability., Comment: 7 pages, 6 figures, 1 table; To be published in MNRAS

Existing algorithms of analysis of radial velocity time series are improved for the purposes of extrasolar planets detection and characterizing. Three important effects are considered: the poorly known radial velocity jitter, periodic systematic errors, and statistical bias due to non-linearity of models. Mathematical tools to account for these effects are developed and applied to a number of real planetary systems. In particular, it is shown that two outer planets of HD37124 are likely trapped in the 2/1 resonance. The dwarf star GJ876 may host an extra, Neptune-mass, planet which is in resonance with two giant planets in this system.

We perform an analysis of ~80 000 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 light curves from the Exoplanet Transit Database, public photometry from the literature, and some proprietary photometry privately supplied by other authors. Half of these light curves 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 transit timing and radial velocity 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 s, although their parameters are model dependent and uncertain, while radial velocities did not reveal statistically significant Doppler signals., Facultad de Ciencias Astronómicas y Geofísicas, Instituto de Astrofísica de La Plata

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., 2 pages, to appear in the proceedings of IAUS310 "Complex Planetary Systems"; the PlanetPack2 package can be downloaded at http://sourceforge.net/projects/planetpack

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., 16 pages, 6 figures; Accepted for publication in MNRAS; the PlanetPack2 code implementing the Keplerian periodogram computing can be downloaded at http://sourceforge.net/projects/planetpack

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., 21 pages, 12 figures, 3 tables; Accepted for publication in MNRAS; the PlanetPack2 code implementing these new Doppler noise models is available at http://sourceforge.net/projects/planetpack/

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., Comment: 4 pages, 1 figure, to appear in the proceedings of IAUS310 "Complex planetary systems"; v2 corrects "ELODIE" to "CORALIE" everywhere

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 $\frac{\pi}{16} W^2 e^{-z} z^2$, 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., Comment: Accepted to MNRAS; 14 pages with 9 figures; the computation package is available at http://sourceforge.net/projects/fredec

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 $\exp(\nu \cos \omega t)$. This simple function with an additional non-linear parameter $\nu$ 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., Comment: 14 pages, 5 figures; published in MNRAS. Version 2 here is the accepted manuscript with a reduced fig. 5 file and without copy-edit changes of the final published version. Notice added with v2: the von Mises periodogram computation package, along with any future updates, can be downloaded at http://sourceforge.net/projects/vonmises/

In this paper, the problem addressed is estimation of the false alarm probability, associated with maximum peaks on the periodograms, which are based on the least-squares fitting of the putative periodic signal. This class of periodograms include, for instance, the well-known Lomb-Scargle periodogram and multi-harmonic periodograms. The evaluation of the related distribution of the maximum periodogram values was performed using the so-called Rice method, based on the analysis of the number of up-crossings. This method allowed to obtain simple and closed approximations to the false alarm probability, associ- ated with maximum peaks on the periodograms. The comparison of these analytic approximations with results of Monte Carlo simulations shows that the precision of the analytic expressions should be suitable in the most practical cases. I. INTRODUCTION In many proctical problems in various reserch fields we of- ten deal with the task of detecting a periodic component, which our observational or experimental data can possibly contain. These input data may have various nature and structure, and the putative periodicity may have different physical sense (de- pending on the research field). For definiteness we will call the independent (one-dimensional) variable as "time" and denote it as t, though in practice its physical sense may differ from the physical time. The data array represent a sequence of discrete (also one-dimensional) measurements xi, taken at timings ti (which may be sampled arbitrarily, but are supposed to be known precisely). In addition, we usually have a sequence of quantities, characterising the measurement uncertainties. These quantities may be, for instance, the standard deviations of the measurement errors, σi, or the weights of observations wi ∝ 1/σ 2 i (so that the proportionality factor is ap riori unknown). These data can possibly contain a deterministic periodic signal of ap rioriunknown frequency f. The task is to detect this periodicity and (further) to estimate its parameters. One of the mostly popular mathematical tools solving this task is based on the periodogram approach. A periodogram is a function of the frequency of the putative periodic signal, which represents, in fact, some estimation of the power spectrum of the variable quantity being observed. High peaks on a periodogram indicate that the data likely contain a periodic signal of the respective frequency. However, the further prob- lem is to rigorously estimate the statistical significance of the observed periodogram peaks. It is this problem, which is addressed in this paper. To claim that the observed peak is statistically significant, we need first to evaluate the associated false alarm probability (hereafter FAP), i.e. the probability that a peak of the same or larger height could be inspired solely by measurement noise and then to check, whether it stays below some small tolerance level. The problem of evaluation of the FAP is directly connected with the problem of evaluation of the distribution function of the maximum periodogram value. This task is a non-trivial one, and in many publications this problem was considered (6), (7), (12)-(14), (17), (18), (20), (21). Recently, a significant progress was attained in this field by the author (2)-(5). In these papers, the approximations to the distribution function of the maximum are obtained using the so-called Rice method, which is based on the analysis of level up-crossings (1), (15). We present these results below.

The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the planetary system are found. In the first one, the outer planets c and d are trapped in the 2/1 mean-motion resonance. The second family of solutions corresponds to the 5/2 mean-motion resonance between these planets. In both families, the planets are locked in (or close to) an apsidal corotation resonance. In the case of the 2/1 MMR, it is an asymmetric apsidal corotation (with the difference between the longitudes of periastra $\Delta\omega\sim 60^\circ$), whereas in the case of the 5/2 MMR it is a symmetric antialigned one ($\Delta\omega = 180^\circ$). It remains also possible that the two outer planets are not trapped in an orbital resonance. Then their orbital eccentricities should be relatively small (less than, say, 0.15) and the ratio of their orbital periods is unlikely to exceed $2.3-2.5$., Comment: 28 pages, 10 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronomy

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' periodogram, which is being used for detection of non-sinusoidal signals, and is based on the least-squares fitting of truncated Fourier series. The recent investigation (Baluev 2008) made for the Lomb-Scargle periodogram is extended to the more general multi-harmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multi-harmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a suitable precision and robustness of these approximations., Comment: 8 pages, 6 figures, 1 table. Accepted to MNRAS

The role of radial velocity (RV) jitter in extrasolar planet search surveys is discussed. Based on the maximum likelihood principle, improved statistical algorithms for RV fitting and period search are developed. These algorithms incorporate a built-in jitter determination, so that resulting estimations of planetary parameters account for this jitter automatically. This approach is applied to RV data for several extrasolar planetary systems. It is shown that many RV planet search surveys suffer from periodic systematic errors which increase effective RV jitter and can lead to erroneous conclusions. For instance, the planet candidate HD74156 d may be a false detection made due to annual systematic errors., Comment: 10 pages, 1 figure, 1 table; accepted to MNRAS; 4th version due to a few extra minor corrections in Sect.11 and Tab.1

We demonstrate that moderate exoplanet radial velocity searches are often subject to the effect of the correlated (red) radial velocity noise. When disregarded, this effect may induce strong distortions in the results of the time series analysis and, ultimately, can even lead to false planet detections. We construct a maximum-likelihood algorithm, which is able to manage this issue rather efficiently.