Resonant chains are groups of planets for which each pair is in resonance, with an orbital period ratio locked at a rational value (2/1, 3/2, etc.). Such chains naturally form as a result of ...convergent migration of the planets in the proto-planetary disk. In this article, I present an analytical model of resonant chains of any number of planets. Using this model, I show that a system captured in a resonant chain can librate around several possible equilibrium configurations. The probability of capture around each equilibrium depends on how the chain formed, and especially on the order in which the planets have been captured in the chain. Therefore, for an observed resonant chain, knowing around which equilibrium the chain is librating allows for constraints to be put on the formation and migration scenario of the system. I apply this reasoning to the four planets orbiting Kepler-223 in a 3:4:6:8 resonant chain. I show that the system is observed around one of the six equilibria predicted by the analytical model. Using N-body integrations, I show that the most favorable scenario to reproduce the observed configuration is to first capture the two intermediate planets, then the outermost, and finally the innermost.
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Using high-contrast imaging with the SPHERE instrument at the Very Large Telescope (VLT), we report the first images of a cold brown dwarf companion to the exoplanet host star HD 4113A. The brown ...dwarf HD 4113C is part of a complex dynamical system consisting of a giant planet, a stellar host, and a known wide M-dwarf companion. Its separation of 535 ± 3 mas and H-band contrast of 13.35 ± 0.10 mag correspond to a projected separation of 22 AU and an isochronal mass estimate of 36 ± 5 MJ based on COND models. The companion shows strong methane absorption, and through fitting an atmosphere model, we estimate a surface gravity of logg = 5 and an effective temperature of ~500–600 K. A comparison of its spectrum with observed T dwarfs indicates a late-T spectral type, with a T9 object providing the best match. By combining the observed astrometry from the imaging data with 27 years of radial velocities, we use orbital fitting to constrain its orbital and physical parameters, as well as update those of the planet HD 4113A b, discovered by previous radial velocity measurements. The data suggest a dynamical mass of 66−4+5 $66^{+5}_{-4}$ 66−4+5 MJ and moderate eccentricity of 0.44−0.07+0.08 $0.44^{+0.08}_{-0.07}$ 0.44−0.07+0.08 for the brown dwarf. This mass estimate appears to contradict the isochronal estimate and that of objects with similar temperatures, which may be caused by the newly detected object being an unresolved binary brown dwarf system or the presence of an additional object in the system. Through dynamical simulations, we show that the planet may undergo strong Lidov-Kozai cycles, raising the possibility that it formed on a quasi-circular orbit and gained its currently observed high eccentricity (e ~ 0.9) through interactions with the brown dwarf. Follow-up observations combining radial velocities, direct imaging, and Gaia astrometry will be crucial to precisely constrain the dynamical mass of the brown dwarf and allow for an in-depth comparison with evolutionary and atmosphere models.
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Context.
HD 13724 is a nearby solar-type star at 43.48 ± 0.06 pc hosting a long-period low-mass brown dwarf detected with the CORALIE echelle spectrograph as part of the historical CORALIE ...radial-velocity search for extra-solar planets. The companion has a minimum mass of 26.77
−2.2
+4.4
M
Jup
and an expected semi-major axis of ~240 mas making it a suitable target for further characterisation with high-contrast imaging, in particular to measure its inclination, mass, and spectrum and thus establish its substellar nature.
Aims.
Using high-contrast imaging with the SPHERE instrument on the Very Large Telescope (VLT), we are able to directly image a brown dwarf companion to HD 13724 and obtain a low-resolution spectrum.
Methods.
We combine the radial-velocity measurements of CORALIE and HARPS taken over two decades and high-contrast imaging from SPHERE to obtain a dynamical mass estimate. From the SPHERE data we obtain a low-resolution spectrum of the companion from
Y
to
J
band, as well as photometric measurements from IRDIS in the
J
,
H
, and
K
bands.
Results.
Using high-contrast imaging with the SPHERE instrument at the VLT, we report the first images of a brown dwarf companion orbiting the host star HD 13724. It has an angular separation of 175.6 ± 4.5 mas and an
H
-band contrast of 10.61 ± 0.16 mag, and using the age estimate of the star to be ~1 Gyr gives an isochronal mass estimate of ~44
M
Jup
. By combining radial-velocity and imaging data we also obtain a dynamical mass of 50.5
−3.5
+3.3
M
Jup
. Through fitting an atmospheric model, we estimate a surface gravity of log
g
= 5.5 and an effective temperature of 1000 K. A comparison of its spectrum with observed T dwarfs estimates a spectral type of T4 or T4.5, with a T4 object providing the best fit.
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Efficient modeling of correlated noise Delisle, J.-B.; Hara, N.; Ségransan, D.
Astronomy and astrophysics (Berlin),
06/2020, Volume:
638
Journal Article
Peer reviewed
Open access
Correlated noise affects most astronomical datasets and to neglect accounting for it can lead to spurious signal detections, especially in low signal-to-noise conditions, which is often the context ...in which new discoveries are pursued. For instance, in the realm of exoplanet detection with radial velocity time series, stellar variability can induce false detections. However, a white noise approximation is often used because accounting for correlated noise when analyzing data implies a more complex analysis. Moreover, the computational cost can be prohibitive as it typically scales as the cube of the dataset size. For some restricted classes of correlated noise models, there are specific algorithms that can be used to help bring down the computational cost. This improvement in speed is particularly useful in the context of Gaussian process regression, however, it comes at the expense of the generality of the noise model. In this article, we present the
S + LEAF
noise model, which allows us to account for a large class of correlated noises with a linear scaling of the computational cost with respect to the size of the dataset. The
S + LEAF
model includes, in particular, mixtures of quasiperiodic kernels and calibration noise. This efficient modeling is made possible by a sparse representation of the covariance matrix of the noise and the use of dedicated algorithms for matrix inversion, solving, determinant computation, etc. We applied the
S + LEAF
model to reanalyze the HARPS radial velocity time series of the recently published planetary system HD 136352. We illustrate the flexibility of the
S + LEAF
model in handling various sources of noise. We demonstrate the importance of taking correlated noise into account, and especially calibration noise, to correctly assess the significance of detected signals.
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Efficient modeling of correlated noise Delisle, J.-B.; Hara, N.; Ségransan, D.
Astronomy and astrophysics (Berlin),
03/2020, Volume:
635
Journal Article
Peer reviewed
Open access
Periodograms are common tools used to search for periodic signals in unevenly spaced time series. The significance of periodogram peaks is often assessed using false alarm probability (FAP), which in ...most studies assumes uncorrelated noise and is computed using numerical methods such as bootstrapping or Monte Carlo. These methods have a high computational cost, especially for low FAP levels, which are of most interest. We present an analytical estimate of the FAP of the periodogram in the presence of correlated noise, which is fundamental to analyze astronomical time series correctly. The analytical estimate that we derive provides a very good approximation of the FAP at a much lower cost than numerical methods. We validate our analytical approach by comparing it with Monte Carlo simulations. Finally, we discuss the sensitivity of the method to different assumptions in the modeling of the noise.
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The ESA global astrometry space mission
Gaia
has been monitoring the position of a billion stars since 2014. The analysis of such a massive dataset is challenging in terms of the data processing ...involved. In particular, the blind detection and characterization of single or multiple companions to stars (planets, brown dwarfs, or stars) using
Gaia
astrometry requires highly efficient algorithms. In this article, we present a set of analytical methods to detect and characterize companions in scanning space astrometric time series as well as via a combination of astrometric and radial velocity time series. We propose a general linear periodogram framework and we derive analytical formulas for the false alarm probability (FAP) of periodogram peaks. Once a significant peak has been identified, we provide analytical estimates of all the orbital elements of the companion based on the Fourier decomposition of the signal. The periodogram, FAP, and orbital elements estimates can be computed for the astrometric and radial velocity time series separately or in tandem. These methods are complementary with more accurate and more computationally intensive numerical algorithms (e.g., least-squares minimization, Markov chain Monte-Carlo, genetic algorithms). In particular, our analytical approximations can be used as an initial condition to accelerate the convergence of numerical algorithms. Our formalism has been partially implemented in the
Gaia
exoplanet pipeline for the third
Gaia
data release. Since the
Gaia
astrometric time series are not yet publicly available, we illustrate our methods on the basis of H
ipparcos
data, together with on-ground CORALIE radial velocities, for three targets known to host a companion: HD 223636 (HIP 117622), HD 17289 (HIP 12726), and HD 3277 (HIP 2790).
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We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of ...the orbital parameters. The accuracy is mainly limited by the accuracy of the computation of the Fourier decomposition of the signal which is sensitive to sampling and noise. Our method is complementary with more accurate (and more expensive in computer time) numerical algorithms (e.g. Levenberg-Marquardt, Markov chain Monte Carlo, genetic algorithms). Indeed, the analytical approximation can be used as an initial condition to accelerate the convergence of these numerical methods. Our method can be applied iteratively to search for multiple planets in the same system.
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Most Neptune-mass planets in close-in orbits (orbital periods less than a few days) present nonzero eccentricity, typically around 0.15. This is somehow unexpected, as these planets undergo strong ...tidal dissipation that should circularize their orbits in a timescale shorter than the age of the system. In this paper we discuss some mechanisms that can oppose to bodily tides, namely, thermal atmospheric tides, evaporation of the atmosphere, and excitation from a distant companion. In the first two cases, the eccentricity can increase consistently, while in the last one, the eccentricity can only be excited for a limited amount of time (that may nevertheless exceed the age of the system). We show the limitations of these different mechanisms and how some of them could, depending on specific properties of the observed planetary systems, account for their presently observed eccentricities.
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Efficient modeling of correlated noise Delisle, J.-B.; Unger, N.; Hara, N. C. ...
Astronomy and astrophysics (Berlin),
03/2022, Volume:
659
Journal Article
Peer reviewed
Open access
The radial velocity method is a very productive technique used to detect and confirm extrasolar planets. The most recent spectrographs, such as ESPRESSO or EXPRES, have the potential to detect ...Earth-like planets around Sun-like stars. However, stellar activity can induce radial velocity variations that dilute or even mimic the signature of a planet. A widely recognized method for disentangling these signals is to model the radial velocity time series, jointly with stellar activity indicators, using Gaussian processes and their derivatives. However, such modeling is prohibitive in terms of computational resources for large data sets, as the cost typically scales as the total number of measurements cubed. Here, we present
S+LEAF
2, a Gaussian process framework that can be used to jointly model several time series, with a computational cost that scales linearly with the data set size. This framework thus provides a state-of-the-art Gaussian process model, with tractable computations even for large data sets. We illustrate the power of this framework by reanalyzing the 246 HARPS radial velocity measurements of the nearby K2 dwarf HD 138038, together with two activity indicators. We reproduce the results of a previous analysis of these data, but with a strongly decreased computational cost (more than two order of magnitude). The gain would be even greater for larger data sets.
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We study the evolution of two planets around a star, in mean-motion resonance and undergoing tidal effects. We derive an integrable analytical model of mean-motion resonances of any order which ...reproduce the main features of the resonant dynamics. Using this simplified model, we obtain a criterion showing that, depending on the balance of the tidal dissipation in both planets, their final period ratio may stay at the resonant value, increase above, or decrease below the resonant value. Applying this criterion to the two inner planets orbiting GJ 163, we deduce that the current period ratio (2.97) could be the outcome of dissipation in the 3:1 MMR provided that the innermost planet is gaseous (slow dissipation) while the second one is rocky (faster dissipation). We perform N-body simulations with tidal dissipation to confirm the results of our analytical model. We also apply our criterion on GJ 581b, c (5:2 MMR) and reproduce the current period ratio (2.4) if the inner planet is gaseous and the outer is rocky (as in the case of GJ 163). Finally, we apply our model to the Kepler mission’s statistics. We show that the excess of planets pairs close to first-order MMRs but in external circulation, i.e., with period ratios Pout/Pin> (p + 1) /p for the resonance (p + 1):p, can be reproduced by tidal dissipation in the inner planet. There is no need for any other dissipative mechanism, provided that these systems left the resonance with non-negligible eccentricities.
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