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Register a new userDiscovering new worlds: a review of signal processing methods for detecting exoplanets from astronomical radial velocity data
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Exoplanets, short for `extra solar planets, are planets outside our solar system. They are objects with masses less than around 15 Jupiter-masses that orbit stars other than the Sun. They are small enough so they can not burn deuterium in their cores, yet large enough that they are not so called `dwarf planets like Pluto. To discover life elsewhere in the universe, particularly outside our own solar system, a good starting point would be to search for planets orbiting nearby Sun-like stars, since the only example of life we know of thrives on a planet we call Earth that orbits a G-type dwarf star. Furthermore, understanding the population of exoplanetary systems in the nearby solar neighbourhood allows us to understand the mechanisms that built our own solar system and gave rise to the conditions necessary for our tree of life to flourish. Signal processing is an integral part of exoplanet detection. From improving the signal-to-noise ratio of the observed data to applying advanced statistical signal processing methods, among others, to detect signals (potential planets) in the data, astronomers have tended, and continue to tend, towards signal processing in their quest of finding Earth-like planets. The following methods have been used to detect exoplanets.
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The space missions TESS and PLATO plan to double the number of 4000 exoplanets already discovered and will measure the size of thousands of exoplanets around the brightest stars in the sky, allowing ground-based radial velocity spectroscopy follow-up to determine the orbit and mass of the detected planets. The new facility we are developing, MARVEL (Raskin et al. this conference), will enable the ground-based follow-up of large numbers of exoplanet detections, expected from TESS and PLATO, which cannot be carried out only by the current facilities that achieve the necessary radial velocity accuracy of 1 m/s or less. This paper presents the MARVEL observation strategy and performance analysis based on predicted PLATO transit detection yield simulations. The resulting observation scenario baseline will help in the instrument design choices and demonstrate the effectiveness of MARVEL as a TESS and PLATO science enabling facility.
The MINiature Exoplanet Radial Velocity Array (MINERVA) is a dedicated observatory of four 0.7m robotic telescopes fiber-fed to a KiwiSpec spectrograph. The MINERVA mission is to discover super-Earths in the habitable zones of nearby stars. This can be accomplished with MINERVAs unique combination of high precision and high cadence over long time periods. In this work, we detail changes to the MINERVA facility that have occurred since our previous paper. We then describe MINERVAs robotic control software, the process by which we perform 1D spectral extraction, and our forward modeling Doppler pipeline. In the process of improving our forward modeling procedure, we found that our spectrographs intrinsic instrumental profile is stable for at least nine months. Because of that, we characterized our instrumental profile with a time-independent, cubic spline function based on the profile in the cross dispersion direction, with which we achieved a radial velocity precision similar to using a conventional sum-of-Gaussians instrumental profile: 1.8 m s$^{-1}$ over 1.5 months on the RV standard star HD 122064. Therefore, we conclude that the instrumental profile need not be perfectly accurate as long as it is stable. In addition, we observed 51 Peg and our results are consistent with the literature, confirming our spectrograph and Doppler pipeline are producing accurate and precise radial velocities.
The fully marginalized likelihood, or Bayesian evidence, is of great importance in probabilistic data analysis, because it is involved in calculating the posterior probability of a model or re-weighting a mixture of models conditioned on data. It is, however, extremely challenging to compute. This paper presents a geometric-path Monte Carlo method, inspired by multi-canonical Monte Carlo to evaluate the fully marginalized likelihood. We show that the algorithm is very fast and easy to implement and produces a justified uncertainty estimate on the fully marginalized likelihood. The algorithm performs efficiently on a trial problem and multi-companion model fitting for radial velocity data. For the trial problem, the algorithm returns the correct fully marginalized likelihood, and the estimated uncertainty is also consistent with the standard deviation of results from multiple runs. We apply the algorithm to the problem of fitting radial velocity data from HIP 88048 ($ u$ Oph) and Gliese 581. We evaluate the fully marginalized likelihood of 1, 2, 3, and 4-companion models given data from HIP 88048 and various choices of prior distributions. We consider prior distributions with three different minimum radial velocity amplitude $K_{mathrm{min}}$. Under all three priors, the 2-companion model has the largest marginalized likelihood, but the detailed values depend strongly on $K_{mathrm{min}}$. We also evaluate the fully marginalized likelihood of 3, 4, 5, and 6-planet model given data from Gliese 581 and find that the fully marginalized likelihood of the 5-planet model is too close to that of the 6-planet model for us to confidently decide between them.
We briefly review the various proposed scenarios that may lead to nonthermal radio emissions from exoplanetary systems (planetary magnetospheres, magnetosphere-ionosphere and magnetosphere-satellite coupling, and star-planet interactions), and the physical information that can be drawn from their detection. The latter scenario is especially favorable to the production of radio emission above 70,MHz. We summarize the results of past and recent radio searches, and then discuss FAST characteristics and observation strategy, including synergies. We emphasize the importance of polarization measurements and a high duty-cycle for the very weak targets that radio-exoplanets prove to be.
The EXtreme PREcision Spectrograph (EXPRES) is an environmentally stabilized, fiber-fed, $R=137,500$, optical spectrograph. It was recently commissioned at the 4.3-m Lowell Discovery Telescope (LDT) near Flagstaff, Arizona. The spectrograph was designed with a target radial-velocity (RV) precision of 30$mathrm{~cm~s^{-1}}$. In addition to instrumental innovations, the EXPRES pipeline, presented here, is the first for an on-sky, optical, fiber-fed spectrograph to employ many novel techniques---including an extended flat fiber used for wavelength-dependent quantum efficiency characterization of the CCD, a flat-relative optimal extraction algorithm, chromatic barycentric corrections, chromatic calibration offsets, and an ultra-precise laser frequency comb for wavelength calibration. We describe the reduction, calibration, and radial-velocity analysis pipeline used for EXPRES and present an example of our current sub-meter-per-second RV measurement precision, which reaches a formal, single-measurement error of 0.3$mathrm{~m~s^{-1}}$ for an observation with a per-pixel signal-to-noise ratio of 250. These velocities yield an orbital solution on the known exoplanet host 51 Peg that matches literature values with a residual RMS of 0.895$mathrm{~m~s^{-1}}$.
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