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    Optical ray tracing of echelle spectrographs applied to the wavelength solution for precise radial velocities

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    We present moes\texttt{moes}, a ray tracing software package that computes the path of rays through echelle spectrographs. Our algorithm is based on sequential direct tracing with Seidel aberration corrections applied at the detector plane. As a test case, we model the CARMENES VIS spectrograph. After subtracting the best model from the data, the residuals yield an rms of 0.024 pix, setting a new standard to the precision of the wavelength solution of state-of-the-art radial velocity instruments. By including the influence of the changes of the environment in the ray propagation, we are able to predict instrumental radial velocity systematics at the 1 m/s level

    Calibrating echelle spectrographs with Fabry-Pérot etalons

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    Context. Over the past decades hollow-cathode lamps have been calibration standards for spectroscopic measurements. Advancing to cm/s radial velocity precisions with the next generation of instruments requires more suitable calibration sources with more lines and fewer dynamic range problems. Fabry-Pérot interferometers provide a regular and dense grid of lines and homogeneous amplitudes, which makes them good candidates for next-generation calibrators. Aims. We investigate the usefulness of Fabry-Pérot etalons in wavelength calibration, present an algorithm to incorporate the etalon spectrum in the wavelength solution, and examine potential problems. Methods. The quasi-periodic pattern of Fabry-Pérot lines was used along with a hollow-cathode lamp to anchor the numerous spectral features on an absolute scale. We tested our method with the HARPS spectrograph and compared our wavelength solution to the one derived from a laser frequency comb. Results. The combined hollow-cathode lamp/etalon calibration overcomes large distortion (50 m/s) in the wavelength solution of the HARPS data reduction software. The direct comparison to the laser frequency comb shows differences of only 10 m/s at most. Conclusions. Combining hollow-cathode lamps with Fabry-Pérot interferometers can lead to substantial improvements in the wavelength calibration of echelle spectrographs. Etalons can provide economical alternatives to the laser frequency comb, especially for smaller projects

    An independent planet search in the

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    Context. The primary goal of the Kepler mission is the measurement of the frequency of Earth-like planets around Sun-like stars. However, the confirmation of the smallest of Kepler’s candidates in long periods around FGK dwarfs is extremely difficult or even beyond the limit of current radial velocity technology. Transit timing variations (TTVs) may offer the possibility for these confirmations of near-resonant multiple systems by the mutual gravitational interaction of the planets. Aims. We previously detected the second planet candidate in the KOI 1574 system. The two candidates have relatively long periods (about 114 d and 191 d) and are in 5:3 resonance. We therefore searched for TTVs in this particularly promising system. Methods. The full Kepler data was detrended with the proven SARS pipeline. The entire data allowed one to search for TTVs of the above signals, and to search for additional transit-like signals. Results. We detected strong anti-correlated TTVs of the 114 d and 191 d signals, dynamically confirming them as members of the same system. Dynamical simulations reproducing the observed TTVs allowed us to also determine the masses of the planets. We found KOI 1574.01 (hereafter Kepler-87 b) to have a radius of 13.49 ± 0.55 R⊕ and a mass of 324.2 ± 8.8 M⊕, and KOI 1574.02 (Kepler-87 c) to have a radius of 6.14 ± 0.29 R⊕ and a mass of 6.4 ± 0.8 M⊕. Both planets have low densities of 0.729 and 0.152 g cm-3, respectively, which is non-trivial for such cold and old (7−8 Gyr) planets. Specifically, Kepler-87 c is the lowest-density planet in the super-Earth mass range. Both planets are thus particularly amenable to modeling and planetary structure studies, and also present an interesting case where ground-based photometric follow-up of Kepler planets is very desirable. Finally, we also detected two more short-period super-Earth sized (<2 R⊕) planetary candidates in the system, making the relatively high multiplicity of this system notable against the general paucity of multiple systems in the presence of giant planets like Kepler-87 b

    Radial velocity constraints on the long-period transiting planet Kepler-1625 b with CARMENES

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    Context. The star Kepler-1625 recently attracted considerable attention when an analysis of the stellar photometric time series from the Kepler mission was interpreted as showing evidence of a large exomoon around the transiting Jupiter-sized planet candidate Kepler-1625 b. However, the mass of Kepler-1625 b has not been determined independently and its planetary nature has not been formally validated. Moreover, Kepler’s long-period Jupiter-sized planet candidates, like Kepler-1625 b with an orbital period of about 287 d, are known to have a high false-alarm probability. An independent confirmation of Kepler-1625 b is therefore particularly important. Aims. We aim to detect the radial velocity (RV) signal imposed by Kepler-1625 b (and its putative moon) on the host star, or, as the case may be, determine an upper limit on the mass of the transiting object (or the combined mass of the two objects). Methods. We took a total of 22 spectra of Kepler-1625 using CARMENES, 20 of which were useful. Observations were spread over a total of seven nights between October 2017 and October 2018, covering 125% of one full orbit of Kepler-1625 b. We used the automatic Spectral Radial Velocity Analyser pipeline to deduce the stellar RVs and uncertainties. We then fitted the RV curve model of a single planet on a Keplerian orbit to the observed RVs using a χ2 minimisation procedure. Results. We derive upper limits on the mass of Kepler-1625 b under the assumption of a single planet on a circular orbit. In this scenario, the 1σ, 2σ, and 3σ confidence upper limits for the mass of Kepler-1625 b are 2.90 MJ, 7.15 MJ, and 11.60 MJ, respectively (MJ being Jupiter’s mass). An RV fit that includes the orbital eccentricity and orientation of periastron as free parameters also suggests a planetary mass but is statistically less robust. Conclusions. We present strong evidence for the planetary nature of Kepler-1625 b, making it the (confirmed) planet with the tenth longest period known today. Our data do not allow us to make any form conclusions regarding a second, possibly shorter period planet that could be responsible for the observed transit timing variation of Kepler-1625 b
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