The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights (χ 2 fitting). Compared to the Lomb-Scargle periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the date-compensated discrete Fourier transform, the floating-mean periodogram, and the "spectral significance" estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian periodogram that searches for the period of the best-fitting Keplerian orbit to radial velocity data. The systematic and non-random algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.

At a distance of 1.295 parsecs, 1 the red-dwarf Proxima Centauri (α Centauri C, GL 551, HIP 70890, or simply Proxima) is the Sun's closest stellar neighbour and one of the best studied low-mass stars. It has an effective temperature of only ∼ 3050 K, a luminosity of ∼0.1 per cent solar, a measured radius of 0.14 R ⊙ 2 and a mass of about 12 per cent the mass of the Sun. Although Proxima is considered a moderately active star, its rotation period is ∼ 83 days, 3 and its quiescent activity levels and X-ray luminosity 4 are comparable to the Sun's. New observations reveal the presence of a small planet orbiting Proxima with a minimum mass of 1.3 Earth masses and an orbital period of ∼11.2 days. Its orbital semi-major axis is ∼ 0.05 AU, with an equilibrium temperature in the range where water could be liquid on its surface. 5 The results presented here consist of the analysis of previously obtained Doppler measurements (pre-2016 data), and the confirmation of a signal in a specifically designed follow-up campaign in 2016. The Doppler data comes from two precision radial velocity instruments, both at the European Southern Observatory (ESO): the High Accuracy Radial velocity Planet Searcher (HARPS) and the Ultraviolet and Visual Echelle Spectrograph (UVES). HARPS is a high-resolution stabilized echelle spectrometer installed at the ESO 3.6m telescope (La Silla observatory, Chile), and is calibrated in wavelength using hollow cathode lamps. HARPS has demonstrated radial velocity measurements at ∼1 ms −1 precision over time-scales of years, 6 including on low-mass stars. 7 All HARPS spectra were extracted and calibrated with the standard ESO Data Reduction Software, and radial velocities were measured using a least-squares template matching technique. 7 HARPS data is separated into two datasets. The first set includes all data obtained before 2016 by several programmes (HARPS pre-2016 work, and its value is then used to assess the false-alarm probability (or FAP) of the detection. 14 A FAP below 1% is considered suggestive of periodic variability, and anything below 0.1% is considered to be a significant detection. In the Bayesian framework, signals are first searched using a specialized sampling method 16 that enables exploration of multiple local maxima of the posterior density (the result of this process are the gray lines in Figure 1), and significances are then assessed by obtaining the ratios of evidences of models. If the evidence ratio exceeds some threshold (e.g. B 1 /B 0 > 10 3 ), then the model in the numerator (with one planet) is favoured against the model in the denominator (no planet).A well isolated peak at ∼11.2 days was recovered when analyzing all the night averages in the pre-2016 datasets (Figure 1, panel a). Despite the significance of the signal, the analysis of pre-2016 subsets produced slightly different periods depending on the noise assumptions and which subsets were considered. Confirmation or refutation of this signal at 11.2 days was the main driver for proposing the HARPS PRD campaign. T...

We present the ROSAT All-Sky Survey Bright Source Catalogue (RASS-BSC, revision 1RXS) derived from the all-sky survey performed during the first half year (1990/91) of the ROSAT mission. 18,811 sources are catalogued (i) down to a limiting ROSAT PSPC countrate of 0.05 cts/s in the 0.1−2.4 keV energy band, (ii) with a detection likelihood of at least 15 and (iii) at least 15 source counts. The 18,811 sources underwent both an automatic validation and an interactive visual verification process in which for 94% of the sources the results of the standard processing were confirmed. The remaining 6% have been analyzed using interactive methods and these sources have been flagged. Flags are given for (i) nearby sources; (ii) sources with positional errors; (iii) extended sources; (iv) sources showing complex emission structures; and (v) sources which are missed by the standard analysis software. Broad band (0.1−2.4 keV) images are available for sources flagged by (ii), (iii) and (iv). For each source the ROSAT name, position in equatorial coordinates, positional error, source count-rate and error, background count-rate, exposure time, two hardness-ratios and errors, extent and likelihood of extent, likelihood of detection, and the source extraction radius are provided. At a brightness limit of 0.1 cts/s (8,547 sources) the catalogue represents a sky coverage of 92%. The RASS-BSC, the table of possible identification candidates, and the broad band images are available in electronic form (Voges et al. 1996a) via http://wave.xray.mpe.mpg.de/rosat/catalogues/rassbsc . 1

Context. The CARMENES survey is a high-precision radial velocity (RV) programme that aims to detect Earth-like planets orbiting low-mass stars. Aims. We develop least-squares fitting algorithms to derive the RVs and additional spectral diagnostics implemented in the SpEctrum Radial Velocity Analyser (SERVAL), a publicly available python code. Methods. We measured the RVs using high signal-to-noise templates created by coadding all available spectra of each star. We define the chromatic index as the RV gradient as a function of wavelength with the RVs measured in the echelle orders. Additionally, we computed the differential line width by correlating the fit residuals with the second derivative of the template to track variations in the stellar line width. Results. Using HARPS data, our SERVAL code achieves a RV precision at the level of 1 m/s. Applying the chromatic index to CARMENES data of the active star YZ CMi, we identify apparent RV variations induced by stellar activity. The differential line width is found to be an alternative indicator to the commonly used full width half maximum. Conclusions. We find that at the red optical wavelengths (700-900 nm) obtained by the visual channel of CARMENES, the chromatic index is an excellent tool to investigate stellar active regions and to identify and perhaps even correct for activity-induced RV variations.

We monitored the chromospheric activity in the Ca ii H and K lines of 13 solar-type stars (including the Sun): 8 of them over 3 years at the Canada-France-Hawaii Telescope (CFHT) and 5 in a single run at the Very Large Telescope (VLT). A total of 10 of the 13 targets have close planetary companions. All of the stars observed at the CFHT show long-term (months to years) changes in H and K intensity levels. Four stars display short-term (days) cyclical activity. For two, HD 73256 and 1 Cet, the activity is likely associated with an active region rotating with the star; however, the flaring in excess of the rotational modulation may be associated with a hot Jupiter. A planetary companion remains a possibility for 1 Cet. For the other two, HD 179949 and And, the cyclic variation is synchronized to the hot Jupiter's orbit. For both stars this synchronicity with the orbit is clearly seen in two out of three epochs. The effect is only marginal in the third epoch at which the seasonal level of chromospheric activity had changed for both stars. Short-term chromospheric activity appears weakly dependent on the mean K line reversal intensities for the sample of 13 stars. In addition, a suggestive correlation exists between this activity and the M p sin i of the star's hot Jupiter. Because of their small separation ( 0.1 AU ), many of the hot Jupiters lie within the Alfvén radius of their host stars, which allows a direct magnetic interaction with the stellar surface. We discuss the conditions under which a planet's magnetic field might induce activity on the stellar surface and why no such effect was seen for the prime candidate, Boo. This work opens up the possibility of characterizing planet-star interactions, with implications for extrasolar planet magnetic fields and the energy contribution to stellar atmospheres.