Flat-relative optimal extraction. A quick and efficient algorithm for stabilised spectrographs

Optimal extraction is a key step in processing the raw images of spectra as registered by two-dimensional detector arrays to a one-dimensional format. Previously reported algorithms reconstruct models for a mean one-dimensional spatial profile to assist a properly weighted extraction. We outline a simple optimal extraction algorithm including error propagation, which is very suitable for stabilised, fibre-fed spectrographs and does not model the spatial profile shape. A high signal-to-noise, master-flat image serves as reference image and is directly used as an extraction profile mask. Each extracted spectral value is the scaling factor relative to the cross-section of the unnormalised master-flat which contains all information about the spatial profile as well as pixel-to-pixel variations, fringing, and blaze. The extracted spectrum is measured relative to the flat spectrum. Using echelle spectra of the HARPS spectrograph we demonstrate a competitive extraction performance in terms of signal-to-noise and show that extracted spectra can be used for high precision radial velocity measurement. Pre- or post-flat-fielding of the data is not necessary, since all spectrograph inefficiencies inherent to the extraction mask are automatically accounted for. Also the reconstruction of the mean spatial profile by models is not needed, thereby reducing the number of operations to extract spectra. Flat-relative optimal extraction is a simple, efficient, and robust method that can be applied easily to stabilised, fibre-fed spectrographs.

The planet search programme at the ESO CES and HARPS. IV. The search for Jupiter analogues around solar-like stars

In 1992 we began a precision radial velocity (RV) survey for planets around solar-like stars with the Coude Echelle Spectrograph and the Long Camera (CES LC) at the 1.4 m telescope in La Silla (Chile). We have continued the survey with the upgraded CES Very Long Camera (VLC) and HARPS, both at the 3.6 m telescope, until 2007. The observations for 31 stars cover a time span of up to 15 years and the RV precision permit a search for Jupiter analogues. We perform a joint analysis for variability, trends, periodicities, and Keplerian orbits and compute detection limits. Moreover, the HARPS RVs are analysed for correlations with activity indicators (CaII H&K and CCF shape). We achieve a long-term RV precision of 15 m/s (CES+LC, 1992-1998), 9 m/s (CES+VLC, 1999-2006), and 2.8 m/s (HARPS, 2003-2009, including archive data), resp. This enables us to confirm the known planets around Iota Hor, HR 506, and HR 3259. A steady RV trend for Eps Ind A can be explained by a planetary companion. On the other hand, we find previously reported trends to be smaller for Beta Hyi and not present for Alp Men. The candidate planet Eps Eri b was not detected despite our better precision. Also the planet announced for HR 4523 cannot be confirmed. Long-term trends in several of our stars are compatible with known stellar companions. We provide a spectroscopic orbital solution for the binary HR 2400 and refined solutions for the planets around HR 506 and Iota Hor. For some other stars the variations could be attributed to stellar activity. The occurrence of two Jupiter-mass planets in our sample is in line with the estimate of 10% for the frequency of giant planets with periods smaller than 10 yr around solar-like stars. We have not detected a Jupiter analogue, while the detections limits for circular orbits indicate at 5 AU a sensitivity for minimum mass of at least 1 M_Jup (2 M_Jup) for 13% (61%) of the stars.

The M dwarf planet search programme at the ESO VLT + UVES. A search for terrestrial planets in the habitable zone of M dwarfs

We present radial velocity (RV) measurements of our sample of 40 M dwarfs from our planet search programme with VLT+UVES begun in 2000. Although with our RV precision down to 2 - 2.5 m/s and timebase line of up to 7 years, we are capable of finding planets of a few Earth masses in the close-in habitable zones of M dwarfs, there is no detection of a planetary companion. To demonstrate this we present mass detection limits allowing us to exclude Jupiter-mass planets up to 1 AU for most of our sample stars. We identified 6 M dwarfs that host a brown dwarf or low-mass stellar companion. With the exception of these, all other sample stars show low RV variability with an rms < 20 m/s. Some high proper motion stars exhibit a linear RV trend consistent with their secular acceleration. Furthermore, we examine our data sets for a possible correlation between RVs and stellar activity as seen in variations of the Halpha line strength. For Barnards star we found a significant anticorrelation, but most of the sample stars do not show such a correlation.

The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms

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 ($chi^{2}$ 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.

The Discovery of Stellar Oscillations in the K Giant $iota$ Dra

$iota$ Dra (HIP 75458) is a well-known example for a K giant hosting a substellar companion since its discovery by Frink et al. (2002). We present radial velocity measurements of this star from observations taken with three different instruments spanning nearly 8 years. They show more clearly that the RV period is long-lived and coherent thus supporting the companion hypothesis. The longer time baseline now allows for a more accurate determination of the orbit with a revised period of P=511 d and an additional small linear trend, indicative of another companion in a wide orbit. Moreover we show that the star exhibits low amplitude, solar like oscillations with frequencies around 3-4 d$^{-1}$ (34.7-46.3 $mu$Hz).