When applying the barycentric correction to a precise radial velocity measurement, it is common practice to calculate its value only at the photon-weighted midpoint time of the observation instead of integrating over the entire exposure. However, since the barycentric correction does not change linearly with time, this leads to systematic errors in the derived radial velocities. The typical magnitude of this second-order effect is of order 10 cm s$^{-1}$, but it depends on several parameters, e.g. the latitude of the observatory, the position of the target on the sky, and the exposure time. We show that there are realistic observing scenarios, where the errors can amount to more than 1 ms$^{-1}$. We therefore recommend that instruments operating in this regime always record and store the exposure meter flux curve (or a similar measure) to be used as photon-weights for the barycentric correction. In existing data, if the flux curve is no longer available, we argue that second-order errors in the barycentric correction can be mitigated by adding a correction term assuming constant flux.
The goal of this paper is to establish the requirements of a barycentric correction with an RMS of $\lesssim 1$ cm/s, which is an order of magnitude better than necessary for the Doppler detection of true Earth analogs ($\sim9$ cm/s). We describe the theory and implementation of accounting for the effects on precise Doppler measurements of motion of the telescope through space, primarily from rotational and orbital motion of the Earth, and the motion of the solar system with respect to target star (i.e. the "barycentric correction"). We describe the minimal algorithm necessary to accomplish th…
We provide formulae for the calculation of precise Doppler velocities of sunlight, in both the case of direct observations of the Sun and in reflection from the surfaces of solar system objects such as the Moon or asteroids. We discuss the meaning of a "barycentric correction" of measurements of these Doppler velocities, which is a different procedure from the analogous correction for starlight, and provide a formula for reducing such measurements to the component of the Sun's motion in the direction of the Earth or other Solar System object. We have implemented this procedure in the public ba…
One source of error in high-precision radial velocity measurements of exoplanet host stars is chromatic change in Earth's atmospheric transmission during observations. Mitigation of this error requires that the photon-weighted barycentric correction be applied as a function of wavelength across the stellar spectrum. We have designed a system for chromatic photon-weighted barycentric corrections with the EXtreme PREcision Spectrograph (EXPRES) and present results from the first year of operations, based on radial velocity measurements of more than $10^3$ high-resolution stellar spectra. For obs…
It has long been recognized that the finite speed of light can affect the observed time of an event. For example, as a source moves radially toward or away from an observer, the path length and therefore the light travel time to the observer decreases or increases, causing the event to appear earlier or later than otherwise expected, respectively. This light travel time effect (LTTE) has been applied to transits and eclipses for a variety of purposes, including studies of eclipse timing variations (ETVs) and transit timing variations (TTVs) that reveal the presence of additional bodies in the …
We announce barycorrpy (BCPy) , a Python implementation to calculate precise barycentric corrections well below the 1 cm/s level, following the algorithm of Wright and Eastman (2014). This level of precision is required in the search for 1 Earth mass planets in the Habitable Zones of Sun-like stars by the Radial Velocity (RV) method, where the maximum semi-amplitude is about 9 cm/s. We have developed BCPy to be used in the pipeline for the next generation Doppler Spectrometers - Habitable-zone Planet Finder (HPF) and NEID. In this work, we also develop an automated leap second management routi…
Atmospheric effects on stellar radial velocity measurements for exoplanet discovery and characterization have not yet been fully investigated for extreme precision levels. We carry out calculations to determine the wavelength dependence of barycentric corrections across optical wavelengths, due to the ubiquitous variations in air mass during observations. We demonstrate that radial velocity errors of at least several cm/s can be incurred if the wavelength dependence is not included in the photon-weighted barycentric corrections. A minimum of four wavelength channels across optical spectra (380…
Spectrographs nominally contain a degree of quasi-static optical aberrations resulting from the quality of manufactured component surfaces, imperfect alignment, design residuals, thermal effects, and other other associated phenomena involved in the design and construction process. Aberrations that change over time can mimic the line centroid motion of a Doppler shift, introducing radial velocity (RV) uncertainty that increases time-series variability. Even when instrument drifts are tracked using a precise wavelength calibration source, barycentric motion of the Earth leads to a wavelength shi…
The ability to make independent detections of the signatures of exoplanets with complementary telescopes and instruments brings a new potential for robust identification of exoplanets and precision characterization. We introduce PEXO, a package for Precise EXOplanetology to facilitate the efficient modeling of timing, astrometry, and radial velocity data, which will benefit not only exoplanet science but also various astrophysical studies in general. PEXO is general enough to account for binary motion and stellar reflex motions induced by planetary companions and is precise enough to treat var…
We present a possible NASA key project using the iSHELL near-infrared high-resolution echelle spectrograph on the NASA Infrared Telescope Facility for precise radial velocity follow-up of candidate transiting exoplanets identified by the NASA TESS mission. We briefly review key motivations and challenges with near-infrared radial velocities. We present the current status of our preliminary radial velocity analysis from the first year on sky with iSHELL.
The radial-velocity (RV) method is one of the most successful in the detection of exoplanets, but is hindered by the intrinsic RV variations of the star, which can easily mimic or hide true planetary signals. kima is a package for the detection and characterization of exoplanets using RV data. It fits a sum of Keplerian curves to a timeseries of RV measurements and calculates the evidence for models with a fixed number Np of Keplerian signals, or after marginalising over Np. Moreover, kima can use a GP with a quasi-periodic kernel as a noise model, to deal with activity-induced signals. The hy…
The Penn State Pathfinder is a prototype warm fiber-fed Echelle spectrograph with a Hawaii-1 NIR detector that has already demonstrated 7-10 m/s radial velocity precision on integrated sunlight. The Pathfinder testbed was initially setup for the Gemini PRVS design study to enable a systematic exploration of the challenges of achieving high radial velocity precision in the near-infrared, as well as to test possible solutions to these calibration challenges. The current version of the Pathfinder has an R3 echelle grating, and delivers a resolution of R~50,000 in the Y, J or H bands of the spectr…
Context: With the announced arrival of instruments such as ESPRESSO one can expect that several systematic noise sources on the measurement of precise radial velocity will become the limiting factor instead of photon noise. A stellar companion within the fiber is such a possible noise source. Aims: With this work we aim at characterizing the impact of a stellar companion within the fiber to radial velocity measurements made by fiber-fed spectrographs. We consider the contaminant star either to be part of a binary system whose primary star is the target star, or as a background/foreground star.…
We have been monitoring 373 very bright (V < 6 mag) G and K giants with high precision optical Doppler spectroscopy for more than a decade at Lick Observatory. Our goal was to discover planetary companions around those stars and to better understand planet formation and evolution around intermediate-mass stars. However, in principle, long-term, g-mode nonradial stellar pulsations or rotating stellar features, such as spots, could effectively mimic a planetary signal in the radial velocity data. Our goal is to compare optical and infrared radial velocities for those stars with periodic radial v…
This chapter describes briefly the key aspects behind the derivation of precise radial velocities. I start by defining radial velocity precision in the context of astrophysics in general and exoplanet searches in particular. Next I discuss the different basic elements that constitute a spectrograph, and how these elements and overall technical choices impact on the derived radial velocity precision. Then I go on to discuss the different wavelength calibration and radial velocity calculation techniques, and how these are intimately related to the spectrograph's properties. I conclude by present…
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 …
Stellar activity can induce signals in the radial velocities of stars, complicating the detection of orbiting low-mass planets. We present a method to determine the number of planetary signals present in radial-velocity datasets of active stars, using only radial-velocity observations. Instead of considering separate fits with different number of planets, we use a birth-death Markov chain Monte Carlo algorithm to infer the posterior distribution for the number of planets in a single run. In a natural way, the marginal distributions for the orbital parameters of all planets are also inferred. T…
A rocky planet orbiting LHS 1140 with a period of 24.7d has been found based on the discovery of transits in its light and high precision radial velocity data (Dittmann et al. 2017). This discovery by two independent methods is an observational tour-de-force, however, we find that a conservative analysis of the data gives a different solution. A three planet system is apparent in the radial velocity data based on our diagnosis of stellar activity. We encourage further targeted photometric and radial velocity observations in order to constrain the mini-Neptune and super-Earth mass objects appar…
Context: In the near future, new instruments such as ESPRESSO will arrive, allowing us to reach a precision in radial-velocity measurements on the order of 10 cm/s. At this level of precision, several noise sources that until now have been outweighed by photon noise will start to contribute significantly to the error budget. The telluric lines that are not neglected by the masks for the radial velocity computation, here called micro-telluric lines, are one such noise source. Aims: In this work we investigate the impact of micro-telluric lines in the radial velocities calculations. We also inve…
A new catalogue of extrasolar planets is presented by re-analysing a selection of published radial velocity data sets using EXOFIT (Balan & Lahav 2009). All objects are treated on an equal footing within a Bayesian framework, to give orbital parameters for 94 exoplanetary systems. Model selection (between one- and two-planet solutions) is then performed, using both a visual flagging method and a standard chi-square analysis, with agreement between the two methods for 99% of the systems considered. The catalogue is to be made available online, and this 'proof of concept' study may be maintained…
Recent and upcoming stabilized spectrographs are pushing the frontier for Doppler spectroscopy to detect and characterize low-mass planets. Specifications for these instruments are so impressive that intrinsic stellar variability is expected to limit their Doppler precision for most target stars (Fischer et al. 2016). To realize their full potential, astronomers must develop new strategies for distinguishing true Doppler shifts from intrinsic stellar variability. Stellar variability due to star spots, faculae and other rotationally-linked variability are particularly concerning, as the stellar…
We present radial velocities of the M8V-type, very low-mass star vB 10 that have been obtained at four different epochs of observations between 2001 and 2008. We use high-resolution (R ~ 20,000) near-infrared (J-band) spectra taken with the NIRSPEC instrument on the Keck II telescope. Our data suggest that vB 10 shows radial velocity variability with an amplitude of ~1 km/s, a result that is consistent with the recent finding of a massive planet companion around the star by Pravdo & Shaklan (2009). More velocity measurements and a better sampling of the orbital phase are required to precisely …
We aim to demonstrate the efficiency of a Bayesian approach in analysing radial velocity data by reanalysing a set of radial velocity measurements. We present Bayesian analysis of a recently published set of radial velocity measurements known to contain the signal of one extrasolar planetary candidate, namely, HD 11506. The analysis is conducted using the Markov chain Monte Carlo method and the resulting distributions of orbital parameters are tested by performing direct integration of randomly selected samples with the Bulirsch-Stoer method. The magnitude of the stellar radial velocity variab…
The abilities of radial velocity exoplanet surveys to detect the lowest-mass extra-solar planets are currently limited by a combination of instrument precision, lack of data, and "jitter". Jitter is a general term for any unknown features in the noise, and reflects a lack of detailed knowledge of stellar physics (asteroseismology, starspots, magnetic cycles, granulation, and other stellar surface phenomena), as well as the possible underestimation of instrument noise. We study an extensive set of radial velocities for the star HD 10700 ($τ$ Ceti) to determine the properties of the jitter arisi…
Radial velocity identification of extrasolar planets has historically been dominated by optical surveys. Interest in expanding exoplanet searches to M dwarfs and young stars, however, has motivated a push to improve the precision of near infrared radial velocity techniques. We present our methodology for achieving 58 m/s precision in the K band on the M0 dwarf GJ 281 using the CSHELL spectrograph at the 3-meter NASA IRTF. We also demonstrate our ability to recover the known 4 Mjup exoplanet Gl 86 b and discuss the implications for success in detecting planets around 1-3 Myr old T Tauri stars.
With Hubble Space Telescope Fine Guidance Sensor astrometry and published and previously unpublished radial velocity measures we explore the exoplanetary system mu Arae. Our modeling of the radial velocities results in improved orbital elements for the four previously known components. Our astrometry contains no evidence for any known companion, but provides upper limits for three companion masses. A final summary of all past Fine Guidance Sensor exoplanet astrometry results uncover a bias towards small inclinations (more face-on than edge-on). This bias remains unexplained by either small num…
We present radial velocity measurements of a sample of M5V-M9V stars from our Red-Optical Planet Survey, ROPS, operating at 0.65-1.025 micron. Radial velocities for 15 stars, with r.m.s. precision down to 2.5 m/s over a week long time scale are achieved using Thorium-Argon reference spectra. We are sensitive to planets with m_psin(i) >= 1.5 MEarth (3 MEarth at 2-sigma) in the classical habitable zone and our observations currently rule out planets with m_psin(i) > 0.5 MJup at 0.03 AU for all our targets. A total of 9 of the 15 targets exhibit r.m.s. < 16 m/s, which enables us to rule out the p…
Context. Searching for extrasolar planets through radial velocity measurements relies on the stability of stellar photospheres. Aims. We aim at characterizing the statistical properties of magnetic activity cycles, and studying their impact on spectroscopic measurements such as radial velocities, line bisectors and line shapes. Methods. We use data from the HARPS high-precision planet-search sample comprising 304 FGK stars followed over about 7 years. We obtain high-precision Ca II H&K chromospheric activity measurements and convert them to R'HK indices using an updated calibration taking into…
This work is part of an ongoing project which aims to detect terrestrial planets in our neighbouring star system $α$ Centauri using the Doppler method. Owing to the small angular separation between the two components of the $α$ Cen AB binary system, the observations will to some extent be contaminated with light coming from the other star. We are accurately determining the amount of contamination for every observation by measuring the relative strengths of the H-$α$ and NaD lines. Furthermore, we have developed a modified version of a well established Doppler code that is modelling the observa…
Bright features have been recently discovered by Dawn on Ceres, which extend previous photometric and Space Telescope observations. These features should produce distortions of the line profiles of the reflected solar spectrum and therefore an apparent radial velocity variation modulated by the rotation of the dwarf planet. Here we report on two sequences of observations of Ceres performed in the nights of 31 July, 26-27 August 2015 by means of the high-precision HARPS spectrograph at the 3.6-m La Silla ESO telescope. The observations revealed a quite complex behaviour which likely combines a …
Variations related to stellar activity and correlated noise can prevent the detections of low-amplitude signals in radial velocity data if not accounted for. This can be seen as the greatest obstacle in detecting Earth-like planets orbiting nearby stars with Doppler spectroscopy regardless of developments in instrumentation and rapidly accumulating amounts of data. We use a statistical model that is not sensitive to aperiodic and/or quasiperiodic variability of stellar origin. We demonstrate the performance of our model by re-analysing the radial velocities of the moderately active star CoRoT-…
Mid-late M stars are opportunistic targets for the study of low-mass exoplanets in transit because of the high planet-to-star radius ratios of their planets. Recent studies of such stars have shown that, like their early-M counterparts, they often host multi-resonant networks of small planets. Here, we reanalyze radial velocity measurements of YZ Ceti, an active M4 dwarf for which the HARPS exoplanet survey recently discovered three exoplanets on short-period (P = 4.66, 3.06, 1.97 days) orbits. Our analysis finds that the orbital periods of the inner two planets cannot be uniquely determined u…
Research in extrasolar-planet science is data-driven. With the advent of radial-velocity instruments like HARPS and HARPS-N, and transit space missions like Kepler, our ability to discover and characterise extrasolar planets is no longer limited by instrumental precision but by our ability to model the data accurately. This chapter presents the models that describe radial-velocity measurements and transit light curves. I begin by deriving the solution of the two-body problem and from there, the equations describing the radial velocity of a planet-host star and the distance between star and pla…
Magnetic activity and surface flows at different scales pertub radial velocity measurements. This affects the detectability of low-mass exoplanets. In these flows, the effect of supergranulation is not as well characterized as the other flows, and we wish to estimate its effect on the detection of Earth-like planets in the habitable zone of Sun-like stars. We produced time series of radial velocities due to oscillations, granulation, and supergranulation, and estimated the detection limit for a G2 star and a period of 300 days. We also studied in detail the behavior of the power when the signa…
The ever increasing level of precision achieved by present and future radial-velocity instruments is opening the way to discovering very low-mass, long-period planets (e.g. solar-system analogs). These systems will be detectable as low-amplitude signals in radial-velocity (RV). However, an important obstacle to their detection may be the existence of stellar magnetic cycles on similar timescales. Here we present the results of a long-term program to simultaneously measure radial-velocities and stellar-activity indicators (CaII, H_alpha, HeI) for a sample of stars with known activity cycles. Ou…
We present the latest and most precise characterization of the architecture for the ancient ($\approx 11$ Gyr) Kepler-444 system, which is composed of a K0 primary star (Kepler-444 A) hosting five transiting planets, and a tight M-type spectroscopic binary (Kepler-444 BC) with an A-BC projected separation of 66 au. We have measured the system's relative astrometry using the adaptive optics imaging from Keck/NIRC2 and Kepler-444 A's radial velocities from the Hobby Eberly Telescope, and re-analyzed relative radial velocities between BC and A from Keck/HIRES. We also include the Hipparcos-Gaia a…
Stellar activity due to different processes (magnetic activity, photospheric flows) affects the measurement of radial velocities (RV). Radial velocities have been widely used to detect exoplanets, although the stellar signal significantly impacts the detection and characterisation performance, especially for low mass planets. On the other hand, RV time series are also very rich in information on stellar processes. In this lecture, I review the context of RV observations, describe how radial velocities are measured, and the properties of typical observations. I present the challenges represente…
We present a technique to extract radial velocity measurements from echelle spectrograph observations of rapidly rotating stars ($V\sin{i} \gtrsim 50$ km s$^{-1}$). This type of measurement is difficult because the line widths of such stars are often comparable to the width of a single echelle order. To compensate for the scarcity of lines and Doppler information content, we have developed a process that forward-models the observations, fitting the radial velocity shift of the star for all echelle orders simultaneously with the echelle blaze function. We use our technique to extract radial vel…
We report multi-epoch radial velocities, rotational velocities, and atmospheric parameters for 37 T-type brown dwarfs observed with Keck/NIRSPEC. Using a Markov Chain Monte Carlo forward-modeling method, we achieve median precisions of 0.5 km s$^{-1}$ and 0.9 km s$^{-1}$ for radial and rotational velocities, respectively. All of the T dwarfs in our sample are thin disk brown dwarfs. We confirm previously reported moving group associations for four T dwarfs. However, the lack of spectral indicators of youth in two of these sources suggests that these are chance alignments. We confirm two previo…
Transit timing variations of Kepler-410Ab were already reported in a few papers. Their semi-amplitude is about 14.5 minutes. In our previous paper, we found that the transit timing variations could be caused by the presence of a stellar companion in this system. Our main motivation for this paper was to investigate variation in a radial-velocity curve generated by this additional star in the system. We performed spectroscopic observation of Kepler-410 using three telescopes in Slovakia and Czech Republic. Using the cross-correlation function, we measured the radial velocities of the star Keple…
The precise radial velocity technique is a cornerstone of exoplanetary astronomy. Astronomers measure Doppler shifts in the star's spectral features, which track the line-of/sight gravitational accelerations of a star caused by the planets orbiting it. The method has its roots in binary star astronomy, and exoplanet detection represents the low-companion-mass limit of that application. This limit requires control of several effects of much greater magnitude than the signal sought: the motion of the telescope must be subtracted, the instrument must be calibrated, and spurious Doppler shifts "ji…
Radial-velocity variations of the K giant star Aldebaran ($α$ Tau) were first reported in the early 1990s. After subsequent analyses, the radial-velocity variability with a period of $\sim 629\,\mathrm{d}$ has recently been interpreted as caused by a planet of several Jovian masses. We want to further investigate the hypothesis of an extrasolar planet around Aldebaran. We combine 165 new radial-velocity measurements from Lick Observatory with seven already published data sets comprising 373 radial-velocity measurements. We perform statistical analyses and investigate whether a Keplerian model …
