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Register a new userTheory of Dispersed Fixed-Delay Interferometry for Radial Velocity Exoplanet Searches
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The dispersed fixed-delay interferometer (DFDI) represents a new instrument concept for high-precision radial velocity (RV) surveys for extrasolar planets. A combination of Michelson interferometer and medium-resolution spectrograph, it has the potential for performing multi-object surveys, where most previous RV techniques have been limited to observing only one target at a time. Because of the large sample of extrasolar planets needed to better understand planetary formation, evolution, and prevalence, this new technique represents a logical next step in instrumentation for RV extrasolar planet searches, and has been proven with the single-object Exoplanet Tracker (ET) at Kitt Peak National Observatory, and the multi-object W. M. Keck/MARVELS Exoplanet Tracker at Apache Point Observatory. The development of the ET instruments has necessitated fleshing out a detailed understanding of the physical principles of the DFDI technique. Here we summarize the fundamental theoretical material needed to understand the technique and provide an overview of the physics underlying the instruments working. We also derive some useful analytical formulae that can be used to estimate the level of various sources of error generic to the technique, such as photon shot noise when using a fiducial reference spectrum, contamination by secondary spectra (e.g., crowded sources, spectroscopic binaries, or moonlight contamination), residual interferometer comb, and reference cross-talk error. Following this, we show that the use of a traditional gas absorption fiducial reference with a DFDI can incur significant systematic errors that must be taken into account at the precision levels required to detect extrasolar planets.
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The dispersed fixed-delay Intereferometer (DFDI) method is attractive for its low cost, compact size, and multiobject capability in precision radial-velocity (RV) measurements. The phase shift of fringes of stellar absorption lines is measured and then converted to an RV shift via an important parameter, phase-to-velocity scale (PV scale), determined by the group delay (GD) of a fixed-delay interferometer. Two methods of GD measurement using a DFDI Doppler instrument are presented in this article: (1) GD measurement using white-light combs gen- erated by the fixed-delay interferometer and (2) GD calibration using an RV reference star. These two methods provide adequate precision of GD measurement and calibration, given the current RV precision achieved by a DFDI Doppler instrument. They can potentially be used to measure GD of an fixed-delay interferometer for submeter- precision Doppler measurement with a DFDI instrument. Advantages and limitations of each method are discussed in detail. The two methods can serve as standard procedures of PV-scale calibration for DFDI instruments and cross- checks for each other.
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.
We present the Exoplanet Simple Orbit Fitting Toolbox (ExoSOFT), a new, open-source suite to fit the orbital elements of planetary or stellar mass companions to any combination of radial velocity and astrometric data. To explore the parameter space of Keplerian models, ExoSOFT may be operated with its own multi-stage sampling approach, or interfaced with third-party tools such as emcee. In addition, ExoSOFT is packaged with a collection of post-processing tools to analyze and summarize the results. Although only a few systems have been observed with both the radial velocity and direct imaging techniques, this number will increase thanks to upcoming spacecraft and ground based surveys. Providing both forms of data enables simultaneous fitting that can help break degeneracies in the orbital elements that arise when only one data type is available. The dynamical mass estimates this approach can produce are important when investigating the formation mechanisms and subsequent evolution of substellar companions. ExoSOFT was verified through fitting to artificial data and was implemented using the Python and Cython programming languages; available for public download at https://github.com/kylemede/ExoSOFT under the GNU General Public License v3.
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$mathrm{~m~s^{-1}}$.
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 1m/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.
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