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Published July 2010 | Published
Journal Article Open

Theory of Dispersed Fixed-Delay Interferometry for Radial Velocity Exoplanet Searches

Abstract

The dispersed fixed-delay interferometer (DFDI) represents a new instrument concept for high-precision radial velocity (RV) surveys for extrasolar planets. A combination of a Michelson interferometer and a 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 instrument's 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.

Additional Information

© 2010 American Astronomical Society. Received 2009 July 3; accepted 2010 May 28; published 2010 June 28. The multiple-object ET instrument was supported by the W. M. Keck Foundation, NSF with grant AST-0705139, NASA with grant NNX07AP14G, the SDSS-III program, and the University of Florida. The development of the single-object ET was supported by NSF with grant AST-0451407, NOAO, and the Pennsylvania State University. J.vE. and S.M. gratefully acknowledge support from the JPL Michelson Fellowship program funded by NASA, and from Kitt Peak National Observatory for travel support for many nights of observing at the 2.1 m telescope. J.vE. also gratefully acknowledges support from the fellowship provided by the Pennsylvania State University, and from the SPIE scholarship program. This work has made use of the IDL Astronomy User's Library (Landsman 1993),12 and Craig Markwardt's IDL library.13 Funding for SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, and the National Science Foundation. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the University of Cambridge, Case Western Reserve University, University of Portsmouth, Johns Hopkins University, Princeton University, the Korean Scientist Group, the Max- Planck-Institute for Astrophysik, New Mexico State University, Ohio State University, University of Pittsburgh, Brazilian RIO Group, German Participation Group, New York University, University of California-Santa Clara, University of Florida, and the University of Washington. The SDSS-III Web Site is: http://www.sdss3.org The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. We gratefully acknowledge our anonymous referee's input which helped substantially improve this paper. J.vE. thanks Peter Plavchan for much useful discussion of the addition approximation error, Dimitri Veras for proofreading of early versions, and Justin Crepp for his helpful suggestions. Facilities: KPNO:2.1m (ET), Sloan (Keck ET), HET

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Created:
August 22, 2023
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October 20, 2023