COMBINING CORONAGRAPHY WITH INTERFEROMETRY AS A TOOL FOR MEASURING STELLAR DIAMETERS

The classical approach for determining stellar angular diameters is to use interferometry and to measure fringe visibilities. Indeed, in the case of a source having a diameter larger than typically λ/6B, B being the interferometer's baseline and λ the wavelength of observation, the fringe contrast decreases. Similarly, it is possible to perform angular diameter determinations by measuring the stellar leakage from a coronagraphic device or a nulling interferometer. However, all coronagraphic devices (including those using nulling interferometry) are very sensitive to pointing errors and to the size of the source, two factors with significant impact on the rejection efficiency. In this work, we present an innovative idea for measuring stellar diameter variations, combining coronagraphy together with interferometry. We demonstrate that, using coronagraphic nulling statistics, it is possible to measure such variations for angular diameters down to λ/40B with 1σ error-bars as low as λ/1500B. For that purpose, we use a coronagraphic implementation on a two-aperture interferometer, a configuration that significantly increases the precision of stellar diameter measurements. Such a design offers large possibilities regarding the stellar diameter measurement of Cepheids or Mira stars, at a 60-80 μas level. We report on a simulation of a measurement applied to a typical Cepheid case, using the VLTI-UT interferometer on Paranal.

[1]  Antoine Labeyrie,et al.  Resolved imaging of extra-solar planets with future 10 100 km optical interferometric arrays , 1996, astro-ph/9602093.

[2]  C. I. O. Technology.,et al.  Diameters of δ Cephei and η Aquilae Measured with the Navy Prototype Optical Interferometer , 2000, astro-ph/0009398.

[3]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[4]  D. Mawet,et al.  Annular Groove Phase Mask Coronagraph , 2005 .

[5]  A. Labeyrie,et al.  The Four-Quadrant Phase-Mask Coronagraph. I. Principle , 2000 .

[6]  C. D. Laney,et al.  Cepheid parallaxes and the Hubble constant , 2007, 0705.1592.

[7]  J. Armstrong,et al.  Theoretical Limb Darkening for Classical Cepheids. II. Corrections for the Geometric Baade-Wesselink Method , 2003, astro-ph/0304084.

[8]  Robert Piessens,et al.  Quadpack: A Subroutine Package for Automatic Integration , 2011 .

[9]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[10]  Robert A. Shaw,et al.  Astronomical data analysis software and systems IV : meeting held at Baltimore, Maryland, 25-28 September 1994 , 1995 .

[11]  Michael W. Feast,et al.  The Luminosities and Distance Scales of Type II Cepheid and RR Lyrae variables , 2008, 0803.0466.

[12]  Albert A. Michelson,et al.  Measurement of Jupiter's Satellites by Interference , 1891, Nature.

[13]  A. Michelson,et al.  Measurement of the Diameter of Alpha-Orionis by the Interferometer. , 1921, Proceedings of the National Academy of Sciences of the United States of America.

[14]  F Reynaud,et al.  Kilometric optical fiber interferometer. , 2001, Optics express.

[15]  A. Goushcha,et al.  Quantum efficiency of silicon photodiodes in the near-infrared spectral range. , 2003, Applied optics.

[16]  Anthony Boccaletti,et al.  The Four‐Quadrant Phase Mask Coronagraph. III. Laboratory Performance , 2003 .

[17]  J. J. Moré,et al.  Levenberg--Marquardt algorithm: implementation and theory , 1977 .

[18]  W. A. Traub,et al.  The angular diameter and distance of the Cepheid ζ Geminorum , 2001, astro-ph/0102359.

[19]  Pierre Riaud,et al.  Coronagraphic search for exo-planets with a hypertelescope: I. In the thermal IR , 2002 .

[20]  D. Bersier,et al.  A New Calibration Of Galactic Cepheid Period-Luminosity Relations From B To K Bands, And A Comparison To LMC Relations , 2007, 0709.3255.

[21]  V. C. D. Foresto.  Optique guidée monomode et interférométrie astronomique , 1997 .

[22]  G. Tinetti.  Characterizing Extrasolar Terrestrial Planets with Reflected, Emitted and Transmitted Spectra , 2007, Origins of Life and Evolution of Biospheres.

[23]  H. Zeng,et al.  Photon-number-resolving detection based on InGaAs/InP avalanche photodiode in the sub-saturated mode. , 2009, Optics express.

[24]  L. Berdnikov,et al.  Galactic Cepheids. Catalogue of light-curve parameters and distances , 2000 .

[25]  David M. Shemo,et al.  Optical Vectorial Vortex Coronagraphs using Liquid Crystal Polymers: theory, manufacturing and laboratory demonstration. , 2009, Optics express.

[26]  Eric Mazur,et al.  Enhancing near-infrared avalanche photodiode performance by femtosecond laser microstructuring. , 2006, Applied optics.

[27]  An Error Analysis of the Geometric Baade-Wesselink Method , 2003, astro-ph/0312349.

[28]  M. Creech-Eakman,et al.  Long-Baseline Interferometric Observations of Cepheids , 2002 .

[29]  C. Jenkins.  Optical vortex coronagraphs on ground-based telescopes , 2007, 0709.0153.

[30]  J. Tonry,et al.  The Discovery of Cepheids and a Distance to NGC 5128 , 2006, astro-ph/0605707.

[31]  Dimitri Mawet,et al.  The development and applications of a ground-based fiber nulling coronagraph , 2008, Astronomical Telescopes + Instrumentation.

[32]  Daniel Durand,et al.  Astronomical Data Analysis Software and Systems XI , 2009 .

[33]  Dinesh Manocha,et al.  Cache-efficient numerical algorithms using graphics hardware , 2007, Parallel Comput..

[34]  E. al.,et al.  Extended Envelopes around Galactic Cepheids. III. Y Ophiuchi and α Persei from Near-Infrared Interferometry with CHARA/FLUOR , 2007, 0704.1825.

[35]  R. Lachaume,et al.  On marginally resolved objects in optical interferometry , 2003, astro-ph/0304259.

[36]  L. Macri,et al.  To appear in the Astrophysical Journal A NEW CEPHEID DISTANCE TO THE MASER-HOST GALAXY NGC 4258 AND ITS IMPLICATIONS FOR THE HUBBLE CONSTANT 1 , 2006 .

[37]  Oswald Wallner,et al.  Alignment tolerances for plane-wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators. , 2002, Applied optics.

[38]  F. Vilardell,et al.  A comprehensive study of Cepheid variables in the Andromeda galaxy. Period distribution, blending, a , 2007, 0707.2965.

[39]  Pierre Riaud,et al.  The Four‐Quadrant Phase‐Mask Coronagraph. II. Simulations , 2001 .

[40]  Anthony J. Peacock,et al.  Darwin ground-based European Nulling Interferometer Experiment (GENIE) , 2003, SPIE Astronomical Telescopes + Instrumentation.

[41]  O. Lay,et al.  Systematic errors in nulling interferometers. , 2004, Applied optics.

[42]  Olivier Guyon,et al.  Imaging Faint Sources within a Speckle Halo with Synchronous Interferometric Speckle Subtraction , 2004 .

[43]  Roberto Biasi,et al.  STRAP for the VLT instruments , 1997, Optics & Photonics.

[44]  Roberto Abuter,et al.  Post-processing the VLTI fringe-tracking data: first measurements of stars , 2009 .

[45]  Eugene Serabyn,et al.  Deep nulling of laser light with a single-mode-fiber beam combiner. , 2006, Applied optics.

[46]  Stuart B. Shaklan,et al.  Fiber optic beam combiner for multiple-telescope interferometry. , 1990 .

[47]  S. Ridgway,et al.  CHARA Array Measurements of the Angular Diameters of Exoplanet Host Stars , 2008, 0803.1411.

[48]  Klaus Ergenzinger,et al.  DARWIN mission and configuration trade-off , 2006, SPIE Astronomical Telescopes + Instrumentation.

[49]  Daniel W. Wilson,et al.  Astronomical demonstration of an optical vortex coronagraph. , 2008 .

[50]  S. R. Kulkarni,et al.  Direct detection of pulsations of the Cepheid star ζ Gem and an independent calibration of the period–luminosity relation , 2000, Nature.

[51]  O. Lay,et al.  Imaging properties of rotating nulling interferometers. , 2005, Applied optics.