Differential Interferometry

Reverberation mapping estimates the size and kinematics of broad line regions (BLR) in Quasars and type I AGNs. It yields size-luminosity relation, to make QSOs standard cosmological candles, and mass-luminosity relation to study the evolution of black holes and galaxies. The accuracy of these relations is limited by the unknown geometry of the BLR clouds distribution and velocities. We analyze the independent BLR structure constraints given by super-resolving differential interferometry. We developed a three-dimensional BLR model to compute all differential interferometry and reverberation mapping signals. We extrapolate realistic noises from our successful observations of the QSO 3C273 with AMBER on the VLTI. These signals and noises quantify the differential interferometry capacity to discriminate and measure BLR parameters including angular size, thickness, spatial distribution of clouds, local-toglobal and radial-to-rotation velocity ratios, and finally central black hole mass and BLR distance. A Markov Chain Monte Carlo model-fit, of data simulated for various VLTI instruments, gives mass accuracies between 0.06 and 0.13 dex, to be compared to 0.44 dex for reverberation mapping mass-luminosity fits. We evaluate the number of QSOs accessible to measures with current (AMBER), upcoming (GRAVITY) and possible (OASIS with new generation fringe trackers) VLTI instruments. With available technology, the VLTI could resolve more than 60 BLRs, with a luminosity range larger than four decades, sufficient for a good calibration of RM mass-luminosity laws, from an analysis of the variation of BLR parameters with luminosity.

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“…3 can be limited to values u ·r < 1. Petrov (1989) shows that the interferometric phase for such a source is given by…”

Section: Differential Interferometry Of Non-resolved Sourcesmentioning

confidence: 99%

“…about ten times below the standard resolution limit of the largest infrared interferometers. Petrov et al (2001) and Marconi et al (2003) have proposed to apply to BLRs the super-resolution capability of differential interferometry (Petrov, 1989). This was one of the design specifications of the VLTI first generation instrument AMBER .…”

Section: Introductionmentioning

confidence: 99%

Differential interferometry of QSO broad-line regions - I. Improving the reverberation mapping model fits and black hole mass estimates

Rakshit

Petrov

Meilland

et al. 2015

Monthly Notices of the Royal Astronomical Society

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“…smaller than λ/B) sources, it is proportional to the variation of the photocenter of the source (Petrov 1989). Given a sufficient SNR, the photocenter variation with λ can be measured on very unresolved sources with many very rich astrophysical applications.…”

Section: Differential Phasementioning

confidence: 99%

AMBER, the near-infrared spectro-interferometric three-telescope VLTI instrument

Petrov¹,

Malbet²,

Weigelt

et al. 2007

A&A

322

210

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Context. Optical long-baseline interferometry is moving a crucial step forward with the advent of general-user scientific instruments that equip large aperture and hectometric baseline facilities, such as the Very Large Telescope Interferometer (VLTI). Aims. AMBER is one of the VLTI instruments that combines up to three beams with low, moderate and high spectral resolutions in order to provide milli-arcsecond spatial resolution for compact astrophysical sources in the near-infrared wavelength domain. Its main specifications are based on three key programs on young stellar objects, active galactic nuclei central regions, masses, and spectra of hot extra-solar planets. Methods. These key science goals led to scientific specifications, which were used to propose and then validate the instrument concept. AMBER uses single-mode fibers to filter the entrance signal and to reach highly accurate, multiaxial three-beam combination, yielding three baselines and a closure phase, three spectral dispersive elements, and specific self-calibration procedures. Results. The AMBER measurements yield spectrally dispersed calibrated visibilities, color-differential complex visibilities, and a closure phase allows astronomers to contemplate rudimentary imaging and highly accurate visibility and phase differential measurements. AMBER was installed in 2004 at the Paranal Observatory. We describe here the present implementation of the instrument in the configuration with which the astronomical community can access it. Conclusions. After two years of commissioning tests and preliminary observations, AMBER has produced its first refereed publications, allowing assessment of its scientific potential.

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“…In addition, spectrally resolved long-baseline interferometry -also called differential interferometry (DI;Petrov 1989;Lachaume 2003) once combined with Earth-rotation synthesis and/or the use of simultaneous baselines from three or more telescopes, offers new possibilities for observing the details of rotationally flattened stars and directly checking whether the von Zeipel effect applies to different spectral types and luminosity classes (van Belle 2012). The application of DI in practice demands, however, special data analysis to access the so-called differential phase (Vakili et al 1998), which in turn needs appropriate calibration procedures that go beyond the usual traditional angular diameter estimates versus visibility curves extrema and/or zeros.…”

Section: Introductionmentioning

confidence: 99%

Beyond the diffraction limit of optical/IR interferometers

Hadjara

Souza

Vakili

et al. 2014

A&A

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Context. As previously demonstrated on Achernar, one can derive the angular radius, rotational velocity, axis tilt, and orientation of a fast-rotating star from the differential phases obtained by spectrally resolved long baseline interferometry using earth-rotation synthesis.Aims. We applied this method on a small sample of stars for different spectral types and classes, in order to generalize the technique to other rotating stars across the H-R diagram and determine their fundamental parameters. Methods. We used differential phase data from the AMBER/VLTI instrument obtained prior to refurbishing its spectrometer in 2010. With the exception of Fomalhaut, which has been observed in the medium-resolution mode of AMBER (λ/δλ ≈ 1500), our three other targets, Achernar, Altair, and δ Aquilae offered high-resolution (λ/δλ ≈ 12 000) spectro-interferometric data around the Brγ absorption line in K band. These data were used to constrain the input parameters of an analytical, still realistic model to interpret the observations with a systematic approach for the error budget analysis in order to robustly conclude on the physics of our 4 targets. We applied the super resolution provided by differential phases φ diff to measure the size (equatorial radius R eq and angular diameter / eq ), the equatorial rotation velocity (V eq ), the inclination angle (i), and the rotation axis position angle (PA rot ) of 4 fast-rotating stars: Achernar, Altair, δ Aquilae, and Fomalhaut. The stellar parameters of the targets were constrained using a semi-analytical algorithm dedicated to fast rotators SCIROCCO. Results. The derived parameters for each star were R eq = 11.2 ± 0.5 R , V eq sin i = 290 ± 17 km s −1 , PA rot = 35.4• ± 1.4• , for Achernar; R eq = 2.0 ± 0.2 R , V eq sin i = 226 ± 34 km s −1 , PA rot = −65.5 • ± 5.5• , for Altair; R eq = 2.2 ± 0.3 R , V eq sin i = 74 ± 35 km s −1 , PA rot = −101.2• ± 14 • , for δ Aquilae; and R eq = 1.8 ± 0.2 R , V eq sin i = 93 ± 16 km s −1 , PA rot = 65.6 • ± 5 • , for Fomalhaut. They were found to be compatible with previously published values from differential phase and visibility measurements, while we were able to determine, for the first time, the inclination angle i of Fomalhaut (i = 90• ± 9 • ) and δ Aquilae (i = 81 • ± 13 • ), and the rotation-axis position angle PA rot of δ Aquilae. Conclusions. Beyond the theoretical diffraction limit of an interferometer (ratio of the wavelength to the baseline), spatial super resolution is well suited to systematically estimating the angular diameters of rotating stars and their fundamental parameters with a few sets of baselines and the Earth-rotation synthesis provided a high enough spectral resolution.

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Differential Interferometry

Cited by 28 publications

References 13 publications

Differential interferometry of QSO broad-line regions - I. Improving the reverberation mapping model fits and black hole mass estimates

Differential interferometry of QSO broad-line regions - I. Improving the reverberation mapping model fits and black hole mass estimates

AMBER, the near-infrared spectro-interferometric three-telescope VLTI instrument

Beyond the diffraction limit of optical/IR interferometers

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