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Register a new userUsing bootstrap to assess uncertainties of VLBI results I. The method and image-based errors
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I.N. Pashchenko
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Very Long Baseline Interferometric (VLBI) observations of quasar jets enable one to measure many theoretically expected effects. Estimating the significance of observational findings is complicated by the correlated noise in the image plane. A reliable and well justified approach to estimate the uncertainties of VLBI results is needed as well as significance testing criteria. We propose to use bootstrap for both tasks. Using simulations we find that bootstrap-based errors for the full intensity, rotation measure, and spectral index maps have coverage closer to the nominal values than conventionally obtained errors. The proposed method naturally takes into account heterogeneous interferometric arrays (such as Space VLBI) and can be easily extended to account for instrumental calibration factors.
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We propose a method to overcome the usual limitation of current data processing techniques in optical and infrared long-baseline interferometry: most reduction pipelines assume uncorrelated statistical errors and ignore systematics. We use the bootstrap method to sample the multivariate probability density function of the interferometric observables. It allows us to determine the correlations between statistical error terms and their deviation from a Gaussian distribution. In addition, we introduce systematics as an additional, highly correlated error term whose magnitude is chosen to fit the data dispersion. We have applied the method to obtain accurate measurements of stellar diameters for under-resolved stars, i.e. smaller than the angular resolution of the interferometer. We show that taking correlations and systematics has a significant impact on both the diameter estimate and its uncertainty. The robustness of our diameter determination comes at a price: we obtain 4 times larger uncertainties, of a few percent for most stars in our sample.
Calibration of radio interferometric observations becomes increasingly difficult towards lower frequencies. Below ~300 MHz, spatially variant refractions and propagation delays of radio waves traveling through the ionosphere cause phase rotations that can vary significantly with time, viewing direction and antenna location. In this article we present a description and first results of SPAM (Source Peeling and Atmospheric Modeling), a new calibration method that attempts to iteratively solve and correct for ionospheric phase errors. To model the ionosphere, we construct a time-variant, 2-dimensional phase screen at fixed height above the Earths surface. Spatial variations are described by a truncated set of discrete Karhunen-Loeve base functions, optimized for an assumed power-law spectral density of free electrons density fluctuations, and a given configuration of calibrator sources and antenna locations. The model is constrained using antenna-based gain phases from individual self-calibrations on the available bright sources in the field-of-view. Application of SPAM on three test cases, a simulated visibility data set and two selected 74 MHz VLA data sets, yields significant improvements in image background noise (5-75 percent reduction) and source peak fluxes (up to 25 percent increase) as compared to the existing self-calibration and field-based calibration methods, which indicates a significant improvement in ionospheric phase calibration accuracy.
A crucial part of a space mission for very-long baseline interferometery (VLBI), which is the technique capable of providing the highest resolution images in astronomy, is orbit determination of the missions space radio telescope(s). In order to successfully detect interference fringes that result from correlation of the signals recorded by a ground-based and a space-borne radio telescope, the propagation delays experienced in the near-Earth space by radio waves emitted by the source and the relativity effects on each telescopes clock need to be evaluated, which requires accurate knowledge of position and velocity of the space radio telescope. In this paper we describe our approach to orbit determination (OD) of the RadioAstron spacecraft of the RadioAstron space-VLBI mission. Determining RadioAstrons orbit is complicated due to several factors: strong solar radiation pressure, a highly eccentric orbit, and frequent orbit perturbations caused by the attitude control system. We show that in order to maintain the OD accuracy required for processing space-VLBI observations at cm-wavelengths it is required to take into account the additional data on thruster firings, reaction wheel rotation rates, and attitude of the spacecraft. We also investigate into using the unique orbit data available only for a space-VLBI spacecraft, i.e. the residual delays and delay rates that result from VLBI data processing, as a means to evaluate the achieved OD accuracy. We present the results of the first experience of OD accuracy evaluation of this kind, using more than 5,000 residual values obtained as a result of space-VLBI observations performed over 7 years of the RadioAstron mission operations.
A possible method for linking the optical Gaia Celestial Reference Frame (GCRF) to the VLBI-based International Celestial Reference Frame (ICRF) is to use radio stars in a manner similar to that in the linking of the Hipparcos Celestial Reference Frame (HCRF) to ICRF. In this work, an obtainable accuracy of the orientation angles between GCRF and ICRF frames was estimated by Monte Carlo simulation. If the uncertainties in the radio star positions obtained by VLBI are in the range of 0.1-4 mas and those obtained by Gaia are in the range of 0.005-0.4 mas, the orientation angle uncertainties are 0.018-0.72 mas if 46 radio stars are used, 0.013-0.51 mas if 92 radio stars are used, and 0.010-0.41~mas if 138 radio stars are used. The general conclusion from this study is that a properly organized VLBI programme for radio star observation with a reasonable load on the VLBI network can allow for the realization of GCRF-ICRF link with an error of about 0.1 mas.
Software spectrometer (SWSpec) developed for spacecraft tracking can be used to assure VLBI signal chain reliability, and phase stability of a VLBI receiver. Testing performed with SWSpec during pre-operations both saves time, and eases the tests as one does not need to gather, couple and setup the hardware.
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