VLBI STUDIES AT THE RADIOPHYSICAL RESEARCH INSTITUTE
M. B. Nechaeva, A. A. Antipenko, A. F. Dement'ev, N. A. Dugin, S. D. Snegirev, and Yu. V. Tikhomirov
Radiophysical Research Institute, Nizhny Novgorod, Russia
Radiophysics and Quantum Electronics, Vol. 50, No. 7, 2007
We consider the state-of-the-art of research in the field of very long baseline interferometry (VLBI) at the Radiophysical Research Institute (Nizhny Novgorod, Russia). In the past decade, the team of the VLBI Laboratory at this institute used the extensive methodological and instrument basis and the accumulated experience of radio-interferometric observations to continue experimental and theoretical studies along several research lines including the studies of the solar wind and radio emission of the Sun, radar studies of the bodies in the solar system, and navigational measurements. We present the main experimental results obtained for the analyzed problems.
The need for achievement of a high angular resolution for studying small-size radio sources and their spatial structure caused the appearance of new radio-astronomical instruments such as very long baseline radio interferometers. The studies in the field of very long baseline interferometry (VLBI) began almost simultaneously in the USSR, USA, and Canada in 1965 [1-3]. In the USSR, such works started almost in parallel at the Lebedev Physical Institute of the Russian Academy of Science (Moscow, Russia) and the Radiophysical Research Institute (Nizhny Novgorod, Russia). For fifty years, many theoretical and experimental works have been performed in the USSR and Russia and a number of research directions in the VLBI field have been developed due to the efforts made by the teams of the Lebedev Physical Institute of the Russian Academy of Sciences, Sternberg Astronomical Institute, Institute of Applied Astronomy of the Russian Academy of Sciences, Space Research Institute of the Russian Academy of Sciences, Radiophysical Research Institute and other institutions. The obtained results are generalized in several comprehensive surveys systematizing the state of VLBI in Russia. In this respect, one should single out the papers collected in . The results obtained by foreign VLBI teams are presented in ample monograph . This paper describes the contribution made by the Radiophysical Research Institute (RRI) to VLBI studies, describes briefly the main works, and reviews the studies of the past decade.
In various periods, VLBI research works at the RRI were headed by V. S. Troitskii, V. A. Alekseev, and B. N. Lipatov. At the initial stage, instrument systems of radio interferometers with independent receiving systems were developed along with the signal processing methods. Pilot experiments were performed using short-baseline instruments available at the RRI radio-astronomical stations. The developed radio interferometers included the receiving systems operated in a wide frequency range (from 9 MHz to 22 GHz) and the systems for coherent conversion, registration, correlation, and spectral analysis of the received signals. Methods for synthesis of a wide reception band, the phase control of receiving channels, data processing algorithms, etc. were proposed [4-15].
Along with that, the VLBI theory and techniques were developed to solve fundamental and applied problems. The methods of aperture-frequency synthesis for obtaining radio images of space sources with super-high spatial resolution and the techniques of measuring angular distances between two sources of quasi-monochromatic radiation were proposed [16-18]. In 1969, experimental astrophysical studies employing large-scale Russian radio telescopes started. The objectives of the first experiments were to measure angular dimensions of the sources of space radio emission and to estimate their correlated flux densities (1969) . The angular dimension of the Cassiopeia A source was measured for the first time in the decameter-wave range in 1971 . In collaboration with the Crimean and Byurakan observatories, the dimensions of several radio sources were estimated with a resolution of 0.1 arcsec at a frequency of 408 MHz (1972) . An angular resolution of 0.001 arcsec was achieved in determining the angular dimensions of space masers at the wavelength λ=1.35 cm (23 GHz) with a baseline of 1100 km (jointly with the Byurakan Astrophysical Observatory of the USSR Academy of Sciences, the Space Research Institute of the USSR Academy of Sciences, the Institute of Radioengineering and Electronics, the Crimean Astrophysical Observatory, and the Lebedev Physical Institute) in 1972-1973 .
The first experiments showed that VLBI makes it possible to solve the classical astronomical problems with accuracy exceeding the accuracy of other measurement methods by more than two orders of magnitude. This fact made VLBI an irreplaceable radio-astronomical tool. The fundamentals of the differential interferometry method were proposed, which was applied in solving many fundamental and applied astronomical problems [23-25]. The problem of establishing the fundamental quasi-inertial system of celestial coordinates and the system of terrestrial coordinates, including express determination of their mutual orientation, was solved [26, 27]. The differential interferometry method was used for measuring the Earth's rotation speed and the motion of the poles, as well as for studying tides in the Earth's crust . Interferometry of space masers by the same method made it possible to synchronize spaced time scales for the first time in the USSR and determine geodetic coordinates of large antennas with an error smaller than one meter for the first time (1973) [29, 30].
Space navigation is an astrometry direction, in which VLBI is also applied. The fundamentals of the method of radio interferometry in determining celestial coordinates of artificial satellites in orbits of different types and interplanetary space payloads were developed to provide high-precision navigation support to their fights. Angular coordinates of the artificial satellite of Venus and an aerostat in the Venerian atmosphere (project "EOS-Venera," 1974), automatic interplanetary station "Vega" (1985-1989), and spacecraft "Phobos" (1989) were measured for the first time [31-34]. The experiments aimed at rapidly determining precise positions of "Astron" and 'Granat" satellites by using the long-baseline narrow-band radio interferometry in combination with distance-Doppler measurements were performed in 1989 and 1990 [35-37].
The methodological and instrument support for radio-interferometric astrometry of pulsars was developed to obtain spatio-temporal characteristics of pulsars (angular coordinates and the period and phase of their emission) [38-40].
The VLBI method revealed new opportunities for studying cosmic media. In 1984, a VLBI experiment was performed, in which the near-solar plasma was probed continuously by electromagnetic signals transmitted by the 'Venera-15" automatic interplanetary station. The baseline in this experiment was 1200 km long (Crimea-to-Moscow region), and the wavelength λ=30 см cm . In 1986, the coma of Halley's comet was probed by radio signals transmitted by the "Vega" spacecraft . Since 1990, VLBI studies of the solar-wind plasma by probing it by radio emission of quasars have become regular [43-46].
One of the most important RRI research lines is the development of receiving and recording systems and individual components of VLBI equipment. It is evident that the wide range of the solved scientific problems requires using a large number of antennas. VLBI observations are performed in close cooperation with the institutions having large antenna facilities. Currently, five VLBI points are equipped with receiving and recording systems developed by the RRI.
Based on an extensive methodological and instrument basis and the accumulated experience of radio-interferometric observations, the RRI continued the experimental and theoretical VLBI studies in the recent decade in the following directions:
In 1996, new opportunities for the experiments pursuing the above-mentioned objectives opened up due to organization of the international low-frequency VLBI network (LFVN) [47, 49]. The main partners of the LFVN are currently the following Russian and foreign VLBI points: Evpatoriya (RT-70; Ukraine), Medvezhyi Ozera (TNA-1500; Russia), Noto (RT-32; Italy), Urumchi (RT-25; China), and Simeiz (RT-25; Ukraine). Along with the above-mentioned VLBI points, various combinations of radio telescopes in 12 countries were used in 24 scientific VLBI experiments in 1996-2006.
Within the framework of the LFVN activities, the functions of the RRI team include formulation of scientific tasks, development of the programs of experiments, and calculation of the observation schedule. The RRI staff members take part in the experiments at several VLBI points and provide operation of the receiving and recording equipment developed and manufactured at the RRI. The data are processed using the "NIRFI-3" correlator.
In what follows we consider the main experimental results obtained in recent years in the above-mentioned directions in more detail.
2. VLBI STUDIES OF THE SOLAR WIND
Studies of cosmic media such as the Earth's ionosphere, solar corona, and interplanetary and interstellar media is a conventional field of radiophysics. Of special interest are the studies of the near-sun plasma and the plasma of the solar wind. These media have the greatest influence on the radiation which passes through them, thereby affecting the results of radio-astronomical and astrometric observations. Studies of the solar wind are also of great importance for solving the problems of the physics of solar-terrestrial coupling. The processes in the solar wind form the space weather in the solar system and affect the atmosphere and biosphere of the Earth. Monitoring of the state of the near-sun plasma is the basis for geoffective forecasts.
Currently, the interstellar and near-sun plasmas are diagnosed using radio-astronomical means based on the radio-probing methods: the scintillation method, the method of probing media by radio signals transmitted by spacecraft and received by ground-based radio telescopes, and the method of Doppler long-baseline interferometry . In the recent decade, the methods of wide-band radio interferometry have been applied in this field.
In the case of radio-interferometric reception, the emission from the source located at a small angular distance from the Sun propagates through the inhomogeneous medium of the solar wind and is received at spaced apart ground-based points. The turbulent plasma causes fluctuations of the parameters of the transmitted radiation. The analysis of these fluctuations yields information on the propagation medium. The signal processing procedure characteristic of VLBI consists in multiplication of the antenna-received signals referring to the same wave front of the emission from a radio source. This method of multiplication of the signals makes it possible to exclude internal fluctuations of the source emission (they are completely correlated in the received signals) and study only relative perturbations introduced by the medium on two different propagation paths. Such a procedure has a lot of advantages compared with the conventional single-point reception and the methods of Doppler interferometry and disperse radio interferometry, since it allows one to probe the medium by not only monochromatic signals of spacecraft, but also wideband emission of natural radio sources. The informativeness of VLBI observations increases when the measurements are performed simultaneously at several baselines with different orientations and lengths. In this case, one can also estimate the shape (anisotropy) of inhomogeneities from the difference between the phase perturbations of interference responses at different baselines by making Snapshots" of the responses. Then, the size of the baseline projection onto the wave front determines the maximum scale of inhomogeneities to which this interferometer is sensitive [51-35].
Despite the fact that the first radio-interferometric experiment with probing of the solar wind was made in 1951 , some aspects of this method have not yet been considered in full detail. In particular, insufficient attention has been given to the analysis of complex-field correlations with allwance for the spatial separation of the sources, nor the spectral characteristics of the interferometer output signal comprising both the phase and amplitude fluctuations of the received emission have been analyzed. This circumstance did not make it possible to reveal the advantages of the VLBI method for solving the described problem.
At the RRI, the solar-wind plasma has been studied by using the wideband emission of natural sources since the 1990s . Theoretical and experimental works were aimed at developing the interferometric methods used to diagnose turbulent flows and finding ways to improve the informativeness of such methods when determining the parameters of a turbulent medium. The spectral and energy characteristics of the radio-interferometer signal were analyzed for the case of reception of noise emission from a natural source. A method for reconstruction of information on the parameters of the propagation medium (the electron number density and the velocity of the solar wind) from the spectral composition of the interferometer signal has been proposed [51-53, 55].
The possibilities of the considered method were studied experimentally. In 1994-2000, seven multipurpose international sessions of VLBI observations of extragalactic radio sources and the Sun at frequencies of 327 and 1665 MHz were performed [45, 46, 55, 56]. In the part of the experiment related to the diagnostics of the solar-wind plasma, the spatial region at the distances R>10R☼ (R☼ - from the Sun was studied (here RQ is the radius of the Sun). In this region, the flow of the solar wind is steady-state and the assumptions of the freezing-in hypothesis are valid . To do this, the sources located at angular distances ranging from 4° to 53° from the Sun were observed.
The initial processing of the results obtained in the experiments of 1994-1996 was performed at the Jet Propulsion Laboratory (California Institute of Technology, USA), and those of 1997-2000, on the correlator of the Dominion Radio Astrophysical Observatory (Pentincton, Canada). The secondary processing aimed at solving the problems of solar-wind diagnostics was performed at the RRI using special software.
When processing the experimental data, the power spectrum of the interferometer signal was calculated. When analyzing data, it was assumed that as the emitted radiation propagates in a turbulent medium, the dominant contribution to strong perturbations of the signal phase is given by large-scale inhomogeneities, whereas small-scale ones form a weak background of phase fluctuations of the transmitted radiation .
The index of the spatial spectrum of electron-number density fluctuations was estimated from the measurements of the spectral index for the experimental power spectra of the interferometer signal for weak phase fluctuations of the probing radiation. The velocity of the solar wind was determined from the frequency of the spectrum kink. Based on the experimental results obtained in 2000, the average values of the solar-wind velocity V|=342±17 km/s and the spectral index p=3.57±0.06 were found. The latter quantity is close to the index pk=11/3, of Kolmogorov's spectrum and agrees with the experimental results of solar-wind studies performed by various methods. The used method made it possible for the first time to estimate the solar-wind velocity and the index of the spatial spectrum of electron-number density fluctuations independently of each other in the region of scales from 2000 to 9000 km. The found values of the spectral index and the velocity allow us to confirm the applicability of the 'freezing-in" hypothesis and Kolmogorov's spectrum for the description of spatio-temporal variations in the solar wind at long distances from the Sun, for which R>40R☼ [53,56].
The dependences of the spectrum width on the heliocentric distance of the probing path and on the angle between the solar-wind velocity and the baseline projection onto the front wave were analyzed. Despite the fact that the described method does not provide precise quantitative data about media parameters in the case of strong phase fluctuations, it is possibile to interpret qualitatively the large-scale spatial structure of the solar wind from the relative broadening of spectral responses of the interferometer. The processing results demonstrated the presence of the regions with increased intensity of electron-number density fluctuations, which are extended along the direction of the solar wind and have lengths of hundreds of thousands of kilometers and transverse dimensions ranging from 1500 to 2000 km. The limitations imposed by the solar-wind plasma on the operation of VLBI systems in the decimeter-wave range were analyzed. It was shown that the influence of the inhomogeneities in the near-sun plasma on the operation of VLBI systems is significant in the range of angular distances from the Sun up to 30 ° at a frequency of 1665 MHz and up to 80° at a frequency of 327 MHz. In this case, the phase coherence of the signals is entirely violated if the probing path is close to the Sun, i.e., VLBI measurements are impeded at the distances less than 3° (at a frequency of 1665 MHz) and less than 13° (at a frequency of 327 MHz) [46, 53].
In the process of analyzing the experimental results, the recommendations on optimal planning of observations and processing of the received information were developed. They refer to the selection of the sources suitable for solar-wind studies, durations of observation materials, observation conditions at each reception point and parameters of correlation of the data obtained. The software tools for spectral processing of interferometer signals distorted by the perturbed medium were also developed and debugged.
3. STUDIES OF SOLAR RADIO EMISSION
One of the scientific fields developed at the RRI is studying flare processes manifesting themselves in the solar radio emission. In recent years, such studies were aimed at obtaining more and more detailed characteristics of these processes. Special attention is given to studying their fine spectral, temporal, and spatial structures.
An important role in solar radio physics is played by short-lived microwave bursts with a duration shorter than 1 s, a narrow frequency spectrum (the relative spectrum width Δf/f<0.1), and small angular dimensions (less than 1 arcsec). Such fine-structure events as spikes, blips, various pulsations, etc. are well known . These types of microwave bursts are generated by coherent plasma and cyclotron emission mechanisms. Studying the features of short-lived bursts and the development of theoretical models are not only of scientific interest, but are especially useful for exploration of such fundamental problems of the flare theory as fragmentation of flare energy release and particle acceleration.
The revealed fine temporal and spatial structures of the bursts in the decimeter- and centimeter-wave ranges (with durations t=0.01-0.1 s, and Δf/f<0.05) show that their radio sources are strongly fragmentary. In this case, the expected dimensions of such sources range from 0.001 to 0.1 arcsec, which is far beyond the resolution of the instruments currently used in solar radio astronomy (VLA, WRST, and CCPT) [59-62]. At present, such a high spatial resolution can be achieved only by using radio very longbaseline interferometers.
The experiments on studying fragmentary solar emission by the radio interferometry method started at the RRI in the middle of the 1990s. At the same time, creation of the radio-interferometric facility of the RRI started, which was designed to perform regular studies of fast (shorter than a second) processes on the Sun, weak flare phenomena ('microflares"), and the processes of microwave scattering in the solar corona. The radio-interferometric facility was created on the basis of the existing radio telescopes RT-7, RT-17, and RT-15. It includes a short-baseline interferometer with a baseline length of about 416 m in Staraya Pustyn' and an independent-reception interferometer Zimenki-Staraya Pustyn' with a baseline of about 70 km. The facility makes it possible to study localization, spatial sizes, and dynamics of the sources of solar radio bursts with a high (up to 1 ms) temporal resolution, as well as estimate their brightness temperature.
In 1994, the short-baseline interferometer in Staraya Pustyn' was used to study the spatial dynamics of the sources of solar subsecond bursts in the decimeter-wave range. It was found that in an intense multicomponent radio burst with several maxima, variations in the position of the radio-brightness center can reach 8 arcsec and the linear velocities of the visible source shift are close to 30000 km/s. At the same time, no unambiguous temporal correlation between the phase variation (source position) and the density of the flux of individual subsecond components was revealed. It was found that the positions of the sources of some neighboring subsecond peaks in a multicomponent burst differ strongly, and this difference can reach 3-8 arcsec for peaks separated in time by 0.3-0.5 s [63-66].
In 1995, 1998, and 2000, the RRI participated in VLBI experiments on observation of solar radio bursts in the decimeter-wave range, in which VLBI facilities with baselines from 200 to 400 km were used. Among all the registered (over 30) short radio bursts (with durations shorter than 1 s), interferometric responses were detected in two cases only (in the experiment of 1995; Medvezhyi Ozera-Pushchino). The temporal resolution used in the processing (2 s) did not allow one to associate these events with a certain burst type. However, the presence of interference evidences that sources of these bursts have small dimensions (less than 1 arcsec). Estimations of their brightness temperature on the basis of the signal-to-noise ratio and the size of the interference lobe yield a value of about 109 К for a 2-s burst and 1011 К for a 20-ms burst.
Observations of small-size solar flares with the use of the independent-reception interferometer Zimenki-Staraya Pustyn' started in 2006. In May and November 2006, two cycles of VLBI observations of the Sun and cosmic radio sources were performed at frequencies of 610 and 325 MHz. Using observation results, about 10 radio bursts with subsecond temporal structures were registered. Initial correlation processing of the radio-interferometric data at a frequency of 325 MHz, obtained during the burst in November 5, 2006 at 07:02:25 UT, showed the presence of several strong peaks in the interferometer response, which was indicative of the fact that the size of the source is rather small.
Thus, the VLBI experiments and their results demonstrated the possibility to obtain new scientific data about fast flare processes on the Sun by using radio-interferometric measurements. In the future, it is planned to obtain more detailed information about the observed small-size sources of solar radio emission (dimensions, number of simultaneous spikes in a limited region, distance between sources, velocity of their motion, etc.) by making observations simultaneously at 2 or 3 frequencies and upgrading the existing two-element radio interferometer to a multi-element facility containing at least three VLBI receiving points. Moreover, the problem of studying fragmentary flare emission of the Sun is planned to be included in the program of international experiments performed regularly with participation of the RRI on the basis of the international VLBI network LFVN along with simultaneous observations using the RRI Zimenki-Staraya Pustyn' interferometer.
4. NAVIGATIONAL MEASUREMENTS
Since the beginning of the space exploration era, artificial satellites and automatic interplanetary stations have been the most efficient instruments used to study the interplanetary and interstellar environments and objects in the solar system. Modern space projects include the programs of studying the Earth's atmosphere, the near-sun plasma, planets and their atmospheres, as well as other programs with geodynamic, astrophysical, and astrometric applications. The functions of satellites become wider: along with performing scientific tasks, they ensure operation of the routine communication systems and navigational systems.
Analysis of the problems solved by spacecraft shows the necessity of improving the accuracy and operation efficiency of the navigational equipment. Enhancement of the accuracy of spacecraft-based coordinate measurements allows one to reduce the number of corrections of spacecraft orbits, and use aerodynamic retardation in the planetary atmospheres to correct the orbits. Improvement of the accuracy of measuring the spacecraft coordinates changes the solved problems qualitatively and extends the scope of considered problems. Development of technical methods of tracking spacecraft and measuring the parameters of their motion at interplanetary distances is one of priority fields of modern space exploration.
Navigational interferometric studies, which started in 1969 [31-37, 68], show that by supplementing distance-Doppler methods with radio interferometry, one can achieve high accuracy (up to 0.001 arcsec) of determining the spacecraft position, which corresponds to several kilometers at the distance from the Earth to the Mars.
Example of power spectra of the interferometer response to the signal from the spacecraft "Mars Express" at a frequency of 2.3 GHz, obtained on October 10, 2005 at three baselines in the МЕХ 05.3 experiment. The frequency is plotted on the horizontal axis, and the normalized value of the power spectrum, on the vertical axis. The interference frequencies Ft = (523.81-0.12) Hz, Ft = (1693.11-0.12) Hz, and Ft = (1693.18-0.12) Hz were calculated from the spectrum-maximum frequency for the baselines Medvezhyi Ozera-Evpatoriya (a), Evpatoriay-Urumchi (b), and Medvezhyi Ozera-Urumchi (c), respectively
Based on the experience of radio-interferometric measurements, accumulated by the RRI within the framework of the missions "Vega," "Astron,", 'Granat," and "Phobos" [31-37], the RRI team continued navigational studies in the past decade. Determination of spacecraft positions in the quasi-inertial radio reference frame is based on the method of differential radio interferometry . This method includes (i) quasi-simultaneous observation of spacecraft signals and the emission from an extragalactic radio source (a quasar or the nucleus of a radio galaxy) having precisely known coordinates and located at a short angular distance (of about several degrees) from the spacecraft at the session time and (ii) determination of the difference between the time delays and the interference frequencies for the signals received by the interferometer receivers from the spacecraft and the radio source. These parameters measured differentially serve as the informative basis for calculations of the angular distance between the spacecraft and the radio source.
In October 2005, jointly with the European Space Operations Center, the RRI performed an LFVN-based VLBI experiment with radio signals from the interplanetary spacecraft "Mars-Express" at frequencies of 2.3 and 8.4 GHz [69, 70]. As a result of the data processing performed by the RRI, the spectra of the mutually correlated signal performed on the baselines Medvezhyi Ozera-Evpatoriya, Medvezhyi Ozera-Urumchi, and Evpatoriya-Urumchi were plotted (Fig. 1). This yielded the interference frequencies used to refine the spacecraft orbit by the M. V. Keldysh Institute of Applied Mechanics of the Russian Academy of Sciences.
5. VLBI RADAR OBSERVATION OF SPACE OBJECTS
Solving fundamental problems of cosmogony and celestial mechanics related to studies of the origin and evolution of the solar system, requires complete data about bodies in the solar system and the parameters of their motion, including the precise orbital parameters, rotation periods, spatial orientations, shapes, and sizes of the studied objects. Studies of the motion of bodies in the solar system are necessary for the solution of applied problems including preparation and successful implementation of interplanetary space missions.
An important applied problem is monitoring of the near-Earth space aimed at detection, determination of the motion parameters, and classification of artificial and natural cosmic objects that are potentially dangerous for the Earth. Primarily, such objects include fragments of space debris (used satellites, rocket stages, etc.). Technogenic pollution of the near-Earth space is currently dangerous for spacecraft fights and terrestrial ecology due to potential falls of radioactive or large-size fragments.
The problem of the asteroid threat is topical due to the discovery of the population of small planets whose trajectories cross the Earth orbit. A collision of the Earth with an asteroid can cause a global catastrophe. The studies of dynamics of the motion of such objects and of their physico-mineraloglcal properties will be the basis for long-term predictions of dangerous events and estimating the consequences of possible collisions.
At the end of the 1990s, the RRI proposed a method for studying objects in the solar system using VLBI radar . This method consists in irradiation of the studied objects by the signal of a high-power monochromatic or chirp transmitter and reception of the refected signals by a set of antennas in the VLBI regime. The object trajectories are measured using a combination of the VLBI radar method and the differential-interferometry method , when signals from an extragalactic radio source with known coordinates and echo signals from the studied objects are received sequentially. The VLBI radar method can be applied to solve the following problems: determination of precise trajectories along which the centers of gravity of the terrestrial planets move in the quasi-inertial radio reference frame, measurement of the parameters of self-rotation vectors of terrestrial planets, including their short-term variations, and refinement of the trajectories of asteroids and space debris objects.
The experiments on development of the VLBI radar method have been performed since 2001 on the basis of the LFVN network only [48, 70-77]. The data interpretation (determination of parameters of the object orbits) is performed at the M. V. Keldysh Institute of Applied Mechanics of the Russian Academy of Sciences. As a result of the performed works, echo signals from several tens of space-debris objects moving along orbits of different types and from Mars, Venus, and asteroid 2004 XP14 have been recorded.
Since the study of space debris by using the VLBI radar method is a relatively new problem, the majority of the works in this field required the development of all stages of the experiment such as selection of the objects, methods of observation in different radar regimes, procedures of data recording and processing. During the VLBI-radar sessions, echo signals from classified objects were studied and the measurement and data processing techniques were developed to search for unknown bodies in the near-Earth orbits.
Main tasks of the processing included the measurements of the Doppler shift of the interference frequency. The results of the measurements were used further to calculate the orbit parameters. Currenty, the procedure of measuring the distance from the geometric delay with the use of a chirp signal is underway. In addition, a method has been proposed for obtaining information on the general state of a spacecraft, including its rotation velocity, direction and stability of the rotation axis, sizes, the presence of individual refecting fragments on the object body, etc. This method is based on analyzing the temporal dynamics of the frequency spectrum of the interferometer correlation signal the in the VLBI and bistatic-radar regimes [76, 77].
A method for processing the data obtained in VLBI experiments has also been developed. Currently, the processing procedure is performed in several stages using the established scheme [75-77].
Example of the power spectrum resulting from autocorrelation of the echo received at Medvezhyi Ozera from object 95035 in July 28, 2004 in the experiment VLBR 04.2. A high-power response from the studied object was received at the frequency Fv = 251 kHz.
At the first stage, autocorrelation of the recorded signal and its spectral analysis are performed at each VLBI point to determine the presence of a signal reflected from the detected object at the expected frequency. The autocorrelation results are also used to determine the presence of noise and parasitic signals in the receiving system. An example of the power spectrum resulting from autocorrelation of the echo received at Medvezhyi Ozera is shown in Fig. 2. It should be noted that before recording, the received signal undergoes a number of frequency transformations in the receiving channel. The scheme of these transformations is organized in such a way that the useful signal appear at a frequency of about 254 kHz in the registration band after its translation to the low-frequency region. Figure 2 shows a high-power response from the studied object at the frequency Fv = 251 kHz. The shift of the spectrum maximum along the frequency axis is caused by the Doppler effect due to the motion of the object. The accuracy of determination of the Doppler shift from the autocorrelation signal is not high (about 3 kHz). Therefore, the cross-correlation analysis is then performed to obtain information on the velocity of the source.
At the second processing stage, correlation of the signal of the transmitter (or the emitted-signal model) and the echo signal received at each receiving point is ensured (the bistatic-radar regime). The correlation result is subjected to spectral processing. From the frequency of the maximum spectral response, the Doppler frequency shift comprising the information on the object velocity is determined with high accuracy (hundreds of a hertz). Figure 3 shows a spectrogram for a part of the correlation signal if the echo from a large object in a geostationary orbit is received at Medvehyi Ozera. In addition, the possibility of estimating the rotation period of objects from the analysis of the amplitude of mutually correlated spectra of the transmitter signal and the signal reflected from the object and received at each point of the VLBI network.
Spectrogram of the correlation signal for the echo received at Medvezhyi Ozera from large-size object 95017 in a geostationary orbit in the experiment VLBR 05.2 of September 15, 2005. The Doppler frequency shift F = (17845.23±0.23) Hz was measured from the maximum of the spectrum calculated for the interval 12:31:08.00-12:31:12.27 UT.
At the final processing stage, the mutual correlation function of the echo signals is calculated for all baselines of the network (VLBI regime) and is then subjected to spectral analysis. The measured parameters are the interference frequency, which carries information on the velocity of the object, and the delay used to determine the coordinates of the object (if a chirp signal is used). Examples of cross-correlation spectra of the echo signals from the "Kosmos-1366" satellite received in the VLBI regime simultaneously at three baselines of the Medvezhyi Ozera-Noto-Urumchi complex are shown in Fig. 4.
Plots of the signal power spectrum simultaneously obtained by the interferometer for three baselines when detecting the satellite "Kosmos-1366" in the experiment VLBR 03.1 of July 25, 2003 at 22:22 UT. The interference frequencies Ft = (-176.5 ± 0.12) Hz, Ft = (-373.7 ± 0.23) Hz, and Ft = (-195.9 ±0.23) Hz were estimated for the baselines Urumchi-Noto (a), Medvezhyi Ozera-Noto (b), and Medvezhyi Ozera-Urumchi (c), respectively.
Thus, the techniques of measuring the Doppler frequency shifts simultaneously at several receiving points measuring the interference frequency, and determining the rotation period (from variations in the spectrum maximum) have been developed. The Ballistic Centre of the M. V. Keldysh Institute of Applied Mechanics of the Russian Academy of Sciences refines the orbital parameters of the studied objects. The results of the a posteriori estimation of the accuracy of determining the elements of the orbit of the "Kosmos-1366" satellite are shown in Table 1 [74, 75]. The radial velocity of the "Kosmos-1366" satellite in the geostationary orbit was estimated from the measurements of the Doppler frequency shift on the baselines Evpatoriya-Urumchi and Evpatoriya-Medvezhyi Ozera and were processed jointly with optical measurements of the satellite right ascension and declination. For comparison, Table 1 also presents the errors of determination of the orbit, which were obtained from optical measurements only. It follows from the presented estimates that the use of the radial-velocity measurements ensures a significant increase in the accuracy of determination of the orbit parameters.
The VLBI radar experiments with participation of the RRI have regularly been performed for several last years until recently. For example, in July 2006, the international VLBR 06.1 session on detection and ranging of Mercury, the Moon, asteroid 2004 XP14, and space-debris objects was performed [70, 77]. Along with main VLBI points of the LFVN (Evpatoriya, Simeiz, Urumchi, and Noto), the points in Kalyazin (Special Design Bureau of the Moscow Energy Institute and Lebedev Physical Institute) and Zelenchuk (Institute of Applied Astronomy) were used for the first time. The RRI researchers took part in maintaining the operation of the RRI receivers mounted in Evpatoriya and Kalyazin.
The results of processing the experimental data revealed echo signals from 13 fragments of space debris. In particular, an echo signal from a small-size fragment in a geostationary orbit was received for the first time.
Radar experiments aimed at detection of unknown space debris fragments were performed in the beam-park regime, in which the directional patterns of the transmitting and receiving antennas overlap at a given point, and the number of the objects passing it per unit time is recorded in the observation process. The experimental data were used to perform mutual correlation processing of the echo signal received in Kalyazin and the signal of the transmitter in Evpatoriya. The results of the further spectral analysis made it possible to detect the passage of five objects through the directional pattern. For them, the Doppler frequency shifts were measured. In the described experiment, echo signals from the fragments formed as a result of destruction of low-orbit objects 82055AS and 61015BE were detected for the first time and precise measurements of the Doppler frequency shift for them were performed. Spectrograms of the correlation signal at the time of detection of object 82055AS are shown in Fig. 5.
Spectral responses of time-serial (bottom to top) parts of the cross-correlation signal in the VLBR 06.1 session of July 4, 2006 (the "beam-park" regime). At 19:55:33 UT, a strong response from object 82055AS passing through the area under consideration was detected. For each spectrum, the time interval and (if there was a response from the object) the measured Doppler frequency shift are shown at the right.
One of the tasks of the experiment VLBR 06.1 was detection and ranging of an asteroid. At its rendezvous with the Earth at 04:25 UT in July 3, 2006 , asteroid 2004 XP14 was at a distance of only 432338 km from the Earth (this distance is equal approximately to that between the Earth and the Moon). The estimated diameter of the asteroid is 430 m. Before that, neither the conventional, nor VLBI radar observations of a large asteroid had been performed at such short distances.
Asteroid 2004 XP14 was detected at frequencies of 5010.024 and 8560.000 MHz by the radars in Evpatoriya and Goldstone (USA), respectively. The correlation and spectral analysis of VLBI information showed the presence of responses from the asteroid at both frequencies. The results of mutual correlation processing of the emitted signal and the echo received from the asteroid were used to perform precision measurements of the Doppler frequency shift to refine the parameters of the orbit. It should be noted that it was the first time when responses from an asteroid were received in the VLBI radar experiments.
To conclude, we will emphasize the most important results in the VLBI field, obtained at the RRI in the past decade.
The VLBI method of diagnosing the solar-wind plasma probed by with wideband radiation from space radio sources was developed and tested experimentally. For the first time, the measurements of the solar-wind velocity and the index of the spatial spectrum were performed independently of each other in the region of inhomogeneity scales comparable with the length of the interferometer baseline, which made it possible to confirm the validity of the freezing-in hypothesis in the case where angular distances from the Sun exceed 10°.
The method of radar long-baseline interferometry of bodies in the solar system and space-debris objects in the near-Earth space was developed. Parameters of the motion of several tens of space-debris objects were measured, which made it possible to reduce the error of determining their orbits. Parameters of rotation of some non-operating satellites in a geostationary orbit were measured.
The works on development and creation of special VLBI equipment go on. Owing to the efforts of the staff of divisions and radio-astronomical observatories of the RRI, the new instrument (independent-reception interferometer Zimenki-Staraya Pustyn') was created and put into operation in 2006. The interferometer is equipped with irradiating systems with operating frequencies 327, 610, and 1660 MHz and receiving systems operating at frequencies 327 and 610 MHz. The length of the interferometer baseline is about 70 km, and its spatial resolution in the range near 610 MHz is about 1.5 arcsec. The interferometer is intended for studying cosmic media (interplanetary and interstellar media and the solar wind) and small-size flares of solar radio emission.
The RRI has created and maintains the data processing center "NIRFI-3," which is a hardware-software complex for correlation and spectral processing of VLBI data. Currently, the correlation center "NIRFI-3" is actively used for processing radio-interferometric data obtained in joint Russian and international experiments.
The comprehensive materials accumulated in the last decade facilitated the development of methods for solution of some problems and ensured a high level of the results of radio-astronomical studies, fundamental astrometry, space navigation, and studies of the properties of cosmic media and bodies of the solar system. The scope of the problems described in the paper determines the lines for further research in the VLBR field.
The authors are grateful to all staff members of the Russian and foreign observatories, who took part in the organization and implementation of joint VLBI experiments and whose data were used in the paper, and to I. E. Molotov who undertook a great deal of effort to create LFVN and maintain its operation. The authors thank V. A. Razin, V. F. Mel'nikov, V. M. Fridman, T. S. Podstrigach, and other researchers from the RRI divisions and the radio-astronomical observatories in Staraya Pustyn' and Zimenki for help with the radio-interferometric experiments. The authors are grateful to V. D. Krotikov for valuable advice during the preparation of this paper.
The VLBI studies of the RRI were supported by the Russian Foundation for Basic Research (project Nos. 05-02-16838 and 06-02-16981).
Размещен 12 марта 2008.
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