Phase-referencing Technique Research Articles

Applications of the Source-Frequency Phase-Referencing Technique for ngEHT Observations

The source-frequency phase-referencing (SFPR) technique has been demonstrated to have great advantages for mm-VLBI observations. By implementing simultaneous multi-frequency receiving systems on the next-generation Event Horizon Telescope (ngEHT) antennas, it is feasible to carry out a frequency phase transfer (FPT) which could calibrate the non-dispersive propagation errors and significantly increase the phase coherence in the visibility data. Such an increase offers an efficient approach for a weak source or structure detection. The SFPR also makes it possible for high-precision astrometry, including the core-shift measurements up to sub-mm wavelengths for Sgr A*, M 87*, etc. We also briefly discuss the technical and scheduling considerations for future SFPR observations with the ngEHT.

Millimeter-VLBI Observations of Low-luminosity Active Galactic Nuclei with Source-frequency Phase Referencing

Abstract We report millimeter-VLBI results of low-luminosity active galactic nuclei (M84 and M87) up to 88 GHz with source-frequency phase-referencing observations. We detected the weak VLBI core and obtained the first image of M84 at 88 GHz. The derived brightness temperature of the M84 core was about 7.2 × 109 K, which could serve as a lower limit because the core down to 30 Schwarzschild radii was still unresolved in our 88 GHz observations. We successfully determined the core shifts of M87 at 22–44 GHz and 44–88 GHz through the source-frequency phase-referencing technique. The jet apex of M87 could be deduced at ∼46 μas upstream of the 43 GHz core from core-shift measurements. The estimated magnetic field strength of the 88 GHz core of M87 is 4.8 ± 2.4 G, which is at the same magnitude of 1–30 G near the event horizon probed by the Event Horizon Telescope.

Performance of VERA in 10 micro-arcsecond astrometry

Abstract Very Long Baseline Interferometry (VLBI) astrometry using the phase-referencing technique remains an open issue for the quantitative characterization of the observing conditions to achieve a feasible parallax precision of 10 micro-arcseconds (μas). To address this issue, we evaluated the astrometric performance of the VLBI Exploration of Radio Astrometry (VERA) through the parallax measurements of five distant star-forming regions under good observing conditions of close separations (${0{^{\circ}_{.}}5}$–${1{_{.}^{\circ}}3}$) and high elevations (≥50°). Their parallaxes measured 89–200 μas, corresponding to distances of 5–11 kpc with an error of 11–20 μas. Furthermore, we investigated the contributions to the position error budget and concluded that the tropospheric residual contribution is the dominant error source. We also confirmed that the astrometric error propagation strongly depends on the term $\Delta \sec Z$, which stands for the difference between $\sec Z$ of the target and its reference source, where Z is the zenith angle during the observations. We found that for a source pair with a $\Delta \sec Z$ less than 0.01 (for example, a set of a close separation of $\le {{0{^{\circ}_{.}}5}}$ and a high elevation of ≥50°), we can achieve the parallax precision of 10 μas using a typical monitoring program comprising 10 observing epochs over a span of two years.

AGN astrometry: A powerful tool for galaxy kinematic studies

AbstractThis article highlights the successes of the high resolution astrometric VLBI observations used for measuring proper motion of galaxies in the Local group. The required, high accuracies, often in the μ as yr−1 regime, are only attainable through the use of the phase-referencing technique. These require either a compact radio source (AGN) or strong maser emission in the target galaxy and, additionally, some compact extra-galactic radio sources (quasars) to serve as ideal background reference source. The derived proper motions can lead to lower limits on the orbital lower estimates to the mass of the host galaxy, promise a new handle on dynamical models of interacting galaxy systems and offer insights on the spatial distribution of dark matter in the near universe.

Correlation between SiO v = 3 J = 1 → 0 maser excitation and the light curve of a long-period variable star

Abstract In order to understand the excitation mechanisms of silicon monoxide (SiO) masers around long-period variables (LPVs), we have investigated distributions of the SiO v = 2 and v = 3 J = 1 → 0 masers around 12 LPVs by very long baseline interferometry (VLBI) observations with the VLBI Exploration of Radio Astrometry (VERA) and the Nobeyama 45 m telescopes. VLBI fringes of the v = 3 maser emission were detected for five LPVs. The composite maps of the v = 2 and v = 3 masers were made for T Cep, W Hya, WX Psc, and R Leo using the spectral line phase-referencing technique. The v = 2 maser spots were distributed in a ring-like form around the central stars, while it is difficult to recognize any specific morphology in the v = 3 maser distributions due to the small number of v = 3 spots detected. However in T Cep, we find that the distribution of the v = 3 maser spots correlates well with the v = 2 masers within a few milliarcseconds (0.2–0.3 au) in position and 1 km s−1 in line-of-sight velocity at the light curve phase of ϕ = 0.28 (ϕ = 0.0 and 1.0 correspond to the visible light maxima). This correlation implies that the mechanism of line-overlapping between the mid-infrared lines of H2O and SiO molecules works in T Cep at ϕ = 0.28. We discuss the possibility that the line-overlapping may work at the limited duration from the maximum to the minimum of the stellar light curve.

VLBI Imaging of M81* at λ = 3.4 mm with Source-frequency Phase-referencing

Abstract We report on the first VLBI image of the M81 nucleus (M81*) at a wavelength of 3.4 mm, obtained with the source-frequency phase-referencing (SFPR) technique. Thanks to the SFPR calibration, the coherent integration time eventually could be increased by more than an order of magnitude, which enabled the detection of fringes at the level of 45 mJy beam−1 with a dynamic range higher than 130:1. This paves the way toward future millimeter/submillimeter VLBI observations of weaker sources. From the analysis of the M81* visibilities, a core size of ∼50 μas at 3.4 mm was estimated. This follows the power-law relationship with wavelength, , reported previously at lower frequencies. These results constrain the core size (at 3.4 mm) to a minimum of ∼80 Schwarzschild radii of M81*.

Dynamics of SiO Masers around VX Sgr

Abstract We performed Very Long Baseline Array (VLBA) observations of SiO masers ( ) toward VX Sgr from 2006 July to 2008 August. With the application of a phase reference technique, the accurate relative positions of maser spots at the two transitions can be acquired. The relative positions enable us to obtain more matched masers in the same coordinate frame to better study the dynamics of the maser shell. We adopt two different methods to investigate the global motions of the maser shell, which is found to expand in a decelerated manner. At the beginning of this process, the decelerative force can be interpreted as a force dominated by the gravitational attraction of the star. However, in the later epochs, the deceleration has a smaller magnitude, suggesting that an outward force is combating the stellar gravity. In addition, we construct a model of a rotating and expanding maser shell. The consistency of the model and observations at the first two epochs suggests approximate Keplerian rotation of the shell with a period of 46.9 years. However, other explanations, such as an axisymmetric outflow, are also possible. We also find two matched maser spots with double-peak spectra moving at a velocity of 6.8 km s−1. The special spectra provide direct observational evidence that the motion of a maser spot reflects the real gas stream, rather than changes in physical conditions. Finally, the distance to VX Sgr is calculated to be 1.10 ± 0.11 kpc using a statistical parallax method. This value is within the range reported in the literature.

High-resolution measurement of differential mode delay of few-mode fiber using phase reference technique for swept-frequency interferometry

Abstract A method is described for the high-resolution measurement of the differential mode delay (DMD) of few-mode fiber based on the frequency-modulated continuous wave (FMCW) technique. With the conventional approach, a wider optical bandwidth is required for higher resolution, however, the effect of chromatic dispersion becomes critical and limits the actual resolution. This paper proposes and demonstrates a phase reference technique for FMCW signals that achieves high-resolution measurements without increasing the optical bandwidth. We can also further improve the resolution of our proposed method by reducing the phase fluctuation with signal averaging. The feasibility of the proposed method is confirmed experimentally with several kinds of FMFs including an offset-spliced fiber where mode couplings occur.

MultiView High Precision VLBI Astrometry at Low Frequencies

AbstractObservations at low frequencies (<8GHz) are dominated by distinct direction dependent ionospheric propagation errors, which place a very tight limit on the angular separation of a suitable phase referencing calibrator and astrometry. To increase the capability for high precision astrometric measurements an effective calibration strategy of the systematic ionospheric propagation effects that is widely applicable is required. The MultiView technique holds the key to the compensation of atmospheric spatial-structure errors, by using observations of multiple calibrators and two dimensional interpolation. In this paper we present the first demonstration of the power of MultiView using three calibrators, several degrees from the target, along with a comparative study of the astrometric accuracy between MultiView and phase-referencing techniques. MultiView calibration provides an order of magnitude improvement in astrometry with respect to conventional phase referencing, achieving ~100micro-arcseconds astrometry errors in a single epoch of observations, effectively reaching the thermal noise limit.

VLBI Monitoring of the Sub-parsec-scale Jet in the Radio Galaxy 3C 66B at 22 GHz

Abstract We present measurements of the proper motion of the sub-parsec scale jet at 22 GHz in the nearby FR I galaxy 3C 66B. Observations were made using Very Long Baseline Array (VLBA) at six epochs over four years. A phase-referencing technique was used to improve the image quality of the weak and diffuse jet components. We find that the inner knots are almost stationary, although one of them was expected to be detected with an apparent speed of 0.2 mas yr−1, according to 8 GHz monitoring at the same observation epochs. Clear flux variations are not observed in the core at 22 GHz; in contrast, clear flux enhancement is observed in the core at 8 GHz. We discuss a possible explanation: if the jet has helical structure, the viewing angles of the jet at 8 and 22 GHz differ by a few degrees, if the jet direction is almost along our line of sight. Although these results may imply the existence of a two-zone jet, which has been suggested in certain radio galaxies, it cannot explain the fact that the jet at the higher frequency is slower than that at the lower frequency.

MultiView High Precision VLBI Astrometry at Low Frequencies

Abstract The arrival of the Square Kilometer Array (SKA) will revitalize all aspects of Very Long Baseline Interferometry (VLBI) astronomy at lower frequencies. In the last decade, there have been huge strides toward routinely achieving high precision VLBI astrometry at frequencies dominated by tropospheric contributions, most notably at 22 GHz, using advanced phase-referencing techniques. Nevertheless, to increase the capability for high precision astrometric measurements at low radio frequencies (<8 GHz), an effective calibration strategy of the systematic ionospheric propagation effects that is widely applicable is required. Observations at low frequencies are dominated by distinct direction-dependent ionospheric propagation errors, which place a very tight limit on the angular separation of a suitable phase-referencing calibrator. The MultiView technique holds the key to compensating for atmospheric spatial-structure errors, by using observations of multiple calibrators and two-dimensional interpolation in the visibility domain. In this paper we present the first demonstration of the power of MultiView using three calibrators, several degrees from the target, along with a comparative study of the astrometric accuracy between MultiView and phase-referencing techniques. MultiView calibration provides an order of magnitude improvement in astrometry with respect to conventional phase referencing, achieving ∼100 μas astrometry errors in a single epoch of observations, effectively reaching the thermal noise limit. MultiView will achieve its full potential with the enhanced sensitivity and multibeam capabilities of SKA and the pathfinders, which will enable simultaneous observations of the target and calibrators. Our demonstration indicates that the 10 μas goal of astrometry at ∼1.6 GHz using VLBI with SKA is feasible using the MultiView technique.

The Power of (Near) Simultaneous Multi-Frequency Observations for mm-VLBI and Astrometry

Simultaneous or near-simultaneous observations at multiple frequency bands have the potential to overcome the fundamental limitation imposed by the atmospheric propagation in mm-VLBI observations. The propagation effects place a severe limit in the sensitivity achievable in mm-VLBI, reducing the time over which the signals can be coherently combined, and preventing the use of phase referencing and astrometric measurements. We present two demonstrations of the power of (near) simultaneous multi-frequency observations with the KVN and VLBA, and our recently developed analysis strategies to enable new measurements at mm-VLBI. The first case comprises simultaneous observations at 22, 43, 87 and 130 GHz of a group of five AGNs, the weakest of which is ∼200 mJy at 130 GHz, with angular separations ranging from 3.6 to 11 degrees, using the KVN. We analysed this data using the Frequency Phase Transfer (FPT) and the Source Frequency Phase Referencing (SFPR) techniques, which use the observations at a lower frequency to correct those at a higher frequency. The results of the analysis provide an empirical demonstration of the increase in the coherence times at 130 GHz from a few tens of seconds to about twenty minutes, with FPT, and up to many hours with SFPR. Moreover the astrometric analysis provides high precision relative position measurements between two frequencies, including, for the first time, astrometry at 130 GHz. The second case is a variation of the above, whereby adding dedicated wide-band cm-wavelength observations to measure the ionosphere eliminates the need for a second, calibrator, source. This addresses the scarcity of calibrators at mm-VLBI. We dubbed this technique Multi Frequency Phase Referencing (MFPR). We present bona fide astrometrically aligned VLBA images of BL Lacertae at 22 and 43 GHz using MFPR, which, combined with results from conventional phase referencing at cm-wavelengths, suggests the VLBI core has a recollimation shock that is revealed at mm-wavelengths. These shocks could be responsible for the γ-ray emission in blazar jets.

THE POWER OF SIMULTANEOUS MULTIFREQUENCY OBSERVATIONS FOR mm-VLBI: ASTROMETRY UP TO 130 GHz WITH THE KVN

Simultaneous observations at multiple frequency bands have the potential to overcome the fundamental limitation imposed by the atmospheric propagation in mm-VLBI observations. The propagation effects place a severe limit in the sensitivity achievable in mm-VLBI, reducing the time over which the signals can be coherently combined, and preventing the use of phase referencing and astrometric measurements. We carried out simultaneous observations at 22, 43, 87 and 130 GHz of a group of five AGNs, the weakest of which is ca. 200 mJy at 130 GHz, with angular separations ranging from 3.6 to 11 degrees, using the KVN. We analysed this data using the Frequency Phase Transfer (FPT) and the Source Frequency Phase Referencing (SFPR) techniques, which use the observations at a lower frequency to correct those at a higher frequency. The results of the analysis provide an empirical demonstration of the increase in the coherence times at 130 GHz from a few tens of seconds to about twenty minutes, with FPT, and up to many hours with SFPR. Moreover the astrometric analysis provides high precision relative position measurements between two frequencies, including, for the first time, astrometry at 130 GHz. Finally we demonstrate a method for the generalised decomposition of the relative position measurements into absolute position shifts for bona fide astrometric registration of the maps of the individual sources at multiple frequencies, up to 130 GHz.

A High-Resolution Continuous-Scan Acoustic Measurement Method for Turbofan Engine Applications

Detailed mapping of the sound field produced by a modern turbofan engine, with its multitude of overlapping noise sources, often requires a large number of microphones to properly resolve the directivity patterns of the constituent tonal and broadband components. This is especially true at high frequencies where the acoustic wavelength is short, or when shielding, scattering, and reflection of the sound field may be present due to installation effects. This paper presents a novel method for measuring the harmonic and broadband content of complex noncompact noise sources using continuously moving (referred to here as continuous-scan (CS)) microphones in conjunction with a state-of-the-art phase-referencing technique. Because the microphones are moving through the sound field produced by the noise sources, they effectively provide infinite spatial resolution of the sound directivity over the scan path. In this method, harmonic (i.e., shaft-coherent) content at the integer multiples of the instantaneous shaft rotational frequency is first extracted from the time signal using a tachometer signal and the Vold-Kalman (VK) filter. The residual broadband signal is then filtered in the time domain in fractional octave bands. The broadband spectra of the signals from the moving microphones are then computed at arbitrary positions along their scan paths using weighted averages (based on Chebyshev polynomial zero-crossings) and the assumption of a complex envelope that varies slowly over a spatial scale whose lower bound is set by the acoustic wavenumber. A benefit of this method is that the decomposition of the total measured sound field into a stochastic superposition of components preserves a meaningful phase definition for each “partial field” associated with a given shaft order (SO). This preservation of phase data enables the forward or backward projection of each of these partial fields using acoustical holography (AH). The benefits of the CS method are demonstrated using acoustic data acquired for a 22-in. scale-model fan stage run at the NASA Glenn Research Center's 9-foot by 15-foot wind tunnel. Two key outcomes of the work include (1) significant improvement in the spatial resolution of the measured sound field and (2) reduction in the overall data acquisition time. Additionally, the methods described here lead to new opportunities for noise source diagnostics and visualization.

New high-accuracy spacecraft VLBI tracking using high data-rate signal: A demonstration with Chang’E-3

As the scientific data volume in deep-space exploration rapidly grows, spacecraft heavily relies on high data-rate signals that span several megahertz to transmit data back to Earth. Employing high data-rate signals for high-accuracy radiometric interferometry can simultaneously deal with data transmission and spacecraft navigation. We demonstrate very long baseline interferometry (VLBI) tracking of the Chang’E-3 lander and rover to determine their relative lunar-surface position using downlink high data-rate signals. A new method based on the VLBI phase-referencing technique is proposed to obtain the differential phase delay, which is much more accurate than the differential group delay acquired by conventional VLBI approaches. The systemic errors among different signal channels have been well calibrated using the new method. The data from the Chang’E-3 mission were then processed, and meter-level accuracy positions of the rover with respect to the lander have been obtained. This demonstration shows the feasibility of high-accuracy radiometric interferometry using high data-rate signals. The method proposed in this paper can also be applied to future deep-space navigation.

Demonstration of KVN phase referencing capability

We present the results of Very Long Baseline Interferometry (VLBI) observations using the phase reference technique to detect weak Active Galactic Nuclei (AGN) cores in the Virgo cluster. Our observations were carried out using the Korean VLBI Network (KVN). We have selected eight representative radio galaxies, seven Virgo cluster members and one galaxy (NGC 4261) that is likely to be in the background. The selected galaxies are located in a range of density regions showing various morphology in 1.4GHz continuum. Since half of our targets are too weak to be detected at K-band we applied a phase referencing technique to extend the source integration time by calibrating atmospheric phase fluctuations. We discuss the results of the phase referencing method at high frequency observations and we compare them with self-calibration on the relatively bright AGNs, such as M87, M84 and NGC 4261. In this manuscript we present the radio intensity maps at 22GHz of the Virgo cluster sample while we demonstrate for first time the capability of KVN phase referencing technique.

DETERMINATION OF CENTRAL ENGINE POSITION AND ACCRETION DISK STRUCTURE IN NGC 4261 BY CORE SHIFT MEASUREMENTS

We report multifrequency phase-referenced observations of the nearby radio galaxy NGC 4261, which has prominent two-sided jets, using the Very Long Baseline Array at 1.4-43 GHz. We measured radio core positions showing observing frequency dependences (known as "core shift") in both approaching jets and counter jets. The limit of the core position as the frequency approaches infinity, which suggests a jet base, is separated by 82$\pm$16 ${\mu}$as upstream in projection, corresponding to (310$\pm$60)Rs (Rs: Schwarzschild radius) as a deprojected distance, from the 43 GHz core in the approaching jet. In addition, the innermost component at the counter jet side appeared to approach the same position at infinity of the frequency, indicating that cores on both sides are approaching the same position, suggesting a spatial coincidence with the central engine. Applying a phase referencing technique, we also obtained spectral index maps, which indicate that emission from the counter jet is affected by free-free absorption (FFA). The result of the core shift profile on the counter jet also requires FFA because the core positions at 5-15GHz cannot be explained by a simple core shift model based on synchrotron self-absorption (SSA). Our result is apparently consistent with the SSA core shift with an additional disk-like absorber over the counterjet side. Core shift and opacity profiles at the counter jet side suggest a two-component accretion: a radiatively inefficient accretion flow at the inner region and a truncated thin disk in the outer region. We proposed a possible solution about density and temperature profiles in the outer disk on the basis of the radio observation.

Accurate relative positioning of Yutu lunar rover using VLBI phase-referencing mapping technology

Real-time high-accuracy VLBI techniques played an important role in the Chinese lunar exploration mission in executing the soft landing of the ChangE-3 probe on the lunar surface. To make this possible, in-beam phase referencing was used to obtain accurate relative positioning between the Yutu rover and the lander. The visibilities outputted by the correlator software were initially converted to the uniform FITS-IDI format. Astronomical mapping software, such as AIPS and Difmap, was then used to complete the mapping and angular positioning of the Yutu antenna. A new positioning algorithm was developed to determine the three dimension positions of the rover on the lunar surface. We took advantage of the in-beam observations, for which the signals from lander and rover were received in the same digital terminal, to eliminate system errors. Theoretical analysis, null position testing, and comparisons with visual localization results show that an accuracy of about one meter is achieved in relative positioning. The in-beam phase-referencing technique has potential for use in accurate positioning, navigation, and visual location calibration in future lunar and/or planetary exploration.

VERIFICATION OF THE ASTROMETRIC PERFORMANCE OF THE KOREAN VLBI NETWORK, USING COMPARATIVE SFPR STUDIES WITH THE VLBA AT 14/7 mm

The Korean VLBI Network (KVN) is a new mm-VLBI dedicated array with capability for simultaneous observations at multiple frequencies, up to 129 GHz. The innovative multi-channel receivers present significant benefits for astrometric measurements in the frequency domain. The aim of this work is to verify the astrometric performance of the KVN using a comparative study with the VLBA, a well established instrument. For that purpose, we carried out nearly contemporaneous observations with the KVN and the VLBA, at 14/7 mm, in April 2013. The KVN observations consisted of simultaneous dual frequency observations, while the VLBA used fast frequency switching observations. We used the Source Frequency Phase Referencing technique for the observational and analysis strategy. We find that having simultaneous observations results in a superior performance for compensation of all atmospheric terms in the observables, in addition to offering other significant benefits for astrometric analysis. We have compared the KVN astrometry measurements to those from the VLBA. We find that the structure blending effects introduce dominant systematic astrometric shifts and these need to be taken into account. We have tested multiple analytical routes to characterize the impact of the low resolution effects for extended sources in the astrometric measurements. The results from the analysis of KVN and full VLBA datasets agree within 2-$\sigma$ of the thermal error estimate. We interpret the discrepancy as arising from the different resolutions. We find that the KVN provides astrometric results with excellent agreement, within 1-$\sigma$, when compared to a VLBA configuration which has a similar resolution. Therefore this comparative study verifies the astrometric performance of KVN using SFPR at 14/7 mm, and validates the KVN as an astrometric instrument.

VLBI observations of the radio quasar J2228+0110 atz= 5.95 and other field sources in multiple-phase-centre mode

A patch of sky in the SDSS Stripe 82 was observed at 1.6 GHz with Very Long Baseline Interferometry (VLBI) using the European VLBI Network (EVN). The data were correlated at the EVN software correlator at JIVE (SFXC). There are fifteen known mJy/sub-mJy radio sources in the target field defined by the primary beam size of a typical 30-m class EVN radio telescope. The source of particular interest is a recently identified high-redshift radio quasar J222843.54+011032.2 (J2228+0110) at redshift z=5.95. Our aim was to investigate the milli-arcsecond (mas) scale properties of all the VLBI-detectable sources within this primary beam area with a diameter of 20 arcmin. The source J2228+0110 was detected with VLBI with a brightness temperature T_b>10^8 K, supporting the active galactic nucleus (AGN) origin of its radio emission, which is conclusive evidence that the source is a radio quasar. In addition, two other target sources were also detected, one of them with no redshift information. Their brightness temperature values (T_b >10^7 K) measured with VLBI suggest a non-thermal synchrotron radiation origin for their radio emission. The detection rate of 20% is broadly consistent with other wide-field VLBI experiments carried out recently. We also derived the accurate equatorial coordinates of the three detected sources using the phase-referencing technique. This experiment is an early attempt of a wide-field science project with SFXC, paving the way for the EVN to conduct a large-scale VLBI survey in the multiple-phase-centre mode.