On the coherence loss in phase-referenced VLBI observations
I. Marti-Vidal, E. Ros, M. A. Perez Torres, J. C. Guirado, S. Jimenez-Monferrer, J. M. Marcaide
aa r X i v : . [ a s t r o - ph . I M ] A p r Astronomy&Astrophysicsmanuscript no. 14203 c (cid:13)
ESO 2018November 5, 2018
Coherence loss in phase-referenced VLBI observations
I. Mart´ı-Vidal ⋆ , E. Ros , , M.A. P´erez-Torres , J. C. Guirado , S. Jim´enez-Monferrer , and J. M. Marcaide Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, D-53121 Bonn (Germany)e-mail: [email protected] Departament d’Astronomia i Astrof´ısica, Universitat de Val`encia, E-46100 Burjassot, Val`encia (Spain) Instituto de Astrof´ısica de Andaluc´ıa, CSIC, Apdo. Correos 2004, E-08071 Granada (Spain)Submitted on 5.02.2010. Accepted on 11.03.2010.
ABSTRACT
Context.
Phase-referencing is a standard calibration technique in radio interferometry, particularly suited for the detection of weaksources close to the sensitivity limits of the interferometers. However, e ff ects from a changing atmosphere and inaccuracies in thecorrelator model may a ff ect the phase-referenced images, and lead to wrong estimates of source flux densities and positions. Asystematic observational study of signal decoherence in phase-referencing and its e ff ects in the image plane has not been performedyet. Aims.
We systematically studied how the signal coherence in Very-Long-Baseline-Interferometry (VLBI) observations is a ff ected bya phase-reference calibration at di ff erent frequencies and for di ff erent calibrator-to-target separations. The results obtained should beof interest for a correct interpretation of many phase-referenced observations with VLBI. Methods.
We observed a set of 13 strong sources (the S5 polar cap sample) at 8.4 and 15 GHz in phase-reference mode with 32di ff erent calibrator / target combinations spanning angular separations between 1.5 and 20.5 degrees. We obtained phase-referencedimages and studied how the dynamic range and peak flux-density depend on observing frequency and source separation. Results.
We obtained dynamic ranges and peak flux densities of the phase-referenced images as a function of frequency and separationfrom the calibrator. We compared our results with models and phenomenological equations previously reported.
Conclusions.
The dynamic range of the phase-referenced images is strongly limited by the atmosphere at all frequencies and forall source separations. The limiting dynamic range is inversely proportional to the sine of the calibrator-to-target separation. Notsurpriseingly, we also find that the peak flux densities decrease with source separation, relative to those obtained from the self-calibrated images.
Key words.
Techniques: interferometric – Atmospheric e ff ects
1. Introduction
Phase-referencing is a standard calibration technique in radiointerferometry. It allows the detection of a weak source (targetsource) by using quasi-simultaneous observations of a closebystrong source (calibrator) (see e.g., Ros 2005 and referencestherein). This technique also allows the user to recover theposition of the target source relative to that of the calibrator;a position otherwise lost by the use of closure phases in theimaging. Basically, phase-referencing consists of estimating theantenna-based complex gains with the calibrator fringes, time-interpolating these gains to the observations of the target, andcalibrating the visibilities of the target with the interpolatedgains. Therefore, it is assumed that for each antenna the opticalpaths of the signals from both sources are similar. However, at-mospheric turbulences and / or inaccuracies in the correlator geo-metrical model may introduce errors in the estimates of the opti-cal paths of the signals and severely a ff ect the phase-referencing.These errors can be partially corrected by applying the self-calibration algorithm (see, e.g., Readhead & Wilkinson 1978)after phase-referencing. However, self-calibration, specially onobservations of weak sources, may a ff ect the resulting images inundesirable ways (see, e.g., Mart´ı-Vidal & Marcaide 2008).The correlator model includes contributions from the drytroposphere, the Earth orientation parameters, gain corrections ⋆ Alexander von Humboldt Fellow for the sampling, and feed rotation of the alt-azimuthal mountsof the antennae. An imperfect modelling in any of these con-tributions and the loss of coherence of the radio waves withinthe time elapsed between consecutive observations of a givensource, have an impact on the quality of phase-referencing.Some authors have stated that the loss of signal coherence inphase-referencing is linearly dependent on the separation be-tween the calibrator source and the target source (Beasley &Conway 1995). However, in a recent publication Mart´ı-Vidal etal. (2010) suggest a phenomenological model di ff erent from thatof Beasley & Conway (1995), based on Monte Carlo simulationsof atmospheric turbulences.To empirically establish this dependence, we need to com-pare phase-referenced images to those obtained from the self-calibrated visibilities (i.e., the images obtained by applying the optimum phase gains; those that maximize the signal coherenceof the target sources). For this purpose, both calibrator and tar-get must be strong enough to generate fringes with a signal-to-noise ratio (SNR) high enough to allow for an accurate estimateof the phase, delay, and rate of the fringe peaks, thus avoidingthe bias e ff ects related to self-calibration of weak signals (e.g.,Mart´ı-Vidal & Marcaide 2008).The S5 polar cap sample (a subset of 13 sources from theS5 survey, see K¨uhr et al. 1981, Eckart et al. 1986) is an idealset of sources to perform such a study. The spectra of thesesources are relatively flat at radio wavelenghts and their fluxdensities range from hundreds of mJy to several Jy. Therefore I. Mart´ı-Vidal et al.: Coherence loss in phase-referenced VLBI observations it is possible to study the loss of phase coherence as a func-tion of observing frequency and source separation. We observedthe S5 polar cap sample at 8.4 GHz and 15 GHz. These observa-tions are part of a large astrometry programme (Ros et al. 2001,P´erez-Torres et al. 2004, Mart´ı-Vidal et al. 2008, and Jim´enez-Monferrer et al. in preparation) and were performed in phase-reference mode with many di ff erent calibrator / target combina-tions. From these observations, we studied the loss of signal co-herence in phase-referenced observations by comparing phase-referenced and self-calibrated images for all possible calibra-tor / target combinations allowed by the observations.In the next section we describe our observations and the pro-cess of data calibration and reduction. In Sect. 3 we report on theresults obtained. In Sect. 4 we summarize our conclusions.
2. Observations and data reduction
We observed the 13 sources of the S5 polar cap sample withthe complete Very Long Baseline Array (VLBA) at 8.4 GHz on2001 February 3 and at 15 GHz on 2000 June 15. At each epoch,8 bands of 8 MHz bandwidth each were recorded, obtaining asynthesized bandwidth of 64 MHz in one polarization (LCP). Allthree epochs consisted of 24 hr of observations. The observationstook place in phase-referenced mode with di ff erent subsets ofthree or four radio sources in di ff erent duty cycles (see Mart´ı-Vidal et al. 2008 for more details on the observing schedule).The sources of each subset were observed cyclically for abouttwo hours. Each radio source was observed a total of about fourhours. Data were cross-correlated at the Array Operation Centerof the National Radio Astronomy Observatory (NRAO). Detailson the source images at 8.4 GHz and 15 GHz can be found inRos et al. (2001) and P´erez-Torres et al. (2004), respectively. Theresults of the high-precision astrometry analysis at 15 GHz canbe found in Mart´ı-Vidal et al. (2008). Those at 8.4 GHz will bepublished elsewhere (Jim´enez-Monferrer et al. in preparation).The data calibration and reduction was performed using ParselTongue (Kettenis et al. 2006), a Python interface to theNRAO Astronomical Image Processing System ( aips ). We gen-erated a script in ParselTongue to automatize the calibration andimaging of the phase-referenced images between all source pairsthat were observed within the same duty cycles. A total of 32source pairs were obtained, covering a range of source separa-tions between 1.5 and 20.5 degrees. We checked the quality ofthe automated calibration and imaging by re-generating man-ually phased-referenced images of some pairs of sources andcomparing them to the automated images. The results obtainedwere compatible within 0.1 σ . Below we summarize the processof calibration followed in our analysis. – Step 1. A correction of the the Earth Orientation Parameters(EOP) as estimated by the United States Naval Observatory(USNO) was applied to the data. – Step 2.
The visibility phases were aligned between the sub-bands, through the whole 64 MHz band for all sources andtimes by fringe-fitting the sub-band delays of a selected scanwith high-quality fringes and applying the estimated delaysand phases to all visibilities. – Step 3.
A second fringe fitting, using now the delays deter-mined from the whole band, provided new phase correctionsfor all the observations. The visibility amplitude calibrationwas performed with the system temperatures and gain curvesfrom each antenna. – Step 4.
The calibrated data were exported into the pro-gramme difmap (Shepherd et al. 1995) to obtain images of all sources. The CLEAN algorithm and several iterations ofphase and gain self-calibration were applied to each sourceuntil high-quality images (with residuals close to the thermalnoise) were obtained. – Step 5.
These images were imported back into aips for a sec-ond fringe fitting, now taking into account the contributionof the source structures in the estimates of the residual de-lays and phases. The amplitude calibration was also refinedby estimating the amplitude gains based on the source struc-tures (one gain solution for all antennae every 10 minutes).Once the data were calibrated as described above, we pro-ceeded with the analysis. For each pair of sources (A and B), foursets of data were generated. On the one hand, the self-solutionsof A (B) in the time range when this source was observed in thesame duty cycles as B (A). On the other hand, the set of vis-ibilities of A (B) phase-referenced to B (A), obviously for thesame time range as that of the corresponding self-calibrated datasets. Each of these data sets was used to generate an image us-ing natural weighting of the visibilities (to optimize the sensi-tivity) and the same CLEAN windows that were used to obtainthe images in Step 4 of the data calibration procedure. For thephase-referenced images, the position of the peak flux-densitywas first estimated and the CLEAN windows were accordinglyshifted before CLEANing.
3. Results and discussion
The dynamic ranges of the images obtained as described in theprevious section were computed as the peak flux-density per unitbeam divided by the root-mean-square (rms) of the image resid-uals (i.e., after subtracting the CLEAN model). The peak fluxdensities of the images obtained from the self-calibrated visi-bilities range between 0.16 and 2.60 Jy at 8.4 GHz and between0.16 and 1.86 Jy at 15 GHz. The typical rms of these images are1 mJy beam − at 8.4 GHz and 2 mJy beam − at 15 GHz.A total of 64 phase-referenced images were obtained at eachfrequency. These are two images for each pair of sources (i.e.,image of source A phase-referenced to B and image of source Bphase-referenced to A). We then discarded the images with dy-namic ranges lower than 10, because in these cases there is a highchance of confusion of the source with a spurious noise peak.Applying this cuto ff to the dynamic ranges, 53 phase-referencedimages were left at 8.4 GHz and 31 images at 15 GHz. The dy-namic ranges of the phase-referenced images are typically a fac-tor ∼
40 smaller than those obtained from the self-calibratedvisibilities (see Figs. 1 and 2). A first conclusion is that the lossof phase coherence strongly a ff ects the dynamic range of thephase-referenced images, regardless of the calibrator-to-targetseparation. A similar conclusion was reported by Mart´ı-Vidal et al.(2010) based on Monte Carlo simultations of phase-referencedobservations under a turbulent atmosphere. These authors mod-elled the dynamic range of a phase-referenced image consider-ing the addition in quadrature of two sources of noise; one dueto the thermal noise of the receiving system, σ th , and the otherdue to the atmosphere. σ at . The latter was assumed to be equalto a given percentage of the source flux-density, i.e. σ at = f at S .In this expression, S is the flux density and f at is a factor thatdepends on the calibrator-to-target separation, θ , the observingfrequency, ν , and the on-source observing time ∆ t . We noticethat a similar expression is usually employed in the estimate . Mart´ı-Vidal et al.: Coherence loss in phase-referenced VLBI observations 3 Dyn.Range H Norm. L H deg L Dyn.Range H Norm. L Fig. 1.
Dynamic ranges (normalized to an observing time of 10hours) of the phase-referenced images as a function of distanceto the calibrators. The error bars are proportional to the flux den-sities of the calibrators. Lines represent a model of the maximumachievable dynamic range (Eq. 2). H deg L Dyn.Range H Norm. L Fig. 2.
Dynamic ranges (normalized to an observing time of 10hours) of the images obtained from self-calibrated visibilities.Stars are data at 8.4 GHz and diamonds at 15 GHz. This figurecan be compared to Fig. 1 to see the e ff ect of coherence lossesin the phase-referenced images.of the (instrumental) systematic amplitude-calibration errors inVLA and VLBI observations. However, in our case the factor f at depends on the calibrator-to-target separation and on the to-tal on-source observing time, while the factors for the estimateof systematic amplitude-calibration errors in VLA and VLBI ob- servations only depend on the observing frequency. The dynamicrange is thus D = S q σ th + f at S . (1)The dynamic range of a phase-referenced image is limited toa given value, D l , D l = f at . (2)This limit is independent of both S and the sensitivity of thearray. It is achieved when the flux density of the target sourceis much higher than the thermal noise of the interferometer. Thelimiting dynamic range only depends on θ , ν , and ∆ t , and it canbe several orders of magnitude smaller than the correspondingdynamic range due to the thermal noise of the receiving sys-tem, indicating that the atmosphere strongly limits the sensitiv-ity of the observations. Mart´ı-Vidal et al. (2010) propose a phe-nomenological model for f at based on their Monte Carlo simu-lations (see their Sect. 5.3). This model takes the form f at = K ν √ ∆ t sin ( θ ) , (3)where K is a constant to be determined.We can compare this phenomenological model to our obser-vations by plotting the dynamic range of all our phase-referencedimages as a function of calibrator-to-target separation. The im-ages obtained for each source pair correspond to data withslightly di ff erent on-source observing times. Therefore, we cor-rected (i.e., we normalized) the dynamic ranges of all the im-ages by applying the factor √ N / N v , where N v is the numberof visibilities for each image and N is the number of visibil-ities corresponding to a on-source observing time of 10 hourswith the VLBA. We show in Fig. 1 the normalized dynamicranges and the model resulting from Eq. 3. We find that for K ∼ . . GHz − the model predicts the limiting dynamicranges obtained with the VLBA at both frequencies, althoughthe results at 8.4 GHz are of higher quality; the results at 15 GHzare noisier. The dynamic ranges (also normalized to an observ-ing time of 10 hours) obtained from the self-calibrated imagesare shown in Fig. 2 for a comparison with those obtained fromphase-referencing. The error bars in Fig. 1 are set to be propor-tional to the flux density of the calibrator. This way the readerhas information in a single figure on the quality of the phase-referenced images and the quality of the calibrator visibilities. We show in Fig. 3 the peak flux densities of the phase-referencedimages relative to those obtained from the images correspond-ing to the self-calibrated visibilities as a function of distanceto the calibrator. The systematics in the loss of flux density isclear for the 8.4 GHz data. The flux density recovered is about80% of the real flux density for separations of ∼ I. Mart´ı-Vidal et al.: Coherence loss in phase-referenced VLBI observations
PeakRatio H deg L PeakRatio
Fig. 3.
Peak flux densities of the phase-referenced images nor-malized to the peak flux densities of the images obtained fromthe self-calibrated visibilities. Lines represent the model givenby Eq. 4.(these points correspond to sources B1803 +
784 and B1150 + P ph , relativeto the real peak flux-density of the source, P s f , can be estimatedas P ph P s f = + k f k at , (4)where k is a constant to be determined. From the Monte Carlosimulations, the exponent k takes the value 1 . ± .
02. In Fig.3 we also show the predictions of the model given by Eq. 4for k ∼
63. The model roughly predicts the behaviour of the8.4 GHz data, although for separations larger than ∼
15 degrees,the observed peak ratios clearly saturate at ∼ .
5, while themodel predictions monotonically decrease. A similar conclusionis obtained for the 15 GHz data, where a saturation around 0.4 isappreciated. The saturation in the ratio of flux-density peaks atlarge calibrator-to-target separations is not modelled using Eq.4 and could be due to the saturation of the power-spectrum ofthe tropospheric turbulences at large scales (see, e.g., Thomson,Moran, & Swenson 1991), which was not considered in the sim-ulations reported in Mart´ı-Vidal et al. (2010). This saturation ofthe power spectrum of the turbulences would stabilize the phasedi ff erence between target and calibrator for large separations andtherefore enhance the signal coherence (and peak flux-density)of the target source.
4. Conclusions
We report how phase referencing a ff ects the signal coherence(and the fidelity of the images) in VLBI observations at di ff erentfrequencies (8.4 GHz and 15 GHz) and for di ff erent calibrator-to-target separations (from 1.5 to 20.5 degrees). We determinedthe loss of dynamic range and peak flux-density of the phase-referenced images and compared the results with the model pre-dictions given in Mart´ı-Vidal et al. (2010).The dynamic range of the phase-referenced images isstrongly limited by the atmosphere at all frequencies and forall calibrator-to-target separations. The maximum achievable dy-namic range using the VLBA is given by Eqs. 2 and 3, with K ∼ . ν is given in GHz and ∆ t in hours). If the targetsource is not strong (as is usually the case), the thermal noise ofthe receiving system cannot be ignored and the dynamic rangeshould be estimated with Eqs. 1 and 3.The flux-density (computed as the peak flux density of thephase-referenced image in units of the real peak flux-densityof the source) decreases as the separation to the calibrator in-creases and is given by Eqs. 4 and 3, with k ∼
63 and k ∼ . ∼
15 degrees (the re-sults at 15 GHz are too noisy to reach a robust conclusion). Forseparations larger than 15 degrees, the observed peak ratios arehigher than the model predictions, possibly due to a saturationin the power spectrum of the tropospheric turbulences at largescales, which was not considered in Mart´ı-Vidal et al. (2010).It is remarkable that for relatively small separations (below5 degrees), which are typical in many phase-referencing obser-vations, the flux-density loss can be as large as 20% at 8.4 GHzand 30 −
40% at 15 GHz (and even larger at higher frequencies,according to Eq. 4). It must be also taken into account that thephase-referenced observations here reported were performed un-der good weather conditions and when the sources were close totheir transits at nearly all stations (except Mauna Kea and St.Croix, see Mart´ı-Vidal et al. 2008 for details on the observingschedule). Therefore even larger flux-density losses and lowerdynamic ranges may be obtained when the observing conditionsare far from optimal.However, we must also notice that the typical calibrator-to-calibrator cycle times in our observations were about 120 − −
240 seconds in VLBIobservations). Therefore it is not expected that a changing atmo-sphere may have introduced strong e ff ects in the coherence of thephase-referenced visibilities at 8.4 GHz. At 15 GHz, the shortercoherence time (which takes typical values of 100 −
140 secondsin VLBI observations) might be short enough to imply an addi-tional phase degradation in the phase-referenced visibilities dueto a changing atmosphere. Nevertheless, this issue is unlikely tosignificantly a ff ect the results of our analysis, because the timeevolution of the self-solutions of the antenna-based phase gainsat 15 GHz are smooth, which indicates that the weather condi-tions were good enough to allow for a well-behaved phase con-nection between contiguous scans of each source. Acknowledgements.
IMV is a fellow of the Alexander von HumboldtFoundation in Germany. The Very Long Baseline Array is operated by theUSA National Radio Astronomy Observatory, which is a facility of the NationalScience Foundation operated under cooperative agreement by AssociatedUniversities, Inc. Partial support was obtained by Generalitat Valenciana(Prometeo 2009 P104) and from Spanish grant AYA 2005-08561-C03-02.MAPT acknowledges support by the MEC through grant AYA 2006-14986- . Mart´ı-Vidal et al.: Coherence loss in phase-referenced VLBI observations 5
C02-01, and by the Consejer´ıa de Innovaci´on, Ciencia y Empresa of Junta deAndaluc´ıa through grants FQM-1747 and TIC-126.
References
Beasley, A. J., Conway, J. E. 1995, in ASP Conf. Ser. 82, Very Long BaselineInterferometry and the VLBA, eds. J. A. Zensus, P. J. Diamond, & P. J.Napier (San Francisco: ASP), p. 327Eckart, A., Witzel, A., Biermann, P., et al. 1986, A&A, 168, 17Mart´ı-Vidal, I., Marcaide, J. M., Guirado, J. C., P´erez-Torres, M. A., Ros, E.2008, A&A 478, 267Mart´ı-Vidal & I., Marcaide, J. M. 2008, A&A 480, 289Mart´ı-Vidal, I., Guirado, J. C., Marcaide, J.M., & Jim´enez-Monferrer, S. 2010,A&A, accepted (arXiv:1004.1624)P´erez-Torres, M. A., Marcaide, J. M., Guirado, J. C., Ros, E. 2004, A&A, 428,847Kettenis, M., van Langevelde, H. J., Reynolds, C., & Cotton, B. 2006, ASPC,351, 497K¨uhr, H., Witzel, A., Pauliny-Toth, I. I. K., et al. 1981, A&AS, 45, 367Readhead, A. C. S., & Wilkinson, P. N. 1978, ApJ, 223, 25Ros, E., Marcaide, J. M., Guirado, J. C., P´erez-Torres, M. A. 2001, A&A, 348,381Ros, E., in ASP Conf. Ser. 340, Future Directions in High ResolutionAstronomy: The 10th Anniversary of the VLBA, ASP ConferenceProceedings, eds. J. Romney & M. Reid (San Francisco: ASP), p. 482, 2005Shepherd, M. C., Pearson, T. J., & Taylor, G. B. 1995, BAAS, 26, 987Thomson, A. R., Moran, J. M., & Swenson, G. W. 1991,