On significance of VLBI/Gaia position offsets
aa r X i v : . [ a s t r o - ph . GA ] J a n MNRAS , 1–6 (2017) Preprint 16 July 2018 Compiled using MNRAS L A TEX style file v3.0
On significance of VLBI/Gaia position offsets
L. Petrov ⋆ , and Y. Y. Kovalev , Astrogeo Center, 7312 Sportsman Dr., Falls Church, VA 22043, USA Astro Space Center of Lebedev Physical Institute, Profsoyuznaya 86/32, 117997 Moscow, Russia Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany
Accepted 2017 January 2; Received 2016 December 15; in original form 2016 November 6
ABSTRACT
We have cross matched the
Gaia
Data Release 1 secondary dataset that containspositions of 1.14 billion objects against the most complete to date catalogue of VLBIpositions of 11.4 thousand sources, almost exclusively active galactic nuclei. We found6,064 matches, i.e. 53% radio objects. The median uncertainty of VLBI positions isa factor of 4 smaller than the median uncertainties of their optical counterparts. Ouranalysis shows that the distribution of normalized arc lengths significantly deviatesfrom Rayleigh shape with an excess of objects with small normalized arc lengthsand with a number of outliers. We found that 6% matches have radio optical offsetssignificant at 99% confidence level. Therefore, we conclude there exists a populationof objects with genuine offsets between centroids of radio and optical emission.
Key words: galaxies: active – radio continuum: galaxies – astrometry: referencesystems
The secondary dataset of the first release of astrometricdata from the European Space Agency mission
Gaia con-tains positions of 1.14 billion objects (Lindegren et al. 2016).Of them, the vast majority are stars, though over one hun-dred thousands of extragalactic objects, namely active galac-tic nuclei (AGN), were also included in the catalogue. Theposition uncertainty of the
Gaia
DR1 secondary dataset,2.3 mas median, is two orders of magnitude higher thanthe uncertainty of previous large all-sky catalogue in opticalwavelengths NOMAD (Zacharias et al. 2004) of 1.17 billionobjects. The only technique that can determine positions oftarget sources with comparable accuracy is very long base-line interferometry (VLBI). The first insight on compari-son of
Gaia and VLBI position catalogues can be found inMignard et al. (2016), who found that the overall agreementbetween the optical and radio positions is excellent, thougha small number of sources ( ∼ Gaia and VLBI positions beyond that reported in Mignard et al.(2016). Several factors motivated us. Firstly, the authors ofthe cited paper ran their comparison against the auxiliary
Gaia quasar solution for some 135,000 quasars. This solu-tion is not yet published in full, and only positions of 2% ofthe objects were reported. The question of how results of thecomparison against this auxiliary solution are representativeto the main solution of one billion objects remained opened. ⋆ E-mail: [email protected] (LP)
Secondly, Mignard et al. (2016) used the ICRF2 cat-alogue (Fey et al. 2015) for their comparison. This cat-alogue assembled in 2008–2009 represented the state ofthe art by 2008 and comprised of sources observed ingeodetic programs (Ma et al. 1998; Petrov et al. 2009) andsix Very Long Baseline Array (VLBA) Calibrator Sur-veys (Beasley et al. 2002; Fomalont et al. 2003; Petrov et al.2005, 2006; Kovalev et al. 2007; Petrov et al. 2008). Sincethat, there was an explosive growth of absolute astrometryVLBI programs: VLBA and European VLBI network Galac-tic plane surveys (Petrov et al. 2011a; Petrov 2012); VLBAImaging and Polarimetry Survey (VIPS) (Petrov & Taylor2011); Australian Long Baseline Calibrator Survey (LCS)(Petrov et al. 2011b); the VLBA Calibrator Search for theBeSSel Survey (Immer et al. 2011); the VLBA survey ofbright 2MASS galaxies (V2M) (Condon et al. 2016); theVLBA+EVN survey of optically bright extragalactic radiosources (OBRS–1,OBRS–2) (Petrov 2011, 2013); the sec-ond epoch VLBA calibrator survey observations (VCS-ii),(Gordon et al. 2016). Besides, there is a number of ongoingsurveys: the VLBI Ecliptic Plane Survey (VEPS) (Shu et al.2016), the wide-band VCS7,VCS8,VCS9 surveys (Petrov2016), and the VLBI survey of
Fermi detected γ -ray sources(Schinzel et al. 2015). By September 14, 2016, the date of Gaia
DR1 release, the total number of sources with positionsdetermined with absolute astrometry using VLBI reached11,444, a factor of 3.5 increase with respect to the ICRF2. c (cid:13) Petrov and Kovalev
Thirdly, the analysis of Mignard et al. (2016)showed that there exist sources with significant radio-optical offsets. Early comparisons of source positionsfrom VLBI and ground optical observations promptedZacharias & Zacharias (2014) and Orosz & Frey (2013) tosurmise there is a population of radio optical offset objectswith position differences in a range of 10–100 mas. Largeoffsets can occur either due to unaccounted errors in opticalpositions or a gross oversight in deriving VLBI coordinates,or due to an offset between the centroids of radio and opticemission. We call latter objects genuine radio optical offset(thereafter, GROO) sources. An increase in the accuracy ofthe optical positions by two orders magnitude allows us tore-examine the question of the GROO population existence.If such a population exists, it poses a challenge to explainsignificant radio-optical offsets.
Our study is based on the analysis of the catalogue called
Gaia
DR1 secondary dataset. We used for our work posi-tions, their uncertainties, correlations between right ascen-sion and declination for 1,142,679,769 objects. We did notanalyze
Gaia data and took the catalogue as it is. On theother hand, we reprocessed all publicly available VLBI datalisted in the previous section from the level of visibilitiesusing VLBI data analysis software
PIMA . Detailed de-scription of the analysis strategy and comparison with themethods adopted in the past and those used for processingthe data can be found in Petrov et al. (2011a). An importantconclusion of that comparison was that it does not introducesystematic differences at least above the 0.2 mas level withrespect to the old processing pipeline. The specific VLBIcatalogue used in our study is rfc 2016c . It is based on allgeodesy and absolute astrometry VLBI data since April 1980through July 2016, including all observations used for deriv-ing the ICRF2 catalogue and those that became publiclyavailable since 2008.At the first step we identified all Gaia sources thatlie within 5 ′′ of VLBI objects and found 6954 preliminarymatches. We should note the source density of Gaia
DR1 issubstantially heterogeneous (see Figure 9 in Lindegren et al.2016): the density in the Galactic plane exceeds by two orderof magnitude the density near the Galactic poles. To takeinto account variations of
Gaia spatial source density, wecounted
Gaia sources on the regular 0 . ◦ × . ◦ grid andnormalized the count to the number of sources per steradian.Then for a given match we computed the probability of falseassociation (PFA) as the product of local Gaia source den-sity and the area πd where d = L V G +3 max( σ g , maj , σ v , maj ), L V G is the arc length VLBI/
Gaia , σ g , maj and σ v , maj aresemi-major error ellipse axes for Gaia and VLBI respectively.This conservative estimate of the PFA takes into accountpossible errors that affect d and represents rather its up-per limit. The total number of matches with the PFA lessthan 2 · − is 6064. Of them, 9 are radio stars. We have See http://astrogeo.org/pima Available online at http://astrogeo.org/rfc
Figure 1.
The fraction of sources found in
Gaia catalogue asa function of the total flux density at 8.4 GHz integrated overparsec-scale image in logarithmic scale. excluded them from further analysis. According to the se-lected PFA cutoff criterion, the mathematical expectationof the number of spurious matches within our conservativesample is 0.03, i.e. less than one object. We certainly missedsome real matches, but for the purpose of this letter it ismore important to prevent false matches in the sample.In total, 53% VLBI sources are associated with a
Gaia counterpart. The fraction of VLBI/
Gaia matches monoton-ically decreases with a decrease of radio flux density: from0.8 for sources with flux density > Gaia
DR1 is not complete inany sense, we defer analysis why the share of VLBI/
Gaia matches drops with a decrease of flux density till deep op-tical surveys, such as Pan-STARRS that is expected to becomplete at least to 23 mag, will become available.
We computed the normalized arc lengths between VLBI po-sitions from rfc 2016c solution and the
Gaia auxiliary quasarsolution. We normalize the arc lengths exactly the same wayas Mignard et al. (2016): q = ( d α , d δ ) · (cid:18) σ g,α + σ v,α Cov( α, δ ) g + Cov( α, δ ) v Cov( α, δ ) g + Cov( α, δ ) v σ g,δ + σ v,δ (cid:19) − · ( d α , d δ ) ⊤ , where d α , d δ are VLBI/ Gaia offsets in right ascension mul-tiplied by factor cos δ and declination, σ g,α and σ v,α arereported uncertainty in right ascensions (including the fac-tor cos δ ) of Gaia and VLBI positions respectively, and σ g,α , σ v,α are reported uncertainties in declinations.The distribution of normalized arc lengths, square rootof q of that sub-sample denoted as QS is shown in theleft part of Figure 2. The distribution is very close to thatshown in Figure 8 of Mignard et al. (2016) based on anal-ysis of the auxiliary Gaia quasar solution and the ICRF2catalogue. The blue line in the left part of Figure 2 shows
MNRAS , 1–6 (2017) n significance of VLBI/Gaia position offsets L3 Figure 2.
Left: normalized arc length among the 2080 VLBI/
Gaia matches of QS sub-sample from the
Gaia quasar solution. Thecontinuous blue line shows the best fit Rayleigh distribution with parameter σ = 1 . Right: the distribution of normalized arc lengthsamong all 6055 matches from the
Gaia
DR1 solution. The thick blue line is the best fit to the Rayleigh distribution, which is certainlyinadequate.
Figure 3.
Cumulative distribution function of semi-major erroraxes P ( σ maj < a ): green (upper) curve for VLBI and blue (low)curve for Gaia . the Rayleigh distribution with σ = 1 .
15 that fit best to thehistogram that again is very close to the value 1.11 reportedby Mignard et al. (2016). This confirms our previous asser-tion that the differences in positions of sources common forthe ICRF2 and rfc 2016c catalogues are not essential for thepresent study.However, the distribution of normalized arc lengths be-tween positions from the
Gaia
DR1 secondary solution andVLBI is remarkably different (right part of Figure 2). It isdefinitely very far from the Rayleigh distribution.The normalized arc lengths depend on both arc lengthsand uncertainties in
Gaia and VLBI position estimates. Fig-ure 3 demonstrate that the
Gaia position errors dominateover VLBI positions in normalized arc lengths. In particular,the median σ v , maj of the matches is 0.50 mas, while the me-dian σ g , maj is 2.15 mas (compare with 2.3 mas for the total Gaia
DR1 sample), i.e. a factor of four greater. The shapeof the distribution remains non-Rayleighian even when wepreform analysis of
Gaia
DR1 and VLBI rfc 2016c solutionsamong 2088 matches of the QS sample. Therefore, we con-clude the shape of the distribution is due to a peculiarity ofthe
Gaia
DR1 secondary solution errors that did not affectstrongly the
Gaia quasar auxiliary solution. If position errors over each coordinate obey the Gaussian dis-tribution, then the normalized arc lengths obey the Rayleigh dis-tribution.
It is important to note that proper motions and paral-laxes were estimated in the
Gaia secondary solution. Sincethe time span of the dataset used in producing the
Gaia
DR1solution, 14 months, in general is not sufficient for providinggood estimates of parallax and proper motions, constraintswere applied. The reciprocal weights of constraints were ad-justed to make realistic errors of positions and parallaxesof stars (Michalik et al. 2015) that do have proper motionsand parallaxes. This disfavored treatment of AGNs that havenegligible parallaxes and proper motion. Estimating propermotions and parallaxes in addition to positions of AGNs in-flated their formal uncertainties. See Michalik et al. (2015)for further details.In order to check this hypothesis, we examined the pa-rameter called the number of good observations along scandirection (NgAL) provided in the
Gaia catalogue. NgALvaries from 2 to 1875 among the matches with the medianvalue of 80. This parameter is proportional to the numberof view crossings. We split the sample of matches into twoequal sub-samples with NgAL below and above the median.The distributions among these sub-samples are indeed verydifferent (Figure 4). The distribution in the sub-sample withNgAL ≥ median fits reasonably well to the Rayleigh distri-bution with σ = 1 .
38, but the sub-sample with NgAL < me-dian does not. This confirms our conjecture that estimationof parallaxes and proper motions is responsible for inflationof the reported uncertainties.We sought for a simple smooth function close to theRayleigh distribution that can approximate the empiricaldistribution of normalized arc lengths. Our further analysisshowed that the distribution has different shape for smalland large Gaia position uncertainties. We found that the dis-tribution of normalized arc lengths q of the sub-samples withGaia semi-major error axes shorter and longer 5 mas can berepresented as the Rayleigh distribution after applying thepower law transformation q λ with different power and scaleparameters. The Table 1 shows parameters of the transfor-mation and Figure 5 illustrates the distributions of two sub-samples after the power law transformation and their bestfit to the Rayleigh distributions.We split the matches into the bulk subset which dis-tribution obeys the the power-law Rayleigh functions and asubset of matches with the probability to belong to the bulk MNRAS , 1–6 (2017) Petrov and Kovalev
Figure 4.
Normalized arc length distributions.
Left: the sub-sample of 3001 matches with the number of good observations along scanbelow the median value 80.
Right: the same for the sub-sample of 3054 matches with the number of good observations along scan at orabove the median. The thick blue line shows the best fit to the Rayleigh distribution with parameter σ = 1 . Figure 5.
Left: the distribution of normalized arc lengths among VLBI/
Gaia matches with σ g , maj < λ = 0 . σ = 1 .
240 to the transformed distribution.
Right: similardistribution among VLBI/
Gaia matches with σ g , maj ≥ λ = 0 . σ = 0 .
622 to the transformed distribution.
Table 1.
Parameters of the empirical model of normalized arcVLBI/
Gaia for two ranges
Gaia semi-major error axes. The sec-ond column shows the best fit to the power transformation param-eter. The third column shows the scaling parameter of the bestfit to the Rayleigh distribution after the power transformation.The last column shows the root mean square (rms) of residualsafter fitting. Range λ σ rms < ≥ subset below some threshold, i.e. outliers. We consider theoffsets from the bulk subset are due to the random noise.Since the probability P ( x > x ) = e − x σ for theRayleigh distribution, we compute the probability for a givensource to have the normalized power-law scaled arc length q λ equal or greater than a given value due to the randomnoise as P ( q λ ) = e − q λ σ , where σ and λ are parameters fromTable 1. We consider an offset between VLBI and
Gaia positions sta-tistically significant if both the PFA is less than 0.0002 andthe probability that the position offset is caused by the ran-dom noise (RNP) is less than 0.01. There are 384 matches(6%) that satisfy these criteria. See their cumulative distri-bution in Figure 6. Table 2 shows these sources. Table 3with remaining 5671 matches with PFA < . ≥ .
01 is given in the electronic attachment only. It shouldbe noted the share of outliers among matches with the
Gaia
DR1 solution is very close to the share of outliers with the
Gaia auxiliary quasar solution (also 6%).A number of reasons may result in statistically signifi-cant offsets: a) errors in
Gaia positions; b) errors in VLBIpositions; c) genuine radio optic offset (GROO). We will con-sider both
Gaia and VLBI errors that led to significant off-sets as failures of quality control rather than random errors.We investigated which objects are more common among thesources with statistically significant offsets and found threegroups: 1) sources with σ v , maj > σ g , maj < . some sources in that group. Position un- MNRAS , 1–6 (2017) n significance of VLBI/Gaia position offsets L5 Table 2.
The first 4 rows of the table of 384 VLBI/
Gaia matches with statistically significant offsets: probability of false association(PFA) less than 0.0002 and the random noise probability (RNP) less than 0.01. The fifth column contains the normalized arc lengths,and two last columns contain positions of
Gaia minus VLBI over right ascensions, including cos δ factor, and declination. The full tableis available in the electronic attachment.VLBI ID Gaia ID PFA RNP q d α (mas) d δ (mas)RFC J0000 − . · − . · − − . · − . · − . · − . · − − . · − . · − Figure 6.
Cumulative distribution function of VLBI/
Gaia offsetsin logarithmic scale: green (lower) curve for the GROO populationand blue (upper) curve for remaining sources. certainties greater than 5 mas are usually obtained when asource was close to the detection limit and too few observa-tions were collected. The weaker the signal to noise ratio, themore chances that a wrong maximum in the delay resolutionfunction will be selected. Errors in group delay that corre-spond to the wrong maximum are significantly greater thantheir formal uncertainty computed assuming a correct max-imum was found. The fewer observations, the more chancesthat a failure in fringe fitting will remain undetected. Dur-ing past iterations of VLBI data analysis, a number of groupdelay estimates that correspond to an incorrect maximum inthe delay resolution function were identified and fixed, whichresulted in a change of source coordinate estimates. It isconceivable that not all such observations have been identi-fied and eliminated. But such oversights in quality controlaffects noticeably only positions of sources with too few ob-servations, usually less than 20. The share of sources with40 or less VLBI observations is 36% among the objects withstatistically significant offsets. That means that more than2/3 matches with significant offsets cannot be affected byoversights in VLBI quality control.A greater share of optically bright sources with small
Gaia position errors favours a hypothesis that at least apart of objects with significant radio optic offsets are GROO:smaller position uncertainties make position offsets statisti-cally more significant if they are real.Analysis of the group of sources with statistically sig-nificant offsets revealed there several gravitation lenses anda number of optically bright galaxies, but did not show anyoutstanding features that singles out these objects. The ev-idence collected so far supports the presence of the GROOpopulation since observed significant radio/optic offsets can- not be explained only by failures in quality control. In orderto explain the phenomenon of GROO, additional informa-tion should be examined. Kovalev et al. (2016) investigateda connection between directions of AGN jets and offset di-rections. More studies focused on explanation of the GROOpopulation are anticipated in the future.
We explored offsets between
Gaia
DR1 and VLBI positions.We used the secondary dataset for optical positions and re-cent VLBI solution rfc 2016c based on analysis of all avail-able observations suitable for absolute astrometry collectedsince 1980 through July 2016. We have found 6055 matchedAGNs using the criterion set on their arc lengths, such thatthe mathematical expectation of the number of spuriousmatches in this sample is less than one object. When weused the
Gaia auxiliary quasar solution, we were able toreproduce closely results of Mignard et al. (2016).Comparison of
Gaia
DR1 and VLBI solutions revealedthe following. • The median position offset is 2.2 mas — very close tothe median semi-major axis of the error ellipse of
Gaia po-sitions in the entire dataset. • The median semi-major axis of the error ellipse of
Gaia positions among the matches, 2.1 mas, is a factor of 4 greaterthan the median semi-major axis of the error ellipse of VLBIpositions. • The distribution of normalized arc lengths is signifi-cantly non-Rayleighian. We found evidence that the anal-ysis strategy implemented in
Gaia
DR1 disfavored sourceswith negligible parallaxes and proper motions, which in-flated their uncertainties. • There exits a population of sources with offsets statis-tically significant at the 99% confidence level (6% of thematches). We admit that some these objects may have sta-tistically significant offset due to failures in quality controlin both VLBI and
Gaia but certainly, not all: at maximum1/3. An increased share of optically bright objects with smallposition uncertainties in this population suggests that somethese objects have genuine radio optical offsets (GROO).The emission center in optic and in radio may not al-ways coincide for a number of reasons. Firstly, the centroid ofthe core may be shifted with frequency (e.g., Lobanov 1998;Kovalev et al. 2008). Secondly, unaccounted radio structuremay cause an offset of the reference point with respect tothe jet base, although such a shift is usually below 1 mas.
MNRAS , 1–6 (2017) Petrov and Kovalev
Thirdly, as Condon et al. (2016) shown, there exist interact-ing galaxies within an optically weaker component hosting abright radio source. In the era of ground optical astrometry,a study of such objects was limited to pairs at least 1 ′′ apart. Gaia astrometry has a potential to find such objects sepa-rated at milliarcsecond level. Finally, the presence of brightcomponents along the jet may shift the optic centroid. Atthe moment, little is known about properties of jets at mil-liarcsecond scales in optic wavelengths. Investigation of theGROO population opens a new window into study of AGNs.We should stress that this analysis is based on
Gaia
DR1 secondary dataset and we expect statistics of compar-ison VLBI positions and future
Gaia releases will be sig-nificantly different because of anticipated changes in dataanalysis strategy of
Gaia observations.
ACKNOWLEDGMENTS
It is our pleasure to thank Alexey Butkevich, Sergei Klioner,Alexandr Plavin, and Eduardo Ros for fruitful discussions.We are very grateful to Lennart Lindegren for a detailedreferee report and suggestions that helped us greatly to im-prove the manuscript and fix an error in numerical tables.This work is supported by the Russian Science Foundationgrant 16–12–10481.
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