Multi-source self-calibration: Unveiling the microJy population of compact radio sources

1.6 MB·

by  Jack F. Radcliffe

Astronomy&Astrophysicsmanuscriptno.Multi_source_self_calibration_final (cid:13)cESO2016
January26,2016
Multi-source self-calibration: Unveiling the microJy population of
compact radio sources
J.F.Radcliffe∗1,2,3,M.A.Garrett2,4,R.J.Beswick1,T.W.B.Muxlow1,P.D.Barthel3,A.T.Deller2,and
E.Middelberg5
1 JodrellBankCentreforAstrophysics/e-MERLIN,TheUniversityofManchester,M139PL,UnitedKingdom
2 ASTRON,theNetherlandsInstituteforRadioAstronomy,Postbus2,7990AA,Dwingeloo,TheNetherlands
3 KapteynAstronomicalInstitute,UniversityofGroningen,9747ADGroningen,TheNetherlands
4 LeidenObservatory,LeidenUniversity,POBox9513,2300RALeiden,TheNetherlands
5 AstronomischesInstitut,Ruhr-UniversitätBochum,Universitätsstr.150,44801Bochum,Germany
6
1 Received<date>/Accepted<date>
0
2
ABSTRACT

n
a Context. Very long baseline interferometry (VLBI) data are extremely sensitive to the phase stability of the VLBI array. This is
J especiallyimportantwhenwereachµJyr.m.s.sensitivities.Calibrationusingstandardphase-referencingtechniquesisoftenusedto
5 improvethephasestabilityofVLBIdata,buttheresultsareoftennotoptimal.Thisisevidentinblankfieldsthatdonothavein-beam
2 calibrators.
Aims.Wepresentacalibrationalgorithmtermedmulti-sourceself-calibration(MSSC)whichcanbeusedafterstandardphaserefer-
] encingonwide-fieldVLBIobservations.Thisistestedona1.6GHzwide-fieldVLBIdatasetoftheHubbleDeepFieldNorthand
M theHubbleFlankingFields.
Methods. MSSCusesmultipletargetsourcesthataredetectedinthefieldviastandardphasereferencingtechniquesandmodifies
I thevisibilitiessothateachdatasetapproximatestoapointsource.Thesearecombinedtoincreasethesignaltonoiseandpermit
.
h self-calibration.Inprinciple,thisshouldallowresidualphasechangescausedbythetroposphereandionospheretobecorrected.By
p meansoffaceting,thetechniquecanalsobeusedfordirection-dependentcalibration.
- Results.Phasecorrections,derivedusingMSSC,wereappliedtoawide-fieldVLBIdatasetoftheHDF-N,whichcomprisesof699
o
phasecentres.MSSCwasfoundtoperformconsiderablybetterthanstandardphasereferencingandsinglesourceself-calibration.All
r
t detectedsourcesexhibiteddramaticimprovementsindynamicrange.UsingMSSC,onesourcereachedthedetectionthreshold,taking
s thetotaldetectedsourcestotwenty.Thismeans60%ofthesesourcescannowbeimagedwithuniformweighting,comparedtojust
a
45%withstandardphasereferencing.Inprinciple,thistechniquecanbeappliedtoanyfutureVLBIobservations.TheParseltongue
[
code,whichimplementsMSSC,hasbeenreleasedandmadepubliclyavailabletotheastronomicalcommunity(https://github.
3 com/jradcliffe5/multi_self_cal).
v Keywords. <Techniques:interferometric-Radiocontinuum:galaxies>
2
5
4
41. Introduction tocovertheentireprimarybeam(e.g.Rampadarathetal.2015).
0 Asaresult,thepracticalnumberofsourcesthatcanbedetected
.WiththeexpandedperformanceandcapabilitiesofVLBIarrays, andimagedinoneobservationhasdramaticallyincreased.These
1
such as the European VLBI Network (EVN), r.m.s sensitivities
0 improvementshaveenabledtheentireprimarybeamofatypical
oftheorderafewmicro-Janskyareattainableinjustafewhours.
6 VLBItelescopetobecompletelymappedouttomilliarcsecond
Thisallowscompactsourceswithbrightnesstemperaturesofjust
1 resolutionsandmicroJysensitivities.
104-105 K to be detected. Improvements in correlator capabili-
:
vtieshaveenabledthepossibilityofwide-fieldVLBIoperations. VLBIobservationsareparticularlysensitivetothetemporal
XiOriginally,datasetswerecorrelatedatasinglephasecentrewith andspatialvariationsofthetroposphereandionosphere.These
cause phase variations over the course of an observation. To
anultrahightemporalandfrequencyresolutiontoallowtheen-
r account for these, calibration on bright, nearby, and compact
atire primary beam to be mapped (e.g. Garrett et al. 2001; Chi
sourcesisessential.Thisiscalled‘phasereferencing’.Itinvolves
etal.2013).However,thesekindsofmethodsresultinlargedata
employing one or more compact sources nearby (or within the
volumesandadegradationinimagequalitytowardstheedgeof
primary beam of) the target field to correct for gain and phase
theprimarybeam.
fluctuations.However,manytargetfieldsoftendonothavecom-
In recent years, the introduction of software-based correla-
pactsources,whichcanbeuseddirectlyforcalibration.
torshasestablishedtheconceptof‘multiplesimultaneousphase
centre observing’ (Deller et al. 2011; Keimpema et al. 2015). Ifthisisthecase,achainoftwoormoresourcescanbeused,
This method uses multiple phase centres with a coarser tempo- whichincreaseinbrightnesswithrespecttothedistancefromthe
ral and frequency resolution to produce a narrow field data set targetfield.This‘boot-strapping’approachallowsphasecalibra-
perphasecentre.Thismethodparallelisesthecorrelationprocess tioncorrectionstobederivedfromthebrightestcalibratorwhich
and,assuch,thecorrelationspeedisnowlimitedbythenumber is the furthest away and passed onto the next calibrator which
of nodes in the correlator. These phase centres can be arranged isclosertothetarget.Self-calibrationisusedateachsteptore-
Articlenumber,page1of7
A&Aproofs:manuscriptno.Multi_source_self_calibration_final
1.2 1.2
62°12'58.04" 62°12'58.04"
1.0 1.0
00) 58.02" 0.8 y) 00) 58.02" 0.8 y)
Declination (J20 5587..0908"" 000...246 Flux Density (J Declination (J20 5587..0908"" 000...246 Flux Density (J
0.0 0.0
57.96" 57.96"
0.2 0.2
57.94" 57.94"
12h36m50.085s 50.080s 50.075s 12h36m50.085s 50.080s 50.075s
Right Ascension (J2000) Right Ascension (J2000)
Fig. 1: Left panel: J123646+621405 when divided by the CLEAN model of the source. The low signal to noise results in an
imperfect CLEAN model. This creates deviations from a normalised point source and, as a result, the peak brightness is ∼ 1.4
Jy/beam.Becausethemodelcannotfullycharacterisethesourcestructure,someofthefluxdensitywillbescatteredintotheside
lobes.ThisresultsinaslightlyreducedS/Nof7.7comparedto7.9beforedividingtheCLEANmodel.Rightpanel:Deconvolved
imageof9different,combinedtargetsources,includingthesourceintheleftpanel.EachsourcehasbeendividedbyitsCLEAN
modelandcombinedtocreateapointsourcewithahighersignaltonoise.Thedeviationsfromaperfect,normalisedpointsource
havereducedandthepeakbrightnessis∼ 1.1Jy/beam.Thisisthesourceusedtoself-calibratetheHDF-NdatasetinMSSC.The
sourcemorphologyismorerepresentativeofapointsourceandtheS/Nhasvastlyincreasedto93.1whichallowsself-calibration
tobeperformed.
finethecorrections.Thisisrepeateduntilthecorrectionsderived their CLEAN model divided into the visibilities, which results
forthenearestphasecalibratorcanthenbeappliedtothetarget inmultiplepointsources.ThesearestackedintheUVplaneto
field.Wenotethatamplitudecalibrationisonlyperformedonthe increasetheS/N,whichallowsself-calibrationtobecomefeasi-
brighter calibrators with a sufficient signal to noise ratio (S/N). ble. The corrections derived can then be applied to the original
The phase corrections applied to the target field reduce in ac- phase-referenced data. It is worth noting that this process only
curacywithrespecttotheangularseparationbetweenthetarget appliestowide-fieldVLBIdatasetsthatdetectandimagemul-
field and the final phase calibrator source because of the atmo- tiplesourceswithinoneepoch.Recentimprovementsintheca-
spheric inhomogeneities. If the angular separation is too large, pabilitiesofVLBIcorrelatorsareensuringthatwide-fieldVLBI
thephasecorrectionsderivedarenotfullyrepresentativeofthe isarealityand,asaresult,therewillbeanincreasednumberof
atmosphereinfrontofthetargetfield.Asaresult,thedynamic experimentswhichutiliseMSSC.
rangeofmanyVLBItargetscanoftenbelimitedbyphaseerrors. MSSChasbeenreleasedandmadepubliclyavailabletothe
Accuratephasecalibrationbecomesevermoreimportantasthe astronomicalcommunityasaParseltonguescript(Kettenisetal.
r.m.s.sensitivitiescontinuetowardsthefaintµJyregime. 2006).Inthispaper,wedemonstratethepowerofthiscalibration
techniqueupononeofthelargestandmostsensitivewide-field
Inprinciple,theseerrorscanbecorrectedbyperformingself-
VLBIsurveyseverconducted,whichtargetstheHDF-N.
calibrationonthetargetfield(Trottetal.2011).Ordinarily,the
responseofasingle,faintsourceisnotsufficienttoemployself-
calibration. However, Rioja & Porcas (2000) and, in particular,
2. HubbleDeepField-NorthandHubbleFlanking
Garrettetal.(2004)firstdemonstratedthepotentialofemploy-
ingmultiplesourcesdetectedacrosstheprimarybeamasinputs Fieldwide-fieldVLBIobservations
fortheself-calibrationoflargewide-fieldVLBIdatasets.Apre-
We have completed the first of three 24-hour epochs of a 1.6
vious VLBI survey of the Lockman Hole by Middelberg et al.
GHzwide-fieldVLBIsurveyusingtheEVNarray.Theobserva-
(2013) developed the fundamentals of the technique presented
tionstargeta15arcminutediameterareacentredontheHDF-N.
here and has recently been employed in the analysis of VLBI
Thissurveyimplementsthe‘multiplesimultaneousphasecentre
observationsoftheHubbleDeepField-North(HDF-N).
observing’modeoftheSFXCcorrelator(Keimpemaetal.2015)
Known as Multi-Source Self-Calibration (MSSC), this is a toimagea7.5arcminuteradiusareabysimultaneouslycorrelat-
calibrationtechniquethatprovidesanadditionalsteptostandard ing on 582 phase centres. This enables us to achieve µJy r.m.s.
phase referencing. MSSC is designed to be used for multiple noise levels with milliarcsecond resolution across the whole of
phase centre correlated VLBI observations but, in principle, it the primary beam. An additional 127 phase centres were used
can be used on any observation that targets multiple sources. to target bright sources up to 12 arcminutes from the pointing
MSSC uses multiple faint sources that are detected within the centre.Thetotalnumberofphasecentrescorrelatedis699.The
primary beam and combines them. The combined response of phasecentresinclude607sourceswhichweredetectedinthee-
manysourcesacrossthefieldofviewisgenerallymorethansuf- MERLINeMERGEsurvey(Wrigleyetal.inprep.)andtheVLA
ficienttoallowphasecorrectionstobederived.Eachsourcehas (Morrisonetal.2010).
Articlenumber,page2of7
J.F.Radcliffeetal.:Multi-sourceself-calibration
Detection (J123642+621331) Non-detection
105 Dσ=at9a.58,µ=-0.032 1σ 3σ 5σ 6σ 7σ 105 Dσ=at9a.76,µ=-0.023 1σ 3σ 5σ 6σ 7σ
104
104
Pixels 103 Pixels 103
er of 102 er of 102
b b
m m
Nu 101 Nu 101
100 100
10-1 10-1
80 60 40 20 0 20 40 60 80 80 60 40 20 0 20 40 60 80
el)/hist01..80 Residuals el)/hist01..80 Residuals
d0.6 d0.6
mo0.4 mo0.4
hist - 00..0280 60 40 20 0 20 40 60 80 hist - 00..0280 60 40 20 0 20 40 60 80
( Peak Flux Density µJy/beam ( Peak Flux Density µJy/beam
Fig.2:Upperpanelsshowhistogramsofthepeakbrightnessdistributionsforfieldswithdetectedsourcesandnodetectedsources.
Each histogram is derived from 1024x1024 pixel, uniformly weighted image and has a Gaussian distribution fitted to the noise
profile. The vertical dashed lines indicate the values of ±1σ, ±3σ, ±5σ and ±7σ and the red dot-dashed line represents the 6σ
detectionthreshold.Thebottompanelsshowtheresidualswhicharenormalisedtothehistogram.Leftpanel:Histogramofthefield
including the source J123642+621331. The fitted Gaussian approximates an r.m.s. noise level of 9.58 µJy/beam. There are large
deviationsfromtheGaussianmodelatthenegativeextremaofthefluxdistribution,whichsuggeststhatgainandphaseerrorsare
thecause.Thedeviationsatthepositiveextremaisduetosourcestructure.Rightpanel:Histogramofablankfieldwithphasecentre
coordinatesR.A.12:36:05.0andDec.+62:12:30.0.AGaussianwitha1σr.m.s.noiselevelof9.76µJy/beamisfitted.Theresiduals
showsmallerdeviationsfromaGaussianattheextremaofthefluxdistribution.Thismaybeduetosomeresidualradiofrequency
interference.
Each phase centre produces a narrow-field (averaged) data calibratorwasusedtoobtainphaseandgaincorrections.Theso-
setthatcanbecalibratedinanidenticalfashionusingtheMSSC lutionsobtainedwerethenappliedtothefaintersource.Further
solutions.Comparedtoimagingtheentireprimarybeam,thisis roundsofself-calibrationwereconductedtorefinethephasecor-
bothconsiderablylesscomputer-intensiveandmuchmoreeasily rectionsandthenthecalibrationwasappliedtothetargetfield.
parallelisable.SincebruteforcesurveyingatVLBIresolutionis WenotethattherewasinsufficientS/Ntoperformgaincalibra-
computationally bound, this provides a way to greatly increase tiononthissource.
the effective (computationally feasible) survey speed of VLBI The fields were searched for emission using a 6σ detection
observations. threshold.Figure2showsthepixelbrightnessdistributionfora
After standard phase referencing there were 19 detected blankfieldandafieldwithasourcedetected.Thefigureshows
sources,18ofwhicharelocatedinthecentral7.5arcminutera- thatthenoiseinbothfieldsexhibitnon-Gaussianitytowardsthe
diusarea.Theinnerfewarcminutesreachr.m.s.sensitivitiesof extremaofthefluxdistribution.Thissuggeststhattheremaybe
5µJy/beamandthisisexpectedtoreach1σthermalnoiselevels some residual RFI in these data. However, the non-Gaussianity
of ∼1.5-4 µJy/beam (depending on telescope availability) with appearstobecorrelatedwiththefluxdensityofthesource.This
theadditionoftwofurtherepochs.Thescientificresultsofthis suggeststhatresidualgainandphaseerrorsarepresentinthese
surveywillbepresentedinafuturepublication(Radcliffeetal. data, which scatters some of the flux density from the bright
inprep.).Thisrepresentsasubstantialimprovementwhencom- sourcedetectionintothesidelobes.Theexcessofpixelsatthe
pared with the previous VLBI observations of the field which extremaofthefluxdistributionresultsinthedetectionthreshold
hadacentralr.m.s.sensitivityof7.3µJy/beam,presentedbyChi beingplacedat6σ.
etal.(2013).
Nine sources were used in MSSC. These were sources
that were detected when imaged with both uniform and natu-
ral weighting. If a source was detected in both images, it is
3. Multi-sourceself-calibration
highlysuggestivethatthesourcecanbedetectedonallbaselines.
The HDF-N field was an ideal candidate for MSSC. This is a Sourcesoutsidetheprimarybeamofthelargesttelescopeswere
fieldwithfewbrightsourcesinallwavebands.Intheradio,the alsoavoidedduetoa-projectioneffects.Thea-projectionarises
brightestsourceshaveintegratedfluxdensitiesoftheorderofa as a result of an intrinsic optical path difference of the radio
fewmJy.BeforeMSSCcanbeutilised,phasereferencinghasto wavesacrosstheprimarybeamofatelescope,alongwithtime-
beconducted.AllcalibrationstepswereconductedusingtheAs- varyinggainsthatarecausedbyantennapointingerrorsandrota-
tronomicalImageProcessingSystem(AIPS)anditsPythonin- tionofasymmetricantennapowerpatterns(seeRauetal.2009).
terface,Parseltongue(Kettenisetal.2006).IntheHDF-Ndata, TheMSSCprocedurelargelyfollowsthetechniquesoutlinedin
this is comprised of two sources, J1241+602, a bright 0.4 Jy Middelbergetal.(2013)andisdescribedbelow.
sourcelocated2◦awayfromthepointingcentre,andJ1234+619, Eachdatasetwasre-imagedwithuniformweightingandwas
afaint20mJysourcelocated23.5arcminutesaway.Thebrighter de-convolvedwiththesynthesisedbeamusingtheCLEANalgo-
Articlenumber,page3of7
A&Aproofs:manuscriptno.Multi_source_self_calibration_final
900 900+
800 800
62°18'32.60" 62°18'32.60"
700 700
600 600
000) 32.58" 500 Jy)µ 000) 32.58" 500 Jy)µ
Declination (J2 32.56" 340000 Flux Density ( Declination (J2 32.56" 340000 Flux Density (
200 200
32.54" 32.54"
100 100
0 0
32.52" 32.52"
100 100
12h36m59.340s 59.335s 59.330s 12h36m59.340s 59.335s 59.330s
Right Ascension (J2000) Right Ascension (J2000)
Fig. 3: Compact radio source J123659+621833, which illustrates the effect MSSC has on the structure, fluxes, and noise levels
achieved.Thecolourscaleisfixedtothescaleofthephase-referencedimagestohighlightchangesinpeakbrightnessandthenoise
profiles. Contours start at the noise level and are evenly spaced to the peak brightness of each image. Left panel: Source when
calibratedwithonlystandardphasereferencing.Thishasapeakbrightnessof824µJy/beam,integratedfluxdensityof1.35mJy
andanr.m.s.noiselevelof14.7µJy/beam.ThisgivesamaximumS/Nof56.1.Notethattheimagesuffersfromsignificantsidelobe
negativesnexttothesource.Rightpanel:ThesourcewithMSSCapplied.Thepeakbrightnessisnow1.28mJy/beam,integrated
fluxdensityof1.73mJyandanr.m.s.noiselevelof11.1µJy/beam.ThisresultsinagreatlyimprovedS/Nof115.8.Thesidelobe
structurehasreducedinamplitudeandthesourceismorecompact.
rithm (Clark 1980). Each set of visibilities were divided by the datasetwasimaged withthephasecorrectionsappliedand the
CLEAN model using the AIPS task UVSUB. This produced a subsequent image was then used as a model for the next round
point source with normalised amplitude, located in the centre ofself-calibration.Thiswasiterateduntilthephasecorrections
of the target field (see Figure 1, left panel). We note that there converged on zero. To get enough S/N, there is the option of
was a small reduction in S/N when this step was undertaken. combiningspectralwindows,polarisations,orincreasingtheso-
The CLEAN model cannot fully characterise the source struc- lution interval. All of these can be changed depending on the
tureand,asaresult,someofthefluxdensityisscatteredintothe flux-densitydistributioninthetargetfieldandthesensitivityof
sidelobes.ThisisshownintheleftpanelofFigure1.Anyoffsets theobservations.PhasecorrectionsderivedwerewrittentoAIPS
in the location of the peak brightness compared to the centroid SN tables, which were attached to a dummy UV file using the
ofthephasecentrewereremovedwhentheCLEANmodelwas taskFITTP.Thesesolution(SN)tableswerethencopiedandap-
dividedthrough.UVSUBadjustedtheweights(w)ofeachdata pliedinAIPStoalloftheotherphase-referenceddatasets.This
i
set (i) by the inverse square of the amplitude adjustment such processcanberepeatedifnecessary.
that
w =(cid:32) 1Jy (cid:33)2. 4. Results
i A Jy
i
In our example application, phase corrections derived us-
For example, a source with S/N of 5 will only contribute ing MSSC were applied to the HDF-N data set. Three self-
1/100 of the combined signal relative to a source with S/N of calibration iterations were conducted using a two minute solu-
50.Thiseffectivelymaximisesthesignaltonoisewhenthedata tioninterval.Allspectralwindowsandpolarisationswerecom-
setsarecombined. bined.Theresultingvisibilitieswereimagedasbeforewithboth
Thesourcecoordinatesineachdatasetwerechangedtothe naturalanduniformweighting.ThesourcesdetectedwithMSSC
centreoftheprimarybeamandthedatasetswereconcatenated were compared to a standard phase-referenced data set (as de-
into one set using the AIPS task DBAPP. The choice of source scribed in Section 2) and a data set with an additional single
coordinatesisarbitrary.Allofthesourcepositionswerechanged source self-calibration applied. The source chosen for this was
tothesamecoordinatessotheycouldbestackedeffectively.This J123658+621833, which has an integrated flux density of 1.4
resultedinadatasetwithvisibilitiesthatrepresentanormalised mJy. The single source self-calibration comprised of three iter-
pointsource.Eachbaseline,time,andfrequencystampnowcon- ations with asolution interval of 6 minutes. A solution interval
tains multiple measurements of a normalised point source. The was selected which was long enough to provide sufficient S/N
combinationofalldetectedsourcesincreasestheS/Nandmakes for accurate phase-solution determinations and acceptably low
self-calibrationpossible(seeFigure1,rightpanel). solutionfailurerates,whilstbeingshortenoughtocorrectforthe
The visibilities were then self-calibrated in phase using the residual phase errors still left in the data set after initial phase-
task CALIB. A normalised point source was used as a model referencingtoanearbycalibrator.
for just the first iteration of self-calibration. These corrections For example, using MSSC the combined S/N of the point
were then applied to the point source data set. The combined source was 93, which is lower than the theoretical S/N of 113.
Articlenumber,page4of7
J.F.Radcliffeetal.:Multi-sourceself-calibration
Table1:Comparisonbetweenstandardphasereferencing,singlesourceself-calibrationandMSSCcalibrationtechniques.
Phasereferencing Singlesourceself-calibration MSSC
SourceID P(µJy/bm) I(µJy) N(µJy/bm) S/N P(µJy/bm) I(µJy) N(µJy/bm) S/N P(µJy/bm) I(µJy) N(µJy/bm) S/N
123608+621036 41.8 50.8 6.3 6.6 45 65.6 6.3 7.1 63.5 78.8 5.6 11.4
123618+621541 61 75.2 9.7 6.3 63.7 75 9.9 6.4 75.3 90.0 9.7 7.8
123620+620844 60 60 6.9 8.7 37.6 49 6.1 6.2 83.4(76.5) 83.4(82.1) 9.7(6.8) 8.6(11.3)
123622+620654 42.8 68.7 6.4 6.7 N-D N-D 5.91 - 40.8 56.5 5.9 6.9
123624+621643 97.1 131.3 9.7 10.0 126.9 130.6 9.9 12.8 131.3 156.8 9.8 13.4
123641+621833 37.2 60.8 5.7 6.6 48.3 59.8 5.5 8.8 53.6 58.4 5.8 9.3
123642+621331 88.2 101.6 5.9 14.8 85.9(96.3) 106.2(115.5) 9.7(6.8) 8.9(14.2) 72.9(113.2) 153.1(141.2) 9.6(6.0) 7.6(18.9)
123644+621133 195 197.1 9.7 20.1 155.1 168.7 9.9 15.7 262.1 256.0 9.7 27.0
123646+621405 76 115.2 9.6 7.9 68.7 100.5 9.6 7.2 114.1 135.0 9.5 12.0
123653+621444 45.9 53.3 5.3 8.6 49.3 56.2 5.6 8.8 58.3 62.9 5.4 10.8
123659+621833 824 1348 14.7 56.1 1284 1743.9 18.1 70.9 1284.9 1732.7 11.1 115.8
123700+620910 63 79.1 5.8 10.8 48.8 63.4 5.7 8.5 63.4(77.4) 89.2(91.1) 9.5(5.7) 6.7(13.6)
123709+620838 34.5* 41.7* 5.9* 5.8* 28.4* 34.1* 5.4* 5.2* 44.9 55.5 5.5 8.2
123714+621826 170.5 181.2 10.0 17.1 185.1 216.2 10.4 17.8 235.1 252.5 10.1 23.3
123715+620823 840.8 946.8 13.5 62.3 524.4 701 14.6 35.9 1242.6 1300.6 15.6 79.7
123716+621512 50.1 54.3 5.6 8.9 49.6 59.5 6.1 8.2 59.4 75.1 5.9 10.1
123717+621733 68.3 76.2 9.7 7.0 71.8 102.8 9.7 7.4 86.3 99.3 9.6 9.0
123721+621130 110.7 153 9.9 11.1 112 143.9 9.8 11.5 182.0 195.1 9.9 18.5
123726+621128 49 63.7 5.6 8.8 N-D N-D 6.43 - 57.3 66.5 5.6 10.2
123701+622109 55.6 80.4 5.6 10.0 57.7 73.1 5.7 10.1 64.0 77.8 5.6 11.4
Phasereferencing SSSC MSSC
Detectedwithnaturalweighting 19 17 20
Detectedwithuniformweighting 9 10 12
Failedsolutions(Iteration3) - 7% 2%
Notes.Toppanel:Comparisonofthepeakfluxdensityperbeamorbrightness(P)inµJy/beam(shortenedtoµJy/bm),integratedfluxdensity(I),
inµJy,r.m.s.noise(R),inµJy/beam,andtheS/Nofthepeakbrightnesstother.m.s.noiseforthreedifferentcalibrationmethods.Thepeakflux
densitiesandintegratedfluxdensitiesweredeterminedusingtheAIPStaskJMFITandthenoisewasmeasuredusingtheAIPStaskIMSTAT.The
phasereferencingusesonlythetwodesignatedcalibratorsJ1241+602andJ1234+619.Singlesourceself-calibrationhasanadditionalcalibration
step.Onlythebrightestdetectedsource(J123659+621833)isusedforself-calibrationwithasolutionintervalof6minutesandMSSCuses9
sourcesinMSSC.Allentriescorrespondtovalueswithcalibratedweights,apartfromentriesinboldwhicharedetectionswithnaturalweighting.
The*representssourceswhichdidnotreachthedetectionthresholdof6σbuttheirfluxdensitiescouldbemeasured,whereasN-D(non-detection)
indicatessourcesthatdidnotreachthedetectionthresholdandtheirfluxdensitiescouldnotbemeasured.Bottompanel:Asummaryofthetotal
numbersourcesthatreachedthe6σdetectionthresholdwitheachcalibrationtechniquealongwiththepercentageoffailedsolutionsduringthe
lastiterationofself-calibration.
This is most likely caused by the inaccuracies in the CLEAN In the single source self-calibrated data, ten sources can be
model that was used to characterise the source structure. As a imagedwithuniformweighting.WhencomparedtoMSSC,we
result,somefluxdensityisscatteredintothesidelobeswhenthe seeanaverageincreaseinS/Nof36%inthenaturallyweighted
visibilitiesaredividedbytheCLEANmodel. imageand69%intheuniformlyweightedimages.Threesources
donotreachthedetectionthresholdineithernaturaloruniform
We adopt a solution acceptance threshold of 5σ i to reduce weighting schemes. We note that single source self-calibration
scatter in the solutions. The S/N of the combined point source performsworsethanstandardphasereferencing.Evenwithaso-
wasscaledtothesolutionintervalof2mins,whichresultedina lutionintervalofsixminutes,7%ofallphasesolutionsfailand,
S/Nof∼3.2.Thismeansthatthemajorityofsolutionsdonotget therefore, there are not enough good solutions to improve the
rejectedbyouracceptancethresholdand,asaresult,thenumber image.WhereaswithMSSC,wecanreducethesolutioninterval
offailedsolutionsisonly2%.Forexample,witha1-minuteso- totwominuteswithonlya2%failurerateandgaincorrections
lutionintervalweacquireascaledS/Nof2.3andthereismuch that dramatically improve the S/N. Table 1 summarises the re-
higherscatter,whichresultsin25%failedsolutions.Withhigher sultspresented.
solutionintervals,wefoundthatsolutionfailuresratesremained
constantbutthepeakbrightnessofthetargetsourcesdecreased,
hence a 2-minute interval was found to be optimal. This argu- 5. Futureapplications
mentwasalsousedtosetthesolutionintervalforsinglesource
self-calibration. With wide-field VLBI becoming more accessible, MSSC can
be used as a direction-dependent calibration tool. Direction-
When MSSC was compared to standard phase referencing, dependentcalibrationtechniquesaredesignedtoaccountforat-
it was found that all sources exhibited an increase in S/N. On mosphericinhomogeneitiesandprimarybeamvariationsacross
average, the S/N increase was found to be 27% in naturally thefieldofview.Thesehavebeenusedextensivelyatlowerfre-
weighted images and 63% in the uniformly weighted images. quencies where data are particularly susceptible to errors from
Twelve sources can be imaged with uniform weighting com- ionosphericvariations.LOFAR,forexample,usesthealgorithm
pared to nine with standard phase referencing. MSSC enabled SAGECal which has been used to great effect to reduce errors
one more source to reach the detection threshold set at 6σ. from both the ionospheric variations and beam variations (see
MSSCcorrectionsalsoprovideanimprovementinthedynamic Yatawatta et al. 2013). MSSC can also be used as a direction-
ranges and the noise profiles of the images. Figure 3 illustrates dependent algorithm by means of faceting. We note that this is
thisbycomparingthephase-referencedsetofJ123658+621833 differenttomethodslikeSAGECalbuttheintentionisthesame.
tothecorrespondingMSSC-calibrateddata. InMSSC,phasesolutionsareessentiallytheaverageofthecor-
Articlenumber,page5of7
A&Aproofs:manuscriptno.Multi_source_self_calibration_final
Fig. 4: MSSC algorithm illustrating the various AIPS tasks used to perform the calibration. The final result is the AIPS solution
(SN)tablesthatcontainthephasecorrections,whichcanthenbeappliedtothedata.
rections derived for each target source weighted by the square MSSCshouldperformadequately.Estimatingtheminimuman-
of the brightness of each source. If the target field is split into gular area needed to use MSSC is extremely inaccurate owing
facets, each of which is an isoplanatic patch, we can separate tothespatialvariabilityofcompactsourcesandthepoorlycon-
theskyintosubsetsofsourcescorrespondingtodifferentareas. strainedsub-mJyVLBIflux-densitydistribution.However,ifthe
MSSCcanthenberunoneachsubsetofsource,whichwillpro- sourcesinthetargetfieldfarexceedthisrequiredS/N,thenthe
videdifferentcorrectionsforeachareaofthesky. sourcescanbesplitupintofacetscontainingsubsetsofsources
forwhichdirection-dependentcorrectionscanbederivedusing
Using the HDF-N observations, we can approximate the MSSC.UsingtheseHDF-Nobservationsasanexampleofafield
minimumS/NrequiredforMSSCinatypicalEVNobservation. with relatively few bright radio sources, we suggest that obser-
TheminimumS/Ncanbeusedtoderivetheoptimalsolutionin- vations that cover areas greater than 200 arcminute2 would al-
tervalasdescribedinSection4.Theobservationshaveatheoret- low direction-dependent solutions to be obtained using MSSC
icalcombinedS/Nof113.1overthedurationoftheobservation, bymeansoffaceting.
whichcanbemoreusefullyexpressedastheS/Nratiorequired Inprinciple,MSSCcanbeusedforanyfutureVLBIobser-
forasuitablesolutioninterval.WecanscalethecombinedS/N vation.ThegrowingnumberofcataloguesofmJysources,most
by the square root of the ratio between the solution interval (2 notably from the mJIVE survey (Deller & Middelberg 2014),
mins)tothetimeonthetargetfield(18hours)toacquireathe- meanthatVLBIdetectedsourcesareclosetoalmosteverytarget
oretical minimum array S/N of 3.2. This is, of course, depen- field.Bytargetingthesesources,inmultiplesimultaneousphase
dent on the number of telescopes and the sources in your field. centre observing mode, MSSC can be used on their combined
HoweveritcanbeusedasaguidefordecidingifMSSCcanbe responsetoimprovecalibrationcorrections.MSSCcanproveto
used for the EVN. The combined S/N for any typical EVN ob- beanextremelypowerfultooltoimprovethedynamicrangeof
servation can be determined by adding, in quadrature, the peak anyfutureVLBIdataset.
brightness of all target sources within a target field or facet di-
videdbyther.m.s.noise.Thiscanbescaledbythesquareroot
6. Conclusions
oftheratioofthesolutionintervaltothetotalobservingtimeto
acquiretheS/Npersolutioninterval.Ifthisvalueislargerthan We present a new calibration technique termed ‘multi-source
the minimum value of 3.2, derived from the HDF-N data, then self-calibration’ which can be used on wide-field VLBI data
Articlenumber,page6of7
J.F.Radcliffeetal.:Multi-sourceself-calibration
sets to increase the phase stability of the target sources. This
technique combines in-beam sources to permit phase self-
calibrationofthetargetfield.Itcanbeusedtoimprovethetradi-
tionalphase-referencingtechniquesusedinVLBIobservations.
The multi-field self-calibration algorithm is outlined in Fig. 4.
A Parseltongue script is available at https://github.com/
jradcliffe5/multi_self_cal, which could be used on any
wide-fieldorfutureVLBIdatasetafterstandardcalibrationhas
beenapplied.Thescriptincludesoptionstochangevariouspa-
rameters such as the number of self-calibration iterations and
willberevisedconstantlyinthefuture.
The MSSC technique is designed for observations of spe-
cificfaintsourcessuchasGRBs,supernovaeremnants,andlow-
luminosity AGN. In this paper we demonstrated the power of
multi-fieldself-calibrationona1.6GHzwide-fieldVLBIobser-
vation of the HDF-N. With just standard phase referencing, 20
sourcesweredetectedbutmanyoftheimageswerelimitedindy-
namicrangeoronlydetectedusingnaturalweighting.Whenap-
plied,thetechniquesignificantlyimprovedtheS/Nofallsources
imaged(seeSection3)andallowedthreemoresourcestobede-
tectedwhenimagedwithuniformweighting.
With rapidly improving sensitivities and correlator capabil-
ities of VLBI arrays, observations of multiple primary beams
is now possible. MSSC permits VLBI observations to be con-
ducted in any direction on the sky and can allow directional-
dependent calibration to be performed. New instruments, such
asthee-EVNandpossiblyVLBIwiththeupcomingSKA,will
make µJy source detection on VLBI baselines routine and, as
such,increasethewealthofpotentialcalibratorsthatcanbeused
inmulti-sourceself-calibration.MSSCcouldprovetobeavery
powerfultoolinunveilingthemicroJyregimeofcompactradio
sources.
Acknowledgements. The research leading to these results has received fund-
ingfromtheEuropeanCommissionSeventhFrameworkProgramme(FP/2007-
2013)undergrantagreementNo283393(RadioNet3).
The European VLBI Network is a joint facility of European, Chinese, South
African,andotherradioastronomyinstitutesfundedbytheirnationalresearch
councils.We’dliketothanktheanonymousrefereefortheirhelpfulcomments.
References
Chi,S.,Barthel,P.,&Garrett,M.2013,Astronomy&Astrophysics,550,A68
Clark,B.1980,AstronomyandAstrophysics,89,377
Deller,A.,Brisken,W.,Phillips,C.,etal.2011,PublicationsoftheAstronomical
SocietyofthePacific,123,275
Deller,A.&Middelberg,E.2014,TheAstronomicalJournal,147,14
Garrett,M.A.,Muxlow,T.W.B.,Garrington,S.T.,etal.2001,A&A,366,L5
Garrett,M.A.,Wrobel,J.M.,&Morganti,R.2004,inEuropeanVLBINetwork
onNewDevelopmentsinVLBIScienceandTechnology,ed.R.Bachiller,
F.Colomer,J.-F.Desmurs,&P.deVicente,35–38
Keimpema,A.,Kettenis,M.,Pogrebenko,S.,etal.2015,ExperimentalAstron-
omy,1
Kettenis,M.,vanLangevelde,H.J.,Reynolds,C.,&Cotton,B.2006,inAstro-
nomicaldataanalysissoftwareandsystemsXV,Vol.351,497
Middelberg,E.,Deller,A.T.,Norris,R.P.,etal.2013,A&A,551,A97
Morrison,G.E.,Owen,F.N.,Dickinson,M.,Ivison,R.J.,&Ibar,E.2010,The
AstrophysicalJournalSupplementSeries,188,178
Radcliffe,J.,Garrett,M.,Muxlow,T.,Beswick,R.,&Barthel,P.inprep.
Rampadarath,H.,Morgan,J.S.,Soria,R.,etal.2015,MNRAS,452,32
Rau,U.,Bhatnagar,S.,Voronkov,M.A.,&Cornwell,T.J.2009,IEEEProceed-
ings,97,1472
Rioja,M.J.&Porcas,R.W.2000,A&A,355,552
Trott,C.M.,Wayth,R.B.,Macquart,J.-P.R.,&Tingay,S.J.2011,TheAstro-
physicalJournal,731,81
Wrigley,N.,Muxlow,T.,&Beswick,R.inprep.
Yatawatta,S.,deBruyn,A.G.,Brentjens,M.A.,etal.2013,A&A,550,A136
Articlenumber,page7of7