Spectral index properties of milliJansky radio sources

2.5 MB·English

by  Kate Randall

Mon.Not.R.Astron.Soc.000,1–18(2011) Printed4January2012 (MNLATEXstylefilev2.2)
Spectral index properties of milliJansky radio sources
K. E. Randall1,2⋆, A. M. Hopkins3, R. P. Norris2, P.-C. Zinn4, E. Middelberg4,
M. Y. Mao2,3,5, R. G. Sharp6
1SydneyInstituteforAstronomy,SchoolofPhysics,TheUniversityofSydney,NSW2006,Australia
2CSIROAstronomyandSpaceScience(CASS),P.O.Box76,EppingNSW,1710,Australia
3AustralianAstronomicalObservatory,POBox296,Epping,NSW,1710,Australia
4AstronomischesInstitutderRuhr-Universita¨tBochum,Universita¨tsstr.150,44801Bochum,Germany
5SchoolofMathematicsandPhysics,UniversityofTasmania,PrivateBag27,Hobart,Tasmania7001,Australia
2
6ResearchSchoolofAstronomyandAstrophysics,TheAustralianNationalUniversity,CotterRoad,Weston,ACT2611,Australia
1
0
2
Accepted2011December20.Received2011December16;inoriginalform2011October17
n
a
J
ABSTRACT
3 At the faintest radio flux densities (S1.4 < 10mJy), conflicting results have arisen regard-
ingwhetherthereisaflatteningoftheaveragespectralindexbetweenalowradiofrequency
]
O (325or610MHz),ande.g.1.4GHz.We presentanewcatalogueof843MHzradiosources
in the ELAIS-S1field thatcontainsthe sources,their ATLAScounterparts,andthe spectral
C
indexdistributionsofthesourcesasafunctionoffluxdensity.Wedonotfindanystatistically
.
h significantevidencefora trend towardsflatter spectralindiceswith decreasingflux density.
p We then investigate the spectral index distribution with redshift for those sourceswith reli-
- able redshiftsand explore the infraredproperties.An initial sample of faintCompact Steep
o
SpectrumsourcesinATLASisalsopresented,withabriefoverviewoftheirproperties.
r
t
s Keywords: catalogues—galaxies:active—galaxies:evolution—radiocontinuum:galax-
a
ies.
[

1
v
8
1 INTRODUCTION levels(Hilletal.1999,2001).Therelativeproportionsofthesetwo
6
5 populationswillhaveaneffectontheaverageradiospectralindex
0 Thedesiretounderstandthepropertiesofthefaintestradiosource (α)1asafunctionoffluxdensity,andatthefaintestfluxdensities,
populations has led to numerous surveys pushing to ever fainter
. core-dominatedAGNmaybemoreprevalent,andmayflattenthe
1 levels. There are now a large number of deep and wide area
averagespectralindextoα>−0.7.
0 radio surveys available, such as the Australia Telescope Large
Conflicting evidence has arisen over the nature and proper-
2 AreaSurvey(ATLAS;Norrisetal.2006;Middelbergetal.2008),
1 tiesofsourcesatfrequenciesbelow 1.4GHz,particularlyoftheir
the Cosmic Evolution Survey (COSMOS; Scovilleetal. 2007;
: spectral index properties, and whether there is a flattening of the
v Smolcˇic´etal. 2008), the ATESPSurvey (Prandonietal. 2000a,b,
i 2006),thePhoenixDeepSurvey(Hopkinsetal.2003),andmany average spectral indices for faint (S1.4 < 10mJy) radio sources.
X Prandonietal. (2006, 2011) found sources with fluxes less than
others(Seymouretal.2008;Owen&Morrison2008;Owenetal.
a few milliJansky had an average spectral index which was flat-
r 2009; Ibaretal. 2009, 2010). The bright radio source population
a terthanthatofthebrighter radiosources(α ∼ −0.7).Similarly,
(S1.4 >10mJy)iswellstudied,andispredominantlycomposedof Owen&Morrison(2008)foundaflatteningoftheaveragespectral
activegalacticnuclei(AGN)(Condon1984;Gruppionietal.1999;
index between 325MHz and 1.4GHz for 1.4GHz selected radio
Magliocchettietal. 2000; Georgakakisetal. 1999; Afonsoetal.
2006).Atfainterfluxdensities,star-forminggalaxies(SFGs)begin sourceswithS1.4 < 10mJy,andangularsizes> 3′′.Theyfound
though, that thespectral indices steepen again at the faintest flux
todominatetheradiosourcepopulation, particularlyintotheµJy
density end of the 20cm survey (∼ 0.5mJy). In contrast, in the
regime (Windhorstetal. 1985; Hopkinsetal. 1998; Afonsoetal.
deepestradiofield,theLockmanHole(Ibaretal.2009),noflatten-
2005;Seymouretal.2008).Understandingthesefaintradiosource
ingofthespectralindicesbetween610MHzand1.4GHzwasseen
populationsisessentialforunderstandinggalaxyevolution,therole
ofstarformation,AGNandtherelationshipbetweenthetwo.The forfluxdensitiesS1.4>100µJy.
Aflatteningoftheaveragespectralindicesimpliesthatthere
useofmultiwavelengthdatatocomplementradiosurveysisvitalin
isaflatorinvertedspectrumpopulationofsourcesatthesemilli-
ordertodistinguishbetweenAGNandstarformationprocessesas
Jansky flux densities, at fluxes fainter than where the steep spec-
theoriginoftheradioemissiondowntothefaintestfluxdensities,
althoughthereislikelyalsoacompositepopulationatthesefaint
1 AssumingSν ∝ να,whereSisthemeasuredfluxdensityandνisthe
⋆ E-mail:[email protected] observer’sframefrequency.
(cid:13)c 2011RAS
2 Randalletal.
trum star-formingpopulation emerges (∼ 0.5mJy). Investigating 2.1.2 Spitzer/SWIRE
the milliJansky and microJansky radio source populations at dif-
TheELAIS-S1fieldwasobservedbytheSpitzerSpaceTelescope
ferentfrequenciesallowsustoinvestigatethissuspectedflattening
aspartofthelargestLegacyProgram,theSpitzerWide-areaInfra-
oftheaveragespectralindices,andthepopulationofsourcescaus-
Red Extragalactic survey (SWIRE; Lonsdaleetal. 2003, 2004).
ingtheflattening,particularlyifwecanfillinthefrequencyregime
SWIRE aimed to trace the evolution of dusty SFGs, AGN, and
fromverylowfrequencies(∼ 100MHz)upto1.4GHz.Itisnec-
evolvedstellarpopulations out toaredshift ofz ∼3,byimaging
essarytounderstandthespectralindexpropertiesofthesefaintra-
largeareasofskyinsevendifferentinfraredbands.Incombination
diosourcesformanyreasons,suchasthez-αrelation,usedtofind
withopticalimaging, thiswouldallowSEDmodelingandexplo-
themostdistantradiogalaxies(deBreucketal.2004;Klameretal.
ration of galaxy evolution with environment. The seven imaging
2006;Ishwara-Chandraetal.2010),identifyingyoungradioAGN,
bands of SWIRE used two different instruments aboard Spitzer,
such as Gigahertz Peaked Spectrum (GPS) and Compact Steep
theMultibandImagingPhotometer(MIPS;Riekeetal.2004),and
Spectrum(CSS)sources(O’Dea1998;Polatidis&Conway2003;
the Infrared Array Camera (IRAC; Fazioetal. 2004), covering
Morgantietal.2009)ordeterminingtheemissionmechanisminra-
∼ 7deg2 over the ELAIS-S1 region. The 24µm MIPS imaging
diogalaxies,whetheritisfromstarformation,orthecentralAGN
reachesa5σsensitivityof350µJy,andtheIRACbandsof3.6,4.5,
(Prandonietal.2006).
5.8and8.0µmhave5σ sensitivitiesof3.7,5.3,48and37.75µJy
Herewepresentradioobservationsat843MHzintheELAIS-
respectively.
S1field,forwhichwehavecomplementary1.4and2.3GHzdata
from ATLAS that we can use to investigate the possible spectral
indexflatteningatafrequencynearertotheubiquitous1.4GHzra-
diosurveys.Section2brieflyreviewstheexistingmultiwavelength 2.1.3 ESIS
datacoveringtheELAIS-S1regionandATLAS,andinSection3
TheESO-SpitzerImagingextragalacticSurvey(ESIS)istheopti-
we describe our observations, the data reduction, and the cross-
calfollow-uptoSWIRE,consistingofopticalimagingintheB,V,
matching process to the ATLAS 1.4 and 2.3GHz catalogue. We
RbandswiththeWideFieldImager(WFI;Bertaetal.2006),andI
present the catalogue in Section 4. Our results and analysis are
andzbandimagingwithVIMOS(Bertaetal.2008).Currently,the
explored in Section 5, and a new faint sample of candidate CSS
VIMOSobservationshavebeencompleted, buttheWFIobserva-
sources is presented in Section 6, discussing the initial selection
tionsarenotyetfullyprocessed.TheBVRobservationsdescribed
and properties of these sources. Our results and plans for future in Bertaetal. (2006) cover 1.5deg2, in the central region of the
workarediscussedinSection7andourconclusionsarepresented
ELAIS-S1field.Thecatalogue of BVRsources is95%complete
inSection8.Throughoutthisanalysis,unlessotherwisenoted,we
to25m inBandV,and24.5m inR.132712sourcesareincluded
use the cosmological parameters, ΩM = 0.27, ΩΛ = 0.73 and inthiscatalogue, withanrmsuncertaintyof ∼ 0.15′′ fortheco-
H0=71kms−1Mpc−1(Komatsuetal.2011). ordinatesofthesources.TheVIMOSdatacovers∼ 4deg2 inthe
Ibandand∼ 1deg2 inthezband,resultinginacompletenessof
90%at23.1mintheIband,and22.5minthezband.Over300,000
2 THEELAIS-S1REGION sources were catalogued in the I band, and over 50,000 in the z
band,withanrmsof∼0.2′′inbothbands.
TheEuropeanLargeAreaISOSurvey-South1Region(ELAIS-
S1) has been a target for many multiwavelength surveys and tar-
getedobservationsoverthelastdecade.TheELAIS-S1fieldcovers
2◦×2◦,centredonRA=00h34m44s.4andDec=−43◦28′12′′.0 2.1.4 PreviousRadioObservations
(J2000.0). Observations covering the ELAIS-S1 field include ra- Prior to the ATLAS observations (detailed below in §2.2),
dioimaging,opticalimagingandspectroscopicredshifts,infra-red Gruppionietal. (1999, G99) observed the ELAIS-S1 field using
observations(near,midandfar-infrared),UV,andX-rayobserva- theAustraliaTelescopeCompactArray(ATCA)in1997,covering
tions.Partoftheattractionforthemultiwavelengthsurveysinthis ∼ 7deg2.Theobservations consisted ofamosaicof 49different
regionisthatthisfieldhasthelowestGalactic100µmcirrusemis- pointings, resultinginanimagermsof∼ 80µJy at1.4GHz,and
sioninthesouthern sky(Schlegel,Finkbeiner&Davis1998),in- acatalogueof581radiosources. Thelowestfluxdensitysources
cludingtheabsoluteminimum. werecatalogueddowntoa5σlevelof0.2mJyinthecentreofthe
field,and0.4mJyintheremainingarea.
2.1 MultiwavelengthdatainELAIS
2.1.1 ISO 2.1.5 X-rayObservations
The field was first observed as part of a deep, wide-angle sur- BeppoSAX,anX-raysatellite,firstobserved40%oftheELAIS-S1
vey with the Infrared Space Observatory (ISO) at 15 and 90µm fieldin1999(Alexanderetal.2001).Theseobservationsreacheda
(Oliveretal.2000).Follow-upobservationsweredoneat6.7µm, sensitivityof∼ 10−13ergcm−2s−1 inthe2−10keVrange, cov-
and the catalogue covering the S1 Region at these three wave- ering ∼ 1.7deg2. The central ∼ 0.6deg2 were then surveyed
lengths is discussed in Rowan-Robinsonetal. (2004). The com- by XMM-Newton in four deep pointings (Puccettietal. 2006).
plete 15µm catalogue contains all the sources from the ELAIS TheXMMobservations weretaken inbothsoftandhardX-rays,
regions: N1, N2, N3, S1, S2, and was finalized by Vaccarietal. and each pointing had a net exposure time of ∼ 60ks. A total
(2005).Thethreebandsofthissurveyhavermsnoiselevelsof1.0, of 478 sources were detected, with 395 in the soft X-ray band
0.7and70mJyrespectivelyforthe6.7,15and90µmbands.Photo- (0.5−2keV)and205inhardX-ray(2-10keV).Thefluxlimitsare
metricuncertaintiesforallbandswere∼10%,andtheastrometric ∼ 5.5×10−16ergcm−2s−1 and ∼ 2×10−15ergcm−2s−1 re-
accuracyis∼0.5′′. spectivelyforthesoftandhardbands.
(cid:13)c 2011RAS,MNRAS000,1–18
Spectralindexpropertiesof mJyradiosources 3
Figure1.ThegreyscaleMOST843MHzimage,withoverlaysindicatingtheapproximatebordersoftheATCA1.4GHzand2.3GHzobservations.Thelarger,
redboundaryrepresentsthe1.4GHzmosaic.
2.1.6 UVObservations inprep.;Banfieldetal.inprep.).ATLAShasmanyscientificgoals,
primarily focussed on investigating the evolution of galaxies and
TheultravioletGalaxyEvolutionExplorer(GALEX;Martinetal.
AGN. Specific goals include distinguishing between AGN and
2005) observed the ELAIS field in two of its observing
SFGsanddeterminingthecontributionofeachtoagivengalaxy’s
modes;theDeepImagingandWideSpectroscopicSurveymodes
luminosity,searchingforhigh-z radiogalaxiestotracetheforma-
(Burgarellaetal.2005).Thebandsobservedwerecentredon153
tionofclustersathighredshift(Maoetal.2010),andfindingnew
and 231nm, and the current data release (GR62) covers 70% of
typesofraresources(N06,M08,Middelbergetal.2011).TheAT-
theskyintheimagingmode,andhas61439spectroscopicsources.
LAS survey regions were chosen because of the large amount of
TheELAISfieldwasobservedfor∼ 9hoursinthespectroscopic
multiwavelengthdatacoveringthesetwofields,includingnearand
surveymode,and∼3hoursintheimagingmode.
far-infrared, and deep optical data, and in some areas, X-ray and
Intheanalysisbelowwefocusontheinfrareddataasthepri-
UV. We aim to create the most comprehensive multiwavelength
mary complement to our radio data, although in future work we
survey of faint radio sources to date. ATLAS currently contains
willalsotakeadvantageoftheX-rayandUVmeasurements.
∼ 2000radiosources,andweestimatewewillhave∼ 16000ra-
diosourcesfollowingfinalanalysisofnewobservationscompleted
in 2010 from ATCA with the Compact Array Broadband Back-
2.2 TheAustraliaTelescopeLargeAreaSurvey(ATLAS)
end(CABB;Wilsonetal.2011).Thesenewobservationsconsistof
ATLASisthewidest,deepradiosurveytodate(Norrisetal.2006; 1000hoursofintegrationtime,andcoverabandwidthof0.5GHz
Middelbergetal. 2008, N06, M08), covering ∼ 7deg2 over two centredon1.4GHz.
fields,ELAIS-S1,andtheChandraDeepFieldSouth(CDFS).The
rmsof the1.4GHzimagingdataiscurrently30µJy, andtheaim In ELAIS-S1, 1276 radio sources have been catalogued,
is to achieve an rms of 10µJy across both fields (Banfieldetal. comprising1366radiocomponents, at1.4GHz(Middelbergetal.
inprep.).ATLASobservationshavebeencompletedat1.4and2.3 2008, M08). The 2.3GHz image has a lower sensitivity, with an
GHzwithATCAfrom2006to2010,withonedatareleasein2008, rmsnoiselevelof∼60µJyinthecentral∼ 1deg2 and∼100µJy
and subsequent data releases to begin in late 2011 (Halesetal. overtheentirefield.Wefindonly576radiosourceshaveawell-
defined counterpart at 2.3GHz, mainly because the resolution is
∼ 3 times coarser at this frequency than at 1.4GHz as a conse-
2 http://galex.stsci.edu/GR6/ quenceof thecompact configuration ofATCAusedfortheseob-
(cid:13)c 2011RAS,MNRAS000,1–18
4 Randalletal.
Figure2.(a)GreyscaleMOST843MHzimageofATELAISJ003306.30-431029.8,(b)originalATCA1.4GHzgreyscaleimage,and(c)theoriginalATCA
2.3GHzgreyscaleimage.Thewhitecrossindicatesthe1.4GHzradiopositionofthissource.
servations. For the purposes of this paper and catalogue, we use andobservingmode, theseartifactsaretechnicallydifficulttore-
thecross-matchesbyZinnetal.(inprep.,Z11),wherewetakethe move.Theartifactsremaininourimage,andduecarewastakento
1.4GHz sources matched to the poorer resolution 2.3GHz data, ensureallobjectsinourfinalcataloguewerenotspurioussources
andextractthefluxesfromtheseimagesforeachsource.M08also associatedwiththeartifacts.Anin-depthdiscussionofthesearti-
compared their flux densities and positions to G99 by repeating factsisgiveninMauchetal.(2003).
theirsourceextractionontheG991.4GHzradioimage.Thedif-
ferences in radio positions were determined to be negligible, but
thefluxdensitiesofM08,whilewithin∼ 3%oftheearliermea- 3.2 Source-finding
surements,wereconsistentlyhigherthanG99.
SourcefindingforthefinalMOSTimagewasdoneusingthetask
SFIND (Hopkinsetal. 2002) in MIRIAD. This produces a cata-
logue of source positions, peak and total flux density and errors,
plus the attributes of the Gaussian fits for each source. The final
3 OBSERVATIONS,DATAREDUCTIONAND
cataloguecontains325radiosources,afterremovalof≈100spu-
CROSS-MATCHING
rioussources associated withthe grating ringsand radial spokes.
To obtain low-radio frequency (843MHz) data within ATLAS, Thespurioussourceswereidentifiedandremovedbyvisualinspec-
we used the Molonglo Observatory Synthesis Telescope (MOST; tion(mostlaydirectlyonastrongradialspokeordiffractionring),
Mills1981;Robertson1991).TheMOSTisa1.6kmlongcylindri- andbycomparisontotheSydneyUniversityMolongloSkySurvey
calparaboloidreflector,withitsaxisalignedinaneast-westdirec- (SUMSS;Bocketal.1999;Mauchetal.2003)images(see§5.1for
tion.Itoperatesatafrequencyof843MHz,andhasafieldofview details).EachMOSTATLASsourcewasidentifiedintheSUMSS
of2◦.7cosec(δ)×2◦.7deg2(Largeetal.1981;Bocketal.1999).We imageswithalowsignal-to-noisesourcethatwasbelowthedetec-
have 31 separate 12 hour observations taken with MOST, which tionleveloftheSUMSScatalogue.TheMOSTimageislargerthan
were combined into a single image. The CDFS field (centred at theATLASsurveyregion,soourcatalogueencompasses alarger
RA=03h32m28s andDec=−27◦48′31′.′0(J2000.0))wasnotob- number ofsourcesintotalthanwesubsequently analysetogether
served, due to strong radio frequency interference (RFI) that in- withtheotherATLASdata.
creasedwithlowerelevation. WeusetheprocessoutlinedinHopkinsetal.(2003)tocalcu-
latetheerrorsassociatedwithourmeasuredfluxdensities,anduse
Equation5ofHopkinsetal.(2003)withonesmallmodification:
3.1 Processing
The data reduction pipeline for MOST data is highly automated σ2
σ =I 2.5 +0.052, (1)
andreliable.Unfortunately,thetelescopewassubjecttosevereRFI I r I2
atthetimeofourobservations.TheprocesstoremovetheRFIre-
where I is the total integrated flux density, σ is the rms error in
quiredmanualidentificationandexcisionoftheaffecteddata.Once
the image at the source location, and σ is the total error on the
completed, wewereabletore-runthedatapipeline, andproduce I
integratedfluxdensity.Weuse0.052 asthesumofthesquaresof
finalcleanedimages.Sevenofour31observationsweresubjectto
the instrumental and pointing errors as given in M08, instead of
RFIthatwewereunabletoremovecompletely,andthesewerenot
0.012 as given in Hopkinsetal. (2003). We have used the more
includedinourfinalimaging.Theremaining24imageswereadded
conservativeestimateof theseerrorsasgivenbyM08, duetothe
together in MIRIAD, first by re-gridding the images to ensure a
calibrationaccuracyofMOSTbeingcomparabletothatofATCA.
common astrometry and pixel grid, and then using the task IM-
COMBtocombinetheimages.Thefinalimagehasanrmssensitiv-
ityof≈0.6mJy,ahighervaluethanexpectedduetothepresence
3.3 Cross-matchingtoATLAS
oflow-level RFIthatcouldnot beexcised. Wecataloguesources
downtoa5σlevelof3mJy.ThefinalimageisshowninFigure1 Thefinal MOSTcatalogue waspositionally cross-matched tothe
withtheapproximatebordersoftheATLAS1.4and2.3GHzmo- combined 1.4 and 2.3GHz catalogue produced by Z11, that in-
saicsoverlaid. cluded the relevant SWIRE and optical data. As mentioned pre-
TheMOSTimagewassubjecttotwokindsofartifacts,grating viously in §2.2, only 576 of the 1276 1.4GHz radio sources in
ringsandradialspokes. Duetothenatureofthetelescopedesign ELAIShaveareliablesingle2.3GHzcounterpart,whilst460have
(cid:13)c 2011RAS,MNRAS000,1–18
Spectralindexpropertiesof mJyradiosources 5
Figure 3. (a) Thegreyscale MOST 843MHzimage ofATELAISJ003306.30-431029.8, (b) the convolved ATCA1.4GHz greyscale image, and (c) the
convolvedATCA2.3GHzgreyscaleimage.Thewhitecrossindicatesthe1.4GHzradiopositionofthissource,andthe1.4GHzcontoursareoverlaidatlevels
of2.5,5and12mJy
nocounterpart,and240areblendedorpoorlyfittedsources(where 3.4.1 FluxDensityComparisonsandCorrections
the 2.3GHz counterpart encompasses multiple 1.4GHz sources).
Fromourcross-matching,105MOSTsourceswerematchedtosin-
To ensure our measured 1.4 and 2.3GHz flux densities from the
glesourcesintheZ11catalogue.Another30MOSTsourceswere
convolved, coarser-resolution, images were robust, we compared
matchedtoconfusedorblendedsourcesfromZ11,and31MOST
thesetothefluxdensitiesinM08andZ11.Wefindthatourmea-
sourceswerefoundtohavemultipleisolatedZ11sourcesmatched
surementsintheimagesconvolvedtoaresolutionconsistentwith
toasingleMOSTsource.
theMOSTimagetendtosystematicallyoverestimatethe1.4GHz
flux densities compared to M08, and underestimate the 2.3GHz
fluxdensitiescomparedtoZ11.
The issue at 2.3GHz arises from negative CLEAN bowls
3.4 ResolutionMatching
aroundsourcesintheoriginalimage.Theseartifactsgiverise,after
TheresolutionoftheMOSTimage,62′′ × 43′′,ismuchcoarser convolution, to our observed systematic decrease in flux density.
than the resolution of the 1.4GHz image (10′′ × 7′′), and the The2.3GHzbeamsize(33′′×20′′)isclosetothatofourMOST
2.3GHz image (33′′ × 20′′). To determine accurate spectral in- images(62′′ × 43′′),andthebulkof thesourcesareunresolved,
dicesacross thethreefrequencies, it isnecessary toconvolve the meaning that there is likely to be little flux missed on extended
ATLAS 1.4 and 2.3GHz images to the same size as the MOST scales.Consequently,wechoosetousethefluxdensitiesestimated
beamtoensuretherecoveredfluxforsourcesatallfrequenciesin- byZ11 inthe original 2.3GHzimagefor our spectral index esti-
cludesanyemissionextendedonscalesuptothoseconsistentwith mates.
theMOSTbeam.Figure2showsanexampleofacomplexsource
fromtheATLAS1.4GHzcatalogueingreyscaleinthethreeradio At1.4GHz,thedifferenceinresolutionfromtheMOSTim-
frequencies,tohighlightthedifferencesinresolution.InFigure3, age is sufficient that we need to use the flux densities from the
thesamesourceisshownafterconvolvingthe1.4and2.3GHzim- convolvedimage.ThefluxdensityoverestimatecomparedtoM08,
agestothesameresolutionastheMOSTimage.Althoughconvolu- which is limited to the fainter sources (S843 < 10mJy), is typi-
tionremovesmostofthesmallscalestructurevisibleintheoriginal callyoftheorderof10%.Thisexistsforclearlyunresolvedsources,
ATLAS1.4GHzimage,itensureswearedetectingemissionfrom whichshouldbeidenticalbeforeandafterconvolution.Thisissue
thesamespatialregionfromeachsource. isassociatedwithside-lobesfromtheradiosourcesineachindivid-
For consistency, weused SFIND todetect sources withinthe ualtelescopepointing,belowtheleveltowhichtheimagehasbeen
convolved1.4and2.3GHzimages.Thisallowsustomeasureer- CLEANed,beingsummedintheconvolvedimage.Whilethisisa
rorsonourfluxdensitiesthatareconsistent forthethreeimages, smalleffect,withaminimalimpactonourderivedspectralindices
whichisimportantforproducingaccuratespectralindicesandas- (quantifiedbelow),wecanmakeanempiricalcorrectionthatmini-
sociated uncertainties. Rather than rejecting blended sources en- mizesanyimpactfurtherstill.Thisisimplementedthroughaleast-
tirely, we account for them carefully in our catalogue. These are squaresfitofourconvolvedfluxdensitiesagainstthoseofM08,and
singleorpointsourcesinthe843MHzMOSTimage(andthe1.4 scalingour convolvedfluxdensitiesusingthisfittobeconsistent
and 2.3GHzconvolved ATLASimages) that encompass multiple withthoseofM08.Thisaccountsfortheflux-densitydependence
ATLAS1.4GHzsourcesfromtheM08catalogue(Figure4).The oftheimagingsystematicswhileretainingcontributionsfromany
M08fluxdensitiesforthesesourcesreportedinourcatalogueare realextended fluxcomponents, andatthesametime,minimizing
thesummedvalues oftheindividual M081.4GHzfluxdensities. anypossibleoverestimateofthefluxdensity.Thiscorrectiontypi-
As the contribution to the total flux density from each individual callyresultsinachangeofonlyαfit ∼0.02.
componentwithinablendedsourcecannotbedetermined,wetreat
themasasingleentityforthepurposeofthecurrentanalysis,even Theimpactonourderivedtwo-pointspectralindexestimates
thoughtheymaybephysicallyunrelated.Weincludethesesources ofpotentialremainingfluxdensityuncertaintiesat1.4and2.3GHz
inouranalysisforcompleteness,butcautionthattheirspectralin- of∼10%is∼0.1.Thisuncertaintyisincludedinourestimatesof
dices should not be considered as accurate estimates of those for spectralindexerrorsbelow,bybeingaddedinquadraturewiththe
theunderlyingsourcecomponents. fluxdensityerrors(givenbyEquation1).
(cid:13)c 2011RAS,MNRAS000,1–18
6 Randalletal.
Figure4.Anexampleofablendedsource.Thecontoursarefromthecon- Figure 5. The single example of a blended source where the ATLAS
volved1.4GHzimage(atlevelsof5,10and20mJy),andthegreyscaleis 1.4GHzradiopositionisnotwithintheGaussian(shownbythewhiteel-
the843MHzimage.Thewhitecrossesindicatethe1.4GHzradioposition lipse)fittedtothissource,butthereisclearlycontaminationfromtheneigh-
ofthetwosources,wheretheobjectinthecentreoftheimageistheMOST bouringsource.
cross-matchedsource,andtheblendedobjectindicatedbytheothercross.
4 THEMOSTATLASSOURCECATALOGUE
The total catalogue consists of 325 MOST sources, limited to
3.4.2 Blendedsources sourcesabovethe5σcutoffof3mJy,ofwhich166haveanATLAS
1.4or2.3GHzcounterpart.Theremaining159sourcesareoutside
Anothereffectoftheconvolutionisthatmostobjectsclassifiedas
theATLASsurveyarea.Intotal,thereare310ATLASsourcesin
radio doubles, triples, or core-jet morphology by M08, appear as
ourcatalogue,with205classifiedasblendedsources.Theremain-
oneMOSTobject(singleorblended).Onlytwocore-jetmorphol-
ing105 ATLASsources correspond tosingleMOSTsources. An
ogysourcesappearslightlyelongatedinthedirectionofthejetin
extract of thecatalogue inshown inTable1, andthe fullversion
theMOSTandconvolved1.4and2.3GHzimages.
is available online. The MOST radio position is listed first, fol-
DuetothelowerresolutionoftheMOSTimage,thereare61
lowedbythefluxdensityanderrorat843MHz.ForMOSTsources
instances where there are ATLAS sources within the beam for a
with a single ATLAS counterpart, the ATLAS source name (e.g.
MOSTradiosource.These61MOSTsourcescorrespondtoato-
ATELAIS J002905.22−433403.9), and ID (e.g. S100) is listed;
tal of 144 ATLAS M08 1.4GHz sources. Of the 61, 30 sources
for blended sources the given ATLAS IDs correspond to all Z11
wereclassifiedasblendedbyZ11duetohavingmultiple1.4GHz
sourcescross-matchedtotheMOSTsource,andtheATLASsource
sourceswithinthe2.3GHzbeam(33′′×20′′).Theremaining31
namecorrespondstothefirstATLASIDlisted.AllATLASsource
areclassifiedasblendedinthispaperduetomultiple1.4or2.3GHz
names and IDs are from M08. The corrected convolved 1.4GHz
sourceswithintheMOSTbeam. Thecross-matched 1.4GHzAT-
andZ112.3GHzfluxdensitymeasurementsandassociatederrors
LAS source (positionally closest to the MOST radio position) is
aregiven,alongwiththethreespectralindices(describedin§5.2
generallybrightwhilethesecond,blended,sourcecontributingto
below).
thefluxdensityistypicallymuchfainter(S1.4 <1mJy).Asacon-
sequence, themajorityof suchblended sourcesarelikelytohave
little contribution to the MOST flux density from the secondary
component,andthespectralindexestimatefortheblendedsources 5 RESULTSANDANALYSIS
canbeconsideredasthatfortheprimaryATLAScounterpart,even
5.1 FluxDensityDistribution
thoughtheuncertaintiesonthisestimatewillclearlybelargerthan
theformaluncertaintiesprovidedinourcatalogue.Blendedsources The flux density distributions (Figure 6) do not show any major
areflaggedinthecatalogue. differencesbetweenthesingle,blended,andnon-ATLASsources.
Forblendedsourcesinourconvolvedimages,whichwerenot The location of the median of the entire catalogue is shown in
classifiedasblendedsourcesbyZ11,thefluxdensitiesfromsepa- Figure6a.Thedistributionsappear consistent withother faintra-
ratesourcesintheATLASZ11cataloguearesummed.Asourceis diosamples,suchastheoriginalATLAScatalogues(Norrisetal.
definedasbeingpartofablendedobjectifthe1.4GHzradioposi- 2006;Middelbergetal.2008).
tionlaywithinanellipsethesizeoftheGaussianusedtofindthe The Sydney University Molonglo Sky Survey (SUMSS;
totalfluxdensityintheconvolvedimage.Anexampleofablended Bocketal. 1999; Mauchetal. 2003) is an 843MHz survey with
sourceisshowninFigure4wherethecross-matchedATLAScoun- MOST, that covers the sky south of δ < −30◦ with |b| > 10◦.
terpartisinthecentreoftheMOSTsource,andtheblendedobject SUMSShassimilarresolutionandsensitivitytotheNationalRa-
iswithintheMOSTsynthesized beam. Thereisone exceptionto dio Astronomy Observatories (NRAO) Very Large Array (VLA)
this, shown in Figure 5, where the blended object is outside the SkySurvey(NVSS;Condonetal.1998).SUMSScontains211063
Gaussianfit,buttheradioemissionclearlyextendsfromS120into radio sources, with an rms of ∼ 1mJy. Our observations probe
S107. sourcesfainterthanSUMSSbyafactorof∼ 2.Ofourcatalogue,
(cid:13)c 2011RAS,MNRAS000,1–18
Spectralindexpropertiesof mJyradiosources 7
20
25 (a) (b) Single/Point Sources
Blended Sources
15
20 10
5
Count15 Count 0(c) Non-ATLAS Sources
10 20
15
5 10
5
0 0
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
Log10(S0.843 (mJy)) Log10(S0.843 (mJy))
Figure6.(a)ThefluxdensitydistributionforourentirecatalogueofMOSTsourceswiththemedianofthecatalogueastheverticaldashedline.(b)Distribution
offluxdensitiesforsingleandblendedMOSTATLASsources,and(c)theMOSTsourcesoutsidetheobservedATLASELAISfield.
(a) (b) (c)
1 1 1
0 0 0
1 1 1
fit(cid:0) fit(cid:3) fit(cid:7)
(cid:1) (cid:4) (cid:8)
2 2 2
(cid:0) (cid:3) (cid:7)
3 3 Median (cid:5)fit Single Sources 3 Median (cid:9)fit Single Sources
(cid:0)(cid:0)4 MSBilenedgnildaeen Sd o (cid:2)Sufoirtuc Sericsnegsle Sources (cid:3)(cid:3)4 51SB(cid:6)(cid:6)ilne SSgnppldeeee Sccdtto rrSuaaorll ucIIennrcsddeeesxx//FFlluuxx LLiimmiitt (cid:7)(cid:7)4 51SB(cid:10)(cid:10)ilne SSgnppldeeee Sccdtto rrSuaaorll ucIIennrcsddeeesxx//FFlluuxx LLiimmiitt
101 102 100 101 102 100 101 102
S0.843 (mJy) S1.4 (mJy) S2.3 (mJy)
Figure7.(a)Spectralindexαfitversus843MHzfluxdensity,(b)1.4GHzfluxdensity,and(c)2.3GHzfluxdensity.Thedottedblacklineindicatesthe1σ
spectralindexlimit,andthesolidblacklinerepresentsthe5σspectralindexlimitforeachfluxdensity.Thedashedblacklineisthemedianαfitvaluefor
singlesourcesonly.
liers,likelyduetointrinsicsourcevariability.Itisknownthatafew
40 percentofmJyradiosourcesarevariableonthetimescaleofyears
Single Sources
Blended Sources (Oort&Windhorst1985).Attributingouroutlierstovariabilityis
35 consistentwiththiswork,asourdatawastakenoverseveralyears.
30
5.2 SpectralIndexDistributionsandProperties
25
unt20 Wehavecalculatedspectralindicesforallsourcesforwhichflux
o
C densitiesareavailableattwoorthreefrequencies.α isathree-
fit
15 pointpower-lawfit,andα10..4843 andα21..34 aretwo-pointpower-law
fits for the respective frequencies. Distributions of these spectral
10
indicesaregiveninFigures7and8.Spectralindexα10..4843 versus
5 spectralindexα21..34 isalsoshowninFigure9,whichindicatesthat
most of our sources are steep-spectrum, with a small fraction of
0
2.5 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 inverted, peaked, and flat spectrum objects, discussed further be-
(cid:11) (cid:11) (cid:11) S0.843(cid:11) to S2.3 S(cid:11)pectral Index (cid:12)fit low.Alargeproportionofsteep-spectrumsourcesareseenbecause
of the low radio frequency selection, and steep spectrum sources
Figure8.Distributionofαfitforourcatalogue.
arebrighteratlowerfrequencies.Themedianspectralindexα
fit
forthesinglesourcesisshownoneachofthepanelsinFigure7.
Only single sources are included in this calculation. The spectral
178sourcesarecross-matchedtoSUMSSsources.Onlyonesource indexlimitsareshowninFigure7b,carisingfromthelimitingflux
inSUMSSdoesnothaveacounterpartinourobservations,asitis density of the least-sensitive frequency in the relevant two-point
locateddirectlyonanartifactinourimage.Ourmeasuredfluxden- spectralindexcalculation.Althoughthethree-pointspectralindex
sities,positions, andradiodifferentialsourcecounts(see§5.5for
details) are consistent with those of SUMSS, with only two out-
(cid:13)c 2011RAS,MNRAS000,1–18
8
Table1. Extractfromthe843MHzMOSTATLASCatalogue
MOSTRA MOSTDec Sm0.J8y43 ∆Sm0J.y843 ATLASName ATLASID/s Type Sm1J.y4 ∆mSJ1y.4 Sm2J.y3 ∆mSJ2y.3 αfit ∆αfit α10..4843 α12..43 Ra
n
d
a
0:28:45.438 −42:51:39.46 15.12 1.5 ... ... ... ... ... ... ... ... ... ... ... ll
0:28:54.063 −43:12:18.30 6.80 1.8 ... ... ... ... ... ... ... ... ... ... ... e
t
0:28:56.980 −42:18:15.37 40.52 3.2 ... ... ... ... ... ... ... ... ... ... ... a
0:29:05.054 −43:34:07.05 11.34 1.3 ATELAISJ002905.22−433403.9 S749 p 9.01 1.16 5.11 0.34 −0.81 0.06 −0.45 −1.14 l
.
0:29:05.968 −44:42:00.59 14.18 1.6 ... ... ... ... ... ... ... ... ... ... ...
0:29:09.167 −43:44:02.10 11.13 1.3 ATELAISJ002909.26−434356.3 S617 p 12.52 1.27 4.63 0.27 −0.93 0.09 0.23 −2.00
0:29:13.163 −44:52:23.32 5.33 1.4 ... ... ... ... ... ... ... ... ... ... ...
0:29:15.437 −43:26:36.78 9.51 1.3 ATELAISJ002915.52−432638.3 S868 p 5.45 1.10 3.56 0.25 −0.97 0.03 −1.10 −0.86
0:29:21.471 −42:55:45.26 44.87 2.6 ... ... ... ... ... ... ... ... ... ... ...
0:29:25.667 −44:08:25.68 15.37 1.8 ATELAISJ002925.66−440822.8 S293,S304 b 9.12 1.13 3.51 0.35 −1.49 0.06 −1.03 −1.92
0:29:27.845 −43:16:15.59 6.61 1.2 ATELAISJ002927.69−431614.4 S1014 p 3.85 1.16 2.03 0.18 −1.18 0.01 −1.06 −1.29
0:29:36.620 −42:25:41.20 64.07 8.4 ... ... ... ... ... ... ... ... ... ... ...
0:29:37.206 −42:34:18.69 5.05 1.4 ... ... ... ... ... ... ... ... ... ... ...
0:29:38.084 −44:23:21.78 42.38 2.7 ATELAISJ002939.19−442319.3 S100,S101.1 b 34.1 2.29 18.82 1.88 −0.74 0.06 −0.43 −1.20
0:29:43.820 −42:37:47.77 17.83 1.7 ... ... ... ... ... ... ... ... ... ... ...
0:29:45.687 −43:21:50.03 24.18 1.6 ATELAISJ002945.64−432149.5 S943 p 16.25 1.41 10 0.52 −0.87 0.06 −0.78 −0.98
0:29:46.493 −43:15:57.34 41.67 2.4 ATELAISJ002946.52−431554.5 S1018 p 27.89 1.78 18.49 0.94 −0.81 0.05 −0.79 −0.83
0:29:47.622 −44:16:15.59 6.62 1.1 ATELAISJ002947.37−441607.0 S181 p 3.90 1.65 1.75 0.15 −1.33 0.01 −1.04 −1.62
0:29:50.398 −44:05:48.45 7.16 1.1 ATELAISJ002949.89−440541.4 S345,S342,S339 b 5.26 1.07 5.13 0.51 −0.31 0.03 −0.61 −0.05
0:29:51.452 −43:45:28.25 8.23 1.3 ATELAISJ002951.48−434528.0 S598 p 4.93 1.13 3.23 0.18 −0.93 0.02 −1.01 −0.85
0:29:53.062 −42:50:17.87 5.16 2.0 ... ... ... ... ... ... ... ... ... ... ...
0:30:03.253 −42:18:22.97 20.81 8.4 ... ... ... ... ... ... ... ... ... ... ...
0:30:04.749 −42:09:58.88 19.10 5.9 ... ... ... ... ... ... ... ... ... ... ...
0:30:10.595 −44:09:12.06 6.49 1.1 ATELAISJ003010.82−440907.3 S288 p 7.60 0.72 8.96 0.46 0.32 0.04 0.31 0.33
0:30:17.439 −42:24:47.35 436.20 22.4 ... ... ... ... ... ... ... ... ... ... ...
0:30:18.530 −45:26:42.05 12.79 2.5 ... ... ... ... ... ... ... ... ... ... ...
0:30:18.793 −44:04:35.34 13.70 1.2 ATELAISJ003019.22−440438.3 S355 p 9.83 0.78 5.57 0.23 −0.89 0.08 −0.65 −1.14
0:30:20.948 −43:39:44.51 69.27 3.7 ATELAISJ003020.95−433942.8 S694 p 51.99 2.55 33.92 1.7 −0.66 0.04 −0.57 −0.86
0:30:21.663 −45:05:09.55 16.15 3.3 ... ... ... ... ... ... ... ... ... ... ...
0:30:22.709 −42:37:02.29 14.25 2.4 ... ... ... ... ... ... ... ... ... ... ...
0:30:27.017 −42:35:14.14 7.34 3.1 ... ... ... ... ... ... ... ... ... ... ...
0:30:29.096 −42:13:50.96 18.19 6.2 ... ... ... ... ... ... ... ... ... ... ...
0:30:34.835 −45:29:47.20 15.73 4.1 ... ... ... ... ... ... ... ... ... ... ...
0:30:35.339 −44:37:11.21 3.69 1.1 ATELAISJ003035.77−443707.2 S18,S19 b 6.53 3.21 2.07 0.21 −0.68 0.01 1.13 −2.31
0:30:35.937 −43:23:39.75 8.95 3.1 ATELAISJ003035.03−432341.6 S926,S923,S930,S930.1 b 5.03 0.62 4.76 0.48 −0.32 0.02 −1.14 −0.11
0:30:38.957 −44:09:56.34 3.95 0.9 ATELAISJ003039.03−441000.0 S279 p 3.04 0.62 1.23 0.13 −1.29 0.01 −0.52 −1.82
0:30:39.015 −45:07:07.04 33.29 2.7 ... ... ... ... ... ... ... ... ... ... ...
0:30:39.621 −44:42:01.21 28.43 1.9 ATELAISJ003039.68−444159.5 S7 p 26.00 3.44 17.02 0.95 −0.49 0.05 −0.18 −0.85
0:30:40.860 −43:23:40.55 11.17 2.4 ATELAISJ003042.10−432335.4 S923,S930,S930.1 b 6.02 0.64 5.47 0.55 −0.53 0.03 −1.22 −0.19
0:30:42.041 −43:18:42.39 4.52 1.0 ATELAISJ003041.88−431840.7 S987 p 3.26 0.61 2.12 0.13 −0.77 0.01 −0.64 −0.87
NOTES.–αfitisthespectralindexfittedacrossthethreefluxdensitymeasurementsat0.843,1.4and2.3GHz.Type(Column7)referstowhetherthesourceisasinglepointsource(p)atallfrequencies,orablendedsource(b).
(cid:13)c
2
0
1
1
R
A
S
,
M
N
R
A
S
0
0
0
,
1
–
1
8
Spectralindexpropertiesof mJyradiosources 9
Table2.SpectralClassifications
Single Sources
Type Total Point Blended Percentage 2 Blended Sources
Number Sources Sources
1
Steep-Spectrum 143 89 54 86%
Inverted 3 2 1 2%
0
Peaked 12 8 4 8%
Upturn 6 4 2 4% 2.31.4 1
(cid:15) (cid:13)
NOTES.–Thepercentagesofeachsourceareonlyforthesingleorpoint
sources. (cid:13)2
3
(cid:13)
αfit is shown in the figure, the limit associated with the two- (cid:13)4
pointspectralindexcalculationprovidesaclearindicationofwhere 2.0 1.5 1.0 0.5 0.0 0.5 1.0
(cid:13) (cid:13) (cid:13) (cid:13)1.4
weareselection-limitedagainstparticularlysteeporflatspectrum (cid:14)0.843
sources. Distributions of α10..4843, split into three flux density bins Figure9.Spectralindexα21..34 versusα10..4843 forMOSTATLASsources.
arealsoshowninFigure10,analogoustoFigure8ofMauchetal. Theblack symbolsineach outercorner oftheplotrepresent thetypeof
(2003). A flattening of the spectral index α10..4843 is suggested by sourceineachquadrantoftheplot,e.g.steep,inverted,peakedorupturn.
Figure 10; however this is primarily due to different numbers of
sourcesineachfluxdensitybin.Thisisfurtherdiscussedin§5.4.
14
5.3 Radiospectralclassifications 12 Single Sources (a) S0.843<10mJy
10 Blended Sources
Figure9showsoursampleofsources,inaradiocolour-colourdia- 8
6
gram(Kesteven,Bridle&Brandie1977;Murphyetal.2010),that 4
2
wenowconsiderinfourclasses: 0
10 (b) 10mJy<S0.843<20mJy
(i) Steep-spectrum objects, with a steep radio spectrum from 8
843MHzto2.3GHz(thelower-leftquadrantofFiguCountre9), 46
(ii) Peakedsources,whereweseetheradiospectrumturnover 2
0
between 843MHz and 2.3GHz (the lower-right quadrant of Fig- 12 (c) S0.843>20mJy
ure9), 10
8
(iii) Inverted (or rising) sources, where the radio flux density 6
4
increases with increasing frequency (the upper-right quadrant of 2
Figure9),and, 02.5 2.0 1.5 1.0 0.5 0.0 0.5 1.0
(iv) Upturnsources,thathaveanupturnintheirradiospectrum (cid:16) (cid:16) (cid:16) S(cid:16)pectral I(cid:16)ndex (cid:17)01..8443
(theupper-leftquadrantofFigure9). Figure10.Distributionofα10..4843,inthreefluxdensitybins,0-10mJy(a),
10-20mJy(b),and> 20mJy(c).Thesolidverticallinesarethemedian
Thisdistributionhighlights the fact that our sample isdominated
by steep-spectrum sources. The statistics are given in Table 2, spectralindexα10..4843foreachfluxdensitybinforthesinglesourcesonly.
split into single and blended sources, noting that any statistics
fromtheblendedsourcesarenotreliable.Incomparison,theAus-
tralia Telescope 20 GHz Survey (AT20G; Murphyetal. 2010),
a high-frequency-selected sample (20GHz), produced a colour-
5.4 Spectralindexasafunctionoffluxdensity
colour plot contained 3763 sources, with 14% inverted (rising)
spectrumsources,57%steep-spectrumobjects,21%peakedspec- Wehaveinvestigatedthepropertiesofoursamplewithfluxdensity.
trumsources,and8%sourceswithanupturnintheirspectra. Figure11showsmedianspectralindexasafunctionoffluxdensity,
As indicated by Table 2, 8% of our MOST ATLAS sample bothforoursample(Figure11a),andforacompilationofsamples
appear to be possible Gigahertz Peaked Spectrum (GPS) sources fromtheliteraturealongwithours(Figure11b).Whiletheuncer-
(see§6.1foradescription).O’Dea(1998)suggestthat∼ 10%of taintiesarelarge,thereisevidence foramildtrendtowardaflat-
brightradiosourcesareGPSsources,whereasRandalletal.(2011) terspectralindiceswithdecreasingfluxdensity(Figure11a).Fig-
found less than1% of their sample to beGPSsources. Although ure11bshowsthecomparisonofourmedianspectralindiceswith
boththesesamplesarenotcomplete,itisinterestingtonotethatat Windhorstetal. (1993); Prandonietal. (2011); Ibaretal. (2009),
faintradiofluxes,theproportionofGPSsourcesappearstobesim- andOwenetal.(2009).Ourdataisingeneralconsistentwiththese
ilartothebrightsampleofO’Dea(1998)ratherthantheunbiased previousresults,andsowecannotruleoutthepossibilitythatthere
brightsampleofRandalletal.(2011).Thissampleofsourceswill is a flattening of the median spectral index with decreasing flux
beexploredfurtherinafuturepaper,Randalletal.(inprep.). density. Wenote that the very steep median spectral index in the
Interestingly, thereisoneverysteepspectrumsinglesource, faintest fluxdensity binof many surveys isaconsequence of the
S1256, which has α01..8443 = −2.92, that is not detected in the flux density limits preventing the detection of flatter spectral in-
2.3GHzimage.Thisobjectisdiscussedinmoredetailin§7.3.5. dicesclosetothesurveylimits.
(cid:13)c 2011RAS,MNRAS000,1–18
10 Randallet al.
0.0
(a) x (b)
de 0.0
n
(cid:18)0.2 al I
al Index(cid:18)0.4 Hz Spectr(cid:20)0.5
pectr(cid:18)0.6 1.4 G
1.4 SMedian 0.843(cid:19) (cid:18)(cid:18)(cid:18)1101....4082 Median 843/610 MHz to (cid:20)(cid:20)211...005 WMMMMMeeeeeinddddddiiiiiaaaaahnnnnno r(cid:21)(cid:21)(cid:21)(cid:21)(cid:21)s00000t11111.......... 3368844444e2514450033t OPIMTabrhwlaaa.i usren1 cndew9h to9eo na23tri kl0 .aFe 1l2it.t1 0 2a t0(o0lP.9 0r(cid:21)2i90v05.4.1/ C01.6omm)
(cid:18) 101 102 (cid:20) 10-1 100 101 102 103
843 MHz Flux Density (mJy) 1.4 GHz Flux Density (mJy)
Figure11.(a)Medianspectralindexα10..4843foroursamplewith843MHzfluxdensity.(b)Medianspectralindexα10..4843foroursample,comparedtomedian
spectralindicesfromtheliterature.TheWindhorstetal.1993solidlineindicatesafittothemedianspectralindexα5 fortheirdata.Theothervalues
0.4/0.6
aretakenfromtabulatedresultsinIbaretal.,2009,Owenetal.,2009,Prandonietal.,2011,andMauchetal.2011(Priv.Comm).Thehorizontalerrorbars
representthefluxdensitybinforeachmedianpoint;theverticalerrorbarsarethe25thand75thpercentiles.
Table3.MedianSpectralIndexα10..4843Statisticsasafunctionoffluxden- hinedreex.,usingtheKellermanncorrection,discussedinfurtherdetail
sity
RangeinS843 Median MeanFlux Number 25th 75th
orS1.4(mJy) α01..8443 (mJy) ofsources perc. perc. 5.5.1 TheKellermannCorrection
S1.4 Kellermann (1964) noted that any observed spectral index distri-
butionisnotindependent oftheobservingfrequency.Thecorrec-
0.81-3.7 −1.134 2.50 21 −1.390 −0.676
3.7-6.4 −0.717 4.89 21 −1.016 −0.355 tionaccountsfortherelationshipbetweenobservedspectralindex
6.4-9.8 −0.533 7.68 22 −0.876 −0.275 distributionsatdifferentfrequencies. Athigher radiofrequencies,
13.5-26 −0.584 13.65 21 −0.769 −0.332
26-95.4 −0.775 36.21 20 −0.945 −0.656 wetend toseemoreflatspectrum objectsasproportionally more
sourcesareabovethefluxlimit.Incontrast,aswemovetolower
S0.843 radiofrequencies,wetendtoseemoresteepspectrumobjectsbe-
3.3-4.52 −0.818 4.04 18 −1.273 −0.825 causetheyarebrighteratthelowerradiofrequencies.Thecorrec-
4.52-6.7 −0.488 5.54 18 −1.203 −0.733
tionstatedintheAppendixofKellermann(1964)describestheoff-
6.7-11 −0.676 8.76 17 −1.210 −0.817
11-15 −0.671 12.68 18 −1.045 −0.795 setbetweenmeanvaluesofspectralindicesatdifferentfrequencies.
15-35 −0.687 22.71 18 −0.872 −0.575 WeuseEquationA5ofKellermann(1964),whereweassumewe
35-204 −0.921 62.42 16 −0.930 −0.741
havetwodistributionsofspectralindices(P(α)andQ(α)),attwo
NOTES.–Errorsonthemedianspectralindicesarecalculatedfromthe different frequencies, ν1 and ν2 respectively. Also required is x,
25thand75thpercentile.Themeanfluxdensitiesarecalculatedasthe theslopeofthenumber-fluxpower-lawN(>S)=kSx(Longair
meanofthefluxdensitiesofallthesourcesineachbin.
1966),wherek isaconstant scalingfactor, andN represents the
numberofsourcesaboveagivenfluxdensity,S.
5.5 RadioSourceCounts Q(α)=A(ν2)−αxP(α), (2)
Thedifferentialradiosourcecountsforour843MHzdataarepre- ν1
sentedinTable4.Aweightingfactorhasbeenappliedtothesource ∞
countstocorrectforincompletenessduetothenoiselevelincreas- Q(α)dα=1. (3)
Z
ingattheedgesofthefield(seeHopkinsetal.1998).Wedonotap- −∞
plyaresolutioncorrection,astheMOSThasalargebeam,andhas P(α)istheknowndistributionofspectralindicesatonefrequency
a high sensitivity to extended diffuse radio emission (Bocketal. and Q(α) is the distribution of spectral indices we wish to in-
1999;Mauchetal.2003).Thedifferentialsourcecountsareshown fer,givenbyEquation2.FollowingKellermann(1964)weassume
in Figure 12, with the SUMSS (Mauchetal. 2003) differential thespecialcasewherethesetwodistributionsareGaussian(area-
source counts, and a compilation of 1.4GHz differential source sonable assumption given the shapes of the distributions in Fig-
counts(Hopkinsetal.2003)asareferencesample.Ourdataprobes ures8and 10), andhave thesamedispersion σ,andA ischosen
the843MHzsourcecountsafactorof2fainterthanSUMSS,but such that Equation A6 of Kellermann (1964) (Equation 3) issat-
westillclearlyunderestimatethecountsinourfaintestfluxdensity isfied.Thisspecial case scenario resultsinthemean value of the
bin,duetoincompleteness. inferredspectralindexdistribution(Q(α))beingshiftedbyafac-
The reference differential source count sample at 1.4GHz tor of xσ2ln(ν1/ν2). For our sample, to shift the distribution of
from Hopkinsetal. (2003) has been shifted to 843MHz assum- the1.4GHzsourcecountcompilationto843MHz,weusedα10..4843
ing an average spectral index value. We have determined that to determine the value of the Kellermann correction for only the
α = −0.5istheappropriatevaluetousefortheaveragespectral single sources. The dispersion was found to be σ = 0.56 and
(cid:13)c 2011RAS,MNRAS000,1–18