Table Of ContentMon.Not.R.Astron.Soc.000,1–5(2001) Printed5February2008 (MNLaTEXstylefilev1.4)
A SCUBA Scan-map of the HDF: Measuring the bright
end of the sub-mm source counts
Colin Borys1, Scott C. Chapman2, Mark Halpern1, Douglas Scott1
1Department of Physics and Astronomy, Universityof British Columbia, Vancouver BC CANADA V6T 1Z1
2California Institute of Technology, Pasadena CA USA 91125
2 2001July24
0
0
2
ABSTRACT
n Using the 850µm SCUBA camera on the JCMT and a scanning technique different
a from other sub-mm surveys, we have obtained a 125 square arcminute map centered
J ontheHubbleDeepField.Theone-sigmasensitivitytopointsourcesisroughly3mJy
1 and thus our map probes the brighter end of the sub-mm source counts. We find 6
2 sources with a flux greater than about 12mJy (>4σ) and, after a careful accounting
of incompleteness and flux bias, estimate the integrated density of bright sources
2 N(>12mJy)=164+77degree−2 (68 per cent confidence bounds).
v −58
5 Key words: – galaxies: statistics – methods: data analysis – infrared: galaxies
1
5
7
0
1 1 INTRODUCTION In this paper, we present a new estimate for the num-
0 ber density of sources which are brighter than 12mJy at
h/ Detections of submillimetre emission from high redshift 850µm. A general discussion of how sources are detected
p galaxies highlight the importance of dust in the early his- is presented in the next section. To convert the detections
- tory of galaxy formation. Observations using the Submil- into a source count requires a careful study of the flux bias
o limetreCommonUserBolometerArray(Hollandetal.1999) andincompleteness,whichareunavoidableduetoconfusion
tr of small fields down to the confusion limit allow us to es- andnon-linearthresholding.SectionthreedescribesMonte-
s timate the source counts of 850µm sources below 10mJy. Carlo studies used to estimate and correct for these effects
a
: In order to learn more about source counts (and hence to andprovideapropernumbercountestimate.Finallywedis-
v constrain models), the next step is to search for brighter cuss correlations between the SCUBA scan-map and other
Xi (>10mJy) objects over somewhat larger (>100square ar- sub-mm data sets. Comparison with data from other wave-
cminute) fields. lengthsis reserved for a longer paperin preparation (Borys
r
a Thepopulationofbrightsub-mmsourcesisnotwellun- et al. 2002).
derstood. Current models (Fall, Charlot & Pei 1996; Blain
& Longair 1996; Blain 1998; Eales et al. 2000; Rowan-
Robinson 2001) for source countsin the sub-mmhave been
2 DATA COLLECTION AND ANALYSIS
able to account for the observed sources by invoking evo-
lution which follows the (1+z)3 form required to account The SCUBA detector is a hexagonal array of bolometers
forIRASgalaxies at60µm,andthepowerfulradio-galaxies withafieldofviewofabout2arcmin.Usingadichroicfilter,
and quasars (Dunlop & Peacock 1990). Euclidean mod- theradiation isseparatedinto850and450µmbandswhich
els with no evolution have a slope of roughly 1.5 (i.e. are directed toward 37 and 91 element arrays respectively.
N(>S) S−3/2),whichcannotpossiblyaccountfo−rthelack Tosamplealargeregion ofthesky,thetelescopescansthis
∝
of sources observed. With reasonable evolution (in IRAS- array along one of three special directions with respect to
motivatedmodels),thecountssteepensharplyatthe10’sof the array, chosen to ensure that sky is fully sampled. The
mJyleveltoroughly S−2.5.Giventheadditional constraint secondarymirrorischoppedatafrequencyof7Hzbetween
of not overproducing the sub-mm background, the counts a‘source’and‘reference’positioninordertoremovefluctu-
of relatively weak sources lead to little variation between ations dueto atmospheric emission.
themodels.However,atthe10–30mJybrightnesslevelvar- ThestandardSCUBAscan-mapobservingstrategyuses
iousevolutionary models(e.g. Guiderdonietal. 1998) show multiplechopthrowsin twofixeddirections ontheskyand
more parameter dependence. Moreover, given that brighter anFFT-baseddeconvolutiontechnique.Thismaybeappro-
sourcesareeasiertofollowupatotherwavelengths,theirin- priatefor regions wherestructureappears on allscales, but
vestigation may help understand thecomposition of galaxy itisnotoptimalforfindingpointsources.Theoff-beampat-
typesand their evolution. terngetsdiluted(makingitmorechallengingtoisolatefaint
(cid:13)c 2001RAS
2 Borys et al.
sources)andthemapnoisepropertiesaredifficulttounder- systematic pointing errors in our data, we re-analysed the
stand. Our approach is to use a single chop direction and Barger et al. (2000) HDF/radio fields, which are a set of
throw, fixed in orientation on the sky. The result is a map smaller maps taken within the HDF flanking field. These
that has, for each source, a negative ‘echo’ of equal ampli- mapsweretakeninthewell-usedjiggle-mapmodeandwere
tudeinapredictableposition.Althoughthechopwasfixed, accompaniedbyseveralpointingchecksandcalibrationmea-
we scanned in all three directions in order to better distin- surements. We compared the maps against our scan-map
guish signal from instrumental noise and sky fluctuations. using a nulling test, finding a shift of 4 3 arcsec to the
±
Atotalof61scanswereobtainedin3separaterunsbe- west. There is no evidence that this shift is variable across
tween 1998 and 2000. The shape of the region mapped was the field. The source of this pointing offset is not entirely
asquarecentredontheHDFandwasorientedalonglinesof understood, though we note the 3arcsec per sample scan
constantrightascensionanddeclination.UsingSURF(Jen- rateofthetelescopeandthattheshiftisalongthedirection
ness&Lightfoot1998)andourowncustomsoftware,weare of thechop.
able to isolate and remove large scale features in the maps The calibration of our map was determined by fitting
and estimate the per-pixel noise level by a careful account- the beam model to observations of standard calibrators
ingoftheper-bolometernoiseandthefrequencywithwhich taken during the run. However, many of the scan-map cal-
each particular pixel is sampled. ibrations turned out to be unusable and we had to rely on
photometric and jiggle mode calibrations obtained during
the runs. Although scan-map flux conversion factors differ
2.1 Scan mapping versus Jiggle map mosaics for from those measured in other modes, it is reasonable to
large surveys assume that they are related by a constant multiplicative
factor. Hence we were able to derive a relative calibration
Most extra-galactic sub-mm surveys previously done use a
betweennights,andbycomparingthescan-mapagainstthe
seriesofjigglemapstofullysamplealargeareaofthesky.To
Barger data, were were able to determine theabsolute cali-
ensureuniformnoisecoverage,thenumberofintegrationson
bration.
aparticularjiggle-mapfieldhastobeadjustedaccordingto
theweatheratthetimeofobservation.Thenoiselevelacross
a scan-map composed of individual scans is very uniform,
since each pixel is sampled by many different bolometers, 2.3 Source detection
whose noise is constant throughout a scan. One advantage
To construct a model beam-shape we artificially added a
of jiggle-mapping is that it is the most used SCUBA ob-
very bright source into the data and created a map using
serving mode and thus is already well understood. Also, it
our analysis pipeline. The positive lobe of the beam was
is known that the observing efficiency, ǫ (the ratio of time
Gaussian, but the negative lobe showed some evidence of
spentcollectingdatatoelapsedrealtime)forthejiggle-map
smearing.Thisisnotsurprisingconsideringthatsomeofthe
modeis higherthanfor scan-mapping, butthisis aslightly
observations were inadvertently taken using an azimuthal
misleading measure for reasons discussed below.
chop (4 out of 61 scans), and other observations were af-
In section 2.3 we describe how we measure fluxes of
fected by the ‘chop-track bug’, which caused the off-beams
point sources by fitting the beam pattern to the map. We
of some SCUBA datasets to rotate on the sky even though
denote the reduction in noise by fitting the beam pattern,
a fixedcoordinate frame was requested.
as opposed to fitting the positive beam alone, by ξ. In the
Sources were found by fitting the dual beam pattern,
case of scan-mapping, where the beam weights are +1 and
inaleast-squaressense,toeachpixelinthemap.Notethat
1,wehaveξ =√2.Thebeamweightsforjiggle-mapping,
S
− thisisequivalenttoaconvolutionofthemapwiththebeam
0.5,+1, 0.5leadtoξ = 3/2.Wehavedeterminedthat
− − J p (Eales et al. 2000) except that it also accounts for thepixel
the observing efficiencies are ǫ 0.77 and ǫ 0.52 for
J S
≃ ≃ bypixel noise.
jiggleandscan-mappingrespectively.Thenatureoftheloss
A total of six sources were found that have a peak to
of efficiency in both modes is related to the time needed to
error-of-fit ratio greater than 4. We also rotated the dual-
read out data after each exposure. In the scan-map mode,
◦
beam pattern by 180 and used that as a model; only 3
the sky is sampled 8 times more often than in jiggle-mode,
sources were found, two of which are associated with the
and hence thereadout time is longer.
Theoverallsensitivitytopointsourcesis ξǫ−0.5 and, two brightest sources in the map. Monte-Carlo simulations
∝ suggest that the other false positive is not unexpected. As
giventhenumbersabove,thejiggle-mapandscan-mapmode
anadditionalcheck,the3runswerecomparedbyeyetoen-
are found tobe almost equally sensitive.
surethateach sourcewasevidentinall subsetsof thedata.
The advantage of using scan-mapping over jiggle-maps
Anadditional6sourceswererecoveredwithaS/Nbetween
in studies of the clustering of SCUBA sources is that the
3.5and4.0.Thoughmorelikelytobespurioussources,they
latter mode is insensitive to scales larger than the array
arestill relatively bright andare includedtofacilitate com-
size. This, coupled with the uniform noise level and nearly
parison with data at other wavelengths. A complete list of
equivalent effective sensitivity should make scan-mapping
sources is given in Table 1.
thepreferred mode when planninglarge field surveys.
The map shown in Figure 1 is the output from the
sourcefittingalgorithm.Itmustbepointedoutthatbycon-
volving with the beam, the dual-beam pattern is converted
2.2 Pointing and flux calibration
into a triple beam. The positive source now has two nega-
Reliably determining the pointing of scan-maps containing tive echos of half the amplitude spaced by the chop throw
no bright sources is problematic. To check for evidence of on either side.
(cid:13)c 2001RAS,MNRAS000,1–5
A SCUBA Scan-map of the HDF 3
18
16
14
n
o
ti
a
n
cli
e
D 12
62:10
08
30 12:37:00 30 00
Right ascension
Figure1.The850µmHDFscan-map.Blackcorrespondstopositivefluxdensity.Themapsizeisapproximately11.25×11.25arcminutes.
The chop is 40 arcseconds and is roughly east-west. The circles outline the six >4σ sources detected in our survey and the diamonds
the6additiondetections above3.5σ.TheregioncoveredbyHughes etal.(1998) isdenoted bythewhiteoutlinenear thecentre ofthe
map,withtheirstrongestdetection, HDF850.1indicatedbythewhitecross.
Table 1. 850µm detections in the HDF scan-map. The top half of the table lists the
> 4σ sources in order of increasing RA. The last six entries are the weaker detections,
againorderedaccordingtoRA.
ID RA(2000) DEC(2000) S850 (mJy) S/N
HDFSMM−3606+1138 12:36:06.4 62:11:38 15.4±3.4 4.5
HDFSMM−3608+1246 12:36:07.8 62:12:46 13.8±3.3 4.2
HDFSMM−3611+1211 12:36:10.6 62:12:11 12.2±3.0 4.0
HDFSMM−3620+1701 12:36:20.3 62:17:01 13.2±2.9 4.6
HDFSMM−3621+1250 12:36:21.1 62:12:50 11.4±2.8 4.0
HDFSMM−3730+1051 12:37:29.7 62:10:51 14.3±3.2 4.5
HDFSMM−3623+1016 12:36:23.3 62:10:16 10.3±2.9 3.5
HDFSMM−3624+1746 12:36:24.2 62:17:46 12.6±3.4 3.7
HDFSMM−3644+1452 12:36:44.5 62:14:52 11.4±2.9 3.9
HDFSMM−3700+1438 12:37:00.4 62:14:38 10.1±2.9 3.5
HDFSMM−3732+1606 12:37:31.6 62:16:06 12.1±3.3 3.6
HDFSMM−3735+1423 12:37:34.9 62:14:23 13.4±3.8 3.6
(cid:13)c 2001RAS,MNRAS000,1–5
4 Borys et al.
3 SOURCE COUNTS
3.1 Completeness correction
In order to estimate the density of sources brighter than
′ ′
somefluxthresholdS ,N(>S ),wemustaccountforseveral
anticipatedstatisticaleffectsonourlistofdetectedsources.
(i) The threshold for source detection, S = mσ is not
T
uniformacrossthemapduetopixeltopixelnoisevariation.
(ii) Dueto confusion anddetector noise, sources dimmer
than S might be scattered abovethe detection threshold.
T
(iii) Similarly,sourcesbrighterthanS mightbemissed.
T
Item (iii) is simply the completeness of our list of
sources, and must take into account edge effects and pos-
sible source overlaps. For a source density N(S) which falls
with increasing flux, item (ii) typically exceeds item (iii),
resulting in Eddington bias. Thus measured fluxes tend to
bebrighter than the truefluxesof the sources.
Using Monte Carlo simulations, these two effects are
quantified by measuring f (S), the fraction of sources at
m
fluxS whichwewoulddetectabovethethresholdS =mσ.
T
Artificial sources with a range of known fluxes are added
to the time series corresponding to random locations (but Figure 2.The850µm sourcecounts. Thesolidcircleshowsthe
resultfromthecurrentwork.Countsderivedfromclusterstudies
constrained nottooverlap each other)andrunthroughour
by Chapman et al. (2001) and Blain et al. (1999) are shown by
source detection pipeline.
the solid squares and triangles respectively. The UK8 mJy sur-
One can calculate the ratio of the integrated source
veycounts(Scottetal.2001)areshownasopentriangles.Crosses
count to thenumberof sources we detect,
represent the counts fromHughes et al.(1998). Some points are
∞ slightly offset along the flux axis for clarity. Overlaid is the two
N(S)dS
γ(S′)= ∞RS′ (1) power-law model of Scott & White (solid line), and two predic-
R0 fm(S)N(S)dS tionsbasedonthemodelsofRowan-Robinson(2001).Thedashed
linerepresentsauniversewithΩM =1.0andΩΛ=0.0whilethe
where N(S)dS is the number of sources between a flux S
dottedlineisΩM =0.3andΩΛ=0.7.
and S+dS. Note that f (S) ranges between zero to unity
m
′
but γ(S ) can be larger than one depending on the form of
N(S) and choice of S′. flux; Eales et al. estimate a 40 per cent boost for their 3σ
Thecalculationofγ(S′)fromtheMonteCarloestimates sources. Note there is no need to use this factor to adjust
of f (S) requires a model of the source counts. We em- our estimate of the source counts because it is inherently
m
ploythetwopower-lawphenomenologicalformofScottand takencareofintheMonteCarlosimulationandthecounts-
White(1999), weighting; We could equivalently quote a somewhat higher
source density at 10mJy.
S −α S −β
N(>S)=N0(cid:16)S0(cid:17) (cid:16)1− S0(cid:17) . (2)
and use S0 = 10mJy, α = 0.8, β = 2.5, and N0 = 1.55 4 DISCUSSION
104deg−2. ×
We have used other available sub-mm data sets in order to
Obviously the factor γ is influenced by what model is
assess the authenticity of our detections. The map of the
used in thecalculation, and other forms of thesource spec-
HDF itself by Hughes et al. (1998) cannot be used for di-
trumarefoundintheliterature.Wefindγvariesbynomore
rectcomparison becausetheirbrightest sourcesarewell be-
than10percentacrossawiderangeofreasonableparameter
low the noise level of this scan-map. Some of sources in the
values.
BargerHDFfieldspreviouslymentionedarealsoslightlytoo
This calculation combinesall threeeffectslisted above.
fainttobesecurelydetectedgiventhesensitivityofourscan-
In the present case, effects (ii) and (iii) balance out almost
map, but the brighter ones are found. The average 850µm
exactly. We calculate γ(12mJy) = 0.95, and therefore ob-
tain N(> 12mJy) = 164+77deg−2 (68 per cent confidence flux from the seven sub-mm sources in the original Barger
−58 catalogue (Barger et al. 2000) is 8.4 0.6mJy in our re-
limit) based on the six 4σ sources found in the 125 square ±
analysis of those data. The average flux from the scan-map
arcminute map. This value is plotted along with estimates
at thesame seven positions is 8.1 1.1mJy.
from other studies in Figure 2. ±
Perhaps the most striking feature of the scan-map is
the group of three sources on the eastern edge (the first
three sources in Table 1). Since the group fits within a sin-
3.2 Flux bias correction
gle jiggle-map field, we obtained time via the CANSERV
Our Monte-Carlo studies confirm the results of Eales et al. program to confirm the existence of these three sources.
(2000) that detected sources tend to be Eddington biased HDFSMM 3606+1138 and HDFSMM 3611+1211 differ
− −
upwardsin flux.Atthe4σ levelused in thiswork, oursim- by no more than 2.5mJy between thescan-map and jiggle-
ulations indicate that the boost is 20 per cent in apparent map.HDFSMM 3608+1246isfainterbyroughly5mJybut
−
(cid:13)c 2001RAS,MNRAS000,1–5
A SCUBA Scan-map of the HDF 5
is still reasonably consistent with the flux derived from the FallS.M.,CharlotS.,PeiY.C.,1996, ApJ,464
scan-map. GuiderdoniB.,HivonE.,BouchetF.R.,MaffeiB.,1998,MNRAS,
Ifthistrioofsourcesrepresenttrueclustering,thenthe 295
sourcecountderivedheremaybebiasedbycosmicvariance. HollandW.S.,etal.,1999,MNRAS,303
HughesD.H.,etal.,1998,Nature,394
Peacocketal.(2000)havefoundweakevidenceofclustering
JennessT.,LightfootJ.F.,1998, StarlinkUserNote216
in the 2 2 arcminutemap of Hugheset al. (1998). The
∼ × PeacockJ.,etal.,2000,MNRAS,318
UK 8mJy survey (Scott et al. 2000) which covers over 250
Rowan-RobinsonM.,2001, ApJ,549
square arcminutes, also shows signs of clustering. However
ScottD.,WhiteM.,1999,A&A,346
these results are inconclusive, and what is needed is a very ScottS.,etal.,2001,MNRAS,submitted
large ( 1 degree) survey.
∼ ThispaperhasbeenproducedusingtheRoyalAstronomical
We have significantly improved statistics on sub-mm
a
source counts at the > 10mJy level. Because these sources Society/Blackwell ScienceLTEX stylefile.
are brighter than typical SCUBA detections, they may be
easiertofollowupatotherwavelengths.Preliminary analy-
sisalreadyindicatesgoodcorrelationwithµJyradiosources
andhardx-raysources,butlittleindicationofopticalcoun-
terparts (as found in other studies).
Based on there-reduction of theBarger HDFdata, we
have also found that a careful treatment of the noise map
allows us to improve the S/N for point sources by about
15%. Furthermore, we find that scan-mapping is an effi-
cientmethodformakinglargemapsforcosmologicalstudies.
Large-scale spatial instrumentaleffectsdonotappear tobe
a significant limitation for analysis of such maps.
Our careful data-reduction, confirmation in indepen-
dentjiggle-maps and extensiveMonte-Carlo studieslead us
tobequiteconfidentintherealityofoursix4σ sources.We
alsoprovidealistofsixadditionalsourcesbetween3.5 4.0σ
−
to aid in comparison with other studies.
ACKNOWLEDGMENTS
We would like to thank Amy Barger for access to her data
before it was available on the JCMT public archive, and
DougJohnstoneforseveralusefulconversations.Wearealso
gratefultothestaff attheJCMT, particularlyTim Jenness
and Wayne Holland who provided invaluable advice. This
work was supported by the Natural Sciences and Engineer-
ingResearch Councilof Canada. TheJames Clerk Maxwell
TelescopeisoperatedbyTheJointAstronomyCentreonbe-
halfoftheParticlePhysicsandAstronomyResearch Coun-
cil of the United Kingdom, the Netherlands Organisation
for Scientific Research, and the National Research Council
of Canada.
REFERENCES
BargerA.J.,CowieL.L.,RichardsE.A.,2000,AJ,119
BargerA.J.,CowieL.L.,SandersD.B.,1999,ApJ,518L
Blain,A.W.,1998, MNRAS,295
BlainA.W.,LongairM.S.,1996,MNRAS,279
Blain A.W., Smail I., Ivison R., Kneib J., 2000 in A. J. Bunker
&W.J.M.vanBreugheleds,ASPConf.Ser.Vol.193,ASP:
SanFrancisco
BorysC.,ChapmanS.C,HalpernM.,ScottD.2002,inprepara-
tion.
ChapmanS.C.,Scott D.,Borys C.,FahlmanG.,2002, MNRAS,
330
DunlopJ.S.,PeacockJ.A.,1990, MNRAS,247
EalesS.,EdmundsM.G.,1996,MNRAS,280
EalesS.,LillyS.,WebbT.,DunnL.,GearW.,ClementsD.,Yun
M.,2000, AJ,120
(cid:13)c 2001RAS,MNRAS000,1–5
