Calibrated and completeness-corrected optical stellar density maps of the Northern Galactic Plane

6.2 MB·

by  H. J. Farnhill

Mon.Not.R.Astron.Soc.000,1–19(2015) Printed13January2016 (MNLATEXstylefilev2.2)
Calibrated and completeness-corrected optical stellar
density maps of the Northern Galactic Plane
H. J. Farnhill1(cid:63), J. E. Drew1, G. Barentsen1,2, E.A. Gonza´lez-Solares3
1School of Physics, Astronomy & Mathematics, University of Hertfordshire, College Lane, Hatfield, AL10 9AB, U.K.
6 2NASA Ames Research Center, Mail Stop 245-30, Moffett Field, CA 94035, USA
1 3Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 OHA, UK
0
2

n Draftlastcompiled13January2016
a
J

2 ABSTRACT
1 Following on from the second release of calibrated photometry from IPHAS, the
INT/WFC Photometric Hα Survey of the Northern Galactic Plane, we present

] incompleteness-correctedstellardensitymapsintherandiphotometricbands.These
A
have been computed to a range of limiting magnitudes reaching to 20th magnitude
G
in r and 19th in i (Vega system), and with different angular resolutions – the highest
. resolution available being 1 square arcminute. The maps obtained cover 94 percent
h
of the 1800 square-degree IPHAS footprint, spanning the Galactic latitude range,
p
5 < b < +5 , north of the celestial equator. The corrections for incompleteness,
- ◦ ◦
o d−ue to confusion and sensitivity loss at the faint limit, have been deduced by the
r method of artificial source injection. The presentation of this method is preceded by
t
s a discussion of other more approximate methods of determining completeness. Our
a
method takes full account of position-dependent seeing and source ellipticity in the
[
survey database. The application of the star counts to testing reddened Galactic disc

1 models is previewed by a comparison with predicted counts along three constant-
v longitude cuts at (cid:96) 30 , 90 and 175 : some over-prediction of the most heavily
◦ ◦ ◦
3 reddened (cid:96) 30 cou(cid:39)nts is found, alongside good agreement at (cid:96) 90 and 175 .
◦ ◦ ◦
8 (cid:39) (cid:39)
9 Key words: Galaxy: disc – Galaxy: structure – Galaxy: stellar content – dust,
2 extinction – atlases
0
.
1
0
6 1 INTRODUCTION Marshall et al. 2006; Sale et al. 2009, 2014). In the next
1
5-10 years, these advances will complement the astrometric
: The positioning of the Solar System almost in the equato-
v harvest being gathered by the Gaia mission and usher in
rial plane of the Milky Way places a significant obstacle in
i a much better, sharper vision of the 3D Milky Way. Nev-
X the way of understanding the structure of our own galaxy.
ertheless, the anticipated Gaia parallax precision at fainter
r DespitethefactthatthediscoftheMilkyWayiseffectively magnitudes (100µarcsec at G∼19) will still leave stars be-
a the largest object in the night sky, offering vastly superior
yond the first 1–2 kpc with distances known to a precision
angularresolutioncomparedtothatachievableforanyother
nobetterthan∼10-20percent.Accordingly,itremainsuse-
galaxy,sightlinesatlowGalacticlatituderemainachallenge
fultosupplementourknowledgethroughtheapplicationof
to decipher because of large and variable amounts of dust
othermethodsthatcantestpredictiveGalacticmodels.One
extinction. Given that the formation and maintenance of
of these, that puts to good use the uniquely detailed view
galactic discs is an important problem in galaxy evolution
wehaveoftheGalacticdisc,iscomparisonwithmagnitude-
(vanderKruit&Freeman2011),animprovedvisionofour
limitedstarcounts.Thisapproachhasbeenappliedsuccess-
own galactic disc is needed. And as our home in the Uni-
fully in the past and continues to be influential in guiding
verse, it is of interest in its own right.
the content of Galactic models (Robin et al. 2003; Czekaj
The reliable empirical determination of the 3-
et al. 2014).
dimensional (3D) distribution of the Milky Way’s interstel-
lardust,neededtomakesenseofthedisc,isnowbecoming Sofar,deeperopticalstar-countmappinghasonlybeen
possiblethroughincreasinglysophisticatedanalysesofcom- carried out in the southern Galactic plane (Ruphy et al.
prehensive digital survey data (Drimmel & Spergel 2001; 1997). The options to conduct a well-calibrated stellar den-
sity mapping of the northern sky are now appearing in the
wake of data product releases from wide-area digital imag-
(cid:63) E-mail:[email protected] ingsurveys(Stoughtonetal.2002;Magnieretal.2013).The
(cid:13)c 2015RAS
2 H. J. Farnhill et al.
greatestchallengeisatlowGalacticlatitudes,buteventhis 20.0 in i, achieved at a median seeing of 1.1 arcsec. The
isnowbecomingtractableasthe1arcsecangular-resolution typical external photometric precision of DR2 is close to
IPHAS (Drew et al. 2005), and UVEX (Groot et al. 2009) 0.03magnitudes,asjudgedbycomparisonswithSDSSDR9
surveys approach completion. In particular, the recent re- data. In Galactic longitude, this survey spans the range
lease of IPHAS DR2 (Barentsen et al. 2014), offering uni- 30◦ <(cid:96)<215◦.Intimeitwillbefullycomplementedbythe
formphotometryofthenorthernGalacticPlaneinr,i(and VPHAS+ survey (Drew et al. 2014) covering the Southern
Hα),providesthebasisforapreciseanddeepstellardensity Galactic Plane and Bulge.
map across almost 1800 square degrees. A highly characteristic feature of the IPHAS survey,
In this work, we describe the construction of r, i stel- due to its targeting the Galactic Plane, is that the stars
lar density maps at a range of angular resolutions, up to a dominatingthefaintendofthecapturedrandibandmag-
maximum of 1 square arcminute, based on IPHAS DR2. In nitude distributions are typically either intrinsically red or
orderthatthismappingisnothamperedbyvariableobserv- highly reddened. Consequently, a reasonable generalisation
ing conditions and correspondingly variable levels of source to apply is that at r = 19, stars captured by the survey
loss, great care has been taken to make corrections for in- are typically brighter in i by around one magnitude (in the
completenessbyevaluatingtheresultsofartificialsourcein- Vega system, adopted by the survey – see figs. 15 to 17 in
jection tailored to every survey field. In the Galactic Plane Barentsen et al. (2014)). Because of this, in the presenta-
where confusion can present as a significant issue, it is im- tion that follows, comparisons between the r and i density
portant to do this reliably. Because literature presentations maps obtained are generally drawn between those derived
of source injection and other methods of correction have so for r=19 an i=18 limits.
farbeenlimited,(butseee.g.Harveyetal.(2006)formore WhilstIPHASiscertainlyuniforminitsexecution,the
than usual detail), we present a reasonably full description weatheratthetelescoperepresentedanimportantvariable.
ofhowwearriveattheposition-andmagnitude-dependent The observations were obtained via standard allocations of
corrections applied. This is presented in sections 3.3 to 3.7, time, with the result that a wide variety of observing con-
afterabriefrestatementofthemainfeaturesoftheIPHAS ditions are contained within the survey database. Thanks
surveyinsection2andsomeappraisalviatwomoreapprox- to the opportunity to obtain repeats of fields exposed in
imate techniques in sections3.1 and 3.2. poorconditions,itwaspossibletoapplyqualitycutsinthe
Theresultingcorrectedr,istellardensitymapsarede- preparation of IPHAS DR2 so as to omit clearly inferior
scribed and briefly discussed in section 4. The maps them- data, whilst still achieving over 92% coverage of the survey
selves,withmaximummagnitudelimitsofr=19andi=18 footprint.Evenso,thereisstillabroadqualityrangewithin
respectively (Vega system), are presented as plots within DR2 in terms of both measured widths of the point spread
anAppendixandareprovidedwithinmachine-readableon- function(PSF),andlimitingmagnitude(forfulldetails,see
line supplementary material. In section 5, a first purely- Barentsen et al. 2014). This variation, along with over a
illustrativecomparisonismadebetweencountsderivedfrom factor of ten contrast in the typical observed stellar density
the i < 18 map and Galactic model predictions. This uses along the Northern Plane (see Fig. 3 in Gonz´alez-Solares
two distinct reconstructions of the 3D distribution of in- etal.2008),makesitimportanttoachieveuniformityofout-
terstellar extinction in order to gain a first impression of come through careful position-dependent completeness cor-
how influential the choice of extinction map can be. Inter- rections. This task, along with the development and appli-
estingly, the results from this preliminary exploration are cationofanalgorithmthatensuresreliablesourcecounting
alreadymixed:wefindthatat(cid:96)(cid:39)90◦ and175◦,theagree- without duplication and proper accounting for small gaps
mentbetweenthestarcountsandmodelpredictionisgood and other irregularities in the data, is described here (see
–butatthelowestGalacticlongitudeexamined,(cid:96)(cid:39)30◦,a also Farnhill 2015).
significant discrepancy appears. The first step in this process is to establish a working
The paper ends in section 6 with some concluding re- definition of a detected ’star’ in the survey data.
marks, including comment on the best use of these star-
count maps.
2.2 On morphological classification and the
expected number density of extra-galactic
sources
2 OBSERVATIONS AfractionofsourcesdetectedinDR2fieldsareknowntobe
misclassified as non-stellar towards field edges - this is due
2.1 IPHAS broad-band photometry
toprogressivedistortioninthePSFwithincreasingdistance
The most recent release, DR2, of the INT/WFC Photo- from the optical axis (OA) of the INT/WFC system. This
metric Hα Survey of the Northern Galactic Plane (IPHAS) pattern of behaviour has a small impact on the final DR2
was presented by Barentsen et al. (2014), while the ba- catalogue, which provides primary detections that are se-
sic specification of IPHAS was set down by Drew et al. lectedaccordingtoacriterionoflowestdistancetotheOA.
(2005). This survey, conducted using the Wide Field Cam- But whencountingstellar sources (morphological classes -1
era (WFC) mounted on the Isaac Newton Telescope (INT) and -2) from a single field to produce a stellar density map
inLaPalma,providesphotometryofthecompleteNorthern the issue of progressive misclassification has to be tackled.
Galactic Plane within the latitude range −5◦ < b < +5◦, Fig. 1 shows an example of a field exhibiting this problem.
in narrow-band Hα and broadband Sloan r and i. It is the Assuming a constant ratio of stellar to non-stellar
broadbands that are the focus of this paper. The typical sources applies in reality across any one field, comparisons
5σ magnitude limit reached in the survey is 21.2 in r and between5sq.deg.regionsatfieldcentresandedgesrevealed
(cid:13)c 2015RAS,MNRAS000,1–19
Stellar density maps of the Northern Galactic Plane 3
catalogues. We then go on to describe our chosen method
ofincompletenesscorrectionbasedonartificialsourceinjec-
tion.
3.1 Confusion, as estimated from
nearest-neighbour analysis
Confusion, the effect of background noise caused by unre-
solved sources, scales with source density (Condon 1974).
Forrandomlydistributedsources,theprobabilityoffinding
agivennumberofneighbourswithinangulardistanceθ can
Figure 1.Distributionsofsourcesclassifiedasstellar(rClass= be described by a Poisson distribution, which leads to the
−1, blue) and non-stellar (rClass = +1, red) in the r-band for nearest neighbour distribution
IPHASfield4975o aug2004a.
n(θ)=2ρ2Ωπθe−ρπθ2 (1)
where ρ is the density of stars per unit solid angle, and Ω
occasional misclassification of several hundred sources. Of
is the sky solid angle of interest, as presented in Bahcall &
course,someoftheseobjectsarenotmisclassified–theycan
Soneira (1983).
be genuine examples of galaxies presenting as extended ob-
Fig. 2 shows this distribution for a sky area matching
jects.Todeterminetheexpectednumberofgalaxiesdetected
thatoftheWFCfieldofview(0.29sq.deg.)containingdif-
inasimilararea,galaxycountsweretakenfromYasudaetal.
ferentnumbersofsources.Itcanbeseenthatincreasingthe
(2001), down to the 5σ r- and i-band limits of IPHAS, and
density of sources increases the number of nearest neigh-
then extinguished by the median Schlegel et al. (1998) ex-
bours at small separations, while lowering the number at
tinction values for all fields (corrected using the Schlafly &
greater separations, thereby pulling in the peak separation
Finkbeiner (2011) recalibration). Based on median limiting
magnitudes, ∼1 extragalactic source is predicted per 5 sq. value, θmax. Equation 1 holds for a population of sources
randomly distributed regardless of brightness. A posteriori
deg.region.Againststellardensitiestypicallyordersofmag-
checkshaverevealedthat,atthe∼1arcsecresolutionchar-
nitude larger, this is very small. It was therefore regarded
acteristicof IPHAS,theangular distribution ofstars inthe
assafetoinclude’non-stellar’+1classifiedsourcesforden-
northern Galactic plane conforms quite well to the random
sitymappingpurposes-thelossesthatwouldbesufferedon
case: essentially we find that the Rn statistic or the ratio
leavingthemout,infieldssimilartothatdepictedinFig.1,
of observed mean nearest-neighbour separation to the pre-
aremuchlargerthanisthelikelycontributionfromgalaxies.
dicted (random) value is commonly between 1 and 1.1, per
field.Ifclusteringweresignificant,orindeedclosepairsdue
to stellar multiplicity were frequent, Rn would be pulled
3 COMPLETENESS CORRECTION
down well below unity. In this context it is worth noting
Genuine astronomical sources falling within IPHAS detec- the following feature of IPHAS star counts: the magnitude
tion limits can fail to appear in the resulting photometric range from ∼ 13th to 20th begins to sample the Galactic
catalogues for a number of reasons. Planefromdistancesof0.5–1kpc,atthebrightend,outto
Detector issues can prevent sources from being picked 4 or more kpc depending on sightline. Accordingly IPHAS
up: the WFC is a 4-CCD mosaic leaving gaps between the starcountssayprobetheGalacticdiskbeyondthefirstkilo-
component detectors, and there are also bad columns and parsec, rather than the solar neighbourhood.
regions of vignetting that will hinder detection. In the ma- Inordertoreproducethetheoreticaldistribution(Eqn.
jority of such cases (but not quite all), missing sources will 1), all sources in the area Ω would need to be recovered.
bepickedupintheoffsetpartnerpointing,orintheoverlap This will never be the case in dense fields, which will mod-
with a neighbouring field. ify the observed distribution in the sense that the smallest
More significant and pervasive losses affecting the final separations will be under-reported - appearing to relatively
star counts are those due either to confusion promoted by boost the proportion of nearest neighbours at larger values
highstellardensitiesortostatisticalsensitivitylossesatthe of θ.
faintlimitfordetection.IntheGalacticplaneatlowerlongi- ThreetestcasesareshowninFig.3:theseIPHASfields,
tudes,wherethestellardensityinIPHAScanreachtomore locatedaround(cid:96)∼32◦,werechosenbecausetheylieinare-
than100,000persquaredegree,confusionwillbeespecially gionofthesurveycontainingfieldsspanningawiderangeof
important and liable to determine the effective magnitude densities.Then(θ)distributionsweregeneratedbyselecting
limit.OutsidetheSolarCirclewherethetypicalstellarden- subregionsoftheCCDssuchthataborderofwidth30(cid:48)(cid:48) was
sity is around 20,000 per square degree, confusion has only excluded – the nearest neighbour would then be identified
marginal significance: in this domain the median 1.1 arcsec foreachsourcewithinthecentralsubregion.Thisapproach
point spread function (PSF) implies 70 ’beams’ per source, eliminates from consideration sources close to CCD edges
to be compared with the rule of thumb confusion threshold whosenearestneighboursarelikelytobelocatedintheim-
of 30 per source (see Hogg (2001)). Both kinds of incom- ageplanebeyondthedetectoredge,whilstitrightlypermits
pletenessareexacerbatedbyrelativelypoorseeing.Wefirst the nearest-neighbour search for each central-region source
considerapproximatemethodsofcorrection,togaininsight to extend into the borders. The border width was set at
into the role source confusion is playing within the IPHAS 30(cid:48)(cid:48) after obtaining initial nearest neighbour distributions
(cid:13)c 2015RAS,MNRAS000,1–19
4 H. J. Farnhill et al.
0.06 0.16 0.25
θ = 10.0 θ = 4.0 θ = 3.0
max max max
0.14
0.05
0.20
0.12
0.04
0.10
0.15
n(θ)0.03 n(θ)0.08 n(θ)
0.10
0.06
0.02
0.04
0.05
0.01
0.02
0.00 0.00 0.00
0 5 10 15 20 0 5 10 15 20 0 5 10 15 20
θ(arcsec) θ(arcsec) θ(arcsec)
Figure3.NearestneighbourdistributionsforthreeIPHASfields,normalisedtoallowtheoverplottingoftheoreticaldistribution(dashed
line).Densityoffieldsincreasefromlefttoright.
close to describing the field as if confusion were not an is-
6000 sue. We have exploited this property as a means to gauge
No. sources confusionlossatsmallseparations.Wehavefitteddistribu-
5000 35000 tionsgeneratedfromEqn.1totheobserveddistributionsat
30000 >10(cid:48)(cid:48) separation,varyingρsuchthatthenumberofsources
4000 25000 in a field ranged from half to twice its observed value. By
20000 calculating χ2 for each fit at large separations, the best fit-
15000
(θ) 3000 10000 tingvalueofρwasfoundforeach,identifyingthecorrection
n that should be applied for confusion.
2000 Fig. 4 shows the effect of confusion on the survey as a
whole.Thebestfittingn(θ)distribution(correspondingtoa
1000 theoretical unconfused source count) was obtained for each
IPHASfield,allowingapicturetobebuiltupoftheimpact
0 ofconfusion.Thestatisticchosentorepresentthemagnitude
0 5 10 15 20 25 of the correction is the ratio of observed sources, where the
predicted
θ (arcsec) “predicted” source count is the count corresponding to the
bestfittheoreticaln(θ)distribution.Inordertounderstand
Figure 2. Theoretical distribution (see Equation 1) of nearest the variation in confusion at different limiting magnitudes
neighbourdistancesforanareawiththeeffectiveareaofaWFC
m ,fitswereperformedonsourcesbrighterthanrespectively
0
image,forfieldscontainingvaryingnumbersofsources.
18th, 19th and 20th magnitudes in r, in addition to fits
across all sources.
In a perfect survey capable of deblending overlapping
whichshowedthatthegreatmajorityofnearestneighbours sources, all fields would exhibit zero confusion, with their
occurred at smaller separations than this (see e.g. Fig. 2). curves jumping from zero to 100% of all fields at a ratio
The fields are displayed in order of increasing density. of 1.0. In reality some sources will always be lost to con-
The left-most field, shown contains 3,966 sources - a num- fusion, with the impact increasing – the higher the density
bersufficientlylowthatconfusionwouldnotbeexpectedto ofobjects.Fainterobjectssuffermorefromconfusionlosses
makeasignificantcontributiontoincompleteness.Thefields as their PSFs are more likely to be lost in the vicinity of
presented in the middle and right panels, containing 24,291 brightersources,inadditiontotheirintrinsicallyhigherden-
and49,150sourcesrespectively,sufferfromincreasinglevels sities(seeFig.6forexamplesofthemagnitudedistributions
of confusion. The overplotted theoretical distribution gives of IPHAS fields). Fig. 4 demonstrates this behaviour as the
an idea of the amount of confusion; at low field densities, incompleteness takes hold for a greater number of fields as
the empirical and theoretical distributions agree quite well, the cut-off magnitude m0 is increased.
whileathigherdensitiesthetheoreticaldistributionsclearly Forafractionoffieldsatallvaluesofm ,thebestfitto
0
predict closer nearest neighbours than measured. their nearest neighbour distributions indicates a lower pre-
While the observed nearest neighbour distribution is dicted number of sources than is actually observed. Indeed
affected by confusion most significantly at smaller ((cid:46) 10(cid:48)(cid:48)) themediancompletenessatbrighterm0 showssignsofcon-
separations, the observed number of nearest neighbours at vergingto0.98–0.99.However,wenoticethatthemaximum
larger separations will be less affected. Hence, the theoreti- ratio returned is an unphysical ∼1.1, for fields which lie in
cal distribution best fitting the tail at large θ values comes regions of lowest density in the map of the Plane. We take
(cid:13)c 2015RAS,MNRAS000,1–19
Stellar density maps of the Northern Galactic Plane 5
1.0 n
0.8 FaintNliomne. CFOV112400000000 irHα 10−1onfusio
ctionoffields00..46 rrr===211098 objectsinWF1068000000000000 1100−−32bjectslosttoc
Fra0.2 umberof 2400000000 1100−−54ctionofo
N a
0.0 0 Fr
0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.0 1.5 2.0 2.5
Ratioofobservedtopredictedobjectcounts Seeing(arcsec)
1.0 Figure5.CorrectionterminEqn.2fortherangeofnsrc=ρ(cid:48)×
Faintlim. ΩWFC and θFWHM. Median seeings for each filter are marked
by vertical lines. The white region denotes the domain where
0.8 None
Equation3istrueandEquation2breaksdown.Notethatvertical
fields0.6 ii==2109 sbcyaltehecoWnvFeCrtsfotootpthrientsooufr0ce.29cosuqnutapreerdesqgrueaerse.degree on dividing
of i=18
n
ctio0.4 i=17
a
Fr
3.2 Other approximate measures of completeness
0.2
A formula for correcting for the number of sources lost to
0.0 confusion, that is based upon Eqn. 1, may be written
0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10
Ratioofobservedtopredictedobjectcounts ρ=−ρ(cid:48)log(cid:0)1−4ρ(cid:48)πθF2WHM(cid:1) (2)
observed 4πθ2
Figure 4. Cumulative histogram of source counts in FWHM
predicted
r (upper panel) and i (lower panel), where the predicted counts where ρ is the actual source density, ρ(cid:48) is the observed
were estimated by fitting Equation 1 to the tail of the nearest density, and θFWHM is the seeing in which the field was
neighbour distribution. The curves in both panels represent the observed. The expression was derived by Irwin & Trimble
ratioasdeterminedforsourcesdowntodifferentlimitingmagni- (1984), and it was used to correct the observed n(θ) distri-
tudes,plusaninstancewherenolimitwasplacedonthemagni- butions directly in Gonza´lez-Solares et al. (2008). Clearly
tudeofsources. fieldswithpoorerseeingandhigherdensitieswillbesubject
tolargercorrections;Gonza´lez-Solaresetal.(2008)reported
that the IPHAS Initial Data Release fields suffering from
thisasanindicationthatthefittingtothen(θ)distribution greatest confusion were missing 41% of their sources.
tails has an associated uncertainty of ∼10% . So large an However Eqn. 2 does not hold for for the entire [ρ(cid:48),
uncertaintyindicatesthatthismethodforcorrectingsource θFWHM] space covered by all IPHAS DR2 fields - it breaks
counts isnot itselfsufficiently exactto adopt itfor applica- down in dense fields, where the seeing is appreciably worse
tion across the survey. A significant contributing factor to thanthemedian.Fig.5showsthevariationofthecorrection
this uncertainty is the adoption of a single nearest neigh- termfortherangeofparametersrelevanttoDR2.Thewhite
bour distribution for each IPHAS field. Marked variations region shows the parameter space in which Eqn. 2 is not
or gradients in stellar density (due particularly to changing applicable, where
extinction) onscales of several arcminuteswithin fields will 4πρθ2 >1 (3)
introduce error into the corrected count inferred from the
tail of the nearest-neighbour distribution – this is behind Althoughthisdomainisonlystrictlyenteredbyfewerthan
theunphysicalunder-predictionnotedabove.Cuttingfields 20 fields, the performance of this approximate formalism –
up into smaller subregions would bear down on this source well-suited to low density halo fields – degrades as the do-
oferror,atthepriceofreducingthenumbersofobjectscon- main is approached at the high densities encountered away
tributing to each distribution. The more fundamental lim- from the mid-Plane inside the Solar Circle. For this reason,
itation on the utility of this technique is that it does not itsdeploymentacrossthesurveyisnotthepreferredoption.
easilyprovidecompletenessasafunctionofstellarapparent An approach used in several previous large-area sur-
magnitude. veys (Ruphy et al. 1997; Cambr´esy et al. 2002; Lucas et al.
Nevertheless, Fig. 4 can be regarded as a first demon- 2008) is to estimate the completeness limit by taking the
stration that, as a general rule, at r < 19 the impact of magnitude distribution of sources and identifying at which
confusion in IPHAS is small while, as might be expected, magnitude the distribution begins to drop off. As part of
it is close to ubiquitous at r > 20. Source counts in the i a study of stellar populations in the Galactic Plane nearly
band are higher thanks to the lower extinction – the same two decades ago, Ruphy et al. (1997) noted that evaluating
plot for this band shows that confusion becomes a minor completeness based on recovery from simulated images is
consideration once i<18. quantitativelythesuperioroption,butforsimplicitykeptto
(cid:13)c 2015RAS,MNRAS000,1–19
6 H. J. Farnhill et al.
the alternative of a completeness limit based on star-count alogues of CCD 4 only. Using only one of the WFC CCDs
histograms of uncrowded fields. This approach may serve perfieldcutstheprocessingtimebyafactoroffour,bring-
well in studies of limited sky regions, or if sources fainter ing the total time necessary to compute the completeness
than the deduced completeness limit can be set aside with- of the entire survey down to a little over one week (using a
out causing problems. In this same study, confusion due to high-performance multi-node cluster). Due to the fact that
crowding was recognized as the dominant source of incom- DR2 preferentially selects sources from around field centres
pleteness,whilst“slightvariationsduetotheobservingcon- (closer to the OA), CCD 4 – the most central of the mo-
ditions”werejudgedtoberelativelyunimportant.Thislast saic – was selected as the chip to represent each field (see
presumption would be unsafe here. Section 3.7 for further discussion).
Cambr´esy et al. (2002) estimated their completeness Themainstepsofthecompletenesscalculationwereas
from the turnover of 2MASS magnitude distributions, and follows. First the typical properties of an image were deter-
reason that their density maps would show imprints of in- mined, and used to generate synthetic sources that closely
dividual observations had they overestimated their limiting resemble genuine stellar sources (Section 3.4). The parame-
magnitudes. This would certainly be the case for IPHAS - ters of these synthetic sources were recorded and then cat-
withoutanymagnitudecutinplace,thefield-to-fieldvaria- alogues were generated, via the pipeline software, from the
tion of densities is extremely obvious. In applying a similar new frames with the added synthetic objects. The tables of
treatment of incompleteness, Lucas et al. (2008) quote the syntheticsourceparameterswerecross-matchedagainstthe
90%completenesslimitoftheUKIDSSGalacticPlaneSur- newly generated catalogues, and the rate of recovery was
vey, noing that in uncrowded fields the modal depths vary measured (Section 3.6). The fraction recovered at different
by 0.25 mag due to observing conditions. This method still magnitudes will allow a completeness curve to be built up
depends heavily on the turnover in the magnitude distribu- foreachfield,resultingintailoredcorrectionsthatcanthen
tion, and relies on “visually extrapolating” the histogram. be applied across the entire survey.
A single completeness statistic as provided by Lucas
etal.(2008)couldbeusedtoapplyauniformcompleteness
3.4 Simulating stellar sources
correction, although this assumes that all fields in a survey
sufferfromthesamepatternofincompleteness.Evenifthis
Thecomplexityofsimulatingstellarsourcesdependsonthe
wereindeedthecase,onlythecountofsourcesbrighterthan
accuracywithwhichtherealsourcesaretoberecreated.The
the given completeness limit could be corrected; it is not
simplestapproximationofstellarimagestotwo-dimensional
possible with this information to correct the count going
Gaussians,canbeseentobeoverlysimplisticfromacursory
deeper.
glance at the reduced IPHAS images. Almost all IPHAS
Fig. 6 shows the magnitude distributions for three
frames exhibit some degree of ellipticity (up to e=0.2 (see
IPHAS fields. A visual inspection would suggest that in-
Barentsen et al. (2014)), requiring non-symmetric artificial
completeness sets in at ∼20th mag or fainter in r and at
sources. Elliptical 2D Gaussians were therefore chosen as
∼19th in i and Hα. Attempts to automate the determina-
sufficiently realistic profiles for artificial stellar sources (see
tion of turnover magnitude for all fields are hampered by
Section 3.6 for further discussion).
thefactsthatthemodeofthesedistributionsaredependent
The parameters returned by the aperture photometry
on the chosen binning, and that the magnitude distribu-
performedontheDR2imagesindicatethefollowingshould
tions of many fields plateau before dropping off. But it is
be included to accurately recreate a stellar source:
already clear from the previous section and Fig. 4 that the
full picture is more complicated, with some small residual • Flux
sourcelossstillaffectingmagnitudesasbrightas18to19.In • FWHM
short, there is good reason to address correction rigorously • Ellipticity
on a field by field basis. • Position angle
• Coordinates (or pixel position on detector).
3.3 Artificial source injection The choice of each is described below.
A thorough treatment of incompleteness in any survey re-
quires measuring its sensitivity to sources over the entire 3.4.1 Flux
magnitude range of interest - this is best achieved by sim-
The relation between total flux and magnitude was deter-
ulating observations and then processing these simulated
mined per field by fitting a power law to the photometry
framesinthesamewayastheoriginaldata.Thismethod(in
returned by imcore.
additiontothemagnitudedistributionmethoddiscussedin
In order to insert a source of a given magnitude m ,
Section3.2)wasusedanddescribedbyHarveyetal.(2006) 0
it is necessary to understand what flux in counts per unit
aspartofastudyofinterstellarcloudsobservedbySpitzer.
time that source should have. The magnitude of an object
Such an approach is much more powerful, as statistics
is determined by
can be returned on magnitude bins, rather than on the en-
c
tire magnitude distribution down to a specified faint limit. m=ZP −2.5×log −APCOR−PERCORR (4)
It entails the simulation of sources of all magnitudes, re- 10 t
semblingtherealdataascloselyaspossible,whilstavoiding where ZP is the photometric zeropoint of the image as de-
undue cost in terms of both computing power or time. termined via the DR2 uniform calibration (Barentsen et al.
Forthepurposesofcorrectingthedensitymap,thecom- 2014),cisthemeasuredcountswithinthedefinedaperture,t
pletenessofeachfieldwasassessedusingtheimagesandcat- isexposuretimeinseconds,whileAPCORandPERCORR
(cid:13)c 2015RAS,MNRAS000,1–19
Stellar density maps of the Northern Galactic Plane 7
3533 dec2006 4450 jul2009 4378 jul2009
1400 9000 14000
1200 r-band 8000 12000
bjects 1000 iH-bαand 67000000 10000
o 800 5000 8000
of
r 600 4000 6000
e
b 3000
m 400 4000
u 2000
N
200 1000 2000
0 0 0
10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24
Magnitude
Figure 6. Magnitude distributions for three IPHAS fields of increasing density. From left to right, fields have r-band source counts of
18,113,99,061and153,430.ArequirementthatsourcescountedherehavenBands>1placesthegreatestconstraintoni-bandcounts,
asreddersourcesarepickedupinthei-bandonly.
are small correction terms. APCOR is an aperture correc- spectively). As with FWHM, the imcore ellipticity value
tiontermcalculatedbythepipelinesoftware,imcore,which per field was used in artificial source generation.
uses the curve-of-growth of stellar sources to determine the
correction required to transform the chosen aperture mea-
surement to total flux (Irwin & Lewis 2001). PERCORR 3.4.3 Position angle
is a sky calibration correction, obtained by comparing dark
skyregionswiththemedianacrosseachCCD.ZP,APCOR Thetypicaldistributionofpositionangle(PA)withinafield
and PERCORR are all taken from the pre-existing cata- isquitebroadandnon-Gaussianinappearance.Inpractice,
logue headers. thereisnoreasontoexpectthechoiceofPAtosignificantly
influencetheabilitytorecoveranartificialsource–henceit
issetatzeroforfieldswherenoobviouspeakinthePAdis-
3.4.2 PSF shape parameters: Full-width at half-maximum tributionwasobserved,otherwiseartificialsourcePAswere
and ellipticity drawn from the best fit to the peak of the PA distribution.
InitiallytheparametersofgenuinesourcesinIPHASframes
were determined by fitting elliptical two-dimensional Gaus-
sian profiles to each source detected by imcore, building 3.4.4 Position
up lists of best fit parameters for the purpose of generating Object x and y pixel positions were drawn randomly from
realistic artificial sources. Parameters of sources were ex- uniform distributions across the 2048×4096 pixels of the
cludedfromtheselistsiftheyexhibitedoneofthefollowing WFC CCDs.
behaviours: The completeness calculated for the unvignetted CCD
• The source position returned is further than 5 pixels 4ofeachfieldwastakentorepresentthecompletenessover
from the position reported by imcore - these fits are likely all four CCDs. This allowed the border zone – which can
complicate the appraisal of completeness – to be easily de-
to have been disturbed by nearby sources
• The peak value of the best-fit Gaussian is > 55000 fined: a rectilinear zone 10 arcsec (or 30 pixels) wide inside
the CCD edges was imposed such that no artificial source
counts-thisistheregimefortheWFCwherebrightsources
could be placed within it. This made sure that no injected
saturate, distorting the PSF.
artificial source would lose flux across the CCD edge.
The best fit full-width half maximum (FWHM) val-
uesreturnedforthesemi-majorandsemi-minoraxesofthe
sourcesweregatheredforeachofthefieldsenteringthisex-
3.5 Practical implementation of artificial source
ploration, and Gaussians were then fit to the distribution
injection
to recover the distribution mean and σ. The FWHM value
representative of each field returned by imcore fell within Ideally measuring the completeness using artificial sources
1σ ofthemean,confirmingthatthepipeline-specifiedvalue would be done by adding a single source at a time, veri-
can be re-used safely for articial source generation. fying whether or not it is detected. This process would be
Similarly, the measure of field-wide ellipticity returned repeated as many times as required to obtain decent statis-
by imcore was found to agree with the typical ellipticities tics, for the entire magnitude range of interest. This would
obtained in the process of fitting Gaussians to each object be the route taken in the absence of any limitations on ei-
across the field using the relation ther time or computing resources. The limiting factor here
is the computing time taken for the basic step of catalogue
e=1− FWHMmin (5) generation (20 sec). To generate the number of sources de-
FWHMmaj tailed in Table 1 it would take ∼ 65 hours to process just
(where FWHMmin and FWHMmaj are the full-width half- one field.
maxima along sources’ semi-minor and semi-major axes re- To reduce the cost, multiple sources must be inserted
(cid:13)c 2015RAS,MNRAS000,1–19
8 H. J. Farnhill et al.
minimize noise where the most significant corrections arise,
Magnitudebin
M increases from 10 to 15 at m = 19.5, and then to 20
0
Start End N M No.sources at m = 20.0. This setup requires around 2.2 hours (∼20
0
s × 410 imcore runs). For the 14,115 fields that make up
11.0 11.25 10 10 100
DR2,thisresultsinatotalcomputingtimeof∼31000hours.
11.25 11.5 10 10 100
.. .. .. .. .. Utilizing128CPUssimultaneously,aswasdonehere,brings
. . . . .
thetotaltimetoestimatecompletenessfortheentiresurvey
13.5 13.75 10 10 100
in a single band to ∼10 days.
13.75 13.0 10 10 100
14.0 14.25 20 10 200
. . . . .
. . . . .
. . . . . 3.6 Recovery of simulated sources
15.25 15.5 20 10 200
15.5 15.75 30 10 300 Cross-matching the recovered sources to the added artifi-
.. .. .. .. .. cial sources required the imposition of matching thresholds
. . . . .
in both position and brightness. While, ideally, a recovered
16.75 17.0 30 10 300
source should lie centred on the exact x,y pixel position
17.0 17.25 40 10 400
.. .. .. .. .. where it was added, there is no guarantee that imcore will
. . . . .
report unchanged centroid coordinates. Background varia-
17.75 18.0 40 10 400
tions in the original image, pixel binning and blending may
18.0 18.25 50 10 500
18.25 18.5 50 10 500 cause the reported centroid to shift by a small amount:
18.5 18.75 50 15 750 hence, a generous upper limit of 5 pixels (compared to a
18.75 19.0 50 15 750 typicalshiftoflessthanonepixel)wassetonthisdisplace-
19.0 19.25 50 20 1000 ment.
. . . . .
.. .. .. .. .. Simplycross-referencingtherecordedpositionofanar-
19.75 20.0 50 20 1000 tificial source with the regenerated catalogue is not suffi-
cient to confirm successful recovery. A constraint on the
Total: 410 12300
difference between the recovered magnitude, mrecovered of
the source and its insertion value msynthetic is essential,
Table1.Numberofartificialsourcesaddedperi-bandmagnitude
in order to reduce spurious crossmatches between added
bin.No.sourcesdenotestotalnumberthatwillbegeneratedover
sources and pre-existing nearby sources (typically of dif-
M runs. N is the number of sources that will be added to each
image,whichwillberepeatedMtimes.Atotalof12300areadded ferent brightness). Choosing a bound on this offset, ∆m =
per field, across 410 images containing artificial sources. For the msynthetic −mrecovered, was more involved than for pixel
r-band,thebinswereshifted1magfainter. position. Previous attempts to use artificial photometry to
understandincompletenesshavefacedsimilarissues.Forex-
ample,Mateo&Hodge(1986),aspartofastudyofaglob-
ular cluster in the Large Magellanic Cloud, added artificial
into each image simultaneously. In practice, it was neces- starstoimagesusingDAOPHOT:theyconsideredasource
sarytoalsoensurethattoomanysourceswerenotinserted
recovered if it was returned at the same coordinates at a
at any one time, since too high a number would modify
magnitude within 0.5 of the inserted value. Harvey et al.
the intrinsic properties of the image. For example, prob-
(2006)usedthisapproachinastudyofstellarsourcesinthe
ing the completeness of an originally sparse image with a
Serpensmolecularcloud,andplottedthemodulusoftheav-
high number of artificial sources inserted would not return
eragedifferenceforartificialsourcesinjectedintotheirdata,
statistics useful for understanding the original image. The finding a range from 0.1 mag at ∼10-13 mag to more than
valueof nimδnage neededtobekeptsufficientlylow,whereδn 0.5 mag at ∼15 mag.
is the number of artificial sources added to the image, and For each field, the distribution of the modulus of ∆m
nimageisthenumberofsourcespresentoriginally.Thequal- wasbinnedupandthemodalvaluedetermined.Foranum-
ity control information available for DR2 fields report that ber of fields, the modal value reached ≈0.4 mag - an effect
the most sparsely populated fields contain more than 1000 thatwouldrequirea∆mtoleranceof>0.5mag.Suchalarge
stars. This is not an extremely constraining limit; a maxi- tolerancewouldlikelyresultinmanyspuriouscross-matches
mumofupto50starswaschosenasavaluethatwouldkeep and hence an unduly optimistic estimate of completeness
δn below 0.05 for all fields. Allowing up to 50 sources fractions,especiallyatfaintermagnitudes.Tobetterunder-
nimage
perartificialsourceinjectionincreasesprocessingefficiency, standthis,themodal∆m foreachfieldwasplottedagainst
butofferstoofewtosamplethepre-existingmagnitudedis- a number of field parameters. The resulting plots, seen in
tribution of the sources in each image faithfully. Hence, the Fig. 7, clearly show this quantity correlates most strongly
approachadoptedwastosplitthemagnituderangeofinter- with the PSF FWHM (the ‘seeing’). Indeed, the relation-
estintobins0.25magwide,insertingsourcesfromonlyone ship underlying the tight trend is that the returned magni-
bin at a time in each catalogue regeneration. tudes from a regenerated catalogue are offset by a system-
Table 1 details N, the number of sources inserted per atic amount rather than spread widely around the mode -
image, and M, the number of artificial images generated a pattern that persists, up to the highest PSF FWHM en-
for reprocessing and recovery for each magnitude bin. N counteredinthesurvey.Thisfindinghasmotivatedtheap-
rises with increasing magnitude and is capped at 50 at the plicationofaseeing-dependentuniformshifttoallrecovered
faint end for the reasons discussed above. To accumulate a magnitudesfromanimage,appliedtobringthemedian∆m
larger number of sources injected in the faintest bins, and ofafieldbacktozero.Theoriginofthisoffsetislikelytobe
(cid:13)c 2015RAS,MNRAS000,1–19
Stellar density maps of the Northern Galactic Plane 9
10..05 0.5
0.4 0.4
0.3 0.3
0.8
0.2 0.2
d
re 0.1 0.1
e
v
eco 00..60 0.0
rr 0 50000 100000 20 21 22
− Numberofstars r5σdepth(mag)
hetic 00..45 0.5
ynt 0.4 0.4
s
r
0.3 0.3
0.2
0.2 0.2
0.1 0.1
00..00 0.0
0.0 1.0 0.21.5 2.00.4 0.00.6 0.1 0.80.2 10..03
Seeing(arcsec) Ellipticity Figure 10.Bestfitstocompletenesscurvesforbothr (upper)
andi(lower)catalogues.
Figure7.Modaldifferencebetweenartificialinsertedandrecov-
eredmagnitudeperfield,plottedagainstfieldparameters.
3.7 Completeness fractions
Fig. 9 shows the completeness curves of all DR2 fields; the
discrete quantisation of completeness is more prominent at
1.0
the bright end due to fewer artificial sources being injected
to assess the incompleteness of bright sources. The upper
0.8 twocumulativehistogramsshownintheuppersetofpanels
in Fig. 9 show that incompleteness remains low at bright
s magnitudes,withamediancompletenessof99.5%atr=15.
s
ne 0.6 At 18th magnitude the median completeness of IPHAS is
e
et 97.7% , falling to 93.1% at 20th magnitude. The pattern in
mpl 0.4 theiband(lowerpanels)issimilar,exceptthatcompleteness
o declines more rapidly with increasing magnitude such that
C
the data for i at 19th magnitude more closely resembles r
0.2 0.50mag at 20th than r at 19th.
0.25mag Inordertoapplycompletenesscorrectionswhengener-
0.10mag ating the density map, each detected source needs to con-
0.0
tribute to the map by a factor that takes into account the
17 18 19 20 21
incompletenessofsourcesofsimilarmagnitudefromitsfield
Magnitude
of origin. In order to characterize the incompleteness frac-
tion of each field as a quantity varying continuously with
Figure 8. An example of r-band completeness fractions for a
magnitude (r as written below), a function was fit to the
singlefieldexposureobtainedusingoffsettolerancesbetweenin-
serted and recovered magnitudes of 0.5 (blue solid), 0.25 (green measured completeness fractions of each field, of the form
dashed), and 0.1 mag (red dotted). The middle value of 0.25 is r
C(r)=α−γ×eβ (6)
theadoptedtolerance.
whereα,β,andγ areparametersallowedtovarytofindthe
best fit for each field. These parameters were collected and
formedalookuptableforuseincorrectingthedensitymap.
The curves of this form can be seen plotted for every field
thedifferencebetweenthestellarprofilesoftheartificialand
inbothr andiinFig.10.Medianvaluesforthecoefficients
therealsources.Inthissensetheempiricallydeterminedoff-
setanditscorrectionarethetradeforhavingusedGaussian are α = 0.996,β = 1.20,γ = 8.08×10−9 for the i-band,
profiles in place of more complex Moffat profiles. and γ = 0.999,β = 1.73,γ = 6.89×10−7 for the r-band.
Thecurvescorrespondingtothesemedianvalueshavebeen
After taking out the systematic shifts to ∆m values, a plotted in Fig. 9. A table containing sets of coefficients for
boundontheacceptablecorrecteddifference∆corstillneeds
m all DR2 fields is available online1.
to be set. As illustrated in Fig. 8, the completeness curves
As mentioned in Section 3.4, the completeness curves
remain relatively unchanged at r (cid:46) 19 as the ∆cor limit
m generated from CCD 4 of each field were used to repre-
is varied between 0.5 and 0.1 mag. This limit was set at
sent those of the field as a whole. To ensure that this ap-
0.25 mag, as a compromise between avoiding acceptance of
proach was sensible, a randomly-selected set of fields had
alargenumberofspuriousdetectionsatthefaintendofthe
magnitude distribution, and ensuring that few objects are
missed due to the occasional larger ∆cmor value. 1 http://www.iphas.org/data/dmap
(cid:13)c 2015RAS,MNRAS000,1–19
10 H. J. Farnhill et al.
t
1.0 1.0
a) b)
0.8
0.8
0.6
n
o
cti 0.4
fra 0.6
eness fields 0.2
mplet 0.4 onof 01..00
Co cti c) d)
a
Fr 0.8
0.2
0.6
0.0 0.4
12 13 14 15 16 17 18 19 20
Magnitude
0.2
0.0
100 101 102 103 104 0.6 0.7 0.8 0.9 1.0 0.6 0.7 0.8 0.9 1.0
Numberoffields Completenessfraction
t
1.0 1.0
a) b)
0.8
0.8
0.6
n
o
cti 0.4
fra 0.6
eness fields 0.2
mplet 0.4 onof 01..00
Co cti c) d)
a
Fr 0.8
0.2
0.6
0.0 0.4
12 13 14 15 16 17 18 19 20
Magnitude
0.2
0.0
100 101 102 103 104 0.6 0.7 0.8 0.9 1.0 0.6 0.7 0.8 0.9 1.0
Numberoffields Completenessfraction
Figure 9.Left:AdensityplotincorporatingeverycompletenesscurveinDR2,formagnitudebinsofwidth0.25inbetween12thand
21stmaginr (upper)andi(lower).Theyellowlinesuperposedineachpanelisthefitcurveobtainedusingeqn.6withthemedian
value for each fit parameter. Right: Cumulative histograms of field completeness for magnitude bins a) 15.0-15.25 b) 18.0-18.25, c)
19.0-19.25,d)20.0-20.25.
completeness curves generated for all four CCDs in order 4 THE DENSITY MAPS
to compare completeness curves and ensure that the varia-
tion between chips was acceptably low. For the magnitude 4.1 Source counting and application of the
range 12 < r < 21, standard deviations in the complete- incompleteness corrections
nesscorrectionswerecalculated.Atr=19,thedeviationin
TheIPHASfootprintwassplitinto1(cid:48)×1(cid:48)cells,andforeach
completeness corrections between CCDs reaches as high as
cell,atableidentifyingtheextentofeveryimagecontribut-
0.025, where a bright star appears in one or more CCDs of
ing to DR2 (at the CCD level, i.e. 4 CCD footprints per
the field. But these cases are rare: the median σ at r = 19
WFC exposure) was queried to identify which intersect the
is 0.005.
cell (either completely or in part). In order to calculate the
(cid:13)c 2015RAS,MNRAS000,1–19