The Structure and Metallicity Gradient in the Extreme Outer Disk of NGC 7793

0.48 MB·English

by  Marija Vlajić

DRAFTVERSIONJANUARY5,2011
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
THESTRUCTUREANDMETALLICITYGRADIENTINTHEEXTREMEOUTERDISKOFNGC7793
M.VLAJIC´
AstrophysikalischesInstitutPotsdam,AnderSterwarte16,D-14482Potsdam,Germanyand
SydneyInstituteforAstronomy,SchoolofPhysics,UniversityofSydney,NSW2006,Australia
J.BLAND-HAWTHORN
SydneyInstituteforAstronomy,SchoolofPhysics,UniversityofSydney,NSW2006,Australia
1
AND
1
0 K.C.FREEMAN
MountStromloObservatory,PrivateBag,Woden,ACT2611,Australia
2
DraftversionJanuary5,2011

n
a ABSTRACT
J
Studiesofouterregionsofspiralsdisksarefundamentaltoourunderstandingofboththeprocessofgalaxy

3 assemblyandthesubsequentsecularevolutionofgalaxies.Inanearlierseriesofpapersweexploredtheextent
andabundancegradientin the outerdisk ofNGC 300and foundan extendedpurelyexponentialdisk with a
] metallicitygradientwhichflattensoffintheoutermostregions.Wenowcontinuethestudyofoutskirtsofpure
A
diskspiralswithanotherSculptorGroupspiral,NGC7793. UsingGeminiMultiObjectSpectrographcamera
G atGeminiSouth, we tracethe diskof NGC7793with star countsoutto 9scale lengths, correspondingto
∼
. 11.5kpcatourcalibrateddistanceof3.61 0.53Mpc. TheouterdiskofNGC7793showsnoevidenceofa
h breakinitslightprofiledowntoaneffective±surfacebrightnessof 30magarcsec- 2( 3magarcsec- 2deeper
p ∼ ∼
thanwhathasbeenachievedwithsurfacephotometry)andexhibitsanon-negativeabundancegradientwithin
-
o theradialextentofourdata.
r Subject headings:galaxies: abundances— galaxies: individual(NGC 7793) — galaxies: stellar content —
t
s galaxies:structure
a
[

1. INTRODUCTION testingmodelsofgalaxyformationandevolution.
1
Predictionsthatmodelsofsecularevolutionofspiralsmake
v Thestudyof theextremeouterdisksofnearbyspiralshas
forstellaragesandmetallicitiesindiskoutskirts(Roškaretal.
7 produced some remarkable findings in recent years. These
2008b,a; Sánchez-Blázquezetal. 2009) are still to be con-
0 advanceshave been broughttogetherby a confluenceof ob-
firmed in a sufficiently large sample of galaxies. Age be-
6 servationalandtheoreticaldiscoveries. Onthe observational
havior is very difficult to observe in galaxies too distant for
0 side,starcountsofferasuperiormethodfortracingfaintstel-
. lar populationsin the outskirts of galaxies, comparedto tra- the full star formation history to be modeled. Barkeretal.
1 (2007)andWilliamsetal.(2009)demonstratenicelyhowan
ditionalsurfacephotometry(Pritchet&vandenBergh1994;
0
agegradientcanbederivedoverthewholediskofM33;how-
1 Fergusonetal.2002;Bland-Hawthornetal.2005;Irwinetal.
ever, this kind of work is only possible for the few closest
1 2005;deJongetal.2007;Radburn-Smithetal.2011). While
spirals. On the other hand, abundance gradients in galax-
: surfacephotometryislimitedbydiffusebackgroundsources
v at the level of 27 mag arcsec- 2, observations of re- ies can be studied relatively easily out to a few Mpc using
i ∼ broad-bandphotometry.Ithasbeenwell-establishedthatina
X solved stellar populations do not suffer from the same lim-
diskwhichis growinginside-out,metallicitydecreasesfrom
itations and allow us to reach 3- 5 mag arcsec- 2 deeper
r the center of the galaxy outward (Goetz&Koeppen 1992;
a in effective surface brightness. On the other hand, the N-
Matteucci&Francois 1989). However, an increasing num-
body/SPH and semi-analyticalmodels of disk formation are
berofgalaxiesshowsignsofanabundancegradientflattening
now able to address the importance of secular effects in the
intheiroutermostregions(Andrievskyetal.2004;Yongetal.
evolution of spirals. Scattering of stars by transient spi-
2006;Carraroetal.2007;Pedicellietal.2009;Bresolinetal.
ral arms first studied by Sellwood&Binney (2002) could
2009b; Vlajic´ etal. 2009). While models mentioned above
potentially have a significant effect on evolution of spi-
offer possible explanationsfor the flattening, its exactcause
ral disks (Roškaretal. 2008b,a; Schönrich&Binney 2009;
isnotyetclearandabundancedataonmoregalaxiesofdiffer-
Sánchez-Blázquezetal. 2009; Martínez-Serranoetal. 2009;
entsizes and outer disk structure will help explainthe slope
Minchev&Famaey 2010; Minchevetal. 2010). The ef-
ofabundancegradientintheoutermostregionsofspirals.
fects of the secular evolution of galaxies are expected to be
Asdiscussedinourearlierpapers,theSculptorGroupisan
mostprominentintheoutermostpartsofdisks(Roškaretal.
ideallaboratoryforstudiesofpurespirals: (i)itshighgalac-
2008a). Additionally,duetotheirlongdynamicaltimescales,
tic latitude minimizes foregroundextinction and contamina-
theouterregionsofspiralshavelargelyretainedfossilrecord
tion from Milky Way stars, (ii) most of its galaxies are iso-
fromtheepochofgalaxyassemblyintheformofspatialdis-
lateddisksystems,and(iii)thedistanceoftheSculptorGroup
tributions, kinematics, ages and metallicities of their stars. (2- 4Mpc)allowsfortheresolvedstellarpopulationstudies
Thesefactorsmakeoutskirtsofspiralsparticularlyusefulfor
fromtheground.AtthefarsideoftheSculptorGroup( 3.6
∼
Mpc), NGC7793is a late-typespiralwith anabsolutemag-
[email protected]
2 Vlajic´,Bland-Hawthorn&Freeman
thenightsof2005Aug09UT(hereafter:firstnight)and2005
Aug 10UT (hereafter: second night). Only 5 (outof 13) g′-
bandand21(outof22)i′-bandimageswereobservedonthe
first night and the observing log indicated that a thin cloud
might have affected i′-band observations. In addition, only
one standard star field observation was recorded. Remain-
ingscienceimagesofSEfield,aswellasthreestandardstars
fieldswereobservedthefollowingnight.Thebulkofthedata
oftheNWfieldwascollectedthenightof2005Aug11UT(12
g′-bandand21i′-bandimages;hereafter: thirdnight). How-
ever,nophotometricstandardstarswereobservedthatnight.
Theremainingscienceframes(oneineachofthebands)were
observedthepreviousnightunderphotometricconditions.
Initialanalysisofthephotometryrevealedasuspiciousdis-
crepancy in i′-band magnitude distribution between the two
fields. In correspondence with the Gemini staff it was con-
firmed that this was most likely due to the non-photometric
conditionsonthenightof2005Aug09UT,whenthemajority
ofthescienceframesoftheSEfieldweretaken. Accounting
for this, and the fact that the photometric standard stars ob-
FIG.1.—DSSwide-fieldimageofNGC7793withGMOSfieldsoverlaid. servationwereonlytakenonthesecondnightoftherun,we
decidedtoproceedinthefollowingmanner:
nitudeM=- 18.46,slightlybrighterthanNGC300(- 18.12; - SE field, i′-band: combine 21 images taken on the first
night and compare photometry of this deep image with the
absolute magnitudes were derived using corrected total ap-
photometryextractedfromthe single imageobservedonthe
parentmagnitudefromCarignan(1985)andthedistancede-
secondnight.
rived in §3.1). Carignan (1985) studied the light profile of
NGC 7793 out to 6′ using surface photometry and derived -SEfield,g′-band: combineseparately5imagesobserved
a scale length of 1.10′ (1.16 kpc) in B. A neutral hydrogen onthefirst,and8imagestakenonthesecondnightandcom-
parethephotometrybetweenthetwoimages.
isntugdoyuotftoCa1r1ig.2n′a(n1&1.8Pukcphce),(w19it9h0)arseuvrefaalcseadneHnsIitdyisaktethxetelnads-t - NW field, i′-band: compare the photometry extracted
datapointof∼0.01M⊙pc- 2. fornomthethtehidrdeenpigimhtaogfetchreeartuendwbyithcotmhebisnininggle2i1miamgaegteasketankoenn
The plan of the paper is as follows. In §2 we describe
thesecondnight.
the observations, data reduction, photometry and complete-
-NWfield,g′-band: similarlytothei′-bandcase,compare
ness analysis. Next, we present results for the distance of
acombineddeepimagecreatedfromthe12exposurestaken
NGC 7793 as estimated from the tip of the red giantbranch
onthethirdnight,withthesingleimagetakenonthesecond
(TRGB, §3.1), color-magnitude diagram (CMD, §3.2), star
nightoftherun.
counts profiles (§3.3), surface brightness profile (§3.4) and
Inthefollowingsections,wewillrefertothe(combinations
metallicity gradient (§3.5). Discussion and conclusions fol-
of)imagestakenonthesecondnightoftherunascalibration
lowin§4.
imagesandtotheonesobservedonthefirstandthirdnightas
finalimages.
2. OBSERVATIONS,DATAREDUCTIONANDPHOTOMETRY
2.1. ObservationsandDataReduction 2.2. PhotometryandArtificialStarsTests
The data were obtained using the Gemini Multi Object To extract stellar photometry we used the standalone ver-
Spectrograph (GMOS) on the Gemini South telescope over sionofDAOPHOTandALLSTARpackages(Stetson1987).
three nights in 2005 August as a part of the program GS- FollowingtheinitialrunsofFINDandPHOTOMETRYroutines,
2005B-Q-4. Deep g′ and i′ images of two major axis fields which were used to catalog objects in the image and mea-
on each side of the galaxy were taken; the locations of the sure their aperture photometry, we proceeded to determine
fields (SE and NW) are shown in Figure 1. GMOS field of the point spread function (PSF) for each image. Depending
view is 5′.5 on a side. (At the distance of NGC 7793 (3.61 onthefilterandthefield,80- 220moderatelybrightisolated
Mpc,§3.1),1′correspondsto1.05kpc.)TheaverageFWHM starsineachfieldwereselectedasPSFstarsandusedtoiter-
of the data is 0′′.6 (SE) and 0′′.8 (NW) in g′, and 0′′.5 (SE) ativelycomputethe PSF. The PSF stars were “hand-picked”
and0′′.7(NW)ini′ band. andtheirradial, contourandmeshprofileswerevisuallyex-
ToreducethedataweemployedthestandardIRAF/Gemini aminedwithintheIRAF/DAOPHOTpackage.Thecalculated
routines which included (i) bias subtraction and flat fielding pointspreadfunctionwasusedtosubtractthePSFstarsfrom
(gireduce),(ii)(fori′dataonly)creatingthemasterfringe the originalimage; the positions of the subtracted PSF stars
frame fromthe individualreducedframes(gifringe)and wereinspectedagainandthePSFstarswhichdidnotsubtract
subtracting it from the individual images (girmfringe), cleanlywereexcludedfromthePSFcalculation. Inaddition,
(iii)mosaickingofindividualGMOSCCDsintoasingleref- starswithsubtractionerrorswhichdifferedmorethan3σfrom
erence frame (gmosaic), and (iv) combining the dithered themeanvaluewerealsoexcluded. Thenextiterationofthe
exposuresintoafinalimage(imcoadd). pointspreadfunctionwas calculatedusingimagesin which,
Weobtained13 600sexposuresing′ and22 600sex- within the fitting radius of each PSF star, all but PSF stars
posuresini′bandp×erfield,bringingtotalon-sourc×eexposure havebeensubtracted. Thiswasfollowedwithyetanothervi-
timeto11.7hours.ThedatafortheSEfieldweretakenduring sualinspectionwithinIRAF/DAOPHOTasdescribedabove.
TheOuterDiskofNGC7793 3
Thewholeprocedurewasrepeatedoncemoretoderivethefi- SHARPasafunctionofmagnitudecanberelativelysafelyas-
nalPSF.Finally,ALLSTARwasusedtofitthecalculatedPSF sumed to be semi-resolved galaxies, blends, cosmic rays or
toallstarsintheobjectcatalogsanddeterminetheirphotom- imagedefects. Weremovedfromfurtheranalysisallstarsly-
etry. ing outside the envelope demarcating 3 standard deviations
Comparison of the final and calibration images revealed fromtheartificialstars’mean CHI and SHARP values. These
the following. In the i′-band, we found the difference in cuts, together with a cut on error in color ( 0.15) remove
≈
photometryextractedfromthecalibratedandfinalimagesof 50%ofobjectsfromtheoriginalmatchedcatalogs.
∼
0.396 0.012fortheSEfieldand0.073 0.006fortheNW
field. ±Inthe g′-bandwe found,within un±certainties(2σ), no 3. RESULTS
difference in magnitudes between calibration and final im-
3.1. TipoftheRedGiantBranchDistance
ages. We therefore decided, in the subsequent analysis, to
use the master frames created by combiningthe full sample Stellar evolution models (e.g. Salaris&Cassisi 1997;
of13framesing′,andareducedsampleof21imagesinthe Iben&Renzini 1983) show that below a metallicity of
i′-band. Two i′-bandimages, one ofeach field, takenon the [Fe/H] - 0.7 the brightness of the tip of the red giant
≈
secondnightwereusedtocalibratethephotometryofthefinal branch (TRGB) is expected to be roughly constant, re-
imageswhich were verylikely taken undernon-photometric gardless of stellar age and metallicity. Observationally,
conditions. DaCosta&Armandroff (1990) and Bellazzinietal. (2001)
We performed photometric calibration using the standard confirmedthatforasampleofGalacticglobularclustersspan-
starsobservationstakenduringthesecondnightoftheobserv- ning a large range of abundances (- 2.1 < [Fe/H] < - 0.7)
ingrun. Thederivedzeropointswereinexcellentagreement and ages (2- 15 Gyr), the absolute I-band magnitude of the
with those stated on the Gemini website (28.31 (our value) TRGBisstableandinsensitivetoageandmetallicity,which
vs. 28.33 (GMOS value) for g′ and 27.92 (our value) vs. enablesitsapplicationasanextragalacticdistanceestimator.
27.93 (GMOS value) for i′ band). In addition, we applied In general, there is been a good agreementbetween the dis-
additional offset (0.396 for the SE field, 0.073 for the NW tancesobtainedusing the TRGB and classical methodssuch
field) to the photometryderived from our final i′ images, as asCepheids(Sakaietal.1996;Ferrareseetal.2000).
explainedabove. FollowingLeeetal.(1993)andSakaietal.(1996),weem-
TheDAOGROWsoftwaresuite(Stetson1990)wasusedto ployourdeepi′-bandphotometryoftwofieldsintheoutskirts
calculate aperture corrections. We subtracted fromeach im- of NGC 7793 to determine the galaxy’s distance. Figure 2
ageallbutPSFstarsanddeterminedtheiraperturephotome- showstheresultofthisexercise.Inordertoincreasethesam-
tryinaseriesofapertures. DAOGROWusestheinformation pleofstarsusedinthedetection,wecombinedphotometryof
on aperture photometry to derive the “total” magnitude of a thetwofields. Thisresultsinavalueconsistentwiththeone
star. The weighted mean difference between the PSF-based wederivefromeachfieldseparately,whilehavinganarrower
magnitude(fromALLSTAR)andthe“total”magnitude(from andbetterdefinedpeak.
DAOGROW) of the PSF stars was adoptedas ’aperturecor- The top panel of the Figure shows the i′ band luminosity
rection’ and applied to PSF-based magnitudesof all stars in function,with(solidline)andwithout(dashedline)thecom-
the frame. The uncertaintiesin the aperturecorrection were pleteness correction. In correcting for incompleteness, we
intherange0.006-0.008. onlyconsiderstarsthatareabove50%completenesslimitin
Completeness, crowding and photometric uncertainties of bothg′ andi′. Inthemiddlepanel,thesmoothedluminosity
thedata wereassessed usingartificialstar tests, describedin functionisshown.Incalculatingthisfunction,discretestellar
more detail in Vlajic´ etal. (2009). We added 900 artificial magnitudes are replaced by Gaussians with the width equal
stars to each frame in a 30 30 grid with the cell size of to the star’s photometric error, according to the expression
69 pixels(10′′); for each com×binationof field and filter 100 (Sakaietal.1996):
artificial star test runs were performed with the grid origin
randomly offset between the runs. Photometry (i.e. magni- Φ(m)= N 1 exp - (mi- m)2
tude range and color distribution) of artificial stars was de- √2πσ (cid:20) 2σ2 (cid:21)
terminedbyrandomlysamplingtheoriginalcolormagnitude Xi=1 i i
diagrams. Artificial stars were added to the frames using Asmoothadaptiveedge-detectionfilteroftheform:
the DAOPHOT/ADDSTAR routine and the resulting images
were analyzed with the identical data reduction pipeline as E(m)=Φ(m+σ )- Φ(m- σ )
m m
the original frames. We consider an artificial star recovered
ifitisdetectedinbothfilterswiththedifferencebetweenin- is then applied. Here, σ is the mean photometric error of
m
put and recovered magnitude <0.5 mag. Completeness as all stars in the magnitude range [m- 0.05,m+0.05], as de-
function of magnitude is calculated as a ratio between the terminedfromartificialstar tests. The maximumof the out-
number of recovered and input stars in a given magnitude put of this edge-detection filter (shown in Figure 2c) marks
bin.Ourphotometryis50%completedownto(g′,i′)=(27.35– theTRGB.Relativelysmallphotometricerrorscausetheout-
27.47,26.75–27.10).Wealsocalculateradialcompletenessas put of the edge-detection filter to be noisy. In order to ob-
a ratioof the numberofrecoveredandinputstars in a given tain a smoother output which would yield a more reliable
radialbin; the informationis later used to correctradialstar distanceestimate,wecalculatethesameedge-detectionfunc-
countsandeffectivesurface brightnessprofilesfor crowding tionusingphotometricerrorsthreetimesthoseestimatedfrom
in the innermostregions. Furthermore,we used information the artificial star tests. The result is shown in the bottom
onthe CHI and SHARP parametersofrecoveredartificialstar panel of Figure 2. Apparent i′ magnitude of TRGB is esti-
teststodiscardspuriousobjectsfromtheALLSTARcatalog. mated to be i′ = 24.35 0.30. Uncertainties are deter-
TRGB ±
CHI and SHARP areoftenemployedasindicatorsofthenon- minedashalf-width-half-maximumofthepeakinFigure2d.
stellar nature of an object; outliers in the plots of CHI and Withtheabsolutei′-bandmagnitudeMi′,TRGB=- 3.44 0.10
±
4 Vlajic´,Bland-Hawthorn&Freeman
FIG.3.—Color-magnitudediagramoftwoNGC7793fields.Dashedlines
representthe50%completenesslimit. Photometricuncertainties atagiven
magnitudeandcolorofg′- i′=1areshownontheleftofthepanels.
3.3. StarCountsProfiles
WederiveradialprofilesofNGC7793inordertoexamine
the extent and structure of its outer disk. Star counts pro-
filesarecomputedbycountingupthestarsinellipticalannuli
with inclination and position angle corresponding to that of
FIG.2.—Determinationofthetipoftheredgiantbranch. i′-bandlumi- NGC7793.Theserawcountsarethennormalizedbythearea
nosityfunction(a)andsmoothedluminosityfunction(b)areshownintop
sampledbyeachannulus.
panelsbeforeandaftercompleteness correction (dashedandsolidlinesre-
spectively). Outputsoftheedge-detectionfilterareshowninthebottomtwo The most challenging aspect of studying outer disk light
panels–calculatedusingthephotometricerrorasdeterminedfromartificial profiles is the need to determine a background level that is
startests(c),andcalculatedusingaphotometricerrorfourtimeslargerthan thensubtractedfromtherawprofileinordertocalculatethe
calculatedfromartificialstartests(d);linetypesarethesameasinthetop
truestarcountsorsurfacebrightnessprofileofagalaxy.Inthe
panels.
caseofsurfacephotometrythisismanifestedthroughdifficul-
ties in deriving accurate estimates of sky brightness. When
(Bellazzini2008),wecalculatetheNGC7793distancemod-
resolvedstellar photometryisusedinsteadtostudyoutskirts
ulustobem- M=27.79 0.32,correspondingtothedistance
± ofspirals,theproblemtranslatesintohowtoreliablyevaluate
of3.61 0.53Mpc.Thisisingoodagreementwiththevalues
± the numberof unresolvedfaintbackgroundgalaxiesthatare
obtainedbyKarachentsevetal.(2003,3.91 0.41Mpc)and
± mistakenlyincludedintostellarcatalogs.Unlikeinthecaseof
theGHOSTSsurvey(3.73MpcRadburn-Smithetal.2011).
surfacephotometry,in star countsstudieswe arenotlimited
by the fundamental limits of observations but by the accu-
3.2. Color-MagnitudeDiagram
racywithwhichwecandeterminethegalaxynumbercounts.
Color-magnitudediagrams(CMDs) of two NGC 7793are However,thechallengeisparticularlydifficultwheninforma-
showninFigure3. AlsomarkedintheFigureare50%com- tion on number counts as a function of color (and not only
pletenesslimitandphotometricerrorsasdeterminedfromar- magnitude)isrequired. Wethereforepaycarefulattentionto
tificialstartestsatagiveni′magnitudeandcolorofg′- i′=1. estimatingthenumbercountsoffaintbackgroundgalaxies.
The (g′- i′,i′) CMDs reveal a prominent red giant branch InFigure 5a,e we show star countprofilesconstructedus-
(RGB). RGB stars make up more than 60% of detectionsin ing all stars in the field, irrespective of their colors. We use
each field. Region just blueward of the RGB is most likely theGalaxyCountonlinetool(Ellis&Bland-Hawthorn2007)
populatedbyunresolvedfaintbackgroundgalaxies. Alsopo- to determine galaxy number counts in the magnitude range
tentiallyvisibleintheCMDisamainsequence(MS)andan probedbyourdata;dashedhorizontallineintoppanelsshows
asymptotic giantbranch (AGB) population. Selection boxes theestimatedbackgroundgalaxylevelof120( 12)arcmin- 2
used for derivingpropertiesof individualstellar populations (SE) and 117( 12)arcmin- 2 (NW field). The±openand full
are shown in Figure 4. AGB and MS populations make up symbolsinthe±figurerepresentthestarcountsbeforeandaf-
2%and 10%ofallobjectsinthefield. terthenumbercountsofgalaxycontaminantshavebeensub-
∼ ∼
TheOuterDiskofNGC7793 5
as the counts in the brighter bins used in the fit. We finally
correctthederivedgalaxynumbercountsusingcompleteness
curvesof our data. The resulting backgroundgalaxy counts
are 3.9 2.1, 51 7 (44 7) and 52 8 (49 7) arcmin- 2,
± ± ± ± ±
fortheAGB,RGBandMSselectionregions,respectively,for
theSE(NW)field. (Quotederrorsarevariance,asestimated
by GalaxyCount.) While contamination-subtracted profiles
of RGB stars largely confirm the finding from Figures 5a,e
(with the distinction that the RGB profile for the NW field
fallsoffmoresteeplyandRGBstarsareonlydetectedoutto
10′) we detectnomainsequencestarsandallobjectswithin
ourMS selection boxcan be attributed to the contaminating
backgroundgalaxypopulation(thegalaxynumbercountsfor
theMSselectionboxare 2- 3timeshigherthanthederived
∼
starcountsforthiscolor-magnituderegion). WedetectAGB
stars out to 8- 9′ (8.5- 9.5 kpc), after which their number
countsfallbellowtheestimatedbackgroundgalaxylevel. As
weshow inVlajic´ etal.(2009), atthehighgalacticlatitudes
of the Sculptor Group, contamination from the Milky Way
starsisnegligible(Robinetal.2003;Sharmaetal.2011).
Radburn-Smith (2011) find a break in the radial profile
of young and intermediate age stars in the outer disk of
NGC 7793 (their HST/ACS fields overlap significantly with
ourSEfield),withthescalelengthofastellarpopulationbe-
ingshorter foryoungerstars. This is largelyconsistentwith
thestarcountsprofileswe derive. Duetothehigherlevelof
contaminationinourgroundbaseddatawe seenoMSstars,
in agreement with the short scale length for this population
foundbyRadburn-Smith(2011);similarly,wefindAGBstars
to be more extendedthan the MS population, with the RGB
starshavingthelargestscalelength.
FIG.4.—Color-magnitudediagramofbothNGC7793fieldswithselection
Comparingthe RGB profilesof NGC 7793 and NGC 300
boxesforRGB,AGB,andMSpopulationsmarked. Dashedlinesrepresent
the50%completenesslimitforSEfield(dashedline)andNWfield(dotted (Vlajic´etal. 2009, Figure 9) we find that the counts in the
line). outermostbinsshownin Figure5bare 2timeslowerthan
∼
corresponding counts in the most distant bins in the outer
tracted. Figure 5e shows that the star counts profile of the diskofNGC300. Thisisyetanotherpieceofevidencesup-
NGC 7793 NW field falls off to practically zero within the porting our earlier finding of an extended exponential disk
extentofourdata,attheradiusofapproximately11′ or11.5 inNGC300(Bland-Hawthornetal.2005;Vlajic´ etal.2009).
kpc. Itisunclearwhethertheupturnreflectedinthetwoout- While our CMD of NGC 300 reaches 4 mag below the tip
ermostdatapointsfortheSEfield(Figure5a)isreal,or(pos- oftheRGB, comparedto only2.5mag inNGC7793,back-
siblymorelikely)aresultofaslightunderestimationofback- ground galaxy number counts increase rapidly with magni-
groundcounts. tude and the counts in the faintest magnitude bins domi-
We also calculate the star counts profiles of distinct stel- nate the total galaxy counts. Our CMDs of NGC 300 and
lar populations in the outer disk of NGC 7793 (Figure 5b- NGC7793reachsameapparentdepth( 26.5- 27mag)and
d,f-h). Selection boxes used to separate stars into differ- hence experience roughly the same co∼ntamination by faint
ent populationsare marked on the color-magnitudediagram backgroundgalaxies.Thedifferenceinstarcountsintheout-
in Figure 4. Since the GalaxyCount tool does not pro- ermostbinsthereforedoesnotreflectthedifferenceingalaxy
vide direct information on the color of background galax- number counts but in star counts, and is an additional in-
ies, we require an alternative method for determining the dependent confirmation of the extended exponential disk in
galaxynumbercounts.FollowingVlajic´etal.(2009),weem- NGC300outtoatleast10diskscalelengths.
ploythedatafromtheWilliamHerschelDeepField(WHDF,
Metcalfeetal. 2001) to estimate the contaminationfrom the
3.4. SurfaceBrightnessProfile
faintbackgroundgalaxypopulation. We determinethenum-
bercountswithintheasymptoticgiantbranch(AGB)boxdi- The power of resolved stellar photometry over sur-
rectlyfromtheWHDFdata,whileforthestellarpopulations face photometry is most easily recognized if star counts
reaching fainter magnitudes than probed with WHDF (i.e. are transformed into measurements of effective surface
main sequence (MS) and red giant branch (RGB) stars) we brightness and compared with existing surface brightness
use the method described in Vlajic´ etal. (2009) to calculate data. It has been shown in a number of works recently
the galaxynumbercounts. We calculate the i′-bandnumber (Bland-Hawthornetal.2005;Irwinetal.2005;deJongetal.
counts of all galaxies in WHDF and fit linearly the (log of) 2007; Radburn-Smithetal. 2011) that this approach allows
differentialnumbercountsin0.5magbins. Inordertodeter- one to reach surface brightnesses 3- 4 mag arcsec- 2 below
minethegalaxycountsbelowthelimitoftheWHDFsurvey thelimitofsurfacephotometry.
weassumethatthecountsinthebins2- 3magnitudesbelow Wedividethedatain0.5′wideannuliandcalculatesurface
thesurveylimitfollowthesamelineartrend(inthelogspace) brightnessineachannulusas:
6 Vlajic´,Bland-Hawthorn&Freeman
FIG.5.—StarcountsprofilesoftheSEfield(leftpanels)andNWfield(rightpanels).Fromtoptobottom,theprofilesshownareofallstars(a&e),RGB(b&
f),AGB(c&g)andMSstars(d&h).Ineachpanelthedashedlinedisplaystheestimatedgalaxycountslevel,determinedusingmethodsdescribedinthetext.
Openandfullsymbolsshowthestarcountsbeforeandafterthebackgroundgalaxycontributionhasbeensubtracted.
whereF′=168887isascalefactorequivalenttoF′′thatcon-
vertsN toarcmin2andN =120( 12)arcmin- 2forSEand
µ=- 2.5log(cid:16)NFp′i′x fg′fi′Xi 10- 0.4mi(cid:17) 1ti1o7n(s±o1fp2ibx)acfokrgrNoWundfiesuldbt(r§a3gca.t3lio).n;Wineen±aecxhtopferthfoersmew1e00rermeaolvizeaa-
randomsetofN starsfromeachannulusandcalculatesur-
cont
Here, Npix is a numberof pixels in an annulus, fg′ and fi′ facebrightnessusingtheremainingstarsasdescribedabove.
areradialcompletenessfactorsandm aremagnitudesofstars Thefinalsurfacebrightnessprofileisthe meanofa hundred
i
within a given annulus. Radial completeness of our data is realizations.Wefindthestandarddeviationofthewholesetof
lowestintheinnermostannulus(45%)duetocrowding,and realizationsfora givenannulusnotto besignificant(<0.03
increasestoanaverageof87%intheoutermostdisk.Tocon- mag arcsec- 2 in g′ and <0.05 mag arcsec- 2 in i′) confirm-
vertsurface brightnessto units of mag arcsec- 2 we multiply ing that the derivation of surface brightness profile is robust
the effectivefluxunderthelogarithmwith the inverseof the againstthechoiceofobjectsweexcludeascontamination.
squareoftheGMOSpixelsize(1pix=0.146′′)whichisequal The derived g′ and i′ effective surface brightness profiles
toF′′=1/0.1462=47. areshowninFigure6. Theinnerdiskdatapointsinthefigure
In order to take into account the contribution from faint arefromtheCarignan(1985)study.Since,tominimizespuri-
backgroundgalaxies(see§3.3)weestimatecontaminationin ousdetections,weusedthematchedstellarcatalogratherthan
eachannulusas individualg′andi′catalogswhenderivingsurfacebrightness,
it is not surprising to find that g′ and i′ profiles are practi-
NgalNpix callyidentical. Theuncertaintyinthegalaxynumbercounts
N =
cont F′
TheOuterDiskofNGC7793 7
FIG.6.—SurfacebrightnessprofileofNGC7793. Innerdiskdata(fullsquares)aresurfacebrightnessmeasurementsfromCarignan(1985). Emptycircles
(squares)areeffectivesurfacebrightnessmeasurementsing′(i′)band,derivedfromstarcountsandcorrectedforbackgroundgalaxycontamination. Errorbars
reflectuncertaintiesingalaxynumbercounts.Duetodifferentrelativedepthsandcompleteness,datahadtobeshiftedbydifferentamountstomatchtheCarignan
(1985)measurements;seetextfordetails.Resolvedstellarcountsreachmorethan4magarcsec- 2deeperthansurfacephotometryandsignificantlyincreasethe
knownextentofNGC7793.
minationfrombroadbandphotometry.
TABLE1 In calculating the metallicity gradient, we only use stars
NGC7793DISKSCALELENGTH. fromthetop 1magnitudesoftheRGBselectionboxinFig-
ure4(i.e. wi∼thM′<- 2.5).Atfaintermagnitudesstarsatthe
Field Filter scalelength[’] scalelength[kpc] i
red/metal-rich side of the RGB fall below the completeness
Carignan BJ 1.11±0.01 1.17±0.02 limit,andtheresultingMDFisartificiallyskewedtowardsthe
SE g’ 1.12±0.05 1.18±0.05
SE i’ 1.24±0.09 1.30±0.10 metal-poorend. Weadoptfourdifferentsetsofstellarevolu-
NW g’ 1.12±0.07 1.18±0.07 tionarytracksfromVandenBergetal.(2006)(withagesof8
NW i’ 1.05±0.06 1.10±0.07 and12Gyrand[α/Fe]of0.0and0.3)andinterpolatebetween
themtoderivemetallicitiesonastarbystarbasis. Themodel
is reflectedin the errorbarsin Figure 6. Low/higherrorbar gridconsistof16finelyspacedredgianttrackscoveringthe
limits represent surface brightness profiles calculated using rangeofmetallicitiesfrom[Fe/H]=- 2.31to0.00inthesteps
background galaxy number counts that are 1σ lower/higher ofapproximately0.1dex.
thannumbercountsusedtoderivetheoriginalprofile. Inor- Wedividethedataintobinsofatleast200starsandforeach
dertomatchtheinnerdiskresult,effectivesurfacebrightness isochrone set determine median metallicities in these bins.
data points of the NW field have been shifted downward by The metallicity gradient is calculated as a slope of a linear
1.3 and 0.3 mag in g′ and i′, respectively. For the SE field, fit to the binned metallicities. Effects of using stellar tracks
correspondingvaluesare0.9and0.0ing′andi′. withdifferentagesand/orα-enhancementsareshowninFig-
Fitting an exponential to a light profile in Figure 6 we ure 7 and Table 2. The use of older and more α-enhanced
calculate the scale length of the NGC 7793 disk. Carignan isochronesresultsinloweroverallmetallicities,buthasprac-
(1985) data points yield for the disk scale length a value of ticallynoeffectonthederivedabundancegradient.
1.11′ 0.02(1.17 0.02kpc). Thescalelengthsderivedus- Figure 7 reveals two surprising characteristics – a strong
ing ou±r data, exclu±ding data points at 10.5 and 11′, are pre- positivemetallicity gradientin the NWfield andoveralllow
sentedinTable1andarelargelyinagreementwiththeCarig- metallicities in both fields. It becomes clear upon closer in-
nan’svalue. spectionoftheFigure7thattheoutermostbinneddatapointis
In summary, our effectivesurface brightnessderivedfrom primarilyresponsiblefortheoverallsteepgradientintheNW
starcountsreaches 3magarcsec- 2 deeperthanthesurface field.Themostdistantradialbincoversaradialrangeof 3′;
brightnessprofileof∼Carignan(1985). Wetracetheexponen- asubstantialfractionofdetectionsintheseoutermostfew∼ar-
tiallightprofileoutto 9diskscalelengths,greatlyincreas- cminutescanbeattributedtobackgroundcontamination(Fig-
∼
ing the known extent of the disk from the Carignan study. ure 5f), making the number count of actual RGB stars very
Thereisnodetectablebreakinthesurfacebrightnessprofile low.Ifthemostdistantdatapointisdiscarded,theabundance
andthediskremainsexponentialoutto11′(11.5kpc). gradientbecomes flat, with the slope and overall metallicity
consistent with that derived for the SE field. However, the
3.5. MetallicityDistributionFunctionandMetallicity valueoftheslopedoesnotchangewiththechangeofthebin
GradientintheOuterDisk size, suggesting that the positive abundance gradient in the
NWfieldisreal.
UsingthepositionofstarsontheRGBasaproxyfortheir
Ontheissueofverylowmetallicities,weseetwopossible
metallicities, we derive the metallicity distribution function
causes for such behavior. Errors in the photometriccalibra-
(MDF) and the metallicity gradient of the stars in the outer
tionwouldmanifestasadisplacementoftheRGBwithinthe
disk of NGC 7793. Due to higher sensitivity of the color
color-magnitudediagram,whichwouldinturnresultinfalse
of RGB stars on metallicity than age (e.g. VandenBergetal.
metallicity estimates. We reject this possibility, since due
2006),theage-metallicitydegeneracydoesnothaveasignif-
to the initial problems with the photometry (§2), photomet-
icanteffectontheshapeofthederivedMDFandmetallicity
riccalibrationwascheckedextensivelyandindependentlyby
gradient,andallowsforarelativelyaccurateabundancedeter-
8 Vlajic´,Bland-Hawthorn&Freeman
FIG.7.— Metallicity gradient in NGC 7793. Filled triangle symbols are inner disk [O/H] abundances from the works of Edmunds&Pagel (1984)and
Webster&Smith(1983); thesolid line shows alinear fitto these abundances. Outer diskmetallicity profiles are linear fits toradially binned metallicities
presentedinthiswork.Differentlinestylesdenoteabundanceprofilesderivedusingdifferentisochronesets;agesand[α/Fe]ratiosoftheseisochronesareshown
inthetopright. Forclarity,weonlyshowbinnedmetallicities thatwereusedtoderivetheabundanceprofileforoneisochroneset(filledcircles). Errorbars
representmeanvalueofabundanceuncertaintiesineachbin.
Geminipersonnel,andtheiranalysisconfirmedourzeropoint
values.Alternatively,itispossiblethatthecomponentweare TABLE2
seeingintheoutskirtsofNGC7793isnotanouterdisk,buta METALLICITYGRADIENTINNGC7793.
galactichalo. However,the effectivesurfacebrightnesspro- Field Age(Gyr) [α/Fe] a σa b σb
file we derivefollowstheinnerdisk profile(Figure6) andit
seems very unlikely that the transition from the disk to the SE 8 0.0 0.004 0.011 -1.49 0.10
halooccursalreadyat6′,wherewederivestellarmetallicities SE 8 0.3 0.006 0.011 -1.69 0.11
SE 12 0.0 0.005 0.012 -1.64 0.11
of[Fe/H] - 1.5. Moreover,Radburn-Smithetal.(2011)de- SE 12 0.3 0.005 0.011 -1.82 0.11
rivemetal≈licitiesintheouterdiskofNGC7793andfindlow NW 8 0.0 0.095 0.023 -2.17 0.20
meanabundancesrangingfrom- 1.23to- 1.64intheirFields NW 8 0.3 0.097 0.024 -2.37 0.21
NW 12 0.0 0.100 0.023 -2.35 0.21
01and02(whichlargelyoverlapwithourSEfield).
NW 12 0.3 0.100 0.024 -2.53 0.21
Inordertoassessthemagnitudeoftheapparentdiscontinu-
ityintheregionwheretheinnerandtheouterdiskmetallici- andNtOhTeEc.o—rreGsproanddieinngtsearrreorinhtahveefuonrmitsooff[αde/xFek]p=ca- 1R.+Abb,uwnhdearnecae
tiesoverlap( 6arcmin,Figure7)itisnecessarytotakeinto gradientfortheinnerdiskusingthedataon[O/H]abundancesof
account(i)th∼e[α/Fe]ratio,whichcorrectsforthefactthatin- HIIregionsfromEdmunds&Pagel(1984)andWebster&Smith
nerandouterdiskabundancesrefertodifferentelements,and (1983)is- 0.11±0.02dexkpc- 1
(ii)theage-metallicityrelation,whichreconcilesabundances
the works of Andrievskyetal. (2002b), Andrievskyetal.
inyoungHIIregionswithmetallicitiesofthestarsonthered
(2002a), Andrievskyetal. (2002c), Lucketal. (2003), and
giantbranchwhichwehaveassumedtobeatleast8Gyrold.
Andrievskyetal.(2004)areshownascrosses. Cepheidsfol-
Despitenumerousresultspointingtoaflatage-metallicityre-
low the well-defined negative gradient out to 15 kpc. On
lationship in the Solar neighborhood (e.g. Edvardssonetal. ∼
thecontrary,oldstarsexhibitsteepergradientintheinnerdisk
1993),theseworksfindthattherelationsteepensfortheoldest (outto10- 12kpc)andaflatteningintheoutermostparts. In
stars. Assumingthatthe differencein metallicities of young theregion10- 15kpcthereisacleardisconnectofupto0.4
HII regionsand 8- 12 Gyrold RGB stars is 0.3- 0.5dex dexbetween the Cepheid abundancesandthose of old stars,
and [α/Fe]=0.0- 0.3, it is possible to accoun∼tfor the abun- similartowhatweobserveinNGC7793.
dance difference of 0.5- 0.8 dex in the transition region in
Figure7. Atthehighend(i.e.0.8dex),thismakeshighinner 4. DISCUSSION&CONCLUSIONS
diskmetallicitiesconsistentwiththeverylowabundanceswe
Wecansummarizetheresultspresentedthusfarasfollows:
derive.
(i) The outer disk of NGC 7793 is primarily old with red
Furthermore, in deriving metallicities of H II regions, giant branch stars as the dominant stellar population and a
Edmunds&Pagel (1984) and Webster&Smith (1983) use
smallcontributionfromasymptoticredgiantbranchstars.
strong-line abundance indicators. These have been shown
(ii)Afterthecontaminationfromfaintbackgroundgalaxies
to result in metallicities which are a factor of two (0.3
hasbeentakenintoaccount,numbercountsofRGBstars,as
dex) higher than nebular (T based) or stellar abundances
e well as those derivedusing a matched catalog of all stars in
(Bresolinetal. 2009a) and likely enhance the difference be- thefield,extendoutto 10- 11′,or 10.5- 11.5kpc.
tween the inner (strong-line) and outer disk (stellar) abun- ∼ ∼
(iii) The effective surface brightness profile derived from
dancesinFigure7.
star counts traces the disk of NGC 7793 out to 9 disk scale
Similarabundancebehavior(althoughofasmallermagni- lengthsandis 3magarcsec- 2 deeperthanthesurfacepho-
tude) is observed in the Milky Way. In Figure 8 we repro- ∼
tometrydata ofCarignan(1985). Anypotentialbreakinthe
duce Figure 4 from Carneyetal. (2005). Old open clusters
lightprofilemaybeassociatedwithaspecificstellarpopula-
areshownasdiamonds(fromTwarogetal.1997;Chenetal.
tion,butweseenoevidenceofatruncationinoldstars.
2003)andsquares(fromYongetal.2005). Circlesarethree
(iv)ThemetallicitygradientintheouterdiskofNGC7793
field red giants from Carneyetal. (2005). Cepheids from
does not exhibit a negative profile, characteristic of the in-
TheOuterDiskofNGC7793 9
consistent with the inside-out scenario for galaxy formation
(Larson 1976; Matteucci&Francois 1989; Chiappinietal.
1997;Naab&Ostriker2006;Muñoz-Mateosetal.2007). In
this picture, a galaxy’s inner regions are built up at ear-
lier times than outer parts, and as a result contain on aver-
age older stars than outermost regions. However, recent re-
sults from resolved stars (Barkeretal. 2007; Williamsetal.
2009,2010)andsurfacephotometry(Bakosetal.2008)seem
to suggest that positive age gradients are frequently ob-
served in outer disks of spirals. This is supported by re-
cent simulations of disk evolution (Roškaretal. 2008b,a;
Sánchez-Blázquezetal. 2009), which find that radial migra-
tionsofstarswithinthediskareresponsibleforthereversed
age profile at large radii. If the same holds in NGC 7793,
thetrueabundancegradientwouldbenegative,flatormildly
FIG.8.—Metallicity gradientinthediskoftheMilkyWay. Plotted are
data for (i) old open clusters Twarogetal. (from 1997); Chenetal. (from positive,dependingonthemagnitudeofthiseffect.
2003) as diamonds and Yongetal. (2005) as squares, (ii) field red giants There is a broad agreement that negative stellar abun-
(Carneyetal. 2005) as circles, and (iii) Cepheids from Andrievskyetal.
dance gradients, easily explained in the context of inside-
(2002a),Andrievskyetal.(2002c),Lucketal.(2003),andAndrievskyetal.
(2004)ascrosses. Thediscrepancyisobviousbetweenoldstarabundances out models for galaxy formation (Goetz&Koeppen 1992;
(diamonds,squaresandcrossed)andCepheids(crosses)intheregion10- 15 Matteucci&Francois 1989), are a common feature of
kpc. disk galaxies (Zaritskyetal. 1994; Fergusonetal. 1998;
Gogartenetal.2010). Surfacedensity,yield andstar forma-
ner galactic regions. The value of the slope is independent tionalldecreasewithradius,resultinginmetallicitydistribu-
of the exact set of stellar evolutionarytracks used (although tionthatismoremetal-richincentralpartsanddecreasespro-
theolder,moreα-enhancedisochronesresultinloweroverall gressivelytowards the outer disk. However, abundancepro-
metallicities). filesinfaintouterdisksaremoredifficulttoderiveandthere
(v) The outer disk metallicity gradient is in disagreement is no generalconsensus on their shape and origin. Growing
with the inner disk slope. The inner and outer disk abun- body of evidence suggests that (most) spirals exhibit a flat-
dances in the overlap region are potentially in agreement teningoftheirmetallicitygradientintheoutermostdisk. Ob-
after [α/Fe] ratio, age-metallicity relationship and the use servationally,thestrongestcasehasbeenmadefortheGalaxy
ofspecificabundanceindicatorshavebeentakenintoaccount. (Andrievskyetal.2004;Yongetal.2006;Carraroetal.2007;
Pedicellietal. 2009), M83 (Bresolinetal. 2009b), and M31
Results presented in §3.5 suggest that the abundance gra- (Wortheyetal.2005). InthemodelsofRoškaretal.(2008b),
dientderivedfromouter disk stellar [Fe/H] metallicitiesdif- Roškaretal. (2008a) and Sánchez-Blázquezetal. (2009),
fersin slope from the gradientcalculatedusing [O/H] abun- stellarradialmixinghasbeenshowntobeabletoproduceflat
dancesfrominnerdiskHIIregions(Figure7). However,the abundance profiles by ’smoothing out’ the underlying nega-
two cannotbe directly comparedas the latter dataset probes tivegradient. Ontheotherhand,amildlypositivemetallicity
recent gas abundances, while the former refers to chemical gradienthasbeenobservedinNGC300(Vlajic´etal.2009).
compositionin starsthatare atleast a coupleofGyr old. In As mentioned earlier, a positive age gradient in the outer
addition,giventheresultsofRoškaretal.(2008a),whichsug- disk of NGC 7793 would bias our derivation of abundance
gestthatgasandstellarmetallicitiesaredecoupledandfollow profileanda flatunderlyingmetallicity profilewouldbe ob-
oppositetrends,itisdifficulttoconcludewhetherourresults served as a positive gradient instead. Our positive metallic-
pointtoanoverallabundancegradientthatgetsshalloweror itygradientintheNWfieldcouldthereforebeinterpretedas
steeper with time. (Models of galactic chemical evolution a combinationof a flat abundanceand positiveage gradient.
are successful in reproducing both trends, e.g. Mollaetal. This particular combination of age and metallicity behavior
1997; Boissier&Prantzos 1999; Portinari&Chiosi 1999; hasbeenfoundtoariseasaconsequenceofstellarmigrations
Tosi 1988; Chiappinietal. 2001) However, our results sup- (Roškaretal. 2008a; Sánchez-Blázquezetal. 2009). On the
portthescenariopresentedbyRoškaretal.(2008a)inwhich otherhand,itispossiblethatthepositivemetallicitygradient
gas abundancesbecome steeper with time (this is consistent in NGC 7793 is real and does not reflect the effects of age-
with relatively steep inner disk slope in NGC 7793) and the metallicity degeneracy. Minchevetal. (2010) find that the
stellar abundancegradientin old stars is shallower than that overlapof spiral and bar resonancesin the disk triggerssig-
inyoungstars. nificant migration of stars and results in positive abundance
Althoughthestellarmetallicityistheprimaryfactorinflu- profile in the outermost regions, similar to what we observe
encing colors of RGB stars, age-metallicity degeneracy and inNGC7793.
the assumption of single age in calculating the metallicity Alternatively, an external mechanism could be responsi-
distribution function introduce uncertainties in the derived ble for the shape of the metallicity gradient in outer disks
MDF. As shown in Figure 7, the derived metallicity gradi- of spirals. In NGC 7793 in particular, the origin of a par-
entispracticallyindependentonadoptedisochrones,assum- ticular abundanceprofile could be explainedby the fact that
ing that age gradient over the extent of the disk is close to the galaxy harbors a surprisingly small H I disk. While a
constant; a non-zeroage gradientwould result in a different greatmajorityofspiralshavemoreorlessextendedHIdisks,
metallicity profile. Negative age gradient in the outer disk sometimesstretchingoutfarbeyondtheknownopticaledges,
of NGC 7793 would suggest that the real abundance gradi- neutralhydrogeninNGC7793isdetectedonlyoutto 11.5′
∼
ent has a higher slope than derived under a constant age as- (Carignan&Puche 1990; Walteretal. 2008), coveringprac-
sumption. Stellarageswhichdecreasewithradiusareindeed tically the same radial extent as our stellar photometry. (In
10 Vlajic´,Bland-Hawthorn&Freeman
chemical evolution, while the signs of the early gradient re-
mainintheoutskirtsofgalaxies.
Fromtheperspectiveofpotentialforstarformationorradial
migrationinagivenregionofaspiraldisk,itisinterestingto
examinetheradialbehavioroftheToomreQparameter. Ina
thindifferentiallyrotatingdisk,rotationandpressureworkto
stabilizethediskagainstaxisymmetricperturbations. Onthe
otherhand,thediskisdestabilizedbyitsownsurfacedensity.
Thedisk isconsideredunstableagainstaxisymmetricmodes
ifQ,givenas:
σ(r)κ(r)
Q(r)=
14.45Σ(r)
islessthanunity. Here,σ isradialvelocitydispersioninkm
s- 1,κisepicyclicfrequencyintheunitsofkms- 1 kpc- 1,and
Σ is gas surfacedensity in M⊙ pc- 2. We employH I obser-
vationsof Pucheetal. (1990) to estimate κ(r) and Σ(r). We
approximatevelocitycurveandlogofHIsurfacedensitybe-
yond 4′ as linear functions of radius (Figure 9a,b) and use
thesefitsto calculateκ andQ. Epicyclicfrequencyκiscal-
culatedas:
v2 vdv
κ2=2 +
r2 rdr
(cid:16) (cid:17)
anditsradialdistributionisshowninFigure9c. Weestimate
velocitydispersionin the outerparts ofNGC 7793fromthe
THINGS survey (Walteretal. 2008) and adopt σ(r)=6 km
s- 1 as a mean velocitydispersion in our observedfield. Ra-
dial distribution of the Q parameter is shown in Figure 9e.
Whileusingadecliningvelocitydispersion(ratherthancon-
stant as we do here) would result in a slower increase of Q,
FIG.9.—(a)LogarithmofsurfacedensityintheouterdiskofNGC7793.
Toomre parameter in the outer disk of NGC 7793 seems to
Filled circles are data from Pucheetal. (1990); solid line is alinear fitto
thesedatapoints. (b)Sameas(a),butforrotationalvelocity. (c)Epicyclic besignificantlyaboveunity andassuch doesnotsupportan
frequency derived fromthevelocity curve in(b). (d)Surface density. (e) environmentinwhichthereisanongoinglargescalestarfor-
ToomreQparameter.
mation. Itis possiblehoweverthattheazimuthallyaveraged
addition, NGC 7793 exhibits a decreasing velocity curve in Qprofiledoesnotadequatelydescribestarformationinouter
itsoutermostparts,whichishighlyunusualforagalaxyofits disk. At very low gas densities in outskirts of spirals, star
size.)ThereasonforarelativelymodestHIdiskinNGC7793 formation might have proceeded in a stochastic manner and
is unclear, particularly given that the galaxy has no obvious insmallclumps,ratherthanonglobalscalesaddressedbyQ
interactions that could have potentially stripped the gas and as calculated here. This is supported by GALEX results of
truncated its H I distribution. Evidence for stripped stars in clumpy star formation in outer disks of nearby spirals (e.g.
the outer disk of NGC 7793 is also lacking. However, it is Thilkeretal. 2007). The high value of Q presents a poten-
possible to imagine that the upturn in the abundance gradi- tial problemfor radialmigration as well. Externalperturba-
ent in the NW field is a consequence of a dispersed stream tions, e.g. from a passing satellite galaxy, have been shown
ofstarsthathavelongfallenbelowthedetectabilitythreshold tobeabletocauseradialmixinginaMilkyWay-typegalaxy
insurfacebrightness,butstillpollutetheouterdiskmetallic- (Quillenetal. 2009) and couldbe responsiblefor stellar mi-
ities. Similartostellarage,positivegradientin[α/Fe]would grationsinhigh-Qenvironments.
– underthe assumptionof constant[α/Fe] – be disguised as
a positive gradientin metallicity. Accountingfor the [α/Fe]
increasefromzeroto0.3overtherangecoveredbyourdata We would like to thank the referee for detailed comments
wouldlikelynotresultinaflatabundancegradient,butwould which contributed to the quality of the paper. Based on ob-
certainlylowertheslopeofthegradientwederivefortheNW servationsobtainedat the Gemini Observatory,which is op-
field. eratedbytheAssociationofUniversitiesforResearchinAs-
Finally, the shape of the metallicity gradient in the outer tronomy,Inc.,underacooperativeagreementwiththeNSFon
disk could be primordial, originating in specific galaxy for- behalfoftheGeminipartnership:theNationalScienceFoun-
mation processes taking place at high redshift. Crescietal. dation(UnitedStates),theScienceandTechnologyFacilities
(2010)showthatrotatingsystemsatz 3showpositiveabun- Council (United Kingdom), the National Research Council
≈
dancegradients. Thesearepresumedtobegeneratedbycold (Canada),CONICYT(Chile),theAustralianResearchCoun-
streamsdepositingpristinematerialintothecentersofgalax- cil (Australia), Ministério da Ciência e Tecnologia (Brazil)
ies. In today’s galaxies the early positive gradient in galac- andMinisterio deCiencia, Tecnologíae InnovaciónProduc-
ticcenterisreversedthroughprocessesofstarformationand tiva(Argentina)