Hubble Space Telescope observations of the Kepler-field cluster NGC 6819. I. The bottom of the white dwarf cooling sequence

1 MB·English

by  L. R. Bedin

Mon.Not.R.Astron.Soc.000,1–11(2015) Printed14January2015 (MNLATEXstylefilev2.2)
Hubble Space Telescope observations of the Kepler-field
cluster NGC 6819. I. The bottom of the white dwarf
⋆
cooling sequence
5
1
0
2 L. R. Bedin1†, M. Salaris2, J. Anderson3, S. Cassisi4, A. P. Milone5, G. Piotto6,1,

n I. R. King7, and P. Bergeron8.
a
J 1INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
2Astrophysics Research Institute, Liverpool John Moores University,146 Brownlow Hill, Liverpool L3 5RF, UK
3 3Space Telescope Science Institute, 3800 San Martin Drive, Baltimore, MD 21218
1 4INAF-Osservatorio Astronomico di Collurania, viaM. Maggini, 64100 Teramo, Italy
5Research School of Astronomy and Astrophysics, The Australian National University,CotterRoad, Weston, ACT, 2611, Australia
R] 6Dipartimento di Fisica e Astronomia “Galileo Galilei”, Universita`di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy
7Department of Astronomy, Universityof Washington, Box 351580, Seattle, WA 98195-1580
S 8D´epartement de Physique, Universit´e de Montr´eal, C.P. 6128, Succ. Centre-Ville,Montr´eal, Qu´ebec H3C 3J7, Canada
.
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p
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Accepted 2015January12.Received2015January9;inoriginalform2014November27
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[ ABSTRACT
WeuseHubbleSpace Telescope (HST)toreachtheendofthewhitedwarf(WD)cool-

1 ingsequence(CS)inthesolar-metallicityopenclusterNGC6819.Ourphotometryand
v
completeness tests show a sharp drop in the number of WDs along the CS at magni-
3
tudes fainter than mF606W = 26.050±0.075. This implies an age of 2.25±0.20 Gyr,
5
consistent with the age of 2.25±0.30 Gyr obtained from fits to the main-sequence
9
turn-off. The use of different WD cooling models and initial-final-mass relations have
2
0 a minor impact the WD age estimate, at the level of ∼0.1 Gyr.
. As animportantby-productofthis investigationwe alsorelease,inelectronic format,
1
both the catalogueof allthe detected sourcesandthe atlasesof the region(in twofil-
0 ters).Indeed,thispatchofskystudiedbyHST (ofsize∼70arcmin2)isentirelywithin
5
the mainKepler-missionfield, so the high-resolutionimagesand deepcatalogueswill
1
: be particularly useful.
v
i Key words: open clusters and associations:individual (NGC6819)— Hertzsprung-
X
Russell diagram — white dwarfs
r
a
1 INTRODUCTION of the observed WD luminosity function (LF – star counts
asafunctionofmagnitude)withtheoreticalonescalculated
During the last few decades both observations and theory
fromWDisochrones.Whenconsideringstarclusters,owing
have improved to a level that has made it possible to em-
to the single (and finite) age of their stars, the more mas-
ploy white dwarf (WD) stars for estimating ages of stellar
sive WDs formed from higher-mass short-lived progenitors
populations in the solar neighbourhood (i.e., Winget et al.
pileupatthebottomofthecoolingsequence(CS),produc-
1987; Garc´ıa-Berro et al. 1988; Oswalt et al. 1996), open
ing a turn to the blue (a turn towards lower radii) in the
(i.e.,Richeretal.1998;vonHippel2005;Bedinetal.2008a,
isochrones. At old ages, when the WD Teff decreases below
2010) and globular (i.e., Hansen et al. 2004, 2007; Bedin et ≈5000 K, the contribution by collision-induced absorption
al. 2009) clusters.
of molecular hydrogen (Hansen 1998) to the opacity in the
Methodstodeterminestellarpopulationagesfromtheir
atmospheres reduces the infrared flux and increase the flux
WDcooling sequencesareusually based on thecomparison
at shorter wavelengths. This produces a turn to the blueof
the colours of individual cooling tracks, that enhances the
⋆ BasedonobservationswiththeNASA/ESAHubbleSpaceTele- blue excursion at the bottom of old WD isochrones. The
scope, obtained at the Space Telescope Science Institute, which existence of a minimum WD luminosity due to the cluster
isoperatedbyAURA,Inc.,underNASAcontractNAS5-26555, finiteage, togetherwiththeaccumulation ofWDsof differ-
underGO-11688&GO-12669. entmassesandageneralincreaseofWDcoolingtimeswith
† E-mail:[email protected]
2 L. R. Bedin et al.
decreasing luminosity (at least before the onset of Debye intwofiltersduringOctober2009,whilethesecondepoch(4
cooling) translates into a peak and cut-off in theLF. Com- orbits)wasinOctober2012andusedonlytheredderofthe
parisons of observed and predicted absolute magnitudes of two filters. As primary instrument the Ultraviolet-Visible
theWD LF cut-off provides thepopulation age. (UVIS)channeloftheWideField Camera 3(WFC3) gath-
The discovery of a second, brighter peak in the WD eredimagesinfourcontiguousfields(each162′′×162′′)orga-
LF of the metal-rich open cluster NGC6791 (see Bedin et nizedina2×2arraycenteredonthecoreofNGC6819.The
al.2005a, 2008a, 2008b forthediscoveryandpossibleinter- same number of fields were also observed in parallel, with
pretations)hasraisedquestionsaboutourunderstandingof the Wide Field Channel (WFC) of the Advanced Camera
theCSinsimplesystemslikeopenclusters,andtheirusefor for Surveys (ACS) (each 202′′×202′′), which is located in
age dating of stellar populations. In particular, this bright the HST focal plane at about 6′ from UVIS, and with the
peak hasbeeninterpretedbyKalirai et al. (2007) asdueto detectoraxes oriented at ∼45◦ from theWFC3 axes.Thus
a population of massive He-core WDs, whilst Bedin et al. theprimaryplusparallelexposurescoveredatotalofabout
(2008b)haveexplaineditintermsofasizablepopulationof 70arcminsquareinNGC6819(seetop-leftpanelofFig.1).
WD+WD binaries. As for the fainter peak –expected to be All collected images were taken in thefilters F606W &
therealageindicator–theageobtained from standardWD F814W,whicharetheoptimalchoiceforourscientificgoals,
models is in conflict (∼ 2Gyr younger) with that derived i.e., the study of the faintest WDs in a relatively-old open
fromtheclustermain-sequence(MS)turn-off(TO),andthe cluster, and are available for both instruments (although
age later obtained from the cluster eclipsing binaries stud- with different zero points and slightly different colour re-
iedbyBrogaard et al.(2012). Thisdiscrepancyhasled toa sponses).Datawereorganizedin1-orbitvisitsperfilterand
detailedreevaluation oftheeffectofdiffusionof22Neinthe perfield.Eachorbitconsistsofone10sshortand4×∼600s
COcorebeforecrystallizationsetsin(e.g.,Bravoetal.1992, long exposures for the primary instrument, and 3×∼470s
Deloye & Bildsten 2002). As shown by Garc´ıa-Berro et al. longexposuresforACS.Withineachorbitbothinstruments
(2010, 2011) with full evolutionary calculations, at the old use analogous filters. The bottom panels of Fig.1 show a
age and high metallicity of this cluster (about twice solar), stacked image of the regions, after removal of cosmic rays
the extra-energy contributed by Ne-diffusion in the liquid and most of theartifacts.
phase slows down substantially the cooling of the models All images were treated with the procedures described
andcanbringintoagreementWD,TOandeclipsingbinary in detail by Anderson & Bedin (2010), to correct positions
ages. andfluxesforimperfectionsinthecharge-transferefficiency
This result highlights very clearly the need for further (CTE) ofbothACS/WFCandWFC3/UVIS.Finally,inall
observations, and the importance of studying WD ages in images, we masked-out by hand the ghosts of the brightest
comparison with TO estimates in individual clusters. As stars in thefields.1
WDs lie in one of the least-explored regions of the colour- Photometry and relative positions were obtained with
magnitude diagram (CMD), we are carrying out a cam- the software tools described by Anderson et al. (2008). In
paign to find out whether the case of NGC6791 is unique addition to solving for positions and fluxes, we also com-
orwhetherotherclusterswithsimilar WDCSsmightexist. puted two important diagnostic parameters: quality-fit and
Our purpose is to extend our knowledge of the dependence rmsSKY. The quality-fit essentially tells how well the flux
of WD LFs on cluster age and metallicity. So far we have distributionresemblestheshapeofthePSF(definedinAn-
investigated two other open clusters: NGC2158 from space derson et al. 2008); this parameter can be very useful for
(Bedinetal.2010),andM67fromtheground(Bellinietal. eliminating the faint blue galaxies that plague studies of
2010); both of them show canonical WD CSs (henceLFs). WDs (see Bedin et al. 2009 for detailed discussions). The
The aim of the present work is to investigate the WD sky-smoothness parameter rmsSKY is the rms deviation
CS of another open cluster, NGC6819, that is within the fromthemean,forthepixelsinanannulusfrom3.5to8pix-
Kepler-mission field. NGC6819 has solar metallicity (Bra- els from each source. As discussed in Bedin et al. (2008a),
gaglia et al. 2001), is about a fourth as old as NGC6791 rmsSKY is invaluable in measuring a more effective com-
(Anthony-Twarog et al. 2013), and somewhat less massive pleteness than has been used in most previousstudies.
(ascanbeinferredfromtheirimagesintheDigitalSkySur- ThephotometrywascalibratedtotheVega-magsystem
vey). following the procedures given in Bedin et al. (2005b), and
Section 2 will describe our observations and WD selec- using the most updated encircled energy curves and zero
tion,whilstSection3presentsthetheoreticalanalysisofthe points2. In the following we will use for these calibrated
WD LF. Sections 4 and 5 discuss our proper motion anal- magnitudesthesymbolsmF606W andmF814W.Theabsolute
ysis and present the electronic material we make publicly accuracy of the calibration should be good to about 0.02
available. Conclusions close thepaper. magnitudeper filter.
TheACS/WFCparallelfields,althoughusefultoderive
2 OBSERVATIONS, MEASUREMENTS AND 1 (from WFC3 instrument handbook, Sect. 6.5.3): The WFC3
SELECTIONS UVIS channel exhibits three different types of optical ghosts: a)
those due to reflections between the CCD front surface and the
Alldatapresentedherewerecollectedwithtwodifferentin-
twodetectorpackagewindows;b)thoseduetoreflectionsbetween
strumentsatthefocusoftheHubbleSpaceTelescope(HST)
the window surfaces; and c) those due to reflections within the
under two programs taken at different epochs, GO-11688
particular filterin use.
and GO-12669 (on both PI: Bedin). 2 http://www.stsci.edu/hst/wfc3/phot zp lbn;
For the first epoch (GO-11688) 8 orbits were allocated http://www.stsci.edu/hst/acs/analysis/zeropoints.
HST observations of the WD CS in NGC6819 3
Figure 1. (Top-Right:) Over-imposed on the DSS is the location of the eight primary and secondary HST fields employed in
this work. (Top-Left:) The same region as seen in one of the periodic full-frame images collected by the Kepler-mission (image:
kplr2009114174833 ffi-cal c50.fits. (Bottom:) Stacked images of deep exposures in the filter F814W. On the left we display the
four primary WFC3/UVIS fields (blue outline), on the right the four parallel ASC/WFC fields (magenta outline). On both panels we
showreferencegridsofequatorial coordinatesatJ2000.0.Theseimagesarereleasedinelectronicformat,aspartofthiswork.
thepresent-daymassfunctionintheoutskirtsoftheclusters field. In particular, the long exposures of the primary field
fromtheMSstars,arenotveryusefultostudytheWDCS, will be used to study the WD CS of NGC6819, while the
as the handful of WDs are outnumbered by the field stars short exposures will allow us to study the brightest and
and background galaxies. There are also fewer ACS/WFC evolved cluster members. The photometry obtained from
images than WFC3/UVIS images, and their larger pixels the short exposures was corrected for differential redden-
sizecomplicatestheidentificationoftruepoint-sources,and ingasinMiloneetal.(2012,seetheirSect.3),andcarefully
themeasurementofpropermotions.Also,therearenoshort registeredtothezeropointsofthelongexposuresusingun-
exposuresfortheWFCimages,makingthesedatauselessfor saturated common stars. A precision of ∼0.01 magnitude
studying the evolved members of NGC6819. Nevertheless, per filter was estimated for this operation; this means that
for completenessand giventheinterest inthispatch ofsky, the photometry from short and long exposures should be
which falls inside the Kepler field, we release the catalogue consistent to thislevel.
and atlases for theACS/WFC fields as well (see Sect.5).
Artificial-star(AS)testswereperformedusingthepro-
Hereafter, we will use only the WFC3/UVIS central cedures described by Anderson et al. (2008). We chose to
4 L. R. Bedin et al.
Figure 2. (a) and (a′): The parameter quality-fit as a function of magnitude, for real stars and ASs. Objects that we consider to be
realstarslietotherightofthebluelines.Thediscardedsourcesarehighlightedinred.[Inallcaseshereexcept(d),thebluelineswere
drawnbyhandinthe lowerpanel andcopiedintothe upper panel.](b) and(b′): Theparameter rmsSKY as afunction ofmagnitude.
Stars that lie on an acceptable background are located to the left of the blue lines. (c) and (c′): The CMD, with blue lines bounding
the WD region. The red lines show the fiducial line along which the ASs were added. (d): Black points and line show the traditional
“completeness”thatignoresthermsSKY criterion,whilethebluepointsandlineshowthecompletenessintheregionswherefaintstars
canbedetectedandmeasured.Theredlineshowsthesizeofthismeasurableareaintermsoffractionoftotalarea.(e)and(e′):Spatial
distributionoftherealandASdetections. Theassumedclustercenterisindicatedbythereddashed-lines.Panels(f1,2,3,4),displaythe
recovered minus added residual biases inmagnitudes and positions. The red line marks a difference equal to zero, while the blue lines
marktheintervalwithinwhichastarisconsideredrecovered.Thegreenlinedenotes the68.27thpercentileofthedistributions.
cover the magnitude range ∼23 < mF606W <∼28.5, with et al. 2009, 2010 for a detailed description of the selection
colours thatplaced theartificial starson theWDsequence. procedures.)Panelswithunprimedlabelsrefertorealstars,
Thesetestsplayedanimportantroleinshowinguswhatse- while those with primed labels refer to theartificial stars.
lectioncriteriashouldbeusedfortherealstars.Thequality We used the AS tests to show what combinations of
of our results depends very much on making a good selec- magnitude and quality-fit are acceptable for valid star im-
tion, the details for which are shown in Fig.2. (See Bedin ages [panel (a′)], and we drew the blue lines to isolate the
HST observations of the WD CS in NGC6819 5
acceptableregion.Wethendrewidenticallinesinpanel(a), for [Fe/H]=+0.06, consistent with [Fe/H]=+0.09±0.03 de-
toseparatetherealstarsfromblendsandprobablegalaxies. termined spectroscopically for a sample of cluster red
We went through similar steps for the rmsSKY parameter clump stars by Bragaglia et al. (2001 – but see Anthony-
(panelsb′andb).FinallyweplottedCMDsanddrewdivid- Twarog et al. 2014 for a slightly different estimates,
inglinesinasimilarwaytoisolatethewhitedwarfs(panels [Fe/H]=−0.06±0.04, obtained from uvbyCaHβ observa-
c′ and c) from field objects. Thankfully, WDs occupy a rel- tions).
atively uncontaminated region of the CMD (Bedin et al. First wedetermined thecluster distancemodulusfrom
2009). isochrone fitting to the MS. Given that stars above the
Asonecanseefrompanels(a)and(a′),theshape(i.e., MSTO are saturated, we could not use the magnitude of
thequality-fit)oftheobjectsbecomesincreasinglyconfused the red clump and the colour of red giant branch stars
with thenoise at magnitudes fainterthan mF606W∼26, and as constraints. We have considered the unevolved cluster
therefore a few blue compact background galaxies might MS between mF606W=17 (about two magnitudes below the
have fallen in the list of selected objects. However, these MSTO) and 19, and derived a fiducial line by taking the
cannot affect the location of the drop of WD star counts, mode of the (mF606W−mF814W) colour distribution of MS
which is the relevant feature studied in our work. Further- stars in 0.25mag wide mF606W bins. Before performing a
more, the proper motions described in Sect.4, confirm the leastsquarefittingoftheisochroneMSstothefiducialline,
WD LF cut-off magnitude. we fixed the cluster E(B−V) to values between 0.10 and
Our final step was to deal with completeness, a con- 0.18 mag, in steps of 0.01 mag. We explored this range fol-
cept that appears in two different contexts: (1) The ob- lowing the estimate by Bragaglia et al. (2001), who used
served number of WDs must be corrected for a magnitude- temperaturesof threered clump stars derived from line ex-
dependentincompleteness.(2)Itiscustomarytochoosethe citation (a reddening-free parameter) and the appropriate
limiting reliable magnitude at the level where the sample theoretical spectra, to determine their intrinsic (B − V)
is 50% complete. In a star cluster these two aims need to colours. Comparison with the observed colours provided
be treated in quite different ways. (1′) To correct for in- E(B−V)=0.14±0.04 (Anthony-Twarog et al. 2014 deter-
completeness the WD LF, we use the traditional ratio of mined E(B −V)=0.160±0.007 from uvbyCaHβ observa-
AS recovered to the number inserted. (2′) For the limit to tions, within the range spanned by Bragaglia et al. esti-
whichmeasuresoffaintstarsarereliable,however,the50%- mate). These E(B−V) valuesbetween 0.10 and 0.18 mag-
completeness level needs to be chosen in a quite different nitudes were then transformed into E(mF606W −mF814W)
way, because in a crowded star cluster more faint stars are andAmF606W asdescribedbyBedinetal.(2009),andassum-
lost in the brightness fluctuations around the bright stars, ingRV=3.1.ForeachE(mF606W−mF814W)wefinallyfitted
thanarelosttothefluctuationsoftheskybackground.The isochronesofvariousagestothefiducialline.Theprocedure
completeness measure that we should use to set the 50% workedasfollows.ForagivenchoiceofE(B−V)thevertical
limit is therefore the recovered fraction of ASs only among shift requiredtofit theisochrones totheobserved MS fidu-
those ASs whose value of rmsSKY, as a function of mag- ciallineprovidedtheapparentdistancemodulus.Thisisun-
nitude, indicates that it was possible to recover the star. affectedbytheisochroneage,giventhatwewerefittingthe
[For a more detailed discussion, see Sect. 4 of Bedin et al. unevolvedMS.Oncederivedtheapparentdistancemodulus
(2008a), and for other two similar applications and further foragivenE(B−V),wecomparedmagnitudeandshapeof
discussions see Bedin et al. 2009, 2010]. the isochrones’ TO with the observed CMD, for ages vary-
Thedistinctionbetweenthetwocompletenessmeasures ing between 1.0 and 4.0 Gyr. This comparison allowed us
is illustrated in panel (d) of Fig.2, where the black line tobothestimate theTOage andnarrowdowntherangeof
shows the overall completeness, while the blue line shows reddeningsconsistentwiththeisochrones.Itturnedoutthat
thecompletenessstatisticsthattakermsSKY intoaccount; forsomeE(B−V)values(andtheassociateddistancemod-
its 50% completeness level is at mF606W = 27.11, rather uli), around the TO region the shape of the isochrone that
than26.87magwiththetraditionalstatistics.Toemphasize matchedtheobservedTOmagnitudewasverydifferentfrom
thecontrast,theredlineshowsthefractionofthearea(i.e., theshapeoftheCMD.Thisimplied thattheisochronewas
with low-background) in which faint stars could have been toooldortooyoungcomparedtotherealclusterage,sothat
found. theTOmagnitudehadmatchedonlyonaccountofanincon-
sistentdistancemodulus,andhenceaninconsistentredden-
ing.OurisochronefittingprovidedE(B−V)=0.17±0.01,
(m−M)0 = 11.88±0.11 [corresponding to a distance of
3 COMPARISON WITH THEORY 2377pc,andto(m−M)V =12.41±0.12] andaMSTOage
Asinourprevioussimilarworksonotherclusters,thecom- tMSTO =2.25±0.30Gyr. The total age range was fixed by
parison with theory comprises the determination of a MS the youngest and oldest isochrones that bracketed the TO
TO age, and theage implied by theWD LF. region in the observed CMD for, respectively, the shortest
BaSTI3 scaled-solar isochrones for both WD (Salaris and largest distance moduli obtained from the MS fitting.
et al. 2010) and pre-WD (Pietrinferni et al. 2004) evolu- The error on the distance modulus is an internal error of
tionary phases, including MS convective-core overshooting, our isochrone MS-fitting method that combines in quadra-
wereusedtodeterminebothMSTOandWDages.Wecon- turetheerrorof theleast squarefit at fixedreddening,and
sidered the available BaSTI (pre-WD and WD) isochrones the effect of the error on the reddening on the least square
fit value.
The reliability of our derived distance can be as-
3 http://www.oa-teramo.inaf.it/BASTI sessed by comparisons with completely independent meth-
6 L. R. Bedin et al.
LF, and matched with theoretical WD LFs of varying age
theobservedcut-offofthestarcounts.TheobservedLF–see
pointswith error bars in Fig. 4– exhibitsjust one peak and
acut-off(atmF606W=26.050±0.0.075 atitsfaintend,asex-
pectedforastandardclusterCS.TheoreticalLFshavebeen
calculated with the Monte Carlo (MC) techniquedescribed
in Bedin et al. (2008b), employing the BaSTI WD models
for both DA and DB objects, and considering a Salpeter
mass function (MF) for the progenitors. Our MC calcula-
tions account for the photometric error as found from the
data-reduction procedure and arbitrary fractions of unre-
solvedWD+WDbinariesandDAandDBWDs.Theeffect
ofrandomfluctuationsofthesyntheticLFareminimizedby
using ∼100 times as many WDs as the observed sequence
(which comprises about 200 objects after the completeness
correction).
To give some more details, the MC code calculates the
syntheticCMDofaWDpopulationoffixedage(andinitial
chemical composition) by selecting first a value of the pro-
genitormassforagenericWDalongthecorrespondingWD
isochrone(weassumeaburstofstarformationwithnegligi-
bleageandmetallicitydispersion,appropriateforopenclus-
ters),accordingtoanIMFthatissettoSalpeterasdefault
choice.Thecorrespondingmassandmagnitudesofthesyn-
Figure3. (Upperpanel:)Fitoftheoreticalisochrones[1.95Gyr, thetic WD are then determined by quadratic interpolation
(m−M)0 =11.99, E(B−V)=0.18 and 2.55 Gyr, (m−M)0 = along the isochrone, that has been calculated assuming a
11.77, E(B − V)=0.16] to the cluster MS in the mF606W- WDinitial-finalmassrelation(seeSalarisetal.2010forde-
(mF606W−mF814W)CMD(seetextfordetails).(Lower panel:) tailsabouttheWDisochrones)4.Forthefractionofobjects
Fit of WD isochrones to the observed CS, for the same age-
assumed to be in unresolved binaries, we extract randomly
distance-reddening combinations. Solid lines denote DA WDs,
dottedlinesDBobjects. also a value for the ratio q between the initial mass of the
companionandthemassoftheWDprogenitor,accordingto
a specified statistical distribution. If the initial mass of the
ods. Sandquist et al. (2013) obtained (m−M)V =12.39± companion hasproduced aWD,we determineits mass and
0.08 [employing E(B−V) = 0.12±0.01] from the cluster magnitudesasforsingleWDs.Incasethecompanionisina
eclipsing binary WOCS 23009, whilst Jeffries et al. (2013) differentevolutionarystage,wedetermineitsmagnitudesby
determined (m−M)V = 12.44±0.07 for the eclipsing bi- interpolatingalongthepre-WDisochrone.Thefluxesofthe
nary WOCS 40007. Wu, Li & Hekker (2014) determined two components are then added, and the total magnitudes
(m−M)0=11.88±0.14[assumingE(B−V)=0.14±0.04] and colours of the composite system are computed.
through theglobal oscillation parameters ∆ν and νmax and We finally add the distance modulus and extinction to
V-bandphotometry of thecluster red giants. the magnitudes of both single and unresolved binary stars,
Ourisochrone-baseddistanceestimateisingoodagree- and perturbe them randomly by using a Gaussian photo-
ment with these independent results based on completely metricerrorwiththeσ derivedfromtheartificial-startests.
different methods. A theoretical LF is then computed for the synthetic
Regardingtheage,ourestimatefromtheMSTOagrees population to becompared with theobserved one.
with t = 2.2 ±0.2Gyr obtained by Jeffries et al. (2013) In general, the exact shape of the WD LF (and of the
by comparing the MS mass-radius relationship of the same WDsequenceintheCMD)dependsonanumberofparame-
BaSTI isochrones used here, with the masses and radii de- tersinadditiontotheclusterage,e.g.,theinitial-final-mass
termined for thecomponents of thecluster eclipsing binary relationship, the mass function of the progenitors, the rel-
WOCS 23009. ative fraction of the (dominant) DA and DB objects, the
The upper panel of Fig. 3 shows the result of the fraction of WD+WDbinaries (and their mass distribution)
isochronefits,withthetwoisochronesthatbestbracketthe and, very importantly, the dynamical evolution of the clus-
MSTO region, i.e., 1.95Gyr [for (m− M)0 = 11.99 and ter, which selectively depletes the WDs according to their
E(B−V)=0.18] and 2.55Gyr [for (m−M)0 = 11.77 and massandtheirtimeofformation.Also,inopenclusters,ifa
E(B−V)=0.16], respectively.WDisochrones(forbothDA WDreceivesasufficientvelocitykickfromasymmetricmass
andDBobjects)withthesameage-distance-reddeningcom- loss during its pre-WD evolution, it may become unbound
binationsaredisplayedinthelowerpanelofthesamefigure. (see, e.g., the introduction in Williams 2004).
Notice how the termination of the DB sequence is brighter
than that for the DA WDs, contrary to the result for typi-
calglobularclusterages,becauseinthisregimeHe-envelope 4 WDisochronetablesforagivenageandinitialchemicalcom-
WDs cool down more slowly that the H-envelope counter- positionprovidethemassoftheWDprogenitor,thecorrespond-
parts (see, e.g., Salaris et al. 2010). To compare WD and ingWDmass,andtheWDmagnitudesinthechosenphotometric
MSTO ages we have used the completeness corrected WD filtersalongtheCS.
HST observations of the WD CS in NGC6819 7
almost the whole predicted WD mass spectrum (hence the
presenceofablueturntowardslowerstellarradii).Amass-
dependentlossmechanismduetodynamicalevolutionwould
therefore alter the number distribution of WDs around the
blue-turn,butitshouldhavenomajoreffectontheobserved
location of the cut-off in the WD LF. Figure 4 compares
thecompleteness-correctedobservedmF606W WDLF(filled
circles with error bars) with theoretical LFs calculated to
explore some of the other effects listed above.
Panela)displaysthetheoreticalLFforDAWDs(with
thesamenumberofobjectsastheobservedcandidateWDs),
an age of 2.25 Gyr[(m−M)0=11.88 and E(B−V)=0.17],
and two different fractions of progenitor binaries – no bi-
naries, and 22% respectively (dotted and solid lines in the
figure)– corresponding to zero, and 14% WD+WD binary
(supposedtobeunresolved)systemsonthefinalcoolingse-
quence. The mass ratio q for the binary companions (the
primary components are assumed to follow a Salpeter MF)
was chosen with a flat distribution between 0.5 and 1.0. As
discussed, e.g., in Podsiadlowski (2014), the distribution of
q in binary systems is not well determined and appears to
depend on the mass range. Massive binaries favour stars
of comparable mass (q≈1) whilst the situation is less clear
for low-mass stars, and most studies show that q is possi-
Figure 4. Comparison of the completeness-corrected observed bly consistent with a flat distribution. The 22% fraction of
mF606W WD LF (filled circles with error bars) with theoretical progenitor binaries was chosen after the recent results by
2.25GyrLFs,calculatedwithaSalpeterMFanddifferentchoices
Millimanetal.(2014),whodeterminedapresentfractionof
ofparameters,forE(B−V)=0.17and(m−M)0=11.88.Panel 22±3% MS binaries with period less than 104 days.
a)displaysDALFswithnounresolvedWD+WDbinaries(dotted
line),witha22% fractionofprogenitor binaries(solidline–our The unresolved systems show up in the LF at mF606W
referencecase),andwiththesamefractionofprogenitorbinaries between 25 and 25.2 (the variation of the star counts at
butadifferentdistributionofmassratiosofthetwocomponents fainter magnitudes is a consequence of keeping the to-
(dashedline–seetextfordetails).Panelb)displaysourreference tal number of objects fixed at the observed value) about
theoretical LF(solidline),andaLFwith85% DA and15% DB 0.75 mag brighter than the LF cut-off, as for the case of
objects, leaving everything else unchanged (dashed line). Panel NGC6791(Bedinetal.2008b). Theinclusion ofunresolved
c) displays the reference LF and one calculated with a flat MF WD+WDbinariesimprovesthefitoftheLFat thosemag-
(dashedline–seetextfordetails).Paneld)displaysourreference
nitudes and leaves completely unchanged the magnitude of
LF (solid line) and a 2.5Gyr old LF, everything else being the
theLF cut-off.
same(dashedline).
Wehavealso tested theeffectof changingthedistribu-
tionofqbyfixingtheprogenitorbinaryfractionto22%,but
On one hand, this is why we are not attempting to thistimeemployingaflat distribution between0.1 and 1.0.
matchpreciselytheshapeofthewholeWDLF,bytryingto TheresultingLF(dashedline)hasaslightlychangedshape,
determine simultaneously the cluster age, the precise frac- thelocalmaximumbetween25and25.2islesspronounced,
tion of WD+WD binaries, DB objects, and the progenitor but the magnitude of the cut-off is not affected. Note how
MF. These effects are difficult to disentangle using just the thefew contaminant sources in thesample thatmight alter
observed LF, and complicated by the limited statistic (to- ourobservedWDLFbelowmF606W∼26.5,donotaffectthe
tal number of observed WDs, compared for example with location of the WD LF drop-off.
thecasesofM4orNGC6791) andbyapotential(although Panel b) shows the effect of including a 15% fraction
mild) residual field contamination. of DB objects (dashed line – DB isochrones are also from
On the other hand, the observed position of the WD Salaris et al. 2010) for an age of 2.25 Gyr, and a reference
LF cut-off, which is the primary WD age indicator, should 22% binary progenitor fraction. Also in this case the mag-
have been affected very little by any of these parameters. nitude of the LF cut off is unchanged, and the signature
In the following we quantitatively demonstrate how all the of DB WDs appears at mF606W ∼25.5 (the variation of the
aboveuncertainties,althoughpotentiallyaffectingtheshape star counts at fainter magnitudes is again a consequence of
of the WD LF, do not alter the magnitude location of the keepingthetotalnumberofobjectsfixed).Accordingtothe
LF cut-off. observed LF there is no room for a much higher fraction of
First of all, the effect of the dynamical evolution (see DBobjects,andactually avalueclosetozerowouldproba-
Yang et al. 2013 for indications about the dynamical evo- bly bea better match to the observations.
lution of this cluster) should be negligible, for thefollowing Panelc)investigatesthecombinedeffectofvaryingthe
reason. The WD isochrones predict that the brighter WDs progenitor initial MF plus the cluster dynamical evolution
should havenearly a single mass, whereas the region of the thatprogressivelydepletesthelowermass(bothprogenitors
WD LF cut-off — i.e., at the blue-turn at the bottom of andWDs)objects.TothispurposewedisplaytheLFforthe
the CS — is expected to be populated by objects spanning standardSalpeterMF(solidline–noDBs,22%ofWD+WD
8 L. R. Bedin et al.
Figure 5. (Left:) (mF606W −mF814W) vs. mF814W CMD of stars in panel (b) of Fig. 2 (small dots). The stars for which it was
possibletocompute aproper-motionarehighlightedwithempty circles.Bluedots marktheMSstars usedtocompute theinter-epoch
transformationsnecessarytocomputepropermotions.(SecondpanelfromLeft:)mF814W vs.totalpropermotionsinmasyr−1relativeto
themeanpropermotionofthecluster.Errorsincreasetowardfaintermagnitudes.Theredlineisolatetheobjectsthathavemember-like
motions(black)fromfieldobjects(reddots).(ThirdpanelsfromLeft:)arevectorpointdiagramsforthosestarsinfourmagnitudebins.
(Right panels:) resultingdecontaminated CMDs.NotehowthesharpdropoftheWDCSresultsevenclearerthanintheleftpanel.
unresolvedbinaries)andaLFcalculatedwithaclosetoflat isduetothedifferentsensitivityofTOandWDmagnitude
MF for the WD progenitors (dashed line), i.e., a power law cut-off to thepopulation age (Salaris 2009a).
with exponent −0.15. Progenitor masses are between ∼1.7
We close our theoretical analysis presenting two addi-
and ∼6.5 M⊙ at our reference age of 2.25 Gyr, whilst the tional tests about our derived WD ages. First, we have re-
finalWDmassesrangebetween∼0.61and1.0M⊙according calculated the BaSTI WD isochrones considering the WD
totheinitial-final massrelation adopted bytheBaSTI WD
initial-final mass relation (IFMR) byKalirai (2009) instead
isochrones (see Salaris et al. 2010 for details).
of the default IFMR employed by the BaSTI isochrones
(Salaris et al. 2009b). In the WD progenitor mass range
The comparison of the two LFs shows that the mag-
nitude of the cut-off is unchanged, as expected. Only the typical of NGC6819 (progenitor masses above ∼1.6 M⊙),
thisdifferentIFMRpredictsgenerallyslightlylowerprogen-
overall shape is affected and the width of the peak of the
itor masses at fixed WD mass, compared to the BaSTI de-
theoreticalLFisincreased,butnottheposition ofthedrop
faultIFMR.Thisimpliesthatwith theKalirai etal.(2009)
of the star counts beyond the peak, that is the age indi-
IFMR WDs of a given mass start to cool along the CS at
cator. Finally, panel d) displays the effect of age (2.25 and
a later time, hence they reach somewhat brighter magni-
2.5Gyr,respectively),keepingtheDBfraction tozero, and
tudesforagivenWDisochroneage(werecall thattheWD
the reference 22% of progenitor binaries. The older LF has
isochroneageisequaltothesumoftheprogenitorageplus
a fainter termination, and can beexcludedby means of the
theWDcoolingage),comparedtothecaseoftheSalariset
comparison with theposition of theobserved cut-off.
al.(2009b) IFMR.Comparisons withtheobservedLFshow
thattheuseof theKalirai etal. (2009) IFMRincreases the
Afterthisreassessment of thesolidity of theLFcut-off
estimate of theWD age by just 40 Myr.
as age indicator, we have varied the cluster apparent dis-
tancemoduluswithintherangeestablishedwiththeMSfit- As a second test, we have considered the DA WD
tingandobtainedarangeofWDagestWD=2.25±0.20Gyr. cooling tracks by Renedo et al. (2010 – their calcula-
This age range has been determined by considering all the- tions for metallicity approximately half-solar, theclosest to
oretical LFs thatdisplay after thepeak asharp drop in the NGC6819 metallicity in their calculations), that are com-
starcountsatthebincentredaroundmF606W=26.05.Notice pletely independent from the BaSTI WD models employed
that the range is narrower than the MSTO age range, but here. Renedo et al. (2010) calculations follow the complete
completelyconsistent withtMSTO.Thisnarroweragerange evolution of theWD progenitors through thethermalpulse
HST observations of the WD CS in NGC6819 9
phases and include the effect of CO phase separation upon It can be seen that at high-signal-to-noise ratio, clus-
crystallization, like BaSTI WD models. The CO stratifica- ter stars have a sharp proper motion distribution which is
tionandenvelopethicknessofRenedoetal.models(aswell consistent with a few times 0.1masyr−1, but embedded in
asthemodelinputphysics)areslightlydifferentfromBaSTI the middle of a cloud of field objects, mainly thin disk and
models,butthecoolingtimesdowntotheluminositiesofthe thick disk stars [NGC6819 is at (l,b)≃(74◦,8◦)]. Note the
bottom of the observed CS of NGC6819 are similar. From increasing size of random errors with decreasing signal-to-
their calculations, the match of the cut-off of the observed noise ratio.
LF provide an age older by ∼100Myr compared to the age In order to separate members from non-members we
determined with our reference BaSTI WD models. used the results of the artificial star test illustrated in (f3
andf4)andderivethe1-Dσ asthe68.27thpercentileofthe
added−recovered positions for each coordinate at different
magnitudesteps. The red line marks the2.5σ level.
4 PROPER MOTIONS
Non-members,totherightoftheredline,aremarkedin
In principle a mild contamination from field objects, might red.Inthethirdpanelsfromleft,usingthesamesymbols,we
also affect the shape of the WD LF, but again, it cannot show the vector-point diagrams (in mas yr−1) for four dif-
change the magnitude location of the sharp drop off in the ferent magnitudebins(mF606W =18-20.5, 20.5-23, 23-25.5,
WDLF.Inthissectionweusepropermotionstostrengthen and25.5-28).TheCMDsthatresultsfromthecleaningcrite-
theclustermembershipoftheobservedstarsintheexpected rionofthesecondpanelareshownintherightmostpanelsof
CMD location of theWD CS. thesamefigure,usingbothfilters. Nomatterhowtight the
Proper motionswere determinedbymeansof thetech- circleis,evenatthebrightestmagnitudes,therewillalways
niques described in Bedin et al. (2003, 2006, 2009, 2014). be field objects that accidentally have the same motions of
We used the deep exposures in F814W collected in Octo- NGC6819 members.Thankfully,theWDsof NGC6819 oc-
ber2009asfirstepoch,whileweusedtheF814Wexposures cupyalow-contaminationregionoftheCMD,werefewblue
takeninOctober2012assecondepoch.Thepropermotions faint stars exist, field WDs and bluecompact galaxies both
arecalculatedasthedisplacementbetweentheaverageposi- being generally significantly fainter (Bedin et al. 2009).
tionsbetweenthetwoepochs,dividedbythetimebase-line Although affected by low completeness, it seems even
(about3years),andfinallymultipliedbythepixelscale.We more clear that the sharp drop at mF606W ≃ 26.05 (i.e.,
assumed a WFC3/UVIS pixel scale of 39.773 maspixel−1 mF814W ≃25.6) inFig.2(c)isrealandthatthefewobjects
(Bellini, Anderson & Bedin 2011). As the proper motions along thecontinuation of theWD CS at mF606W ∼27 (i.e.,
signalsareafunctionoftheF814Wmagnitudeonly,weplot mF814W ≃ 26) are most likely field WDs or background
proper motions properties as a function of this magnitude, unresolved galaxies.
rather than F606W. Finally, in Fig. 6 we show the CMDs of the decontam-
Unfortunately, the cluster has a proper motion that is inated WD CS. Although very incomplete, these contain
not significantly different from thebulk ofthefield objects, the best measured WDs in our sample, offering a higher-
and our precision is too low for an accurate discrimination photometric-precision version of the complete sample used
betweenfieldobjectsandclustermembers,especiallyatthe to derive the WD LF. Indeed, the shape of the observed
magnitudes of the faintest WDs. Furthermore, proper mo- blue-turn here appears to be significant, and most impor-
tionsarenotavailableforallsources,withanincompleteness tantly consistent with the shape of the WD DA isochrones
that ishard toassess quantitatively(and reliably);thepre- (indicatedin red)andwith thesyntheticCMDsfor theref-
cision of the derived proper motions is also heterogeneous erence LF of panel b) in Fig. 4. Very interestingly, thesyn-
across thesample. thetic CMDs show around mF606W ∼ 25 and (mF606W −
Even though we cannot do quantitative work with the mF814W)∼0.5afeaturecausedbytheunresolvedWD+WD
propermotions,wecanstillusetheminaqualitativewayto binaries included in the simulation (see Sect. 3 for details),
confirm:(i) thetruncationoftheWDLF,(ii) theobserved that corresponds to the end of the DA cooling sequence
shape of theend of theWD CS (as thestars havingproper shifted 0.75mag brighter (see upper panels of the same fig-
motions are also the ones with the best photometry), and ure). The observed CMDs exhibit a very similar feature lo-
(iii)thegoodnessoftheemployedisochrones(howwellthey catedatthesamemagnitudeandcolour,hintingatthepres-
reproduce theblue-turn). enceofasmallfraction ofunresolvedWD+WDsystems,as
The left panel of Fig. 5 shows as small dots all stars suggested also by thefit of theLF (see Section 3).
in panel (c) of Fig. 2, but this time plotting the colour A future paper (involving other team-members) will
vs.mF814W instead of vs.mF606W. Stars for which it was dealwiththeabsolutemotionsofNGC6819withrespectto
possible to estimate a proper motion are highlighted with backgroundgalaxiesinordertocomputetheclusterGalactic
open circles. Only members along the MS were used to de- orbit using as input the sources in the catalogue described
fine the transformations between the two epochs, and they in the next section. [Similar to the study of the orbit of
are marked in blue. In the second panel, we show for this NGC6791 donein Bedin et al. 2006.]
sub-sample of stars the magnitudes of the proper motions
vs. mF814W. Cluster members should have a dispersion of
the order of ∼1 km s−1, which at a distance of ∼2.4kpc
5 ELECTRONIC MATERIAL: WFC3/UVIS
would correspond to a proper motion internal dispersion of
AND ACS/WFC
less than 0.1masyr−1, making them an ideal almost-fixed
reference frame. For this reason our zeroes of the motion ThecatalogueisavailableelectronicallyinthisJournal(and
will coincide with the cluster bulkmotion. also under request to the first author). In the catalogue,
10 L. R. Bedin et al.
Figure 7. Colour-Magnitude diagrams obtained from the
Figure 6. A zoom-in of the decontaminated CMDs in Fig. 5 ACS/WFC parallel fields shown in the bottom-right panel of
centred on the WD CS, with colour vs. mF814W in left panels Fig.1.Thebottomandleftaxesdisplayinstrumentalmagnitudes,
and vs. mF606W in the right panel. The top panels display the whilethetopandrightthecalibratedones.Dashedlinesindicate
observedCMDs,withover-imposedtheWDisochronesemployed the level where saturation sets-in. Note that it is possible to re-
in Fig. 3 (solid lines: DA in red, DB in blue). We also display, cover photometry forsaturated starsuptoabout3.5magnitude
as dotted lines, the same isochrones but 0.75 mag brighter, to abovetheselimits(seeGilliland2004fordetails),butnotenough
markapproximately themagnitude andcolourrangecovered by toobservetheMSTOstarsreliably.
apopulation ofunresolvedWD+WD binaries.Thebottom pan-
elsdisplaythesyntheticCMDscorrespondingtothereferenceLF
shownasasolidlineinpanelb)ofFig.4(seeSect.3fordetails) forUVIS,25maspixel−1forWFC).Wehaveincludedinthe
with approximately the same number of stars of the decontami- headeroftheimage,asWorldCoordinateSystemkeywords,
natedCMDs(seeSect. 3fordetails). ourabsoluteastrometricsolutionbasedonthe2MASSpoint
source catalogue. As part of the material of this article, we
also electronically release these astrometrized stacked im-
Col.(1) containstherunningnumber;Cols.(2) and(3)give ages.
the J2000 equatorial coordinates in decimal degrees for the
epoch J2000.0, while Cols.(4) and (5) provide the pixel co-
ordinates x and y in a distortion-corrected reference frame.
6 CONCLUSIONS
Columns(6)to(11)givephotometricdata,i.e.,mF606W and
mF814W magnitudesandtheirerrors.Ifphotometryinaspe- WehaveusedHubbleSpaceTelescope toobservetheWDse-
cific band is not available, a flag equal to 99.999 is set for quencein NGC6819, a nearsolar-metallicity old open clus-
the magnitude and 0.999 - for the error. In Fig. 7 we show ter within the Kepler mission field of view. By means of
the CMDs obtained from the unselected catalogue of the ourphotometryandcompletenesstestswehavedetermined
ACS/WFC parallel fields, which we have not analysed and the LF of the cluster WD CS, which exhibits a sharp drop
used in this article. For ACS/WFC we provide the entire at mF606W = 26.050±0.075, and a shape consistent with
list of all detections,thesestill includeblendsand otherar- theoretical predictions for a canonical cluster CS.
tifacts.ForthecaseofWFC3/UVISmaincataloguewealso Isochrone fits to the cluster MS have provided E(B−
provide the subset of the selected stars as shown in Fig.2 V) = 0.17±0.01, (m−M)0 = 11.88±0.11, and a MSTO
andaWDflag.Wealsoprovidethephotometryfrom short age tMSTO =2.25±0.30Gyr. These distances and ages are
exposures. in agreement with independent constraints from eclipsing
The stack images shown in the bottom panels of Fig.1 binary and asteroseismological analyses.
provide a high-resolution representation of the astronom- WehavereassessedtherobustnessoftheWDLFcutoff
ical scene that enables us to examine the region around magnitudeasageindicatoranddeterminedanageof2.25±
each source. Indeed, the pixel-based rapresentation of the 0.20GyrfromtheCS,completelyconsistentwiththeageof
composite data set provides a nice objective cross-check on 2.25±0.30Gyr obtained from the MSTO. We have tested
thecatalog-based representations,whichisaproductofour theeffectofadifferentIFMRonourWDages,obtainingan
subjectivefindingandselectioncriteria.Thestackedimages agelargerbyjust40MyrwhenusingtheKaliraietal.(2009)
are 20000×20000 for UVIS (and 24000×24000 for WFC) IFMR instead of our reference Salaris et al. (2009) IFMR.
super-sampled pixels (by a factor of 2, i.e., 20maspixel−1 We have also employed the completely independent set of