Rocky Planetesimals as the Origin of Metals in DZ Stars

0.87 MB·English

by  J. Farihi

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed27January2010 (MNLATEXstylefilev2.2)
Rocky planetesimals as the origin of metals in DZ stars
J. Farihi1, M. A. Barstow1, S. Redfield2, P. Dufour3, N. C. Hambly4
1Department of Physics & Astronomy, Universityof Leicester, LeicesterLE1 7RH, UK; [email protected]
2Astronomy Department, Van Vleck Observatory, Wesleyan University,Middletown, CT 06459, USA
3D´epartement de Physique, Universit´e de Montr´eal, Montr´eal, QCH3C 3J7, Canada
4Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK
0
1
0
2

n
ABSTRACT
a
The calcium and hydrogen abundances, Galactic positions and kinematics of 146 DZ
J
white dwarfs from the Sloan Digital Sky Survey are analyzed to constrain the possi-
7
ble origin of their externally polluted atmospheres. There are no correlations found
2
between their accreted calcium abundances and spatial - kinematical distributions

] relative to interstellar material. Furthermore, two thirds of the stars are currently lo-
P cated above the Galactic gas and dust layer,and their kinematics indicate multi-Myr
E residences in this region where interstellar material is virtually absent.
. Where detected, the hydrogenabundancesfor37DZA starsshowlittle orno cor-
h
relationwithaccretedcalciumorspatial-kinematicaldistributions,thoughthereis a
p
- generaltrend with cooling age. It is found that Eddington type accretion of interstel-
o lar hydrogen can reproduce the observed hydrogen abundances, yet simultaneously
r fails to account for calcium. The calcium-to-hydrogen ratios for the DZA stars are
t
s dominated by super-solar values, as are the lower limits for the remaining 109 DZ
a stars. All together, these polluted white dwarfs currently contain 1020±2g of calcium
[
in their convective envelopes, commensurate with the masses of calcium inferred for

1 large asteroids.
v A census of current Teff .12000K, helium-rich stars from the Sloan Digital Sky
5 Survey suggests the DZ and DC white dwarfs belong to the same stellar population,
2
with similar basic atmospheric compositions, effective temperatures, spatial distribu-
0
tions, and Galactic space velocities. Based on this result, pollution by the interstel-
5
lar medium cannot simultaneously account for both the polluted and non-polluted
.
1 sub-populations. Rather, it is probable that these white dwarfs are contaminated by
0 circumstellar matter; the rocky remains of terrestrial planetary systems.
0
In this picture, two predictions emerge. First, at least 3.5% of all white dwarfs
1
harbor the remnants of terrestrial planetary systems; this is a concrete lower limit
:
v and the true fraction is almost certainly, and perhaps significantly, higher. Therefore,
i onecaninfer thatatleast3.5%ofmain-sequenceA-andF-typestarsbuildterrestrial
X
planets. Second, the DZA stars are externally polluted by both metals and hydrogen,
r and hence constrain the frequency and mass of water-rich, extrasolar planetesimals.
a
Key words: circumstellar matter— minor planets, asteroids— stars: abundances—
stars: chemically peculiar— stars: evolution— planetary systems— white dwarfs
1 INTRODUCTION metal-linedwhitedwarfslikevMa2mustbeexternallypol-
luted.
Owing to a relatively low atmospheric opacity, the de-
The curious presence of heavy elements in the atmospheres tection of calcium in the optical spectra of more than one
of cool white dwarfs has been known since the discovery of dozen cool, single, helium-rich (DZ) white dwarfs preceded
the first degenerate stars; van Maanen 2 is the prototype the availability of 8m class telescopes and high resolution
DZ white dwarf (van Maanen 1917). For more than half a CCD spectrographs (Sion et al. 1990b). Although the sink-
century it has been understood that, in the absence of ra- ing timescales are always orders of magnitude shorter than
diative forces, elements heavier than hydrogen and helium the white dwarf cooling age, heavy elements can persist for
shouldrapidlysinkbelowthephotosphereinthehighgrav- up to 106yr in the sizable convection zones of helium-rich
ity environment of white dwarfs (Schatzman 1948); hence degenerates (Paquette et al. 1986). This fact led somewhat
(cid:13)c 0000RAS
2 J. Farihi et al.
naturally to the hypothesis that the source of the accreted 2 COOL HELIUM-RICH WHITE DWARFS
heavyelementswastheinterstellarmedium(ISM),encoun- FROM THE SDSS DR4
teredinsufficientdensityafewtoseveraltimesperGalactic
The SDSS fourth data release (DR4;
orbit(onaverage)fortheSolarneighborhood(Dupuiset al.
Adelman-McCarthy et al. 2006) contains a prodigious
1993a,b, 1992).
number of new white dwarfs, in the neighborhood of
SeveralfactorshavecontinuallychallengedtheISMpol- 6000 (Eisenstein et al. 2006). Excluding multiple entries
lution scenario. First, the typical dearth of hydrogen rel- for the same source, binaries or binary candidates, and
ative to calcium in DZ stars argues for the accretion of uncertain classifications, there are 95 DZ and 142 DC
volatile depleted material (Dufour et al. 2007; Wolff et al. stars within the DR4 white dwarf catalog. Under further
2002; Sion et al. 1990a). Second, the firm establishment of scrutiny, Dufour et al. (2007) has expanded the number of
the hydrogen-rich DAZ spectral class, with heavy element confirmed, uniqueDZ stars to 146, providing effective tem-
diffusion timescales as short as a few days, and Galactic peratures, calcium abundances, and photometric distances
positions far from known interstellar clouds (Koester et al. under the assumption of log[g(cms−2)] = 8.0. Of these
2005a; Zuckerman et al. 2003). Third, the increasing num- 288 cool, helium-rich white dwarfs in DR4, only one was
ber of metal-contaminated white dwarfs with infrared ex- known previously; G111-54 or SDSS J080537.64+383212.4
cessesandcloselyorbitingringsofdustyandgaseousdebris (Dufouret al. 2007; Greenstein 1975).
(Farihi et al. 2009; Jura et al. 2009a; G¨ansicke et al. 2008). Perhaps surprisingly, the current number of DC and
Thus,whilethereisfirmobservationalevidenceofpollution DZ stars in the SDSS are nearly identical. The DR4 cat-
via circumstellar material, as yet there is none favoring the alog autofit temperatures for helium-rich stars are gener-
ISM. ally unreliable near or below 10000K, as their helium at-
mosphere models do not extend below this temperature
Aannestad et al. (1993) provided an extensive spatial,
(Eisenstein et al. 2006). Owing to this fact, the DC star
kinematical, and calcium abundanceanalysis against which
spectroscopic and photometric data were fitted using the
theytestedlikelyscenariosofinterstellaraccretionbasedon
same technique and helium-rich (metal-free) models as in
the best available data at that time, concluding interstellar
Dufouret al. (2007), yielding effective temperatures and
accretion could not explain the abundances in any of their
photometricdistances,againassuminglog g=8.0.Allpho-
15DZwhitedwarfs.However,theirlandmarkstudywaslim-
tometricdataweretakenfromtheDR4whitedwarfcatalog
ited to targets within 50pc for the most part, and to stars
(Eisenstein et al. 2006), with stellar parameters for the DZ
that were proper-motion selected, and hence biased toward
stars from Dufouret al. (2007) and the DC model fits per-
higher space velocities (Sion et al. 1988). Kilic & Redfield
formed for thiswork.
(2007) examined possible correlations between the current
Spatial and kinematical data for these white dwarfs
positions of 35 DAZ white dwarfs and models of the sur-
were obtained from the SDSS seventh data release (DR7;
roundingISMas inferred from nearbycolumn densitymea-
Abazajian et al.2009).Thislatest datareleaseincludesthe
surements, finding a lack of sufficient material to account
USNO-SDSS derived proper motion catalog of Munn et al.
for most polluted stars.
(2004) anditsrecentamendments(Munnet al. 2008),with
This paper returns to the question of the origin of the statistical errors around 3masyr−1. For a handful of white
DZ spectral class. Historically, the DZ stars outnumbered dwarfs, propermotions were not available in theDR7cata-
theirhydrogen-richcounterpartsstarsby25:1(Dupuiset al. log;forthesestarsmeasurementsweretakenfromtheSuper-
1993b) until high resolution, spectroscopic searches with COSMOS Science Archive (SSA; Hambly et al. 2001), the
largetelescopesuncoveredacommensuratenumberofDAZ LSPM catalog (Lepine& Shara 2005), or were calculated
stars (Koester et al. 2005a; Zuckerman et al. 2003). Today, for this work based on two or more positions on archival
theratioofknownDZtoDAZstarsisgreaterthan4:1,due photographicplatesandSDSSimagesseparatedbyapprox-
almost exclusively to the Sloan Digital Sky Survey (SDSS; imately 50 years. These proper motions are listed in Table
Eisenstein et al. 2006). The ability to detect mild levels of 1.
heavy element pollution in these stars, combined with the
relative lack of circumstellar material at both the DZ and
coolDAZwhitedwarfs(Farihi et al.2009),makestheorigin
of the DZ stars challenging to constrain. 3 ABUNDANCE ANALYSIS
It is argued here that thehundredsof newly identified, TheSDSSwhitedwarfsofferadeepersnapshotoftheSolar
cool, helium-rich white dwarfs from the SDSS provide an neighborhood and beyond. Owing to the g > 22 AB mag-
excellent,spatiallyandkinematicallyunbiasedsampleupon nitude limit of the survey, and its general avoidance of the
whichtotesttheISMaccretionhypothesis.Thesestarsform Galactic plane, these white dwarfs typically represent dis-
a large statistical sample that favors an alternative to the tant stars (tens tohundredsofpc) at intermediate Galactic
accretion of Galactic gas and dust; as a whole the SDSS latitudes. Hence the SDSS DZ stars are an excellent probe
DZ stars do not show the spatial, kinematical, or elemen- of thelocal ISM(LISM) both within and beyond theLocal
talabundancecorrelationsexpectedfromaccretionepisodes BubbleorChimney(Welsh et al.1999,1994),whichextends
within theplane of the Galaxy. Furthermore,the SDSSDZ roughly to 100pc (Redfield& Linsky 2008).
andDC(helium-rich,featureless) starsappeartobesimilar A number of relevant quantities were calculated from
populationsofpollutedandnon-pollutedstarsbroadlyshar- the DZ and DC white dwarf spatial and kinematical data:
ing all relevant characteristics save photospheric calcium, tangential speed vtan, height above (or below) the Galactic
and perhaps hydrogen. mid-plane z, space velocities UVW (assuming zero radial
| |
(cid:13)c 0000RAS,MNRAS000,000–000
The origin of metals in DZ stars 3
Table1.WhiteDwarfProperMotionsUnavailableinSDSSDR7 plotsthecalcium abundances(throughoutthispaper[X/Y]
=log[n(X)/n(Y)]),relativetohelium,ofthe146DZstarsas
SDSSWhiteDwarf µ P.A. Sources afunctionofeffectivetemperature,heightabovetheGalac-
(masyr−1) (deg) tic mid-plane, and tangential speed. A low abundance cut-
off at higher effective temperatures and larger distances is
J000557.20+001833.3 209.3 93.5 1,2,3
apparentintheupperandmiddlepanels;theseareobserva-
J020001.99+004018.4 33.2 87.7 1
tional biases arising from higher atmospheric opacities and
J020132.24−003932.0 90.7 184.1 1
lower spectroscopic sensitivity, respectively (Dufour et al.
J080211.42+301256.7 59.4 199.8 3
2007;Koester et al. 2005a).Theclassical conundrumof the
J082927.85+075911.4 168.0 258.7 1
J083434.68+464130.6 225.1 133.2 1,2,3 DZwhite dwarfs presentsitself well in theupperpanel; the
J084911.86+403649.7 96.3 233.8 1 majorityofstarshavenodetectedhydrogen,includingthose
J093545.45+003750.9 66.2 227.0 1 with thehighest calcium abundances.
J094530.20+084624.8 67.4 255.7 1
The middle and lower panels of Figure 1 are notewor-
J113711.28+034324.7 176.5 230.3 2,3
J122204.48+634354.5 66.6 251.1 1 thy because they fail to reveal a physical correlation be-
J140316.91−002450.0 63.6 96.9 3 tween accreted calcium and height above the Galactic disk
J144022.52−023222.2 224.3 271.8 3 ortangentialspeed.TheGalacticgasanddustlayerextends
J153032.05+004509.0 71.7 249.7 1 roughly 100pc above theGalactic mid-plane, and yet some
of most highly polluted DZ white dwarfs lie well abovethis
Sources:(1)SSA;(2)LSPMcatalog; (3)thiswork. region. The lower panel is relevant in the context of gravi-
tationally driven accretion, expected if the DZ stars obtain
their heavy elements while moving through the ISM. The
Table 2. Statistical Properties of SDSS DZ and DC White
lackofcorrelationbetweenspeedandthemetalabundances
Dwarfs
argues, qualitatively but strongly, against fluid accretion of
Parameter 146DZStars 142DCStars ISM.
Teff (K) 8700±1330 9040±1610 Figure 2 plots the masses of calcium contained in the
g−z −0.29±0.23 −0.18±29 convection zones of these metal-enriched stars using their
d(pc) 196±91 206±96 abundancestogetherwiththeconvectiveenvelopemassesfor
|z|(pc) 140±67 148±72 log g=8 helium-rich whitedwarfs (Koester2009).The fig-
ureshows that the most highly polluted DZ stars currently
vtan (kms−1) 48±32 52±25 harborupto1022gofcalciumintheirconvectionzones.This
U (kms−1) 2±35 −4±38
is a truly remarkable amount of a single heavy element, a
V (kms−1) −12±28 −12±24
W (kms−1) 1±25 −1±25 mass in calcium alone that is roughly equivalent to the to-
|W|(kms−1) 18±17 19±15 tal mass of a 200km diameter asteroid(!). A more typical
T (kms−1) 43±29 48±23 DZ star appears to contain around 1020g of calcium, still
a prodigious amount, and corresponds to a time-averaged
Spacevelocitieswerecalculatedassumingzeroradialvelocityand metalaccretionrateof2 108gs−1 (Farihi et al.2009),and
correctedtotheLSR(otherwiseT =vtan). a total accreted mass of×metals of just under1022g.
Figure 3 plots the hydrogen abundances in 37 of
velocity), and total space velocity T2 = U2 + V2 +W2.
the 146 DZ stars where hydrogen is detected or inferred
SpacevelocitieswerecorrectedtotheLocalStandardofRest
(Dufouret al. 2007), versus height above the Galactic mid-
(LSR;Dehnen & Binney 1998), with U positive toward the
plane and tangential speed. No obvious pattern is seen, al-
Galactic anticenter, V positive in the direction of Galactic
thoughtheremaybeahigherdensityofDZAstarsnearthe
rotation,andW positivetowardthenorthGalacticpole.In
Galacticdiskandperhapsalsotowardmoremodest speeds,
theabsenceofcorrectiontotheLSR,theassumptionofzero
but the former may be an observational bias due to dimin-
radial velocity is equivalent to T = vtan. Tangential speeds ished spectroscopic sensitivity. In any case, one should ex-
were calculated from
pect a correlation between these quantities if the hydrogen
vtan(kms−1)=4.7405 d(pc) µ(arcsecyr−1) (1) were accreted from ISM.
× ×
As discussed by Dupuiset al. (1993a), white dwarfs
The Sun does not have zero velocity relative to the LSR; accreting Solar abundance matter within the ISM at 3
depending on viewing direction, the Solar motion con- 1011gs−1 for106yrcanaccumulatetheheavyelementmas×s
tributes vtan = 10 15kms−1 (Dehnen& Binney 1998; fractions observed in the convective envelopes of DZ stars,
−
Mihalas & Binney1981).Table2liststhecalculatedparam- such as plotted in Figure 2 (however, this cannot account
eter means for the SDSSDZ and DC white dwarfs. for their hydrogen abundances, discussed in detail below).
Yet some care must be taken not to invoke such high ac-
cretion rates without skepticism; while these rates are suf-
3.1 A Glance at the Data
ficient to account for the calcium data (that is the nature
As a first attempt to establish the relationship, if any, be- of the hypothesis), the physical plausibility is of equal im-
tween the DZ stars and the ISM, one can search for spa- portance. Below, the problem of interstellar accretion onto
tial or kinematical correlations with calcium abundance white dwarfs is reviewed in some detail and updated with
(Zuckerman et al. 2003; Aannestad et al. 1993). Figure 1 old and new theoretical and empirical considerations.
(cid:13)c 0000RAS,MNRAS000,000–000
4 J. Farihi et al.
Figure 2. Mass of calcium and hydrogen in the convective en-
velopes of the SDSS DZ stars; envelope masses were taken from
Koester(2009).Atypicalcalciummassintheconvectionzoneof
these stars is 6×1019g, roughly the same as that contained in
the asteroid Minerva, whose mean diameter is 146km and total
massis3×1021 g.
lasting around 105yr would suffice to transform a DB (or
DC)starintoaDA(Koester1976).Therefore,theexistence
ofmorethan1000hydrogen-poorwhitedwarfsintheSDSS
(Eisenstein et al. 2006) argues strongly against the Bondi-
Hoyletypeaccretion of interstellar hydrogen.
Regardless of particulars relevant only to the metal-
enriched white dwarf varieties, the lack of hydrogen in
helium atmosphere white dwarfs is of great observational
Figure1.Calciumabundancesforthe146DZstarsplottedver- significance. High resolution and high signal-to-noise spec-
sus effective temperature, height above the Galactic mid-plane, troscopy reveals roughly equal numbers of DB stars where
and tangential speed. Those stars with detected hydrogen are hydrogen is either undetected or detected but deficient by
plottedasfilledcircles,whilethosewithoutareplottedwithopen a few to several orders of magnitude relative to helium
circles.
(Vosset al. 2007). The highest mass of hydrogen seen in a
DB(metal-free)atmosphereisaround8 1022gina12000K
×
star, while the older and cooler counterparts studied here
3.2 A Closer Look at the Interstellar Accretion
(theDZAstars)containupto4 1024g.Thishighermassof
Hypothesis: Hydrogen atmospheric hydrogen would be×accreted in under106yrat
Both Koester (1976) and Wesemael (1979) were among the interstellar Bondi-Hoyle rate assumed by Dupuiset al.
the first to consider the issue of interstellar accretion onto (1993a),andhencethiscannotbethecorrectpicturedueto
helium-rich white dwarfs, both concluding that the atmo- thelack of such hydrogen masses in DB stars.
spheres of these stars (both typeDB and DC) were incom- Gravitational accretion of ISM particles by a star of
patible with Bondi-Hoyle accretion of interstellar hydrogen. mass M and radius R, in the supersonic regime follows the
That is, in most cases a single interstellar cloud encounter mathematical form (Alcock & Illarionov 1980)
(cid:13)c 0000RAS,MNRAS000,000–000
The origin of metals in DZ stars 5
(Bondi1952),yieldinganaccretion rateforinteractingpar-
ticles
M˙BH = 4πG2sM3 2ρ∞ (6)
Thismass infall raterepresentsthemaximal, idealized case
where themean free path of theparticles is such that colli-
sionsareimportantandtransversemomentumiseffectively
destroyed downstream from the star. It is also physically
unrealistic in perhaps all situations excepting an ionized
plasma, as it assumes no net angular momentum between
the accreting star and its surrounding medium (Koester
1976), and it certainly does not apply to neutral atoms or
large particles (Alcock & Illarionov 1980). The ratio of the
Bondi-Hoyle to Eddington accretion rates is v2R/2GM for
v c,oraround104fortypicalwhitedwarfsizesandspeeds
≫
(Koester1976).Table3liststypicaldensities andotherrel-
evantparametersforfourfundamentaltypesofISM:molec-
ular clouds, diffuse clouds, warm ionized, and hot ionized.
Listed also are the expected high-end mass infall rates for
white dwarfs moving through these regions following either
Bondi-Hoyle (fluid) or Eddington (geometric) type accre-
tion.
The two-phase accretion-diffusion scenario as laid out
by (Dupuiset al. 1993a), invokes106yr within a cloud (ac-
cretion),and5 107yrbetween clouds(diffusion).Fordisk
×
starswithGalacticorbitssimilartotheSun,thesetimescales
imply about five cloud encounters per 240Myr orbit. The
motions of interest are the relative motions between stars
and the ISM, the latter which should be moving within
the relatively low velocity spiral arms of the Galactic disk
(Jahreiß & Wielen 1997).
Figure 3. Hydrogen abundances for the 37 DZA stars plotted
Ifcorrect,thisimpliesatypicalhelium-richwhitedwarf
versusheightabovetheGalacticmid-plane,andtangentialspeed. moving at 50kms−1 relative to the LSR and (presumably)
the ISM travels, on average, 240pc within clouds during a
single Galactic rotation. This timescale corresponds to the
M˙ =π(RA+R)Rsρ∞ (2) cooling age for a log g = 8.0, 14500K helium-rich white
dwarf, and hence such a star should, according to this sce-
whereRA istheaccretion radius,s=√v2+cs2 forrelative nario,obtain upto5 1022gof hydrogenviageometric ac-
×
stellar velocity v and ambient sound velocity cs, while ρ∞ cretion,or[H/He]= 4.4.Thisvalueiscommensuratewith
−
is the unperturbed density of material being accreted. The thehighesthydrogenabundancesobservedinDBstars,and
accretion radius is definedas wellabovethelowerlimitofdetectability(Voss et al.2007).
This comparison implies 1) the densities and corre-
2GM
RA (3) spondingEddingtonaccretion ratesinTable3aretoohigh,
≡ s2 or 2) cloud encounters last less than 106yr or are less fre-
and is often referred to the as the Bondi or Bondi-Hoyle quent than once per 5 107yr, but is otherwise consistent
×
radius. For all possible speeds considered here, RA R, withthegeometriccaptureofhydrogenwithintheISM,and
≫
and the accretion rate is given by inconsistent with fluid accretion. Ignoring the fact that all
hydrogen will be ionized within the Bondi-Hoyle radius of
M˙ =2πGMRARsρ∞ (4) the white dwarf, and hence should accrete as a plasma at
thefluidrate(Alcock & Illarionov1980),itisclearthatfluid
or accretion of hydrogen does not occur in helium atmosphere
white dwarfs, if and when passing through dense ISM.
M˙ = 2πGMRρ∞ (5)
Edd
s
3.3 Super-solar Calcium to Hydrogen Abundances
This is the Eddington rate (Eddington 1926), the accre-
tioninducedonnon-interactingparticlesbythegeometrical- The average DZ star in the sample has an effective tem-
gravitational cross section of the star as it travels through perature of 9000K and a cooling age around 860 Myr
theISM. (Fontaineet al. 2001). A hydrogen abundance of [H/He]
Bondi-Hoyle theory (i.e. including gas pressure; Edgar = 3.8 was detectable in all 146 DZ stars (Dufour et al.
2004)demonstratesthattheeffectivecrosssectioninEqua- 200−7),equivalenttoabitlessthan1024gofhydrogenatthe
tion 4, πRAR becomes πRA2 in the fluid dynamical limit averageDZtemperature.Inordertoavoidsuchahydrogen
(cid:13)c 0000RAS,MNRAS000,000–000
6 J. Farihi et al.
Table 3.Representative HighISMAccretionRatesforWhiteDwarfs
ISMType Gas ρ∞ T cs M˙BH M˙Edd
(cm−3) (K) (kms−1) (gs−1) (gs−1)
MolecularCloud H2 1000 20 0.3 1012 108
DiffuseCloud H 100 80 1 1011 107
WarmIonized H+ 1 8000 1 109 105
HotIonized H+ 0.01 106 100 107 103
Accretion rates listed are order of magnitude estimates calculated for the
listedparametersandv=50kms−1,aspeedtypicalofboththeDZandDC
samples.
mass within its outer envelope, a helium-rich white dwarf 3.4 A Closer Look at the Interstellar Accretion
must eschew 1) fluid accretion in any region similar to the Hypothesis: Metals
relativelylowdensityLISMfor99.9%ofitscoolingage,and
Interstellargas–bothcoldandwarm–ismetal-poor;heav-
2) geometrical accretion in any molecular cloud, for around
ierelementstendtobelockedupingrains,leavingonlylight
90%ofitscoolingage.Only12oftheDZstarsor8%ofthe
andvolatileelements(Venn & Lambert1990).Thisfactwas
samplehavehydrogenabundances[H/He]> 3.8,implying
− not considered by Dupuiset al. (1993a), whose accretion-
such avoidance has occurred for the remaining 134 DZ(A)
diffusion scenario explicitly assumes 1) accretion based on
stars.IfthephotosphericcalciumoriginatesintheISM,then
fluid rates for hydrogen also apply to heavy elements, and
aprocessthataccretesmetal-richdustgrainswhileeschew-
2) elements are accreted in Solar proportions. Aboveit was
ing hydrogen (and other gaseous volatiles) is necessary to
shownthatfluidaccretion ratesforISMaccretion ofhydro-
accountfor theDZwhitedwarfs withlittle ornohydrogen.
gen over predict the observed abundances in DB stars by a
Historically, the super-solar [Ca/H] abundances of DZ few to several orders of magnitude. But more importantly
whitedwarfswerequalitativelyaccountedforbypreferential forheavyelementaccretion isthefact thatinterstellar dust
accretionofdustgrains(Dupuiset al.1993b).Ahypothesis grains should not accrete at the fluid rate.
topermittheincursionofdustgrainsyetrepulselightgasis Solid particles will follow trajectories independent of
thepropellermechanism,wherebychargedionspeciesarere- surrounding gas whether neutral, or charged and electri-
pelledattheAlfv´enradius(Wesemael & Truran1982).This callyormagneticallycoupledtothegas(Alcock & Illarionov
model fails to explain a number of very hydrogen-deficient 1980). However, dust grains approaching the stellar surface
DZ-typestars,includingGD40with[H/He]= 6.0,awhite will be separated into their constituent elements via sub-
−
dwarfforwhichFriedrich et al.(2004)failedtofindevidence limation that proceeds at slightly different rates according
of magnetism sufficient to drive a propeller. Rather, in the to the particular chemical species, resulting in significant
samestudytheDZAstarLHS235,with400timesmorehy- ingress prior to becoming gaseous. The gradual evapora-
drogenthanGD40wasfoundtohavea7kGmagneticfield tion of approaching interstellar dust has two major conse-
– essentially the exact opposite of what might be expected quences.First,gaseousheavyelementscannotaccreteatthe
if hydrogen was screened efficiently by a propeller. Perhaps fluid rate, as the effective gravitational cross section is sig-
thecoupdegrˆaceforthepropelleristhemagneticDZAstar nificantly reduced bythe close approach necessary for their
G165-7; with a 650 kG field, [Ca/He] = 8.1, and [H/He] evaporation out of grains. Second, the process of sublima-
−
= 3.0 (Dufouret al. 2006), it has everythinga ‘fan’ could tion will spatially and temporally separate heavy elements
−
hope for. But should this star haveso much hydrogen? Ac- accordingtotheirspecificevaporationtemperatures,result-
cording to theory, its propeller failed around 660 Myr ago inginpreferentiallyhigheraccretionratesforvolatilespecies
asa7500Kstar(Wesemael & Truran1982),andcouldhave suchas icemantles, as opposed tometallic atoms orrefrac-
amassed at most 2 1024gin 660 Myrofcontinuous accre- torymaterial.Thislatterconsequenceisinterestingbecause
×
tion at the high Eddington rate, corresponding to [H/He] it predicts a relatively high volatile to refractory element
= 4.0.Clearly,thisstarwasneverapropeller.Thismecha- accretion mixture; in stark contrast both to the observed
−
nismisunsupportedbyobservations(Friedrich et al.2004), abundancesandtothoseexpectedfromtheaccretionofcir-
andisfundamentallyatoddswiththeexistenceDBAZand cumstellar material (Sion et al. 1990a).
DZA stars (Voss et al. 2007). The radius at which dust grains are evaporated,
The upper panel of Figure 4 plots the hydrogen ver- Rev, and become part of the ambient, interacting gas
sus calcium abundances of all 37 DZA stars. The lack of is substituted for R in Equation 2 which then becomes
any correlation between the two elements suggests either (Alcock & Illarionov 1980)
1) disparate origins, or 2) a common origin with intrinsic
variations in [Ca/H]. Neither of these two possibilities is M˙gr =π(RA+Rev)Revsρ∞ (7)
consistent with ISM accretion. The middle and lower pan-
Ifthegrainsabsorbandradiateenergyasblackbodies,they
els of Figure 4 display the inferred [Ca/H] abundances and
will evaporate at temperature Tev at a distance from the
lowerlimitsforthe37DZAand109DZstars.Inbothcases,
star given by (Chen & Jura 2001)
thevast majority of these values are super-solar by at least
an order of magnitude (see also Figure 12 of Dufour et al. R T 2
2007). Rev eff (8)
≈ 2 (cid:16)Tev(cid:17)
(cid:13)c 0000RAS,MNRAS000,000–000
The origin of metals in DZ stars 7
M˙gr = πGMRρ∞ Teff 2 (9)
s (cid:16)Tev(cid:17)
All else being equal, this rate should be around 10 to 18
times the Eddington rate for refractory-rich dust grains,
suchasinterstellarsilicates.Aspointedoutmorethanthirty
yearsagobyKoester(1976),theaboveanalysisignoresany
netangularmomentumbetweenthestarandthesurround-
ing ISM, which will work to reduce the effectiveness of ac-
cretionexceptingwherematerialisfullyionized,asituation
unlikelytoberealizedforgaseousheavyelements.Thephys-
ical considerations discussed in this section have been, for
the most part, overlooked in several major studies of DZ
stars, and their absence has biased outcomes favoring the
interstellar origin of metals in cool white dwarfs in general
(Koester & Wilken 2006; Wolff et al. 2002; Friedrich et al.
2000; Dupuiset al. 1993b).
ApplyingEquation8tothehighestdensity,Solarabun-
danceISM(i.e.adusttogasratioof1:100, [Ca/H]= 5.6,
ρ∞ =1000gcm3),awhitedwarfcanaccreteheavyelem−ents
from the ISM at up to 2 107gs−1. Over 106yr of sus-
×
tained accretion at this rate, a typical white dwarf would
accumulate 7 1018g of calcium in its convectiveenvelope;
×
longer timescales are irrelevant because diffusion begins to
compete with accretion. This quantityof calcium is able to
accountforasmallminorityoftheobservedenvelopemasses
plotted in the upperpanel of Figure 2; the average calcium
massis10timeshigher,withafewvalues3ordersofmagni-
tudegreater. Thiscalculation assumes1)thehighest accre-
tion rate for dust grains within dense ISM regions, and 2)
starsthatcurrentlyretaintheirpeakcalciumabundancesto
withinanorderofmagnitude.Hence,thecalculationshould
overpredicttheamountofcalciumpollutingthestellarcon-
vectionzonesbyonetoafewordersofmagnitude.Therefore,
if this analysis is valid to within an order of magnitude, it
is all but certain that the photosphericcalcium in DZ stars
cannot have interstellar origins.
TheDAZwhitedwarfsmakethispointevenmorestrik-
ing.Forthesepolluted,hydrogenatmospherestarswiththin
convection zonesandshort metaldiffusion timesrelative to
theDZstars,Koester & Wilken(2006)infercontinuousand
ongoing mass accretion rates based on a highly probable,
current steady state balance between accretion and diffu-
sion. Theinferred DAZaccretion rates for Solar abundance
matter, up to 2 1011gs−1, are quite similar to the high
×
rateassumedbyDupuiset al.(1993a)fortheDZstars.Yet
no correlation is found between the implied DAZ accretion
Figure 4. The upper panel plots the hydrogen versus calcium rates and the total space velocity of the stars as expected
abundances for the 37 DZA stars, while the middle panel plots inthecaseoffluidaccretion(Koester & Wilken2006).Fur-
ahistogramoftheir[Ca/H]ratios.Thelowerpanelplots[Ca/H] thermore, there are no known regions of enhanced LISM
ratio lower limits forthe 109 DZ white dwarfs without detected density in the vicinity of the DAZ stars (Kilic & Redfield
hydrogen.TheSolarabundance is[Ca/H]=−5.6. 2007; Koester & Wilken 2006; Zuckerman et al. 2003), and
Table 3 reveals that accretion rates of 1011gs−1 are only
even theoretically possible within relatively dense clouds,
Taking a typical DZ effective temperature of 9000K from
which are not seen. Lastly, there is firm evidence that the
Table 3 and Tev between 1500 and 2000K, the resulting nearby DAZ G29-38 does not accrete matter at the fluid
evaporation radius is between 10 and 18 white dwarf radii
rate,butratherhasanupperlimit basedonX-rayobserva-
(or 0.13 to 0.23R⊙). This is a few hundred times smaller tions that is 25 times lower (Jura et al. 2009b).
thanatypicalBondi-Hoyleradius,around0.5AUforawhite
There is no physical reason why helium and hydrogen
dwarf,andhenceheavyelementswillaccreteataratemuch
atmosphere white dwarfs should become polluted via sep-
closer to the Eddington rate. In this situation RA ≫ Rev, arate mechanisms; in fact, Occam’s razor argues against a
and the resulting mass infall becomes
bimodal theory. The fact that some examples of both va-
(cid:13)c 0000RAS,MNRAS000,000–000
8 J. Farihi et al.
rieties of metal-contaminated stars are found with closely from the Galactic mid-plane, and 2) have not traveled sig-
orbiting dust is testament to this fact (Farihi et al. 2009). nificantlyfurtherthanaround18pcabovethegasanddust
In this regard, the only real difference between the DZ and layer,on average. Thisdistanceconstraint corresponds toa
DAZstarsisthatthelattergroupiscurrentlyaccretingfrom star traveling at the sample mean W = 18kms−1 speed
| |
its immediate surroundings, while the former group carries (see Table 2) overa typical Myr diffusion timescale.
their metallic scars long after a pollution event has ended However, these requirements do not match the obser-
(Koester 2009). vations. First, more than half the sample (81 stars or 58%)
currentlysitmorethan120pcabovethediskoftheGalaxy.
Second, and rather damningly, nearly half of the sample is
movingbackintothediskratherthanaway.Theupperpanel
4 SPATIAL - KINEMATICAL ANALYSIS of Figure 5 reveals 67 polluted white dwarfs that are cur-
rentlymovingbacktowardtheGalacticmid-plane.Manyof
4.1 Polluted White Dwarfs in the Local Bubble
these stars are among the most highly polluted in the sam-
ple, and many have z & 100 pc. The middle panel of the
While Koester & Wilken (2006) obtain capture rates up to
| |
1011gs−1 inthewarm,ionizedLISMwithintheLocalBub- same figure shows the height above the disk as a function
oftotalspacevelocity;surprisinglysomeofthefasteststars
blewhichassumesfluidaccretionisvalidforheavyelements,
arealsohighabovetheplane.Theseresultsstronglyconflict
there are still serious problems with this picture when ap-
with expectations from ISM accretion models.
plied to the DZ stars. The individually identified parcels
In order to estimate how much time high z DZ stars
of LISM span at most a few pc (Redfield& Linsky 2008),
| |
corresponding to several 104yrof traversal by a typical DZ spend above the spiral arms and interwoven disk material,
one can use the Solar motion as a first estimate. Depend-
whitedwarf. Suchan encounterin atypicalregion of LISM
withρ∞ =0.1cm−3(Redfield& Linsky2000)leadstoM˙BH ing on the Galactic model potential, and whether it in-
rates of 108gs−1, and would provideonly 1016g of calcium cludes dark disk matter, the Sun oscillates about z = 0
every 60 to 90Myr (Matese et al. 1995; Bahcall & Bahcall
pollution if accreting Solar abundance matter. While such
1985; Mihalas & Binney 1981), the former and latter val-
modest an amount of metal can effectively pollute the rel-
uesderivedusingmodelscontainingsubstantialandnodark
atively thin outer layers of DAZ stars, this paltry calcium
diskmatter,respectively.Kuijken & Gilmore(1989)provide
mass requires 10000 LISM encounters to account for the
average calcium mass in the DZ star envelopes. Of course, Wmax and zmax data for 100pc 6 z 6 2000pc based on a
sample of K dwarfs toward the South Galactic Pole and
this presumes fluid accretion is viable for heavy elements,
a Galactic model which contains no dark disk component.
which has been shown above to be physically implausible,
Using a simple harmonic oscillator model, a period can be
thus making legion fluid infall episodes unlikely in the ex-
computedfromthesemaximumheightsandspeedsforstars
treme.Therefore,itissafetoconcludethatwithintheLocal
withinseveralhundredpcofthedisk.Theperiodofasimple
Bubble,ISMaccretionisinconsistentwiththephenomenon
oscillator is
of DZ stars, which on average travel only 50pc during a
106yrmetal sinkingtimescale.
Kz
Pz =2π (10)
r m
4.2 ISM Accretion Above the Galactic Disk? where
P(Trior 6to 12th0e00SKD)SwS,hittehedrewarwfsereknofewwn b(iefyoanndy)20c0opocl Kz =m Wmax 2 (11)
eff (cid:16) zmax (cid:17)
(McCook & Sion 1999). Generally a hindrance for both
magnitude limited as well as proper motion surveys, such In reality, the period is a function of z due to the disk
distant cool degenerates would have V > 18mag, while component of the Galaxy, which acts as a linear term
100km s−1 tangential speeds only yield µ . 100masyr−1. in the vertical gravitational potential, while the spherical
The DZ sample of Aannestad et al. (1993) was limited to component (including the inferred dark halo) acts as a
within 50pc of theSun,but theSDSSDZ sample stretches quadratic term, equivalent by itself to a harmonic poten-
out to 300pc above the disk of the Milky Way (see Figure tial(Bahcall et al.1999).Usingtheaboveequationsandthe
1). While the single DZ outlier at z > 400pc is likely to dataofKuijken & Gilmore (1989)forstarswithin500pcof
| |
be a higher than average mass white dwarf (i.e. its pho- theplane,themeanperiodisPz =80 10Myrandcompares
±
tometric distance is overestimated), the sample as a whole favorably to rigorously derived values for the Sun. Taking
contains 96 (66%) and 26 (18%) stars situated more than Pz = 80Myr, one can then use the same simple model to
100 and 200pc above the plane of the Galaxy. This fact calculate thelength of timeaDZ starwith currentvelocity
alone perhaps provides an insurmountable challenge to the W and height z has spent outside the 100pc Galactic gas
ISMaccretion hypothesis. and dust layer.
ThescaleheightofmoleculargasasmeasuredbyCOis The lower panel of Figure 5 plots a histogram of the
75 25pc(Dame& Thaddeus1985),while thatof neutral, outward- and inward- bound DZ white dwarfs which are
±
atomichydrogenisroughly135pcwithsubstantialirregular- currently at least 100pc above the Galactic mid-plane. All
ities(Lockman et al.1986).Taking100pcasafiducialscale 96 of these stars have spent more than 3 Myr in a region
heightforinterstellargasanddust,andassumingtheentire of space where the accretion of interstellar matter can be
sampleof DZstarsobtained theirmetals from thismedium likely ruled out, 91 of these metal-polluted stars have been
requiresthestars:1)arecurrentlytravelingthroughoraway out of the Galactic disk for over 6 Myr. As can be seen by
(cid:13)c 0000RAS,MNRAS000,000–000
The origin of metals in DZ stars 9
If the majority of these DZ white dwarfs have traveled
away from where they were polluted for a few to several
diffusion timescales, the extant photospheric metals repre-
sent only a fraction of their peak abundances. This picture
dramatically exacerbates the original problem of the metal
origins in the following manner. Instead of accounting for
1022±2g of total accreted metals, a viable theory must now
account for nearly 1024±2g – Ceres and Moon masses of
heavy elements – for a sample which has traveled for 4 to
5 diffusion timescales in the absence of accretion. This pos-
sibility would greatly strengthen the need for efficient de-
livery of planetesimal-size masses of heavy elements, and
combinedwiththehydrogendeficiency,ismoreratherthan
lesschallengingtoexplainwithinterstellaraccretion.Hence
thispossibility is not considered further.
4.3 ISM Accretion At High Speed?
Throughout the preceding sections, a nominal 50kms−1
tangential speed was used for relevant calculations; this
valuebeingsomewhatfriendlytoISMaccretionmodelsand
also themean among the146 DZ starsin thesample. How-
ever, there are 13 stars with vtan > 100kms−1 (and total
space velocities, T > 100kms−1 since their radial veloc-
ities are unknown and assumed to be zero), which would
imply a decrease in the Table 3 fluid accretion rates by an
order of magnitude. There appears to be no correlation be-
tweenthesespeedsandtheaccreted calcium abundancesin
the DZ stars (see Figure 1), and hence there seems little
or no chance that these stars have accreted in this man-
ner.Koester & Wilken(2006)findsasimilarlackofcorrela-
tionamongtheknownDAZstars;amorestrikingstatement
given their necessary ongoing accretion.
While the dependence of geometrical accretion on ve-
locity is milder by comparison, for ISM accretion scenarios
itisreasonabletoexpectamildcorrelation shouldexistbe-
tweenaccreted massand velocity,yetnosuchcorrelation is
seen in Figures 1 or 3. In themiddle panel of Figure 5, one
would expect to find milder velocities necessary to capture
moreISMmaterialasstarsmoveawayfromtheGalacticgas
anddustlayerandintoregionswheretheISMistenuousat
best, yet this pattern is not observed.
5 THE SDSS DZ AND DC WHITE DWARFS
COMPARED
Figure 5.Theupperpanelreveals67DZstarsmovingbackto- IftheISMaccretionhypothesisiscorrect,thentheonlydif-
wardtheGalacticmid-plane,manyamongthemosthighlymetal- ference between a DZ and a DC star is its recent (within
polluted stars in the sample. The middle panel shows the total a few Myr) spatial and kinematical history. That is, dur-
space velocity as a function of height above the Galactic disk, ing that time a DZ star has recently exited a relatively
withmanystarsexhibitinghighvaluesalongbothaxes.Thelower dense patch of ISM, while a DC star has not (the con-
panel is a histogram of Myr spent at |z|>100pc for the 96 DZ
tinuous, warm-phase ISM accretion scenario forwarded by
starscurrentlylocatedinthisregion.
Koester & Wilken(2006)doesnotworkfortheDZstars,as
demonstrated above). Is this thecorrect picture?
ThereareasimilarnumberofDZandDCwhitedwarfs
reviewing Figure 1, these high z DZ stars are not anoma- intheSDSSandacomparison oftheirmodeleffectivetem-
| |
lous in terms of their abundances,but rathermundaneand peratures, g z colors (the longest baseline possible which
−
trulyrepresentativeofthesampleatlarge.Ifanythingthese is unaffected by calcium H and K absorption), Galactic
whitedwarfshavehigherabundancesthanthelower z stars heights, and tangential speeds is shown in Figure 6. There
| |
(butthisislikelyabiasresultingfromspectroscopiccalcium appear to be a few modest differences between the sample
detection sensitivity). distributions;asmallgroupofrelativelylowertemperatures,
(cid:13)c 0000RAS,MNRAS000,000–000
10 J. Farihi et al.
Figure6.Effectivetemperature,g−zcolor,Galacticheight,andtangentialspeedhistogramsfortheDZandDCwhitedwarfs.Forthe
mostpart,thesetwospectral classesappeartorepresentthesamepopulationofhelium-richwhitedwarfs.
and a flatter color distribution are found among the DC the DZ and DC white dwarfs is total; there does not exist
stars, while the z and vtan distributions are fairly similar. anyregionwhereDZstarsarefoundinhigherconcentrations
| |
Table 2 demonstrates the two spectral classes have mean thantheirDCcounterparts.However,thistypeofprojection
parameters which agree rather well despite the relatively is very dense on paper while the actual sky is rather vast,
large standard deviations; their average effective tempera- and it necessarily ignores the third dimension, namely the
tures, distances, Galactic heights, and tangential speeds all distance from the Sun. Therefore a pertinent question to
agree to within 4% to 8%. ask is whether any of these stars are pc-scale neighbors. A
Figure 7 plots the UVW space velocities of the DZ searchwasconductedaroundeachDZandDCstarforother
and DC samples (assuming v = 0), supporting the idea sample stars within a r = 10pc radius, and the results are
rad
theyarebothbasicallythindiskpopulations,eachwithsev- listed in Table 4.
eral possible thick disk members. Table 2 shows the two
groups share the same mean space velocities and velocity
All together 18 pairs of stars were identified in this
dispersions,thelatterbeingthemostimportantindicatorof
manner, three of which lie together within a 5pc region
kinematicalage(Jahreiß & Wielen1997;Mihalas & Binney
of space. There are nine DZ-DC, 4 DZ-DZ, and 5 DC-DC
1981). Together these analyses suggest DZ and DC white
pairs; exactly half the pairs are of mixed spectral type. Of
dwarfsbelongtothesamepopulationofheliumatmosphere,
the DZ-DC pairs, there are three where the total space ve-
thin (and a few thick) disk stars.
locitiesagreetowithin12kms−1,pairs#1,6,and10.Inthe
latter case, each space velocity component by itself agrees
within 3kms−1(!). These three pairs of stars have traveled
5.1 Convergent and Divergent Pairs of DZ and
the last 106yr in adjacent regions of interstellar space, yet
DC White Dwarfs
eachcomponentstarhasevolveddistinctlyfrom itspartner
Figure 8 projects the Galactic longitude and latitude of all –onemetal-polluted and theothernot.Furthermore,there
the DZ and DC stars onto the plane of the sky. While it are two DZ-DZ pairs whose total space velocities differ by
is true that the SDSS observes only certain areas of the more than 100kms−1, thus implying their current spatial
sky, and hence one can a priori expect these two groups to convergenceisincontrast totheirdivergentinterstellarhis-
occupy overlapping regions, the degree of overlap between tory over the last 106yr. Therefore, these two DZ-DZ pairs
(cid:13)c 0000RAS,MNRAS000,000–000