Hot star wind models with new solar abundances

0.07 MB·English

by  Jiri Krticka

Astronomy&Astrophysicsmanuscriptno.spravnez February5,2008
(DOI:willbeinsertedbyhandlater)
Hot star wind models with new solar abundances
J.Krticˇka1 andJ.Kuba´t2
1 U´stavteoreticke´fyzikyaastrofyzikyPˇrFMU,CZ-61137Brno,CzechRepublic,e-mail:[email protected]
2 Astronomicky´ u´stav,AkademieveˇdCˇeske´republiky,CZ-25165Ondˇrejov,CzechRepublic
7 Received20thNovember2006/Accepted11thJanuary2007
0
0
Abstract. We compare the hot-star wind models calculated by assuming older solar-abundance determination with models
2
calculatedusingtherecentlypublishedvaluesderivedfrom3Dhydrodynamicalmodelatmospheres.Weshowthattheuseof

n newabundances withlowermetallicityimprovestheagreement betweenwindobservationandtheoryinseveralaspects. (1)
a Thepredictedwindmass-lossratesarelowerbyafactorof0.76.Thisleadstobetteragreementwithmass-lossratesderived
J
fromobservational analysisthat takestheclumpingintoaccount. (2)Asaresult oftheloweringof mass-lossrates,thereis

7 betteragreementbetweenthepredictedmodifiedwindmomentum-luminosityrelationshipandthatderivedfromobservational
1 analysisthattakestheclumpingintoaccount.(3)Boththelowermassfractionofheavierelementsandlowermass-lossrates

leadtoadecreaseinopacityintheX-rayregion.ThisinfluencesthepredictionoftheX-raylineprofileshapes.(4)Thereis
2 betteragreementbetweenpredictedPionizationfractionsandthosederivedfromobservations.
v
1
Keywords.stars:winds,outflows–stars:mass-loss–stars:early-type–hydrodynamics
1
4
1
0 1. Introduction 2. Basicassumptions
7
0 Massivehotstarsloseasubstantialpartoftheirmassviatheir 2.1.Windmodels
/ stellarwinds.Windparameters,especiallythewindmass-loss
h
p rate(theamountofmasslostbythestarpertimeunit),arethe We used our own NLTE wind models to predict the hot-
- functionsofbasicstellarparameters,forexamplethestellarlu- star wind structure (Krticˇka & Kuba´t 2004, recent improve-
o minosity (see, e.g., Kudritzki & Puls 2000; Krticˇka & Kuba´t mentsinourcalculations,especiallytheinclusionoftheAuger
r
t 2006,forareview).Thewindmass-lossrateisthemostimpor- ionization, will be described elsewhere). Our models enabled
s
a tant wind parameter, because the presence of strong hot-star us to self-consistently solve the hydrodynamicalequations in
: winds influences not only the emergent spectra, but also, for the spherically-symmetric, stationary, radiatively-driven stel-
v
i example,stellarevolution(e.g.,Chiosi&Maeder1986). lar wind. The radiative force (in the Sobolev approximation,
X Sincehot-starwindsaremainlyacceleratedbytheabsorp- Castor 1974)and the radiativeheating/coolingtermwere cal-
r tion (or scattering) of radiation in lines of heavier elements culated using the solution of NLTE equations, for which we
a
(like carbon, nitrogen, or iron), the radiative force and wind mainly used the atomic data available from the Opacity and
mass-loss rate also depend significantly on metallicity. With Iron Projects (Seaton et al. 1992; Hummer et al. 1993). This
increasing metallicity, the mass-loss rate and the wind ter- enabledustochangetheabundanceofeachelementseparately
minal velocity increase (Kudritzki & Puls 2000; Vink et al. according to its new value, and not only via the common pa-
2001; Krticˇka 2006). Frequently, the solar abundance values rametercalledthemetallicity.Usingourmethodwewereable
ofAnders&Grevesse(1989)areusedforthewind-modelpre- topredictwinddensityandvelocitystructure,namelythewind
dictions. However, the solar metallicity was recently reduced mass-lossrateM˙ andthewindterminalvelocity3∞.
following the calculations by Asplund et al. (2005) based on
improved (self-consistent) treatment of the outer solar con-
2.2.Modelstars
vectiveregion(using3Dhydrodynamicalmodelatmospheres,
Nordlund&Dravins1990;Steffenetal.1995;Asplund2004). ForouranalysisweselectedOstarswithT . 40000K(see
eff
The difference between older abundance determinations and Table1), for which the stellar parameters were derived using
recent, more realistic ones is very striking, as the estimate of the models with line blanketing. Effective temperatures and
the mass fraction of heavier elements decreased from 0.0194 radii were taken from Repolust, Puls, & Herrero (2004,here-
to0.0122.Consequently,itwouldbeinterestingtotestthein- afterR04),Markovaetal.(2004,hereafterM04),andMartins
fluenceofthenewsolarabundancedeterminationonthewind etal.(2005,hereafterM05).Stellar masseswereobtainedus-
models. To do so, we compare wind models calculated with ingevolutionarytrackseitherbyus(usingSchalleretal.1992
botholdandnewabundancedeterminations. tracks)orbyM05.
2 J.KrticˇkaandJ.Kuba´t:Hotstarwindmodelswithnewsolarabundances
Table1.StellarparametersoftheOstars. 3.5
Anders & Grevesse (1989)
Asplund et al. (2005)
Star HD Sp. R∗ M Teff Source observation
number type [R⊙] [M⊙] [K] 3 LSL
ξPer 24912 O7.5IIIe 14.0 36 35000 R04
ιOri 37043 O9III 21.6 41 31400 M04 c
s
15Mon 47839 O7Ve 9.9 32 37500 M04 ve 2.5
/∞
54662 O7III 11.9 38 38600 M04 v
93204 O5V 11.9 41 40000 M05
2
ζOph 149757 O9V 8.9 21 32000 R04
68Cyg 203064 O8e 15.7 38 34500 R04
19Cep 209975 O9Ib 22.9 47 32000 R04
1.5
Data sources: M04 – Markova et al. (2004), R04 – Repolust et al. 30000 32000 34000 36000 38000 40000
(2004),M05–Martinsetal.(2005) T [K]
eff
Fig.1.Comparisonoftheratiooftheterminalvelocitytotheescape
Table2.ComparisonofwindparameterscalculatedassumingAnders
velocity calculated using terminal velocities either from theoretical
&Grevesse(1989)andAsplundetal.(2005)solarabundances.
calculations(withdifferentsetsofabundance determinations) orde-
rivedfromobservations(valuesadoptedfromPulsetal.1996,M04,
HD Anders&Grevesse(1989) Asplundetal.(2005)
M05).LSLdenotestheaverageratioderivedbyLamersetal.(1995).
number M˙ 3∞ M˙ 3∞
[M⊙yr−1] [kms−1] [M⊙yr−1] [kms−1]
24912 5.7·10−7 2440 4.4·10−7 2270 derivedfromobservation.However,suchacomparisoniscom-
37043 7.3·10−7 2440 6.2·10−7 2340 plicatedbytheeffectofclumping.
47839 3.7·10−7 2450 2.2·10−7 3080
54662 1.1·10−6 2350 7.9·10−7 2190
93204 1.8·10−6 2490 1.3·10−6 2290 4.1.Windclumping
149757 5.9·10−8 2310 4.7·10−8 2040
203064 7.4·10−7 2270 5.7·10−7 2080 Therearetwowaystoderivewindmass-lossrates.Sincemany
209975 1.0·10−6 2510 8.4·10−7 2430 spectral features are sensitive to wind density (or mass-loss
rate),itispossibletoderivetheirvaluesfromobservationsus-
ingwindmodelswherethemass-lossrateisafreeparameter.
3. WindmodelswithAsplund,Grevesse,&Sauval These values are sometimes called ‘observed’, but we prefer
solarabundancedetermination to call them ‘derived from observations’. On the other hand,
the mass-loss rate can be calculated ab initio from dedicated
With decreasing metallicity the radiative force decreases wind models where stellar parameters (the effective tempera-
and, consequently, the wind mass-loss rate also decreases.
ture, mass, radius, and metallicity) serve as input parameters.
Moreover, the decrease in metallicity leads to a slight lower-
Thisvalueofthemass-lossrateisusuallycalled‘predicted’.It
ingofthewindterminalvelocity(Kudritzki&Puls2000;Vink
isclearthatbothwaysofdeterminingthewindmass-lossrate
et al. 2001; Krticˇka 2006). Both these effects are apparent in
shouldbeincloseagreement.
Table 2,wherewe comparewind parameterscalculatedusing
However,recentspectroscopicstudies(Bouretetal.2003;
differentdeterminationsofsolarabundances(see alsoFig. 1).
Martins et al. 2005; Puls et al. 2006) indicate that there may
On average,the mass-loss rate changesby a factor 0.76.This
be significant disagreementbetween the wind mass-loss rates
roughlycorresponds(theabundancechangeswerenotuniform
derivedfromobservationsandpredictedones.Theproblemis
forallelements)tothedependence M˙ ∼ Z0.60,whereZ isthe
thattheemergentspectrumis,inmanycases,notdirectlysen-
massfractionofheavierelements.Thisdependenceisslightly sitive to the wind mass-loss rate M˙, but to the wind density
lowerthanthe onereportedbyVinket al.(2001)andKrticˇka
squared.This means that, if it happensthat the wind is struc-
(2006).Note,however,thattheseresultsarenotdirectlycom-
turedonsmallscales(“clumped”),thenthelinesoriginatingin
parable, since the relative change in the abundance of differ-
theclumpedwindwitharelativelylowmeanwinddensitymay
ent elements is not uniform in this study, whereas results by
mimic those with a much higher mass-loss rate. If the winds
both Vink et al. (2001) and Krticˇka (2006) were obtained for
are really significantly clumped in all regionsfrom which we
a uniform relative change in the abundance. On average, the
observe the emergent radiation, as seems to follow from the
windterminalvelocityalsodecreaseswithdecreasingmetallic-
comparison of synthetic wind spectra with the observed ones
ity(see Fig.1).However,notethatthechangein theterminal
(e.g.,Bouretetal.2003;Martinsetal.2005),thentherealwind
velocitydueto the decreasein the metallicityis mostlylower
mass-lossratesaresignificantlylowerthanthepredictedones.
thantheerrorintheterminalvelocitydetermination.
From the studies of wind spectra that include clumping
(M05),it followsthat wind mass-loss rates are roughlylower
by a factor ∼ 0.3 than those derived from the standard wind
4. Implicationsofnewabundancedeterminations
models of Vink et al. (2001). Consequently, the reduction of
Thenextlogicalstepwouldbetocompareourpredictedwind windmass-lossratebyafactor0.76duetothereducedmetal-
parameters(especiallythemass-lossrates)withthe quantities licity represents an improvement in the agreement between
J.KrticˇkaandJ.Kuba´t:Hotstarwindmodelswithnewsolarabundances 3
31 Table3.Comparisonofcontinuumopacity(opacityperunitofmass
GS) AKAsnrtpdičleukrnas d && e KGt uarbel.áv (te2 (s02s00e50 )(41)989) iXn-ruanyitsreogfiocnmf2ogr−s1evaevrearlagdeiffdefroerntthwearvaedlieunsg1th.5sRca⊙lc<ulrate<d5foRr⊙t)hienttwhoe
C 30 Vink et al. (2001) abundancedeterminations(forHD24912).
1/2] ( MR0045
)⊙ wavelength[Å] 8.1 12.0 15.8 20.0 24.0
R 29
/* Anders&Grevesse(1989) 31 83 141 228 154
R Asplundetal.(2005) 20 52 91 150 125
(∞
v
.M 28
g[
o
l
terminationpredictlowerwindmomentumthanthosederived
27
4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 fromobservations.
log(L / L )
⊙
4.3.X-raycontinuumopticaldepth
Fig.2. Comparison of modified wind-momentum calculated for in-
dividual starsinthispaper assumingsolar abundances byAnders & Another painful problem of the hot-star wind theory is con-
Grevesse(1989)withmorerecentloweronesbyAsplundetal.(2005). nected with the shape of X-ray line profiles. While the wind
Wealsoplotthelinearfitsofthetheoreticalpredictions,derivedwith theorybasedoncurrentlyavailabletheoreticalmass-lossrates
olderabundances(Krticˇka&Kuba´t2004;Vinketal.2001),andvalues
predicts asymmetric X-ray line profiles due to the continuum
derivedfromobservationsbothbyM05(individualstarsforwhichthe
absorptionwithinthewind(see,e.g.,Owocki&Cohen2006;
clumpingwastakenintoanaccount)andbyR04(linearfitforgiant
Oskinovaetal.2006),theobservationsmostlyshowsymmetric
anddwarfs,forwhichtheclumpingwasnottakenintoanaccount).
X-raylineprofiles.Thisindicatesthatthewind’sopticaldepth
incontinuumforX-rayfrequenciesissmallintheregionwhere
wind mass-loss rates derived from observation (that take the X-raysform.
clumpingintoaccount)andpredictedones. To inferthe impactof newsolar abundancesonthe X-ray
lineprofiles,wecomparedthemass-absorptioncoefficientscal-
culated with solar abundances from both Anders & Grevesse
4.2.Modifiedwindmomentum-luminosityrelationship
(1989)andAsplundetal.(2005).Apparently,sinceheavierel-
It follows from both wind theory and observations that the ements dominate the continuum opacity in the X-ray region
value of the modified wind momentum M˙3∞(cid:0)R/R⊙(cid:1)1/2 de- (especiallyduetoAugertransitions),themassabsorptioncoef-
pendsmainlyonthestellarluminosity(Kudritzki&Puls2000, ficientdecreaseswithdecreasingmetallicity(seeTable3).The
andreferencestherein).Especiallythemass-dependencenearly decrease in the optical depth is not equal for all wavelengths
cancelsout.Consequently,thewindmomentum-luminosityre- because different elements dominate the opacity for different
lationship is suitable for comparing observations and theory. wavelengths and the relative change of the metallicity is not
Here we compare this relationship derived using theoretical the same for all elements. The influence of new solar abun-
models with both older and new abundance determinations dance determinationon the total continuumopacity in the X-
withvaluesfromM05,whoderivedwindmass-lossratesfrom ray region is amplified by the fact that the wind density also
theobserveddataandwhoaccountforclumping,andR04,who decreaseswithdecreasingmetallicity.
neglectedthepossibilityofwindclumping(seeFig.2). Asaresultoftheseeffects,theX-rayopticaldepthislower
Thepredictedwindmomentumislowerformodelscalcu- roughlybyafactorof2.TheuseoflowerX-rayopticaldepth
lated using improved solar metallicity determination, mainly in the calculation of Owocki & Cohen (2006) leads to better
due to the decrease in wind mass-loss rate with metallicity agreementbetweenpredictedandobservedX-raylineshapes.
and, to a lesser extent, due to the lower terminal velocities Conversely, the effect of scattering in these lines (Ignace &
that are derived. The theoretical modified wind momentum- Gayley2002)mightdecreasewithmetallicity.
luminosityrelationshipcalculatedusingimprovedabundances
hastheform
4.4.Phosphoruslineprofiles
loghM˙3∞(cid:0)R/R⊙(cid:1)1/2i=1.91 log(L/L⊙)+18.1 (CGS). (1) The ion P is assumed to be a dominant phosphorus ion in
Ourresultstosomeextentimprovetheagreementbetweenthe thestellarwind.Sinceitsabundanceisverylow,itsresonance
theoryandobservationalanalysisthattakestheclumpinginto linesasobservedinthehotstarwindspectraaregenerallyun-
account(M05andalsoFig.2).However,theyarenotabletore- saturated.Consequently,these linesare assumed notto be in-
movethedifferencebetweenthetheoryandobservationscom- fluenced by clumping and are ideal for determining the wind
pletely. Note that there is good agreement between theoreti- mass-loss rate. This was done by Fullertonet al. (2006),who
calpredictionsderivedusingAnders&Grevesse(1989)abun- showed that the mass-loss rate determined from the P lines
dances(Vinketal.2001;Krticˇka&Kuba´t2004,andtheempty is much lower than when derived from the Hα line or radio
circles in the Fig. 2) and observationsby R04. Consequently, emission.
if the influence of clumping on the observed wind spectra is This discrepancy can have two explanations: either P is
negligible,thenthewindmodelswithimprovedabundancede- nota dominantphosphorusion or the windsare clumpedand
4 J.KrticˇkaandJ.Kuba´t:Hotstarwindmodelswithnewsolarabundances
their mass-loss rates are much lower. However, the phospho- realistic solarabundancedeterminationsmaybea partialway
rusline profilesare sensitiveto phosphorusabundanceandto to solvethe problembecauseitimprovestheagreementin all
the overall stellar metallicity (due to the dependence of wind aspectsstudiedhere.
mass-loss rates on the metallicity). Both these effects lead to
Acknowledgements. ThisresearchmadeuseofNASA’sADSandthe
theweakeningof Plineprofiles.Thephosphorusabundance
SIMBAD database, operated at the CDS, Strasbourg, France. This
changesbyafactorof0.81whenusinganewabundancedeter- workwassupportedbygrantGACˇR205/04/1267.TheAstronomical
minationand,togetherwiththedecreaseinwindmass-lossrate InstituteOndˇrejovissupportedbytheprojectAV0Z10030501.
causedbythedecreaseinthemetallicity,leadstothechangein
P lineopticaldepthbya factorofabout0.62.Althoughthis
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