Absolute-Magnitude Calibration for W Uma-Type Systems. II. in Uence Of

AbsoluteMagnitude Calibration for W UMatype Systems I I

Inuence of Metallicity

Slavek Rucinski

Longb ow Drive Scarb orough Ontario MW W Canada

ABSTRACT

A mo dication to the absolute magnitude calibration for W UMatype systems

taking into account dierences in metal abundances is derived on the basis of contact

binary systems recently discovered in metalp o or clusters A preliminary estimate of

the magnitude of the metallicitydependent term for the B V based calibration

is M F eH The calibration based on the V I color is

exp ected to b e less sensitive with the correction term F eH

Need for a metallicitydependent term in the calibration

Searches for gravitational microlenses are currently giving large numbers of serendipitously

discovered variable stars Among these variables there are many W UMatype contact binaries

On the basis of the rst part of the catalog of variable stars discovered during the OGLE pro ject

Udalski et al one can estimate the total number of contact binaries which will b e

discovered in the Baade Window during OGLE at well over one thousand This estimate is based

on discoveries of such systems in the rst part of the catalog which covered one of the OGLE

elds ie less than of the whole area searched the Central Baade Window BWC and

reached I The newly discovered systems will provide excellent statistics for the p erio d color

and amplitude distributions of contact binaries much b etter than those based on the skyeld

sample which is heavily biased towards largeamplitude variables Kaluzny Rucinski

Rucinski Kaluzny They can b e also utilized as calibrators of distances into the inner

galactic disk Rucinski with their absolute magnitudes estimated using the p erio dcolor

calibration derived recently by Rucinski a CAL The large numbers of contact binaries

which are now b eing discovered should b e compared with W UMatype systems in the most

recent General Catalogue of Variable Stars Among those only systems have go o dquality

data but only for half of that in standard photometric systems

Stars visible toward the Galactic Bulge show a large spread in metallicity While the Bulge

stars might show a range of metallicities as large as F eH Frogel all contact

Aliated with the Department of Astronomy University of Toronto and Department of Physics and Astronomy

York University

binary systems visible in BWC Rucinski are at distances kp c from us and thus

b elong to the Disk p opulation For this p opulation the range in metallicities is exp ected to b e

The calibration presented in CAL utilized the observational dereddened B V color as

the temp erature index Since redbased color indices should b ecome more p opular in the future

and the OGLE pro ject provides data in V and I sp ectral bands an additional very preliminary

calibration based on the V I color was also given in CAL This calibration was derived

assuming that the relation b etween the B V and V I colors is identical to that for the Main

Sequence stars an assumption which do es not necessarily have to b e correct for the W UMatype

systems b ecause of their strong chromospheric activity The relations given in CAL for predicting

the absolute magnitudes M at maximum light together with an indep endent calibration for M

Rucinski are

M log P B V

M log P V I

The p erio d P is in days and b oth colors are reddeningfree The predictive p ower of these relations

was estimated in CAL to b e at a level of ab out mag Extensive MonteCarlo exp eriments

show that the uncertainty dep ends on a particular p erio dcolor combination and is smaller

typically mag within the strict range of p erio ds and colors used to derive the calibrations

P day B V V I

The metallicity dep endence has b een bypassed in CAL as the calibration was based on a

few nearby W UMa systems which presumably have solar abundances and on four nearby op en

clusters with mo derate underabundances F eH see Table in CAL The

B V based version of the calibration was applied also in CAL to three distant clusters with a

larger range of metallicities In this case the goal was to sieve out nonmember foreground and

background Milky Way interlopers from these low galacticlatitude clusters Mazur et al

applied recently the calibration for the same purp ose to establish membership of among

W UMatype systems in the eld of Cr and Yan Mateo used it for systems in the

globular cluster M see b elow

The three lowlatitude clusters analyzed in CAL had F eH b etween and It was

noted that the most metalp o or cluster To showed consistently p ositive deviations M from

obs obs

where M is derived simply from the brightness of a the calibration M M M

system at maximum light and the assumed distance mo dulus of the cluster The metallicity of

To is denitely low but is p o orly known at this moment it might b e as low as F eH

Geisler We would like to establish if the deviations observed for To could b e caused by

the low metallicity of the cluster

This pap er addresses the metallicity dep endence of the absolute magnitude calibrations given

by Equations and in view of recent discoveries of W UMatype binaries in metalp o or

globular clusters

Determination of the correction on the basis of metalp o or globular clusters

Little is known ab out metal abundances of isolated W UMa systems mostly b ecause of the

extreme rotational blending of sp ectral lines which prevents application of traditional techniques

Mo dern metho ds of sp ectral synthesis could p ossibly shed light on this matter but have not b een

yet applied ubv y photometry of a sample of bright W UMa systems Rucinski Kaluzny

Rucinski has not lead to clearcut results as it was imp ossible to exclude the presence

of intrinsic activityrelated p eculiarities in ultraviolet parts of sp ectra Fortunately recent

discoveries of contact systems in very metalp o or stellar systems oer a p ossibility of a preliminary

lo ok into the dep endence of absolute magnitudes on metal abundances

Mo dications to the periodcolor relation resulting from metallicity dierences were already

discussed by Rucinski b POP This study concentrated on limits imp osed by the

fullconvection condition for Population II stars but implicitly discussed observed mo dications to

p erio ds and colors for low metallicity systems It was shown there that two systems in NGC

NH and NH Mateo et al and four systems in NGC Kaluzny Krzeminski

V V V and V are bluer and have shorter p erio ds than the common Population I

W UMa systems Application of the M M l og P B V calibration conrmed that these

systems were slightly fainter than exp ected as should b e for Population II stars Thus six bona

de representatives of metalp o or p opulations were identied at that time It was argued in POP

that the remaining systems in NGC were Milky Way foreground interlopers

It should b e stressed that data for the contact systems in b oth of the metalp o orest clusters

NGC and NGC are of medio cre quality due to diculties of observing faint variable

stars However b oth clusters are so metalp o or that even crude data could give information on

ma jor trends due to metallicity variations

Recently Yan Mateo discovered contact binaries in M increasing the sample of

W UMatype systems in the globular clusters from to This is a very imp ortant discovery as

the relatively mo derate metal underabundance of the cluster estimated at ab out F eH

p ermits to bridge the large gap b etween the solarabundance systems and the metalp o or ones

for The data were obtained in the V and I lters so that Eq must b e used to calculate M

systems in M This forces us to discuss together results based on the B V color with results

based on the V I color We address the sp ecic question of relative sensitivities of b oth colors

to metallicities in the last section of the pap er

The assumptions made to determine the absolute magnitudes M and the reddeningcorrected

colors of systems in the three globular clusters were as follows For NGC m M

E B V for NGC m M E B V with additional corrections for

patchy extinction as describ ed by Kaluzny Krzeminski and for M m M and

E B V The values of p erio ds and colors for the W UMa systems were taken from the

discovery pap ers and are listed in Table

Figure shows the deviations M from the Population I calibration as function of F eH

for systems in stellar systems of low metal abundance These are the systems in three

globular clusters new systems M and systems as in POP and the systems in the

op en cluster To as in CAL The values of F eH for these clusters were taken from Geisler

and Geisler et al for To for NGC and for NGC

F eH was assumed for M Less extreme values of F eH have b een also given in the

literature for To Kubiak et al assumed F eH and the database of Webbink

gave and for NGC and NGC resp ectively The systems which

we consider as members of the clusters have b een marked in Figure by lled symbols The

broken lines give the approximate range for the membership acceptancerejection for Population I

systems estimated at mag in CAL On the basis of Figure we conclude

The globular cluster data suggest a weak dep endence of the absolute magnitude M on

F eH a linear relation should suce for the relatively p o or data which are available now

Inclusion or rejection of M would have only a minor inuence on the slop e of a linear

relation as this cluster provides a to o small baseline in F eH Besides the deviations for

this cluster were derived from the calibration based on V I and not on B V as for the

remaining clusters As we show in Section the metallicity dep endence entering through

the color term is exp ected to b e dierent for these two color indices

Assuming that the dep endence is linear and using the data for the metalp o or globular

cluster systems with metallicities based on Geisler et al publications we obtain the slop e

M F eH for the set of lessextreme metallicity data as mentioned

ab ove the slop e is

The four systems in To deviate to o much from the linear relation shown in Figure to

maintain that their underluminosity is due to low metallicity the most likely reason for the

deviations is the p o orly known reddening of the cluster Kubiak et al

It is suggested that until additional data are available the calibration based on the observed

B V color Eq should b e augmented by a term F eH We do not

have sucient data to determine observationally the co ecient for the calibration based on

V I but on the basis of the mo del atmospheres see next section we estimate that the

dep endence should b e ab out times weaker

We note that the new discovery for M by Yan Mateo for M has resulted in an

identication of the rst known contact binary systems which are located below the turno point

of a globular cluster This should b e contrasted with our calibrating systems al l six of them being

Blue Stragglers as is clearly visible in Figure which shows the globularcluster systems in the

colormagnitude diagram We are left as in POP with only the Blue Stragglers systems when

we reject binaries which probably are foreground interlopers as they are much to o bright

mag relative to the M calibration see Figure and have p erio dcolor combinations such

as for Population I systems At the time of writing POP we were condent that this way one

can eectively remove Population I eld interlopers from the sample such systems are marked by

op en symbols in Figures and In the case of the systems in M this approach encounters a

complication While the agreement of absolute magnitudes is basically p erfect the p erio dcolor

relation do es not indicate any obvious blue deviations As we can see in Figure all four

systems fall into the main band dened by skyeld presumably olddisk Guinan Bradstreet

W UMatype systems We do not have a ready explanation for this discrepancy Possibly

F eH is to omild a deciency to aect the colors or the transformation of V I to

B V is not applicable here or and this would b e most unfortunate the systems used in this

pap er to nd the F eH dep endence are not representative for the whole p opulation b ecause of

their Blue Straggler status

The metallicity dep endence of the color term

The previous section gives us some idea ab out a correction to the absolute magnitude

calibrations based on the B V color but we have no observational data to establish how sensitive

to metallicity is the calibration based on the V I color We should stress that it is a loworder

simplication to describ e prop erties of contact binaries by only two terms in the calibration log P

and the color cf derivations of the exp ected relationships in CAL But if we really want to use

very simple terms we can exp ect that when metallicity of a contact system is varied its p erio d

will b e mo died according to changes in radii driven by internal structure mo dications while its

color will change through changes in the atmospheric prop erties The situation is reminiscent to

that for sub dwarfs which are known to b e less luminous than Population I stars partly b ecause of

smaller radii and partly b ecause large eects of metallicity on their sp ectra and colors

To place the result of the previous section in a predictive context we can assume that the

metallicity mo dication to our calibration is entirely due to the color term This dep endence is

much easier to predict than the mo dication to the orbital p erio ds which would require calculation

of detailed structure mo dels with several unavoidable assumptions on the way Whereas the

metallicity dep endence of U B and B V colors for solartype stars has attained a textb o okcase

status similar intercomparisons involving the V I color are rare A convenient tabulation has

b een recently provided by Buser Kurucz who computed mo del atmosphere colors for

several combinations of parameters for solartype stars with T K We used only

the metallicity dep endence of these theoretical mo dels and disregarded the stillexisting problems

of matching the theoretical colors to the observed ones The dierences b etween these colors for

various values of metallicities F eH and for the solar metallicity are shown in Figures and

On the basis of these gures we conclude the following

For the range of mo derate deviations from the solar metallicity F eH

the corrections to colors scale approximately as B V / F eH and

V I / F eH

There exists practically no dep endence on the gravity but there is some dep endence on the

stellar eective temp erature with the V I colordeviation relatively more dep endent

For strong metal underabundances the relations tend to saturate and b ecome less

sensitive to F eH For F eH the corrections b ecome B V ' and

With these mo del results we are in p osition to check consistency of the assumption that

the metallicity correction to the M log P B V calibration is dominated by the color term

Comparing the colorterm co ecient in Eq with the approximate slop e of the B V

metallicity dep endence describ ed ab ove F eH we indeed approximately recover the

correction term / F eH This close agreement must b e partly fortuitous b ecause the data

are not accurate but it do es conrm that the the metallicity enters mainly through the color term

of the calibration

We can now apply the same argument to the calibration based on V I Eq The color

term of this calibration is smaller and the V I color is ab out times less sensitive to changes

in metallicity than the B V color Thus we guess at this p oint that the correction to the

M log P V I should include a metallicity term whose magnitude is smaller than for

the B V based calibration ie F eH This is a very preliminary estimate

requiring an observational conrmation

Conclusions

The correction term to the M calibration based on the observational dereddened color

B V M ' F eH has b een obtained on the basis of W UMatype systems which

are certain members of two very metalp o or globular clusters All systems are Blue Stragglers

which inserts a degree of uncertainty into applicability of the present results to all observable

contactbinary systems Comparison of the metallicity correction M with the mo delatmosphere

results on synthetic colors suggests that the largest eect in the calibration is through the color

term This p ermits us to formulate a prediction that the absolute magnitude calibration based on

the V I color is ab out times less sensitive to metallicity variations than the one based on

the B V color

Thanks are due to my wife Anna for her supp ort of my research The research grant from the

Natural Sciences and Engineering Council of Canada is acknowledged with gratitude

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This preprint was prepared with the AAS L T X macros v E

W UMatype Systems in Globular Clusters

System P d B V M M Comment

NGC F eH

V B V from V I

V nonmember

M V I F eH

Fig Deviations from the M calibration for W UMatype systems in metalp o or clusters

the op en cluster To crosses and the globular clusters NGC circles NGC triangles

and M asterisks The systems which we think are members of globular clusters are marked by

lled symbols Note that two dierent M calibrations were used for most systems it was the

one based on B V but for M the one based on V I was used it is assuring that these

calibrations seem to give consistent results V in NGC has b een marked by a smaller symbol

since its B V was not measured directly but was derived from V I The F eH values for

NGC and NGC are from the pap ers by Geisler et al The dotted line gives the linear t

for member systems in metalp o or globular clusters with the slop e of

Fig The same systems as in Figure are shown in a combined color magnitude diagram

The iso chrones for years and for values of F eH as lab eled are from Bergbusch

VandenBerg For M the B V values were derived from the dereddened V I colors

using the Main Sequence relation

Fig The p erio dcolor for bright W UMatype systems from the compilation of Mo chnacki

crosses and for systems in globular clusters same symbols as in Figures and but

the data p oints for To are not plotted Note that the systems in M asterisks do not have

abnormally blue colors

Fig Dep endence of B V on F eH for solartype stars following the mo del atmosphere

results of Buser Kurucz

Fig Dep endence of V I on F eH for solartype stars following the mo del atmosphere

results of Buser Kurucz