New intrinsic-colour calibration for uvby -- β photometry
aa r X i v : . [ a s t r o - ph . GA ] D ec The
Harvard
Family of Bibliography Styles
Peter Williams([email protected])Thorsten Schnier([email protected])June 8, 2018
Contents
This document describes the harvard family of bibliographic styles which areprovided in addition to those described in ? and ? . This style is primarilyintended for use with the B ib TEX bibliographic database management system.However, provision is also made for hand coding of bibliographies.
There are two primary forms of citation in the harvard style dependent uponwhether the reference is used as a noun or parenthetically. Additionally, where1here are more than two authors, all authors are listed in the first citation andin subsequent citations just the first author’s name followed by ‘et al.’ is used.The following example from ? illustrates these points.The major improvement concerns the structure of the interview (Ul-rich & Trumbo 1965, p. 112) . . . . Later reports (Carlson, Thayer,Mayfield & Peterson 1971) record greatly increased interviewer re-liability for structured interviews. Wright (1969, p. 408) commentsthat ‘undoubtedly interviewer skill is directly related to the validity,quantity and quality of the interview output’, and this would sug-gest some sort of interviewer training is called for. Rowe (1960), forexample, found that trained interviewers are better able to evalu-ate applicants with some measure of reliability. In addition Wexley,Sanders & Yukl (1973) showed that by extensive interviewer train-ing all significant contrast effects could be eliminated. The resultsof the 1971 study (Carlson et al. 1971) are still relevant, but effortsto . . . .To facilitate using a citation as a noun a new command \ citeasnoun hasbeen created which has the same syntax as the \ cite command except thatmultiple citations are not permitted. The effect of this command is that As \citeasnoun{btxdoc} and \citeasnoun[Annex~B]{latex} describe \ldots producesAs ? and ? describe . . .whereas The \BibTeX\ \cite{btxdoc} and \LaTeX\ \cite[Annex~B]{latex} manuals \ldots producesThe B ib TEX ( ? ) and L A TEX ( ? , Annex B) manuals . . .A second new command \ possessivecite is provided for those instances whereit is desired to use the citation as a possessive noun phrase. This is a variationon the \ citeasnoun command and multiple citations are not permitted. As anexample of its use \possessivecite{latex} description of this feature is \ldots produces ? description of this feature is . . .A third new command \ citeaffixed allows text to be affixed inside the beginningof the parenthesis of a parenthetical citation. This command is like the the \ cite command except that it takes a second argument – the text to be affixed afterthe opening parenthesis. For example \BibTeX\ manuals \citeaffixed{latex,btxdoc}{e.g.} describe \ldots producesB ib TEX manuals (e.g. ? , ? ) describe . . .2 .2 Citation Modes By default, where appropriate, citations are abbreviated automatically after thefirst reference when bibliographies are produced by B ib TEX. Provision is alsomade for this feature to be accessed during manual coding. This feature maybe overridden by using the \ citationmode command which takes full , abbr or default as its single argument. The command \ citationmode { full } makesthe system use full citations, \ citationmode { abbr } makes the system use ab-breviated citations and \ citationmode { default } causes the default behaviourof using full citations for the first instance and abbreviated citations thereafter.Alternatively, the citation mode may be selected as an full , abbr or default option to the \ usepackage command that invokes the harvard package. Use ofthe default option is redundant in that, if no citation mode option is used, thatmode will be selected automatically. In addition to the primary forms of citation, the citation commands \ citeyear and \ citename are provided as building blocks for more complex citations thatauthors may (from time to time) require. \ citeyear behaves like the \ cite command except that only the year portion of the citation label is used. Forexample, \citeyear{btxdoc,latex} produces ( ? , ? ). The parenthesis around the year list may be omitted by mod-ifying the command name with a single asterisk (e.g. \citeyear*{btxdoc} ). \ citename behaves like the \ citeasnoun command except that only the authorname(s) portion of the citation label is used. For example, \citename{btxdoc} produces ? .The use of these commands does not trigger the use of abbreviated citations forsubsequent \ citeasnoun and \ cite references. Occasions arise where an author wishes to override the default behaviour for anindividual citation (e.g. she may wish the citation to use the full list of authorswhere the default would use the abbreviated form). All commands that intro-duce authors’ names into a document (i.e. \ cite , \ citeasnoun , \ citeaffixed , \ possesivcite and \ citename ) may be modified with the addition of a singleasterisk in order to force them to use the full list of authors names and by adouble asterisk to force them to use the abbreviated form.3 Styles
There are six bibliography styles currently available within the harvard family, agsm (used in this document) which is based on ? , dcu which is based upon theconventions in use in the Design Computing Unit, Department of Architecturaland Design Science, University of Sydney, jmr for the Journal of ManagementResearch, jphysicsB for the Journal of Physics B, kluwer which aspires to con-form to the requirements of Kluwer Academic Publishers and nederlands whichconforms to Dutch conventions. They are invoked by the \ bibliographystyle as described in ? and effect the layout of the entries in the bibliography.Provided there is no name clash with other harvard options the bibliographystyle may be selected by passing it as an option to the \ usepackage commandthat invokes the harvard package. There are two citation styles currently available within the harvard family, agsm (used in this document) and dcu which for the previous example would produce:The B ib TEX ( ? ) and L A TEX ( ? , Annex B) manuals . . .and for multiple citations such as The original documentation \cite{btxdoc,latex} say \ldots the agsm citation style producesThe original documentation ( ? , ? ) say . . .and the dcu citation style producesThe original documentation ( ? ; ? ) say . . .The default citation style is agsm and both styles have no effect on the appear-ance of the \ citeasnoun citation format.These styles are invoked by the \ citationstyle command, for example: \citationstyle{agsm}. Because these styles affect the format of parenthetical citations, this commandshould appear before any \ cite commands. Additionally the citation style maybe selected by passing an option to the \ usepackage command that invokes the harvard package. In order to avoid name clashes with the agsm and dcu bibliog-raphy styles the options agsmcite and dcucite are used with the \ usepackage command in order to select agsm and dcu citation modes respectively. The type of parenthesis used in citations may be set using the \ harvardparenthesis command which takes one argument. The argument to this command must beone of round , curly , angle , square or none . The default value is round .4f it is a requirement that different parenthesis types are required for paren-thetical cites that for the year portion for a \ citeasnoun citation then thecommand \ harvardyearparenthesis may be used to set the year parenthe-sis seperately. This command must be issued after any \ harvardparenthesis command as that command sets both parenthetical and year parenthesis. Ifthe bibliographic style chosen is agsm or dcu then the parenthesis style chosenusing \ harvardyearparenthesis is used with the year portion of the entries inthe bibliographic listing. The options round , curly , angle , square and none may also be used with the the \ usepackage command that invokes the harvard package.Authors of style files for use with the harvard family who wish to make use ofthis feature should use the strings " \harvardleft " and " \harvardright " instead of the respective parenthesis characters where they wish them to beeffected by the selection made with \ harvardparenthesis . In the previous examples for the agsm bibliographic style a “&” characteris used to signify conjunction between a pair of names or between the lasttwo names of a list of names. Similarly the word “and” is used for the dcu style. With these two styles this convention may be overwritten by using \ renewcommand to redefine the command \ harvardand . This should bedone after the \ citationstyle command (if used) as this command resets it tothe default for the style selected. The agsm , dcu , jmr , jphysicsB and kluwer bibliographic styles support anew bibliographic entry field URL for specifying the
URL of documents thatare available via the World Wide Web. An example of this is the reference to ? documentation for his L A TEX2 html package in the file harvard.bib that isenclosed with the source for this document. When processed by L A TEX2 html documents using the harvard bibliographic package will have hypertext linkscreated from the citation within the text to the reference list. If an entry in thereference list has an
URL field then a hypertext link to the document will becreated using the data in that field.
Hand coding is accomplished much the same as described in ? except that thenew command \ harvarditem is used in place of \ bibitem . The syntax of thiscommand is \ harvarditem [ abbr-citation ] { full-citation }{ citation-year }{ cite-key } where abbr-citation is the (optional) abbreviated citation (minus the year) to beused in the text subsequent to the first mention of a particular reference,5 ull-citation is the full citation (minus the year) to be used in the text on thefirst mention of a particular reference, citation-year the year portion of the citation including any suffices requiredto disambiguate citations, and cite-key is the key used in the \ cite and \ citeasnoun commands. The motivation for this style came from Fay Sudweeks of the Design ComputingUnit who also originated the formats for the dcu style and proofread theirimplementation.The nederlands bibliographic style was implemented by Werenfried Spit([email protected]).The idea for \ citeyear came from Renate Schmidt ([email protected]).The solution to the mysterious \ enddocument problem came from BerwinA. Turlach ([email protected]) as did the identification of a subtle problemwith sorting entries in the reference list.6 r X i v : . [ a s t r o - ph . GA ] D ec New intrinsic-colour calibration for uvby – β photometry Y¨uksel Karata¸s a , , William.J. Schuster b a ˙Istanbul University, Science Faculty, Department of Astronomy and SpaceSciences, 34119 University, ˙Istanbul, Turkey b Observatorio Astron´omico Nacional, Instituto de Astronom´ıa, UniversidadNacional Autonoma de M´exico,Apartado Postal 877, C.P. 22800, Ensenada, B.C., M´exico
Abstract
A new intrinsic-colour calibration (( b – y ) o – β ) is presented for the uvby – β photo-metric system, making use of re-calibrated Hipparcos parallaxes and published red-dening maps. This new calibration for ( b – y ) o – β , our Equation (1), has been basedupon stars with d Hip <
70 pc in the photometric catalogues of Schuster et al. (1988,1993, 2006), provides a small dispersion, ± . . β coefficient, which is not too different from the coefficients of Crawford(+1.11; 1975a) and of Olsen (+1.34; 1988). For 61 stars with spectra from CASPEC,UVES/VLT, and FIES/NOT databases, without detectable Na I lines, the averagereddening value h E ( b − y ) i = − . ± .
002 shows that any zero-point correctionto our intrinsic-colour equation must be minuscule.
Key words:
ISM: dust, extinction: ISM: general: stars: distancesPACS 97.10 Wn; 97.80.Fk; 97.80.Hn
Intrinsic-colour, metallicity and absolute magnitude calibrations from uvby – β photometry for F-, G- and early K-type dwarf and turn-off stars are of vitalimportance for studying several very important astrophysical problems, suchas age-metallicity relations, metallicity gradients, and interstellar reddeningin the Galaxy. The uvby – β photometric system was specifically devised byStr¨omgren (1951) for studying B, A, and F stars. A recent evaluation of the E-mail: [email protected]
Preprint submitted to New Astronomy 8 June 2018 mportance and capacity of the uvby – β photometric system has been presentedby Bessell (2005). For this photometry, several photometric indices, or colours,are defined: ( b – y ), which measures the continuum slope and is sensitive tostellar temperatures for B, A, F, and G stars; m = ( v – b ) − ( b – y ), a colourdifference designed to measure the blanketing due to metal lines near 4100˚ A (this index is also referred to as a metal or metallicity index); c = ( u – v ) − ( v – b ), a colour difference designed to measure the strength of the Balmerdiscontinuity; and β = β w − β n , an intermediate-narrow index measuring thestrength of the hydrogen β line, which is also sensitive to stellar temperaturesfor B, A, and F stars, and which is free of the effects of interstellar extinctionand reddening.Since the β index is independent of interstellar reddening, ( b – y ) is not, andboth β and ( b – y ) measure stellar temperatures for B, A, F, and G stars, thisenables us to obtain an intrinsic-colour calibration, ( b – y ) o – β , which is quiteimportant for de-reddening the photometric indices ( b – y ), m , and c usedfor deriving the astrophysical parameters T eff , M v , and [ F e/H ] from uvby – β photometry. For dwarf and turn-off stars, some of the first calibrations forintrinsic-colour for uvby – β photometry have been given by Crawford (1975a)(hereafter C75), and Olsen (1988) (hereafter O88). C75 presents all threetypes of calibration (intrinsic-colour, metallicity, and absolute magnitude) forPopulation I type stars in the solar neighbourhood, with spectral types F2–G0 and luminosity classes III–V. O88 gives only an intrinsic-colour (( b – y ) o – β )calibration good for all F0–G2 stars of luminosity classes III–V, except perhapsthe more metal-poor Population II stars. An intrinsic-colour calibration (( b – y ) o – β ) was also derived by Schuster & Nissen (1989) (hereafter SN89) interms of the standard (non-differential) indices ( b – y ), m , c , and β .Thanks to re-calibrated Hipparcos parallaxes (ESA 1997) by van Leeuwen(2007), the reddening maps of Schlegel, Finkbeiner & Davis (1998) (hereafterSFD98), and the large photometric data base of Schuster & Nissen (1988)(hereafter SN88), Schuster, Parrao & Contreras-Mart´ınez (1993) (hereafterSPC93), and Schuster et al. (2006) (hereafter SMM06) a new relation forintrinsic-colour (( b – y ) o – β ) based on uvby – β photometry for F-, G-, and earlyK-type dwarf and turn-off stars has been obtained. The calibration is updatedand improved compared to those which have been available in the literatureand used in uvby – β photometric surveys to derive abundance distributions,effective temperatures, age-metallicity relations, and stellar kinematics for theGalaxy (for example, see Nissen & Schuster (1991), SPC93, SMM06, and Nord-str¨om et al. (2004)). This new intrinsic-colour calibration also has the advan-tage that its zero-point is tested here using stars observed spectroscopicallywith the CASPEC, UVES/VLT, and FIES/NOT echelle spectrographs andshown to have no interstellar Na I lines.This paper is organized as follows: Section 2 describes the data catalogues,2arallaxes, and cleansing of binary stars. In Section 3 the de-reddening proce-dure is presented in detail. In Section 4 the ( b – y ) o – β relation from the Schusteret al. photometric catalogue is presented, some comparisons are made, a dis-cussion of these, and finally the conclusions in Section 5. Our new ( b – y ) o – β calibration has been based mainly on the uvby – β cataloguesof Schuster & Nissen (1988) (hereafter SN88), and Schuster et al. (SPC93;SMM06). First, a catalogue which includes 1475 dwarf and turn-off stars fromthe SN88, SPC93 and SMM06 catalogues has been created, and this uvby – β catalogue will be referred to as the “Schuster” catalogue. Photometric rangesfor this catalogue are as follows: 0 . ≤ ( b – y ) ≤ . . ≤ m ≤ . . ≤ c ≤ . . ≤ β ≤ . β values taken from an outside source (“HM”), or stars near oroutside the color limits of our photometric transformations (“R” or “R?”).Similarly for the catalogue of SPC93, and in addition stars labelled with “++”have been omitted; these are the redder subgiant/giant stars whose uvby – β photometry probably contains small systematic transformation errors. Starswith “+” from this same SPC93 catalogue are not as red, ( b – y ) < .
50, andhave been retained. Also, for the catalogue of SMM06 stars with similar binaryindications in the notes, as well as “++”, have been excluded, and in additionthose with the note “fainter star in diaphragm”, but stars with “fainter star(just) outside diaphragm” have been retained.Since binaries and anomalous stars have an impact not only on the intrinsic-colour calibration, but also on the metal-abundance, and absolute-magnitudecalibrations, the Schuster catalogue has been cleansed of these type of stars.SMM06 identified binaries by using various catalogues, including primarilythose of Carney et al. (1994), Carney (2003), and Dommanget & Nys (1994).235 stars which are doubled-lined spectroscopic binaries (SB2), other typesof binaries, or photometrically variable stars have been removed from this Based on observations collected at the H. L. Johnson 1.5m telescope at the Ob-servatorio Astron´omico Nacional at San Pedro M´artir, Baja California, M´exico, andat the Danish 1.5m and 0.5m telescopes at La Silla, Chile. Based on observations collected at the H.L. Johnson 1.5m telescope at the Ob-servatorio Astron´omico Nacional at San Pedro M´artir, Baja California, M´exico E ( B – V )reddening values from SFD98 have been collected for this uvby – β Schustercatalogue. For this intrinsic-colour calibration, parallaxes ( π ), their associateduncertainties ( σ π ), and Galactic coordinates ( l , b ) of stars have been takenfrom van Leeuwen (2007). Understanding the local interstellar reddening is of vital importance in thederivation of the ( b – y ) o – β calibration, and likewise for stellar metallicities,distances and ages. The region which lies at 50–100 pc from the Sun is speciallyinteresting. The nearest interstellar dust patches are at about 70 pc in somedirections; this region devoid of dust is commonly identified with the LocalHot Bubble. There are several works about reddening within the limits ofthis Local Bubble: very weak interstellar polarization caused by magneticallyaligned dust grains has perhaps been observed within ≈
35 pc by Tinbergen(1982), but Leroy (1999) finds almost no polarization up to 50 pc. Leroy (1999)also showed that significant dust clouds appear at 70–80 pc, slightly beyondthe Local Bubble boundary defined with the help of X-ray measurements.Holmberg, Nordstr¨om & Andersen (2007) consider that real reddening within40 pc is negligible. The older intrinsic-colour calibration of SN89 was derivedwith a distance limit of about 80 pc, and an over-correction for interstellarreddening of about +0 .
005 was suggested by Nissen (1994) using stars withoutdetectable interstellar Na I lines. Additionally, Vergely et al. (1998), Sfeir etal. (1999), Breitschwerdt et al. (2000), Lallement et al. (2003), Luck & Heiter(2007) state that the extinction within 65–75 pc of the Sun is essentially nil.From all these works concerning the Local Bubble, the reddening values within70 pc are seen to be insignificant.To derive the intrinsic-colour (( b – y ) o – β ) calibration, as a first step, only starswith relative-parallax errors, σ π /π ≤ .
10, are considered, corresponding tothe near-solar vicinity, where interstellar reddenings are small or negligible. Tocheck the distribution of reddening in the solar neighbourhood, E ( B – V )( l, b ) ∞ values for individual stars in the Schuster and Olsen catalogues are taken fromthe reddening maps of SFD98 via the web page of NED (NASA ExtragalacticDatabase). The reddening E ( B – V ) for a given star is reduced compared tothe total reddening E ( B – V )( l, b ) ∞ by a factor { − exp [ − d sin | b | /H ] } , where b and d are the Galactic latitude and distance, respectively, assuming that thedust layer has a scale height H = 125 pc (Bonifacio, Monai & Beers 2000).However, Arce & Goodman (1999) caution that the SFD98 reddening mapsoverestimate the reddening values when the colour excess E ( B – V ) is more4han about 0 .
15, or even as low as 0 .
10 (Schuster et al. 2004). Hence, accordingto Schuster et al. (2004), a slight revision of the SFD98 reddening estimates hasbeen adopted via an equation, E ( B – V ) A = 0 .
10 + 0 . E ( B – V ) − .
10) when E ( B – V ) > .
10, otherwise E ( B – V ) A = E ( B – V ), where E ( B – V ) A indicatesthe adopted reddening estimate.Graphs of E ( B – V ) versus Hipparcos distance ( d Hip ) and versus Galactic lat-itude ( b ) for 551 stars with σ π /π ≤ .
10 from the Schuster catalogue areplotted in Figs. 1(a) and 1(b), respectively, for the Galactic latitude rangeof 0 o ≤ | b | ≤ o . Figs. 1(a)–(b) allow us to appreciate the reddening inthe solar vicinity for the derivation of the ( b – y ) o – β calibration. It can be seenfrom Fig. 1(a) that the majority of stars have reddening values less than E ( B – V ) ≈ .
02 (the horizontal line), and most reddenings are small up to distancesof d Hip ≈
70 pc. E ( B – V ) = 0.02 corresponds approximately to E ( b – y ) = 0 . E ( B – V ) = 1 . E ( b – y ) from Crawford (1975b). Althoughthere are a few stars with reddenings up to E ( B – V ) ≈ .
10 in Figs. 1(a)–(b), the reddening values of most stars are less than 0 .
02 for 0 ≤ | b | ≤ .In Figs. 1(a)–(b) strict limits are put on the reddening in the solar vicinityfor the derivation of our intrinsic-colour calibration. M´endez & van Altena(1998)(their figure 3) show that reddening values for three low-latitude di-rections are zero for distances less than about 100 pc. SN89 consider thatreddening is negligible within a distance limit of 100 pc following the works ofC75 and Crawford (1979); their actual distance limit may be more like 80 pcfrom a more exact photometric distance scale. Olsen used the criteria d < E ( b – y ) < .
03 for his intrinsic-colour calibration.Metal-poor stars ([
F e/H ] < − .
00 dex) are of vital importance for the intrinsic-colour calibration from the Schuster catalogue, since this calibration is in-tended for a full range of stellar population types, from thin disk to ex-treme halo. Having taken into consideration the distance limit for the red-dening of Local Bubble, reddening is considered to be negligible for stars with d Hip <
70 pc from the distributions displayed in Figs. 1(a)–(b), and accordingto the references mentioned above. According to these publications concern-ing the Local Bubble, this d Hip <
70 pc criterion, which is slightly beyondthe Local Bubble boundary, can be justified as an upper limit. Also, a smallerdistance limit would leave too few metal-poor stars for an adequate intrinsic-colour calibration.In summary, the strict criteria from Figs. 1(a)–(b), plus reddening studiesconcerning the Local Bubble, allow us to derive an intrinsic-colour calibrationusing stars from the Schuster catalogue out to distances of 70 pc, with E ( B – V ) < .
02. 5
The Intrinsic-colour Calibration from the Schuster Catalogue
The ( b – y ) o – β calibration has been carried out utilizing a mathematical packagecalled “Minitab” which allows the regression of a dependent variable againstseveral independent variables. From the Schuster catalogue, 405 stars with E ( B – V ) < .
02 and d Hip <
70 pc, according to panels (a) and (b) of Fig. 1,have been used for the derivation of the present intrinsic-colour calibration.(These calibration stars are assumed to be unreddened, and so m = m o and c = c o .) For these 405 stars, sixteen terms from simple ones to higher-ordercross terms have been tested, as follows: m o , m o , c o , c o , ∆ β , ∆ β , m o ∆ β , m o c o , m o c o , m o c o , c o ∆ β , m o ∆ β , m o ∆ β , c o ∆ β , c o ∆ β , and m o c o ∆ β , where ∆ β =2 . − β . The t-ratios, the ratios between a coefficient and its estimated er-ror, were used to eliminate non-significant terms. The solutions were iterated;at each step the term with the smallest t-ratio was omitted until all termswere significant. During the Minitab regression analyses, 13 stars have beenremoved, those with residuals greater than ± . m o ∆ β , c o , m o ∆ β , m o , m o , and m o c o .The final solution, with a dispersion of ± . b − y ) o = +0 . ± . − . ± . c o +2 . ± . β − . ± . β +6 . ± . m o c o − . ± . c o ∆ β − . ± . m o c o + 53 . ± . c o ∆ β +9 . ± . m o ∆ β + 27 . ± . c o ∆ β − . ± . m o c o ∆ β (1)Equation (1) is valid for the ranges, +0 . ≤ ( b – y ) ≤ +0 . . ≤ m ≤ +0 . . ≤ c ≤ +0 . . ≤ β ≤ . ± . β coefficient, +2 . m , c , and β arelisted for Equation (1); average residuals, numbers, and standard deviationsfrom Equation (1) are listed in Columns 2, 3, and 4, respectively. Note thatthe ranges in the average residuals for m , c , and β for Equation (1) are[ − . , +0 . − . , +0 . − . , +0 . m o term, whereas the new calibration in Equation (1),392 stars and 11 terms, without m o , but the m o dependence is available in amore complicated form, in four cross terms: m o c o , m o c o , m o ∆ β , and m o c o ∆ β ;during the iterations of the calibration process, the simple m o term has beeneliminated according to the empirical criteria discussed above. Here, sixteenterms have been considered while producing the new intrinsic-colour calibra-tion as compared to only twelve terms for the one of SN89. Moreover, thenumber of calibration stars in Equation (1) and the metal-poor-star contentis superior to that of SN89, and finally this new intrinsic-colour calibrationextends to somewhat cooler stellar temperatures as shown by the applica-ble ranges in ( b – y ), m o , and β for these two calibrations; stellar spectra arebecoming more complicated at cooler temperatures. E ( b – y ) distributions for stars from the Schuster catalogue are displayed inFigs. 2(a) and (b) as calculated from Equation (1); the stars included fall inthe ranges of validity given above. Panel 2(a) includes 1062 stars within theabove limits of ( b – y ), m , c , and β in the Schuster catalogue, while 2(b) onlythose stars with [ F e/H ] < − .
0. (For program stars which may be reddened, m is substituted for m o and c for c o in Equation (1), and then the solutionis iterated to consistency in ( b – y ) o , m o , and c o ; see SN89.) The hatched areasof both panels in Fig. 2 fulfill the distance limit d Hip <
70 pc, which corre-sponds to the near-solar vicinity and negligible reddenings, as argued above.Qualitative agreements can be seen in Figs. 2(a) and (b); all open histogramshave positive tails extending to E ( b – y ) ≈ .
07, showing slightly reddened starswithin distributions which are mostly symmetric about E ( b – y ) = 0 .
00. As ex-pected, the hatched histograms of Fig. 2 show E ( b – y ) distributions mostlysymmetric about E ( b – y ) = 0 .
00, and no obvious reddening tails; this is truefor both the sample of 515 stars including all stars in panel (a), and for the21 stars with lower metallicities of panel (b). In fact, the 21 hatched, low-metallicity stars all have E ( b – y ) less than 0 . d Hip <
70 pc and metallicities [
F e/H ] < − .
0, there are 21stars in the Schuster catalogue; mean h E ( b – y ) i values for these metal-poorstars are presented in Table 2. h E ( b – y ) i values are +0 .
004 and +0 .
010 fromEquation (1) for [
F e/H ] spec < − .
0, and [
F e/H ] spec < − .
5, respectively.In Table 3, Column 3, h E ( b – y ) i values from Equation (1) are compared withthose from SN89, or from O88, for different metallicity groups within thelimits of these calibrations. Here, h ∆ E ( b – y ) eq. (1) − SN i = E ( b – y ) eq. (1) − E ( b – y ) SN , and correspondingly for h ∆ E ( b – y ) eq. (1) − O i . When our E ( b – y ) valuesare compared to those of SN89, the zero point in the Equation (1) of SN89 hasbeen taken both with and without the small zero-point correction of +0 . E ( b – y ) values of 23stars with undetectable Na I lines; the left half of Column 3, Table 3, gives the7 ∆ E ( b – y ) i differences with this correction and the right half (in parentheses),without. The mean h ∆ E ( b – y ) i differences are quite small, as can be seen in theleft half of Column 3, and are 0 .
005 smaller without this zero-point correction.Note that the average ∆ E ( b – y ) differences show no systematic trend with[ F e/H ].For the comparisons of Table 3, E ( b – y ) values are estimated for stars in theSchuster catalogue considering the appropriate limits of the intrinsic-colourequations of SN89 and O88. The equation of O88 is valid for the ranges of δc = [ − .
02, +0 .
25] and δm = [ − .
01, +0 . b – y ) = [0.254, 0.550], m =[0.033, 0.470], c = [0.116, 0.540], and β = [2.550, 2.681]. SN89 showed that the average difference of E ( b – y ) betweentheir calibration and O88 had a systematic trend with metallicity, and confirmthe need of a correction of +0 .
015 mag over − . < [ F e/H ] < − . E ( b – y ) between Equation (1) andO88 agree with those in table 4 of SN89. In the lower part of Table 3, at highmetallicity, there is a non-negligible ( ≈ − .
02) difference between the E ( b – y )values of Equation (1) and those from O88, and this varies by almost 0.02mag in passing from the metal-rich to the metal-poor regime; such a variationof about 0.02 mag is also seen in the comparison of SN89 (table 4). Bothcomparisons in the lower part of Table 3 have negative values, suggestingan overestimation of the reddening by O88, while the comparison to SN89suggests a small underestimation by their calibration.Our intrinsic-colour calibration, Equation (1), is based in part on the COBE/DIRBE, IRAS/ISSA full-sky dust maps of SFD98, by using the selection cri-teria of E ( B – V ) < .
02, plus the distance criteria of d <
70 pc, derived byconsidering the reddening values within the Local Bubble, while the corre-sponding calibration of SN89 depends mostly on a distance criterion, d . ± .
025 during the iterations. The +0 .
005 zero-point correction of Nis-sen94 is based on the histogram of his figure 2, which shows an expected rmsscatter in E ( b – y ) of ± . E ( b – y ) = 0 .
00, buta slight asymmetry leading to a small positive h E ( b – y ) i = +0 .
005 for the23 metal-poor stars observed with the ESO 3.6m telescope and its CASPECechelle spectrograph and showing no interstellar Na I lines.Such a procedure assumes that stars without interstellar Na lines are notaffected by interstellar extinction, i.e. E ( b – y ) = 0 .
00. Munari & Zwitter(1997)(their fig. 4) have shown there is a good correlation between EW(Na I)and E(B-V) for single-lined systems. The works of Hobbs (1974), Sembach etal. (1993), Sembach & Danks (1994), and N94 have also shown correlationsbetween the interstellar Na I gas and dust. In fact, equation (2) of Hobbs(1974), equation (1) of N94, and figure 4 of Munari & Zwitter (1997) all pointto the probability that the interstellar dust abundance goes to zero together8ith the interstellar Na I gas abundance. These works point out that cold gasand dust probably occur together, and that the absence of cold interstellar gasimplies the absence of dust. These results strengthen greatly our assumptionthat the absence of interstellar Na I lines proves the absence of interstellardust, i.e. E ( b – y ) = 0 . E ( b − y ) values for the 23 CASPEC stars are presented in panel (a) of Fig.3; these are calculated via Equation (1) using each star’s values of ( b – y ), m , c , and β . Panel (a) gives h E ( b − y ) i = +0 . ± .
002 (mean error), whichis very close to the value of +0 . ± . b – y ), m , c , and β photometry. These give the E ( b − y )distribution in panel (b) of Fig. 3, which shows an average reddening value of h E ( b − y ) i = − . ± .
003 (mean error) from our Equation (1), and thisvalue is insignificantly different from E ( b – y ) = 0 . E ( b − y ) distribution for61 stars is presented in panel (c) of Fig. 3. The average reddening value h E ( b − y ) i = − . ± .
002 (mean error) is obtained, which again is insignif-icantly different from E ( b – y ) = 0 .
00. These new F- and G-type metal-poorstars without interstellar Na I lines suggest that any zero-point correction toour intrinsic-colour equation must be very small.9ur new intrinsic-colour calibration has been applied to the main-sequencestars of the open clusters NGC 2548 and M67, which have CCD uvby – β pho-tometry published by Balaguer-N´u˜nez, Jordi & Galad´ı-Enr´ıquez (2005) (here-after B05) and Balaguer-N´u˜nez, Galad´ı-Enr´ıquez & Jordi (2007) (hereafterB07). For 124 main sequence stars of the M67 cluster within the applica-ble limits of Equation (1), our intrinsic-colour calibration gives the averagereddening h E ( b − y ) i = +0 . ± . . ± .
030 for M67,derived using standard photometric relations to obtain the stellar parameters,as described in Jordi et al. (1997). Also for M67, Nissen, Twarog & Crawford(1987)(hereafter N87) obtained h E ( b − y ) i = +0 . ± .
004 from uvby – β pho-tometry of main-sequence stars, again showing very good agreement; they usedseveral methods of C75, Crawford (1978), Crawford (1979) and of Hilditch etal. (1983), depending on the spectral range of the main sequence stars. For21 main sequence stars of the open cluster NGC 2548, which fall within theapplicable limits of our Equation (1), our calibration gives the average red-dening h E ( b − y ) i = +0 . ± . . ± . Our main conclusions are as follows:(1) The intrinsic-colour calibration of our Equation (1) has a small dispersion, ± . . β term is a standard positive one like those ofCrawford (+1.11; 1975a) and Olsen (+1.34; 1988). Equation (1) also hasthe advantage of being useful over a wider range of stellar-populationtypes, from metal-rich to quite metal-poor ( − . ≤ [ F e/H ] ≤ +0 . E ( b − y ) distribution of 23 CASPEC stars, as can be seen frompanel (a) of Fig. 3, shows E ( b − y ) = +0 . ± . .
005 zero-point correction of N94. As discussed by Nissen,this suggests that the zero point of our intrinsic-colour equation shouldbe increased by +0 . h E ( b − y ) i = − . ± . h E ( b − y ) i = − . ± . E ( b – y ) = 0 .
00. These more recently observed F- and G-10ype metal-poor stars help prove that any zero-point correction to ourintrinsic-colour equation must be very small.(5) For the main sequence stars of M67 and NGC 2548, the estimated averagereddenings, +0 . ± .
004 for M67 and +0 . ± .
011 for NGC 2548,are in good concordance with the ones found by B05 and B07, and byN87.(6) The intrinsic-colour calibration of our Equation (1) can be used for de-reddening uvby – β photometry for measuring photometric effective tem-peratures, metal abundances, absolute magnitudes, distances, stellar clas-sifications, and ages for dwarf and turn-off stars, in the field and in clus-ters of the Galaxy, over a wide range in metallicity. This work was supported by the CONACyT project 49434-F (M´exico), andby the Research Fund of the University of Istanbul, project number: BYP-781/05102005. We sincerely thank P. E. Nissen for providing his special spec-troscopic results, as well as ideas and references. This research has been madepossible by the use of the SIMBAD database, operated at the CDS, Stras-bourg, France, and the web site of the General Catalogue of PhotometricData, Geneva, Switzerland.
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70 pc in the SchusterCatalogue, Calculated from Equation (1).[
F e/H ] range h E ( b – y ) eq. (1) i N[ F e/H ] < − . F e/H ] < − . able 3Mean h ∆ E ( b – y ) i Differences between Equation (1) and SN89, or O88, for MetallicitySubsets. Col. 1: [
F e/H ] intervals; Col. 2: the number of stars in each interval;Col. 3: first part, h ∆ E ( b – y ) i differences with respect to SN89, with (and without)the +0.005 zero-point correction of Nissen (1994); second part, with respect to O88;Col. 4: standard deviations for the comparisons.[ F e/H ] range N h E ( b – y ) eq. (1) − SN i Std.dev.[+0.42, +0.00] 19 +0.0057 (+0.0007) 0.0074( − − − − − − − − − − − − − − − − − − − − − F e/H ] range N h ∆ E ( b – y ) eq. (1) − O i Std.dev.[+0 . − .
50] 342 − .
024 0.030( − . − .
22] 42 − .
007 0.007 ig. 1. For the Schuster catalogue: (a) E ( B – V ) versus d Hip ; and (b) E ( B – V ) versusGalactic latitude. For this catalogue, the criteria, E ( B – V ) < .
02 plus d Hip < b – y ) o – β )calibration. See Section 4 for details. ig. 2. E ( b – y ) distributions for stars from the Schuster catalogue are displayed inpanels (a) and (b) as calculated from Equation (1); the stars fall within the ranges ofvalidity: +0 . ≤ ( b – y ) ≤ +0 . . ≤ m ≤ +0 . . ≤ c ≤ +0 . . ≤ β ≤ . b – y ), m , c , and β , while (b) only those stars with [ F e/H ] < − .
0. In both panels thedistribution is quite symmetric about E ( b − y ) = 0 .
00. The hatched areas meet therestriction, d Hip <
70 pc, which corresponds to the negligible-reddening, near-solarvicinity. ig. 3. E ( b – y ) distributions for: panel (a), 23 CASPEC stars; panel (b), 44UVES/VLT + FIES/NOT stars; and panel (c), 61 stars, the combined sample;all without detectable interstellar Na I lines. As calculated from our Equation (1),panels (a), (b), and (c) give the average reddenings of h E ( b − y ) i = +0 . ± . h E ( b − y ) i = − . ± . h E ( b − y ) i = − . ± .002, respectively.