The problem of the Pleiades distance CERN

The Problem Of The Pleiades Distance Cern-Free PDF

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2 D Stello and P E Nissen The problem of the Pleiades distance. modulus of 5 60 0 05 mag based on an extensive multi 2 MS fitting with Stro mgren photometry. color MS fitting analysis They make use of several open. clusters to check for different possible error sources and The Pleiades shifted to the distance inferred from the. both isochrones and an empirical Hyades MS are used as Hipparcos mean parallax are compared to nearby field. the zero point of the ZAMS Pinsonneault et al 1998 stars of the same metallicity in a color magnitude dia. suggest that the discrepancy between the results from gram This is done to see if the ZAMS defined by the field. Hipparcos and the MS fitting method is due to spatial stars hereafter denoted ZAMSField does coincide with. systematic errors on small angular scales in the Hipparcos the Pleiades MS Further the distance modulus of the. data Pinsonneault et al 1998 Fig 20 which are larger Pleiades is inferred from a best fit by the comparison of. than expected Lindegren 1988 1989 1997 From a com the Pleiades MS and the ZAMSField This investigation. parison of the Pleiades MS with those of the Hyades and also includes a sensitivity analysis of the ZAMSField locus. Persei clusters Eggen 1998 also concludes that the to changes in Fe H The analysis is performed for F type. Hipparcos parallax distance of the Pleiades may be in er stars and in three color temperature indices b y v y. ror by some 10 An investigation of the possible spatial and to check for robustness and possible hidden errors. systematic errors in the Hipparcos data is performed by in the MS fitting technique. Narayanan Gould 1999 who confirm the distance mod The advantage of using field stars to define the zero. ulus of around 5 6 mag by an estimate of 5 58 mag though point of the distance modulus is that the investigation. with a fairly large error of 0 18 mag Their investigation will be purely empirical and not affected by some possi. is based on a variant of the moving cluster method to get ble lacking ingredients in the theoretical calculations of the. distances for each individual cluster member On the ba isochrones So this investigation only relies on the Vogt. sis of the stated spatial systematic errors in the Hipparcos Russell theorem Sect 1 The shape of the Pleiades MS. data Robichon et al 1999 make an extensive investiga turns out to be very similar to the ZAMSField shape and. tion of this problem which makes use of the method of hence we avoid the problem of fitting to isochrones which. analyzing Hipparcos intermediate data described by van do not match the cluster MS at every temperature inter. Leeuwen Evans 1998 They recalculate the Hipparcos val Using F type stars gives the opportunity to correct. parallaxes and find a distance modulus of 5 36 0 06 mag for interstellar reddening and to estimate Fe H based. for the Pleiades which is the value adopted in this paper on the Stro mgren indices and available empirical calibra. for comparisons tion formulas The assumed shape of the ZAMSField used. for the comparison between the Pleiades MS and the field. stars is found by a second order robust least squares fit to. Recently Grenon 1999 has claimed that the Pleiades the Pleiades stars. distance problem is solved by adopting a cluster metallic. ity of Fe H Pleiades 0 11 as determined from Geneva. photometry instead of Fe H Pleiades 0 0 as determined 2 1 Data. from high resolution spectroscopy Boesgaard Friel The uvby data for the Pleiades is taken from Table. 1990 In particular Geneva photometry points to a large II of Crawford Perry 1976 hereafter CP76 which. difference in the metallicity of Praesepe and Pleiades contains members classified as F type stars by CP76 The. Fe H 0 28 To a large extent this explains the off mean error of one observation was determined from the. set between the two clusters in various color magnitude internal scatter in the measurements of all the Pleiades. diagrams Robichon et al 2000 stars Table I CP76 and were given as follows. 0 011 b y 0 009 m1 0 011 and c1, The purpose of the current study is to investigate the 0 012 CP76 Taking into account that each star has been. discrepancy between the Pleiades distance inferred from observed about 5 times we obtain the following typical. the Hipparcos mean parallax and from the MS fitting mean errors of the mean indices of one star 0 005. method by comparing Stro mgren uvby photometry b y 0 004 m1 0 005 and c1 0 005 mag. of Pleiades F type stars with field stars having the same The magnitudes of the stars in CP76 were adopted. metallicity as the Pleiades We start out with a presen from Johnson Mitchell 1958 based on the U BV. tation of the Pleiades cluster and field star data followed system so to get the Stro mgren values y transformed. by the calibration formulas and selection of stars used for to V the star magnitudes are taken from the WEBDA. the rest of the reductions Then the MS fitting analysis is database Mermilliod 2000 For about half of the stars. described including the fitting technique which has been the Stro mgren value is not available and the magnitudes. developed to locate the ZAMS of the field star sample and are taken to be the average of the V values from U BV. how we test the age range of the field stars Furthermore a observations also given in the WEBDA database It is. metallicity sensitivity analysis is presented and finally we noted that for stars with both uvby and U BV photometry. discuss possible answers to the Pleiades problem including the V magnitudes agree within 0 02 mag. the suggestion that the discrepancy in the derived distance The field star data has been taken from a catalogue of. moduli could be a real effect caused by the structure of 30 000 stars observed in uvby Olsen 1999 This. the cluster catalogue has been made by merging five published cata. D Stello and P E Nissen The problem of the Pleiades distance 3. logues all by E H Olsen The sample used in this investi where. gation F type stars is based on three of these catalogues. Olsen 1983 1988 1994 The overall RMS internal er c0 c0 c0 ZAMS m0 m0 Hyades m0 2. ror of one observation is V 0 005 b y 0 004,c0 c1 0 20 E b y m0 m1 0 30 E b y 3. m1 0 006 c1 0 007 and 0 007 These, errors are the conservative ones in some of the catalogues and 2 72 The standard relation between. they were in fact 0 002 mag smaller but the conserva m0 Hyades and c0 ZAMS is found by interpolation between. tive ones are adopted in this investigation The majority of the data points given in Table I by Crawford 1975a The. the stars were observed only once and a few 2 or 3 times iterative procedure uses the four Stro mgren indices for. so the errors in the mean photometric values per star are each star and an initial guess for the color excess as input. not significantly different from the errors stated above data The output individual color excesses was obtained. The absolute magnitudes are derived using the redden when E b y converged at the 0 0001 level The expected. ing corrected apparent magnitudes V0 transformed from error for E b y is found as. y and the Hipparcos parallaxes ESA 1997 The men, tioned possible spatial systematic error in the Hipparcos E b y 2 b y 2 b y 0 4. parallaxes does not affect the locus of the ZAMSField be. cause it can only have effects on small angular scales and where. the field stars are distributed randomly all over the sky. 2 b y 0 2 1 11 5 4 3 6 m0 2 5, Thus the error contributions from the parallaxes in the.
zero point for the ZAMSField is the global parallax error 2 m0 0 1 3 6 2 0 052 2 c0. which is less than 0 1 mas Arenou et al 1997 with m0 m1 and c0. In addition to the internal errors for the Pleiades pho c1 An estimate of this error is obtained by inserting. tometry by CP76 and for the field stars by Olsen 1999 the mean values of and m0 from the samples For the. there could be systematic differences between the two Pleiades stars it is E b y Pleiades 0 008 mag while. sources Especially the index is critical because the red it for the field stars is E b y Field 0 010 mag. dening and hence the corrected color indices b y 0 and. v y 0 is determined from Sect 2 2 1 It is however, very unlikely that systematic errors in could be large 2 2 2 Fe H calibration. enough to explain the offset between the Pleiades and the To be able to select nearby field stars with the same metal. field stars which is of the order of 0 02 mag in if we licity as the Pleiades Fe H is calculated for the Pleiades. adopt the Hipparcos distance modulus of the Pleiades In using the empirical calibrations of Nissen 1981 The cal. this connection we note that photometric observations of ibration formula is as follows. the index is quite straightforward no extinction cor. rection is needed and the transformation to the stan Fe H 10 5 50 2 626 m0 0 12 6. dard system is linear without color terms As discussed. by Olsen 1983 systematic differences in obtained with where m0 is like in Eq 2 and the constant of 0 12 is. different telescopes and filter sets are 0 005 mag at most the adopted Fe H Hyades The adopted Fe H Hyades does. Furthermore we note that two of the Pleiades F type not affect the result of the comparison of the Pleiades with. stars from CP76 Hz II 739 and 948 happen to be in the field stars because it is only relative But the estimate. Olsen 1999 The differences Olsen CP76 are 0 007 and of the absolute Fe H Pleiades value is of course depen. 0 008 respectively This does not point to any large sys dent on the assumed Fe H Hyades The expected error in. tematic errors and a correction for this difference would this calibration is obtained by a procedure similar to that. in fact increase the offset of the Pleiades with respect to presented in Sect 2 2 1 but this time m0 m0. the field stars but of course we cannot draw any strong is used The results are Fe H Pleiades 0 07 and. conclusions from two stars only Fe H Field 0 07,2 2 3 Reduction step by step. 2 2 Calibration and selection, The criterion for being an F type star is set to be 2 59. 2 2 1 Reddening 2 72 which is the range used by Crawford 1975a. and Nissen 1981 for their calibration formulas redden. To correct for reddening the color excess is determined. ing and metallicity,for individual stars as E b y b y b y 0 where. To keep as many Pleiades members as possible no, b y 0 is found by an iterative calculation based on the.
stars from Table II CP76 are rejected as a start ex. empirical calibration given by Crawford 1975a, cept Hz II 948 which appear to be a non member in both. CP76 and the WEBDA database For each member star, b y 0 0 222 1 11 2 7 2 1 the reddening is calculated by the procedure described. 0 05 c0 0 1 3 6 m0 in Sect 2 2 1 and their photometry measurements are. 4 D Stello and P E Nissen The problem of the Pleiades distance. individually corrected The mean reddening obtained is y Field 2 1 2 0 044 mag The size of the effect on MV0. hE b y iPleiades 0 031 0 004 mag1 and the star from b y 0 depends on the slope of the ZAMS in. to star RMS scatter is S E b y Pleiades 0 022 mag the color region of interest A test plot is made to find. Compared with the expected error of the E b y de the approximate slope and it is found to be 12 The. termination E b y Pleiades 0 008 mag this indi effect from on the distance modulus is found by. cates significant star to star reddening differences across differentiating the relation m M 5 log 1 5 with. the cluster The mean color excess for the Pleiades ob respect to 1 where m M is the distance modulus. tained here is in quite good agreement with former results This now leads to the following expression. obtained from other investigations which in general are. 2 MV0 2 V0 12 b y 0 2 2 17 2 7, in the range of about 0 03 0 04 mag e g Pinsonneault et. al 1998 used E b y 0 7 0 04 mag 0 03 mag here The optimized choice of the upper limit of is. using the relation between E b y and E B V from when 2 17 max V0 12 b y 0 0 12. Crawford 1975b mag where b y 0 Field 0 010 mag Eq 6 which. The reddening corrected m0 values together with the suggests 0 05 If a similar consideration is made. observations are then used as input in Eq 6 to in the MV0 vs v y 0 or MV0 vs diagram the sug. get the Pleiades metallicity The mean value derived is gestion would be 0 04 To avoid different sam. h Fe H iPleiades 0 01 0 021 This value is in very good ples of field stars in the three investigation parts parallax. agreement with spectroscopic results which mostly come measurements to a 5 accuracy are chosen which left a. out with a near solar metallicity for the Pleiades e g sample of 782 stars This seems to be the most reason. Boesgaard Friel 1990 The star to star RMS scatter able choice since the sample is large enough to make a. is S Fe H Pleiades 0 13 which is somewhat larger than clear definition of the ZAMS and a lower error always is. the expected error Fe H Pleiades 0 07 desirable, From the catalogue of field stars used in this investi. gation there are 12658 stars which have 2 59 2 72 2 3 MS fitting analysis. thus F type stars but 1194 stars of this group do not. have Hipparcos parallaxes so the absolute magnitude The MS fitting analysis is carried out in three diagrams. could not be derived and they are therefore rejected For MV0 vs b y 0 MV0 vs v y 0 and MV0 vs Often. each star in the remaining sample the reddening is cal only the b y 0 case will be illustrated in the figures but. culated as described in Sect 2 2 1 and the photometry the results of the other diagrams will be given Though. D Stello and P E Nissen The problem of the Pleiades distance 3 logues all by E H Olsen The sample used in this investi gation F type stars is based on three of these catalogues Olsen 1983 1988 1994 The overall RMS internal er ror of one observation is V 0 005 b y 0 004 m1 0 006 c1 0 007 and 0 007 These errors are the conservative ones in some of the

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