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Mon Not R Astron Soc000 1ndash9 (2002) Printed 5 November 2018 (MN LATEX style file v22)

Variable Stars in the Magellanic CloudsResults from OGLE and SIRIUS

Yoshifusa Ita1⋆ Toshihiko Tanabe1 Noriyuki Matsunaga1 Yasushi Nakajima2 ChieNagashima2 Takahiro Nagayama2 Daisuke Kato2 Mikio Kurita2 Tetsuya Nagata2Shuji Sato2 Motohide Tamura3 Hidehiko Nakaya4 and Yoshikazu Nakada151Institute of Astronomy School of Science The University of Tokyo Mitaka Tokyo 181-0015 Japan2Department of Astrophysics Nagoya University Chikusa-ku Nagoya 464-8602 Japan3National Astronomical Observatory of Japan Mitaka Tokyo181-8588 Japan4Subaru Telescope National Astronomical Observatory of Japan 650 North Arsquoohoku Place Hilo HI 96720 USA5Kiso Observatory School of Science The University of Tokyo Mitake Kiso Nagano 397-0101 Japan

Received ndash Accepted ndash

ABSTRACTWe have performed a cross-identification between OGLE-II data and single-epoch SIRIUSnear-infrared (NIR)JHK survey data in the Large and Small Magellanic Clouds (LMC andSMC respectively) After eliminating obvious spurious variables variables with too few gooddata and variables that seems to have periods longer than theavailable baseline of the OGLE-II data we determined the pulsation periods for 9681 and 2927 variables in the LMC andSMC respectively

Based on these homogeneous data we studied the pulsation properties and metallicityeffects on period-K magnitude (PK) relations by comparing the variable stars in the Largeand Small Magellanic Clouds The sample analyzed here is much larger than the previousstudies and we found the following new features in thePK diagram (1) variable red giantsin the SMC form parallel sequences on thePK plane just like those found by Wood (2000)in the LMC (2) both of the sequencesA andB of Wood (2000) have discontinuities and theyoccur at theK-band luminosity of the TRGB (3) the sequenceB of Wood (2000) separatesinto three independent sequencesBplusmn andCprime (4) comparison between the theoretical pulsationmodels (Wood amp Sebo 1996) and observational data suggests that the variable red giants onsequencesC and newly discoveredCprime are pulsating in the fundamental and first overtonemode respectively (5) the theory can not explain the pulsation mode of sequencesAplusmn andBplusmn and they are unlikely to be the sequences for the first and second overtone pulsatorsas was previously suggested (6) the zero points ofPK relations of Cepheids in the metaldeficient SMC are fainter than those of LMC ones byasymp 01 mag but those of SMC Mirasare brighter than those of LMC ones byasymp 013 mag (adopting the distance modulus offsetbetween the LMC and SMC to be 049 mag and assuming the slopes of the PK relations arethe same in the two galaxies) which are probably due to metallicity effects

Key words galaxies Magellanic Clouds ndash stellar content ndash stars AGB and post-AGB ndashvariables ndash infrared stars ndash surveys

1 INTRODUCTION

The Large and Small Magellanic Clouds offer us the opportunityto study the stellar evolution They are close enough to resolveeach stellar populations with relatively small telescopesand yet farenough to neglect their depth so that we can reasonably considerthat all stars in them are at the same distance from us

Many observations have been carried out toward the LMC

⋆ E-mail yitaioasu-tokyoacjp

and SMC especially for the variable stars to study the relation-ship between the pulsation period and the luminosity (PL relation-ship) There is a long standing question related to thePL rela-tionship whether it depends on metallicity or not A controversystill exists between observations and theories (eg Alibert et al1999 and references therein for Cepheid variables Wood amp Sebo1996 Glass et al 1995 Feast Whitelock amp Menzies 2002 forlong-period variables) Because thePL relationship is of fundamen-tal importance for the determination of the extragalactic distance

ccopy 2002 RAS

2 Y Ita et al

scale a homogeneous survey of variable stars in different environ-ments is needed

Thanks to the gravitational microlensing search projects(OGLE eg Udalski Kubiak amp Szymanski 1997 MACHO egAlcock et al 2000 EROS eg Afonso et al 1999 MOA egBond et al 2001) a large number of variable stars have beenfound in the Magellanic Clouds Wood et al (1999) analyzed thedata from MACHO survey in the 025 square degree area of theLMC bar and showed that the variable red giants form paral-lel sequences in the period-magnitude plane Cioni et al (2001)and Lebzelter Schultheis amp Melchior (2002) confirmed the resultsof Wood (2000) using data from EROS microlensing survey andAGAPEROS variable star catalog (Melchior Hughes amp Guibert2000) respectively both in the 025 square degree area of the LMCbar

In this paper we study the OGLE variables in the 3 squaredegrees along the LMC bar (see figure 1 of Ita et al 2002) and inthe 1 square degree area of the central part of the SMC (figure 1)The OGLE variables have been cross-identified with the SIRIUSNIR survey data and their pulsation periods were determinedby ap-plying the Phase Dispersion Minimization technique to the OGLEdata We classify the variable stars on thePK plane and discussthe properties of each group The environmental effect onPK re-lations is discussed by comparing variable stars in the Large andSmall Magellanic Clouds

2 DATA

21 IRSFSIRIUS

We are now conducting a NIRJHK monitoring survey toward theMagellanic Clouds using the InfraRed Survey Facility (IRSF) atSutherland South African Astronomical Observatory The IRSFconsists of a specially constructed 14m alt-azimuth telescope towhich is attached a large-format 3-channel infrared camera SIR-IUS (Simultaneous three-colour InfraRed Imager for Unbiased Sur-veys)The SIRIUS can observe the sky inJ H andKs bands simul-taneously and has a field of view of about 77 arcmin square witha scale of 045 arcsecpixel Details of the instrument are found inNagashima et al (1999) and Nagayama et al (2002)

We have been monitoring a total area of 3 square degreesalong the LMC bar since December 2000 and a total area of 1square degree around the SMC center since July 2001 Figure 1shows the monitoring area in the SMC Details and some first re-sults of the LMC survey are found in Ita et al (2002) (hereafterreferred to as Paper I) In the present paper we deal with the single-epoch data from the monitoring survey

211 Photometry

All data were reduced in the same way using the SIRIUS pipeline(Nakajima private communication) and a single image comprises100 dithered 5 sec exposures Photometry was performed onthe dithered images with DoPHOT in the fixed position mode(Schechter Mateo amp Saha 1993) The magnitudes are referredtothe Las Campanas Ovservatory (LCO) system ones based on obser-vations of a few dozen stars from Persson et al (1998) In thesys-tem conversion colour terms have been considered by observingred stars in table 3 of Persson et al The photometry has a signal-to-noise ratio (SN) of about 20 at 169 168 and 160 mag inJ H and

Figure 1 A schematic map of the monitoring region in the SMC Each meshhas a side of 20 arcmin and consists of 9 sub-meshes which correspond tothe field of view of the SIRIUS The background stars are drawnfrom theGSC22 catalog Stars brighter than 16th magnitude at Fgsc located in the

total area of 25 square degree centered on (α2000 δ2000) = (0h 55m 000s-70 30prime 000primeprime) are plotted

K respectively Typical photometric errors are tabulated in table 1of Paper I

212 Source selection

LMCIn the three square degree survey area 1593248 sources were de-tected by DoPHOT Because of the scan overlaps there shouldbemany multiple entries of a single source in the original sampleWe eliminated such multiple entries based on (1) spatial proximity(|∆r|6 05primeprime) and (2) difference in photometry (|∆mJHandK|6 01mag) It leaves 1305983 sources Further requiring detections atleast two of the three wave bands leaves 789929 sources

In Paper I we used the allowed discrepancy|∆r| of 15primeprime in-stead of the present value of 05primeprime This was because the celestialcoordinates were calculated by referencing the USNO catalog in-stead of the Guide Star Catalog II (GSC22 see section 213) Wecan find substantial number of positional reference stars byusingthe GSC22 catalog and this greatly improved the accuracy of thepositioningSMCIn the one square degree survey area 257637 sources were de-tected by DoPHOT Multiple entries were eliminated in the samemanner as we did in the LMC It leaves 210566 sources Furtherrequiring detections at least two of the three wave bands leaves107376 sources

213 SIRIUS data

In table 1 we summarize the number of sources detected in eachwave band Hereafter we refer these 789929 and 107376 sourcesas the SIRIUS data Although many stars were detected only intwo wave bands these stars hardly affect the results of thispaper

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Variable Stars in the Magellanic Clouds 3

Table 1 Breakdown list of the SIRIUS data

NumberWavebands LMC SMC

J + H + K 596913 85491J + H 75812 15173

H + K 114827 6693J + K 2377 19Total 789929 107376

Also although SIRIUSJHK photometries are single-epoch onesit should not affect the results so much because the pulsation am-plitudes of variable stars are usually small in the infrared(exceptfor Mira variables but still the results should be statistically fairbecause of large number of available data)

The SIRIUS data were corrected for the interstellar absorp-tion based on the relations in Koornneef (1982) assumingR =32 We adopted (AJ AH AK) = (0129 0084 0040) and(0082 00530025) corresponding to the total mean reddeningsof EBminusV = 0137 and 0087 as derived by Udalski et al (1999a) forthe OGLErsquos observing fields in the LMC and SMC respectively

214 Astrometry

Celestial coordinates of the sources detected by the SIRIUSweresystematically calculated in the International CelestialReferenceSystem (ICRS) by referencing the Guide Star Catalog II (STScI2001) The astrometric precision of the SIRIUS data is expected tobe the same as that of GSC 22 catalog ie better than 05primeprime in mostcases (Tanabe et al in preparation)

22 OGLE

Thanks to the microlensing surveys (OGLE MACHO EROSMOA) a large number of variable stars were found as the naturalby-products In particular the Optical Gravitational Lensing Ex-periment (OGLE) project has been monitoring the central parts ofthe Magellanic Clouds in theBVI wave bands and theI band time-series data (OGLE-II Udalski et al 1997) is now available over theInternet (OGLE homepage httpsiriusastrouweduplsimogle)

221 Cross-identification of the SIRIUS sources and the OGLEvariables

The SIRIUS data and all the stars found by the OGLE survey inthe Magellanic Clouds have been cross-identified using a simplepositional correlation In the very strict sense the OGLE surveydoes not fully cover the SIRIUS survey area and some very smallareas are not included in the OGLE However it never affect anyconclusions in this paperLMCThere are 49008 OGLE variables in the OGLESIRIUS overlapped3 square degree area in the LMC The identification was made intwo steps First a search radius of 3primeprime was used finding 35726matches Plotting the offsets between the SIRIUS coordinates andthe OGLE coordinates revealed that there are small median astro-metric shifts between them the median differences are -080primeprime inright ascension (RA) and 010primeprime in declination (DEC) Second theOGLE coordinates were corrected for these offsets and a search ra-dius of 3primeprime was used again We finally found 35783 matches with an

Figure 2 Histogram of the positional difference between the SIRIUS co-ordinates and the OGLE coordinates in 005primeprime bins for the cross-identifiedstars in the LMC (upper panel) and the SMC (lower panel)

rms error in the difference between SIRIUS and OGLE coordinates068primeprime in RA and 063primeprime in DEC respectivelySMCThere are 7345 OGLE variables in the OGLESIRIUS overlapped1 square degree area in the SMC The identification was made inthe same way as we did in the LMC First a search radius of 3primeprime

was used finding 6118 matches The offsets between the SIRIUScoordinates and the OGLE coordinates are 002primeprime in RA and -040primeprime

in DEC After correcting the OGLE coordinates for these medianoffsets a search radius of 3primeprime was used again We finally found 6103matches with an rms error in the difference between SIRIUS andOGLE coordinates 041primeprime in RA and 038primeprime in DEC respectively

We show the histogram of positional differences of the finallyidentified stars in Figure 2 It is clear that the positional differencesare smaller than 1primeprime for most of the identified stars (29228 out of35783 stars or 817 in the LMC and 5745 out of 6103 stars or941 in the SMC)

222 Period determination

We applied the Phase Dispersion Minimization (PDM) techniqueto the OGLE data to determine the light variation periods ofthe cross-identified stars This technique is described in detail byStellingwerf (1978) and here we show only the outline of the tech-nique we used

We represent the observational dataset as(xi ti) wherex is themagnitudet is the observation time andi denotes theith observa-tion We assume that there areN observations in all (i = 1N) LetV be the variance of the magnitude of the original dataset given by

V =N

sumi=1

(xi minus x)2(Nminus1) (1)

wherex is the meansumxiN First thexi andti are folded with atrial period and the full phase space[01) is divided into an appro-priate (user-specified) number of bins (there areNB bins in all iej = 1NB) Second the variancev j of magnitude of each bin andthe mean variance macrv of them are calculated namely

v=NB

sumj=1

v jNB (2)

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Variable Stars in the Magellanic Clouds 3

Table 1 Breakdown list of the SIRIUS data

NumberWavebands LMC SMC

J + H + K 596913 85491J + H 75812 15173

H + K 114827 6693J + K 2377 19Total 789929 107376

Also although SIRIUSJHK photometries are single-epoch onesit should not affect the results so much because the pulsation am-plitudes of variable stars are usually small in the infrared(exceptfor Mira variables but still the results should be statistically fairbecause of large number of available data)

The SIRIUS data were corrected for the interstellar absorp-tion based on the relations in Koornneef (1982) assumingR =32 We adopted (AJ AH AK) = (0129 0084 0040) and(0082 00530025) corresponding to the total mean reddeningsof EBminusV = 0137 and 0087 as derived by Udalski et al (1999a) forthe OGLErsquos observing fields in the LMC and SMC respectively

214 Astrometry

Celestial coordinates of the sources detected by the SIRIUSweresystematically calculated in the International CelestialReferenceSystem (ICRS) by referencing the Guide Star Catalog II (STScI2001) The astrometric precision of the SIRIUS data is expected tobe the same as that of GSC 22 catalog ie better than 05primeprime in mostcases (Tanabe et al in preparation)

22 OGLE

Thanks to the microlensing surveys (OGLE MACHO EROSMOA) a large number of variable stars were found as the naturalby-products In particular the Optical Gravitational Lensing Ex-periment (OGLE) project has been monitoring the central parts ofthe Magellanic Clouds in theBVI wave bands and theI band time-series data (OGLE-II Udalski et al 1997) is now available over theInternet (OGLE homepage httpsiriusastrouweduplsimogle)

221 Cross-identification of the SIRIUS sources and the OGLEvariables

The SIRIUS data and all the stars found by the OGLE survey inthe Magellanic Clouds have been cross-identified using a simplepositional correlation In the very strict sense the OGLE surveydoes not fully cover the SIRIUS survey area and some very smallareas are not included in the OGLE However it never affect anyconclusions in this paperLMCThere are 49008 OGLE variables in the OGLESIRIUS overlapped3 square degree area in the LMC The identification was made intwo steps First a search radius of 3primeprime was used finding 35726matches Plotting the offsets between the SIRIUS coordinates andthe OGLE coordinates revealed that there are small median astro-metric shifts between them the median differences are -080primeprime inright ascension (RA) and 010primeprime in declination (DEC) Second theOGLE coordinates were corrected for these offsets and a search ra-dius of 3primeprime was used again We finally found 35783 matches with an

Figure 2 Histogram of the positional difference between the SIRIUS co-ordinates and the OGLE coordinates in 005primeprime bins for the cross-identifiedstars in the LMC (upper panel) and the SMC (lower panel)

rms error in the difference between SIRIUS and OGLE coordinates068primeprime in RA and 063primeprime in DEC respectivelySMCThere are 7345 OGLE variables in the OGLESIRIUS overlapped1 square degree area in the SMC The identification was made inthe same way as we did in the LMC First a search radius of 3primeprime

was used finding 6118 matches The offsets between the SIRIUScoordinates and the OGLE coordinates are 002primeprime in RA and -040primeprime

in DEC After correcting the OGLE coordinates for these medianoffsets a search radius of 3primeprime was used again We finally found 6103matches with an rms error in the difference between SIRIUS andOGLE coordinates 041primeprime in RA and 038primeprime in DEC respectively

We show the histogram of positional differences of the finallyidentified stars in Figure 2 It is clear that the positional differencesare smaller than 1primeprime for most of the identified stars (29228 out of35783 stars or 817 in the LMC and 5745 out of 6103 stars or941 in the SMC)

222 Period determination

We applied the Phase Dispersion Minimization (PDM) techniqueto the OGLE data to determine the light variation periods ofthe cross-identified stars This technique is described in detail byStellingwerf (1978) and here we show only the outline of the tech-nique we used

We represent the observational dataset as(xi ti) wherex is themagnitudet is the observation time andi denotes theith observa-tion We assume that there areN observations in all (i = 1N) LetV be the variance of the magnitude of the original dataset given by

V =N

sumi=1

(xi minus x)2(Nminus1) (1)

wherex is the meansumxiN First thexi andti are folded with atrial period and the full phase space[01) is divided into an appro-priate (user-specified) number of bins (there areNB bins in all iej = 1NB) Second the variancev j of magnitude of each bin andthe mean variance macrv of them are calculated namely

v=NB

sumj=1

v jNB (2)

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4 Y Ita et al

Table 2 Used resolution in period search

trial period [day]start(gt) end(lt) resolution [day]

01 10 00000110 50 0000150 100 0001

100 1000 0011000 10000 01

Third the statistic parameterθ which is defined as

θ = vV (3)

is calculated for the trial period These three processes are thenrepeated for the next trial period (iePtrial new= Ptrial old+resolution see below) Theθ is a measure of the regularity of thelight variation or the scatter about the mean light curve being hope-fully near 0 for the very regular light variation with true period andnear 1 for the irregular light variation without any distinctive pe-riodicity or for the incorrect period Hereafter we call stars withsmallθ (6 055) as ldquoregularly pulsating variablesrdquo and the others(gt 055) as ldquoless regularly pulsating variablesrdquo

We searched the minimum of theθ throughout the trial peri-ods that start from 01 and end in 1000 days The trial periods wereincremented by variable step values (= resolution) which are sum-marized in table 2 For all of the 35783 (LMC) and 6103 (SMC)matched stars their original light curveθ spectra and the foldedlight curve are carefully eye-inspected and the obvious spuriousdata points were eliminated We assigned one pulsation period toeach variable star and the multi-periodic stars (eg Bedding et al1998) were not analyzed in this paper It should be noted thatthetotal available baseline of the OGLE-II data is about 1200 days andwe did not try to determine the light variation period for thevari-ables that seem to have the period longer than 1000 days Alsowe did not try to determine the period for the variables that havetoo few good data points and that seem to hardly show any pe-riodicity The OGLE-II survey data has yearly blank phases thatcould be a problem for variable stars with pulsation period of abouta year However experimentations showed that these yearlygapshardly affect the period determination and it is the virtueof thePDM technique In very rare cases the yearly gaps may unfortu-nately coincide with the timing of the peak luminosities They canaffect the determination of pulsation amplitude but still such casesshould be very rare Finally we determined the light variation pe-riods for 9681 and 2927 OGLE variables in the LMC and SMCrespectively

3 DISCUSSION

31 K magnitude distribution

Many low-amplitude variables were newly discovered by the afore-mentioned optical surveys The vast majority are at the luminositiesbelow the TRGB Alves et al (1998) suggested that they are AGBstars in the early evolutionary phase prior to entering the thermal-pulsing phase of the AGB In Paper I we found that theK mag-nitude distribution of the variable red giants in the LMC hastwopeaks one is well above the TRGB consisting genuine AGB vari-ables and the other is just around the TRGB

In figure 3 we show theK magnitude distributionN(K) (dK=005 mag) of the SIRIUS data The discontinuity in theN(K) isclearly seen aroundK asymp 121 (upper panel) andasymp 127 (lower

Figure 3 TheK magnitude distribution differentiated by 005 mag bins ofthe SIRIUS data in the LMC (upper panel) and the SMC (lower panel)Closeup around the TRGB is shown in the inset

panel) which corresponds to the TRGB of the LMC and SMCrespectively Figure 4 is the same diagram as the figure 3 butthe9681 and 2927 OGLESIRIUS variables in the LMC and SMC areshown It is clear that there is a ldquopile-uprdquo around theK-band lumi-nosity of the TRGB in both two galaxies In Paper I we concludedthat a significant fraction of the constituent variable stars of the sec-ond peak could be on the RGB Of course there may be faint AGBvariables but there is no reason to assume according to modelsthat they accumulate at the TRGB

32 Period-K magnitude diagram

Wood (2000) found that radially pulsating red giants in the LMCform ldquothreerdquo distinctive parallel sequences in thePK plane Hecharacterized the complex variability of the red giants by thepulsation modes which are an important probe of the internalstructure of the stars Wood et al (1999) suggested that Miravariables are fundamental mode pulsators while so-calledsemi-regular variables can be pulsating in the first second or evenhigher overtone mode by comparison of observations with the-oretical models However a controversy still exists on thepul-sation mode of Mira variables Diameter measurements of Miravariables in the Milky Way indicates first overtone pulsation (egHaniff Scholz amp Tuthill 1995 Whitelock amp Feast 2000) while ob-servations of radial velocity variation favor fundamentalmode pul-sation for Mira variables (eg Bessell Scholz amp Wood 1996)

We show the relationship between the determined pulsationperiods and theK magnitudes of the cross-identified variables infigure 5 We found that the variable red giants in the SMC formparallel sequences on thePK plane just like those found by Wood

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Variable Stars in the Magellanic Clouds 5

Figure 4 The K magnitude distribution differentiated by 01 mag bins ofthe OGLESIRIUS 9681 and 2927 variables in the LMC (upper panel) andthe SMC (lower panel) respectively

(2000) in the LMC In the LMCPK diagram bunch of variablestars exist in the faint magnitude (K 150) and very short pe-riod (logP minus01) region Considering their location on thePKplane they are likely to be RR Lyrae variables Compared to theLMC PK diagram the SMC one is a bit scattered This is probablydue to the difference in the intrinsic depth of the two galaxies be-cause the LMC has a nearly face on orientation (Westerlund 1997)and Groenewegen (2000) obtained the total front-to-back depths of0043 mag for the LMC and 011 mag for the SMC respectively

In figure 6 we again show thePK relationship of variable starsin the Magellanic Clouds In this diagram we divided variable starsinto four types according to theirJminusK colours andθ as is shown onthe upper-left corner of the figure The labels of the sequences arenamed in analogy to the ones found in the LMC by Wood (2000)(exceptCprime F andG) While Cioni et al (2001) found no objects onsequenceA from their EROSDENIS variables in the LMC this se-quence is clearly seen in both galaxies This is essentiallythe samediagram as the one obtained by Wood (2000) However the sampleused here is much larger than those of previous studies and we cansee new features in the figure (1) the sequencesA andB of Wood(2000) are found to be composed of the upper and lower sequencesA+B+ andAminusBminus (2) the sequenceB of Wood (2000) separatesinto three independent sequencesBplusmn andCprime (3) radially pulsatingred giants form actually ldquofourrdquo parallel sequences (ABCprime andC)

321 Less regularly pulsating variables

Most of the less regularly pulsating variables reside in these-quencesA andB and show small pulsation amplitudes (∆I 02mag but some of theB stars have∆I of about 04 mag) Al-

Figure 5 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel)

though it is not mentioned in Wood (2000) his sequencesA andBare densely populated at fainter magnitudes and a discernible gaparound the TRGB can be seen in his diagram (see his figure 1) Thisgap also presents in our diagram around theK-band luminosity ofthe TRGB (K sim 121 in the LMC andsim 127 in the SMC) whichwe roughly estimated in section 31 Also in the LMC a horizontalmisalignment of the sequences apparently occurs at the TRGB Onepossible explanation for the discontinuity is that neithersequencesA nor B are single sequences but each of them is composed of twoindependent sequences So we subdivided the sequencesA andBinto A+B+ andAminusBminus where the+ andminus correspond to the lu-minosity being brighter thanK = 121 (LMC) or 127 (SMC) andfainter than it respectively

Since the sequencesA+ andB+ exceed theK-band luminosityof the TRGB they consist of intermediate-age population andormetal-rich old population AGB stars However the interpretationof the sequencesAminus andBminus is difficult If the metal-poor and oldAGB stars pulsate in the same mode as the more massive stars onthe sequencesA+ or B+ they should be located on the sequencesAminus or Bminus because they do not exceed the TRGB luminosity Thequestion is whether the sequencesAminus andBminus contain RGB pul-sators or not If AGB stars alone make up theAminus andBminus as wellasA+ andB+ sequences the small gap and the horizontal shift be-tween them needs to be explained IfAminus andBminus stars at least someof them are pulsating on the RGB then the discontinuity betweenthe minus and+ sequences is understood in terms of different evo-lutionary stages If we could apply the same period-temperaturerelation as that for Mira variables (Alvarez amp Mennessier 1997)to theAminus and A+ stars the period shift ofδ logP = minus0083 be-tween the two sequences at the TRGB (K = 121 see table 3) cor-responds to the temperature difference ofδ logTeff asymp 0015 This

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6 Y Ita et al

Figure 6 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) Variable stars are classified intofour types according to theirJminusK colours andθ The labels of the se-quences are named in analogous to the sequences found by Wood(2000) inthe LMC (exceptCprime F andG see text)

is in good agreement with the temperature difference between theAGB and RGB stars with the TRGB luminosity predicted by thestellar evolutionary model for stars with 1sim2 M⊙ in the LMC(Castellani et al 2003) Though we prefer the RGB interpretationit should be noted that a definitive answer has not been obtained

322 Regularly pulsating variables

Figure 7 shows the comparison between the observational period-K magnitude sequences of pulsating red giants in the LMC andthe theoretical models calculated by Wood amp Sebo (1996) Thelo-cation of sequenceC is consistent with the LMC Mira sequence(Feast et al 1989) After classifying stars by their regularity of lightvariation we discovered a new sequenceCprime Most of the stars onsequenceCprime are regularly pulsating just like those onC but theiramplitudes are smaller than those of theC stars We note howeverthat the amplitudes of stars on sequenceCprime are larger than thoseof stars onB The observed periods luminosities and period ratioof sequencesC andCprime agree very well with those of the theoreti-cal fundamental (P0) and first overtone mode (P1) pulsation models(Wood amp Sebo 1996) Also the theory predicts that overtone pul-sators have smaller amplitudes than fundamental ones Thereforeall of the above observational facts and the agreements withthetheory could be naturally explained if we consider that the stars ofsequencesC andCprime are Mira variables pulsating in the fundamentaland first overtone mode respectively However the pulsation the-ory cannot reproduce the period ratio of the observed sequencesAandB To explain their pulsation modes a new theoretical model isneeded

Figure 7 Period-K magnitude relations of variable red giants comparedwith theoretical model of Wood amp Sebo (1996) Their models for stars ofmasses of 08 10 and 15 M⊙ pulsating in the fundamental (P0 they forcedtheoretical fundamental mode period to fit the observed Mirarelation ofFeast et al (1989) (dot-dashed line)) and first (P1) second (P2) and third(P3) overtone modes are shown Colours of the points are as in figure 6

It is interesting that with only a few exceptions all of theredgiants with red colours (JminusK gt 14) reside in the brighter magni-tudes of sequencesC andCprime According to Nikolaev amp Weinberg(2000) stars withJminusK gt 14 in the LMC are primarily carbon-rich AGB stars being considered as the descendants of oxygen-rich AGB stars We subdivided stars on sequencesC andCprime intotwo subgroups on the basis of theirJminusK colour being redder than14 and the others Table 3 (see section 33) infers that those twopopulations may follow the differentPK relations and the carbon-rich (JminusK gt 14) stars could define a line of somewhat shallowerslope with brighter zero point than that of the oxygen-rich starsFeast et al (1989) obtainedPK relations for carbon- and oxygen-rich stars in the LMC The calculated slopes and zero-pointsarein good agreement with their results In figure 8 we plotted colour-magnitude and colour-colour diagram of probable carbon-rich starson sequenceC andCprime Interestingly all of the carbon-rich stars withJminusK colour redder than 20 are on the sequenceC meaning that allof them are pulsating in the fundamental mode However it shouldbe emphasized that the obscured oxygen-rich stars such as OHIRstars could have redder colours So it could be dangerous toas-sume that all of the stars with redder colours are carbon-rich starsInfrared spectroscopic work would provide the definite conclusionon these issues

The sequenceD is thought to be populated by the longer pe-riod of a binary system (Wood 2000) However the explanation ofthis sequence is not clear yet The periods of the groupD stars arevery long and more long-term observations are needed for theclearexplanation Wood et al (1999) suggested that stars on the loosesequenceE are contact and semi-detached binaries Interestinglytheir distribution seems to extend to the TRGB Stars on sequencesF and G are very regularly pulsating and have periods rangingfrom less than 1 day to more than 30 days suggesting that theyare Cepheid variables pulsating in fundamental and first overtonemode respectively

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Variable Stars in the Magellanic Clouds 7

Figure 8 Colour-magnitude (upper panel) and colour-colour (lower panel)diagram of the carbon-rich stars on sequenceC (crosses) andCprime (dots) Twostars that are on sequenceC are excluded from the colour-colour diagrambecause they are outside the range

33 Period-K magnitude relations

In order to determine thePK relations we defined boundary linesas in figure 9 that divide the variable stars into nine (LMC) andeight (SMC) prominent groups (sequenceE is excluded) ForgroupsC Cprime andD the slopes of the boundary lines were chosento be -385 which is obtained by Hughes amp Wood (1990) for theslope of thePK relation for the blend populations of carbon- andoxygen-rich Miras in the LMC The slope of the right side of groupB+ was also chosen to be -385 For groupsAminusBminus A+B+ andFGthe slopes of the boundary lines were chosen to be -335 -345 and-336 respectively after the rough estimation of the slopes of eachsequence The width of the each box was chosen so that each ofthem contains the most probable body of a sequence and it mini-mizes the miss-classifications as much as possible

Because the scattering is rather large due probably to theSMCrsquos intrinsic front-to-back depth we did not tried to separateCprime stars fromB+ ones in the SMC Also we did not calculate thePK relations of variable red giants in the SMC The dotted linesinfigure 9 are the least square fits of linear relation to each group andtable 3 summarizes the calculatedPK relations

331 Metallicity effects on the period-K magnitude relations

Gascoigne (1974) empirically obtained the period-visual magni-tude relation for Cepheid variables and found that Cepheidsin

Figure 9 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) with classification boxes Thedotted lines are the least-square fits of linear relation to stars in each box

the metal deficient environment would be fainter than those withthe same periods in the metal rich one Based on this result theCepheids in the metal-deficient SMC should be fainter than thosein the LMC if compared with the same period On the other handWood (1990) suggested that if there was a factor of 2 differencein metal abundance between LMC and SMC long period variables(eg Miras) the LMC stars were fainter by 013 magnitudesin Kthan those in the SMC with the same period Therefore Cepheidsand long period variables are expected to express completely dif-ferent reactions to the metal abundance

One possible way to test this anticipation is to compare thePK relations in the LMC and SMC and it is done in figure 10The distances to the Magellanic Clouds are still uncertainandwe can only say with confidence that the SMC lies some 04-06mag beyond the LMC (Cole 1998) We adopted the distance mod-uli to the LMC and SMC as 1840 (Nelson et al 2000) and 1889(Harries Hilditch amp Howarth 2003) respectively These distancemoduli were obtained by using the eclipsing binary systems in theMagellanic Clouds and the technique while not entirely geometri-cal (reddening estimates are required) is free from the metallicity-induced zero point uncertainties So we shifted theK magnitudesof the SMC stars byminus049 magnitude to account for the differentdistance moduli of the SMC and LMC The red dots represent theLMC stars and the green dots correspond to the SMC stars

The figure shows just as expected that Cepheids in the SMCare fainter but red giants in the SMC are brighter than thosein theLMC if compared with the same period Also it is likely that theslopes of thePK relations are almost the same in the two galax-ies and only the zero points seem to differ To estimate the dif-ferences quantitatively we fixed the slopes of thePK relations ofSMC Cepheids and Miras to the corresponding LMC ones and cal-

ccopy 2002 RAS MNRAS000 1ndash9

8 Y Ita et al

Table 3 Period-K magnitude relations for variable stars in the MagellanicClouds of the formK = atimes logP+ b The K magnitudes are referred tothe LCO system (Persson et al 1998) Theσ is the standard deviation inK andN is the number of stars being used in the least square fitting afterapplying 30σ clipping Stars on sequencesC andCprime in the LMC weresubdivided into two subgroups according to theirJminusK colour and theirperiod-K magnitude relations were also calculated

Group a b σ N JminusKLMC

Aminus -3284plusmn0047 17060plusmn0065 0114 1142 AllA+ -3289plusmn0047 16793plusmn0077 0125 510 AllBminus -2931plusmn0057 17125plusmn0091 0100 584 AllB+ -3356plusmn0052 17634plusmn0099 0160 502 AllCprime -3768plusmn0023 18885plusmn0046 0110 693 AllCprime -3682plusmn0109 18720plusmn0245 0122 135 gt14Cprime -3873plusmn0031 19081plusmn0060 0105 558 614C -3520plusmn0034 19543plusmn0082 0198 975 AllC -3369plusmn0099 19165plusmn0250 0200 447 gt14C -3589plusmn0055 19698plusmn0126 0196 528 614D -3635plusmn0078 21718plusmn0207 0198 472 AllF -3188plusmn0019 16051plusmn0013 0095 540 AllG -3372plusmn0041 15574plusmn0016 0091 317 All

SMCF -3350plusmn0020 16722plusmn0010 0139 606 AllG -3280plusmn0035 16133plusmn0009 0147 403 All

Figure 10 Period-K magnitude diagram of variable stars in the LMC (reddots) and SMC (green dots) TheK magnitudes of SMC stars are shiftedby minus049 magnitude (see text) to account for the difference in the distancemoduli between the LMC and the SMC

culated the zero points The fixed-slope solutions yielded the zeropoints of 19409plusmn0018 16170plusmn0006 and 15659plusmn0007 mag forsequencesC F andG in the SMC respectively (after shifting theirK magnitudes byminus049 mag) Comparing these zero points withthose of the LMC Cepheids and Miras Cepheids in the SMC arefainter byasymp 01 mag and Miras in the SMC are brighter byasymp 013mag than the LMC ones with the same period

4 SUMMARY

We cross-identified the OGLE-II survey data and the SIRIUS NIRdata in the Magellanic Clouds Based on the large and homoge-

neous data1 we studied the pulsation properties of variable starsin the Magellanic Clouds We discovered a new sequence on theperiod-K magnitude plane and identified it as the one for Miravariables pulsating in the first overtone mode We also foundthatthe variable red giants in the SMC form parallel sequences intheperiod-K magnitude plane just like those found by Wood (2000)in the LMC The period-K magnitude relations were derived es-pecially for both fundamental mode and overtone Cepheids intheMagellanic Clouds These results are obtained with the greatestnumbers of available stars and most deep photometric data intheinfrared up to now Metallicity effects on period-K magnitude re-lations are studied by comparing variable stars in the MagellanicClouds The result suggested that Cepheids in the metal-deficientSMC are fainter than the LMC Cepheids while Miras in the SMCare brighter than the LMC ones if compared with the same period

ACKNOWLEDGMENTS

The authors thank the referee Dr Albert Zijlstra for constructivecomments It is a pleasure to thank Dr Michael Feast for valu-able and helpful comments on the first version of this paper Wealso thank Dr Ian Glass for useful comments This research is sup-ported in part by the Grant-in-Aid for Scientific Research (C) No12640234 and Grant-in-Aids for Scientific on Priority Area (A) No12021202 and 13011202 from the Ministry of Education ScienceSports and Culture of Japan The IRSFSIRIUS project was initi-ated and supported by Nagoya University National AstronomicalObservatory of Japan and University of Tokyo in collaboration withSouth African Astronomical Observatory under a financial supportof Grant-in-Aid for Scientific Research on Priority Area (A)No10147207 of the Ministry of Education Culture Sports Scienceand Technology of Japan The Guide Star Catalogue-II is a jointproject of the Space Telescope Science Institute and the Osserva-torio Astronomico di Torino Space Telescope Science Institute isoperated by the Association of Universities for Research inAstron-omy for the National Aeronautics and Space Administrationundercontract NAS5-26555 The participation of the Osservatorio Astro-nomico di Torino is supported by the Italian Council for Researchin Astronomy Additional support is provided by European South-ern Observatory Space Telescope European Coordinating Facilitythe International GEMINI project and the European Space AgencyAstrophysics Division

REFERENCES

Afonso C et al 1999 AampA 344 L63Alcock C et al 2000 ApJ 541 734Alibert Y Baraffe I Hauschildt P Allard F 1999 AampA344551

Alvarez R Mennessier M-O 1997 AampA 317 761Alves D et al 1998 in Takeuti M Sasselov D D eds ProcIAU JD 24 Pulsating Stars Recent Developments in Theory andObservation Universal Academic Press Tokyo p 17

Bedding T R Zijlstra Albert A Jones A Foster G 1998MN-RAS 301 1073

Bessell M S Scholz M Wood P R 1996 AampA 307 481Bond I A et al 2001 MNRAS 327 868

1 Data of the variable stars will be published in the separate paper

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 9

Castellani V DeglrsquoInnocenti S Marconi M Prada MoroniP GSestito P 2003 AampA 404 645

Cioni M-R L Marquette J-B Loup C Azzopardi M HabingH J Lasserre T Lesquoy E 2001 AampA 377 945

Cole A A 1998 ApJ 500 L137Feast M W Glass I S Whitelock P A Catchpole R M 1989241 375

Feast M W Whitelock P A Menzies J 2002 MNRAS 329L7

Gascoigne S C B 1974 MNRAS 166 25Glass I S Whitelock P A Catchpole R M Feast M W 1995MNRAS 273 383

Groenewegen M A T 2000 AampA 363 901Haniff C A Scholz M Tuthill P G 1995 MNRAS 276 640Harries T J Hilditch R W Howarth I D 2003 MNRAS 339157

Hughes S M G Wood P R 1990 AJ 99 784Ita Y et al 2002 MNRAS 279 L32Koornneef J 1982 AampA 107 247Lebzelter T Schultheis M Melchior A L 2002 AampA 393573Melchior A-L Hughes S M G Guibert J 2000 AampAS 14511

Nagashima C et al 1999 in Nakamoto T ed Star formation1999 Nobeyama Radio Observatory p 397

Nagayama T et al 2002 Proc SPIE 4841-51 2002Nelson C A Cook K H Popowski P Alves D R 2000 AJ119 1205

Nikolaev S Weinberg M D 2000 ApJ 542 804Persson S E Murphy D C Krzeminski W Roth M Rieke MJ 1998 AJ 116 2475

Schechter P L Mateo M Saha A 1993 PASP 105 1342Stellingwerf B F 1978 ApJ 224 953STScI 2001 VizieR Online Data Catalog 1271Udalski A Kubiak M Szymanski M 1997 AcA 47 319Udalski A Szymanski M Kubiak M Pietrzynski G SoszynskiI Wozniak PZebrun K 1999a AcA 49 201

Westerlund B E 1997 The Magellanic Clouds Cambridge UnivPress Cambridge

Whitelock P A Feast M W 2000 MNRAS 319 759Wood P R 1990 in Mennessier M O Omont A ed FromMiras to Planetary Nebulae Editions Frontieres Gif-sur-Yvettep67

Wood P R Sebo K M 1996 MNRAS 282 958Wood P R et al 1999 IAU symp 191 151Wood P R 2000 PASA 17 18

ccopy 2002 RAS MNRAS000 1ndash9

• Introduction
• DATA
• • IRSFSIRIUS
  • OGLE
  • • Discussion
    • • K magnitude distribution
      • Period-K magnitude diagram
      • Period-K magnitude relations
      • • Summary

Variable Stars in the Magellanic Clouds 5

Figure 4 The K magnitude distribution differentiated by 01 mag bins ofthe OGLESIRIUS 9681 and 2927 variables in the LMC (upper panel) andthe SMC (lower panel) respectively

(2000) in the LMC In the LMCPK diagram bunch of variablestars exist in the faint magnitude (K 150) and very short pe-riod (logP minus01) region Considering their location on thePKplane they are likely to be RR Lyrae variables Compared to theLMC PK diagram the SMC one is a bit scattered This is probablydue to the difference in the intrinsic depth of the two galaxies be-cause the LMC has a nearly face on orientation (Westerlund 1997)and Groenewegen (2000) obtained the total front-to-back depths of0043 mag for the LMC and 011 mag for the SMC respectively

In figure 6 we again show thePK relationship of variable starsin the Magellanic Clouds In this diagram we divided variable starsinto four types according to theirJminusK colours andθ as is shown onthe upper-left corner of the figure The labels of the sequences arenamed in analogy to the ones found in the LMC by Wood (2000)(exceptCprime F andG) While Cioni et al (2001) found no objects onsequenceA from their EROSDENIS variables in the LMC this se-quence is clearly seen in both galaxies This is essentiallythe samediagram as the one obtained by Wood (2000) However the sampleused here is much larger than those of previous studies and we cansee new features in the figure (1) the sequencesA andB of Wood(2000) are found to be composed of the upper and lower sequencesA+B+ andAminusBminus (2) the sequenceB of Wood (2000) separatesinto three independent sequencesBplusmn andCprime (3) radially pulsatingred giants form actually ldquofourrdquo parallel sequences (ABCprime andC)

321 Less regularly pulsating variables

Most of the less regularly pulsating variables reside in these-quencesA andB and show small pulsation amplitudes (∆I 02mag but some of theB stars have∆I of about 04 mag) Al-

Figure 5 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel)

though it is not mentioned in Wood (2000) his sequencesA andBare densely populated at fainter magnitudes and a discernible gaparound the TRGB can be seen in his diagram (see his figure 1) Thisgap also presents in our diagram around theK-band luminosity ofthe TRGB (K sim 121 in the LMC andsim 127 in the SMC) whichwe roughly estimated in section 31 Also in the LMC a horizontalmisalignment of the sequences apparently occurs at the TRGB Onepossible explanation for the discontinuity is that neithersequencesA nor B are single sequences but each of them is composed of twoindependent sequences So we subdivided the sequencesA andBinto A+B+ andAminusBminus where the+ andminus correspond to the lu-minosity being brighter thanK = 121 (LMC) or 127 (SMC) andfainter than it respectively

Since the sequencesA+ andB+ exceed theK-band luminosityof the TRGB they consist of intermediate-age population andormetal-rich old population AGB stars However the interpretationof the sequencesAminus andBminus is difficult If the metal-poor and oldAGB stars pulsate in the same mode as the more massive stars onthe sequencesA+ or B+ they should be located on the sequencesAminus or Bminus because they do not exceed the TRGB luminosity Thequestion is whether the sequencesAminus andBminus contain RGB pul-sators or not If AGB stars alone make up theAminus andBminus as wellasA+ andB+ sequences the small gap and the horizontal shift be-tween them needs to be explained IfAminus andBminus stars at least someof them are pulsating on the RGB then the discontinuity betweenthe minus and+ sequences is understood in terms of different evo-lutionary stages If we could apply the same period-temperaturerelation as that for Mira variables (Alvarez amp Mennessier 1997)to theAminus and A+ stars the period shift ofδ logP = minus0083 be-tween the two sequences at the TRGB (K = 121 see table 3) cor-responds to the temperature difference ofδ logTeff asymp 0015 This

ccopy 2002 RAS MNRAS000 1ndash9

6 Y Ita et al

Figure 6 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) Variable stars are classified intofour types according to theirJminusK colours andθ The labels of the se-quences are named in analogous to the sequences found by Wood(2000) inthe LMC (exceptCprime F andG see text)

is in good agreement with the temperature difference between theAGB and RGB stars with the TRGB luminosity predicted by thestellar evolutionary model for stars with 1sim2 M⊙ in the LMC(Castellani et al 2003) Though we prefer the RGB interpretationit should be noted that a definitive answer has not been obtained

322 Regularly pulsating variables

Figure 7 shows the comparison between the observational period-K magnitude sequences of pulsating red giants in the LMC andthe theoretical models calculated by Wood amp Sebo (1996) Thelo-cation of sequenceC is consistent with the LMC Mira sequence(Feast et al 1989) After classifying stars by their regularity of lightvariation we discovered a new sequenceCprime Most of the stars onsequenceCprime are regularly pulsating just like those onC but theiramplitudes are smaller than those of theC stars We note howeverthat the amplitudes of stars on sequenceCprime are larger than thoseof stars onB The observed periods luminosities and period ratioof sequencesC andCprime agree very well with those of the theoreti-cal fundamental (P0) and first overtone mode (P1) pulsation models(Wood amp Sebo 1996) Also the theory predicts that overtone pul-sators have smaller amplitudes than fundamental ones Thereforeall of the above observational facts and the agreements withthetheory could be naturally explained if we consider that the stars ofsequencesC andCprime are Mira variables pulsating in the fundamentaland first overtone mode respectively However the pulsation the-ory cannot reproduce the period ratio of the observed sequencesAandB To explain their pulsation modes a new theoretical model isneeded

Figure 7 Period-K magnitude relations of variable red giants comparedwith theoretical model of Wood amp Sebo (1996) Their models for stars ofmasses of 08 10 and 15 M⊙ pulsating in the fundamental (P0 they forcedtheoretical fundamental mode period to fit the observed Mirarelation ofFeast et al (1989) (dot-dashed line)) and first (P1) second (P2) and third(P3) overtone modes are shown Colours of the points are as in figure 6

It is interesting that with only a few exceptions all of theredgiants with red colours (JminusK gt 14) reside in the brighter magni-tudes of sequencesC andCprime According to Nikolaev amp Weinberg(2000) stars withJminusK gt 14 in the LMC are primarily carbon-rich AGB stars being considered as the descendants of oxygen-rich AGB stars We subdivided stars on sequencesC andCprime intotwo subgroups on the basis of theirJminusK colour being redder than14 and the others Table 3 (see section 33) infers that those twopopulations may follow the differentPK relations and the carbon-rich (JminusK gt 14) stars could define a line of somewhat shallowerslope with brighter zero point than that of the oxygen-rich starsFeast et al (1989) obtainedPK relations for carbon- and oxygen-rich stars in the LMC The calculated slopes and zero-pointsarein good agreement with their results In figure 8 we plotted colour-magnitude and colour-colour diagram of probable carbon-rich starson sequenceC andCprime Interestingly all of the carbon-rich stars withJminusK colour redder than 20 are on the sequenceC meaning that allof them are pulsating in the fundamental mode However it shouldbe emphasized that the obscured oxygen-rich stars such as OHIRstars could have redder colours So it could be dangerous toas-sume that all of the stars with redder colours are carbon-rich starsInfrared spectroscopic work would provide the definite conclusionon these issues

The sequenceD is thought to be populated by the longer pe-riod of a binary system (Wood 2000) However the explanation ofthis sequence is not clear yet The periods of the groupD stars arevery long and more long-term observations are needed for theclearexplanation Wood et al (1999) suggested that stars on the loosesequenceE are contact and semi-detached binaries Interestinglytheir distribution seems to extend to the TRGB Stars on sequencesF and G are very regularly pulsating and have periods rangingfrom less than 1 day to more than 30 days suggesting that theyare Cepheid variables pulsating in fundamental and first overtonemode respectively

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 7

Figure 8 Colour-magnitude (upper panel) and colour-colour (lower panel)diagram of the carbon-rich stars on sequenceC (crosses) andCprime (dots) Twostars that are on sequenceC are excluded from the colour-colour diagrambecause they are outside the range

33 Period-K magnitude relations

In order to determine thePK relations we defined boundary linesas in figure 9 that divide the variable stars into nine (LMC) andeight (SMC) prominent groups (sequenceE is excluded) ForgroupsC Cprime andD the slopes of the boundary lines were chosento be -385 which is obtained by Hughes amp Wood (1990) for theslope of thePK relation for the blend populations of carbon- andoxygen-rich Miras in the LMC The slope of the right side of groupB+ was also chosen to be -385 For groupsAminusBminus A+B+ andFGthe slopes of the boundary lines were chosen to be -335 -345 and-336 respectively after the rough estimation of the slopes of eachsequence The width of the each box was chosen so that each ofthem contains the most probable body of a sequence and it mini-mizes the miss-classifications as much as possible

Because the scattering is rather large due probably to theSMCrsquos intrinsic front-to-back depth we did not tried to separateCprime stars fromB+ ones in the SMC Also we did not calculate thePK relations of variable red giants in the SMC The dotted linesinfigure 9 are the least square fits of linear relation to each group andtable 3 summarizes the calculatedPK relations

331 Metallicity effects on the period-K magnitude relations

Gascoigne (1974) empirically obtained the period-visual magni-tude relation for Cepheid variables and found that Cepheidsin

Figure 9 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) with classification boxes Thedotted lines are the least-square fits of linear relation to stars in each box

the metal deficient environment would be fainter than those withthe same periods in the metal rich one Based on this result theCepheids in the metal-deficient SMC should be fainter than thosein the LMC if compared with the same period On the other handWood (1990) suggested that if there was a factor of 2 differencein metal abundance between LMC and SMC long period variables(eg Miras) the LMC stars were fainter by 013 magnitudesin Kthan those in the SMC with the same period Therefore Cepheidsand long period variables are expected to express completely dif-ferent reactions to the metal abundance

One possible way to test this anticipation is to compare thePK relations in the LMC and SMC and it is done in figure 10The distances to the Magellanic Clouds are still uncertainandwe can only say with confidence that the SMC lies some 04-06mag beyond the LMC (Cole 1998) We adopted the distance mod-uli to the LMC and SMC as 1840 (Nelson et al 2000) and 1889(Harries Hilditch amp Howarth 2003) respectively These distancemoduli were obtained by using the eclipsing binary systems in theMagellanic Clouds and the technique while not entirely geometri-cal (reddening estimates are required) is free from the metallicity-induced zero point uncertainties So we shifted theK magnitudesof the SMC stars byminus049 magnitude to account for the differentdistance moduli of the SMC and LMC The red dots represent theLMC stars and the green dots correspond to the SMC stars

The figure shows just as expected that Cepheids in the SMCare fainter but red giants in the SMC are brighter than thosein theLMC if compared with the same period Also it is likely that theslopes of thePK relations are almost the same in the two galax-ies and only the zero points seem to differ To estimate the dif-ferences quantitatively we fixed the slopes of thePK relations ofSMC Cepheids and Miras to the corresponding LMC ones and cal-

ccopy 2002 RAS MNRAS000 1ndash9

8 Y Ita et al

Table 3 Period-K magnitude relations for variable stars in the MagellanicClouds of the formK = atimes logP+ b The K magnitudes are referred tothe LCO system (Persson et al 1998) Theσ is the standard deviation inK andN is the number of stars being used in the least square fitting afterapplying 30σ clipping Stars on sequencesC andCprime in the LMC weresubdivided into two subgroups according to theirJminusK colour and theirperiod-K magnitude relations were also calculated

Group a b σ N JminusKLMC

Aminus -3284plusmn0047 17060plusmn0065 0114 1142 AllA+ -3289plusmn0047 16793plusmn0077 0125 510 AllBminus -2931plusmn0057 17125plusmn0091 0100 584 AllB+ -3356plusmn0052 17634plusmn0099 0160 502 AllCprime -3768plusmn0023 18885plusmn0046 0110 693 AllCprime -3682plusmn0109 18720plusmn0245 0122 135 gt14Cprime -3873plusmn0031 19081plusmn0060 0105 558 614C -3520plusmn0034 19543plusmn0082 0198 975 AllC -3369plusmn0099 19165plusmn0250 0200 447 gt14C -3589plusmn0055 19698plusmn0126 0196 528 614D -3635plusmn0078 21718plusmn0207 0198 472 AllF -3188plusmn0019 16051plusmn0013 0095 540 AllG -3372plusmn0041 15574plusmn0016 0091 317 All

SMCF -3350plusmn0020 16722plusmn0010 0139 606 AllG -3280plusmn0035 16133plusmn0009 0147 403 All

Figure 10 Period-K magnitude diagram of variable stars in the LMC (reddots) and SMC (green dots) TheK magnitudes of SMC stars are shiftedby minus049 magnitude (see text) to account for the difference in the distancemoduli between the LMC and the SMC

culated the zero points The fixed-slope solutions yielded the zeropoints of 19409plusmn0018 16170plusmn0006 and 15659plusmn0007 mag forsequencesC F andG in the SMC respectively (after shifting theirK magnitudes byminus049 mag) Comparing these zero points withthose of the LMC Cepheids and Miras Cepheids in the SMC arefainter byasymp 01 mag and Miras in the SMC are brighter byasymp 013mag than the LMC ones with the same period

4 SUMMARY

We cross-identified the OGLE-II survey data and the SIRIUS NIRdata in the Magellanic Clouds Based on the large and homoge-

neous data1 we studied the pulsation properties of variable starsin the Magellanic Clouds We discovered a new sequence on theperiod-K magnitude plane and identified it as the one for Miravariables pulsating in the first overtone mode We also foundthatthe variable red giants in the SMC form parallel sequences intheperiod-K magnitude plane just like those found by Wood (2000)in the LMC The period-K magnitude relations were derived es-pecially for both fundamental mode and overtone Cepheids intheMagellanic Clouds These results are obtained with the greatestnumbers of available stars and most deep photometric data intheinfrared up to now Metallicity effects on period-K magnitude re-lations are studied by comparing variable stars in the MagellanicClouds The result suggested that Cepheids in the metal-deficientSMC are fainter than the LMC Cepheids while Miras in the SMCare brighter than the LMC ones if compared with the same period

ACKNOWLEDGMENTS

The authors thank the referee Dr Albert Zijlstra for constructivecomments It is a pleasure to thank Dr Michael Feast for valu-able and helpful comments on the first version of this paper Wealso thank Dr Ian Glass for useful comments This research is sup-ported in part by the Grant-in-Aid for Scientific Research (C) No12640234 and Grant-in-Aids for Scientific on Priority Area (A) No12021202 and 13011202 from the Ministry of Education ScienceSports and Culture of Japan The IRSFSIRIUS project was initi-ated and supported by Nagoya University National AstronomicalObservatory of Japan and University of Tokyo in collaboration withSouth African Astronomical Observatory under a financial supportof Grant-in-Aid for Scientific Research on Priority Area (A)No10147207 of the Ministry of Education Culture Sports Scienceand Technology of Japan The Guide Star Catalogue-II is a jointproject of the Space Telescope Science Institute and the Osserva-torio Astronomico di Torino Space Telescope Science Institute isoperated by the Association of Universities for Research inAstron-omy for the National Aeronautics and Space Administrationundercontract NAS5-26555 The participation of the Osservatorio Astro-nomico di Torino is supported by the Italian Council for Researchin Astronomy Additional support is provided by European South-ern Observatory Space Telescope European Coordinating Facilitythe International GEMINI project and the European Space AgencyAstrophysics Division

REFERENCES

Afonso C et al 1999 AampA 344 L63Alcock C et al 2000 ApJ 541 734Alibert Y Baraffe I Hauschildt P Allard F 1999 AampA344551

Alvarez R Mennessier M-O 1997 AampA 317 761Alves D et al 1998 in Takeuti M Sasselov D D eds ProcIAU JD 24 Pulsating Stars Recent Developments in Theory andObservation Universal Academic Press Tokyo p 17

Bedding T R Zijlstra Albert A Jones A Foster G 1998MN-RAS 301 1073

Bessell M S Scholz M Wood P R 1996 AampA 307 481Bond I A et al 2001 MNRAS 327 868

1 Data of the variable stars will be published in the separate paper

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 9

Castellani V DeglrsquoInnocenti S Marconi M Prada MoroniP GSestito P 2003 AampA 404 645

Cioni M-R L Marquette J-B Loup C Azzopardi M HabingH J Lasserre T Lesquoy E 2001 AampA 377 945

Cole A A 1998 ApJ 500 L137Feast M W Glass I S Whitelock P A Catchpole R M 1989241 375

Feast M W Whitelock P A Menzies J 2002 MNRAS 329L7

Gascoigne S C B 1974 MNRAS 166 25Glass I S Whitelock P A Catchpole R M Feast M W 1995MNRAS 273 383

Groenewegen M A T 2000 AampA 363 901Haniff C A Scholz M Tuthill P G 1995 MNRAS 276 640Harries T J Hilditch R W Howarth I D 2003 MNRAS 339157

Hughes S M G Wood P R 1990 AJ 99 784Ita Y et al 2002 MNRAS 279 L32Koornneef J 1982 AampA 107 247Lebzelter T Schultheis M Melchior A L 2002 AampA 393573Melchior A-L Hughes S M G Guibert J 2000 AampAS 14511

Nagashima C et al 1999 in Nakamoto T ed Star formation1999 Nobeyama Radio Observatory p 397

Nagayama T et al 2002 Proc SPIE 4841-51 2002Nelson C A Cook K H Popowski P Alves D R 2000 AJ119 1205

Nikolaev S Weinberg M D 2000 ApJ 542 804Persson S E Murphy D C Krzeminski W Roth M Rieke MJ 1998 AJ 116 2475

Schechter P L Mateo M Saha A 1993 PASP 105 1342Stellingwerf B F 1978 ApJ 224 953STScI 2001 VizieR Online Data Catalog 1271Udalski A Kubiak M Szymanski M 1997 AcA 47 319Udalski A Szymanski M Kubiak M Pietrzynski G SoszynskiI Wozniak PZebrun K 1999a AcA 49 201

Westerlund B E 1997 The Magellanic Clouds Cambridge UnivPress Cambridge

Whitelock P A Feast M W 2000 MNRAS 319 759Wood P R 1990 in Mennessier M O Omont A ed FromMiras to Planetary Nebulae Editions Frontieres Gif-sur-Yvettep67

Wood P R Sebo K M 1996 MNRAS 282 958Wood P R et al 1999 IAU symp 191 151Wood P R 2000 PASA 17 18

ccopy 2002 RAS MNRAS000 1ndash9

• Introduction
• DATA
• • IRSFSIRIUS
  • OGLE
  • • Discussion
    • • K magnitude distribution
      • Period-K magnitude diagram
      • Period-K magnitude relations
      • • Summary

6 Y Ita et al

Figure 6 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) Variable stars are classified intofour types according to theirJminusK colours andθ The labels of the se-quences are named in analogous to the sequences found by Wood(2000) inthe LMC (exceptCprime F andG see text)

is in good agreement with the temperature difference between theAGB and RGB stars with the TRGB luminosity predicted by thestellar evolutionary model for stars with 1sim2 M⊙ in the LMC(Castellani et al 2003) Though we prefer the RGB interpretationit should be noted that a definitive answer has not been obtained

322 Regularly pulsating variables

Figure 7 shows the comparison between the observational period-K magnitude sequences of pulsating red giants in the LMC andthe theoretical models calculated by Wood amp Sebo (1996) Thelo-cation of sequenceC is consistent with the LMC Mira sequence(Feast et al 1989) After classifying stars by their regularity of lightvariation we discovered a new sequenceCprime Most of the stars onsequenceCprime are regularly pulsating just like those onC but theiramplitudes are smaller than those of theC stars We note howeverthat the amplitudes of stars on sequenceCprime are larger than thoseof stars onB The observed periods luminosities and period ratioof sequencesC andCprime agree very well with those of the theoreti-cal fundamental (P0) and first overtone mode (P1) pulsation models(Wood amp Sebo 1996) Also the theory predicts that overtone pul-sators have smaller amplitudes than fundamental ones Thereforeall of the above observational facts and the agreements withthetheory could be naturally explained if we consider that the stars ofsequencesC andCprime are Mira variables pulsating in the fundamentaland first overtone mode respectively However the pulsation the-ory cannot reproduce the period ratio of the observed sequencesAandB To explain their pulsation modes a new theoretical model isneeded

Figure 7 Period-K magnitude relations of variable red giants comparedwith theoretical model of Wood amp Sebo (1996) Their models for stars ofmasses of 08 10 and 15 M⊙ pulsating in the fundamental (P0 they forcedtheoretical fundamental mode period to fit the observed Mirarelation ofFeast et al (1989) (dot-dashed line)) and first (P1) second (P2) and third(P3) overtone modes are shown Colours of the points are as in figure 6

It is interesting that with only a few exceptions all of theredgiants with red colours (JminusK gt 14) reside in the brighter magni-tudes of sequencesC andCprime According to Nikolaev amp Weinberg(2000) stars withJminusK gt 14 in the LMC are primarily carbon-rich AGB stars being considered as the descendants of oxygen-rich AGB stars We subdivided stars on sequencesC andCprime intotwo subgroups on the basis of theirJminusK colour being redder than14 and the others Table 3 (see section 33) infers that those twopopulations may follow the differentPK relations and the carbon-rich (JminusK gt 14) stars could define a line of somewhat shallowerslope with brighter zero point than that of the oxygen-rich starsFeast et al (1989) obtainedPK relations for carbon- and oxygen-rich stars in the LMC The calculated slopes and zero-pointsarein good agreement with their results In figure 8 we plotted colour-magnitude and colour-colour diagram of probable carbon-rich starson sequenceC andCprime Interestingly all of the carbon-rich stars withJminusK colour redder than 20 are on the sequenceC meaning that allof them are pulsating in the fundamental mode However it shouldbe emphasized that the obscured oxygen-rich stars such as OHIRstars could have redder colours So it could be dangerous toas-sume that all of the stars with redder colours are carbon-rich starsInfrared spectroscopic work would provide the definite conclusionon these issues

The sequenceD is thought to be populated by the longer pe-riod of a binary system (Wood 2000) However the explanation ofthis sequence is not clear yet The periods of the groupD stars arevery long and more long-term observations are needed for theclearexplanation Wood et al (1999) suggested that stars on the loosesequenceE are contact and semi-detached binaries Interestinglytheir distribution seems to extend to the TRGB Stars on sequencesF and G are very regularly pulsating and have periods rangingfrom less than 1 day to more than 30 days suggesting that theyare Cepheid variables pulsating in fundamental and first overtonemode respectively

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 7

Figure 8 Colour-magnitude (upper panel) and colour-colour (lower panel)diagram of the carbon-rich stars on sequenceC (crosses) andCprime (dots) Twostars that are on sequenceC are excluded from the colour-colour diagrambecause they are outside the range

33 Period-K magnitude relations

In order to determine thePK relations we defined boundary linesas in figure 9 that divide the variable stars into nine (LMC) andeight (SMC) prominent groups (sequenceE is excluded) ForgroupsC Cprime andD the slopes of the boundary lines were chosento be -385 which is obtained by Hughes amp Wood (1990) for theslope of thePK relation for the blend populations of carbon- andoxygen-rich Miras in the LMC The slope of the right side of groupB+ was also chosen to be -385 For groupsAminusBminus A+B+ andFGthe slopes of the boundary lines were chosen to be -335 -345 and-336 respectively after the rough estimation of the slopes of eachsequence The width of the each box was chosen so that each ofthem contains the most probable body of a sequence and it mini-mizes the miss-classifications as much as possible

Because the scattering is rather large due probably to theSMCrsquos intrinsic front-to-back depth we did not tried to separateCprime stars fromB+ ones in the SMC Also we did not calculate thePK relations of variable red giants in the SMC The dotted linesinfigure 9 are the least square fits of linear relation to each group andtable 3 summarizes the calculatedPK relations

331 Metallicity effects on the period-K magnitude relations

Gascoigne (1974) empirically obtained the period-visual magni-tude relation for Cepheid variables and found that Cepheidsin

Figure 9 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) with classification boxes Thedotted lines are the least-square fits of linear relation to stars in each box

the metal deficient environment would be fainter than those withthe same periods in the metal rich one Based on this result theCepheids in the metal-deficient SMC should be fainter than thosein the LMC if compared with the same period On the other handWood (1990) suggested that if there was a factor of 2 differencein metal abundance between LMC and SMC long period variables(eg Miras) the LMC stars were fainter by 013 magnitudesin Kthan those in the SMC with the same period Therefore Cepheidsand long period variables are expected to express completely dif-ferent reactions to the metal abundance

One possible way to test this anticipation is to compare thePK relations in the LMC and SMC and it is done in figure 10The distances to the Magellanic Clouds are still uncertainandwe can only say with confidence that the SMC lies some 04-06mag beyond the LMC (Cole 1998) We adopted the distance mod-uli to the LMC and SMC as 1840 (Nelson et al 2000) and 1889(Harries Hilditch amp Howarth 2003) respectively These distancemoduli were obtained by using the eclipsing binary systems in theMagellanic Clouds and the technique while not entirely geometri-cal (reddening estimates are required) is free from the metallicity-induced zero point uncertainties So we shifted theK magnitudesof the SMC stars byminus049 magnitude to account for the differentdistance moduli of the SMC and LMC The red dots represent theLMC stars and the green dots correspond to the SMC stars

The figure shows just as expected that Cepheids in the SMCare fainter but red giants in the SMC are brighter than thosein theLMC if compared with the same period Also it is likely that theslopes of thePK relations are almost the same in the two galax-ies and only the zero points seem to differ To estimate the dif-ferences quantitatively we fixed the slopes of thePK relations ofSMC Cepheids and Miras to the corresponding LMC ones and cal-

ccopy 2002 RAS MNRAS000 1ndash9

8 Y Ita et al

Table 3 Period-K magnitude relations for variable stars in the MagellanicClouds of the formK = atimes logP+ b The K magnitudes are referred tothe LCO system (Persson et al 1998) Theσ is the standard deviation inK andN is the number of stars being used in the least square fitting afterapplying 30σ clipping Stars on sequencesC andCprime in the LMC weresubdivided into two subgroups according to theirJminusK colour and theirperiod-K magnitude relations were also calculated

Group a b σ N JminusKLMC

Aminus -3284plusmn0047 17060plusmn0065 0114 1142 AllA+ -3289plusmn0047 16793plusmn0077 0125 510 AllBminus -2931plusmn0057 17125plusmn0091 0100 584 AllB+ -3356plusmn0052 17634plusmn0099 0160 502 AllCprime -3768plusmn0023 18885plusmn0046 0110 693 AllCprime -3682plusmn0109 18720plusmn0245 0122 135 gt14Cprime -3873plusmn0031 19081plusmn0060 0105 558 614C -3520plusmn0034 19543plusmn0082 0198 975 AllC -3369plusmn0099 19165plusmn0250 0200 447 gt14C -3589plusmn0055 19698plusmn0126 0196 528 614D -3635plusmn0078 21718plusmn0207 0198 472 AllF -3188plusmn0019 16051plusmn0013 0095 540 AllG -3372plusmn0041 15574plusmn0016 0091 317 All

SMCF -3350plusmn0020 16722plusmn0010 0139 606 AllG -3280plusmn0035 16133plusmn0009 0147 403 All

Figure 10 Period-K magnitude diagram of variable stars in the LMC (reddots) and SMC (green dots) TheK magnitudes of SMC stars are shiftedby minus049 magnitude (see text) to account for the difference in the distancemoduli between the LMC and the SMC

culated the zero points The fixed-slope solutions yielded the zeropoints of 19409plusmn0018 16170plusmn0006 and 15659plusmn0007 mag forsequencesC F andG in the SMC respectively (after shifting theirK magnitudes byminus049 mag) Comparing these zero points withthose of the LMC Cepheids and Miras Cepheids in the SMC arefainter byasymp 01 mag and Miras in the SMC are brighter byasymp 013mag than the LMC ones with the same period

4 SUMMARY

We cross-identified the OGLE-II survey data and the SIRIUS NIRdata in the Magellanic Clouds Based on the large and homoge-

neous data1 we studied the pulsation properties of variable starsin the Magellanic Clouds We discovered a new sequence on theperiod-K magnitude plane and identified it as the one for Miravariables pulsating in the first overtone mode We also foundthatthe variable red giants in the SMC form parallel sequences intheperiod-K magnitude plane just like those found by Wood (2000)in the LMC The period-K magnitude relations were derived es-pecially for both fundamental mode and overtone Cepheids intheMagellanic Clouds These results are obtained with the greatestnumbers of available stars and most deep photometric data intheinfrared up to now Metallicity effects on period-K magnitude re-lations are studied by comparing variable stars in the MagellanicClouds The result suggested that Cepheids in the metal-deficientSMC are fainter than the LMC Cepheids while Miras in the SMCare brighter than the LMC ones if compared with the same period

ACKNOWLEDGMENTS

The authors thank the referee Dr Albert Zijlstra for constructivecomments It is a pleasure to thank Dr Michael Feast for valu-able and helpful comments on the first version of this paper Wealso thank Dr Ian Glass for useful comments This research is sup-ported in part by the Grant-in-Aid for Scientific Research (C) No12640234 and Grant-in-Aids for Scientific on Priority Area (A) No12021202 and 13011202 from the Ministry of Education ScienceSports and Culture of Japan The IRSFSIRIUS project was initi-ated and supported by Nagoya University National AstronomicalObservatory of Japan and University of Tokyo in collaboration withSouth African Astronomical Observatory under a financial supportof Grant-in-Aid for Scientific Research on Priority Area (A)No10147207 of the Ministry of Education Culture Sports Scienceand Technology of Japan The Guide Star Catalogue-II is a jointproject of the Space Telescope Science Institute and the Osserva-torio Astronomico di Torino Space Telescope Science Institute isoperated by the Association of Universities for Research inAstron-omy for the National Aeronautics and Space Administrationundercontract NAS5-26555 The participation of the Osservatorio Astro-nomico di Torino is supported by the Italian Council for Researchin Astronomy Additional support is provided by European South-ern Observatory Space Telescope European Coordinating Facilitythe International GEMINI project and the European Space AgencyAstrophysics Division

REFERENCES

Afonso C et al 1999 AampA 344 L63Alcock C et al 2000 ApJ 541 734Alibert Y Baraffe I Hauschildt P Allard F 1999 AampA344551

Alvarez R Mennessier M-O 1997 AampA 317 761Alves D et al 1998 in Takeuti M Sasselov D D eds ProcIAU JD 24 Pulsating Stars Recent Developments in Theory andObservation Universal Academic Press Tokyo p 17

Bedding T R Zijlstra Albert A Jones A Foster G 1998MN-RAS 301 1073

Bessell M S Scholz M Wood P R 1996 AampA 307 481Bond I A et al 2001 MNRAS 327 868

1 Data of the variable stars will be published in the separate paper

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 9

Castellani V DeglrsquoInnocenti S Marconi M Prada MoroniP GSestito P 2003 AampA 404 645

Cioni M-R L Marquette J-B Loup C Azzopardi M HabingH J Lasserre T Lesquoy E 2001 AampA 377 945

Cole A A 1998 ApJ 500 L137Feast M W Glass I S Whitelock P A Catchpole R M 1989241 375

Feast M W Whitelock P A Menzies J 2002 MNRAS 329L7

Gascoigne S C B 1974 MNRAS 166 25Glass I S Whitelock P A Catchpole R M Feast M W 1995MNRAS 273 383

Groenewegen M A T 2000 AampA 363 901Haniff C A Scholz M Tuthill P G 1995 MNRAS 276 640Harries T J Hilditch R W Howarth I D 2003 MNRAS 339157

Hughes S M G Wood P R 1990 AJ 99 784Ita Y et al 2002 MNRAS 279 L32Koornneef J 1982 AampA 107 247Lebzelter T Schultheis M Melchior A L 2002 AampA 393573Melchior A-L Hughes S M G Guibert J 2000 AampAS 14511

Nagashima C et al 1999 in Nakamoto T ed Star formation1999 Nobeyama Radio Observatory p 397

Nagayama T et al 2002 Proc SPIE 4841-51 2002Nelson C A Cook K H Popowski P Alves D R 2000 AJ119 1205

Nikolaev S Weinberg M D 2000 ApJ 542 804Persson S E Murphy D C Krzeminski W Roth M Rieke MJ 1998 AJ 116 2475

Schechter P L Mateo M Saha A 1993 PASP 105 1342Stellingwerf B F 1978 ApJ 224 953STScI 2001 VizieR Online Data Catalog 1271Udalski A Kubiak M Szymanski M 1997 AcA 47 319Udalski A Szymanski M Kubiak M Pietrzynski G SoszynskiI Wozniak PZebrun K 1999a AcA 49 201

Westerlund B E 1997 The Magellanic Clouds Cambridge UnivPress Cambridge

Whitelock P A Feast M W 2000 MNRAS 319 759Wood P R 1990 in Mennessier M O Omont A ed FromMiras to Planetary Nebulae Editions Frontieres Gif-sur-Yvettep67

Wood P R Sebo K M 1996 MNRAS 282 958Wood P R et al 1999 IAU symp 191 151Wood P R 2000 PASA 17 18

ccopy 2002 RAS MNRAS000 1ndash9

• Introduction
• DATA
• • IRSFSIRIUS
  • OGLE
  • • Discussion
    • • K magnitude distribution
      • Period-K magnitude diagram
      • Period-K magnitude relations
      • • Summary

Variable Stars in the Magellanic Clouds 7

Figure 8 Colour-magnitude (upper panel) and colour-colour (lower panel)diagram of the carbon-rich stars on sequenceC (crosses) andCprime (dots) Twostars that are on sequenceC are excluded from the colour-colour diagrambecause they are outside the range

33 Period-K magnitude relations

In order to determine thePK relations we defined boundary linesas in figure 9 that divide the variable stars into nine (LMC) andeight (SMC) prominent groups (sequenceE is excluded) ForgroupsC Cprime andD the slopes of the boundary lines were chosento be -385 which is obtained by Hughes amp Wood (1990) for theslope of thePK relation for the blend populations of carbon- andoxygen-rich Miras in the LMC The slope of the right side of groupB+ was also chosen to be -385 For groupsAminusBminus A+B+ andFGthe slopes of the boundary lines were chosen to be -335 -345 and-336 respectively after the rough estimation of the slopes of eachsequence The width of the each box was chosen so that each ofthem contains the most probable body of a sequence and it mini-mizes the miss-classifications as much as possible

Because the scattering is rather large due probably to theSMCrsquos intrinsic front-to-back depth we did not tried to separateCprime stars fromB+ ones in the SMC Also we did not calculate thePK relations of variable red giants in the SMC The dotted linesinfigure 9 are the least square fits of linear relation to each group andtable 3 summarizes the calculatedPK relations

331 Metallicity effects on the period-K magnitude relations

Gascoigne (1974) empirically obtained the period-visual magni-tude relation for Cepheid variables and found that Cepheidsin

Figure 9 Period-K magnitude diagram for OGLE variables in the LMC(upper panel) and the SMC (lower panel) with classification boxes Thedotted lines are the least-square fits of linear relation to stars in each box

the metal deficient environment would be fainter than those withthe same periods in the metal rich one Based on this result theCepheids in the metal-deficient SMC should be fainter than thosein the LMC if compared with the same period On the other handWood (1990) suggested that if there was a factor of 2 differencein metal abundance between LMC and SMC long period variables(eg Miras) the LMC stars were fainter by 013 magnitudesin Kthan those in the SMC with the same period Therefore Cepheidsand long period variables are expected to express completely dif-ferent reactions to the metal abundance

One possible way to test this anticipation is to compare thePK relations in the LMC and SMC and it is done in figure 10The distances to the Magellanic Clouds are still uncertainandwe can only say with confidence that the SMC lies some 04-06mag beyond the LMC (Cole 1998) We adopted the distance mod-uli to the LMC and SMC as 1840 (Nelson et al 2000) and 1889(Harries Hilditch amp Howarth 2003) respectively These distancemoduli were obtained by using the eclipsing binary systems in theMagellanic Clouds and the technique while not entirely geometri-cal (reddening estimates are required) is free from the metallicity-induced zero point uncertainties So we shifted theK magnitudesof the SMC stars byminus049 magnitude to account for the differentdistance moduli of the SMC and LMC The red dots represent theLMC stars and the green dots correspond to the SMC stars

The figure shows just as expected that Cepheids in the SMCare fainter but red giants in the SMC are brighter than thosein theLMC if compared with the same period Also it is likely that theslopes of thePK relations are almost the same in the two galax-ies and only the zero points seem to differ To estimate the dif-ferences quantitatively we fixed the slopes of thePK relations ofSMC Cepheids and Miras to the corresponding LMC ones and cal-

ccopy 2002 RAS MNRAS000 1ndash9

8 Y Ita et al

Table 3 Period-K magnitude relations for variable stars in the MagellanicClouds of the formK = atimes logP+ b The K magnitudes are referred tothe LCO system (Persson et al 1998) Theσ is the standard deviation inK andN is the number of stars being used in the least square fitting afterapplying 30σ clipping Stars on sequencesC andCprime in the LMC weresubdivided into two subgroups according to theirJminusK colour and theirperiod-K magnitude relations were also calculated

Group a b σ N JminusKLMC

Aminus -3284plusmn0047 17060plusmn0065 0114 1142 AllA+ -3289plusmn0047 16793plusmn0077 0125 510 AllBminus -2931plusmn0057 17125plusmn0091 0100 584 AllB+ -3356plusmn0052 17634plusmn0099 0160 502 AllCprime -3768plusmn0023 18885plusmn0046 0110 693 AllCprime -3682plusmn0109 18720plusmn0245 0122 135 gt14Cprime -3873plusmn0031 19081plusmn0060 0105 558 614C -3520plusmn0034 19543plusmn0082 0198 975 AllC -3369plusmn0099 19165plusmn0250 0200 447 gt14C -3589plusmn0055 19698plusmn0126 0196 528 614D -3635plusmn0078 21718plusmn0207 0198 472 AllF -3188plusmn0019 16051plusmn0013 0095 540 AllG -3372plusmn0041 15574plusmn0016 0091 317 All

SMCF -3350plusmn0020 16722plusmn0010 0139 606 AllG -3280plusmn0035 16133plusmn0009 0147 403 All

Figure 10 Period-K magnitude diagram of variable stars in the LMC (reddots) and SMC (green dots) TheK magnitudes of SMC stars are shiftedby minus049 magnitude (see text) to account for the difference in the distancemoduli between the LMC and the SMC

culated the zero points The fixed-slope solutions yielded the zeropoints of 19409plusmn0018 16170plusmn0006 and 15659plusmn0007 mag forsequencesC F andG in the SMC respectively (after shifting theirK magnitudes byminus049 mag) Comparing these zero points withthose of the LMC Cepheids and Miras Cepheids in the SMC arefainter byasymp 01 mag and Miras in the SMC are brighter byasymp 013mag than the LMC ones with the same period

4 SUMMARY

We cross-identified the OGLE-II survey data and the SIRIUS NIRdata in the Magellanic Clouds Based on the large and homoge-

neous data1 we studied the pulsation properties of variable starsin the Magellanic Clouds We discovered a new sequence on theperiod-K magnitude plane and identified it as the one for Miravariables pulsating in the first overtone mode We also foundthatthe variable red giants in the SMC form parallel sequences intheperiod-K magnitude plane just like those found by Wood (2000)in the LMC The period-K magnitude relations were derived es-pecially for both fundamental mode and overtone Cepheids intheMagellanic Clouds These results are obtained with the greatestnumbers of available stars and most deep photometric data intheinfrared up to now Metallicity effects on period-K magnitude re-lations are studied by comparing variable stars in the MagellanicClouds The result suggested that Cepheids in the metal-deficientSMC are fainter than the LMC Cepheids while Miras in the SMCare brighter than the LMC ones if compared with the same period

ACKNOWLEDGMENTS

The authors thank the referee Dr Albert Zijlstra for constructivecomments It is a pleasure to thank Dr Michael Feast for valu-able and helpful comments on the first version of this paper Wealso thank Dr Ian Glass for useful comments This research is sup-ported in part by the Grant-in-Aid for Scientific Research (C) No12640234 and Grant-in-Aids for Scientific on Priority Area (A) No12021202 and 13011202 from the Ministry of Education ScienceSports and Culture of Japan The IRSFSIRIUS project was initi-ated and supported by Nagoya University National AstronomicalObservatory of Japan and University of Tokyo in collaboration withSouth African Astronomical Observatory under a financial supportof Grant-in-Aid for Scientific Research on Priority Area (A)No10147207 of the Ministry of Education Culture Sports Scienceand Technology of Japan The Guide Star Catalogue-II is a jointproject of the Space Telescope Science Institute and the Osserva-torio Astronomico di Torino Space Telescope Science Institute isoperated by the Association of Universities for Research inAstron-omy for the National Aeronautics and Space Administrationundercontract NAS5-26555 The participation of the Osservatorio Astro-nomico di Torino is supported by the Italian Council for Researchin Astronomy Additional support is provided by European South-ern Observatory Space Telescope European Coordinating Facilitythe International GEMINI project and the European Space AgencyAstrophysics Division

REFERENCES

Afonso C et al 1999 AampA 344 L63Alcock C et al 2000 ApJ 541 734Alibert Y Baraffe I Hauschildt P Allard F 1999 AampA344551

Alvarez R Mennessier M-O 1997 AampA 317 761Alves D et al 1998 in Takeuti M Sasselov D D eds ProcIAU JD 24 Pulsating Stars Recent Developments in Theory andObservation Universal Academic Press Tokyo p 17

Bedding T R Zijlstra Albert A Jones A Foster G 1998MN-RAS 301 1073

Bessell M S Scholz M Wood P R 1996 AampA 307 481Bond I A et al 2001 MNRAS 327 868

1 Data of the variable stars will be published in the separate paper

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 9

Castellani V DeglrsquoInnocenti S Marconi M Prada MoroniP GSestito P 2003 AampA 404 645

Cioni M-R L Marquette J-B Loup C Azzopardi M HabingH J Lasserre T Lesquoy E 2001 AampA 377 945

Cole A A 1998 ApJ 500 L137Feast M W Glass I S Whitelock P A Catchpole R M 1989241 375

Feast M W Whitelock P A Menzies J 2002 MNRAS 329L7

Gascoigne S C B 1974 MNRAS 166 25Glass I S Whitelock P A Catchpole R M Feast M W 1995MNRAS 273 383

Groenewegen M A T 2000 AampA 363 901Haniff C A Scholz M Tuthill P G 1995 MNRAS 276 640Harries T J Hilditch R W Howarth I D 2003 MNRAS 339157

Hughes S M G Wood P R 1990 AJ 99 784Ita Y et al 2002 MNRAS 279 L32Koornneef J 1982 AampA 107 247Lebzelter T Schultheis M Melchior A L 2002 AampA 393573Melchior A-L Hughes S M G Guibert J 2000 AampAS 14511

Nagashima C et al 1999 in Nakamoto T ed Star formation1999 Nobeyama Radio Observatory p 397

Nagayama T et al 2002 Proc SPIE 4841-51 2002Nelson C A Cook K H Popowski P Alves D R 2000 AJ119 1205

Nikolaev S Weinberg M D 2000 ApJ 542 804Persson S E Murphy D C Krzeminski W Roth M Rieke MJ 1998 AJ 116 2475

Schechter P L Mateo M Saha A 1993 PASP 105 1342Stellingwerf B F 1978 ApJ 224 953STScI 2001 VizieR Online Data Catalog 1271Udalski A Kubiak M Szymanski M 1997 AcA 47 319Udalski A Szymanski M Kubiak M Pietrzynski G SoszynskiI Wozniak PZebrun K 1999a AcA 49 201

Westerlund B E 1997 The Magellanic Clouds Cambridge UnivPress Cambridge

Whitelock P A Feast M W 2000 MNRAS 319 759Wood P R 1990 in Mennessier M O Omont A ed FromMiras to Planetary Nebulae Editions Frontieres Gif-sur-Yvettep67

Wood P R Sebo K M 1996 MNRAS 282 958Wood P R et al 1999 IAU symp 191 151Wood P R 2000 PASA 17 18

ccopy 2002 RAS MNRAS000 1ndash9

• Introduction
• DATA
• • IRSFSIRIUS
  • OGLE
  • • Discussion
    • • K magnitude distribution
      • Period-K magnitude diagram
      • Period-K magnitude relations
      • • Summary

8 Y Ita et al

Table 3 Period-K magnitude relations for variable stars in the MagellanicClouds of the formK = atimes logP+ b The K magnitudes are referred tothe LCO system (Persson et al 1998) Theσ is the standard deviation inK andN is the number of stars being used in the least square fitting afterapplying 30σ clipping Stars on sequencesC andCprime in the LMC weresubdivided into two subgroups according to theirJminusK colour and theirperiod-K magnitude relations were also calculated

Group a b σ N JminusKLMC

Aminus -3284plusmn0047 17060plusmn0065 0114 1142 AllA+ -3289plusmn0047 16793plusmn0077 0125 510 AllBminus -2931plusmn0057 17125plusmn0091 0100 584 AllB+ -3356plusmn0052 17634plusmn0099 0160 502 AllCprime -3768plusmn0023 18885plusmn0046 0110 693 AllCprime -3682plusmn0109 18720plusmn0245 0122 135 gt14Cprime -3873plusmn0031 19081plusmn0060 0105 558 614C -3520plusmn0034 19543plusmn0082 0198 975 AllC -3369plusmn0099 19165plusmn0250 0200 447 gt14C -3589plusmn0055 19698plusmn0126 0196 528 614D -3635plusmn0078 21718plusmn0207 0198 472 AllF -3188plusmn0019 16051plusmn0013 0095 540 AllG -3372plusmn0041 15574plusmn0016 0091 317 All

SMCF -3350plusmn0020 16722plusmn0010 0139 606 AllG -3280plusmn0035 16133plusmn0009 0147 403 All

Figure 10 Period-K magnitude diagram of variable stars in the LMC (reddots) and SMC (green dots) TheK magnitudes of SMC stars are shiftedby minus049 magnitude (see text) to account for the difference in the distancemoduli between the LMC and the SMC

culated the zero points The fixed-slope solutions yielded the zeropoints of 19409plusmn0018 16170plusmn0006 and 15659plusmn0007 mag forsequencesC F andG in the SMC respectively (after shifting theirK magnitudes byminus049 mag) Comparing these zero points withthose of the LMC Cepheids and Miras Cepheids in the SMC arefainter byasymp 01 mag and Miras in the SMC are brighter byasymp 013mag than the LMC ones with the same period

4 SUMMARY

We cross-identified the OGLE-II survey data and the SIRIUS NIRdata in the Magellanic Clouds Based on the large and homoge-

neous data1 we studied the pulsation properties of variable starsin the Magellanic Clouds We discovered a new sequence on theperiod-K magnitude plane and identified it as the one for Miravariables pulsating in the first overtone mode We also foundthatthe variable red giants in the SMC form parallel sequences intheperiod-K magnitude plane just like those found by Wood (2000)in the LMC The period-K magnitude relations were derived es-pecially for both fundamental mode and overtone Cepheids intheMagellanic Clouds These results are obtained with the greatestnumbers of available stars and most deep photometric data intheinfrared up to now Metallicity effects on period-K magnitude re-lations are studied by comparing variable stars in the MagellanicClouds The result suggested that Cepheids in the metal-deficientSMC are fainter than the LMC Cepheids while Miras in the SMCare brighter than the LMC ones if compared with the same period

ACKNOWLEDGMENTS

The authors thank the referee Dr Albert Zijlstra for constructivecomments It is a pleasure to thank Dr Michael Feast for valu-able and helpful comments on the first version of this paper Wealso thank Dr Ian Glass for useful comments This research is sup-ported in part by the Grant-in-Aid for Scientific Research (C) No12640234 and Grant-in-Aids for Scientific on Priority Area (A) No12021202 and 13011202 from the Ministry of Education ScienceSports and Culture of Japan The IRSFSIRIUS project was initi-ated and supported by Nagoya University National AstronomicalObservatory of Japan and University of Tokyo in collaboration withSouth African Astronomical Observatory under a financial supportof Grant-in-Aid for Scientific Research on Priority Area (A)No10147207 of the Ministry of Education Culture Sports Scienceand Technology of Japan The Guide Star Catalogue-II is a jointproject of the Space Telescope Science Institute and the Osserva-torio Astronomico di Torino Space Telescope Science Institute isoperated by the Association of Universities for Research inAstron-omy for the National Aeronautics and Space Administrationundercontract NAS5-26555 The participation of the Osservatorio Astro-nomico di Torino is supported by the Italian Council for Researchin Astronomy Additional support is provided by European South-ern Observatory Space Telescope European Coordinating Facilitythe International GEMINI project and the European Space AgencyAstrophysics Division

REFERENCES

Afonso C et al 1999 AampA 344 L63Alcock C et al 2000 ApJ 541 734Alibert Y Baraffe I Hauschildt P Allard F 1999 AampA344551

Alvarez R Mennessier M-O 1997 AampA 317 761Alves D et al 1998 in Takeuti M Sasselov D D eds ProcIAU JD 24 Pulsating Stars Recent Developments in Theory andObservation Universal Academic Press Tokyo p 17

Bedding T R Zijlstra Albert A Jones A Foster G 1998MN-RAS 301 1073

Bessell M S Scholz M Wood P R 1996 AampA 307 481Bond I A et al 2001 MNRAS 327 868

1 Data of the variable stars will be published in the separate paper

ccopy 2002 RAS MNRAS000 1ndash9

Variable Stars in the Magellanic Clouds 9

Castellani V DeglrsquoInnocenti S Marconi M Prada MoroniP GSestito P 2003 AampA 404 645

Cioni M-R L Marquette J-B Loup C Azzopardi M HabingH J Lasserre T Lesquoy E 2001 AampA 377 945

Cole A A 1998 ApJ 500 L137Feast M W Glass I S Whitelock P A Catchpole R M 1989241 375

Feast M W Whitelock P A Menzies J 2002 MNRAS 329L7

Gascoigne S C B 1974 MNRAS 166 25Glass I S Whitelock P A Catchpole R M Feast M W 1995MNRAS 273 383

Groenewegen M A T 2000 AampA 363 901Haniff C A Scholz M Tuthill P G 1995 MNRAS 276 640Harries T J Hilditch R W Howarth I D 2003 MNRAS 339157

Hughes S M G Wood P R 1990 AJ 99 784Ita Y et al 2002 MNRAS 279 L32Koornneef J 1982 AampA 107 247Lebzelter T Schultheis M Melchior A L 2002 AampA 393573Melchior A-L Hughes S M G Guibert J 2000 AampAS 14511

Nagashima C et al 1999 in Nakamoto T ed Star formation1999 Nobeyama Radio Observatory p 397

Nagayama T et al 2002 Proc SPIE 4841-51 2002Nelson C A Cook K H Popowski P Alves D R 2000 AJ119 1205

Nikolaev S Weinberg M D 2000 ApJ 542 804Persson S E Murphy D C Krzeminski W Roth M Rieke MJ 1998 AJ 116 2475

Schechter P L Mateo M Saha A 1993 PASP 105 1342Stellingwerf B F 1978 ApJ 224 953STScI 2001 VizieR Online Data Catalog 1271Udalski A Kubiak M Szymanski M 1997 AcA 47 319Udalski A Szymanski M Kubiak M Pietrzynski G SoszynskiI Wozniak PZebrun K 1999a AcA 49 201

Westerlund B E 1997 The Magellanic Clouds Cambridge UnivPress Cambridge

Whitelock P A Feast M W 2000 MNRAS 319 759Wood P R 1990 in Mennessier M O Omont A ed FromMiras to Planetary Nebulae Editions Frontieres Gif-sur-Yvettep67

Wood P R Sebo K M 1996 MNRAS 282 958Wood P R et al 1999 IAU symp 191 151Wood P R 2000 PASA 17 18

ccopy 2002 RAS MNRAS000 1ndash9

• Introduction
• DATA
• • IRSFSIRIUS
  • OGLE
  • • Discussion
    • • K magnitude distribution
      • Period-K magnitude diagram
      • Period-K magnitude relations
      • • Summary

Variable Stars in the Magellanic Clouds 9

Castellani V DeglrsquoInnocenti S Marconi M Prada MoroniP GSestito P 2003 AampA 404 645

Cioni M-R L Marquette J-B Loup C Azzopardi M HabingH J Lasserre T Lesquoy E 2001 AampA 377 945

Cole A A 1998 ApJ 500 L137Feast M W Glass I S Whitelock P A Catchpole R M 1989241 375

Feast M W Whitelock P A Menzies J 2002 MNRAS 329L7

Gascoigne S C B 1974 MNRAS 166 25Glass I S Whitelock P A Catchpole R M Feast M W 1995MNRAS 273 383

Groenewegen M A T 2000 AampA 363 901Haniff C A Scholz M Tuthill P G 1995 MNRAS 276 640Harries T J Hilditch R W Howarth I D 2003 MNRAS 339157

Hughes S M G Wood P R 1990 AJ 99 784Ita Y et al 2002 MNRAS 279 L32Koornneef J 1982 AampA 107 247Lebzelter T Schultheis M Melchior A L 2002 AampA 393573Melchior A-L Hughes S M G Guibert J 2000 AampAS 14511

Nagashima C et al 1999 in Nakamoto T ed Star formation1999 Nobeyama Radio Observatory p 397

Nagayama T et al 2002 Proc SPIE 4841-51 2002Nelson C A Cook K H Popowski P Alves D R 2000 AJ119 1205

Nikolaev S Weinberg M D 2000 ApJ 542 804Persson S E Murphy D C Krzeminski W Roth M Rieke MJ 1998 AJ 116 2475

Schechter P L Mateo M Saha A 1993 PASP 105 1342Stellingwerf B F 1978 ApJ 224 953STScI 2001 VizieR Online Data Catalog 1271Udalski A Kubiak M Szymanski M 1997 AcA 47 319Udalski A Szymanski M Kubiak M Pietrzynski G SoszynskiI Wozniak PZebrun K 1999a AcA 49 201

Westerlund B E 1997 The Magellanic Clouds Cambridge UnivPress Cambridge

Whitelock P A Feast M W 2000 MNRAS 319 759Wood P R 1990 in Mennessier M O Omont A ed FromMiras to Planetary Nebulae Editions Frontieres Gif-sur-Yvettep67

Wood P R Sebo K M 1996 MNRAS 282 958Wood P R et al 1999 IAU symp 191 151Wood P R 2000 PASA 17 18

ccopy 2002 RAS MNRAS000 1ndash9

• Introduction
• DATA
• • IRSFSIRIUS
  • OGLE
  • • Discussion
    • • K magnitude distribution
      • Period-K magnitude diagram
      • Period-K magnitude relations
      • • Summary