Determination of the Distance to M33 Based on the Tip of the Red Giant Branch and the Red C

a r X i v :a s t r o -p h /0110006v 1 29 S e p 2001

Draft version February 1,2008

Preprint typeset using L A T E X style emulateapj v.21/08/00

DETERMINATION OF THE DISTANCE TO M33BASED ON THE TIP OF THE RED GIANT

BRANCH AND THE RED CLUMP 1

Minsun Kim,Eunhyeuk Kim,Myung Gyoon Lee

Astronomy Program,SEES,Seoul National University,Seoul,151-742,Korea

Ata Sarajedini

Department of Astronomy,University of Florida,P.O.Box 112055,Gainsville,FL 32611,USA

Doug Geisler

Departamento de F ′?sica,Grupo de Astronom′?a,Universidad de Concepci′o n,Casilla 160-C,Concepci′o n,Chile

Draft version February 1,2008

ABSTRACT

We have determined the distance to M33using the tip of the red giant branch (TRGB)and the red clump (RC),from the V I photometry of stars in ten regions of M33based on HST/W F P C 2images.The regions used in this study are located at R =2.6?17.8arcmin from the center of M33.The distance modulus to M33obtained in this study,for an adopted foreground reddening of E (B ?V )=0.04,

is (m ?M )0,T RGB =24.81±0.04(random)+0.15

?0.11(systematic)from the TRGB,and (m ?M )0,RC =24.80±0.04(random)±0.05(systematic)from the RC,showing an excellent agreement between the two (corresponding to a distance of 916±17(random)kpc and 912±17(random)kpc,respectively).These results are ≈0.3mag larger than the Cepheid distances based on the same HST/W F P C 2data and ground-based data.This di?erence is considered partially due to the uncertainty in the estimates of the total reddening for Cepheids in M33.

Subject headings:galaxies:distances and redshifts —galaxies:individual (M33(NGC 598))—stars:

tip of the red giant branch (TRGB)—stars:red clump(RC)

1.introduction

The accurate determination of the distances to Local Group galaxies is critical in the study of the extragalac-tic distance scale.In particular two spiral galaxies in the Local Group,M31and M33,are primary calibrators for several secondary distance indicators including the Tully-Fisher relation.While the distance to M31has been mea-sured extensively,relatively less attention has been paid to the distance determination of M33(van den Bergh 2000).Recently the tip of the red giant branch (TRGB),a Pop-ulation II distance indicator,has frequently been used for the determination of distances to resolved galaxies in the Local Group;in addition,another Population II distance indicator,the red clump (RC),has come to be used quite often as well.These two methods have an advantage over the classical primary distance indicators such as Cepheids and RR Lyraes in that the distances to galaxies can be determined reliably from single epoch observations.The TRGB has been known to be an excellent standard can-dle for resolved galaxies,because the I -band magnitude of the TRGB for stars older than a few Gyrs with metallicity ?2.1≤[F e/H ]≤?0.7is essentially independent of age and metallicity (Lee,Freedman,&Madore 1993;Lee 1996;Salaris &Cassisi 1998;Ferrarese et al.2000;Cioni et al.2000).

On the other hand,the RC was not widely recognized as a potentially good standard candle until Paczy′n ski &Stanek (1998)recently suggested its use.Since then the reliability of the RC as a standard candle has been contro-versial (see Sarajedini (1999);Girardi &Salaris (2001);Popowski (2000)and the references therein).Paczy′n ski

&Stanek (1998)showed that the mean I -band magni-tude M RC

I of red clump stars is independent of their color in the range 0.8≤(V ?I )0≤1.4and has a small dispersion(≈0.2mag),suggesting that the RC can be a good standard candle as originally pointed out by Can-non (1970).However,the distance to the Large Magel-lanic Cloud obtained using the RC by Stanek,Zaritsky,&Harris (1998)and Udalski et al.(1998)was much shorter than that based on other methods,which became a start-ing point for debate focused on the accuracy of the RC

method.Udalski (1998)claimed that the M RC

I has a weak dependence on metallicity and no dependence on age for an intermediate age population (2–10Gyrs)of stars.On the contrary,Sarajedini (1999)analyzed several galactic open clusters with intermediate-ages and compared the properties of their RCs with the predictions of stellar evo-lution models;this comparison indicates that the M RC

I becomes signi?cantly fainter as the cluster gets older.In addition,a number of studies have argued that stellar evo-lutionary theory predicts a signi?cant dependence of M RC

I on the combination of the age and metallicity of the stel-lar population (Cole 1998;Girardi et al.1998;Girardi 2000;Girardi &Salaris 2001).Castellani et al.(2000)pointed out that the input physics and the dependence of various evolutionary codes should be considered to clarify this discrepancy.Observationally it is also important to attack this problem by investigating the e?ect of age and metallicity on the RC in other nearby galaxies where the properties of the RC can be studied in detail.

In this paper we present an analysis designed to deter-mine the distance to M33using the TRGB and the RC based on photometry of stars in ten M33?elds obtained 1

Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute,which is operated by the Association of Universities for Research in Astronomy,Incorporated,under NASA contract NAS5-26555.

1

2Kim et al.

from HST/W F P C2images.M33is an ideal target to apply both the TRGB and RC methods of distance deter-mination using HST/W F P C2data.

This paper is composed as follows.In§2we present the data and reduction technique.§3displays the color-magnitude diagrams of the measured stars,and estimates the distance to M33using the TRGB and RC methods. Primary results are discussed in§4and are summarized in §5.

2.data and reduction

We have analyzed HST/W F P C2data for ten?elds in M33obtained for Sarajedini et al.(1998)’s cycle5program (GO-5914).Each?eld was observed for four orbits,yield-ing a total exposure time of4800seconds for F555W(V) and5200seconds for F814W(I).These data were ob-tained originally for the study of globular clusters in M33, and a globular cluster is centered in each PC chip.The data from the PC chip were presented by Sarajedini et al. (1998)and Sarajedini et al.(2000).In this study we use all?eld stars in the WF2,WF3,and WF4chips as well as in the PC chip.Hereafter we refer to each observed region using the globular cluster’s designation.Figure1 illustrates the location of the regions in M33used in this study.Considering the number of?elds and the deep ex-posures,these data are ideal for studying the?eld stars as well as the globular clusters in M33.

Table1lists the positions,galactocentric distances,de-projected radial distances,and the reddening values of all the regions used in this study.The position of the re-gion in Table1is the center of the WFPC2.The galacto-centric distance is the distance from the center of M33 (RA(2000)=01h33m51s.02,Dec(2000)=+30?39′36′′.7) (Cotton,Condon,&Arbizzani1999).All the regions were assumed to be in the plane of M33’s disk and were depro-jected to estimate the actual radial distance.An inclina-tion of56?and a position angle of23?for M33were used for deprojection of the positions(Regan&Vogel1994). For foreground reddening correction,the COBE/IRAS ex-tinction maps of Schlegel,Finkbeiner,&Davis(1998) are used.The reddening values of all the regions are as low as E(V?I)=0.06(E(B?V)=0.04).The extinction laws for R V=3.3,A I=1.95E(B?V)and E(V?I)=1.35E(B?V)(Cardelli et al.1989),are adopted in this study.

The photometry of the stars in the CCD images has been obtained using the multiphot routine of the HSTphot pack-age(Dolphin2000a).The HSTphot package was designed for photometry of HST/W F P C2data and employs a li-brary of Tiny Tim point-spread-functions(PSFs)for PSF ?tting to account for variations in the PSF due to loca-tion on the chip and the centering within a pixel.After PSF-?tting,corrections are also made for geometric distor-tion,CTE e?ect,and the34th row e?ect(Dolphin2000b). The multiphot routine gives the magnitudes transformed to the standard system as well as instrumental magnitudes. The HSTphot photometry used zero points from Dolphin (2000b)which provides corrections to the Holtzman et al. (1995)values.

3.results

3.1.Color-Magnitude Diagrams

The number of the measured stars in each region is many tens of thousands(from～60000to～80000stars) which are too many to plot in a color-magnitude diagram (CMD).Therefore,as an example,Fig.2shows the color-magnitude diagram(CMD)for one?eld.In the case of the PC chip,at the center of which a globular cluster is located,the stars at r<2.8arcsec from the center of the cluster are considered to be members while those at r>4.6arcsec are considered to be?eld stars.Figure2 shows a CMD for the measured stars in the C20-region, which happens to be our most distant?eld from the center of M33.Several features are seen in Figure2.(a)There is a broad red giant branch(RGB),the tip of which is seen at I≈21.0mag.The mean color of the RGB of these?eld stars is redder than that of the globular clus-ter C20in the same region(represented by the solid line). The locus of C20was derived from the median color of the stars at r<2.8arcsec from the center of C20.(b) A red clump is distinctively seen at I≈24.5mag and (V?I)≈1.0;(c)Asymptotic giant branch(AGB)stars are also seen along and above the RGB;and(d)There is a blue plume at(V?I)≈0.0extending up to I≈20mag, which consists of massive main sequence stars and evolved supergiants.These features are also seen in the CMDs of the other regions.

In Figure3,the CMDs of all the regions are shown in number density contour maps(Hess Diagrams).The den-sity contour maps are constructed on100×100grids in the CMD domain(the size of each grid is?(V?I)×?I= 0.03×0.1),and are smoothed using Gaussian?lters of2 grid width.Basic features seen in Figure3are similar to those in Figure2.Number density contour maps are useful for revealing the areas with the highest stellar density.All CMDs in Figure3show a strong peak at the position of the red clump(marked by the crosses).The photometry of the stars in the R14-and R12-regions is signi?cantly af-fected by crowding,because they are located close to the center of M33.Therefore only the stars in the PC chip (which has higher spatial resolution than the WF chips) are used to measure the magnitude of the red clump in these regions in the following.

3.2.Estimation of the Distance to M33

3.2.1.Tip of the Red Giant Branch

We have determined the distance to M33using the I-band magnitude of the TRGB,following the description given in Lee,Freedman,&Madore(1993).Figure4dis-plays the I-band luminosity functions of red stars includ-ing the RGB and AGB stars.In Figure4there is a sud-den increase at I T RGB≈20.9in all the regions as marked by the arrow,which corresponds to the TRGB.We have measured the I-band magnitude of the TRGB using this feature in the luminosity function by eye detection(supple-mented by using the edge-detection?lters(Lee,Freedman, &Madore1993)).The values of the I T RGB thus derived for all the regions are listed in Table2.

The distance modulus is given by

(m?M)I=I0,T RGB+BC I?M bol,T RGB(1) where I0,T RGB is the dereddened I-band magnitude of the TRGB.BC I is the bolometric correction to the I magni-

TRGB and RC Distance to M333

tude which depends on color as follows:

BC I=0.881?0.243(V?I)0,T RGB(2) where(V?I)0,T RGB is the dereddened color of the TRGB. The bolometric magnitude of the TRGB,M bol,T RGB,is given as a function of metallicity[Fe/H]by:

M bol,T RGB=?0.19[F e/H]?3.81.(3) Metallicity can be estimated from the(V?I)color at the absolute I-band magnitude of M I=?3.5given by Lee,Freedman,&Madore(1993)(see also Saviane et al. (2000))as follows:

[F e/H]=?12.64+12.6(V?I)0,?3.5?3.3(V?I)20,?3.5.

(4) We have employed an iterative procedure in which an initial guess at the distance is used to estimate the metal-licity which is in turn used to re?ne the distance until the solution converges,which occurs after only a few itera-tions.It is important to note that the regions used for this study are located in various environments including young to old stellar populations;thus,the broad RGBs seen in the CMDs are actually a mixture of intermediate-age to old populations,as well as a range of metallicities. If we simply use the mean color[(V?I)0,?3.5]of the entire apparent RGB in this case,the resulting metallicity will be an underestimate,because there are younger populations with bluer color on the blue side of the RGB.For this rea-son we tried to use the median value of the color of the stars along the RGB to reduce the e?ect of intermediate-age populations.As a check of our method,we have also derived the mean metallicity using the slope of the RGB as calibrated by Sarajedini et al.(2000),obtaining very similar results to those from the median color of the RGB stars.

The mean metallicities resulting from this procedure are listed in Table2.The mean metallicity ranges from[Fe/H]≈–0.6to–0.9dex.Figure5displays the mean metallic-ity versus the deprojected radial distance of the regions (?lled circles).In Figure5there is clearly a negative ra-dial gradient of the metallicity.The mean metallicity data are?t by[Fe/H]=?0.05[±0.01]R dp?0.55[±0.02]([Fe/H] =?0.04[±0.02]R dp?0.51[±0.06],using the metallicity ob-tained with the RGB slope method)for all the data,where R dp is given in terms of kpc(1′=0.27kpc is assumed). If we exclude the two innermost regions where the crowd-ing is severe,we obtain a?t,[Fe/H]=?0.07[±0.01]R dp?0.48[±0.04]([Fe/H]=?0.08[±0.03]R dp?0.34[±0.10]us-ing the metallicity obtained with the RGB slope method), similar to values found in our Galaxy’s disk using open clusters and?eld giants(d[F e/H]/dR=?0.050±0.008 kpc?1)(Janes1979).

In Figure5the metallicity of the red giants is com-pared with that of HII regions in M33.The metallic-ity of the HII regions was converted from[O/H]values given in the literature(Kwitter&Aller1981;McCall,Ryb-ski,&Shields1985;Vilchez et al.1988;Zaritsky,Kenni-cutt,&Huchra1994)using the following relation taken from King(2000):[O/F e]=?0.184[F e/H]+0.019. The deprojected radius for the HII regions was calculated as above.The metallicity of the HII regions is?t by [Fe/H]=?0.12[±0.02]R dp+0.33[±0.07],which is some-what steeper than that for the?eld red giants.The rela-tion for the HII regions shows a trend that is similar to that of the?eld red giants,but with a larger scatter.It is natural that the mean metallicity of the?eld red giants is lower than that of the HII regions,because the red giants are much older than the HII regions.

Then we derive the distance modulus of each region us-ing the information given above.Table2lists the pa-rameters related to the TRGB method;the observed I-band magnitude of the TRGB(I T RGB),the extinction corrected I-band magnitude of the TRGB(I0,T RGB),the mean color of the TRGB[(V?I)0,T RGB],the mean color measured at M I=?3.5[(V?I)0,?3.5],the mean metal-licity([Fe/H])of the RGB,the absolute magnitude of the TRGB(M I,T RGB),and the distance modulus[(m?M)0]. Figure6displays I T RGB versus[Fe/H]for the ten re-gions in M33.The value of I T RGB varies little,with no obvious net metallicity dependence.The mean value of I T RGB for the ten regions is I T RGB=20.88±0.04,show-ing a remarkably small dispersion.

The average value of the distance moduli for all of the?elds is calculated to be(m?M)0,T RGB=24.81±

0.04(random)+0.15

?0.11

(systematic).The errors for the dis-tance modulus are based on the error budget listed in Ta-ble3.

The calibration of the TRGB is based on Galactic globu-lar clusters with[Fe/H]=–2.1to–0.7dex,yet the derived mean metallicities of the four inner regions in our sample ([Fe/H]=–0.61to–0.68dex)are slightly larger than the upper boundary of the calibration range.If we use only the six other regions,excluding these four inner ones,we obtain an average distance modulus of(m?M)0,T RGB=

24.83±0.06(random)+0.15

?0.11

(systematic).If the theoretical calibration given by Salaris&Cassisi(1998)is adopted (M I,T RGB=?3.953+0.437[M/H]+0.147[M/H]2and [M/H]=?39.270+64.687[(V?I)0,?3.5]?36.351[(V?I)0,?3.5]2+6.838[(V?I)0,?3.5]3),the average distance modulus will be(m?M)0,T RGB=24.99±0.04(statistical), which is0.2mag fainter than that derived using the em-pirical calibration of Lee,Freedman,&Madore(1993). However,it has been found that the distance obtained with the theoretical calibration is not consistent with other results as shown by Dolphin et al.(2001)in IC 1613.So we prefer to use the empirical calibration rather than the theoretical one in this study.Finally we adopt

(m?M)0,T RGB=24.81±0.04(random)+0.15

?0.11

(systematic) as the TRGB distance modulus to M33.

3.2.2.Red Clump Stars

We have determined the distance to M33using the red clump as well.Red clumps are clearly found in the CMDs of all the regions,as seen in Figure3.It is important to note that implicit in the subsequent analysis is the as-sumption that the metallicity determined from the RGB stars can be applied to the red clump stars as well.This is based on two assertions.First,based on the absence of a vertical structure of stars blueward of the RC(Girardi &Salaris2001),we claim that the age of the RC stars is likely to be older than～1Gyr.Second,the chemical enrichment in the disk of M33is assumed to have been small in the period between10Gyr and a few Gyr ago.

4Kim et al. To check the variation of the mean magnitude of the red

clump on the color,we have selected red clump stars with

colors and magnitudes in the range0.6<(V?I)<1.6

and23.5

tude of these stars(I RC)versus their(V?I)colors.The horizontal bars on the?lled circles represent the size of the

color bin.Two thousand stars are included in each color

bin.

Figure7shows that the variation of the mean magni-

tudes for the color range of0.8≤(V?I)≤1.2in a given

region(the same range as used for M31by Stanek&Gar-

navich(1998))is smaller than0.1mag in all of the regions;

Fig.7also indicates that the variation of the mean magni-

tudes among the regions is remarkably small(less than0.1 mag).It is rather surprising that the variation of the mean magnitudes of the RC is smaller than0.1mag,considering

that the regions used are located at a large range of dis-

tances from the center of M33with diverse star formation histories and a varying metallicity.However,we note that

the metal abundances vary over a range of less than0.3

dex.Such a small abundance range has a correspondingly

small e?ect on the I-band RC luminosity(less than0.04

mag)(Girardi&Salaris2001;Sarajedini1999).The RC

is also sensitive to age,which further suggests that the dominant stellar populations in our M33disk?elds are all probably similar in age.In uniform populations such as

this,the red clump can potentially be a good standard candle.

We derive then the I-band luminosity functions of these

red clump stars with0.8≤(V?I)≤1.2,as displayed in

Figure8.Figure8shows that there is a strong single peak

above the slowly varying background in the I-band lumi-

nosity functions in all the regions.We measure the peak magnitude of the red clumps?tting the I-band luminosity functions with the combination of a gaussian function(for

the red clump)and a parabolic function(for the red giants

and subgiants)as follows(Paczy′n ski&Stanek1998):

N(I rc)=a+b(I?I rc)+c(I?I rc)2+N RC

2π

exp ?(I?I rc)2

TRGB and RC Distance to M335

on age is likely to be manifested in the dispersion around the dotted line in Fig.9(c).This dispersion amounts to

a root-mean-square deviation of the points from the?t of

0.03mag,which is larger than the typical error in I0,RC of～0.01mag.If taken at face value,this represents an age dispersion of～1.5Gyr among the RC stars(based on0.02mag/Gyr from the models presented by Sarajedini (1999)).

The mean value of the distance moduli for ten re-gions is derived to be(m?M)0,RC=24.80±0.04(random)±0.05(systematic)using eq.(6).The errors are derived following the error budget in Table 5.If we use the calibration by Udalski(2000),we obtain (m?M)0,RC=24.76±0.04(random)±0.05(systematic). These values are in excellent agreement with those from the TRGB.

4.discussion

https://www.sodocs.net/doc/1811316164.html,parison with Other Studies

To date the distance to M33has been studied using a number of standard candles:Cepheid variables(Sandage 1983;Sandage&Carson1983;Christian&Schommer 1987;Mould1987;Madore&Freedman1991;Freedman, Wilson,&Madore1991;Freedman et al.2001;Lee et al. 2001),horizontal branch stars in globular clusters(Sara-jedini et al.2000),red supergiant long-period variables (SLPVs)(Pierce,Jurcevic,&Crabtree2000),the lumi-nosity function of the planetary nebulae(PNLF)(Magrini et al.2000)and the TRGB(Mould&Kristian1986;Lee, Freedman,&Madore1993;Salaris&Cassisi1998),as summarized in Table6(see also van den Bergh(1991),van den Bergh(1999),van den Bergh(2000)).These distance moduli range from as low as24.41to a high of24.85.Our values of24.80,24.81(from the RC with Popowski(2000) calibration and the TRGB)and24.76(from the RC with Udalski(2000)calibration)are at the high end of the pub-lished range of distances.

Among the previous distance estimates,Lee et al.(2001) determined the distance to M33using the single phase I-band photometry of21Cepheids with log P>0.8based on the same data as used in this paper.Lee et al.(2001) obtained(m?M)0=24.52±0.13for for an adopted total reddening of M33,E(B?V)=0.20±0.04(E(V?I)= 0.27±0.05)given by Freedman et al.(2001),the reddening to the LMC,E(B?V)=0.10,and the distance to the LMC,(m?M)0=18.50.This value is～0.3mag smaller than those derived using the TRGB and RC in this study. This di?erence is considered partially due to the uncer-tainty in the estimates of the total reddening for Cepheids in M33.Note that Freedman,Wilson,&Madore(1991) derived the total reddening of M33Cepheids from BV RI photometry to be E(B?V)=0.10±0.09,while Freedman et al.(2001)revised this value to E(B?V)=0.20±0.04 using the di?erent period-luminosity relations for V and I with the same data.Better estimates of the redden-ing of M33Cepheids are needed to investigate further this problem.

4.2.Magnitude di?erence between the TRGB and the RC In the previous section we have examined the depen-dence on metallicity of the I-band magnitude of the red clump and the magnitude of the TRGB.Here we investigate the dependence on metallicity of both to-gether using the di?erence of the I-band magnitude be-tween the RC and the TRGB,?I(RC–TRGB)=I RC?I T RGB.?I(RC–TRGB)can be measured directly from the photometry and has the added advantage of being extinction-free(Bersier2000).Figure10displays?I(RC–TRGB)versus[Fe/H]for the ten regions in M33.It is seen clearly that there is a positive correlation be-tween?I(RC–TRGB)and[Fe/H].The data for the outer8regions in M33are?t well by?I(RC–TRGB)= 0.45[±0.18][Fe/H]+3.95[±0.14].If we use the data for all regions including the inner two regions,we derive?I(RC–TRGB)=0.56[±0.15][Fe/H]+4.04[±0.11].The error for the slope is rather large,because the range of[Fe/H]used for this?t is small.Since the TRGB magnitudes and fore-ground extinctions for all the regions are almost constant,

M T RGB

I

=?4.0and A I=0.08(as given in Table2),the slope in this?t represents basically the dependence of the RC magnitude on[Fe/H].The slope derived from the data of M33is rather steeper than the slope given by Popowski (2000)which is based on the galactic RC stars(shown by the dashed line in Figure10).For a better determination of the dependence of?I(RC–TRGB)on[Fe/H],a large range of[Fe/H]is required.

We have compared?I(RC–TRGB)for M33with those for other nearby galaxies compiled by Bersier(2000)in Figure11.For M33the mean di?erence=3.62±0.05and mean metallicity<[F e/H]>=?0.75±0.07of the outer eight regions(excluding R14and R12)are used from this study.Figure11shows that the data for M33 is consistent with those for other galaxies,following the relation plotted in Figure10.

5.summary

We present V I photometry of?eld stars in ten regions located at R=2.6to17.8arcmin from the center of M33 based on HST/W F P C2images.From this photometry we have determined the distance to M33using the tip of the red giant branch(TRGB)and the red clump(RC). Main results obtained in this study are summarized as fol-lows.

1.Mean metallicities of the RGB in ten regions range

from[Fe/H]=–0.9to–0.6.We?nd a clear negative

radial gradient of the metallicity of the RGB,

which has a smaller slope and much smaller scatter

than that derived from HII regions in M33.

2.I-band magnitudes of the TRGB in ten regions

are almost constant with a very narrow range:

I=20.82to20.92.This result con?rms that the

I-band magnitudes of the TRGB is insensitive to

age or metallicity for old stars with[Fe/H]

(Lee,Freedman,&Madore1993).

3.The distance to M33based on the TRGB of

ten regions is derived to be(m?M)0,T RGB=

24.81±0.04(random)+0.15

?0.11

(systematic)(corre-sponding to a distance of916±17(random)

kpc).

4.Mean colors of the RC in ten regions are almost

constant:(V?I)0=0.89to0.97,and show little

correlation with[Fe/H].

6Kim et al.

5.I-band magnitudes of the RC in ten regions

are almost constant with a very narrow range:

I=24.46to24.57,but they show a correlation with[Fe/H]with a slope similar to that given by Popowski(2000).

6.Assuming the metallicity of the RC stars

is the same as that of the RGB stars,the

distance to M33based on the RC of ten

regions is derived to be(m?M)0,RC=

24.80±0.04(random)±0.05(systematic)(corre-

sponding to a distance of912±17(random)kpc),

which is in excellent agreement with the TRGB

distance obtained in this study.

M.G.L.is in part supported by the MOST/KISTEP In-ternational Collaboration Research Program(1-99-009). M.G.L.is grateful to the Astronomy Group at the Uni-versity of Concepcion for the warm hospitality during his stay for this work.A.S.has bene?ted from?nancial sup-port from NSF CAREER grant No.AST-0094048.D.G. acknowledges?nancial support for this project received from CONICYT through Fondecyt grant8000002.

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TRGB and RC Distance to M337

Table1

A LIST OF THE REGIONS IN M33USED FOR ANALYSIS

Region R.A.(2000)a Dec.(2000)b R c R dp d E(V?I)e

a Right ascension in units of hours,minutes,and seconds.

b Declination in units of degrees,arcminutes,and arcseconds.

c Radial distance in arcminutes from the center of M33.

d Deprojected radial distanc

e in arcminutes from the center o

f M33.

e Foreground reddening from COBE/IRAS maps o

f Schlegel,

Finkbeiner,&Davis(1998).

Table2

ESTIMATED PARAMETERS FOR THE TIP OF THE RED GIANT BRANCH METHOD

Region I T RGB I0,T RGB(V?I)0,T RGB(V?I)0,?3.5[Fe/H]M I,T RGB(m?M)0,T RGB

8Kim et al.

Table3

ERROR BUDGET FOR THE TRGB METHOD

Error Estimation(mag)

2.Systematic Error

A.RR Lyrae distance scale0.11

B.Undersampling in the Galactic globular cluster calibration b0.1

C.Total+0.15

?0.11

a G or H=F/√

R1424.57±0.0224.490.33±0.090.93±0.006–0.61±0.0924.8424.80 R1224.52±0.0224.440.41±0.190.89±0.006–0.65±0.0924.8024.76 U7724.49±0.0124.410.38±0.070.92±0.004–0.68±0.0924.7724.73 U4924.52±0.0124.440.34±0.060.93±0.004–0.67±0.0924.7924.75 M924.49±0.0124.400.24±0.010.94±0.004–0.79±0.0924.7824.74 H1024.56±0.0124.480.26±0.020.97±0.004–0.71±0.0924.8424.80 H3824.53±0.0124.440.25±0.020.89±0.004–0.72±0.0924.8124.76 U13724.53±0.0124.440.25±0.010.93±0.004–0.74±0.0924.8124.76 C2024.46±0.0124.370.21±0.010.92±0.004–0.82±0.0924.7624.71 C3824.49±0.0124.400.21±0.010.92±0.003–0.86±0.0924.8024.75

TRGB and RC Distance to M339

Table5

ERROR BUDGET FOR THE RED CLUMP METHOD

Error Estimation(mag)

2.Systematic error

A1.calibration error in Powposki(2000)0.05

A2.calibration error in Udalski(2000)0.05

a F=E/√

Cepheids m pg24.05±0.1824.320.12Christian&Schommer(1987)

Cepheids I24.82±0.1524.930.12Mould(1987)

Cepheids BVRI24.64±0.0924.750.10Freedman,Wilson,&Madore(1991) Cepheids VI24.56±0.1024.870.20Freedman et al.(2001)

Cepheids VI24.52±0.1524.830.20Lee et al.(2001)

TRGB24.70±0.1024.820.10Mould&Kristian(1986),Lee,Freedman,&Madore(1993) SLPV24.85±0.1324.970.10Pierce,Jurcevic,&Crabtree(2000)

PNLF24.62±0.2524.740.10Magrini et al.(2000)

HB24.84±0.16—0.04b Sarajedini et al.(2000)

TRGB24.81±0.13—0.04b This study

RC24.80±0.14c—0.04b This study

RC24.76±0.14d—0.04b This study

10Kim et al.

Fig. 1.—A?nding chart of M33showing the positions of the ten regions observed with HST/W F P C2(squares).The grayscale map is from the digitized Palomar Sky Survey.

Fig. 2.—Color-magnitude diagrams of the?eld stars in the PC chip(left panel)and in the WF2,WF3,and WF4chips(right panel)of the C20-region.The solid line in the left panel represents the mean locus of the globular cluster C20.Note that the mean color of the RGB of the?eld stars is redder than that of the globular cluster.A compact red clump is found to be at I≈24.4and at(V?I)≈0.9,and the TRGB is seen at I≈21.0.

TRGB and RC Distance to M3311

2826242220(a)R14(ALL)(b)R12(ALL)(e)U77(f)U49

2826242220(g)M9(h)H10(i)H38

-1

0122826242220V-I

(j)U137-1012V-I

(k)C20-1012

V-I

(l)C38

(c)R14(PC)

2826242220(d)R12(PC)Fig. 3.—Color-magnitude diagrams of the observed regions in M33displayed in the density contour map.The panels (c)and (d),for R14and R12regions,are only for the stars in the PC chip.In other panels the CMDs of the ?eld stars in all four chips (PC,WF2,WF3,and WF4)are displayed.Crosses represent the peaks of the density contour map,which correspond to the mean position of the red clumps.Contour levels are at 1,3,10,30,50,70,90,110,and 130stars/grid,respectively.For (c)and (d)contour levels are at 1,3,5,10,15,20,and 25stars/grid,respectively.

12Kim et al.

Fig. 4.—I-band luminosity functions of bright red stars in M33.The I magnitudes of the tip of the red giant branch are marked by arrows.

TRGB and RC Distance to M3313

Fig. 5.—Mean metallicity[Fe/H]of the RGB in each region as a function of the deprojected radial distance derived in this study(?lled circles).The dashed line represents the mean relation between R dp and[Fe/H]derived from the RGB.The mean metallicity decreases as the radial distance increases.For comparison,the solid line represents the mean relation between R dp and[Fe/H]derived for the HII regions in M33from various other studies(open circles).

Fig.6.—The I-band magnitude of the TRGB,I T RGB,as a function of metallicity.The solid line represents the average value of I T RGB, and the dashed lines represent standard deviations of±1σ.

14Kim et al.

Fig.7.—The mean magnitude of the red clump I RC versus(V?I)color.The horizontal bars on?lled circles represent the sizes of color bins,not error bars,while the vertical bars represent?tting errors.Two thousand stars are included in each color bin.Note that I RC varies little in the color range of0.8≤(V?I)≤1.2(between the two vertical dotted lines).The horizontal solid line represents the mean of I RC for all color bins.

TRGB and RC Distance to M3315

Fig.8.—I-band luminosity functions of red clump stars in the color range0.8<(V?I)<1.2and in the magnitude range23.5

16Kim et al.

Fig.9.—Several parameters for the red clump method as a function of metallicity[Fe/H].(a)The mean color of the red clump(V?I)RC. The dashed line represents a mean value of the ten regions.(b)The dispersion of the mean magnitude of red clump.The dashed line represents a mean value of the outer six regions with lower[Fe/H].(c)The extinction corrected I-band magnitudes of the red clump.The dashed line shows the Popowski(2000)’s calibration for a distance modulus of(m?M)0=24.81.

Fig.10.—The di?erence in I-band magnitude between the RC and the TRGB,?I(RC–TRGB),versus mean metallicity of the red giants

in M33.The dashed line represents the expected di?erence,when the TRGB magnitude M T RGB

I =?4.0and Popowski(2000)’s calibration

are assumed.The solid line represents a?tting line to the data when R14and R12regions(open circles)are excluded.

TRGB and RC Distance to M3317

Fig.11.—The di?erence in I magnitude between the RC and the TRGB stars?I(RC–TRGB)versus metallicity for M33and other nearby galaxies.A?lled pentagon represents our mean value of the eight regions in M33.The LMC data are from Zaritsky,Harris,&Thompson (1997)(open square)and Sakai,Zaritsky,&Kennicutt(2000)(?lled square).The solid line represents the expected di?erence when the

=?4.0and Popowski(2000)’s calibration are assumed.

TRGB magnitude M T RGB

I