Reddening and Distance of the Local Group Starburst Galaxy IC 10
Minsun Kim, Eunhyeuk Kim, Narae Hwang, Myung Gyoon Lee, Myungshin Im, Hiroshi Karoji, Junichi Noumaru, and Ichi Tanaka
aa r X i v : . [ a s t r o - ph . C O ] J u l To be published in ApJ, 2009
Reddening and Distance of the Local Group Starburst Galaxy IC10 ∗ Minsun Kim , , Eunhyeuk Kim , , Narae Hwang , , Myung Gyoon Lee , Myungshin Im ,Hiroshi Karoji , Junichi Noumaru , and Ichi Tanaka [email protected], [email protected], [email protected],[email protected], [email protected], [email protected],[email protected], [email protected] ABSTRACT
We estimate the reddening and distance of the nearest starburst galaxy IC10 using deep near infrared
J HK S photometry obtained with the Multi-ObjectInfraRed Camera and Spectrograph (MOIRCS) on the Subaru telescope. Weestimate the foreground reddening toward IC 10 using U BV photometry of IC 10from the Local Group Survey, obtaining E ( B − V ) = 0 . ± .
04 mag. We derivethe total reddening including the internal reddening, E ( B − V ) = 0 . ± . U BV photometry of early-type stars in IC 10 and comparing
J HK S photometry of red giant branch stars in IC 10 and the SMC. Using the 2MASSpoint source catalog of 20 Galactic globular clusters, we derive a relation betweenthe metallicity [Fe/H] CG and the slope of the red giant branch in the K S − ( J − K S ) color-magnitude diagram. The mean metallicity of the red giant branch starsin IC 10 is estimated to be [Fe/H] CG = − . ± .
28. The magnitude of thetip of the red giant branch (TRGB) of IC 10 in the K S band is measured to be International Center for Astrophysics, Korea Astronomy and Space Science Institute, Daejeon 305-348,Korea Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742,Korea National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan Institute of Earth-Atmosphere-Astronomy, Yonsei University, Seoul 120-749, Korea*Based on data collected at Subaru Telescope, which is operated by the National Astronomical Obser-vatory of Japan. K S,T RGB = 18 . ± .
01. Based on the TRGB method, we estimate the distancemodulus of IC 10 to be ( m − M ) = 24 . ± . ± . d = 715 ± ±
60 kpc. This confirms that IC10 is a member of the Local Group.
Subject headings: galaxies: individual (IC 10) — galaxies: irregular — galaxies:starburst — galaxies: tip of the red giant branch — galaxies: distance — LocalGroup
1. Introduction
The dwarf irregular galaxy IC 10 is the nearest starburst galaxy so that it plays an impor-tant role for understanding the formation and evolution of stars in the starburst galaxies. It islocated at the low galactic latitude ( l = 118 ◦ . b = − ◦ .
33) where the foreground reddeningis expected to be large. In addition, the internal reddening of IC 10 may vary spatially due toits strong star forming activity. Therefore, it is difficult to determine reliably the reddeningand distance of IC 10, and published values for reddening and distance of IC 10 have a largerange: E ( B − V ) = 0 . d = 500 kpc to 3 Mpc, respectively(Massey & Armandroff1995; Saha et al. 1996; Wilson et al. 1996; Sakai, Madore, & Freedman 1999; Borissova et al.2000; Hunter 2001; Demers, Battinelli, & Letarte 2004; Vacca et al. 2007; Sanna et al. 2008;Goncalves et al. 2008). During the last decade, these rangeg were decreased but are stilllarge: E ( B − V ) = 0 . d = 500 kpc to 1 Mpc (see Demers, Battinelli, & Letarte(2004) and Table 5 in this study for details).Since Mayall (1935) found that IC 10 is an extra-galactic object, there were severalstudies to determine the distance to IC 10. In the early days the distance to IC 10 was esti-mated to be from 1.3 Mpc to 3 Mpc, based on the size of the HII regions (e.g., Roberts (1962);de Vaucouleurs & Ables (1965); de Vaucouleurs (1978); Sandage & Tammann (1974)). Jacoby & Lesser(1981) determined the upper limit of the distance to IC 10 to be 1.8 Mpc (( m − M ) = 26 . m − M ) =25 .
08 ( d = 1 . ± .
09 Mpc). Massey & Armandroff (1995) used the Wolf-Rayet stars and thebluest stars to obtain a distance modulus of ( m − M ) = 24 . d = 0 .
96 Mpc). Saha et al.(1996) and Wilson et al. (1996) used the Cepheid variables to obtain distance moduli of( m − M ) = 24 . ± .
30 ( d = 0 .
83 Mpc) and ( m − M ) = 24 . ± .
21 ( d = 0 . ± . I band magnitude of the tip of the red giant branch (TRGB) stars to derive a distance of( m − M ) = 24 . ± . d = 600 ±
60 kpc) and 23 . ± . d = 500 ±
50 kpc), respectively. 3 –Borissova et al. (2000) have determined a reddening of E ( B − V ) = 1 . ± .
10 and adistance modulus of ( m − M ) = 23 . ± .
12 for IC 10 by comparing the
J HK phtometryof the red supergiants of IC 10 and IC 1613. Hunter (2001) used the TRGB to determine adistance to IC 10 of ( m − M ) = 24 . ± . E ( B − V ) = 0 .
77, using F W and F W data obtained using the Hubble Space Telescope (HST)/Wide Field andPlanetary Camera 2 (WFPC2). Demers, Battinelli, & Letarte (2004) determined a distancemodulus of ( m − M ) = 24 . ± .
11 (741 ±
37 kpc), using the mean apparent magnitude ofthe C stars. Using the luminosity function of planetary nebula, Kniazev, Pustilnik, & Zucker(2008) obtained a distance modulus of ( m − M ) = 24 . +0 . − . . Vacca et al. (2007) derived adistance modulus of ( m − M ) ∼ . K ′ )- K ′ color-magnitude diagram (CMD) of IC 10 with those of the SMC. They also deriveda distance modulus of ( m − M ) = 24 . ± .
08 by comparing the location of the TRGB inthe CMD of IC 10 with that of the SMC. Sanna et al. (2008) obtained a distance modulusof ( m − M ) = 24 . ± .
08 by comparing the TRGB magnitude of IC 10 to those of theSMC, 47 Tuc, and ω Cen, using the deep HST/WFPC2 and Advance Camera for Surveys(ACS) observations.The purpose of this paper is to estimate the foreground/total reddening toward IC10 and the distance to IC 10 with high accuracy using deep near infrared (NIR)
J HK S photometry obtained with the Subaru telescope and also using the optical photometry of IC10 in the literature. Accurate estimation of the distance to IC 10 is important to understandthe nature of IC 10. This paper is composed as follows. § § K S − ( J − K S ) CMDs of stars in IC 10. § §
5, we derivea relation between metallicity [Fe/H] CG and the red giant branch (RGB) slope in the K S − ( J − K S ) CMD, and we use it to estimate the mean metallicity of the RGB stars in IC10. Then we determine the distance to IC 10 using the J, H, and K S band magnitudes of theTRGB. In §
6, we compare our results to those in the previous studies. Primary results of thisstudy are summarized in §
7. Throughout this paper, quoted errors are for ± σ confidencelevel. 4 –
2. Observation and Data Reduction2.1. Observation
Deep imaging observations were carried out on 2005 December 9, with Multi-ObjectInfraRed Camera and Spectrograph (MOIRCS) , a wide-field imaging camera and spectro-graph on the Subaru telescope. MOIRCS consists of two HAWAII-2 HgCdTe arrays and hasa field of view of 4 ′ × ′ with a spatial resolution of 0 . ′′ / pixel.We observed a field centered at IC 10 (R.A. [J2000.0]= 00 h m . s , Decl. [J2000.0]=+59 o ′ . ′′ ) with a dithering mode using the J , H , and K S band filters . Our observationlog is given in Table 1. Total exposure times are 900 s, 675 s, and 1215 s for the J , H , and K S bands, respectively. Seeing was excellent during the observations, 0 ′′ .5 to 0 ′′ .6. Pre-processing of the images was performed in the standard manner by subtracting darkand bias and by performing flat correction using IRAF/XDIMSUM. We corrected the opticaldistortion of the images that is fit well by the third-order polynomial as a function of thedistance from the optical center ( x c = 858, y c = 1034 on chip 1, x c = 1178, y c = 1012 on chip2) , where x c and y c are coordinates of the center in each chip. Individual long exposureimages were combined with XDIMSUM to make a single mosaic image and to remove thevarying sky fluctuation in each band.Figure 1 shows a gray scale map of the K S band image of IC 10. We note that numerousresolved stars are visible throughout the field with a higher concentration of stars aroundthe middle part of the field, and that little signature of dust feature is visible.We divided the entire observed field (called RA) into three subregions for the followinganalysis as shown in Figure 1: R2 for the central region, and R1 and R3 for the northernand southern outer regions, respectively. We listed the mean surface number density of thestars for each region in Table 2. The mean surface number density of stars in the R2 regionis ∼ . / arcsec , and that of the R1 and R3 regions is ∼ . / arcsec . Therefore, there are http://iraf.noao.edu/iraf/ftp/iraf/extern-v212/xdimsum alf phot , which runs automatically a com-bination of DAOPHOT, ALLSTAR, MONTAGE2, and ALLFRAME (Stetson 1994). Wetransformed the instrumental magnitudes onto standard magnitudes using J HK S photom-etry in the Two Micron All Sky Survey (2MASS) point source catalog for the objects thatare common with those in our observation.We selected several dozens of bright stars in the 2MASS point source catalog with goodquality flags (AAA), and matched these sources with those in our observation. Due to thelarge difference in seeing FWHMs between 2MASS images( ∼ ′′ ) and the present SUBARU J HK S images ( ∼ . ′′ ) we consider the matches with matching distance smaller than 0 . ′′ .Figure 2 displays the difference between the 2MASS magnitudes and the instrumental mag-nitudes for these stars. We used the data points inside the boxes in each panel for calibration.The mean values for the differences (the 2MASS magnitudes minus the instrumental magni-tudes in this study) are: 2 . ± .
06 mag (31 stars), 2 . ± .
09 mag (29 stars), 2 . ± . J , H , and K S , respectively. Therefore the mean errors for calibration are0.010, 0.017, and 0.012 for J , H , and K S , respectively. It is known that the effect of colorterm is negligible between 2MASS photometric system and the NIR photometric system inMauna Kea Observatories (Legget et al. 2006) so that we did not consider any color termfor standard calibration.The final catalog of J HK S photometry of IC 10 includes ∼ ,
000 stars. The magnitudelimits are J ∼ H ∼ .
5, and K S ∼
21 mag, respectively. In Figure 3, we display meanphotometric errors of the stars in the K S , ( J − K S ), and ( J − H ) as a function of the K S magnitude. The photometric errors in Figure 3 represent the mean of the photometricerrors of DAOPHOT/ALLFRAME photometry at a given magnitude range. These errorswere derived from the photometry of the combined images for each filter hence representthe photon noise. We also checked the errors due to frame-to-frame repeatability using thephotometry of individual images, finding that they are similar to those derived from thecombined images. Borissova et al. (2000) presented
J HK photometry of bright stars in a central 3 ′ . × ′ . σ clipping are+0 .
23, +0 .
29, and +0 .
11 mag for the J , H , and K S bands, respectively. If we use only thebright stars with J <
H <
16, and K S <
16 mag, these differences decrease significantly:+0 .
14, +0 .
18, and +0 .
05 mag for the J , H , and K S bands, respectively. Our magnitudesare slightly fainter than Borissova et al. (2000)’s.To understand the cause of this magnitude difference, we estimate the effect of sourceblending due to the difference in the spatial resolution. Note that the data used for Borissova et al.(2000) were obtained under the seeing of 1 ′′ − ′′ . ′′ . K S <
16 mag, there are219 point sources in Borissova et al. (2000), which is similar to the number of sources foundin this study, 295. For the fainter sources with 16 < K S <
17 mag, we found 295 pointsources in Borissova et al. (2000), which is much smaller than the number of sources foundin this study, 739. This is consistent with the incompleteness results given in Borissova et al.(2000).We assume that the faint point sources with K S >
17 mag, which were completely orpartially detected in this study, are merged into the nearby brighter stars with K S < J < , H <
16 mag, and K S <
16 mag) increases by0 . J ) , . H ) , and 0 . K S ). With these correction values the magnitude differencesbetween ours and Borissova et al. (2000) decrease to small values of 0 . J ) , . H ), and0 . K S ), respectively. Therefore the magnitude differences between the two studies aremainly due to difference in the spatial resolution of the images. We note that the J HK S photometry of this study is significantly deeper ( ∼ K S >
16 mag) in Figure 4 is mainlydue to the large photometric errors in Borissova et al. (2000). 7 –
3. Color-Magnitude Diagrams
In Figure 5, we display the K S − ( J − K S ) CMD of the measured stars in the entireobserved region and three subregions. The number density contour maps are overplotted toshow clearly the morphology of the RGB. Several features are noted in Figure 5. First, themost distinguishable feature is an RGB population with 1 < ( J − K S ) <
2, showing thatmost of the resolved stars are red giants with K S = 18 . − . K S magnitudes of 17 to 18 mag. Third, there is a horizontalfeature extended to the redder color from the brightest part of the AGB, which are mostlycarbon stars. Fourth, there is an almost vertical bright sequence with 0 . . ( J − K S ) .
4. Reddening of IC 10
We estimate both foreground and internal reddening of IC 10 using
U BV photometryfrom the Local Group Survey given by Massey et al. (2007) and
J HK S photometry in thisstudy. We adopted the extinction laws for R V = 3 . A J /A V = 0 . A H /A V = 0 . A K S /A V = 0 . We estimate the foreground reddening toward IC 10 using
U BV photometry of theforeground stars in the direction of IC 10. We use
U BV photometry of a 20 ′ × ′ fieldcovering IC 10 given in the Local Group Survey (Massey et al. 2007). Figure 6(a) displaysthe optical V − ( B − V ) CMD of these stars. The majority of point sources seen in theCMD are foreground stars. The blue plume fainter than V ≈
18 mag in the CMD representsmainly the bright MS stars in IC 10. To estimate the foreground reddening toward IC 10,we selected bright foreground MS stars inside the large tilted box in Figure 6(a).Figure 6(b) shows the ( U − B ) − ( B − V ) diagram of these selected foreground MSstars. We adopted E ( U − B ) /E ( B − V ) = 0 .
72, and showed the reddening direction for onemagnitude visual extinction by an arrow in Figure 6(b). Recently Zagury (2007) arguedthat there might be insignificant difference in the extinction law between the Milky Way,LMC, and SMC. We binned the data in ( B − V ) color with a magnitude bin size of 0 .
05 andfitted these with the empirical fiducial relation for the MS (Schmidt-Kaler 1982) using thechi-square minimization method. We obtained the best fit value of E ( B − V ) = 0 . ± .
04 8 –with 90% confidence level. This value is ∼ E ( B − V ) = 1 . r ). Using the same method applied to estimate the foreground reddening for thetotal sample, we obtained the values: E ( B − V ) = 0 . ± .
08, 0 . ± .
06, 0 . ± .
05, and0 . ± .
07 for r < ′ , 5 ′ < r < ′ , 8 ′ < r < ′ , and 10 ′ < r < ′ , respectively. Thisresult shows that there is little spatial variation of the foreground reddening over the fieldin this study. Therefore we adopt the foreground reddening derived using the total sampleof Massey et al. (2007) as a foreground reddening toward IC 10.The value for the foreground reddening of IC 10 derived above would be a lower limit forthe following reasons. First, the ( U − B ) color distribution of the foreground MS stars usedfor the reddening estimate shows a large dispersion of σ = 0 .
13, which is ∼ b = − ◦ . U − B ) color of the foreground stars is mainlyattributed to the differential reddening of stars toward IC 10.Using the relation between U BV photometric system and MK spectral classification ofSchmidt-Kaler (1982) and the derived foreground reddening, E ( B − V ) = 0 .
52, we computedthe V band distance moduli of the foreground MS stars in the tilted box of Figure 6(a). Wefound that 90% of foreground stars are within ∼ ∼ . l = 118 ◦ .
95. We also foundthat the faintest ( V ≈
22 mag) red MS stars are located at the similar distance to that ofthe brightest ( V ≈
16 mag) blue MS stars, while there is a significant spatial spread for starswith intermediate colors. 9 –
The total reddening of IC 10 consists of the foreground reddening (due to the interstellardust in the Milky Way) and the internal reddening (due to the interstellar dust in IC 10).We applied two different approaches to estimate the total reddening: 1) comparing the meanNIR colors of RGB stars in IC 10 and those in the SMC in the K S − ( J − K S ) CMD, and2) using the ( U − B ) − ( B − V ) diagram of the early-type stars in IC 10. Since the mean NIR color of the RGB stars in a galaxy is expected to be similar to thatof another galaxy with a similar metallicity, we can use the mean NIR color of the RGBstars to estimate the reddening of a galaxy. We selected the SMC as a comparison with IC10, because the SMC, a nearby dwarf irregular galaxy, is known to have a similar metallicityto that of IC 10 (Cioni et al. 2000a).We used
J HK S photometry of the SMC stars given by Kato et al. (2007). Their pho-tometry is given in the 2MASS system, and reaches ∼ . . J HK S photometry of IC 10 includes stars ∼ . K S,T RGB < K S < K S,T RGB + 1 .
5, where K S,T RGB is anapparent magnitude of the TRGB in the K S band.The TRGB magnitude for IC 10 is K S,T RGB = 18 .
28 mag as derived in §
5. We estimatedthe K S,T RGB of the SMC as follows. To take advantage of multi-band photometry, weselect the candidate RGB and AGB stars with negligible internal reddening in the SMCusing both optical and NIR photometry of the SMC. Using the deep optical photometry ofthe SMC given by Zaritsky et al. (2002), we selected RGB and AGB stars in the outskirtof the SMC where the internal reddening for the RGB stars is expected to be negligible(Zaritsky et al. 2002). We matched the selected RGB and AGB stars to those in the NIRcatalog of Kato et al. (2007), obtaining an NIR photometric list of RGB and AGB starsin the outer region of the SMC. With these RGB and AGB candidates, we determine themagnitude of the TRGB in the SMC to be K S,T RGB = 12 .
85 mag. This value is very similarto that given in Kato et al. (2007), K S,T RGB = 12 .
80 mag. However, this value is about 0.2mag fainter than that given by Cioni et al. (2000a), K S,T RGB = 12 .
62 mag, who used theDENIS catalog towards the Magellanic Clouds (Cioni et al. 2000b).We derived the mean loci of RGB stars in IC 10 and SMC with 0 . K S band, and estimated the mean and dispersion of the ( J − K S ) colors by fitting the colordistributions of RGB stars with a Gaussian function. Figure 7 displays the K S − ( J − K S )CMD of IC 10 with the mean locus of RGB stars for IC 10 ( solid line ) and that for the SMC( filled circles ). The RGB locus for the SMC was shifted vertically so that the TRGB of theSMC matches that of IC 10. Then the RGB locus of the SMC was shifted horizontally sothat it matches that of IC 10. We found an excellent agreement between two RGB loci.The difference in reddening between IC 10 and the SMC thus derived is ∆ E ( J − K S )(IC10–SMC)= 0 . ± .
02 mag, and ∆ E ( B − V )(IC 10–SMC)= 0 . ± .
03 mag. Here the errorrepresents the mean error of the derived mean color.It is noted that the RGB slope of IC 10 is very similar to that of the SMC, supportingthe assumption employed in this analysis. Adopting the foreground reddening of the SMCof E ( B − V ) = 0 .
04 given in Schlegel et al. (1998), we derive a value for the total reddeningof the RGB stars in IC 10, E ( B − V ) = 1 . ± . Using the
U BV photometry of bright blue MS stars in IC 10 from the Local GroupSurvey (Massey et al. 2007), we directly estimated the total reddening for IC 10. We selectedbright blue stars in IC 10 with the conditions:
B < . − . < ( U − B ) < .
2, and0 . < ( B − V ) < .
0. These stars were plotted as triangles in Figure 6. We obtained thereddening of individual stars comparing the empirical fiducial line of the MS (Schmidt-Kaler1982) and the selected bright blue stars in the ( U − B ) − ( B − V ) diagram, as shown in Figure6(b). The mean value for the total reddening is measured to be E ( B − V ) = 0 . ± . E ( B − V ) = 1 . ± .
03 derivedusing NIR colors of the RGB stars.Taking an average of the two estimates, we derive a value of E ( B − V ) = 0 . ± .
06 forthe total reddening for IC 10, which is used in the subsequent analysis. This result is similarto the values, E ( B − V ) = 1 . ± .
10 given by Borissova et al. (2000) and E ( B − V ) = 1 . E ( B − V ) = 0 .
81 for IC 10, which is smaller than ourestimation, although both studies used the same photometric catalog. 11 –
5. Distance to IC 105.1. The RGB Slope and Metallicity
Lee, Freedman, & Madore (1993) suggested that the absolute magnitude of the TRGBin the I -band is a primary distance indicator for resolved galaxies since it depends little onmetallicity ([Fe/H] < − . > a few Gyrs) of old stellar populations. However,the absolute magnitudes of the TRGB depend on metallicity much more in the J HK S bandsthan in the I band (e.g. Valenti et al. 2004; Ferraro, Valenti, & Origlia 2006). Therefore weneed to know the metallicity of RGB stars when using the NIR TRGB magnitudes for thedistance estimation.It is known that the RGB slope of old stellar populations in the CMD is sensitive tothe metallicity, while insensitive to age, and that the RGB slope has a strong correlation withmetallicity (e.g. Kuchinski & Frogel 1995; Kuchinski et al. 1995; Mighell, Sarajedini, & French1998). Therefore the RGB slope can be used to estimate metallicity of old stellar populations.Since the slope of the RGB does not depend either on reddening or on distance, the meanmetallicity of the RGB stars estimated from the RGB slope is independent of the reddeningand distance of RGB stars. The RGB slope can be measured using RGB stars in a full rangeof magnitudes or in a specific magnitude range: RGB stars with brightness of the top ofhorizontal branch (HB) to 4.6 mags brighter in the K − ( J − K ) CMD ((Kuchinski & Frogel(1995); Kuchinski et al. (1995)) or stars on the RGB from top of the HB to 2.0 and 2.5 magsbrighter in the V − ( B − V ) CMD (Mighell, Sarajedini, & French 1998).We derived a relation between the RGB slope in the K S − ( J − K S ) CMD and themetallicity of Galactic globular clusters, where the RGB slope is measured using the RGBstars in the bright ∼ r h ) of the globular cluster depending on the tidal radii ( r t )of clusters, where the outer boundary is chosen to minimize the background contaminationand to maximize the number of the cluster members. We note that the basic parameters ofGalactic globular clusters such as positions and r h are based on the literature (Harris 1996),unless otherwise noted. In addition, we selected stars having 2MASS rd f lg values of 1, 2,or 3, which indicate the best quality detections, photometry, and astrometry. With theseselection criteria, the number of stars in each globular cluster is 100 ∼ K S − ( J − K S ) CMD by iterative fitting with second order polynomial equations clippingthe stars deviating by 3 σ from the fitted line. We determined the position of the TRGB by 12 –careful visual inspection. We estimated the RGB slopes in several magnitude steps, betweenthe magnitude of the TRGB and the magnitudes fainter than that of the TRGB, using themean locus of the globular cluster.In Table 3 we list the parameters of the Galactic globular clusters that were used forcalibrating the relation between the RGB slope and the metallicity. We note that thevalues of [Fe/H] CG (Carretta & Gratton 1997) come from the literature such as Harris(1996), Ferraro et al. (1999, 2000), and Valenti et al. (2007). We transformed [Fe/H] ZW into[Fe/H] CG using the equation (7) in Carretta & Gratton (1997), [Fe/H] CG = − . − . ZW − . ZW .The RGB slopes as a function of [Fe/H] CG (Carretta & Gratton 1997) are displayed forseveral magnitude steps in Figure 8. The best linear least-squares fit results of the relationbetween [Fe / H] CG and the RGB slope are derived as follows:[Fe / H] CG ,S = 0 . ± . S − . ± .
19) [ σ = ± .
34] (1)[Fe / H] CG ,S = 0 . ± . S − . ± .
18) [ σ = ± .
31] (2)[Fe / H] CG ,S = 0 . ± . S − . ± .
17) [ σ = ± .
28] (3)[Fe / H] CG ,S = 0 . ± . S − . ± .
16) [ σ = ± .
26] (4)[Fe / H] CG ,S = 0 . ± . S − . ± .
15) [ σ = ± .
23] (5)[Fe / H] CG ,S = 0 . ± . S − . ± .
15) [ σ = ± .
22] (6)[Fe / H] CG ,S = 0 . ± . S + 0 . ± .
17) [ σ = ± .
20] (7)[Fe / H] CG ,S = 0 . ± . S + 0 . ± .
13) [ σ = ± .
19] (8)where S , S , S , S , S , S , S , and S are linearly fitted slopes in magnitude rangesbetween the TRGB and 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 magnitude fainter thanthe TRGB, respectively. The uncertainties for parameters and fitting errors are given inparentheses and brackets, respectively. These uncertainties decrease with increasing themagnitude ranges of RGB stars.Our photometric catalog of IC 10 reaches only ≈ S and using equation (3) (see Table 4). The mean metallicity of the RGB stars in the entireregion (RA) is measured to be [Fe/H] CG = − . ± .
28. The [Fe/H] CG of the centralregion (R2) of IC 10 ([Fe/H] CG = − . ± .
28) is very similar with that of outer regions(R1 and R3) ([Fe/H] CG = − . ± . CG = − . J HK S photometry, and foundonly ∼
350 matched sources. This number is negligible compared with the number of theRGB stars used in estimating the RGB slopes and the TRGB.Cioni et al. (2000a) determined [M/H] of the LMC and SMC by fitting isochrones(Girardi et al. 2000) to the K S − ( J − K S ) CMD, finding [M/H]= − .
70 and [M/H]= − . CG using an equationof [Fe/H] CG =[M/H] − log (0 . × . + 0 . M/H ] − . CG = − .
02 for the SMC. Therefore, the mean metallicity of RGB starsin IC 10 determined in this study is similar to that of the SMC estimated by Cioni et al.(2000a). In addition, we estimate the mean metallicity of the SMC using the RGB slopein the K S − ( J − K S ) CMD obtained from Kato et al. (2007) (see Figure 7). Adopting theequation (3) for S and (6) for S , the mean metallicity of the RGB stars in the SMC isderived to be [Fe/H] CG = − . ± .
28 and [Fe/H] CG = − . ± .
22, respectively. Thesevalues agree well with that of the SMC given by Cioni et al. (2000a). Thus the metallicityof the RGB stars in IC 10 is very similar to that of the SMC.
We estimate the distance to IC 10 using the TRGB method (Lee, Freedman, & Madore1993). First we measure the apparent magnitude of the TRGB ( m T RGB ) at which theluminosity function of red giant stars shows a sudden increment. Figures 9, 10 and 11display the luminosity functions N ( m ) of the red giant stars in IC 10 for J , H , and K S bands, respectively. These figures show two types of increments: a slow increment due tothe AGB stars in brighter magnitudes, and a rapid increment due to the RGB stars in faintermagnitudes. The latter represents the TRGB. The TRGB is seen at J ≈ . H ≈ . K S ≈ . N ′′ ( m ) ≡ d N ( m ) /dm , following the method suggested byCioni et al. (2000a), as follows: 1) we derive the luminosity function N ( m ) for the red 14 –stars, 2) we apply a Savitzky-Golay filter (Press et al. 1992) to derive N ′′ ( m ), 3) we findthe highest peak of N ′′ ( m ), fitting it with a Gaussian function, and finally we estimate anapparent magnitude of the TRGB, m T RGB = m g − ∆ m g ( σ g ) where m g and σ g are themean and dispersion of the best fit Gaussian. ∆ m g ( σ g ) is a correction factor as a monotonicfunction of σ g due to a phenomenological model. We used the solid line (∆ f = 0 .
25) inFigure A.2 (b) of Cioni et al. (2000a) to estimate ∆ m g ( σ g ), assuming that the shape ofthe intrinsic magnitude distribution of the stars in IC 10 is not significantly different fromthat of the LMC or SMC. The estimated values for ∆ m g ( σ g ) for the J HK S bands in allregions have a range from − .
09 to − .
14. Details of this method are given in Appendix ofCioni et al. (2000a).We performed Monte-Carlo simulations to estimate the uncertainties of the derivedvalue for m T RGB . We generated a thousand of random realizations having the same numberof stars as the observation. The magnitude of an artificial star in the random realization wasrandomly drawn from a Gaussian distribution with a Gaussian width of the photometric un-certainty centered at an observed stellar magnitude. We perform the same processes appliedfor the observed data to every random realization to detect the TRGB magnitude, and thencalculate the median, ˜ m T RGB,sim , and dispersion, σ T RGB,sim , of the TRGB magnitudes. Theresulting ˜ m T RGB,sim shows an excellent agreement with the observation value m T RGB ( < . σ T RGB,sim is smaller than 0.02 magnitude. We attribute σ T RGB,sim asthe uncertainty of the derived value m T RGB . The TRGB magnitudes estimated in this studyare listed in Table 4 for the
J HK S bands and are displayed in Figures 9, 10, and 11, whichshow N ( m ) and N ′′ ( m ) of stellar populations of IC 10 for the J HK S bands, respectively.These values for The TRGB magnitudes are in excellent agreement with the visual estimateswith differences smaller than 0.05.Valenti et al. (2004) provided empirical calibrations of the absolute magnitude of theTRGB as a function of [Fe/H] CG , based on a homogeneous NIR data of 24 Galactic globularclusters with a wide metallicity range ( − . ≤ [Fe/H] CG ≤ − . M J = − . / H] CG − .
67 [ σ = ± .
20] (9) M H = − . / H] CG − .
71 [ σ = ± .
16] (10) M K S = − . / H] CG − .
98 [ σ = ± .
18] (11)where σ is the dispersion of each relation. We consider this dispersion as the uncertaintyof the absolute magnitude of the TRGB in this study. We note that this uncertainty ismuch larger than that of the apparent magnitude of TRGB ( . .
02 mag). The absolute 15 –magnitudes of the TRGB in the entire observed region (RA) are M J = − . ± .
20 mag, M H = − . ± .
16 mag, and M K S = − . ± .
18 mag, respectively. Using the absolutemagnitude and the apparent magnitude of TRGB stars, we estimate the distance modulusfor IC 10. In Table 4 we list the absolute magnitudes of the TRGB and distance moduliderived for the entire and three subregions for the
J HK S bands. The extinction values usedfor IC 10 are A J = 0 . ± . A H = 0 . ± .
02, and A K S = 0 . ± .
02 mag.The distance moduli for IC 10 derived for three subregions and three different bandsagree well within the uncertainties. Since the crowding in outer regions is lower than thatin the central region and the uncertainty of reddening is the smallest in the K S band,we derive a distance modulus of IC 10 by averaging the distance moduli of R1 and R3regions in the K S band: ( m − M ) = 24 . ± . random ) ± . systematic ). Thiscorresponds to a distance of d = 715 +10 −
10 +62 − kpc. We note that the quoted error of thedistance modulus consists of random and systematic uncertainties. The random error comesfrom the uncertainties of TRGB detection and applied reddening, while the systematic errorcomes from the uncertainty in calibration equation of the absolute magnitude of TRGB.To reduce the uncertainty in the calibration equation in deriving the absolute magnitude ofTRGB stars, higher precision J HK S photometry of the stars in Galactic globular clustersis needed.
6. Discussion
The distance to IC 10 has been derived with various standard candles: the Wolf-Rayetstars and blue plume (Massey & Armandroff 1995), Cepheid variables (Wilson et al. 1996;Saha et al. 1996; Sakai, Madore, & Freedman 1999)), red supergiant stars (Borissova et al.2000), carbon stars (Demers, Battinelli, & Letarte 2004), and the TRGB stars (Sakai, Madore, & Freedman1999; Hunter 2001; Vacca et al. 2007; Sanna et al. 2008). Previous estimates for the distancemodulus of IC 10 range from ( m − M ) = 23 . . m − M ) = 24 . ± . ± .
18, is in the middle of the previous estimates.Since different standard candles suffer from different reddening, it is not simple to figureout what causes the difference in the estimated distances. Therefore we focus on the distanceestimates only based on the TRGB to investigate what causes the difference in the estimateddistances. It is noted that the distance estimates based on the TRGB method also show alarge dispersion: ( m − M ) = 23 . ± .
19 in Sakai, Madore, & Freedman (1999), 24 . ± . . ± . ± .
16 in Vacca et al. (2007), and 24 . ± . ± .
08 inSanna et al. (2008). 16 –All previous studies based on the TRGB method assumed R V = 3 . R V = 3 .
2, while we adopted R V = 3 .
3. We checked how much the dif-ference in the assumed value of R V = A V /E ( B − V ) contributes to the distance modulusestimation. When E ( B − V ) ∼ . ≤ R V ≤ . R V results in the distance scatters of 0.08 and 0.2 mag at maximum for NIR ( J HK )bands and optical (
BV I ) bands, respectively. Therefore, the different value of R V does notcontribute much to the large scatter in distance moduli ( ∼ V I photometry of IC 10 obtained at the Hale 5 m telescope. Theyderived I T RGB = 21 . ± .
15, and obtained a distance modulus of ( m − M ) = 23 . ± . ±
50 kpc), adopting a reddening value of E ( B − V ) = 1 . ± .
08. If the reddeningvalue of E ( B − V ) = 0 .
98 is adopted as in this study, their distance modulus becomes largerby 0 .
27 mag, but it is still smaller than ours by 0 .
50 mag. It is noted that their TRGB mag-nitude is 0.5 mag brighter than that Hunter (2001) derived from the
HST data. Thereforethe TRGB in their estimate may be the tip of the AGB, or their estimate for the TRGBmagnitude may be an overestimate due to the blending effect in the CCD images they used.Hunter (2001) determined the distance to IC 10 based on the TRGB method using F W and F W photometry obtained from HST observation. They derived I T RGB =22 .
2, and estimated a distance modulus of ( m − M ) = 24 . E ( B − V ) = 0 .
77. Their distance modulus is 0 .
63 magnitude larger than that of this study.If the same reddening of E ( B − V ) = 0 .
98 as in this study is used, their distance moduluswill be only 0.09 magnitude larger than ours, agreeing well with our estimate.Vacca et al. (2007) obtained both optical and NIR photometry of IC 10 from the laserguide star adaptive optics (AO) observation at the Keck II telescope and the
HST /ACS observation. They derived a distance modulus of ( m − M ) = 24 . ± . ± .
16 bycomparing the TRGB magnitude of IC 10 to that of the SMC. They adopted a reddening of E ( B − V ) = 0 . ± .
15, and their distance modulus of IC 10 is 0.21 magnitude larger thanthat of this study. If the same reddening of E ( B − V ) = 0 .
98 as in this study is used, theirdistance modulus, ( m − M ) = 24 .
31, will be very similar to ours.Recently Sanna et al. (2008) estimated the distance to IC 10 by comparing the magni-tude of the TRGB in the I band to those of the SMC and two Galactic globular clusters,47 Tuc, and ω Cen. Adopting a total reddening of IC 10, E ( B − V ) = 0 . ± .
06, and adistance to the SMC, ( m − M ) = 18 .
75, they obtained a TRGB distance modulus of IC 10of ( m − M ) = 24 . ± .
08. If the same reddening of E ( B − V ) = 0 .
98 as in this study isused, we derive a value ( m − M ) = 24 .
02. If we take a longer distance scale for the SMC of( m − M ) = 18 .
93 (Keller & Wood 2006), then their distance modulus, ( m − M ) = 24 .
20, 17 –is very close to ours. We note that the reddening value of IC 10 derived by matching visuallythe blue sequence of IC 10 to that of blue stars in the SMC cluster NGC 346 in Figure 3 ofSanna et al. (2008) might be a lower limit, because the reddened RGB sequence of IC 10 isstill bluer than that of the SMC stars.
7. Summary
We estimated the reddening and distance of the sta burst galaxy IC 10 using the
J HK S photometry obtained from the Subaru/MOIRCS and U BV photometry of IC 10 given bythe Local Group Survey (Massey et al. 2007). Primary results are summarized as follows.1. We presented
J HK S photometry of ∼ ,
000 stars in the central 4 ′ × ′ field of IC 10derived from deep images obtained using MOIRCS at the Subaru telescope.2. We estimated the foreground reddening of IC 10 using the U BV photometry of fore-ground MS stars provided by the Local Group Survey (Massey et al. 2007), obtaining E ( B − V ) = 0 . ± .
04. We also derived a value for the total reddening (including theinternal reddening) of E ( B − V ) = 0 . ± .
06, using the ( U − B ) − ( B − V ) diagramof early-type stars in IC 10, and using a comparison of the RGB loci of IC 10 and theSMC in the K S − ( J − K S ) CMD.3. We derived relations between the metallicity [Fe/H] CG and the slope of the RGB inthe K S − ( J − K S ) CMD in several magnitude steps for 20 Galactic globular clusters,using the 2MASS point source catalog. Using these calibrations, we estimated themean metallicity of the RGB stars in IC 10 to be [Fe/H] CG = − . ± . K S = 18 . ± .
01. Then, wederived a distance modulus for IC 10 of ( m − M ) = 24 . ± . ± . E ( B − V ) = 0 .
98, corresponding to the distance of d = 715 +10 − − kpc. This confirms that IC 10 is a member of the Local Group.This work was supported in part by a grant (R01-2007-000-20336-0) from the Basic Re-search Program of the Korea Science and Engineering Foundation. The authors are gratefulto the Director of the Subaru telescope for allocation of the observing time for this project. 18 – REFERENCES
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21 –Table 1. Observation Log for IC 10Filter Exposure Time Date(1) (2) (3) J
13 s, 9 ×
100 s 2005-12-09 H
13 s, 9 ×
75 s 2005-12-09 K S
13 s, 9 ×
135 s 2005-12-09Note. — Col. (1): Filter. Col. (2):Exposure time. Col. (3): Observationdate (UT).Table 2. Parameters for Observed RegionsRegion Area Number of Stars Number Density Remark[ ′′ ] [number] [number/ ′′ ](1) (2) (3) (4) (5)RA 105564 52 ,
054 0.49 the entire regionR1 35354 12 ,
299 0.35 the northern outer regionR2 35190 26 ,
004 0.74 the central regionR3 35019 13 ,
751 0.39 the southern outer regionNote. — Col. (1): Region name. RA indicates the entire observed region, andR1, R2, and R3 indicate three subregions (see Figure 1.). Col. (2): Geometric areaof the selected region in units of arcsec . Col. (3): Number of detected stars ineach region. Col. (4): Surface number density of the stars in each region in units ofnumber/arcsec . Col. (5): Remark. 22 –Table 3. Parameters for Galactic Globular Clusters Name Other Name [Fe/H] CG S S S S S S S S − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . K S − ( J − K S )CMD, respectively.
23 –Table 4. TRGB Distance Estimates for IC 10Filter Region S [Fe/H] CG m T RGB M T RGB ( m − M ) (1) (2) (3) (4) (5) (6) (7)J RA − . − . ± .
28 19 . ± . − . ± .
20 24 . ± . ± .
20J R1 − . − . ± .
28 19 . ± . − . ± .
20 24 . ± . ± .
20J R2 − . − . ± .
28 19 . ± . − . ± .
20 24 . ± . ± .
20J R3 − . − . ± .
28 19 . ± . − . ± .
20 24 . ± . ± .
20H RA − . − . ± .
28 18 . ± . − . ± .
16 24 . ± . ± .
16H R1 − . − . ± .
28 18 . ± . − . ± .
16 24 . ± . ± .
16H R2 − . − . ± .
28 18 . ± . − . ± .
16 24 . ± . ± .
16H R3 − . − . ± .
28 18 . ± . − . ± .
16 24 . ± . ± . S RA − . − . ± .
28 18 . ± . − . ± .
18 24 . ± . ± . S R1 − . − . ± .
28 18 . ± . − . ± .
18 24 . ± . ± . S R2 − . − . ± .
28 18 . ± . − . ± .
18 24 . ± . ± . S R3 − . − . ± .
28 18 . ± . − . ± .
18 24 . ± . ± . K S − ( J − K S ) CMD. Col. (4): Metallicity estimated withequation (3) using the RGB slope in the K S − ( J − K S ) CMD. Col. (5): Apparent magnitudeof the TRGB. Col. (6): Absolute magnitude of the TRGB derived with equations (7)-(9)in Valenti et al. (2004). Col. (7): Distance modulus of IC 10. The quoted errors consistof (random error) ± (systematical error). The random error comes from TRGB detectionuncertainty plus reddening uncertainty. The systematical error is due to the uncertainty inthe calibration equation of the absolute magnitude of the TRGB. 24 –Table 5. A Summary of Distance Estimates for IC 10 Method ( m − M ) E ( B − V ) Filter Reference(1) (2) (3) (4) (5)WR/Blue plume 24 .
90 0 . − .
80 sp/ BV . ± .
30 0 . gri . ± . JHK . ± .
20 1 . ± . VI . ± .
19 1 . ± . VI . ± .
12 1 . ± . JHK . ± .
20 0.77
F555W,F814W . ± .
11 variable
R,I,CN,TiO . ± .
08 0.95
F814W, K ′ . ± .
08 0 . ± . F555W,F814W . ± . ± .
18 0 . ± . J HK S
25 –
E N
R3R2R1
Fig. 1.— A gray scale map of K S band image of IC 10. North is up and east to the left.The size of the field of the view is 4 ′ × ′ . The observed field is divided into three subregions(R1, R2, and R3) for the analysis. 26 –Fig. 2.— Differences between the 2MASS magnitudes (upper cases) and the instrumentalmagnitudes from the present SUBARU observations (lower cases) for the stars commonbetween the 2MASS point source catalog and this study. The data points inside the box ineach panel are used for standard calibration. 27 –Fig. 3.— Mean photometric errors in the K S magnitude and the ( J − K S ) and ( J − H )colors as a function of the K S magnitude. The error bar indicates 1 σ error in each magnitudebin. 28 –Fig. 4.— A comparison of the magnitudes in this study and those in Borissova et al. (2000)for (a) J , (b) H , and (c) K S bands, respectively. In each panel, the solid line represents amean difference with 2 σ clipping for bright stars with J <
H <
16, and K S <
16 mag :∆ J = 0 .
14 mag, ∆ H = 0 .
18 mag, and ∆ K S = 0 .
05 mag, where ∆ means this study minusBorissova et al. (2000). 29 –Fig. 5.— K S − ( J − K S ) CMDs of IC 10 for the entire region RA and three subregions R1,R2, and R3, respectively. The number density contour maps are overlayed with solid linesto show clearly the morphology of the RGB. 30 –Fig. 6.— (a) The V − ( B − V ) CMD of the 550 square arcmin field of IC 10 obtained from theLocal Group Survey (Massey et al. 2007). Open triangles represent the bright MS stars in IC10. The stars inside the tilted box are foreground MS stars belonging to the Galaxy. (b) The( U − B ) − ( B − V ) color-color diagram of IC 10. Open triangles and dots represent the MSstars of IC 10 and the Galaxy, respectively, as selected from (a). The dotted, long dashed,and solid lines represent the intrinsic MS sequence (Schmidt-Kaler 1982) reddened accordingto E ( B − V ) = 0 .