RELATIVE AGE DIFFERENCE BETWEEN THE METAL-POOR GLOBULAR CLUSTERS M53 AND M92

Abstract

CCD photometric observations of the globular cluster (GC), M53 (NGC 5024), are performed using the 1.8 m telescope at the Bohyunsan Optical Astronomy Observatory in Korea on the same nights (2002 April and 2003 May) as the observations of the GC M92 (NGC 6341) reported by Cho and Lee using the same instrumental setup. The data for M53 is reduced using the same method as used for M92 by Cho and Lee, including preprocessing, point-spread function fitting photometry, and standardization etc. Therefore, M53 and M92 are on the same photometric system defined by Landolt, and the photometry of M53 and M92 is tied together as closely as possible. After complete photometric reduction, the V versus B − V , V versus V − I, and V versus B − I color-magnitude diagrams (CMDs) of M53 are produced to derive the relative ages of M53 and M92 and derive the various characteristics of its CMDs in future analysis. From the present analysis, the relative ages of M53 and M92 are derived using the Δ(B − V ) method reported by VandenBerg et al. The relative age of M53 is found to be 1.6 ± 0.85 Gyr younger than that of M92 if the absolute age of M92 is taken to be 14 Gyr. This relative age difference between M53 and M92 causes slight differences in the horizontal-branch morphology of these two GCs.

1. INTRODUCTION

M53 (NGC 5024) is a metal-poor globular cluster (GC) ([Fe/H] = −2.07, Boberg et al. 2016), whose distance from the Sun and the Galactic plane is R⊙ = 17.9 kpc and Z = 17.6 kpc, respectively (Harris 1996, 2010 edition). Its apparent distance modulus and interstellar reddening has been estimated to be (m−M)V = 16.32 mag and E(B − V ) = 0.02 mag, respectively (Harris 1996, 2010 edition). Rey et al. (1998), who carried out a photometric study of M53, reported that M53 has a dominantly blue horizontal branch (BHB) that extends down to ≈1 mag below the mean horizontal-branch (HB) level with some RR Lyrae variable stars. According to Lee et al. (1994), the quantity of the morphology of the HB (B−R)/(B + V + R) of M53 is 0.76, where B, V, and R are the number of BHB stars, RR Lyrae variable stars, and red horizontal-branch (RHB) stars, respectively. According to Rey et al. (1998), M53 has many blue straggler stars (BSSs) throughout its face, showing a bimodal radial distribution. Beccari et al. (2008) examined the BSSs of M53 in great detail using three different telescopes, and confirmed the bimodal radial distribution of the BSSs of M53, identifying almost 200 BSSs.

M92 (NGC 6341) is also one of the most metal-poor GCs ([Fe/H] = −2.34, Sneden et al. 2000; but possibly lower [Fe/H], see Roederer & Sneden 2011), whose distance from the Sun and Galactic plane is R⊙ = 8.3 kpc and Z = 4.7 kpc, respectively (Harris 1996, 2010 edition). Its apparent distance modulus was found to be (m −M)V = 14.65 mag and its interstellar reddening was estimated to be E(B − V ) = 0.02 mag (Harris 1996, 2010 edition). M92 has dominantly BHB stars extending down to ≈1.5 mag below the mean HB level with some RR Lyrae variable stars (Buonanno et al. 1985; Lee et al. 2003; Cho & Lee 2007). According to Lee et al. (1994), the (B − R)/(B + V + R) of M92 is 0.88, which indicates that the HB morphology of M92 is slightly bluer than that of M53. Di Cecco et al. (2010) derived the new absolute age of M92 as 11 ± 1.5 Gyr by fitting isochrones generated by the updated version of the FRANEC stellar evolutionary codes (Chieffi & Straniero 1989; Straniero et al. 1997; Degl’Innocenti et al. 2008) to the three types of photometric data sets obtained by the ground-based telescopes and the Hubble Space Telescope (HST). Roederer & Sneden (2011) reported a clear star-to-star abundance dispersion in some heavy neutron-capture elements (i.e., La, Eu, and Ho) spanning 0.5–0.8 dex in 19 member stars of M92 using the high-resolution spectra obtained from the WIYN 3.5 m Telescope. On the other hand, they provided no explanation for the astrophysical origin(s) responsible for the abundance dispersion in these heavy neutron-capture elements. In contrast to Roederer & Sneden (2011), Cohen (2011) reported that there was no such large star-to-star dispersion using the high resolution spectra of 12 member stars on the red giant branch (RGB) of M92 taken at the Keck Telescope.

Heasley & Christian (1991) first examined the age problem between M53 and M92. Overlaying the fiducial sequence of M92 by Stetson & Harris (1988) on the color-magnitude diagram (CMD) of M53 obtained by themselves, Heasley & Christian (1991) suggested that the ages of M53 and M92 are the same within error. Rey et al. (1998) also argued that there was no significant age difference between M53 and M92 using the Δ(B−V ) method reported by VandenBerg et al. (1990) (Δt < 1 Gyr). Rey et al. (1998), however, used the fiducial sequence by themselves in the case of M53 and the fiducial sequence of Stetson & Harris (1988) in the case of M92. VandenBerg (2000) reported the ages of 26 Galactic GCs including M53 and M92. According to him, the ages of M53 and M92 were 12.5 ± 1.0 Gyr and 14.0 ± 0.8 Gyr, respectively. On the other hand, he used the inhomogeneous photometric data of Galactic GCs in his age derivation. In the case of M53, VandenBerg (2000) used the V versus B − V CMD reported by Rey et al. (1998). In the case of M92, he used the V versus B − V CMD and V versus V − I CMD reported by Stetson & Harris (1988) and Johnson & Bolte (1998), respectively. Anderson et al. (2008) reported homogeneous V I CCD photometric data of 65 nearby Galactic GCs using the HST Advanced Camera for Surveys (ACS). Using this homogeneous data, Marín-Franch et al. (2009) reported the relative ages of 64 nearby Galactic GCs including M53 and M92. According to Marín-Franch et al. (2009), the relative ages of M53 and M92 are similar within error. In addition, Dotter et al. (2010) examined the absolute ages of 61 nearby Galactic GCs using the isochrone fitting method with the homogeneous photometric data of Anderson et al. (2008) including M53 and M92. They suggested that age is the second parameter governing the HB morphology of Galactic GCs. According to Dotter et al. (2010), the absolute ages of M53 and M92 are 13.25 ± 0.50 Gyr and 13.25 ± 1.00 Gyr, respectively, which are similar within error. Recently, VandenBerg et al. (2013) derived the ages of 55 Galactic GCs using an improved method with the data of the HST/ACS reported by Anderson et al. (2008) including M53 and M92. According to VandenBerg et al. (2013), the ages of M53 and M92 are 12.25 ± 0.25 Gyr and 12.75 ± 0.25 Gyr, respectively, where the errors arise from the fitting of zero-age HBs and isochrones. This result is slightly different from that of Dotter et al. (2010). However, considering the error arising from uncertainties in distance and chemical abundance, ~±1.5–2 Gyr, the ages of M53 and M92 are similar within error.

To reconsider the age problem of M53 and M92 in terms of the accurate relative ages, M53 and M92 were observed on the same nights using the same telescope, filter set, and detector. In addition, accurate relative ages of M53 and M92 were derived using the Δ(B −V ) method reported by VandenBerg et al. (1990) with the photometric data of M53 and M92 reduced using the same method and with the same photometric parameters in each reduction step. The reduction steps included preprocessing, point-spread function (PSF) fitting photometry, aperture photometry, aperture correction, and standardization. Rosenberg et al. (1999) reported the importance of obtaining homogeneous photometric data in the relative age measuring studies of Galactic GCs.

Section 2 presents the observations and data reduction procedures of M53. Section 3 reports the CMDs of M53 as well as the fiducial sequences of M53 and M92. Section 4 deals with the relative age derivation of M53 and M92 using the Δ(B − V ) method reported by VandenBerg et al. (1990). Section 5 presents a brief summary.

 

2. OBSERVATIONS AND DATA REDUCTION

2.1. Observations

All observations of M53 and M92 were carried out using the 1.8 m telescope (f/8) and SITe 2048 × 2048 CCD camera at the Bohyunsan Optical Astronomy Observatory (BOAO) in Korea in the BV I bands on the same nights using the same instrumental setup, which was also the same as that used by Cho et al. (2005). Details of the observations of M92 can be found in the report by Cho & Lee (2007).

The BV I CCD observations of the central 11.7′ × 11.7′ regions of M53 and M92 were made using the BOAO 1.8 m telescope on the night of 2002 April 4. Figures 1 and 2 show the observed regions of M53 and M92, respectively. In Figures 1 and 2, the thinner lines indicate the observed regions in the present study and the thicker lines indicate the observed region of M53 by Rey et al. (1998) and that of M92 by Stetson & Harris (1988). In Figure 2, the upper thicker solid line indicates the M92 north region of Stetson & Harris (1988) and the lower thicker solid line indicates the M92 south consortium field and the dashed line indicates the M92 deep northwest field of Stetson & Harris (1988). Table 1 lists the exposure times of M53 for each band. The average seeing (FWHM, Full Width at Half Maximum) during the observations of M53 was 1.2′′ on that night and it was also nonphotometric like during the observations of M92. Additional BV I CCD observations were carried out for the central 11.7′ × 11.7′ regions of M53 and M92, and the PG 1633+099 and SA 107 (centered near the star 107-595) regions of Landolt’s (1992) standard regions on the night of 2003 May 4. They were used for standardization on the photometric night of 2003 May 4. Table 1 lists the exposure times for each band of M53 frames. For these observations, the seeing (FWHM) was between 1.6′′ and 1.9′′.

Figure 1.Comparison of the observed regions of M53. The thinner line indicates the observed region in the present study and the thicker line indicates the observed region reported by Rey et al. (1998). North is upward, and East is to the left.

Figure 2.Comparison of the observed regions of M92. The thinner solid line indicates the observed region in the present study and the thicker solid lines indicate the observed regions reported by Stetson & Harris (1988): the M92 north region of Stetson & Harris (1988) and the M92 south consortium field. The dashed line indicates the M92 deep northwest field of Stetson & Harris (1988). North is upward, and East is to the left.

Table 1Observation Summary of M53

2.2. Data Reduction

Cho & Lee (2007) reported the full data reduction processes for the M92 frames. For accurate relative age measurements of M53 and M92, the same data reduction steps adopted by Cho & Lee (2007) for M92 were used to reduce all the science frames of M53. In addition, the same parameters were used for preprocessing using the IRAF CCDRED package and extracting the instrumental magnitudes of M53 stars by the PSF fitting method using the IRAF version of the DAOPHOT package (Stetson 1987; Stetson et al. 1990) or by aperture photometry using the IRAF APPHOT package, as in the case of M92. The same procedures as for the stars of M92 were followed for an aperture correction of the stars in M53.

To standardize the instrumental magnitudes of the 2003 May 4 frames of M53, the transformation equations (3a), (3b), and (3c) in Cho & Lee (2007) were used after rejecting spurious detections with magnitude errors ϵ(mag) > 0.15 mag, sharpness of fit |sharpness| > 1.0 (or |r0| > 1.0 according to the Stetson & Harris 1988), and goodness of fit χ > 3.0 as in the case of M92, which provided the standard BV I magnitudes for the stars in the M53 and M92 in Johnson-Cousins photometric system defined by Landolt (1992). The transformation equations (3a), (3b), and (3c) in Cho & Lee (2007) were derived using the PG 1633+099 and SA 107 (centered near the star 107-595) regions of Landolt’s (1992) standard regions. The final colors and magnitudes were obtained for the M53 stars in the Johnson-Cousins photometric system in the frames taken on the night of 2002 April 4 from Equations (1), (2), and (3), which were derived from the 483 bright common stars of the M53 frames taken on the nights of 2002 April 4 and 2003 May 4. The spurious detections in the frames of 2002 April 4 were also rejected. The transformation equations of (1), (2), and (3) can be expressed as

where b, v, and i are the instrumental magnitudes after applying the aperture correction and ζV, ζBV, and ζV I are zero points. Therefore, throughout the entire data reduction processes of M53 and M92, the same method was applied for both clusters. And the photometry of M53 and M92 was tied together as closely as possible using Landolt’s (1992) stars as the standard stars to transform the 2003 May 4 data of M53 and M92, which were used to transform the 2002 April 4 data of M53 and M92 to the standard system.

Figure 3 shows the residual differences in the V magnitude and B−V and V −I colors of M53 as a function of the V magnitude of 2002 April 4 between the data of 2002 April 4 and 2003 May 4. Figure 4 also shows the same residual differences of M53 as a function of B−V and V −I colors of 2002 April 4. The differences are in the sense of the 2002 April 4 data minus the 2003 May 4 data. As seen in Figures 3 and 4, no visible trends for the V magnitude and B − V and V − I colors are found between the two data sets for M53.

Figure 3.Residual difference in the V magnitude and B−V and V − I colors for M53 between the data of 2002 April 4 and 2003 May 4 plotted as a function of the V magnitude for 2002 April 4. The difference is in the sense of the data obtained on 2002 April 4 minus that obtained on 2003 May 4.

Figure 4.Same as in Figure 3, but the horizontal axis is plotted as a function of B − V and V − I colors for 2002 April 4.

2.3. Comparison with Other Photometry

To determine if the magnitudes and colors of M53 and M92 in the present study were well transformed and tied to the standard photometric system defined by Landolt (1992), and to determine if there are systematic errors in the magnitudes and colors of M53 and M92 in the present study, the photometry of M53 and M92 in the present study was compared with that reported in the literature. Figures 5 and 6 show the residual differences in the V magnitude and B − V and V − I colors of M53 between the data of the present study and those reported by Stetson (2000, 2012 update) against the V magnitude and B − V and V − I colors of the present study, respectively. The photometric data reported by Stetson (2000) for M53 and M92 are the photometric standard star data tied to the Landolt (1992) photometric system set by CCD photometric observations. The differences are in the sense of the data of the present study minus that reported by Stetson (2000, 2012 update). The mean residual differences were −0.029 ± 0.002 mag in the V magnitude, −0.056 ± 0.003 mag in the B −V color, and −0.028 ± 0.002 mag in the V −I color, where the errors are the standard deviation of the mean. The deviation was large in the B − V color and was caused mainly by the large photometric zero point shift in the B band of the present study. The observations for M53 were carried out sequentially in the B, V, and I bands before observations of the standard regions of Landolt (1992). Therefore, in the case of M53, the changing sky condition in the initial stages of the observations might have caused a large photometric zero point shift in the B band, a slight photometric zero point shift in the V band, and a negligible photometric zero point shift in the I band. On the other hand, the photometric zero point error is not important in relative age dating methods because the photometric zero point shift disappears in the procedures of the relative age dating methods. Figure 5 shows that there were no trends of the V magnitude, and the B−V and V − I colors against the V magnitude of the present study of M53 but there was a large residual difference in the B − V color. According to Figure 6, a slight trend of the B−V color against the B−V color of this study was observed on M53. The trend was that at the bluer B−V color region of M53, the residual difference Δ(B − V ) became slightly larger in the negative sense, and this trend was caused mainly by BHB stars of M53. Figures 7 and 8 show the residual differences in the V magnitude and B − V color of M53 between the data of the present study and those reported by Rey et al. (1998) against the V magnitude and B−V color of the present study, respectively. The mean residual differences were −0.023 ± 0.001 mag in the V magnitude and −0.052 ± 0.001 mag in the B −V color, where the errors are the standard deviation of the mean. Figures 7 and 8 show there were no trends in the V magnitude and the B−V color against the V magnitude and B−V color of the present study of M53 except for the slightly large residual difference in the B−V color. Table 2 lists the residual differences in the V magnitude and B − V and V −I colors of M53 between the data of the present study and that of other studies.

Figure 5.Residual difference in the V magnitude and B−V and V − I colors for M53 between the data of the present study and Stetson (2000, 2012 update) plotted as a function of the V magnitude in the present study. The difference is in the sense of the data of the present study minus that reported by Stetson (2000, 2012 update).

Figure 6.Same as in Figure 5, but the horizontal axis is plotted as a function of B − V and V − I colors in the present study.

Figure 7.Residual difference in the V magnitude and B −V color for M53 between the data of the present study and Rey et al. (1998) plotted as a function of the V magnitude in the present study. The difference is in the sense of the data of the present study minus that reported by Rey et al. (1998).

Figure 8.Same as in Figure 7, but the horizontal axis is plotted as a function of the B−V color in the present study.

Table 2References. — (1) Heasley & Christian 1991; (2) Rey et al. 1998; (3) Stetson 2000 The difference Δ is in the sense of the present study minus other study and errors are standard deviations.

Figures 9 and 10 show the residual differences in the V magnitude and B − V and V − I colors of M92 between the data of the present study and Stetson (2000, 2012 update) against the V magnitude and B −V and V − I colors of the present study, respectively. The differences were also in the sense of the data of the present study minus that reported by Stetson (2000, 2012 update). In the case of M92, the mean residual differences were found to be −0.010 ± 0.001 mag in the V magnitude, −0.028 ± 0.001 mag in the B − V color, and −0.028 ± 0.001 mag in the V − I color, respectively, where the errors are the standard deviation of the mean. Compared to other photometric studies on M92, the photometric data of M92 in Cho & Lee (2007) also showed good photometric qualities, as shown in Table 3. This might be caused by the good sky conditions during the observations of M92, because the observations of M92 were carried out between the observations of the standard regions reported by Landolt (1992) during which the sky conditions were clearly photometric, as shown in Figure 4 in the paper reported by Cho & Lee (2007). According to Figure 9, no trends in the V magnitude and B − V and V − I colors against V magnitude were observed in M92. On the other hand, according to Figure 10, a slight trend of the B−V color against the B −V color was observed on M92, which is similar to that of M53, as shown in Figure 6. This trend was caused mainly by the BHB stars of M92 as in M53. Therefore, these slight trends in the B−V color against the B − V color of M53 and M92 in the present study will not seriously affect the relative age measurements of M53 and M92. Figures 11 and 12 show the residual differences in the V magnitude and B−V color of M92 between the data of the present study and Heasley & Christian (1986) against the V magnitude and B − V color of the present study, respectively. The differences are in the sense of the data of the present study minus that reported by Heasley & Christian (1986). Figure 11 shows that no significant trends of the V magnitude and B−V color against the V magnitude were observed for M92 except for a small zero point difference in the B − V color. Figure 12 also shows that no trends in the V magnitude and B − V color against the B − V color were observed for M92 except for the small zero point difference in the B − V color between the two studies. Figures 13 and 14 also show the residual differences in the V magnitude and V − I color of M92 between the data of the present study and Rosenberg et al. (2000) against the V magnitude and V − I color of the present study, respectively. The differences are in the sense of the data of the present study minus that reported by Rosenberg et al. (2000). The mean residual differences were found to be +0.007 ± 0.002 mag in the V magnitude and −0.007 ± 0.001 mag in the V −I color, where the errors are the standard deviation of the mean. According to Figures 13 and 14, the photometry of the present study and Rosenberg et al. (2000) for M92 almost coincided except for large scatters at faint magnitude due to the increasing internal photometric errors of both studies without a residual trend between the two studies. Table 3 lists the residual differences in the V magnitude and B − V and V − I colors of M92 between the data of the present study and other studies.

Figure 9.Residual difference in the V magnitude and B−V and V − I colors for M92 between the data obtained in the present study and that reported by Stetson (2000, 2012 update) plotted as a function of the V magnitude in the present study. The difference is in the sense of the data of the present study minus that reported by Stetson (2000, 2012 update).

Figure 10.Same as in Figure 9, but the horizontal axis is plotted as a function of B−V and V −I colors in the present study.

Figure 11.Residual difference in the V magnitude and B−V color for M92 between the data obtained in the present study and that reported by Heasley & Christian (1986) plotted as a function of the V magnitude in the present study. The difference is in the sense of the data of the present study minus that reported by Heasley & Christian (1986).

Figure 12.Same as in Figure 11, but the horizontal axis is plotted as a function of the B−V color in the present study.

Figure 13.Residual difference in the V magnitude and V − I color for M92 between the data obtained in the present study and that reported by Rosenberg et al. (2000) plotted as a function of the V magnitude in the present study. The difference is in the sense of the data of the present study minus that reported by Rosenberg et al. (2000).

Figure 14.Same as in Figure 13, but the horizontal axis is plotted as a function of the V −I color in the present study.

Table 3References. — (1) Sandage & Walker 1966; (2) Cathey 1974; (3) Heasley & Christian 1986; (4) Stetson & Harris 1988; (5) Rosenberg et al. 2000; (6) Stetson 2000 The difference Δ is in the sense of the present study minus other study and errors are standard deviations.

In summary, according to Figures 5–14, there were no significant systematic trends of the V magnitude and B − V and V − I colors of M53 and M92 in the present study against V magnitude and B−V or V −I color. This means the photometry of M53 and M92 in the present study was tied to the same photometric system defined by Landolt (1992) as closely as possible. On the other hand, in the case of M53 some significant zero point difference was observed particularly in the B −V color according to Figures 5–8 and Table 2. This photometric zero point difference was probably caused by the zero point shift during the observations of M53 on 2003 May 4. Therefore, photometric zero point errors can be estimated by the data of M92 when the sky condition was clearly photometric. According to Table 3, the photometric zero point errors of the present photometry of M53 and M92 were estimated to be ~0.010 mag in the V magnitude, ~0.025 mag in B − V color, and ~0.015 mag in V − I color, respectively. On the other hand, even the photometric zero points of the standard star data in the field of M92 by Stetson (2000) were changing slightly within ~0.02 mag level in the V magnitude and B −V and V −I colors during twelve years of updating the data according to Table 3.

 

3. COLOR-MAGNITUDE DIAGRAMS

Figure 15 shows the CMDs of M53 for V versus B−V, V versus V − I, and V versus B − I. Owing to the extreme crowding in the central region of M53, the stars within r < 1.22′ from the cluster center were excluded from the photometric list of M53 and are not plotted in Figure 15. In Figures 15a, 15b, and 15c, the stars were matched in all the three bands (BV I) and the total number of stars plotted was 11395. In Figure 15d, the stars were matched only in the BV bands and the total number of stars plotted was 13632. Because there were insufficient exposure times for the I band compared to the BV bands for M53 on 2002 April 4, the limiting magnitude of the star catalog of M53 that matched in the BV I bands was ≈0.5 mag brighter than that of the star catalog of M53 matched in the BV bands, as seen by comparing Figures 15a and 15d in the V versus B−V plane. The small open circles in Figure 15 are 30 RR Lyrae variable stars identified from the variable stars list reported by Clement et al. (2001) in the observed field of M53.

Figure 15.CMDs of M53. Only the stars satisfying the condition, r ≥ 1.22′ , are shown. The small open circles are 30 known RR Lyrae stars from the observed field according to the variable stars list for M53 reported by Clement et al. (2001). (a) V vs. B − V CMD of which the stars are matched in the BV I bands. (b) V vs. V − I CMD of which the stars are matched in the BV I bands. (c) V vs. B − I CMD of which the stars are matched in the BV I bands. In (a), (b), and (c) the total number of stars was 11395. (d) V vs. B − V CMD of which the stars are matched only in the BV bands and the total number of stars was 13632.

The internal photometric errors in the V magnitude and B − V, V − I, and B − I colors were estimated from the photometric errors calculated using the IRAF version of the DAOPHOT package. Then ϵ(V ) was ≈0.005 mag and ϵ(B −V ), ϵ(V −I), and ϵ(B − I) were ≈0.01 mag to V ≈ 18.00 mag. Accordingly, ϵ(V ) was ≈0.01 mag, ϵ(B − V ) and ϵ(V − I) were ≈0.02 mag, and ϵ(B − I) was ≈0.03 mag from V ≈ 18.00 mag to ≈19.50 mag. In addition, ϵ(V ) increased continuously up to ≈0.08 mag, ϵ(B − V ) up to ≈0.12 mag, ϵ(V − I) up to ≈0.14 mag, and ϵ(B − I) ≈0.16 mag from V ≈ 19.50 mag down to V ≈ 22.00 mag.

The characteristics of the CMDs of M53 shown in Figure 15 are as follows. First, although there appears to be some RHB stars and some RR Lyrae stars, the dominant part of HB of M53 was BHB, which extends down to ≈1.0 mag below the mean HB level of M53. Second, the asymptotic giant branch (AGB) is clearly separated in all three kinds of CMDs from the RGB sequence from ~1.0 mag below the RGB tip down to the bottom of the AGB. On the other hand, the AGB bump (Ferraro et al. 1999; Cassisi et al. 2001), which indicates the clump of AGB stars at the beginning of He-shell burning, is difficult to identify because of the sparse distribution pattern of AGB stars in the CMDs compared to the AGB bumps of the GCs M3 (NGC 5272), M13 (NGC 6205), M15 (NGC 7078), and M92 (Cho et al. 2005; Cho & Lee 2007). Finally, as reported by Rey et al. (1998) and Beccari et al. (2008), there are many BSSs that extend diagonally from the main sequence of M53, and the BSSs are delineated most clearly in the V versus B−I CMD due to about a factor of two higher color resolution than in the V versus B−V or V versus V − I CMD.

Figure 16 shows V versus B − V CMD of M92 reported by Cho & Lee (2007) and that of M53 in the present study, of which the stars are matched only in the BV bands for comparison on the same scale. Details of the characteristics of the CMD of M92 in Figure 16b were well summarized by Cho & Lee (2007). In Figure 16b, twenty clear field stars that were brighter than V ≈ 15.5 mag were rejected according to the proper motion data reported by Rees (1992) because they are not members.

Figure 16.(a) V vs. B − V CMD of M53 of which the stars are matched only in the BV bands. (b) V vs. B − V CMD of M92 reported by Cho & Lee (2007). Only the stars satisfying the condition, r ≥ 1.22′, are shown for M53 and M92. The small open circles in each panel are 30 and 10 known RR Lyrae stars from the observed field according to the variable stars list reported by Clement et al. (2001) for M53 and M92, respectively. The total number of stars was 13632 and 13694 for M53 and M92, respectively.

In the present study, V versus B − V CMDs of M53 and M92 were used to examine the relative age difference between M53 and M92, because V versus B − V CMD is the deepest in all three types of CMDs in the case of M53. Indeed, the limiting magnitude of V versus B−V CMD, which matched only in the BV bands, was ≈0.5 mag fainter than those of all three types of CMDs matched in all three BV I bands, as shown in Figure 15. On the other hand, in the case of M92, the limiting magnitudes of all three types of CMDs were similar because of the sufficient exposure times for each BV I band. In most GCs, the extreme central crowding of GCs causes blending of stars and increases the photometric errors of faint stars in the central region of GCs. Therefore, the CMDs of the central part of GCs are not as tight as those of the outer part of GCs in the fainter magnitude regions. To obtain tighter CMDs of M53 and M92, which might allow more accurate fiducial sequences to be derived, a further radial restriction was made in the faint magnitude regions of the CMDs of M53 and M92. In the case of M53, only the stars whose radial distance from the cluster center was r ≥ 2.50′ when V > 18.0 mag were taken. In the case of M92, only the stars whose radial distance from the cluster center was r ≥ 2.50′ when V > 17.5 mag were taken. Figures 17a and 17b show the resulting CMDs for M53 and M92, respectively. In Figure 17, the RR Lyrae variable stars were excluded from the photometric catalogs of M53 and M92 according to the variable stars list reported by Clement et al. (2001) and were not plotted. Therefore, Figures 17a and 17b presents the CMDs for the relative age determination of M53 and M92, respectively. The fiducial sequences of M53 and M92 were made from V versus B − V CMDs in Figure 17a for M53 and Figure 17b for M92. As shown in Figure 17, the faint parts of the CMDs of M53 and M92 become much tighter than the CMDs of M53 and M92 in Figures 16a and 16b, respectively.

Figure 17.(a) V vs. B − V CMD of M53 of which the stars are matched only in the BV bands. (b) V vs. B − V CMD of M92. In each CMD, further radial restriction was applied below the dotted line for a more clear definition of the fiducial sequence in the fainter part of the CMD, as indicated in each figure. In each CMD, the RR Lyrae stars were removed according to the variable stars list reported by Clement et al. (2001) for M53 and M92, respectively. See the text for more details.

The procedures for constructing the fiducial sequences are as follows. First, clear HB and AGB stars were removed from the CMDs of M53 and M92 to speed up the procedure. The RGB and main-sequence parts of M53 and M92 were divided into bins of sizes, 0.125 or 0.250 mag, depending on the number of stars. The mean and standard deviation of each bin of M53 and M92 are calculated to reject the outlying field stars from the RGB sequences and main sequences. After excluding stars deviating by more than 2.5 σ in each bin of M53 and M92, the mean and standard deviation of each bin were recalculated. Stars deviating by more than new 2.5 σ of the new mean value in each bin were also excluded. These procedures were repeated several times until the mean and standard deviation of each bin converged. After performing the outlying field star exclusion processes, the RGB sequences and main sequences of M53 and M92 were divided into bins of sizes 0.1, 0.2, or 0.3 mag considering the number of stars and importance in the fiducial sequences. In addition, the mean and standard deviation of each bin in the V magnitude and B − V color were calculated. Tables 4 and 5 list the resulting unsmoothed fiducial sequences for M53 and M92, respectively.

Table 4Fiducial Sequence of M53

Table 5Fiducial Sequence of M92

Figure 18 compares the CMDs and fiducial sequences of M53 and M92 in the present study. According to Figure 18, the fiducial sequences made using Figure 17 reproduce the entire CMDs of M53 and M92 without further radial restrictions. Figure 19 compares the fiducial sequences of M53 from the present study with those reported by Rey et al. (1998). The solid line with dots denotes the unsmoothed fiducial sequence of the present study in Table 4 and the dashed line is that reported by Rey et al. (1998) in their Table 6. The fiducial sequence of the present study in Figure 19 was shifted according to the photometric zero point differences in the V magnitude and B −V color between the present study and Rey et al. (1998). The photometric zero point differences between the present study and Rey et al. (1998) were −0.023 ± 0.001 mag in V magnitude and −0.052 ± 0.001 mag in B − V color, where the errors are the standard deviation of the mean. With the exception of the photometric zero point differences in magnitude and color, two fiducial sequences coincide very well from the RGB tip down to the main sequence. Figure 20 compares the fiducial sequences of M92 in the present study with those reported by Stetson & Harris (1988), which was used to examine the relative age dating of M53 and M92 by Rey et al. (1998). The solid line with dots is the unsmoothed fiducial sequence of the present study in Table 5 and the dashed line is that reported by Stetson & Harris (1988) in their Table 6. In contrast to the M53, no photometric zero point shifts in the V magnitude and B − V color were applied to the fiducial sequence of M92 in the present study. The two fiducial sequences of M92 coincide well in the main-sequence part but deviate from each other from the subgiant branch to the lower RGB part.

Figure 18.(a) Comparison of the CMD and fiducial sequence of M53 in the present study. (b) Comparison of the CMD and fiducial sequence of M92 in the present study. In both panels, the solid line indicates the fiducial sequence in the present study. Only the stars satisfying the condition, r ≥ 1.22′ , are shown for M53 and M92. The RR Lyrae stars are not plotted according to the variable stars list reported by Clement et al. (2001) for M53 and M92, respectively.

Figure 19.Comparison of the fiducial sequences of M53. The solid line with dots is the fiducial sequence of the present study and the dashed line denotes that reported by Rey et al. (1998) in their Table 6. The fiducial sequence of the present study was shifted according to the photometric zero point differences with respect to Rey et al. (1998). See the text for details.

Table 6Fiducial Sequence of M92 by Stetson (2000, 2012 update)

Figure 20.Comparison of the fiducial sequences of M92. The solid line with the dots is the fiducial sequence of the present study and the dashed line is that reported by Stetson & Harris (1988) in their Table 6.

Figure 21a compares the CMD of M53 reported by Stetson (2000, 2012 update) with the fiducial sequence of M53 in the present study. The fiducial sequence of the present study was shifted according to the photometric zero point differences with respect to Stetson (2000, 2012 update). The mean photometric zero point differences between the present study and Stetson (2000, 2012 update) were −0.029 ± 0.002 mag in V magnitude and −0.056 ± 0.003 mag in B − V color, where the errors are the standard deviation of the mean. The CMD and the fiducial sequence were compared directly in Figure 21a because the number of stars in M53 by Stetson (2000, 2012 update) was too small to derive a reliable fiducial sequence instead of comparing the fiducial sequences themselves. According to Figure 21a, the CMD of M53 by Stetson (2000, 2012 update) and the fiducial sequence of M53 in the present study showed good agreement. From the main sequence to the lower RGB approximately two magnitudes brighter than the main-sequence turnoff point (MSTO), they are almost coincident with each other. On the other hand, in the RGB region, which are two magnitudes brighter than the MSTO, the RGB of Stetson (2000, 2012 update) tends to be slightly bluer than the fiducial sequence of the present study. Figure 21b compares the fiducial sequences of the present study and Stetson (2000, 2012 update) for M92. In this case, the fiducial sequence of Stetson (2000, 2012 update) was shifted according to the photometric zero point differences with respect to the present study. The photometric zero point differences between Stetson (2000, 2012 update) and the present study were +0.010 ± 0.001 mag in V magnitude and +0.028 ± 0.001 mag in B−V color, where the errors are the standard deviation of the mean. The fiducial sequence of M92 by Stetson (2000, 2012 update) was derived using a similar method of derivation as those for M53 and M92 in the present study, as described in this section. On the other hand, the stars within r < 1.22′ from the cluster center of M92 were omitted when the fiducial sequence was derived. Table 6 lists the resulting unsmoothed fiducial sequence for M92 by Stetson (2000, 2012 update) derived in the present study. As in the case of M53, the two fiducial sequences for M92 coincide with each other quite well except for the upper RGB region. In the upper RGB region, which is two magnitudes brighter than the MSTO, the RGB of Stetson (2000, 2012 update) tends to be slightly bluer than the fiducial sequence of the present study, as in the case of M53. These comparisons of the two homogeneous photometry of M53 and M92 in this way clearly suggest that the photometry of M53 and M92 in the present study transformed well to the standard photometric system defined by Landolt (1992) once again. And they also suggest that the present photometry of M53 and M92 is tied together as closely as possible to derive the accurate relative ages of M53 and M92 one more time, except for the small photometric zero point errors. The reason why the fiducial sequence of M92 by Stetson (2000, 2012 update) derived in the present study coincides well with that of the present study rather than that of Stetson & Harris (1988) is that the lower RGB region of the fiducial sequence of Stetson & Harris (1988) was derived from the insufficient number of stars in the outer region of M92.

Figure 21.(a) Comparison of the CMD of M53 by Stetson (2000, 2012 update) and the fiducial sequence of M53 in the present study. The fiducial sequence of the present study was shifted according to the photometric zero point differences with respect to Stetson (2000, 2012 update). (b) Comparison of the fiducial sequences of M92 by the present study and Stetson (2000, 2012 update). The solid line is the fiducial sequence of the present study and the dotted line is the fiducial sequence of Stetson (2000, 2012 update). The fiducial sequence of Stetson (2000, 2012 update) was shifted according to the photometric zero point differences with respect to the present study.

 

4. RELATIVE AGE MEASUREMENT USING THE Δ(B − V ) METHOD

There are two classes of techniques to determine the age of Galactic GCs: the vertical methods and horizontal methods. Vertical methods, such as the so-called ΔV method, use the magnitude difference between the mean HB level and MSTO (Gratton 1985; Peterson 1987). But, in the cases of M53 and M92, the mean HB magnitudes of M53 and M92 could not be measured accurately because they have mainly BHBs in their HBs. Horizontal methods like the so-called Δ(B−V ) method and Δ(V − I) method use the B − V or V − I color difference between the MSTO and lower RGB (VandenBerg et al. 1990; Johnson & Bolte 1998; Rosenberg et al. 1998, 1999) in V versus B − V and V versus V − I CMDs, respectively. The Δ(B − V ) method reported by VandenBerg et al. (1990) was used for the relative age measurements of M53 and M92 in the V versus B − V color-magnitude plane. Techniques to measure relative age are less affected by uncertainties in stellar evolution theory than the absolute age measuring techniques, such as the isochrone fitting method, and are independent of the distance modulus, interstellar reddening, and zero point of the photometric calibrations (Sarajedini & Demarque 1990; VandenBerg et al. 1990) because the absolute terms disappear in a relative comparison. Overall, the Δ(B − V ) method reported by VandenBerg et al. (1990) uses the quantities, (B−V )TO, which is the MSTO color, and V+0.05, which is upper main-sequence magnitude at a point +0.05 mag redder than the MSTO point, to align the fiducial sequences for comparing GCs. After aligning the fiducial sequences of the comparing GCs using the quantities, (B−V )TO and V+0.05, the separation between the fiducial sequences of the lower RGBs gives the relative age difference between the GCs being compared. In this case, the fiducial sequence of the older GC appears bluer, whereas that of the younger GC appears redder.

The (B − V )TO and V+0.05 values of M53 and M92 were determined using the 2.5 σ clipped V versus B−V color-magnitude data of M53 and M92, as described in Section 3. (B − V )TO and VTO of M53 were determined using a parabolic least-squares fit to the stars within ±0.3 mag in the V magnitude of the approximate MSTO region determined by the fiducial sequence of M53 in Section 3. The (B −V )TO of M53 was 0.348 ± 0.003 mag, where the error is the standard deviation of the mean of color of the MSTO region, and the VTO of M53 was 20.24 ± 0.03 mag, where the error is the magnitude error in the MSTO region. The (B −V )TO and VTO of M92 were also determined by a parabolic least-squares fit to the stars within ±0.4 mag in V magnitude of the approximate MSTO region determined by the fiducial sequence of M92 in Section 3. The (B − V )TO of M92 was 0.378 ± 0.002 mag, where the error is the standard deviation of the mean of color of the MSTO region, and the VTO of M92 was 18.66 ± 0.03 mag, where the error is the magnitude error in the MSTO region. The V+0.05 of M53 and M92 were determined by a parabolic least-squares fit to the upper main-sequence stars within ±0.6 mag in V magnitude 0.05 mag redder than the MSTOs of M53 and M92. The V+0.05 of M53 and M92 was 21.10 ± 0.04 mag and 19.50 ± 0.03 mag, respectively, where the errors are the errors propagated by the color errors of the MSTO regions.

Using the (B − V )TO and V+0.05 values of M53 and M92, the fiducial sequences of M53 and M92 were shifted horizontally, making (B − V )TO coincide with each other, and vertically, making the V+0.05 coincide with each other according to the prescription reported by VandenBerg et al. (1990). Figure 22 compares the fiducial sequences of M53 and M92 shifted according to the prescription reported by VandenBerg et al. (1990). On the other hand, further adjustments according to the prescription of footnote 3 of VandenBerg (2000) were abandoned, because such adjustments increased the separation between the lower RGB parts of the fiducial sequences of M53 and M92. In Figure 22, the isochrones reported by VandenBerg et al. (2006) with BV RI color-Teff relations, as described by VandenBerg & Clem (2003), are also shown as a reference after shifting horizontally and vertically to match the (B −V )TO and V+0.05 of M53 and M92. The isochrones of VandenBerg et al. (2006) ranged from 10 to 18 Gyr and were spaced by 1 Gyr with [Fe/H] = −2.14 between those of M53 and M92, and [α/Fe] = +0.30. According to Figure 22, the fiducial sequence of M92 between −4 < (V − V+0.05) < −2.5 was bluer than that of M53 suggesting that M92 is older than M53. This is in contrast to that reported by Rey et al. (1998), implying that there is no large age difference between M53 and M92 (Δt < 1 Gyr) using the same method reported by VandenBerg et al. (1990).

Figure 22.Comparison of the fiducial sequences of M53 and M92. The open triangles are the fiducial sequence of M53 and the filled circles are fiducial sequence of M92. The solid lines are isochrones reported by VandenBerg et al. (2006) ranging from 10 to 18 Gyr and spaced by 1 Gyr with [Fe/H] = −2.14 and [α/Fe] = +0.30 and are shown as a reference. The dashed line is the parabolic least-squares fit line to the fiducial sequence of M53 between −4 < (V −V+0.05) < −2.5, and the dotted line is that of M92 between −4 < (V − V+0.05) < −2.5.

A parabolic least-squares fit to the fiducial sequences of M53 and M92 between −4 < (V − V+0.05) < −2.5 was performed to measure the separation between the lower RGB parts of the fiducial sequences of M53 and M92. The parabolic least-squares fit line to the fiducial sequence of M53 between −4 < (V −V+0.05) < −2.5 is shown in Figure 22 as a dashed line and that of M92 is shown as a dotted line. According to the parabolic least-squares fit, the separation between the fiducial sequences of M53 and M92 between −4 < (V − V+0.05) < −2.5 was Δ(B − V ) ≈ 0.011–0.023 ± 0.009 mag, where the error is a combination in quadrature of the three kinds of errors: the fitting error to the fiducial sequences of M53 and M92 (0.005 mag), the error caused by the VTO error of M53 and M92 (0.006 mag), and the error caused by the (B − V )TO error of M53 and M92 (0.004 mag). If the absolute age of M92 is taken as 14 Gyr, as determined by VandenBerg (2000), the separation, Δ(B − V ) = ±0.01 mag, corresponds to ±0.94 Gyr according to the isochrones reported by VandenBerg et al. (2006) with [Fe/H] = −2.14 and [α/Fe] = +0.30, as shown in Figure 22. VandenBerg (2000) determined the age of M92 using the isochrones reported by Bergbusch & VandenBerg (2001). The isochrones of VandenBerg et al. (2006) are an expanded version of those reported by Bergbusch & VandenBerg (2001) in terms of the metallicity, age, and filter passbands.

On the other hand, according to the literature (Zinn & West 1984; Harris 1996; Carretta et al. 2009), the metallicity difference between M53 and M92 might amount to ≈0.3 dex, which can affect the relative age measurements between M53 and M92, assuming the same metallicity. Therefore, to examine the effect of a slight metallicity difference between the two GCs on the relative age measurement, Figure 23 plots the isochrones reported by VandenBerg et al. (2006) with two different ages (12 and 14 Gyr) and three different metallicities ([Fe/H] = −2.31, −2.14, and −2.01 with [α/Fe] = +0.30). As seen in Figure 23, isochrones with different metallicities and the same age almost coincide. Therefore, the relative age parameter between −4 < (V − V+0.05) < −2.5 is nearly unaffected within the possible metallicity difference between M53 and M92 (≈0.3 dex).

Figure 23.Comparison of the isochrones reported by VandenBerg et al. (2006) with different ages and metallicities. The solid lines are the isochrones reported by VandenBerg et al. (2006) with age = 14 Gyr and [Fe/H] = −2.31, −2.14, and −2.01 and [α/Fe] = +0.30. The dotted lines are those with age = 12 Gyr and the same [Fe/H] and [α/Fe] as in the case of 14 Gyr.

Therefore, the relative age difference between M53 and M92 was ≈1.0–2.2 ± 0.85 Gyr (mean = 1.6 ± 0.85 Gyr) with M92 being older from the color difference between the fiducial sequences of M53 and M92 between −4 < (V − V+0.05) < −2.5, Δ(B − V ) ≈ 0.011–0.023 ± 0.009 mag. In this case, the mean value 1.6 Gyr is not a simple arithmetical mean but a averaged mean in geometrical sense and the error 0.85 Gyr originated from the color difference error 0.009 mag. This result is in contrast to the conclusion reported by Rey et al. (1998) using the same Δ(B − V ) method reported by VandenBerg et al. (1990). The discrepancy might be mainly because in M92 the lower RGB part of the fiducial sequence of the present study was bluer than that reported by Stetson & Harris (1988), as shown in Figure 20, whereas in M53 the fiducial sequence of the present study and Rey et al. (1998) were nearly coincident, as shown in Figure 19. These results were also different from those reported by Marín-Franch et al. (2009), Dotter et al. (2010), and VandenBerg et al. (2013) who suggested that the ages of M53 and M92 coincide within the errors. The discrepancy might be explained by the different methods and photometric data sets used for to derive the age.

According to Figure 22, it seems that the isochrones reported by VandenBerg et al. (2006) do not run parallel with the fiducial sequences of M53 and M92 in the RGB parts and overestimated the ages of M53 and M92 by ~2 Gyr. Moreover, in the case of M92, the age of M92 slightly exceeded the age of the universe (t0) recently measured by the cosmic microwave background radiation (CMB). The age of the universe recently measured by the CMB is t0 = 13.82 ± 0.06 Gyr using the Planck satellite (Ade et al. 2014) and t0 = 13.77 ± 0.06 Gyr using the Wilkinson Microwave Anisotropy Probe (WMAP) satellite (Bennett et al. 2013; Hinshaw et al. 2013). However, this seems due to the fact that the Victoria-Regina isochrones (VandenBerg et al. 2006, 2012, 2014b) are slightly redder than the CMDs of Galactic GCs in the lower to intermediate parts of the RGBs (VandenBerg et al. 2013, 2014a,b, 2016). It seems that other isochrones such as the Dartmouth isochrones (Dotter et al. 2007, 2008) with empirical BV RI color-Teff relations by VandenBerg & Clem (2003), the Yonsei-Yale (Y2) isochrones (Yi et al. 2001; Kim et al. 2002), and the MESA (Modules for Experiments in Stellar Astrophysics) isochrones (Dotter 2016; Choi et al. 2016) will better fit the fiducial sequences of M53 and M92 in the RGB parts. This can be inferred from Figure 11 by Dotter et al. (2007) in the case of the Dartmouth isochrones, from Figures 7 and 8 by Rey et al. (2001) in the case of the Y2 isochrones, and from Figure 28 by Choi et al. (2016) in the case of the MESA isochrones. However, it must be noted that according to the updated Victoria-Regina isochrones reported by VandenBerg et al. (2014b), the current best estimate of the age of M92 is ~12.5 Gyr (VandenBerg et al. 2014a) and compatible with the age of the universe recently measured by the CMB using Planck and WMAP satellites (Ade et al. 2014; Bennett et al. 2013; Hinshaw et al. 2013). This fact suggests that the Victoria-Regina isochrones are not seriously problematic and still reliable at least in terms of age measurement.

 

5. CONCLUSIONS

A BV I CCD photometric study was performed on the central 11.7′ × 11.7′ region of the GC M53 from the RGB tip down to ≈2 mag below the MSTO observed on the same nights of the GC M92 by Cho & Lee (2007) using the same telescope, filter set, and CCD camera at BOAO for an accurate relative age measurement of the GCs M53 and M92. The V versus B −V, V versus V −I, and V versus B−I CMDs of M53 were produced using the same method and photometric parameters in each reduction step, as in the case of M92 reported by Cho & Lee (2007). Therefore, special care was taken to ensure that M53 and M92 were on the same photometric system and the photometry of M53 and M92 was tied together as closely as possible using the Landolt’s (1992) stars as standard stars to transform the 2003 data of M53 and M92, which were used to transform the 2002 data of M53 and M92 to the standard system. The zero point errors were estimated to be at a level of 0.010 mag in V, 0.025 mag in B − V, and 0.015 mag in V − I for the photometry of M53 and M92 of the present study except for the small zero point shift, particularly in the case of M53. According to these CMDs of M53, there are many BSSs in M53, which were most clearly delineated in the V versus B −I CMD. In M53, the AGB stars were separated quite well from the RGB sequence in all three types of CMDs from ~1.0 mag below the RGB tip down to the bottom of the AGB.

The relative ages of M53 and M92 were derived using the Δ(B − V ) method reported by VandenBerg et al. (1990) using the V versus B −V color-magnitude data of M53 and M92 observed during the same observing sessions. The relative age difference between M53 and M92 was found to be 1.6 ± 0.85 Gyr with M92 being older if the absolute age of M92 is taken to be 14 Gyr, as derived by VandenBerg (2000). This result is in contrast to previous results using the inhomogeneous data of M53 and M92 (Heasley & Christian 1991; Rey et al. 1998). If this relative age difference between metal-poor GCs M53 and M92 is real, the older age of M92 might have caused the slightly bluer HB morphology of M92 than M53. This can be explained by the results from the theoretical studies from Lee (1992) and Lee et al. (1994), who reported that an older age makes the HB morphology of metal-poor Galactic GCs bluer.