THE GLOBULAR CLUSTER NGC 6402 (M14). I. A NEW BV COLOR–MAGNITUDE DIAGRAM^*

NGC 6402 (M14, α = 17:37:36.1, δ = −03:14:45, J2000) is a moderately high metallicity globular cluster (GC) with [Fe/H] = −1.28. It is located 9.3 kpc away from the Sun and 4.0 kpc from the Galactic center. M14 has core and half-light radii of 079 and 130, respectively. Being located fairly close to the Galactic plane with ℓ = 2132, b = 1481, it is also fairly highly reddened, with E(B − V) = 0.6. Its fairly high reddening explains why, in spite of its being the 10th brightest Galactic GC, with M_V = −9.1, it has been quite neglected in the literature.⁷

Indeed, very few color–magnitude diagrams (CMDs) of the cluster have been obtained in the past. To our knowledge, there are only five published CMDs. The first two, by Mironov (1973) and Kogon & Wehlau (1974), were barely capable of reaching the horizontal branch (HB) level, being severely dominated by photometric errors. In spite of these limitations, Kogon & Wehlau drew attention to the lack of HB stars near the red end of the instability strip, which is contrary to what is expected for such a high-metallicity cluster. A lack of red HB stars is also apparent in the CMDs of Shara et al. (1986) and Cote et al. (1997); a long extension of the blue HB of the cluster is evident in these studies, particularly the latter. The (snapshot) Hubble Space Telescope (HST) photometry of Piotto et al. (2002) more clearly revealed the unusual HB morphology of M14, with stars extending through the RR Lyrae gap to an extended blue tail reaching the main sequence (MS) turnoff level. M14 is thus a prime example of a second-parameter cluster (see, e.g., Catelan 2009, for a recent review and extensive references), in the sense that it has too blue an HB morphology for its metallicity yet the cluster is not included in any of the recent, extensive studies of GC ages (e.g., Rosenberg et al. 1999; Salaris & Weiss 2002; De Angeli et al. 2005; Marín-Franch et al. 2009; Dotter et al. 2010; D. A. VandenBerg et al. 2013, in preparation). Additional interest in M14 has been generated by the fact that it is an object with a suspected extragalactic origin (e.g., Gao et al. 2007). Several of its properties support this possibility. GCs with long blue HB tails, such as M14, have been found to differ in mass and kinematics with respect to GCs without such blue HB tails, possibly pointing to an extragalactic origin for the former (Lee et al. 2007). In addition, M14 shares with ω Cen (NGC 5139) the peculiar characteristic of possessing a CH star (Cote et al. 1997): such stars are more commonly found in dwarf spheroidal galaxies, and indeed ω Cen has been suggested to be the (present or former) nucleus of one such dwarf (see, e.g., Carretta et al. 2010). In addition, based on the properties of its RR Lyrae stars, M14 is also found to be an Oosterhoff-intermediate GC (C. Contreras Peña et al. 2013, in preparation, hereafter Paper II), which is unusual for Galactic GCs, but not so for nearby extragalactic GCs (e.g., Catelan 2009). A more detailed discussion of the possible extragalactic origin of the cluster will be presented in Paper II.

This is the latest in our series of papers dealing with the CMDs and variable star content in Galactic GCs (e.g., Contreras et al. 2010; Zorotovic et al. 2009, 2010). Here we present a deep CMD for the cluster M14, reaching about 2 mag deeper than the MS turnoff. In Paper II we will describe our comprehensive analysis of the variable star content in the cluster.

Time-series B, V, and I photometry was obtained with the 0.9 m telescope at CTIO during 16 nights between 2007 June 22 and July 12, comprising a total of 67, 65, and 62 images in B, V, and I, respectively. Typical exposure times of 600 s in B, V and 150 s in I were used, and the typical seeing was 18. A 2048 × 2046 CCD detector with a pixel scale of 0369 pixel⁻¹, equivalent to a field size of 135 × 135, was used for image acquisition. The detector has a readout noise and gain of 2.7e⁻ and 0.6e⁻/ADU, respectively. The I-band data were used only to supplement the variability study described in Paper II.

PSF photometry of the images was performed using DAOPHOT II/ALLFRAME (Stetson 1994). For calibration purposes, five different Landolt (1992) standard fields were observed, comprising a total of 39 standard field images in each filter, giving a total of 220 standard star observations. The color range spanned from −0.24 to 2.52 in B − V, and the airmass X varied from 1.07 to 2.27, with a seeing range of 1''–22. Standard IRAF⁸ routines were used to produce the final calibrations for B, V, and I filters. The derived calibration equations are as follows:

$$\begin{eqnarray} b &= B & +1.435(\pm 0.011) +0.090(\pm 0.008)(B-V) \nonumber \\ & & +0.234(\pm 0.005)X, \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} v &= V & +1.275(\pm 0.009)-0.022(\pm 0.006)(B-V) \nonumber \\ & & +0.118(\pm 0.004)X, \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} i &= I & +2.152(\pm 0.010)-0.018(\pm 0.006)(V-I) \nonumber \\ & & +0.023(\pm 0.004)X \end{eqnarray} \tag{ 3 }$$

(where lower-case letters indicate instrumental magnitudes and X is the airmass), with an rms scatter of 0.036, 0.031, and 0.028 mag for the B, V, and I solutions, respectively.

In Figure 1 we show the resulting CMD from the DAOPHOT II/ALLFRAME photometry, after removing stars lying within the innermost regions of the cluster (r ⩽ 086), which are badly affected by crowding. In addition, known variable stars (see Paper II) were also removed from the CMD.

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In order to estimate the physical parameters of the cluster from its CMD, it is necessary to define with high precision the cluster ridgeline. However, it is evident from Figure 1 (upper panels) that there is a significant amount of contamination from field stars. In order to account for this effect, we perform statistical decontamination of the observed CMD following the method described in Gallart et al. (2003), with a maximum distance parameter of d = 0.42. This method requires the use of a control field; ideally we would use stars lying outside the tidal radius (r_t = 80; Harris 2010) of the cluster. Unfortunately, given the small field of view of the telescope compared to the area of M14, this was not possible in practice. For this reason, the control field is defined by using the Besançon Galactic models (Robin et al. 2003), using as input the relevant parameters for M14, i.e., distance, ℓ, b, projected area in the sky, and reddening—with the latter defined as E(B − V) = 0.57 (see Section 3.1). We note that in the method of Gallart et al. (2003) both the ratio between cluster and control field areas and completeness need to be taken into account. As to the first effect, we note that the area of the Besançon control field was chosen to be the same as the area covered by the cluster in the CCD. The second effect becomes important at V ⩾ 21 mag, i.e., the magnitude at which the number of star per magnitude bin started to drop, thus not affecting the general shape of the cluster's CMD—and was thus ignored.

In Figure 1 we present the result of the statistical decontamination. Here it is possible to observe that some branches, particularly the red giant branch (RGB) and the HB, reveal a spread that is larger than would be expected from photometric errors alone. This is especially evident toward the upper part of the CMD. This spread could be caused by the presence of differential reddening, on the order of several millimagnitudes, across the face of the cluster—which would not be unusual given the high level of extinction in the direction of M14.

To correct for the effect of differential reddening, we followed Piotto et al. (1999), dividing the image into one hundred 200 × 200 pixel² subsections and constructing a CMD for each. We arbitrarily selected one of the sections as the reference and extracted its fiducial points by drawing a line by hand. Then, a spline function was fitted to these fiducial points in order to obtain a continuous reference line. Figure 2 illustrates the detected shifts, with respect to this reference line, of stars belonging to two of these small subsections. For clarity the reddening vector is also shown in this plot.

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For each subsection, we determine the distance along the reddening vector (defined by A_V = 3.1 E(B − V)) between each star with (B − V) > 0.8 and V < 21 and the reference fiducial CMD ridgeline. Then, E(B − V) for each star is represented by the abscissa of the distance vector, with the total relative reddening in the corresponding subsection defined as the median value of the abscissa in all of the distances. The resulting differential reddening map is presented in Figure 3, implying a total range in reddening at the level of ΔE(B − V) ≈ 0.17 mag. Every star is then corrected for this differential reddening effect based on its position in the image.

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To further clean our CMD, stars with too large errors compared to what would be expected at their magnitude levels, in both B and V, were excluded. An exponential function was fitted to the median values of the error at each magnitude level (Figure 4), and then all stars with errors falling above the fitted line were excluded. This leads to our final CMD for the cluster, which is shown in Figure 5. The corresponding photometry is given in Table 1.

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3.1. Mean Reddening

3.2. Metallicity and Reddening

In Figure 5 we show the BV CMD of M14, after performing the corrections for field contamination and differential reddening explained above. The morphology of the CMD is consistent with what was found in previous works (Piotto et al. 2002; Cote et al. 1997), confirming that the cluster does indeed contain an extended blue HB. However, our work is the first to clearly reach beyond the MS turnoff level, and to confirm the presence of blue HB stars at least as faint as the turnoff point in V. Conversely, we do not identify a prominent red HB component, contrary to what is commonly seen at such moderately high metallicities—thus confirming that the cluster is indeed a second-parameter object.

Based on our CMD, we estimate the metallicity of M14 by determining the photometric indices from Ferraro et al. (1999). In order to use their equations, we first need to precisely determine the cluster's ridgeline, and most importantly the HB level, since any changes to this level will affect our final results. To determine the ridgeline, we follow the method described in, e.g., Zorotovic et al. (2009) and Stetson et al. (2005): we first determine our fiducial points for the cluster by visual inspection, then we fit a cubic spline to the fiducial points of the derived RGB. The spline fit to the fiducial points of the RGB, along with the mean ridgeline of the MS, can be observed in Figure 6. The fiducial points derived for the cluster are also given in Table 2.

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Table 2. M14 Ridgeline

V	B − V
14.611	2.062
14.800	1.978
14.999	1.889
15.210	1.805
15.499	1.720
15.740	1.668
15.999	1.615
16.240	1.565
16.492	1.516
16.734	1.478
16.993	1.441
17.244	1.408
17.494	1.376
17.735	1.348
17.995	1.321
18.229	1.300
18.495	1.281
18.754	1.263
18.995	1.246
19.214	1.228
19.571	1.207
19.727	1.200
19.978	1.191
20.000	1.190
20.050	1.185
20.100	1.180
20.100	1.167
20.150	1.114
20.200	1.083
20.250	1.060
20.300	1.046
20.350	1.035
20.400	1.025
20.450	1.018
20.500	1.011
20.550	1.007
20.600	1.002
20.650	0.999
20.700	0.997
20.750	0.996
20.800	0.995
20.850	0.996
20.900	0.998
20.950	0.999
21.000	1.000
21.100	1.005
21.200	1.011
21.300	1.019
21.400	1.025
21.500	1.033
21.600	1.042
21.700	1.049
21.800	1.061
21.900	1.073

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Ferraro et al. (1999) use as the HB level the empirical zero-age HB (ZAHB), which is defined by them as the magnitude of the lower envelope of the observed HB distribution in the region with 0.2 < (B − V)₀ < 0.6. This amounts to the "horizontal" part of the HB in the CMD, where, unfortunately, M14 does not contain many stars. Moreover, this region of the CMD may also suffer from statistical decontamination uncertainties in our procedure. In view of these limitations, we decided to use a theoretical ZAHB from VandenBerg et al. (2006) for a chemical composition [Fe/H] = −1.41 (see below), and an enhancement of the α-elements given by [α/Fe] = 0.3, as typically found among Galactic GC stars (e.g., Carney 1996; Sneden 2004). We use E(B − V) = 0.57 (Section 3.1), and vertically shift the theoretical ZAHB to match the lower envelope of our observed blue HB distribution (Figure 7). The HB level is then determined as the mean magnitude of the ZAHB in the region 0.77 < (B − V) < 1.17. This gives V_ZAHB = 17.45.

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Using our mean ridgeline, we derive the RGB parameters (B − V)_{0, g}, ΔV_1.1, ΔV_1.2, ΔV_1.4, S_2.0, and S_2.5. For the first four among these indices we need to correct our observed colors by extinction, which was done by assuming once again E(B − V) = 0.57. The RGB parameters and the respective metallicities derived on the basis of each index are listed in Table 3. A straight average over the derived values gives [Fe/H]_CG97 = −1.15 ± 0.06 on the Carretta & Gratton (1997) scale. This corresponds, following Equation (7) in Carretta & Gratton, to a value of [Fe/H]_ZW84 = −1.38 ± 0.07 on the Zinn & West (1984) scale. This is close to the value listed in the 2003 edition of the Harris (1996) catalog, namely [Fe/H] = −1.39, but slightly lower than the value provided in the 2010 edition of this catalog (Harris 2010), namely [Fe/H] = −1.28. The latter value is, however, in the new UVES spectroscopic scale of Carretta et al. (2009). Using the transformation relations given in Carretta et al., our metallicity value translates into [Fe/H]_UVES = −1.27, in excellent agreement with Harris (2010). Indeed, we obtain a mean value [Fe/H]_UVES = −1.28  ±  0.08, based on the different photometric indicators (Table 3).

Table 3. Photometric Metallicity Indicators in M14^a

Parameter	[Fe/H]CG97	[Fe/H]ZW84	[Fe/H]UVES
(B − V)0, g = 0.81	−1.27	−1.51	−1.42
ΔV1.1 = 1.72	−1.10	−1.32	−1.20
ΔV1.2 = 2.13	−1.14	−1.36	−1.25
ΔV1.4 = 2.63	−1.17	−1.40	−1.29
S2.5 = 4.69	−1.15	−1.37	−1.26
S2.0 = 5.68	−1.12	−1.34	−1.23
Mean	−1.15 ± 0.06	−1.38 ± 0.07	−1.28 ± 0.08

Note. ^aBased on the Ferraro et al. (1999) calibrations.

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The indices S_2.0 and S_2.5 are independent of the assumed reddening of the cluster, and thus can be used as a check of the adopted reddening value and derived metallicity. From Table 3 we can see that the values of [Fe/H] obtained with these two slopes do not differ from those obtained with reddening-dependent indices. Indeed, based on S_2.0 and S_2.5 we derive (B − V)_{0, g} = 0.84 and (B − V)_{0, g} = 0.83, respectively. It is thus possible to conclude that the assumed value of E(B − V) = 0.57, which implies (B − V)_{0, g} = 0.81, must be close to the correct reddening for M14, to within ≈0.02 mag in E(B − V).

3.3. Horizontal Branch Morphology

As mentioned above, NGC 6402 presents an unusually blue HB for its metallicity. We attempt, in the following, to describe its HB morphology through widely used parameters, such as the Lee–Zinn parameter $\mathcal {L}$ (Zinn 1986; Lee 1990; Lee et al. 1990) and the Buonnano parameter $\mathcal {P}_{\mathcal {HB}}$ (Buonanno 1993; Buonanno et al. 1997). These are defined as follows:

$$\begin{eqnarray} \mathcal {L} & = & \mathcal {(B-R)/(B+V+R)}, \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} \mathcal {P}_{\mathcal {HB}} & = & \mathcal {(B{\rm 2}-R)/(B+V+R)}, \end{eqnarray} \tag{ 5 }$$

where $\mathcal {(B{\rm 2}}$ represents the number of blue HB stars bluer than (B − V)₀ < −0.02 and $\mathcal {B,\, R, {\rm and}\; V}$ represent the number of blue, red, and variable stars in the HB (RR Lyrae), respectively. Two other parameters are also presented in this study, both defined by Preston et al. (1991): (B − V)_W, or the mean unreddened color of blue HB stars with −0.02 < (B − V)₀ < 0.18, and $B_{W}/\mathcal {B}$, defined as the number of stars in the given range of color, normalized by the number of blue HB stars with (B − V)₀ < 0.18.

Blue, red, and variable stars in the HB were selected following the boundary regions shown in Figure 8. The criteria adopted can be summarized as follows.

• 1.  
  $\mathcal {R} =$ number of red HB stars: the red HB region is limited, at its red end, by the RGB ridgeline minus 0.08 mag, corresponding to the (somewhat arbitrary) blue limit that was set to select stars in the study of the RGB bump in Section 3.4. The faint limit is set as the lower envelope of the observed RR Lyrae distribution, whereas the bright limit was adopted at V_ZAHB − 0.8, as needed in order to separate HB stars from asymptotic giant branch stars (Buonanno et al. 1994). Finally the blue limit is set by the red limit of the RR Lyrae distribution.
• 2.  
  $\mathcal {V} =$ number of RR Lyrae stars: this quantity is taken from Paper II, corresponding to all RR Lyrae found within the same magnitude limits as defined for red HB stars.
• 3.  
  $\mathcal {B} =$ number of stars contained in the fainter/bluer selection box shown in Figure 8: the limits of this selection box are set by hand in order to include likely faint blue HB stars affected by large photometric errors.

We note that "constant" stars lying within the V selection box are defined as red or blue HB stars, depending on their distance to either one of these groups. The number of stars selected for each region, as explained above, and the resulting parameters of the morphology of the HB are presented in Table 4.

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Table 4. HB Morphology Parameters for NGC 6402

Parameter	Value
$\mathcal {B:V:R}$	191: 106: 39
$\mathcal {B/(B+R)}$	0.83 ± 0.02
$\mathcal {(B-R)/(B+V+R)}$	0.45 ± 0.03
$\mathcal {(B{\rm 2}-R)/(B+V+R)}$	0.14 ± 0.03
(B − V)W	0.078 ± 0.054
$B_W/\mathcal {B}$	0.54 ± 0.14

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The computed value of $\mathcal {L}$ is much lower than the one found in the literature for this cluster ($\mathcal {L}=0.65$; see Catelan 2009 and references therein). The uncertainty is mainly due to the problems involved in accurately evaluating $\mathcal {R}$, given that it is strongly affected by the uncertainties in the CMD decontamination process. Note that the original $\mathcal {L}$ value for this cluster was based on the assumption that $\mathcal {R} = 0$ (Lee et al. 1994).

3.4. Red Giant Branch

One of the most important phases in the evolution of an RGB star is the so-called RGB "bump." This corresponds to a momentary reversal in the evolutionary path of the star, which takes place when its H-burning shell encounters the chemical composition discontinuity left behind by the maximum inward penetration of the giant's convective envelope (see Catelan 2007 for a review and extensive references). In order to determine the position of the RGB bump in M14, we follow the same procedure as applied by Zorotovic et al. (2009) in the case of NGC 5286. The smoothed RGB luminosity function (LF; Figure 9, upper panel) already reveals the presence of a candidate bump at V ∼ 17.3. The significance of the detection is confirmed by subtracting the expected number of stars N_fit given by a power-law fit to the LF from the number of stars in each bin, and comparing this result to the expected 3σ Poisson fluctuation level. As can be seen in the middle panel of Figure 9, the suspected bump clearly stands out as the most prominent feature (the higher peak at V ∼ 20 is due to MS stars). A Gaussian fit to the data around this feature yields V_bump = 17.321 ± 0.003, with σ_{V, bump} = 0.070  ±  0.002. We accordingly estimate the final position of the bump as V_bump = 17.32 ± 0.06, which results from a compromise between the formal error of the position and the width of the Gaussian (see also Zorotovic et al. 2009). The location of the bump is also confirmed by the integrated RGB LF, as shown in the bottom panel of Figure 9.

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The derived position of the RGB bump and ZAHB imply a $\Delta V^{\rm bump}_{\rm HB} = -0.13$ mag. As is well known, this quantity is also strongly sensitive to metallicity, and thus in Figure 10 we present $\Delta V^{\rm bump}_{\rm HB}$ as a function of [Fe/H] (upper panel) and [M/H] (lower panel), using the data from Ferraro et al. (1999). Clearly, the position of the RGB bump in M14 is consistent with our derived metallicity for the cluster, again lending support to our adopted reddening value.

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We make an attempt to determine the age of M14 by comparing it to the GC M5 (Sandquist et al. 1996), using two methods. First we use the so-called ΔV method, based on the magnitude difference between the HB and TO levels. For this method, we follow Chaboyer et al. (1996), using their Equation (2) and assuming M_V(RR) = 0.20 [Fe/H] + 0.98. The latter is assumed as it corresponds to the closest match to the absolute magnitudes of RR Lyrae obtained from the recent calibration by Catelan & Cortés (2008). The HB level of M14 is determined as described in Chaboyer et al. (1996) by using V(HB) = V_ZAHB − 0.05 [Fe/H] − 0.2 (where [Fe/H] = −1.38), which yields V(HB) = 17.32  ±  0.01. The TO level is determined by fitting a parabola to a small region of the MS near the TO point, thus obtaining V_TO = 20.81 ± 0.02 and (B − V)_TO = 0.995 ± 0.030. Then, the corresponding ΔV value for M14 is $\Delta V^{{\rm TO}}_{{\rm HB}}=3.49\,{\pm}\, 0.02$, while for M5, $\Delta V^{\rm TO}_{\rm HB}=3.47\,{\pm}\, 0.06$ (from Sandquist et al. 1996). This implies that M14 is ∼0.3 ± 1.0 Gyr older than M5.

Figure 11 shows the fiducial points of M14 as determined by us and those of M5 taken from Sandquist et al. (1996). In addition, VandenBerg et al. (2006) isochrones for [Fe/H] = −1.41, [α/Fe] = 0.3, and ages ranging from 8 to 18 Gyr are also shown. For comparison with the models, we chose the closest metallicity to the Zinn & West (1984) value determined for M14.

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Following Stetson et al. (1999), the model isochrones and ridgelines are translated horizontally to match each other's turnoff colors, and then shifted vertically to register the point of the upper MS that is 0.05 mag redder than the turnoff. The age is derived using Equation (1) in Vandenberg & Stetson (1991), which requires measuring the color difference between the RGBs. Stetson et al. (1999) measure this difference at the point that lies exactly at V − V_+0.05 = −3, whereas Vandenberg & Stetson (1991) use the value determined at V − V_+0.05 = −2.5; however, the latter authors recommend performing a star-by-star statistical analysis over 1–2 mag along the lower RGB in order to more reliably measure the mean color difference between the RGBs. It is clear from Figure 11 that for our comparison, a value derived from this method will strongly depend on the point where the color difference is evaluated. Thus we make no attempt to derive an age difference. However, the data appear to suggest that M14 is slightly older than M5, and that the age difference could be as high as 2 Gyr. This is consistent with our previous estimate based on the vertical method. A slightly older M14, compared to M5, would help explain the former's bluer HB morphology. However, our data are not sufficient to reach definite conclusions in this regard, and so we are unable to exclude the possibility that M14 and M5 have virtually the same age to within the errors.

We have obtained BVI CCD photometry for the GC M14. A CMD of unprecedented depth is constructed for the cluster based on which we derive several key properties.

The CMD is found to be affected by contamination from field stars, as well as the presence of differential reddening across the face of the cluster. The latter is estimated to be present at the level of ΔE(B − V) ≈ 0.17 mag. After statistically subtracting the field stars, a reddening map is built, and the photometry of M14 is finally corrected for the presence of differential reddening.

RGB photometric parameters are derived as a means of obtaining the cluster's metallicity, implying [Fe/H] = −1.38 ± 0.07 dex on the Zinn & West (1984) metallicity scale, and a mean value [Fe/H] = −1.28 ± 0.08 dex on the more recent UVES scale, in excellent agreement with the value listed in the Harris (2010) catalog. We detect the RGB bump at V_bump = 17.32 ± 0.06 mag, and its position is also fully consistent with the derived metallicity.

The derived photometric parameters allow us to confirm that the absolute reddening of the cluster must be close to E(B − V) = 0.57, to within about 0.02 mag. The latter is significantly higher than implied by the dust maps of Burstein & Heiles or Schlegel et al. HB morphology parameters are also computed, with the main difference between our results and those of previous works arising from the uncertainty in the number of stars belonging to the red part of the HB, caused by the decontamination process.

The so-called ΔV method is used to determine relative ages of M14 and M5, suggesting that M14 is only about 0.3 ± 1.0 Gyr older than M5—a result also qualitatively supported by a comparison with model isochrones and the "horizontal" age method. Therefore, within the uncertainties, M14 and M5 have roughly the same age, although the possibility that M14 may be slightly older (by up to ≈2 Gyr) cannot be ruled out.

We thank an anonymous referee for several useful suggestions that helped us improve the presentation of our results. Support for M.C. and C.C.P. is provided by the Chilean Ministry for the Economy, Development, and Tourism's Programa Iniciativa Científica Milenio through grant P07-021-F, awarded to The Milky Way Millennium Nucleus, by the BASAL Center for Astrophysics and Associated Technologies (PFB-06), by Proyecto Fondecyt Regular #1110326, and by Proyecto Anillos ACT-86.