Deep, Wide-Field Ccd Photometry for the Open Cluster Ngc 3532

Our reductions of the entire NGC 3532 field netted both astrometric positions and $BV(RI{)}_c$ photometry for 316,367 objects within a one square degree area surrounding the cluster center. An example of these data is given in Table 2. From this sample, we will consider a total of 285,990 objects for further analysis since they were detected at least once in each of the $B$, $V$, $R_c$, and $I_c$ filters. The fact that the vast majority of the remaining 30,377 excluded objects ($\sim 93\%$) have $V\gtrsim 20$ implies they likely went undetected in one or more filters due to their extreme faintness and/or the effects of crowding.

In Figure 4, we plot the uncertainties in each magnitude, $\sigma \left(mag\right)$, versus $V$ for the sample of objects with valid measurements in all four filters. These uncertainty values represent the standard error of the mean magnitude as computed by our reductions. Depending on the number of measurements for a particular object, $\sigma \left(mag\right)$ is dominated by either the internal noise estimates in the photometric reductions or by the external frame-to-frame agreement in the calibrated magnitudes. Note the high precision in our photometry, with the majority of stars having $\sigma \left(mag\right)\lesssim 0.1$ for the $V$, $R_c$, and $I_c$ filters over the entire magnitude range. The $B$-band uncertainties, on the other hand, begin to rise above 0.1 mag at $V\sim 19$, indicating that our observing program would have benefited from longer exposure times in $B$ in order to achieve the same depth as the other filters.

The ALLFRAME reductions also supply two image quality parameters known as $\chi$ and $sharp$ that are based on the pixel-to-pixel residuals between the model PSF and the observed brightness profile for any given object (Stetson et al., 2003). While the former can be used to separate out objects that are contaminated by image defects, bad pixels or diffraction spikes, the latter is useful for isolating legitimate stars from background galaxies. The $\chi$ and $sharp$ estimates given in Table 2 for any given entry represent the mean of those determined individually for each frame in which that object was detected. Figure 5 provides a plot of the $\chi$ and $sharp$ values versus $V$ magnitude for the same number of objects shown in Figure 4.

The $[V,(B-V\left)\right]$ and $[V,(V-I_c\left)\right]$ color-magnitude diagrams (CMDs) for NGC 3532 that result from our reductions are shown in Figure 6. In both panels we plot only those stars judged to have the highest quality photometry based on their photometric uncertainties, the number of independent measurements in each filter, and values of the ALLFRAME-computed image quality statistics, $\chi$ and $sharp$. Specifically, we have plotted stars that have at least one measurement in any given filter together with $\sigma \left(mag\right)\le 0.1$ mag, $\chi \le 2.0+{10}^{-0.2(V-13.5)}$, and $|sharp|\le 1.0$ (we have denoted these limits by the dashed lines in Figures 4 and 5).

Upon inspection of the CMDs in Figure 6, a few things are immediately evident. First, a well-defined cluster main sequence can clearly be seen extending from the turnoff at $V\sim 8$ down to $V\sim 16$ where it begins to become lost in field star contamination. The significant number of field stars in the CMDs undoubtedly arises due to the low Galactic latitude of the cluster. Within the field star distribution there appear to be two separate populations; one corresponding to the field dwarfs that lies fainter and blueward of the cluster main sequence, with a second distinct population associated with field giant stars that can be identified as the plume of stars at $(B-V)$ and $(V-I_c)\sim 1.5$. These field stars begin to overlap the cluster population at $V>16$, making it quite difficult to ascertain the exact location of the cluster main sequence at fainter magnitudes.

At the brightest end of each CMD there is a handful of cluster red giants at $(B-V)$ and $(V-I_c)\sim 1$. Such a small population of giant stars, combined with the near-vertical nature of the turnoff and upper main sequence points to the fact that NGC 3532 is a fairly young cluster (i.e., $<1$ Gyr). In addition, there are two objects lying between the turnoff and giant clump at $V\sim 8$ that may be cluster stars transitioning the Hertzsprung gap. A more detailed analysis of the giant star population in NGC 3532 will be given in Section 4.3.

Finally, the $[V,(B-V\left)\right]$ CMD in the left-hand panel of Figure 6 also shows the presence of several faint blue objects that we presume to be part of the white dwarf sequence of NGC 3532. Moreover, it appears that the majority of these stars are positioned in a clump lying at $V\sim$20 and $(B-V)\sim 0$, with only a handful of stars extending fainter. White dwarfs as faint as $V\sim 20$ are known to exist in NGC 3532 based on the investigations of Reimers & Koester (1989) and Koester & Reimers (1993). It may indeed be the case that this clump corresponds to the end of the white dwarf cooling sequence. If so, it would provide an independent method for deriving the cluster age by fitting white dwarf cooling models to the observed population. A more detailed analysis of these faint, blue objects will be given in Section 4.4.

A number of other photometric studies have been published for NGC 3532, though none that provide the depth and coverage of this one. Using the excellent resources available at the WEBDA website⁵, we have been able to cross-identify stars that are in common between our study and the WEBDA database for the purpose of comparing the broadband photometry presented by previous studies for NGC 3532. Specifically, we consider the photometric data given in the following publications: Koelbloed (1959, hereafter K59) (82 stars), Butler (1977, hereafter B77) (26 stars), Fernandez & Salgado (1980, hereafter FS80) (180 stars), Johansson (1981, hereafter J81) (14 stars), Wizinowich & Garrison (1982, hereafter WG82) (68 stars), and Claria & Lapasset (1988, hereafter CL88) (12 stars). All of these investigations provided Johnson $UBV$ photometry for their stars, while the work of WG82 is the only one to include Cousins $RI$ photometry.

Table 3 presents the correspondence between the WEBDA identification system for stars given in these studies and our own numbering system, along with the equatorial coordinates and photometric information derived as part of our analysis. In Table 4 we have listed the previously published photometry from the studies listed above for all stars in Table 3. It should be noted that due to space limitations, Table 4 only includes the data relevant to our comparisons, and excludes any information that has little or no impact on the analysis presented here (e.g., some of these studies provide $(U-B)$ colors, number of individual measurements for each star, magnitude and/or color uncertainties, etc.).

By combining the information listed in both Tables 3 and 4, we are able to create Figures 7 and 8 that show the differences in $V$ magnitudes and $(B-V)$ colors, respectively, for each of the six previous photometric studies of NGC 3532. In both figures, the magnitude and color differences plotted along the ordinates are in the sense of the indicated study minus our present data, while the abscissae give our $V$ magnitudes and $(B-V)$ colors. Some of the panels include open triangles that are meant to point to data lying beyond the ranges of these plots, and a few of these triangles are labeled with their WEBDA identification numbers for further discussion below.

An examination of our finding chart in Figure 1 reveals that WEBDA stars #426, #262, and #255 are situated very close to other bright stars; thus, the $V$ magnitudes presented by the FS80 study are likely too bright when compared with ours since their measuring aperture probably contained too much light from the neighbors. This assumption is supported by our comparisons when considering that the $\Delta V$ values for #426, #262, and #255 are all negative ($\Delta V=-0.705$, $-0.357$, $-0.545$, respectively). However, we cannot rule out that these stars may actually exhibit some variability that is the cause of such large $\Delta V$ values.

In addition to the discussions of these individual stars, we also point to the large scatter in the comparison of our $V$ magnitudes to those of B77 for stars fainter than $V\sim 16$ in panel (b) of Figure 7. Indeed, B77 claims that his photometry for stars with $V>16$ has a high degree of uncertainty among their individual measurements due to their extreme faintness. Given this, along with the large scatter seen at the faint end of panel (b), we do not place any significance on the B77 photometry for stars with $V>16$.

Furthermore, comparisons involving the $(RI{)}_c$ photometry of WG82 exhibit some peculiarities as shown in Figure 9. There are strong systematic differences in both $(V-R_c)$ and $(R-I{)}_c$ between our photometry and theirs as shown in the top row of the figure. Unfortunately, no other studies of NGC 3532 using the Cousins $RI$ filters exist in the literature that would help to identify which set of photometry is at fault. Based on the fact, however, that Figures 2 and 3 of the present investigation show that the recovered $(RI{)}_c$ magnitudes of our observed standards are in very good agreement with those given by Landolt (2009), we conclude that the problem actually lies in the $(RI{)}_c$ photometry tabulated by WG82. Rather than delve too deeply into this, we simply assume that these systematic differences can be corrected using a simple linear relationship. Based on a least-squares fit to the data we find the slopes of the lines shown in the top panels of Figure 9 to be $0.391$ for $(V-R_c)$ and $0.143$ for $(R-I{)}_c$. Using this information to correct the WG82 photometry results in the plots shown in the bottom panels.

Table 5 gives our computed differences in the $V$ magnitudes and colors for the indicated studies. The “Clipped Mean” column represents a determination of the mean based on an iterative clipping scheme where all stars that lie beyond 3 times the standard deviation are rejected from the computation of the average. The stars removed in this way are indicated in both Figures 7 and 8 as open circles or open triangles. The number of stars used in each of these computations is also provided along with the number of stars rejected. Note that our mean values derived for the photometry in the B77 investigation include stars brighter than $V=16$. Also note that the means given for the $(V-R_c)$ and $(R-I{)}_c$ colors of WG82 assume that the systematics shown in the top panels of Figure 9 have been removed.

Among the studies considered here, the one exhibiting the largest differences, both in $V$ magnitude and $(B-V)$ color, is that of WG82. Indeed, WG82 were aware of a zero-point difference between their data when compared to both K59 and FS80, despite all three of these investigations using E-region standards to calibrate their photometry. They cited declination effects in their observing equipment as a possible explanation for these differences. Whatever the reason, our value of $\Delta V\sim +0.07$ for their study is the largest of the six. This fact, together with the earlier discussion regarding the strange systematics in their $(V-R_c)$ and $(R-I{)}_c$ colors (c.f., Figure 9), is an indication that their photometry for NGC 3532 should be used with caution.

The fact that NGC 3532 is projected against a very rich population of disk stars at low galactic latitude is clearly evident by the large amount of field star contamination in the CMDs shown in Figure 6. As a result, we are forced to explore various techniques that would help to reduce the impact of this field population on the CMDs and to better define the cluster main sequence towards fainter magnitudes.

Stellar proper motions can be used as a robust and reliable tool to help determine cluster membership. To this end, we have cross-referenced our photometry list with the stars in the UCAC3 catalog in an effort to better separate the field and cluster populations. There are 18,131 stars in common, with 17,076 of these judged to be legitimate single stars as based on their object classification and double star flags in UCAC3 (see Zacharias et al. 2010 for details). We further reduce the sample by 704 more stars that either have blank or null entries for their proper motions.

In Figure 10 we present the proper motion diagram that results from the UCAC3 data together with the $[V,(V-I_c\left)\right]$ CMD for stars in the NGC 3532 field that have complementary photometry. In the left-hand panels we plot only those stars within a radius of 25 mas yr${}^{-1}$ of the absolute proper motion for the cluster (${\mu }_{\alpha }=-10.04$, ${\mu }_{\delta }=+4.75$; van Leeuwen, 2009), whereas the right-hand panels show stars outside this radius. Although this selection criterion does succeed in removing some of the field star contamination, especially towards the faint end of the CMD, the fact that the cluster’s absolute proper motion does not differ appreciably from that of the background field stars (assumed to be ${\mu }_{\alpha }\approx {\mu }_{\delta }\approx 0$) poses some difficulty for our attempts to isolate the main sequence. While a radius of 25 mas yr${}^{-1}$ may seem to be a bit too generous, additional plots such as these, which are not shown here, that use selection radii of 10, 15, and 20 mas yr${}^{-1}$ did further succeed in reducing the number of field stars, but at the cost of excluding more and more stars that appeared to lie on or near the NGC 3532 main sequence, particularly towards the fainter magnitudes where errors in UCAC3 proper motions begin to become quite large. Moreover, the magnitude limit of the UCAC3 catalog ($V\sim 17$) clearly does not extend to the faintest areas of the CMD where the field star population begins to totally obscure the cluster main sequence (c.f., Figure 6). In the end, we are resigned to accept that we cannot rely solely upon the UCAC3 proper motion information to procure a decent sample of bona fide cluster members, at least towards the fainter end of the CMDs where the field star contamination is the heaviest.

A second attempt to reduce the field star contamination involved isolating the cluster sequence from the background stars by supplementing our data with infrared photometry. To this end, we extracted the $JH{K}_s$ magnitudes and associated uncertainties for 67,670 stars in common between our data set and the 2MASS catalog. Our goal was to ascertain which combination of optical and/or infrared color indices produced the best possible separation between the field and cluster populations. The results of this exercise are shown in Figure 11 where we have plotted two color-color diagrams for stars in the NGC 3532 field. The $\left[\right(V-J),(V-I_c\left)\right]$ diagram in the bottom panel reveals a noticeable separation between two distinct sequences of stars toward the redward end of the plot. Likewise, the $\left[\right(V-K_s),(V-I_c\left)\right]$ diagram in the top panel shows this same separation, but to a somewhat greater degree. To help us better identify which of these sequences actually belong to the cluster itself we have overplotted the standard relations for dwarf stars (solid lines) as given by Bessell & Brett (1988), transformed to the 2MASS system using the relations of Carpenter (2001), in both panels. Based not only on the reddening vectors indicated in the plots, but also the loci of dwarfs predicted by the standard relations, we conclude that the lower branch of stars lying at $(V-I_c)\gtrsim 1.5$ in both panels correspond primarily to the population of field disk stars with various reddenings. The stars in the upper branch, on the other hand, include both legitimate cluster stars as well as some of the field dwarf stars that are situated on the blueward side of the main sequence in Figure 6.

If we exclude stars lying below the dashed lines in Figure 11 and replot the CMDs for NGC 3532, as shown in the top row of Figure 12, then the cluster’s lower main sequence stands out quite clearly against the remaining field star population and can easily be traced down to $V\sim 20$. It is important to note that we have used the same criteria for plotting the CMDs as in Figure 6 but with the addition of excluding stars that have uncertainties greater than 0.2 mag in their $JH{K}_s$ magnitudes. Stars that satisfy these criteria are denoted by black dots in Figure 12, while those that have large uncertainties in $JH{K}_s$, or lack 2MASS photometry entirely, are shown as gray dots. Note that the lack of field stars having $JH{K}_s$ photometry towards bluer colors in each CMD is due to the fact that these stars are just too faint to be detected by the 2MASS survey. Fortunately for us, however, their absence does not inhibit our investigation of the NGC 3532 main sequence since these stars primarily belong to the field population.

While our arbitrary selection of photometry based on the locations of stars in the color-color diagrams in Figure 11 has helped us to better define the cluster main sequence, the question remains as to whether our culling process may have also excluded some legitimate cluster members. For this reason, we show in the bottom panels of Figure 12 the stars that were rejected based on their locations below the lines in Figure 11. Unfortunately, the density of field stars in the vicinity of the lower main sequence is still too high to judge if any stars belonging to the cluster still remain, but based on the $BV(RI{)}_c$ photometry we have derived for the NGC 3532 field, in combination with the 2MASS $JH{K}_s$ magnitudes, this is likely the best method, given the information currently available, for separating the cluster sequence from the field stars at fainter magnitudes.

In order to benefit our analysis of NGC 3532 in later sections, we will further endeavor to isolate the cluster’s main sequence from the field star population using a technique of photometric filtering. Our aim is to identify a sample comprised of stars that have a high probability of belonging to NGC 3532 and is based on the fact that they should remain within a common “envelope” in any given CMD, while the field stars will be scattered in and out of these envelopes depending on their reddenings and/or photometric uncertainties.

A first step in this process involves identifying the location of the main sequence in different CMDs by eye and removing stars that are more than 0.5 mag in color from this initial fiducial. In subsequent iterations the fiducial colors are redetermined by taking the median value over a small range in $V$ magnitude and excluding objects lying more than $3\sigma$ in color away from this median. The final fiducial is produced when these median values do not change appreciably from one iteration to the next, and the number of stars lying within the envelope defined by the fiducial remains constant.

Next, with a trial fiducial, we then compute a ${\chi }^2$ value for each object in a CMD as the following:

Using this definition, we compute three separate ${\chi }^2$ values for each star using its $(B-V)$, $(V-I_c)$ and $(V-K_s)$ colors and $V$ magnitude. We then reject stars if any of their ${\chi }^2$ values is greater than $3\sigma$. Transversely, a given star will be tagged as a member of the cluster by this technique only if all three of its ${\chi }^2$ values determined from its $(B-V)$, $(V-I_c)$, and $(V-K_s)$ colors are within $3\sigma$.

The top row of Figure 13 presents CMDs for the final sample of main sequence stars that have been isolated from the field star population using our technique. Alternatively, the bottom row shows only the rejected stars (i.e., the field stars). Although a few obvious outliers still exist in the upper panels, our filtering has successfully removed a large number of field stars from the cluster main sequence. An important note, however, is that the bottom panels still show the presence of the cluster binary stars lying as much as 0.75 mag above the fiducial. Unfortunately, our filtering technique does not account for the presence of binaries, and our final sample of cluster members will, by design, include predominately single stars.

An alternative means by which to test the robustness of our photometric filtering technique is to examine the distribution of stars as a function of $\Delta color$. Figure 14 shows a few such plots that use $\Delta (V-I_c)$ as the color of choice. The top row of panels show, as a function of $V$ magnitude, the $\Delta (V-I_c)$ values for all the stars, only the field stars, or only the cluster stars from left to right, respectively. The bottom row reveals complementary histograms of these same distributions to illustrate that once the cluster stars are removed using our filtering process, the underlying field star population shows a fairly smooth transition over the cluster main sequence region from $-0.3\le \Delta (V-I_c)\le 0.3$.

One of the main goals in our investigation of NGC 3532 is to derive new estimates for the cluster parameters (e.g., distance, reddening, age, etc.) that are based on the photometry presented herein. Indeed, the depth and precision of our data compared to previous works offers a number of obvious advantages for our analysis. Moreover, the combination of our $BV(RI{)}_c$ data with 2MASS $JH{K}_s$ photometry provides high-quality observations that span a wide wavelength range and allows us to utilize different color indices to better constrain values for the cluster parameters.

Before delving into our own determination of parameters for NGC 3532, however, it is helpful to first consider some of the values for the cluster’s distance, reddening, age, and metallicity that have been derived by previous investigations. Table 6 presents a compilation of the various parameter estimates derived by the studies indicated in the first column. The final column of the table gives a brief explanation of how these parameters were determined. In some cases we also include the uncertainties in the values as quoted in the original investigations.

Interestingly, apart from the distances quoted by Robichon et al. (1999) and van Leeuwen (2009), both of which were derived using $Hipparcos$ parallaxes, virtually all of the values for the distance moduli agree quite well with each other. The one exception to this is the value of $(m-M{)}_0=8.06$ given by Johansson (1981), but this is likely a direct consequence of their higher reddening compared to the other studies listed. If we instead assume $E(B-V)\sim 0.04$, which better corresponds to the other reddening values listed in the third column, their distance modulus would increase to $(m-M{)}_0=8.26$ (assuming a $R_V=3.1$ reddening law). The range in distance moduli tabulated in Table 6 place the cluster between 400 and 500 pc from the Sun, making NGC 3532 one of the closest known open clusters.

The reddening for NGC 3532 likewise seems be well constrained with $E(B-V)$ estimates from the various studies ranging between 0.01 and 0.1. Note that we have converted the $E(b-y)$ values given by Eggen (1981), Schneider (1987), and Malysheva (1997) to $E(B-V)$ assuming $E(B-V)=1.35E(b-y)$ (Crawford, 1975). Despite its position very near the Galactic plane, the low reddening for NGC 3532 is consistent with its proximity to the Sun. For comparison, the reddening maps of Schlegel et al. (1998) give a full line of sight reddening of $E(B-V)\sim 1.20$ at Galactic coordinates corresponding to the center of the cluster. Multiplying this value by a factor of $(1-e^{-|dsinb|/h})$, where $d$ is the cluster’s distance, $b$ is its Galactic latitude, and $h$ the scale height of the typical dust layer (assumed to be 125 pc; Bonifacio et al., 2000) results in $E(B-V)\sim 0.1$ if $d=450$ pc. While this is a somewhat crude upper limit to the reddening for NGC 3532, it serves to support the remarkably low $E(B-V)$ values that have been previously suggested.

Four independent estimates for the cluster’s metallicity exist in the literature. While two of these have been derived from high-resolution spectroscopic analysis of cluster giant stars (Luck, 1994; Gratton, 2000), the other two given by Piatti et al. (1995) and Twarog et al. (1997) are based on calibrations of DDO color indices versus [Fe/H]. Reassuringly, all four [Fe/H] determinations are in good agreement and point to a near-solar metallicity for the cluster. For this reason, we will adopt [Fe/H]=$0.0\pm 0.1$ for NGC 3532 in the subsequent analysis.

We begin our determination of the distance and reddening for NGC 3532 by comparing the locus of cluster stars in the $(B-V)$, $(V-I_c)$, and $(V-K_s)$ CMDs to the well-established main sequence for the Hyades. The Hyades sample used here is based on the collection of so-called “hi-fidelity” members presented by de Bruijne et al. (2001), who derived distances to individual stars based on secular parallaxes. These secular parallaxes are $\sim 2-3$ times more precise than the original parallax estimates given in the $Hipparcos$ catalog, thus providing better constraints on the absolute magnitudes of the Hyades members. The photometry we employ for the Hyades comes from Pinsonneault et al. (2004) who assembled $BV{I}_{c}JH{K}_s$ data from various sources to produce a catalog of color indices for the de Bruijne et al. (2001) “hi-fi” sample. There is, however, one point to make regarding the photometry tabulated by Pinsonneault et al. (2004), in that Taylor & Joner (2005) found systematic differences between their $(V-I_c)$ data and Pinsonneault et al.’s for Hyades stars in common. This result is strengthened when comparing the homogeneous $BV(RI{)}_c$ photometry for a large sample of Hyades stars given by Joner et al. (2006) to the photometry tabulated by Pinsonneault et al. (2004) (c.f., Fig 23 in An et al. 2007). For this reason, we have opted to use the $(V-I_c)$ photometry of Joner et al. (2006) for 42 out of 92 stars in the Hyades sample, while the $(V-I_c)$ photometry for the remaining stars comes from Pinsonneault et al. (2004), but transformed to the Joner et al. (2006) system using a simple linear relationship.

The distance and reddening for NGC 3532 are derived simultaneously by fitting the main sequence fiducial for the cluster, derived in Section 3.3, to a sample of unevolved Hyades members (i.e., stars having $(B-V)>0.39$, $(V-I_c)>0.44$, and $(V-K_s)>0.98$). This technique is akin to the one described by Richer et al. (1997) in their derivation of the distance and reddening to the globular cluster M 4. To account for the metallicity difference between NGC 3532 ([Fe/H]=$0.0\pm 0.1$) and the Hyades ([Fe/H=$0.13\pm 0.01$; Paulson et al., 2003), we adjust the colors of the cluster fiducial redward by $(B-V)=0.029$, $(V-I_c)=0.015$, and $(V-K_s)=0.027$. The ${\chi }^2$ goodness of fit contours are shown in Figure 15 from separately fitting our NGC 3532 fiducial to the empirical Hyades main sequence on the $[M_V,(B-V{)}_0]$, $[M_V,(V-I_c{)}_0]$, and $[M_V,(V-K_s{)}_0]$ planes (i.e., ${\chi }_{(B-V)}^2$, ${\chi }_{(V-I_c)}^2$, and ${\chi }_{(V-K_s)}^2$, respectively). The lower right-hand panel of the same figure shows the combination of ${\chi }^2$ values resulting from all 3 fits (${\chi }_{tot}^2$). The contours in each panel designate the 68.3%, 95.4%, and 99.7% (1, 2, and 3$\sigma$) confidence levels of our fits based on 2 free parameters while the error bars correspond to the uncertainties in distance and reddening when each parameter is considered separately.

Clearly, the combination of fits involving all 3 color indices yields much tighter constraints on the cluster distance and reddening. The parameters that minimize the ${\chi }_{tot}^2$ distribution shown in the lower right-hand panel of Figure 15 occur at $E(B-V)=0.028(\pm 0.006)$ and $(m-M{)}_V=8.54(\pm 0.04)$. This translates to $E(V-I_c)=0.039(\pm 0.008)$, $E(V-K_s)=0.083(\pm 0.018)$, and $(m-M{)}_0=8.45(\pm 0.05)$ when using the reddening coefficients for different bandpasses given by Schlegel et al. (1998) assuming a $R_V=3.1$ reddening law. These values are in superb agreement with most of the modern distance and reddening estimates listed in Table 6 for NGC 3532 that use photometry for their derivations. Moreover, our estimated distance modulus is consistent with those derived from $Hipparcos$ parallaxes to within 2 sigma.

With the good constraints on the distance and reddening for NGC 3532, we can now use theoretical models to estimate the age of the cluster. Generally, this method involves determining which isochrone model of an appropriate metallicity best reproduces both the shape of the cluster turnoff as well as the luminosity of the red giant stars. In practice, this method seems simple, but in reality the reliable modeling of main sequence and giant stars, particularly for a cluster seemingly as young as NGC 3532, is sometimes problematic due to various physics involved in computing the theoretical models for the different types of stars.

Our CMDs for NGC 3532 in Figure 6 show the cluster has a well populated turnoff region, but only a handful of giant stars. In addition, the fact that the cluster is situated in a region of high field star density means that some of the assumed red giant stars in the upper right portion of the CMDs may not belong to the cluster at all. For this reason, we have isolated a sample of candidate red giants from the cluster CMDs for further analysis. Assuming the cluster giants have $(B-V)>0.25$ and $V<8.5$, we find that 14 stars from our database meet these criteria. The photometric, astrometric, and kinematic properties of these 14 candidate giant stars are listed in Table 7. The information presented in this table is meant to include or exclude these stars as bona fide members of the cluster based on their observed properties. We also include $(U-B)$ photometry in the table from FS80. In addition, the proper motion information was extracted from the Tycho-2 catalog (Høg et al., 2000) with radial velocities from González & Lapasset (2002) and Mermilliod et al. (2008).

In Figure 16 we provide several different plots illustrating our membership selection criteria. In the top two panels we use the kinematic information from Table 7 to isolate members from non-members. Specifically, we consider a star to be a member of NGC 3532 if its proper motion is within a radius of 10 mas yr${}^{-1}$ from the cluster mean $({\mu }_{\alpha },{\mu }_{\delta })=(-10.04\pm 0.24,+4.75\pm 0.21)$ (van Leeuwen, 2009) and it has a radial velocity within $\pm 4$ km s${}^{-1}$ of the mean of $V_r=+3.4$ km s${}^{-1}$ (González & Lapasset, 2002). Based on the $\left[\right(U-B),(B-V\left)\right]$ color-color diagram and $[V,(B-V\left)\right]$ CMD in the lower panels of Figure 16, it would appear that the stars we have excluded based on their kinematic properties alone correspond mostly to those that lie far from the primary cluster sequences. As a result of this exercise, we conclude that 9 of the 14 stars in the giant region of the CMD are actual cluster members.

With a sample of giant stars that are legitimate members of the cluster, we can now move to fitting model isochrones to the photometry for NGC 3532 to derive its age. For this purpose, we employ the latest BaSTI stellar evolutionary models (Pietrinferni et al., 2004) for two reasons. First, they are among the most current available in terms of input physics and color-temperature relations and offer models that include convective core overshooting. Secondly, the BaSTI models treat all evolutionary phases, including white dwarf cooling sequences (Salaris et al., 2010); this fact proves advantageous in the next section when we will compare such models to the observed properties of white dwarfs in NGC 3532.

Based on the results presented in previous sections, we have chosen to fix the parameters for NGC 3532 at $(m-M{)}_V=8.54$, $E(B-V)=0.028$, and [Fe/H]=0.0 and explore which isochrones from the BaSTI library provide the best fit to the turnoff. In Figures 17 and 18 we compare such isochrone models, both with and without treatment of convective core overshooting, to the observed CMDs for the cluster. For the $(V-K_s)$ CMD we have transformed the $(V-K{)}_J$ colors of the BaSTI isochrones to the 2MASS system using the relations of Carpenter (2001). The overshooting models with ages of 250, 300, and 350 Myr shown in Figure 17 appear to fit the turnoff and upper main sequence of the cluster quite nicely, but they tend to lie systematically redward of the giant stars (filled circles). The non-overshooting models in Figure 18 with ages of 200, 250, and 250 Myr, on the other hand, arguably do a better job of matching the colors of the giant stars, but they lie consistently on the blueward side of the main sequence for $M_V\le 2.5$ in all three CMDs. Moreover, although not shown here, we have employed the isochrones of Girardi et al. (2002) to fit the observed CMDs and discovered that they provide virtually the same interpretation of the data as the BaSTI models.

Given that the location and shape of the giant branch is greatly influenced by the adopted convective mixing length in the model computations and color transformations, we are inclined to favor a cluster age that is derived mainly from fitting the upper main sequence and turnoff. Therefore, since the overshooting isochrone provides a better fit to the CMDs in these regions, we estimate the age of NGC 3532 to be $\sim 300$Myr.

The existence of white dwarfs in NGC 3532 has been known for quite some time. In their systematic search for white dwarf stars in young open clusters, Reimers & Koester (1989) used deep photographic observations of the cluster to identify 7 objects as candidate white dwarfs. Subsequent spectroscopic followup of these objects revealed 3 of them to be legitimate white dwarfs belonging to the cluster. Spurred by the surprising lack of cluster white dwarfs in their initial study, Koester & Reimers (1993) revisited their search by enlarging the observed area around NGC 3532. Indeed, they identified 3 additional objects as cluster white dwarfs, thus bringing the total number to 6.

More recently, Dobbie et al. (2009) presented a thorough analysis of these 6 known white dwarfs using low-resolution, high signal-to-noise spectroscopy. Their observations allowed them to derive precise temperature and surface gravity estimates by fitting spectral models to the observed Balmer line profiles. Moreover, their inclusion of $V$-band photometry of the cluster field, extending to $V\sim 20.5$, permitted a reevaluation of membership and lead to the conclusion that only four of the six white dwarfs discovered by Reimers & Koester (1989) and Koester & Reimers (1993) have distance moduli comparable to the cluster itself. Furthermore, Dobbie (2010) has identified, via spectroscopy, 3 more faint blue objects as possible white dwarfs that may belong to the cluster.

Given that our $[V,(B-V\left)\right]$ CMD for NGC 3532 in Figure 6 shows an abundance of objects at the faint blue end, it is worthwhile investigating the possibility that a large number of these may be white dwarf members of the cluster. Such an analysis will be beneficial for two reasons. First, increasing the number of known white dwarf stars in open clusters places tighter constraints not only on the masses of their progenitor stars, but also on the initial-final mass relationship. Secondly, the comparison of the location of these stars in the CMD with white dwarf cooling models allows us to derive a cluster age that is free from uncertainties in the treatment of convective core overshooting. Age estimates such as this have only been possible recently with the use of wide field observations obtained on large aperture telescopes that are able to extend faint enough to reach the end of the white dwarf cooling sequence in nearby open clusters (see, for example, the works of Kalirai 2001a, 2001b).

In Figure 19 we present an enlarged portion of the cluster $[V,(B-V\left)\right]$ CMD centered on the region where white dwarfs should reside. To single out potential cluster members, we begin by considering only those objects having $(B-V)\le 0.25$ and $V\ge 17$. As shown in the figure (denoted by dotted vertical and horizontal lines once reddening and distance have been accounted for), these limits exclude the vast majority of the field dwarf stars that contaminate the CMD below the cluster main sequence. These criteria leave us with 78 objects that have photometry of reasonably high precision (i.e., assuming the limits of $\sigma \left(mag\right)\le 0.1$). Upon visually inspecting these candidates in the cluster finding chart (c.f., Figure 1), we can immediately exclude 28 of them as false detections due to their close proximity to much brighter stars, diffraction spikes, or known defects in the CCD.

The remaining 50 objects are shown in the left-hand panel of Figure 19 as either filled or open circles with error bars denoting their photometric uncertainties. Note the prominent clump of objects lying at $(B-V{)}_0\sim -0.1$ and $M_V\sim 11.5$ in the figure. To help us further isolate more of these objects as potential cluster white dwarfs, we overplot the BaSTI cooling models for $M_{WD}=0.54M_{\odot }$ and $1.0M_{\odot }$ (Salaris et al., 2010) in the figure and exclude stars that lie outside of the region they bracket. These 32 remaining stars are shown in the right-hand panel of Figure 19 with filled circles denoting stars that have high probability of being new cluster white dwarfs while open circles shown the location of known white dwarfs in the cluster field from previous studies (Reimers & Koester, 1989; Koester & Reimers, 1993; Dobbie, 2010). Also plotted in this panel are the BaSTI white dwarf isochrones for 200, 300, 400, and 700 Myr. Clearly, the three youngest isochrones terminate at absolute magnitudes comparable to the faintest members of the clump. The 700 Myr isochrone, on the other hand, does terminate at the location of the faintest candidates in our sample, but the bright end of the same isochrone extends too far to the red from the known white dwarfs in the cluster for us to accept such a high age.

Based upon our photometric uncertainties at the faint end (approaching $\sim 0.1$ mag for stars as faint as $V\sim 20$), together with the uncertainty in our derived cluster distance modulus, we can deduce that the white dwarf cooling age for the cluster is somewhere between 200 and 400 Myr. Note that this age range corresponds nicely to the age derived when fitting the cluster turnoff when using either the overshooting or non-overshooting models. However, the quality of our photometry, combined with the paucity of white dwarfs in the faint, blue region of the NGC 3532 CMD, prevents us from placing tighter constraints on the cluster’s age using this technique. Undoubtedly, it would prove useful to obtain high-quality spectroscopic observations of our white dwarf candidates to better locate the termination of the white dwarf cooling sequence.

The impact of unresolved binary stars on a cluster CMD is commonly seen as the broadening of the main sequence towards brighter magnitudes. Indeed, it is well known that clusters containing a large number of equal-mass binary systems exhibit a secondary main sequence displaced by as much as $\sim -0.75$ mag relative to the single-star main sequence (see, for example, the CMDs for M 67 in Montgomery et al. 1993).

The existence of binary stars in NGC 3532 is most clearly evident in Figure 12 as a scattering of dots lying parallel to the cluster main sequence in our CMDs. To determine the approximate binary fraction for NGC 3532 we begin by taking the difference in $V$ magnitude ($\Delta V$) between our derived fiducial sequence and the individual stars within the range of $0.1\le (V-I_c)\le 2.9$. The resulting histogram of the number of stars as a function of $\Delta V$ is shown in the upper panel of Figure 20. While the peak located at $\Delta V=0$ corresponds to the single stars in NGC 3532, the binary population easily reveals itself as the excess in the distribution towards brighter magnitudes with the secondary peak at $\Delta V\sim -0.7$ caused by a small number of equal mass systems. Before we can derive a robust estimate for the binary fraction, however, we must compensate for the field star contribution to the histogram. This has been done by fitting a linear relationship to the distribution of bins outside the area occupied by singles and binaries (specifically, $1.0<|\Delta V|<2.0$). Once the field star contribution is removed, the resulting histogram, shown in the lower panel of Figure 20, $should$ be a reasonable representation of both the single and binary star population in NGC 3532.

Assuming that the distribution of single stars approximates a Gaussian, we have simply reflected the bins at $0.0\le \Delta V\le 0.4$ about the $\Delta V=0$ axis to obtain the dark gray area denoted in the lower panel. The remaining objects situated between 0.0 and $-1.0$ in $\Delta V$ (denoted by the light gray shaded area) should, therefore, approximate the number of binaries in the cluster. The resulting binary fraction can be obtained by simply summing the area indicated by the light gray region of the plot (447 stars) and dividing by the total area below the histogram between $-1.0\le \Delta V\le 0.5$ (1641 stars). Based on this technique, our computed binary fraction for NGC 3532 is therefore $\sim 27\%\pm 5\%$, where the error represents a combination of Poisson statistics and uncertainties associated with the removal of the field star distribution. Due to the fact, however, that a number of spectroscopic binaries show no appreciable brightening relative to the single-star main sequence (see, for example, the HR diagram for the Hyades in Fig. 20 of Perryman et al., 1998), our derived binary frequency for NGC 3532 should be treated as a lower limit.

The unprecedented depth and spatial coverage of our NGC 3532 photometry motivates us to investigate the cluster’s dynamical state via its luminosity and mass functions (LF and MF, respectively). The sample of objects considered for this endeavor is based on the collection of cluster stars that have been isolated from the field population using the photometric filtering technique described in Section 3.3. Constructing the LF for NGC 3532 is simply a matter of counting the number of main sequence stars that lie within the range of $8\le V\le 20$ using a bin size of 1 mag. To account for incompleteness in the photometry toward fainter magnitudes, we have added stars to the original CCD images in an attempt to recover them using our reduction techniques. Briefly, these artificial stars were added uniformly over several trials to the short- and long-exposure $V$-band images for fields 1, 5, 13, 20, and 25 (see Figure 1). The final completeness corrections to our luminosity function represents a combination of the results from these trials for all 5 fields. The results of this exercise imply that our photometry remains $>99\%$ complete at the bright end (i.e., $V\le 15$) and $>75\%$ complete for magnitudes as faint as $V=21$. Note that we also estimate uncertainties in these completeness corrections using the techniques described in Bolte (1989).

The final, incompleteness-corrected LF for the cluster is shown in the top panel of Figure 21 as a solid line. The error bars for denote a combination of uncertainties arising from simple counting statistics and the errors in the completeness corrections. Note that the LF for NGC 3532 exhibits a small “bump” around $4\lesssim M_V\lesssim 6$ where there is a slight overabundance of stars compared to adjacent magnitudes. This feature may be due to an imperfect removal of field stars from our photometric filtering technique. Indeed, inspection of the CMDs shown in Figure 12 reveals that the field disk population crosses over the cluster main sequence within this magnitude range. We argue, however, that the bump is largely a real feature of the LF and that the decrease in the number of stars in the $M_V=7$ magnitude bin corresponds to the so-called “Wielen dip.” This same type of depression, which has been attributed to a change in the slope of the mass-luminosity relation for stars in this magnitude range, can also be seen in the LFs for stars in the solar neighborhood (Wielen, 1974; Wielen et al., 1983; Reid et al., 2002) and other open clusters such as the Pleiades (Lee & Sung, 1995) and Praesepe (Hambly et al., 1995). To better illustrate this, as well as compare our NGC 3532 LF to other stellar populations, we have overplotted the LFs for the Pleiades (Lee & Sung, 1995) and the solar neighborhood (Reid et al., 2002) in the top panel of Figure 21 as dotted and dashed lines, respectively.

Upon integrating the LF and accounting for the handful of giant and white dwarf stars in the cluster, we obtain a cluster population of $\sim 1900$ stars. However, this estimate is predominately based on single stars and does not include the sizable population of binary stars ($\sim 27\%$) that we estimate in Section 4.5. Thus, if we account for binary systems, the total population of stars in NGC 3532 rises to $\sim 2400$.

The MF for NGC 3532 can be derived by using the slope of the mass-luminosity relation predicted from the same 300 Myr overshooting isochrone employed in Section 4.3 to fit the cluster’s main sequence. The result is shown in the bottom panel of Figure 21 and covers a range in mass from $\sim 0.2M_{\odot }$ (the limit of our photometry) to $\sim 3.0M_{\odot }$ (the main-sequence turnoff). The best-fit slope we derive for this mass range is $-1.39\pm 0.14$, which corresponds quite closely to that for the solar neighborhood ($-1.35;$ Salpeter, 1955). We argue, however, that the actual MF for NGC 3532 should be better described by a broken power law with a much shallower slope at the low-mass end (i.e. $\lesssim 2M_{\odot }$) and a steeper slope for more massive stars. Assuming this is the case, we find the best-fit values to be $-1.04\pm 0.22$ and $-2.54\pm 0.41$ for the low- and high-mass stars, respectively. Such a drastic change in slope at the two mass extremes is likely indicative of a mass segregation effect within the cluster. We note, however, that the lowest mass bins of the MF show a very flat distribution. Part of this may be due to the fact that we were forced to extrapolate the BaSTI isochrone beyond its lowest tabulated mass ($0.5M_{\odot }$) for these two bins. Moreover, the bolometric corrections used to translate the isochrone luminosity to $M_V$ could be in error by as much as 0.5 mag for such low-mass stars. The combination of these two effects lead us to doubt the reliability of the MF at the extreme low-mass end.