Main-Sequence Binary Stars in the Core of NGC 6397

Main-Sequence Binary Stars in the Core of NGC 6397

A. S. Bolton, A. M. Cool (San Francisco State University), J. Anderson (U. C. Berkeley)

introduction | data | field star removal | candidate selection | model fitting | results | caveats | discussion | summary and conclusions | references

What we're looking for, and why

The presence and nature of binary star populations within globular star clusters is of great interest. Extensive theoretical and computational research has established that whatever binaries may be present in a given cluster will play a central role in the overall gravitational dynamics of the system. Globular clusters also offer great promise for the study of binary stars (and halo binaries in particular) as such, with the possibility of more uniform samples of binaries than are available in the field.

Previous observational studies of detached binaries in globular clusters have generally fallen into one of three categories: radial velocity surveys of giant stars, searches for eclipsing binaries, and analyses of the location of stars in cluster color-magnitude diagrams (CMD's) (see Hut et al. (1992) and Pryor et al. (1996) for reviews, and Romani and Weinberg (1991) for a detailed analysis of the CMD method). The present study falls into the final category. The CMD method has the advantage of being equally sensitive to any orbital period, and is thus complementary to methods that rely on observing orbital variations.

Here we focus on the isolation of main-sequence/main-sequence binary system candidates using HST WFPC2 data from a central field of the cluster NGC 6397 (Figures 1, 2). Our preliminary results suggest a scarcity of binaries relative to the results of most other studies of globular clusters.

(Note: all figures in this document are linked to full-sized versions.)


Figure 1: 15' x 15' Sky Survey image of globular cluster NGC 6397	Figure 2: HST WFPC2 field with cluster center in PC chip

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Data

HST WFPC2 data sets used
Set	Filter	Exposures	Total Time	Usage
Epoch 2	V₅₅₅	24	960s	Position data for proper motion analysis (all) and binary candidate photometry (V and I)
	I₈₁₄	24	960s
	R₆₇₅	38	1520s
	H-alpha	30	23,900s
Epoch 1	B₄₃₉	20	8400s	Position data for proper motion analysis
	V₅₅₅	6	240s
	I₈₁₄	2	80s

Note: the astrometric analysis was carried out on composite images obtained by averaging co-aligned exposures in each filter: 12 to 15 composite images per filter for the epoch 2 data and 1 or 2 composite images per filter for the epoch 1 data.

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Field star removal by proper motion analysis

The first step in the search for binary candidates was to eliminate field stars from the sample. This was done using the "least-squares linear transformation" method of Anderson and King (2000; also see King et al. 1998).

First, the position data for all stars was corrected for geometric distortion using the method prescribed by Holtzman et al. (1995). Then, the expected position of each star in the epoch 2 images was determined by transforming its epoch 1 position according to the most general linear transformation, minimizing the total square deviation of the transformed positions of its 25 nearest neighbor stars from their actual epoch 2 positions. The difference between the expected and observed positions of the star in the epoch 2 images was used to distinguish cluster stars (small difference) from field stars (larger difference) to sub-PC-pixel accuracy. A distinction between the two populations is clearly visible (see Figure 3). Stars with a total displacement of 0.4 PC pixels (about 18 mas) or greater relative to the average cluster displacement were taken to be field stars and removed from the sample.

Figure 4 shows the V vs. V - I color-magnitude diagram for the original sample as it divides into cluster and field star populations. Notice that the binary sequence (above and to the right of the main sequence), previously somewhat obscured by numerous field stars, is now much more distinct.


Figure 3: Difference between projected and observed epoch 2 star positions (stars from all four WFPC2 chips)	Figure 4: Separation of cluster/field stars by proper motion (reload page to restore figure animation)

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Binary candidate selection based on location in CMD

Those stars taken to be cluster stars were analyzed using an algorithm designed to identify the main-sequence ridgeline (MSRL) for the cluster. We divided the stars into bins of 0.25 magnitude in V and determined the average V - I color for each bin successively. We also determined the number of standard deviations in color outside of which one would statistically expect to find less than 0.5 star out of the entire sample, assuming Gaussian error in color. Stars falling outside of this limit were excluded from the sample for the purposes of determining the average bin color and the procedure was repeated until the number of stars per bin converged for each bin.

This procedure also gave us our initial main-sequence binary (MSB) candidates: those stars falling beyond the limiting number of standard deviations in color to the red side of the MSRL. Any binary star composed of two cluster main-sequence stars will necessarily fall to the red of the MSRL in the CMD. Considering the case of equal mass component stars, the resulting binary system would be unchanged in color but brightened by about 0.75 in magnitude. Given the slope of the main sequence, this "upward" shift would place such binaries to the right (red) side of the MSRL.

Stars identified as binary candidates are marked with triangles in Figure 5.

Figure 5: CMD showing main-sequence ridgeline and main-sequence binary candidate stars

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Fitting of binary candidates to models

The ridgefinding algorithm was also used to determine a MSRL for the outer field 6397 CMD of King et al. (1998) (previously purged of field stars by the same method as above) down to approximately V = 27.3, much fainter than the value of approximately 23 to which the inner field MSRL could be determined. This outer field MSRL was then used to create a grid of model MSB's with grid spacing of about 2 x 10^-3 magnitude in V. Candidate stars were fit to these model binaries by associating with each candidate the model binary with minimum square difference in V and I from the magnitudes of that star. Corresponding component masses were assigned by converting model star component magnitudes using mass-luminosity relations of Alexander et al. (1997) and the values (m - M)_V = 12.6, E(V - I) = 0.19. Error bars were obtained by fitting to two "error stars" at ± 1 standard deviation in color on either side of each candidate star.

Figure 6 shows several model star sequences of distinct mass ratio q = M₂ / M₁ as they fall in the cluster CMD.

Figure 6: Various model binary sequences

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Results: nature of the binary population

Using the CMD cleaned of field stars, we directly identify 81 candidate MS binaries with mass ratios as low as approximately q = 0.4. Considering these 81 observed candidates along with a set of 2437 comparable non-candidates (other stars in the sample within the approximate range 17 < V < 21 spanned by the candidates), we place an upper limit on the MS binary fraction of about 3% for q > about 0.45. (Some fraction of these will be chance coincidences, which will only make the fraction lower; see below).

We measure the distribution in M₁ and q for the 81 MS binary candidates, for primary masses in the approximate range M₁ = 0.46 to 0.82. The binaries appear to uniformly populate the region in M₁ vs q to which we are sensitive (Figure 7).

We extract a distribution in q for the 81 MS binary candidates. Histograms of this distribution can be seen in Figure 8, first binned by 0.05 in q over the range 0.35 < q < 1.0, then by 0.1 over 0.4 < q < 1.0. Numbers of stars per bin for q < 0.6 were weighted to compensate for decreased range of sensitivity in M₁. Error estimates are based on root-N statistics for each bin. The distribution in q is quite flat for q = 0.4 to 1.

If we assume that the q distribution remains flat below q = 0.4, we can place an upper limit on the total MS binary fraction of 5% to 7%.

Figure 9 shows a cumulative histogram of the radial distributions of binary candidates and comparable non-candidates. The candidate binaries appear to be centrally concentrated within the WFPC2 field. A Kolmogorov-Smirnov test of the maximum difference between these two distributions gives a 0.01 chance that the two are drawn from the same parent population. As there are actually fewer stars in the PC field (cluster center) than in the adjacent WF fields, this result could not be obtained if all the binary candidates were due to chance coincidences. Instead, it suggests that a significant fraction of the candidates are likely to be true binaries, and that these binaries are centrally concentrated.


Figure 7: Distribution of binary candidates in M₁ and q, with error bars	Figure 8: Distribution of binary candidates in mass ratio

Figure 9: Radial distribution of binary candidates and comparable non-candidates

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Caveats

An important issue in a study of this kind is the incidence of chance optical superpositions of gravitationally unassociated stars, which will mimic true binaries in the CMD. While the point-spread function fitting photometry we have used in the reduction of these data is less susceptible to producing such superpositions than aperture photometry, it is almost certain that some of our binary candidate stars are in fact not true binaries. A very crude estimate suggests that roughly 1/3 to 2/3 of the candidates could potentially be chance coincidences. The binary fractions stated above should thus rightly be regarded as upper limits.

We will be carrying out detailed artificial star tests to quantify the rate of chance superpositions. These tests will also be important in assessing the impact of chance superpositions on the mass ratio distribution results, which will be biased by the presence of false binaries.

Other possible sources of error are uncertainties in the adopted distance modulus (and thus the mass-luminosity conversion) and in the MSRL-finding procedure. A more thorough exploration of the effects of photometric errors will also be undertaken in the next phase of this project.

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Discussion

Our upper limit of 5% to 7% on the total binary fraction in NGC 6397 is low relative to most previously published results for other clusters. Most notably, in the only other study of MS binaries in the core of a dense cluster (that we know of), Rubenstein and Bailyn (1997) have estimated the binary frequency in the core of NGC 6752 to be in the range 15% to 38%. This is strong evidence of intrinsic differences in globular cluster binary populations.

Most other studies also report higher main sequence binary fractions than those in NGC 6397. Bolte (1992) has reported a value of 10% for the binary fraction with q > 0.7 in NGC 288 (a much less concentrated cluster), implying an even higher overall binary fraction. Based on a distribution in q determined from the field-star radial-velocity study of Duquennoy and Mayor (1991) and on radial-velocity data for 392 stars from several clusters, Pryor et al. (1996) estimate that about 10% of globular cluster stars should appear in the CMD as binary candidates 0.2 mag or greater above the main sequence (corresponding to q > 0.3 or 0.4, approximately). Only the values reported by Romani and Weinberg (1991) appear comparable to ours for NGC 6397: they derive upper limits on the binary fractions in outer fields of M92 and M30 of about 9% and 4%, respectively (all q values included).

Sorting out the causes of these underlying variations would clearly be aided by a larger sample of clusters and additional information about the radial distribution of the binaries within the clusters.

The distribution in mass ratio that we find for the MS binaries in NGC 6397 appears quite flat. We do not see evidence of a steady increase in the distribution toward lower q as seen by Duquennoy and Mayor (1991) and Trimble (1990) for field binaries. However, as noted above, the effects of possible chance superpositions have yet to be quantified.

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Summary and Conclusions

We have isolated 81 main-sequence binary star candidates in the central region of the globular cluster NGC 6397 based on proper-motion membership and their locations in a CMD. By comparing these stars to similarly bright single stars, we derive an upper limit of approximately 3% on the binary fraction for mass ratios of q > about 0.45.
We have measured the distribution of the 81 binary candidates in primary mass (M₁) and mass ratio (q = M₂ / M₁). The candidates appear uniformly distributed within the ranges to which the study is sensitive (M₁ = about 0.46 to 0.82 and q = about 0.4 to 1.0).
The distribution of mass ratios among the 81 binary candidates appears quite flat, i.e., roughly equal numbers of stars fall in bins of width 0.05 or 0.1 in the range q = 0.4 to 1.0.
Extrapolating the above results to lower mass ratios, and assuming the the mass ratio distribution is flat throughout, we place an upper limit of 5% to 7% on the total main-sequence binary fraction in NGC 6397.
The candidate binaries are more concentrated toward the center of the cluster that other stars of similar brightness, at a confidence level of 99%. This behaviour cannot be explained as a result of chance coincidences, as the total number of stars in the PC chip (centered on the cluster) is lower than in any of the adjacent WF chips.

A significant remaining uncertainty concerns the rate of chance superpositions in the WFPC2 images of the cluster. We are undertaking detailed artificial star experiments to determine what fraction of the binary candidates are likely to be chance superpositions. These tests are also needed to assess the effect of chance coincidences on the conclusions regarding the distribution of mass ratios.

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References

Alexander, D. R., Brocato, E., Cassisi, S., Castellani, V., Ciacio, F., & degl'Innocenti, S. 1997, A & A, 317, 90

Anderson, J., & King, I. R. 2000, (in preparation)

Bolte, M. 1992, ApJSS, 82, 145

Duquennoy, A., & Mayor, M. 1991, A & A, 248, 485

Holtzman, J., et al. 1995, PASP, 107, 156

Hut, P., et al. 1992, PASP, 104, 981

King, I. R., Anderson, J., Cool, A. M., & Piotto, G. 1998, ApJL, 492, L37

Pryor, C., et al. 1996, in IAU Symp. No. 174, Dynamical Evolution of Star Clusters: Confrontation of Theory and Observations, ed. P. Hut and J. Makino (Dordrecht: Kluwer), 193

Romani, R. W., & Weinberg, M. D. 1991, ApJ, 372, 487

Rubenstein, E. P., & Bailyn, C. D. 1997, ApJ, 474, 701

Trimble, V. 1990, Mon. Not. RAS, 242, 79

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To express an interest in the preprint of a full article on this project (due sometime in summer 2000), please send an e-mail to that effect to abolton@stars.sfsu.edu

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