IMPLICATIONS FOR THE FORMATION OF BLUE STRAGGLER STARS FROM HST ULTRAVIOLET OBSERVATIONS OF NGC 188^*

Aperture photometry is carried out on redrizzled images with a pixel scale of 0025 pixel⁻¹. We extract count rates using an aperture radius of 6 pixels, or 015, using the IRAF package daophot. We calculate encircled energy fractions for this aperture size using modeled Tiny Tim point sources.⁹ We find corrected count rates by dividing the measured count rate by the encircled energy corrections of 0.83, 0.84, and 0.85 for F140LP, F150LP, and F165LP, respectively.

2.1.1. ACS Red Leak

2.1.2. Magnitude Calculation

Encircled energy-corrected and red leak-subtracted count rates are used to calculate instrumental magnitudes in the STMAG system. We convert the count rates into fluxes (erg cm⁻² s⁻¹ Å⁻¹) using the PHOTFLAM conversion factors for F140LP, F150LP, and F165LP provided in the ACS Data Handbook (Gonzaga et al. 2014). We find the count rates in F140N and F150N by differencing the corrected count rates of the long-pass filters, where F140N = (F140LP − F150LP) and F150N = (F150LP − F165LP). We calculate the flux conversion factors for F140N and F150N using synphot and the F140N and F150N flux errors by combining the flux errors of the long-pass filters in quadrature, scaled by the different exposure times. We calculate instrumental magnitudes in all bandpasses using $\mathrm{STMAG}=-2.5\;{\mathrm{log}}_{10}(\mathrm{flux})-21.1.$ The photometric errors are dominated by Poisson noise due to the low background of the ACS/SBC MAMA detector, although the signal is high enough that the error distributions are approximately symmetric for all but the faintest measurements in F140N and F150N.

The FUV information for the 19 BSSs in this study are presented in Table 2 with the WOCS ID, NUV magnitude, and 5-band FUV magnitudes (F140LP, F150LP, F165LP, F140N, and F150N). A F140N magnitude is only reported for those sources with a higher count rate in F140LP than F150LP. Magnitudes given in italics are less than 3σ detections.

Table 2.  HST FUV Photometry of NGC 188 BSS Population

WOCS ID	NUVa	F165LP	F150LP	F140LP	F150Nb	F140Nb
451	18.38 ± 0.04	18.94 ± 0.04	20.06 ± 0.03	20.54 ± 0.03	${22.2}_{-0.8}^{+0.5}$	23.2+0.7−2.0
1366	20.6 ± 0.2	20.63 ± 0.07	21.83 ± 0.05	22.62 ± 0.06	25.5+1.7−1.7	...
1888	19.39 ± 0.07	19.78 ± 0.05	20.72 ± 0.04	21.37 ± 0.04	${21.9}_{-0.4}^{+0.3}$	...
2679	19.07 ± 0.06	19.22 ± 0.04	20.21 ± 0.03	20.67 ± 0.03	${21.5}_{-0.3}^{+0.3}$	22.7+0.4−0.8
4230	19.49 ± 0.07	19.38 ± 0.04	20.33 ± 0.03	20.77 ± 0.03	${21.5}_{-0.3}^{+0.2}$	22.6+0.4−0.6
4290	19.02 ± 0.06	19.23 ± 0.04	20.32 ± 0.03	20.90 ± 0.03	${22.3}_{-0.7}^{+0.4}$	...
4306	18.00 ± 0.04	18.23 ± 0.03	19.29 ± 0.02	19.81 ± 0.02	${20.9}_{-0.3}^{+0.2}$	...
4348	18.59 ± 0.05	18.64 ± 0.03	19.55 ± 0.02	19.96 ± 0.02	${20.6}_{-0.2}^{+0.2}$	${21.4}_{-0.3}^{+0.2}$
4540	18.17 ± 0.04	17.96 ± 0.02	18.58 ± 0.01	18.80 ± 0.01	${19.07}_{-0.07}^{+0.06}$	${19.29}_{-0.05}^{+0.05}$
4581	18.47 ± 0.04	18.74 ± 0.03	19.82 ± 0.02	20.41 ± 0.03	${21.6}_{-0.5}^{+0.3}$	...
4589	19.77 ± 0.09	20.18 ± 0.06	21.34 ± 0.05	21.86 ± 0.05	24.1+1.0−1.0	...
4970	19.63 ± 0.08	19.95 ± 0.06	20.96 ± 0.04	21.53 ± 0.05	${22.4}_{-0.5}^{+0.4}$	...
5020	18.09 ± 0.04	18.19 ± 0.03	19.21 ± 0.02	19.71 ± 0.02	${20.7}_{-0.2}^{+0.2}$	22.7+0.6−1.6
5325	19.78 ± 0.09	19.96 ± 0.05	20.98 ± 0.04	21.63 ± 0.04	${22.5}_{-0.5}^{+0.4}$	...
5350	17.63 ± 0.03	17.50 ± 0.02	18.49 ± 0.01	18.97 ± 0.01	${19.9}_{-0.1}^{+0.1}$	21.4+0.3−0.4
5379	19.87 ± 0.09	19.13 ± 0.04	19.23 ± 0.02	19.26 ± 0.02	${19.27}_{-0.06}^{+0.05}$	${19.31}_{-0.04}^{+0.04}$
5434	19.00 ± 0.06	19.36 ± 0.04	20.53 ± 0.03	21.13 ± 0.04	23.4+0.9−0.9	...
5671	18.80 ± 0.05	19.09 ± 0.04	20.17 ± 0.02	20.73 ± 0.03	${22.0}_{-0.6}^{+0.4}$	...
8104	19.69 ± 0.02c	21.27 ± 0.11	22.15 ± 0.07	23.01 ± 0.09	${23.1}_{-0.6}^{+0.4}$	...

Notes.

^aGALEX NUV magnitude (AB system), except where noted (Martin et al. 2005). ^bMagnitudes in italics are less than 3σ detections. ^cWFC3 F218W instrumental magnitude (this study).

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Accurate modeling of the BSS population is a key factor in determining the amount of expected FUV emission. We take special care to match modeled and observed near-UV (NUV) photometry (see Section 3.2). We use GALEX NUV photometry for this purpose (Martin et al. 2005). However, one BSS in NGC 188, WOCS 8104, is not detected in GALEX. We obtained NUV photometry for WOCS 8104 using the HST WFC3 in F218W. The observation occurred on 2012 June 19 as part of this program, with a total exposure time of 669 s. We use daophot for source detection and aperture photometry, and calculate the instrumental F218W magnitude for WOCS 8104 (given in Table 2).

Identifying WD companions relies on detecting a FUV excess above the emission expected for a BSS alone. We first compare the observed photometry with modeled BSS photometry for the entire BSS population. This approach best demonstrates the general trend of FUV emission for the type of BSSs found in NGC 188 in comparison to the FUV emission for potential BSS+WD pairs. It also clearly reveals those BSSs with highly significant FUV excesses indicative of hot (temperatures greater than 12,000 K) WD companions.

In Figure 1 we plot a FUV color–magnitude diagram (CMD) for the BSSs in our study along with photometric models of the total BSS population and BSS+WD pairings (described in detail in the next two sections). The observed BSS photometry is shown with black points and 1σ error bars. Since we use F150N–F165LP as our color diagnostic we exclude any BSS with less than a 3σ detection in F150N in Figure 1 and in all subsequent analyses. This removes WOCS 4589 and 5434, both binary stars, and WOCS 1366, a non-velocity variable star. The lack of a F150N detection in these three sources is consistent within 3σ for each of the BSSs given their faint NUV magnitudes.

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The remaining BSS sample used for further analysis includes 16 sources: 13 SB1 binaries and three non-velocity variable stars. The only three sources also having more than a 3σ detection in F140N (WOCS 4540, 4348, and 5379) were presented in Gosnell et al. (2014), and are included in this sample of 16 BSSs.

We calculate the FUV emission of the overall NGC 188 BSS population using a population synthesis approach including a large number of model spectra spanning the entire range of observed BSS temperatures and luminosities. The modeling is done through a three step process: (1) we establish the ranges of physical parameters that define the NGC 188 BSS population, (2) we create a large sample of model spectra constrained by those ranges, and (3) we calculate synthetic photometry for the sample of model spectra.

First, we define the range of parameters for the model spectra using the known temperatures and luminosities of the NGC 188 BSSs.

The BSS temperatures are determined using metallicity-dependent 4- or 5-band color-to-T_eff conversions from Ramírez & Meléndez (2005). The colors used are B − V, V − J, V − H, and V − K (Sarajedini et al. 1999; Skrutskie et al. 2006). V − I is also used when I photometry is available. The resulting temperatures and errors for the non-velocity variable and SB1 BSSs are given in Table 1. The errors given include the error in each color measurement and the systematic error in the temperature calculation as given in Ramírez & Meléndez (2005).

We set the luminosity range based on GALEX NUV magnitudes for the BSSs, which vary from 20.6 M_NUV,AB to 18.0 M_NUV,AB (Martin et al. 2005). As GALEX NUV photometry is the bluest luminosity information available it provides the most accurate normalization for estimating the FUV flux.

Next, we create 50,000 individual model spectra that, together, constitute the BSS-only model population. We create smooth probability density functions (PDFs) modeled after the observed shapes of BSS temperature and NUV luminosity cumulative distribution functions (CDFs). We Monte Carlo sample the PDFs to determine the parameters used for each model spectrum. There is only a weak correlation between temperature and luminosity in the NGC 188 BSS population (r = −0.2), so the two parameters are sampled independently. For each sampling of the PDFs we calculate a model spectrum by interpolating between reddened UVBLUE spectra with temperatures of 6000, 6500, 6750, and 7000 K to match the sampled temperature (E(B − V) = 0.09, [Fe/H] = 0, log(g) = 3.5; Sarajedini et al. 1999; Rodríguez-Merino et al. 2005). We then normalize the interpolated spectrum to match the sampled NUV luminosity. The interpolation and normalization steps are carried out on all 50,000 PDF samples. As a result, we have a BSS-only model composed of a large set of model spectra spanning the range of physical parameters observed in the NGC 188 population.

Finally, after creating the BSS-only model we calculate the expected FUV CMD for the entire model distribution. We convolve each model spectrum with synphot F140LP, F150LP, and F165LP throughput curves to obtain count rates. Since the observed data are red leak-corrected the throughput curves do not include a red leak component. We add Poisson noise to the convolved count rates to mimic photometric errors. The count rates and flux errors in F140N and F150N are calculated in the same manner as the observations. We calculate magnitudes in F140LP, F150LP, F165LP, F140N, and F150N for each of the 50,000 modeled spectra.

We compare the modeled BSS-only FUV photometry with the observed BSSs in Figure 1. The two-dimensional density histogram of modeled photometry is represented by the gray contours encompassing 68%, 95.45%, and 99.73% of the distribution, as labeled. We restrict the density contours to those modeled sources that meet or exceed the same 3σ F150N detection threshold we apply to the observations.¹⁰

In order to demonstrate how the presence of a WD companion changes the expected FUV emission we create representative pairs of BSS+WD binaries. Keeping the BSS luminosity constant at a GALEX NUV magnitude of 18.0 to mimic the brightest BSS in the NUV, we add together the spectra of BSSs between 5750 and 6750 K (Rodríguez-Merino et al. 2005) with WDs of increasing temperature, ranging from 11,000 to 18,000 K. We use WD spectra with a log(g) = 7.75 (Wood 1995, P. Bergeron 2015, private communication). We calculate the synthetic photometry for each BSS+WD pair using the same method as for the BSS-only distribution.

The synthetic photometric results for the BSS+WD pairs are shown in Figure 1 as dotted lines. The rainbow colors indicate the WD temperature, as shown with the color bar. The length of each line shows the photometry of that particular WD temperature with a BSS of 5750 K on the left (blue end) extending to a BSS of 6750 K on the right (red end). Since a higher temperature BSS contributes more light in F165LP it results in an overall redder color. The position of the rainbow tracks changes slightly with the choice of BSS luminosity, but a single BSS luminosity is sufficient to illustrate the general photometric trends for BSS+WD binaries.

Visual analysis of Figure 1 shows there are four sources with obvious FUV excesses: WOCS 4348, WOCS 4540, WOCS 5350, and WOCS 5379. These sources are well separated from the BSS-only distribution and their photometry is consistent with the FUV excesses expected for BSS+WD binaries.

We fit BSS+WD spectra to each of the four FUV excess sources individually to estimate the companion WD temperature. In Figure 2 we show the F140N, F150N, F165LP, and GALEX NUV photometric data for these sources along with the best-fit BSS+WD spectrum found through weighted least squares minimization. A similar figure for WOCS 4348, 4540, and 5379 is shown in Gosnell et al. (2014), although here we employ an improved method of finding the best-fit WD temperature. The grid of WD models (P. Bergeron 2015, private communication) has a temperature resolution of 1000 K. In Gosnell et al. (2014) we restricted our search to grid temperature values while in this work we interpolate between temperatures. Given the uncertainty in the best-fit WD temperatures, the results here and in Gosnell et al. (2014) are consistent. In each case the mean temperature BSS spectrum is shown in orange, the WD spectrum in blue, and the combined spectrum in gray. The synthetic photometry of the combined spectrum is shown with the light gray boxes. The horizontal extent of the boxes shows the filter width while the vertical extent shows the range in photometry, including the BSS and WD temperature uncertainties. The combined spectrum is required to fit the GALEX NUV photometry. The narrowband effective throughputs are shown in the upper left plot as a guide. The observed photometry is shown in black circles at the reference wavelength for each bandpass, and observed 3σ photometric errors are shown when they exceed the symbol size. Measurements in F140N that are less than 3σ are shown with an open circle. The best-fit spectra are also checked for consistency with U-band photometry, when available (Sarajedini et al. 1999).

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We use the estimated temperature and uncertainty from Figure 2 to find the range of WD ages for each source (Holberg & Bergeron 2006; Tremblay et al. 2011). In Table 3 we list the best-fit WD temperature estimates and the age range for each of the four BSSs with a hot WD companion, along with the observed binary period and eccentricity (Geller et al. 2009). Of these BSSs, the maximum age is 230 ± 30 Myr for WOCS 4348, so all four BSSs formed very recently in comparison to the 7 Gyr age of NGC 188.

There are 12 remaining BSSs (nine binaries, three non-velocity variables) within the sample of F150N sources that lack a significant (greater than 3σ) FUV excess. The possibility remains that some of these BSSs have a cool WD companion between 11,000 and 12,000 K. At these temperatures the WD emission would shift the observed photometry to be slightly bluer and brighter than the expected emission for that particular BSS. We cannot detect any WDs with temperatures below 11,000 K. Such "cold" WDs would not have enough FUV emission on their own to exceed the expected emission for any BSS in NGC 188.

We investigate whether any of the 12 FUV-faint BSSs contain a cool (11,000–12,000 K) WD companion by modeling the expected photometry for each BSS individually. Following a similar methodology as in Section 3.2, for each individual FUV-faint BSS we do a Monte Carlo sampling of the temperature range given in Table 1 and luminosity range, as constrained by GALEX NUV photometry for that BSS. The resulting sample is synthetically observed to create a two-dimensional density distribution of expected FUV emission in F150N and F150N–F165LP for that particular BSS. We then find the model density value with the same color and magnitude as the BSS observation, and adopt that value as the probability the BSS is consistent with the expected FUV emission of a BSS without a WD companion (P_BSS). The probability that the BSS has a WD companion is then ${P}_{\mathrm{WD}}=1-{P}_{\mathrm{BSS}}.$

The modeled photometry for each BSS is highly dependent on BSS temperature, which is more uncertain than the NUV luminosity used to normalize the model spectra. We compared the temperatures used here with recently calculated temperatures found from Hα line-profile fits (K. Milliman 2015, private communication). Many BSS temperatures are consistent across the methods, but WOCS 4230 and 4581 have temperature differences of approximately 200 K. Additionally, the temperatures of the non-velocity variable BSSs WOCS 4306 and 5020 vary by 200–300 K. If the actual BSS temperature is different from the modeled BSS temperature the observed BSS photometry could mimic the presence of a cool WD companion. In order to account for potential offsets in the known temperatures, and avoid false identification of a WD companion, we also model each BSS with temperature ranges shifted by ±200 K and adopt the highest P_BSS, or lowest P_WD, for each BSS.

In Table 4 we list each FUV-faint BSS along with the probability that the source has a cool WD companion between 11,000 and 12,000 K. There are three BSS with probabilities greater than 2σ: WOCS 1888 (P_WD = 96%), WOCS 2679 (P_WD = 97%), and WOCS 4230 (P_WD = 99%). The photometry for WOCS 1888, 2679, and 4230 are best fit with BSS+WD composite spectra with WD temperatures between 11 and 12,000 K, as shown in Figure 3. The best-fit temperatures and corresponding ages for these sources, along with binary orbit parameters, are given in Table 5. There is a 2% chance that one of the 12 FUV-faint BSSs has a probability equal to or greater than 96% due to random fluctuations alone, but only a 0.03% chance that all three are due to random fluctuations. We assume that these three BSSs have WD companions and formed through mass transfer between 310 and 360 Myr ago (Holberg & Bergeron 2006; Tremblay et al. 2011).

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For the remaining FUV-faint BSSs, the fit between the observed and modeled photometry is not improved by adding a cool WD of any temperature greater than 11,000 K. The photometry of these sources is consistent with a BSS-only synthetic spectrum, and these sources do not have WD detections. The best fit spectra for the nine remaining BSSs with the corresponding HST and GALEX photometric points are shown in Figure 4.

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Previous work predicted that the majority of the NGC 188 binary BSSs formed through mass transfer (Mathieu & Geller 2009; Geller & Mathieu 2011). The seven WDs detected in this work indicate that more than half of the SB1 BSSs formed through mass transfer. Older mass transfer-formed BSSs have cold WD companions that cannot be detected with this photometric method, so the total number of mass transfer-formed BSSs is greater than seven. Therefore, our results confirm previous predictions that the majority of binary BSSs in NGC 188 formed through mass transfer.

We can further constrain the total frequency of mass-transfer formation by considering how many BSSs may form through other formation mechanisms.

We do not expect any of the non-velocity variable BSSs to form through Case B or C Roche lobe overflow mass transfer. As non-velocity variable objects, these BSSs are either single stars or binary stars with extremely long periods greater than 10,000 days. Case C mass transfer systems have final orbital periods less than about 3000 days (Chen & Han 2008), which is well within the RV binary detection limit in NGC 188 (Geller et al. 2009). (We note that there is a small possibility for a non-velocity variable source to be in a face-on binary that is undetectable using radial velocity methods. Incompleteness studies indicate there is a 24% chance that one of the non-velocity variable BSSs in NGC 188 is in a binary with a period less than 10⁴ days but is not detected due to inclination; Geller & Mathieu 2012.) We propose that the non-velocity variable BSSs formed through other mechanisms, such as collisions or mergers from contact binaries.

Is it possible for any of the remaining eight SB1 BSS binaries to form through non-mass transfer processes? It is unlikely that the SB1 BSSs formed through collisions. BSSs formed through collisions can be in binaries, but the orbital periods tend to be very long and beyond RV sensitivity limits (Geller et al. 2013). In addition, given the observed statistical secondary mass distribution the SB1 BSS secondary masses are between 0.2 and 0.8 M_⊙ (Geller & Mathieu 2011), with a strong peak at 0.5 M_⊙. Models of collisionally formed BSS binaries result in more massive companions than the observed secondary mass distribution allows (Geller & Mathieu 2011).

Some SB1 BSSs may have formed through Kozai-induced mergers in a hierarchical triple (Perets & Fabrycky 2009; Naoz & Fabrycky 2014). The resulting period distribution would be similar to that observed in the NGC 188 BSS binaries, but the secondary masses would differ (Perets 2014). The original tertiary, now the BSS secondary, would be drawn from the cluster initial-mass function (Kroupa 2001).

Without strong observational constraints on the primordial triple population in clusters it is difficult to make confident predictions about the number of Kozai-formed BSSs. Nonetheless, Geller et al. (2013) put limits on Kozai-BSS formation with an N-body model of NGC 188 containing 200 primordial triples—essentially giving every primordial binary with periods between 2 and 50 days a tertiary companion. This model creates an additional 1–2 BSSs at the age of NGC 188, but most of the BSSs result from collisions involving triple systems, not from the Kozai mechanism itself. Approximately 0.5 BSSs per model are created through the Kozai mechanism. However, the Geller et al. (2013) Kozai model prescriptions are possibly inaccurate such that the Kozai origin could be more prevalent than current N-body models suggest. We estimate that one of the BSS SB1 binaries may have formed through a merger in a hierarchical triple system.

We currently have no specific hypothesis for the formation mechanism of the two SB2 short-period BSS binaries. Case B and C mass transfer cannot result in a short-period BSS binary with a mass ratio near unity, as seen in the case of WOCS 5078 and 7782. N-body models fail to create similar systems, even with populations of collisionally formed BSSs (Hurley et al. 2005; Geller et al. 2013). These BSSs may have formed through any of the potential formation pathways and exchanged into their current binaries, but there is no way to know for certain. As they have more complex origins we exclude them from the following discussion of broad BSS population characteristics.

In summary, we detect WD companions to 7 of the 15 SB1 BSSs, establishing a lower limit of the mass-transfer formation frequency of 33%. Given the binary properties and inferred companion masses of the remaining SB1 BSSs in NGC 188, our investigation of the currently hypothesized formation mechanisms suggests that 14 SB1 BSSs were formed through mass transfer. Thus, 14 of the 21 BSSs likely formed through mass transfer, for a total BSS mass-transfer formation frequency in NGC 188 of approximately 67%.

Now that other BSS formation scenarios have been considered we can make an appropriate comparison between our empirical results and the theoretical results of the Geller et al. (2013) N-body model of NGC 188. Geller et al. (2013) present 20 full-lifetime N-body realizations of NGC 188, with complete tracking of the binary populations and dynamical encounters. The models create mass transfer-formed BSSs, and retain information on when the mass transfer ended in each case.

With seven WD detections we can directly compare the empirical and theoretical age distributions for mass transfer-formed BSSs. We create the N-body age distribution using all mass transfer-formed BSSs observable between 6.0 and 7.5 Gyr (Geller et al. 2013), and convert the time since mass transfer ended to a WD temperature (Holberg & Bergeron 2006; Tremblay et al. 2011). The resulting CDF is shown in Figure 6 as a solid black line. The light gray lines are the result of Monte Carlo bootstrap resampling of the N-body CDF, meant to illustrate the inherent error in the N-body age distribution.

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We compare the N-body age distribution with the empirical age distribution, shown in Figure 6 as blue squares with 500 K error bars. A KS test shows the empirical distribution and theoretical distribution are consistent with being drawn from the same parent distribution (p = 0.97). The overall shape of the N-body age distribution is fully consistent with the BSS ages detected in this study.

Adopting a mass-transfer formation frequency of 67% for the BSS population implies there are five BSSs in NGC 188 that formed through other formation mechanisms, such as collisions or the Kozai mechanism, in addition to the two short-period SB2 systems. This number is consistent with the number of collisionally formed BSSs seen in the Geller et al. (2013) N-body model of NGC 188.

The fraction of collisionally formed BSSs in the Geller et al. (2013) study is quite different than observed, however, because the total number of BSSs created is too low. The model results have an average of six BSSs in NGC 188 at 7 Gyr, one of which formed from mass transfer. A separate N-body study of the open cluster M67 also fails to create a high fraction of mass transfer-formed BSSs as observed in NGC 188 (Hurley et al. 2005), although the progenitor binary period distributions used were not realistic.

The lack of BSSs in N-body models (Geller et al. 2013) may be attributed to an incomplete description of mass transfer processes in the binary population synthesis models used within the N-body code. Geller et al. (2013) utilize the NBODY6 code (Aarseth 2003), which relies similar algorithms to those implemented in the Binary Stellar Evolution (BSE) code of Hurley et al. (2002) to track binary evolution.

Although there are too few BSSs, Geller et al. (2013) note that the model produces a large number of long-period post-common envelope (CE) binaries that are not observed at such frequency in NGC 188 or the field. The mass transfer parameterization in BSE may need to be adjusted such that these sources go through stable Roche lobe overflow rather than CE. Converting the post-CE binaries to BSS+WD binaries would bring the total mass transfer BSS population to 10 systems at 7 Gyr, for a mass-transfer formation frequency of 67%. This matches the inferred mass-transfer formation frequency of 67% measured in this study for the total NGC 188 BSS population.

However, if the parameterization of mass transfer is amended in BSE the consistency of the age distributions from the N-body model and these results should be revisited.

Binary population synthesis models are important tools for theoretical astronomy that allow full-N models of rich open clusters to run in a reasonable amount of time. We hope that observations such as these help constrain the parameterizations used so that population synthesis models can be as accurate as possible.