Orbital Parameters and Binary Properties of 37 FGK Stars in the Cores of Open Clusters NGC 2516 and NGC 2422

B16 obtained multiepoch spectroscopy in 2013 and 2014 for all photometric F5V-K5V members (N∼125 each) in the core half degree of the open clusters NGC 2516 and NGC 2422. They obtained ∼12 epochs (∼2 hr exposures) in NGC 2516 and ∼10 epochs (∼2.5 hr exposures) in NGC 2422, providing a temporal baseline of ∼1.1 yr. B16 used Michigan/Magellan Fiber System (M2FS, Mateo et al. 2012), a multiplexed high-resolution optical fiber-fed spectrograph—deployed at the Magellan/Clay 6.5 m telescope at Las Campanas Observatory—in its cross-dispersed echelle mode for order 49 (7160–7290 Å) to obtain a total of ∼2700 spectra. B16 selected order 49 for its combination of stellar and telluric absorption lines to provide a simultaneous RV and wavelength reference. Observations had a median R ∼ 50, 000 and a mean per-pixel signal-to-noise ratio (S/N) of 55. This configuration has a limiting RV precision of 25 m s⁻¹, with a median per-epoch precision of 80 m s⁻¹.

Here we incorporate an additional epoch for 36 stars in NGC 2516 obtained from a 3 hr exposure taken in February 2016 with a median S/N of ∼107, extending 33 of our targets to a baseline of ∼3.25 yr. This epoch benefits from a newer M2FS filter tailored to the measured optical blaze, significantly improving throughput albeit with a slightly different wavelength coverage of 7180–7360 Å. We reduce these spectra following B16.

B18 fit model stellar spectra to the data in order to simultaneously extract each target's T_eff, [Fe/H], [α/Fe], ${v}_{r}\sin i$ (stellar rotational velocity), and line-of-sight RV. They used the relation of Torres et al. (2010) to compute stellar masses, which we adopt herein, albeit updated with new SB2 spectral fits.

To obtain RVs for double-lined systems, we employed the reduction package from B16 in binary mode where the model is constructed using a pair of stellar spectra. In this mode, the model gains a second set of stellar parameters and a flux fraction parameter that sets the normalized flux ratio between the component stellar spectra. We first performed an initial round of fits where we held one T_eff fixed to that in B18, the other with that as a starting guess. We used the [Fe/H] and [α/Fe] values from B18 for both components throughout. The veiling and ${v}_{r}\sin i$ parameters were fixed to unity and zero for both stars. This first round was carefully supervised to determine initial RV guesses within ∼20 km s⁻¹ (∼10 pixels) for all components. The spectra were then refit for stellar parameters, allowing T_eff (and the coupled $\mathrm{log}(g)$), ${v}_{r}\sin i$, and flux fraction to float while still holding veiling fixed (these parameters are presented in Table 2). We ensured component spectra remained associated with the same spectral source by checking stellar parameters (e.g., whether stellar temperatures flipped) and by refitting each spectrum with the adopted stellar properties intentionally flipped to check for an improved chi square. We also separately validated this by fitting Keplerian orbits (Section 2.4) to the absolute value of the RV difference, ∣RV₁ − RV₂∣. This approach obtained the correct orbital parameters even if several spectra were assigned to the wrong source; we could then check the source identification. We adopted stellar parameters and flux fraction as described in B16 but excluding fits with RVs closer than 1.5 resolution elements. We then performed a final round of fits to determine RVs with the adopted stellar parameters and flux fraction constant, but allowing veiling to float for each component.

Table 2. Stellar Properties for SB2 Targets

Target ID	Teff 1	Teff 2	log(g) 1	log(g) 2	[Fe/H]	[α/Fe]	${v}_{r}\sin i$ 1	${v}_{r}\sin i$ 2	Flux 1
	(K)	(K)			(dex)	(dex)	(km s−1)	(km s−1)	(%)
146–012622	5602 ± 22	5473 ± 21	4.54	4.55	−0.57	0.10	7.5 ± 0.2	6.5 ± 0.1	53 ± 1
147–012265	6273 ± 29	5538 ± 88	4.43	4.54	−0.25	0.04	16.4 ± 0.1	13.8 ± 0.6	80 ± 1
147–012499	5242 ± 16	4904 ± 29	4.58	4.62	−0.36	0.06	4.9 ± 0.2	10.1 ± 0.2	61 ± 0
377–035049	4881 ± 30	4756 ± 23	4.61	4.63	−0.24	0.06	2.7 ± 0.5	2.8 ± 0.6	54 ± 1
378–036176	6151 ± 46	5982 ± 19	4.46	4.48	−0.44	0.06	6.6 ± 0.1	5.6 ± 0.1	57 ± 1
378–036252	6281 ± 24	4879 ± 78	4.43	4.63	−0.14	0.02	9.1 ± 0.1	6.0 ± 0.5	89 ± 0

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We got successful two-component fits for targets 146-012622, 147-012265, 147-012499, 377-035049, 378-036176, and of which were identified as SB2s in B18–as well as 379-035982 and 147-012164–two SB2s that were missed in B18. We were not able to get reliable orbits for these last two SB2s, as they appear to be higher-order systems whose details we will discuss in Section 3. Stellar and fit properties of these stars are reported in Table 2.

Two stars reported as SB2 in B18, 147-012424 and 379-035886, proved impossible to fit for a second stellar component. Both were identified as nonmembers by Gaia (see next section). On further review of their spectra we now believe these to be off main sequence, possibly chemically peculiar stars with a significant number of unfit lines. We treated them as SB1s in our analysis, and ultimately excluded 379-035886 for poor data quality.

B16 targeted NGC 2516, a 120–150 Myr cluster (Meynet et al. 1993; Sung et al. 2002; Kharchenko et al. 2005; Fritzewski et al. 2020) at 415 pc (Gaia Collaboration et al. 2018) and NGC 2422, a 74–130 Myr cluster (Loktin et al. 2001; Kharchenko et al. 2005) at 487 pc (Gaia Collaboration et al. 2018) for a balance of astrophysical and instrumental reasons described therein. Gaia Collaboration et al. (2018) used Gaia DR2 photometry to derive cluster ages by fitting color–magnitude diagrams. While this gave an age consistent with prior works for NGC 2422 (130 Myr), it gave NGC 2516 an age of 300 Myr, far above the age range found previously. Moreover, it did not include several luminous, mid-B-type stars confirmed as members in the new Gaia analysis. Fritzewski et al. (2020) find that NGC 2516's rotation period distribution is comparable to that of the Pleiades, confirming an age of ≲150 Myr.

Figures 1 and 2 show all Gaia stars and M2FS targets in 15 × 15 fields centered on NGC 2516 and NGC 2422, respectively. We use red to indicate Gaia astrometric members as determined using EDR3 (for M2FS targets studied in this paper) or DR2 (all else; Gaia Collaboration et al. 2018), with larger symbols indicating M2FS targets and crosses indicating those that are RV variable. The solid black line marks the half-degree M2FS field of view (FOV).

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While B18 used the mean stellar RV to determine membership, we are now able to rely exclusively on the precise astrometry of Gaia EDR3. A target was considered a cluster member if its parallax and proper motions from Gaia EDR3 (Gaia Collaboration et al. 2021) were within 5σ and 2 mas yr⁻¹ respectively of the cluster parallaxes and proper motions from Gaia Collaboration et al. (2018). All of the astrometric member singles have mean stellar RVs within 5 km s⁻¹ of the cluster RV, consistent with the scatter expected from measurement error, intrinsic velocity dispersion, and wide (≳5 au) binaries. In contrast, just 6 of 77 single stars that are astrometric nonmembers have RVs within 5 km s⁻¹ of the cluster RV. The updates to membership in light of Gaia DR3 precision astrometry do not change the binary fraction within the margins of error reported by B18.

We fit Keplerian orbits to our RVs using a custom adaptation of orvara (Brandt et al. 2021), a package for fitting stellar and exoplanet orbits using Markov chain Monte Carlo (MCMC) through the package ptemcee (Foreman-Mackey et al. 2013; Vousden et al. 2016). We ran our fits using 20 temperatures and 200 walkers with 1 million steps each; we fit for the orbital period P, eccentricity e, mean anomaly at a reference epoch λ_ref, argument of periastron ω, RV semiamplitude K, and barycenter radial velocity RV₀. Our adaptation of orvara differs from the published version in its ability to analytically marginalize over K and ω, depending on the choice of prior for K. The fits that we present here adopt a uniform prior on all parameters. With this choice, K and RV₀ enter the likelihood linearly (Wright & Howard 2009) and may be analytically marginalized out. The resulting chain stores the maximum-likelihood values of K and RV₀ at the fixed values of the other parameters.

We fit the SB2 targets with a double-component fit with an additional parameter for the ratio of the RV semiamplitudes of the primary and secondary components, equivalent to their mass ratio:

$$\begin{eqnarray}&&{K}_{\mathrm{ratio}}=-\displaystyle \frac{{\mathrm{RV}}_{2}}{{\mathrm{RV}}_{1}}=\displaystyle \frac{{K}_{2}}{{K}_{1}}=\displaystyle \frac{{M}_{1}}{{M}_{2}}.\end{eqnarray} \tag{ 1 }$$

We calculated a per-star multiplicative factor, σ_χ , which would inflate the B18 RV errors σ_i sufficiently to yield a reduced χ² of 1, equivalent to a χ² of the number of degrees of freedom. The inflation factor σ_χ is simply the square root of the computed reduced χ², and is reported in Tables 3 and 4 in Section 3. This ad-hoc factor accounts for sources of RV uncertainty not previously addressed. For example, a poor estimate of the photon-weighted exposure midpoint could introduce uncertainty due to stellar acceleration throughout the exposure. We fold all of these effects into σ_χ , apply it to σ_i , and rerun our chains a second time in order to derive the parameters and confidence intervals we report.

Table 3. Binary Solutions in the Field of NGC 2516

Target ID	Mem.	$v\sin i$	Period	Ecc.	λ	ω	K	RV0	M	q	σχ
		(km s−1)	(days)				(km s−1)	(km s−1)	(M⊙)	(M2/M1)
146-012358	N	4.48 ± 0.25	14.0683 ± 0.0010	${0.0083}_{-0.0057}^{+0.0081}$	${1.8}_{-1.2}^{+3.4}$	${1.3}_{-3.1}^{+1.2}$	${11.670}_{-0.094}^{+0.10}$	${69.464}_{-0.090}^{+0.086}$	0.81	${0.182}_{-0.023}^{+0.11}$	2.24
146-012365	M	6.339 ± 0.093	${586}_{-21}^{+17}$	${0.865}_{-0.051}^{+0.026}$	${3.35}_{-0.28}^{+0.24}$	$-{0.92}_{-0.20}^{+0.15}$	${16.2}_{-4.1}^{+4.2}$	${23.59}_{-0.57}^{+0.53}$	1.04	${0.47}_{-0.11}^{+0.18}$	1.21
146-012455	M	7.574 ± 0.060	${109.17}_{-2.0}^{+0.80}$ a	${0.252}_{-0.048}^{+0.072}$	${2.16}_{-0.33}^{+0.32}$	$-{1.43}_{-0.20}^{+0.13}$	${15.05}_{-0.17}^{+0.20}$	${25.20}_{-1.0}^{+0.43}$	0.89	${0.488}_{-0.052}^{+0.19}$	1.72
146-012500	M	8.83 ± 0.23	${3.656213}_{-0.000092}^{+0.000094}$	${0.0136}_{-0.0095}^{+0.015}$	${3.3}_{-2.1}^{+1.9}$	${0.2}_{-2.3}^{+2.0}$	${24.15}_{-0.62}^{+0.66}$	${24.31}_{-0.30}^{+0.32}$	0.80	${0.249}_{-0.031}^{+0.14}$	5.43
146-012557	N	4.93 ± 0.17	${601}_{-46}^{+18}$ a	${0.731}_{-0.034}^{+0.012}$	${6.2668}_{-0.0057}^{+0.0032}$	$-{3.048}_{-0.032}^{+0.093}$	${10.346}_{-0.050}^{+0.053}$	$-{26.87}_{-0.31}^{+0.10}$	0.89	${0.401}_{-0.047}^{+0.19}$	1.00
146-012601	M	16.07 ± 0.14	${1.868567}_{-0.000039}^{+0.000043}$	${0.0051}_{-0.0036}^{+0.0060}$	${4.05}_{-1.9}^{+0.89}$	${0.01}_{-0.86}^{+1.8}$	${30.37}_{-0.23}^{+0.22}$	${25.096}_{-0.046}^{+0.057}$	0.82	${0.247}_{-0.031}^{+0.14}$	1.81
146-012622A	M	7.53 ± 0.16	${32.1170}_{-0.0018}^{+0.0017}$	${0.1877}_{-0.0020}^{+0.0021}$	${5.190}_{-0.010}^{+0.011}$	−0.387 ± 0.012	${42.540}_{-0.079}^{+0.080}$	24.0710 ± 0.0020	0.83	0.9659 ± 0.0019	1.19
146-012622B	⋯	6.52 ± 0.14	⋯	⋯	⋯	⋯	${44.040}_{-0.079}^{+0.081}$	−0.81	⋯	⋯
147-012175	M	10.83 ± 0.21	${1033}_{-276}^{+492}$ a	${0.42}_{-0.27}^{+0.34}$	3.6 ± 1.4	$-{1.61}_{-0.92}^{+4.4}$	${5.2}_{-1.2}^{+6.1}$	${24.32}_{-0.72}^{+0.69}$	0.78	${0.35}_{-0.12}^{+0.24}$	3.01
147-012205	N	3.967 ± 0.087	≥ 128.70 a	⋯	⋯	⋯	⋯	${21.3}_{-5.3}^{+9.2}$	1.01	≥0.25	6.34
147-012231	N	4.53 ± 0.44	≥1243.58 a	⋯	⋯	⋯	⋯	${21.0}_{-2.3}^{+6.1}$	0.92	≥0.38	4.96
147-012249	M	6.73 ± 0.10	23.2825 ± 0.0036	${0.1448}_{-0.0084}^{+0.0085}$	${4.542}_{-0.064}^{+0.066}$	$-{2.431}_{-0.072}^{+0.069}$	26.07 ± 0.22	23.898 ± 0.045	0.89	${0.522}_{-0.052}^{+0.19}$	5.20
147-012262	M	4.61 ± 0.30	${27.647}_{-0.027}^{+0.014}$	${0.62}_{-0.22}^{+0.23}$	3.02 ± 0.16	−1.57 ± 0.15	${19.7}_{-6.1}^{+17}$	24.49 ± 0.71	0.76	${0.36}_{-0.11}^{+0.17}$	4.56
147-012265A	M	16.36 ± 0.14	${13.47942}_{-0.00076}^{+0.00095}$	${0.6143}_{-0.0027}^{+0.0028}$	${5.0877}_{-0.0069}^{+0.0070}$	−2.1996 ± 0.0066	${61.18}_{-0.22}^{+0.27}$	23.424 ± 0.040	1.12	0.7255 ± 0.0023	2.46
147-012265B	⋯	13.81 ± 0.63	⋯	⋯	⋯	⋯	${84.33}_{-0.31}^{+0.39}$	⋯	0.81	⋯	⋯
147-012270	M	7.47 ± 0.56	${333}_{-109}^{+247}$ a	${0.43}_{-0.25}^{+0.16}$	${4.9}_{-4.8}^{+1.1}$	${0.6}_{-3.2}^{+2.0}$	${11.4}_{-1.5}^{+3.5}$	${24.50}_{-0.71}^{+0.72}$	0.81	${0.57}_{-0.16}^{+0.21}$	3.95
147-012290	N	3.36 ± 0.12	≥617.62 a	⋯	⋯	⋯	⋯	${11.5}_{-1.1}^{+4.2}$	0.88	≥0.19	2.14
147-012308	M	37.77 ± 0.23	${55.77}_{-0.12}^{+157}$ a	${0.665}_{-0.037}^{+0.18}$	${0.628}_{-0.093}^{+0.51}$	$-{1.850}_{-0.072}^{+0.72}$	${11.93}_{-0.45}^{+13}$	${25.08}_{-0.12}^{+0.76}$	1.24	${0.226}_{-0.056}^{+0.31}$	2.20
147-012424	N	6.39 ± 0.22	${23.1482}_{-0.0046}^{+0.0047}$	${0.4649}_{-0.0061}^{+0.0062}$	3.656 ± 0.012	−0.4886 ± 0.0088	${46.17}_{-0.66}^{+0.69}$	17.79 ± 0.27	1.07	${0.831}_{-0.040}^{+0.092}$	2.99
147-012432	M	5.875 ± 0.089	≥576.26	⋯	⋯	⋯	⋯	${24.36}_{-0.67}^{+0.74}$	0.79	≥0.50	2.36
147-012433	N	4.06 ± 0.30	≥256.90 a	⋯	⋯	⋯	⋯	${26.51}_{-1.6}^{+0.23}$	0.85	≥0.06	1.00
147-012474	N	3.676 ± 0.087	≥844.99	⋯	⋯	⋯	⋯	$-{1.6}_{-11}^{+5.2}$	0.86	≥0.41	2.57
147-012487	M	10.38 ± 0.11	${16.3164}_{-0.0027}^{+0.0026}$	0.034 ± 0.012	${5.70}_{-0.59}^{+0.34}$	${1.52}_{-0.37}^{+0.41}$	${18.27}_{-0.36}^{+0.38}$	${23.77}_{-0.23}^{+0.24}$	1.18	${0.275}_{-0.034}^{+0.16}$	3.73
147-012499A	M	4.95 ± 0.21	${66.313}_{-0.050}^{+0.055}$	0.416 ± 0.012	${1.798}_{-0.036}^{+0.039}$	${0.305}_{-0.021}^{+0.020}$	${30.77}_{-0.54}^{+0.56}$	${24.956}_{-0.079}^{+0.080}$	0.81	${0.943}_{-0.013}^{+0.014}$	3.26
147-012499B	⋯	10.13 ± 0.16	⋯	⋯	⋯	⋯	${32.62}_{-0.60}^{+0.61}$	⋯	0.77	⋯	⋯
148-012906	M	15.3 ± 1.0	${747}_{-99}^{+10}$ a	${0.22}_{-0.16}^{+0.26}$	${4.96}_{-3.4}^{+0.70}$	${0.1}_{-1.5}^{+1.0}$	${8.9}_{-2.0}^{+2.5}$	${24.47}_{-0.54}^{+0.70}$	0.92	${0.55}_{-0.18}^{+0.22}$	2.42
148-012940	N	5.955 ± 0.066	10.75742 ± 0.00019	${0.0021}_{-0.0015}^{+0.0023}$	${3.9}_{-2.4}^{+1.5}$	${0.2}_{-1.7}^{+1.4}$	15.092 ± 0.047	${32.523}_{-0.015}^{+0.016}$	1.13	${0.193}_{-0.025}^{+0.12}$	1.00

Note.

^a Denotes target with a multimodal fit.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We obtain a secondary mass distribution for SB2s directly from the mass ratio parameter distribution. For the remaining systems, we compute a random mass for each step in the MCMC chain by drawing $\cos (i)$ uniformly between 0 and 1. We then use the equation for radial velocity semiamplitude

$$\begin{eqnarray}&&K={\left(\displaystyle \frac{2\pi G}{P}\right)}^{\tfrac{1}{3}}\displaystyle \frac{{M}_{2}}{{({M}_{1}+{M}_{2})}^{\tfrac{2}{3}}}\displaystyle \frac{\sin (i)}{\sqrt{1-{e}^{2}}}\end{eqnarray} \tag{ 2 }$$

to obtain a secondary mass, solving directly for the case of one real root. Values for M₁ were already found in B16, as described in Section 2. Figures 6–8 show secondary mass distributions for systems which returned a usable fit (see Section 3).

Plots of the 37 systems for which we obtained a usable fit may be found in the Appendix. Three examples, Figures 3–5, are included here as they highlight target peculiarities that will be discussed in the following sections. The left column displays the RV time series (top) and the phase-folded RV with the maximum-likelihood fit and its RV residuals (bottom). The black error bars are the original RV errors from B18. The red error margins show the extra error inflation from the per-star multiplicative factor, σ_χ .

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We used eleanor (Feinstein et al. 2019) to download the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) light curves for all available targets. We used these light curves to check for photometric periods of our binary systems and to search for eclipses or tidal ellipsoidal distortion. The right column displays these TESS light curves, with the bottom plot showing the light curve phase folded over the period.

We compute a Lomb–Scargle periodogram for each of the targets, using a maximum period of twice our observational baseline and a minimum period of half a day. We caution that periodogram peaks at or below ∼1.1 day are likely due to aliasing from our observational cadence. The center column shows Lomb–Scargle periodograms of TESS (top) and M2FS data (bottom). The dotted and dashed lines denote 95% and 99% significance, respectively, and the arrow points to the maximum-likelihood period. The faint blue lines represent their respective window functions. The bottom center plot shows a random selection of orbits from the MCMC chains with the maximum-likelihood orbit in red.

The following three subsections discuss targets of note, including those with multimodal posteriors. Corner plots for all targets with reliable orbits can be found in Appendix.

• 1.  
  146-012455 (Figure A1.15), 147-012308 (Figure A1.14), 147-012175 (Figure A1.25), 147-012270 (Figure A1.30), and 148-012906 (Figure A1.13) have multimodal posterior distributions. Several have tails extending to long orbital periods. Longer orbits almost always have higher eccentricities.
• 2.  
  146-012601 (Figure A1.24) Phase-folded TESS data from sectors prior to 2021 suggested ellipsoidal variation, but this smooths out when including later data. A closer examination shows that individual sectors show strong ( 3%) ellipsoidal variation but with a phase and amplitude drift between sectors. For this star only we have median smoothed the phase-folded TESS light curves on a 1.5 hour cadence, coloring them by sector to highlight both the ellipsoidal variation and the phase drift.
• 3.  
  147-012164 is an SB2 for which we could not get a reliable binary fit; its stellar parameters are not stable. This is because it is a higher-order system: we see clear evidence for a third star in its spectra. The data could support a full orbital characterization with substantial extra work.

• 1.  
  378-036328 (Figure A1.16) and 378-036814 (Figure A1.32) have multimodal posteriors; longer-period orbits have higher eccentricity.
• 2.  
  378-036252 (Figure A1.3) has a phase-folded TESS light curve, which clearly shows it to be an eclipsing binary.
• 3.  
  379-035982 is an SB2 for which we could not get a reliable binary fit. While there is no visual evidence for a third star in its spectra, this system's stellar properties and component RVs do not make sense without an additional companion. Further observations are needed in order to fully characterize this system.

• 1.  
  146-012557 (Figure A1.7), 379-036194 (Figure A1.8), and 379-036197 (Figure A1.9) have multimodal posteriors; the longer-period orbits are more eccentric.

We find that our mass ratio distributions of binaries in the clusters as well as the field (see Figure 10) are relatively flat, consistent with previous works (e.g., Raghavan et al. 2010; Duchêne & Kraus 2013). Recently, other works have noted an excess of equal-mass (q ≳ 0.95) twins at close separations (e.g., Pinsonneault & Stanek 2006; Simon & Obbie 2009; Kounkel et al. 2019) on top of a uniform distribution for systems with q < 0.95. While our sample size is insufficient to statistically measure a twin excess, two of our NGC 2516 SB2s, 146-012622 and 147-012499, have mass ratios of 0.97 and 0.93, respectively. Two field SB2s 377-035049 and 378-036176, are close-in binaries with mass ratios of 0.99 and 0.94, respectively.

We note an excess of short-period (P < 100 days) binaries along the cluster members, while most systems with periods exceeding our observational baseline are cluster nonmembers. The physical explanation for this effect is likely that these stars, which have a magnitude consistent with an FGK star at ∼450 pc despite being distant background stars, are giants that cannot physically support short-period companions.

We use the high-precision parallaxes and proper motions from Gaia EDR3 to definitively establish cluster membership. This enables us to impose a prior on the radial velocity of a system's barycenter when fitting the orbit of an astrometric member. As a result, four cluster members which originally had multimodal posteriors ended up with well-constrained and unimodal posteriors following the application of this prior. Stars reported as multimodal have errors encompassing all modes. See the corner plots in Figures A1.15 (target 146-012455) and A1.16 (target 378-036328) for two example multimodal targets. Figure 9 shows an example of this effect for NGC 2516 member 147-012265. The application of a prior effected reliable, unimodal fits for some of our notable systems, examples being 146-012601, a tight circular binary (P∼2 days), and 146-012622, an equal-mass SB2. 147-012265, an eccentric SB2, had over five visible orbital modes originally, but the application of the prior identified the dominant mode. As we discuss in the following section, 147-012265 is the shortest-period eccentric binary in our sample.

Binary stars exert tidal forces on each other, causing them to circularize over time, i.e., approach a state where stellar rotation is synchronous with binary orbital motion and the stellar rotation axis is aligned with the normal to the orbital plane of motion (Mazeh 2008). Eccentricity damps due to the mismatch between the orbital frequency, which varies with orbital phase if e > 0, and the rotational frequency of either star.

Orbital characterization of binary star systems in open clusters enables us to determine the transition period separating circular from eccentric binaries. For example, Mathieu et al. (2004) determined the tidal circularization cutoff period for NGC 188 (∼6 Gyr) to be around 15 days using spectroscopic binaries. Meibom & Mathieu (2005)'s sample of transition periods for 8 coeval systems shows a tendency for longer transition periods in older clusters. Geller et al. (2021) recently found a tidal circularization cutoff period of ${11}_{-1.0}^{+1.1}$ days for open cluster M67 (∼4 Gyr), in agreement with the value of ${12.1}_{-1.5}^{+1.0}$ days found by Meibom & Mathieu (2005). All the clusters in the sample in the age range of NGC 2516 and NGC 2422 have cutoff periods within the 5-15 day window.

We find two binaries within this period window: 147-012265, a SB2 in NGC 2516 (e ∼ 0.61, P ∼ 13.48 days), and 378-036252, a circular binary in NGC 2422 (P ∼ 7.29 days). Both of these systems are consistent with previous work. Meibom & Mathieu (2005) find a tidal circularization cutoff period for M35, a cluster around the same age as NGC 2516 and NGC 2422, of 10.2 days. Notably, all stars in their M35 sample with periods under 20 days are less eccentric than 147-012265. The discovery of other systems in NGC 2516 and NGC 2422 within this period window, particularly short-period eccentric binaries, would help constrain the transition period for these clusters. 147-012265 and 378-036252, however, could contribute to a meta-analysis looking at binaries within this crucial period window along with other systems from clusters of similar ages.

The dearth of stars with a companion mass in the brown dwarf range (5–80 M_Jup) is known as the "brown dwarf desert" (Marcy & Butler 2000). Less than 1% of Sun-like stars have brown dwarf companions according to Grether & Lineweaver (2006).

Consistent with the brown dwarf desert, almost all of our well-constrained binaries have stellar companions. Only one field star, 379-036194, has a secondary with a median derived mass of 0.036 solar masses, which is below the hydrogen-burning limit. Recent work by Fontanive et al. (2019) found that a significant fraction of brown dwarf desert inhabitants are themselves members of higher-order systems. This provides additional motivation for the full characterization of the higher-order systems we introduced in Section 3, 147-012164 and 379-035982, to determine if either of these might have a substellar companion.