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Kareem El-Badry, Hans-Walter Rix, The wide binary fraction of solar-type stars: emergence of metallicity dependence at a < 200 au, Monthly Notices of the Royal Astronomical Society: Letters, Volume 482, Issue 1, January 2019, Pages L139–L144, https://doi.org/10.1093/mnrasl/sly206
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ABSTRACT
We combine a catalogue of wide binaries constructed from Gaia DR2 with [Fe/H] abundances from wide-field spectroscopic surveys to quantify how the binary fraction varies with metallicity over separations 50 ≲ s/au ≲ 50 000. At a given distance, the completeness of the catalogue is independent of metallicity, making it straightforward to constrain intrinsic variation with [Fe/H]. The wide binary fraction is basically constant with [Fe/H] at large separations (s ≳ 250 au) but becomes quite rapidly anticorrelated with [Fe/H] at smaller separations: for 50 < s/au < 100, the binary fraction at |$\rm [Fe/H] = -1$| exceeds that at |$\rm [Fe/H] = 0.5$| by a factor of 3, an anticorrelation almost as strong as that found for close binaries with a < 10 au. Interpreted in terms of models where disc fragmentation is more efficient at low [Fe/H], our results suggest that 100 < a/au < 200 is the separation below which a significant fraction of binaries formed via fragmentation of individual gravitationally unstable discs rather than through turbulent core fragmentation. We provide a public catalogue of 8407 binaries within 200 pc with spectroscopically determined [Fe/H] for at least one component.
1 INTRODUCTION
The statistical properties of the binary star population and their potential variation with metallicity provide powerful diagnostics of the star formation process (White & Ghez 2001; Machida et al. 2009; Duchêne & Kraus 2013; Bate 2014; Badenes et al. 2018; Moe, Kratter & Badenes 2018). Different binary formation mechanisms predict different metallicity dependences of the resulting binary fraction (Moe et al. 2018). Measurements of metallicity dependence as a function of orbital separation can thus constrain the separation regimes in which different formation mechanisms operate.
The close binary fraction is strongly anticorrelated with metallicity; the fraction of primaries that have a companion with a < 10 au decreases by a factor of 4 over |$-1 \lt \rm [Fe/H] \lt 0.5$|, from |$\left(40\pm 6\right){{\ \rm per\ cent}}$| at |$\rm [Fe/H] = -1$| to |$\left(10\pm 3\right){{\ \rm per\ cent}}$| at |$\rm [Fe/H] = 0.5$| (Raghavan et al. 2010; Badenes et al. 2018; Moe et al. 2018). The existence of such anticorrelation was long controversial (Jaschek & Jaschek 1959; Carney 1983; Latham et al. 2002; Hettinger et al. 2015) in large part because the sensitivity of most binary detection methods varies with metallicity. But in a recent reanalysis of the binary populations probed by five surveys, Moe et al. (2018) found that after observational biases are corrected for, all five show consistent evidence of a metallicity-dependent close binary fraction.
On the other hand, studies of the wide binary fraction have found it to be approximately metallicity-invariant (e.g. Chanamé & Gould 2004; Zapatero Osorio & Martín 2004; El-Badry et al. 2018b). Most of the binaries studied in these works have separations of order 1000 au, but the variation of metallicity dependence with orbital separation has yet to be studied in detail. The recent Gaia data releases (Gaia Collaboration et al. 2016, 2018) have substantially simplified the process of reliably identifying spatially resolved binaries, making it possible to study the intermediate-to-wide binary population with unprecedented precision (e.g. Andrews, Chanamé & Agüeros 2017; Oelkers, Stassun & Dhital 2017; Oh et al. 2017). In this Letter, we seek to constrain the transition between the close and wide binary regimes, pinpointing the separation at which metallicity dependence emerges.
2 METHODS
2.1 Wide binary catalogue and extension
We extend the wide binary catalogue described in El-Badry & Rix (2018, hereafter ER18), which was constructed by searching Gaia DR2 for pairs of stars whose positions, proper motions, and parallaxes are consistent with being gravitationally bound. The ER18 catalogue contains ∼50 000 binaries with separations |$50 \lesssim s/{\rm au} \lt 50\, 000$|, with an estimated contamination rate of ∼0.2 per cent. To maintain high purity, it only contains binaries that are within 200 pc of the Sun and have high-quality astrometry and photometry.
To separate main sequence stars and white dwarfs, ER18 required both stars to have a measured bp_rp colour, and to have well-resolved photometry as quantified by the phot_bp_rp_excess_factor (see section 2.1 of ER18). As a consequence of these requirements, the ER18 catalogue has an effective resolution limit of ∼2 arcsec and contains few binaries with separations s < 200 au. To find more binaries with small separations, we now extend the catalogue by removing the restrictions on bp_rp and phot_bp_rp_excess_factor only for pairs with projected separations s < 500 au. We still require both components to pass the other quality cuts in ER18, including having reliable astrometry and precisely measured, mutually consistent parallaxes, and we apply the same procedure for removing members of clusters, moving groups, and resolved higher order multiples.
This extended search yields 23 079 new binaries not included in the initial catalogue. Many of the new additions have angular separations between 0.5 and 2 arcsec. Combining them with the sample from ER18 results in a total of 78 207 binaries, including 8284 with s < 200 au. Although the photometry of the objects that did not pass the ER18 cuts is less clean, we expect essentially all of them to be bona fide binaries, as the contamination rate from chance alignments is negligible at close separations.
2.2 Spectroscopic metallicities
We cross-matched the expanded wide binary catalogue with several wide-field spectroscopic surveys: LAMOST (DR5; Zhao et al. 2012), RAVE (DR5; Kunder et al. 2017), APOGEE (DR14; Majewski et al. 2017, using the abundances derived by Ting et al. 2018), and GALAH (DR2; Buder et al. 2018). We also cross-matched with the Hypatia catalogue (Hinkel et al. 2014), which is a compilation of high-resolution spectroscopic abundances for stars within 150 pc of the Sun. We limit our sample to main-sequence binaries in which the primary has absolute magnitude |$2.5 \lt \rm M_G \lt 9.5$|, corresponding to 0.45 ≲ M/M⊙ ≲ 1.5.
The resulting catalogue is summarized in Table 1. Cross-matching yields a spectroscopic [Fe/H] for at least one component of 8407 binaries; in 440, a spectroscopic [Fe/H] is available for both components. We assign binaries in which both components have a spectroscopic [Fe/H] the mean of the two components; when only one component has a measured [Fe/H], we adopt that value. For stars that were observed by more than one survey, we prioritize abundances from surveys in the reverse order listed in Table 1. The catalogue is available online.
Sample . | |$N_{\rm in\, binary}$| . | |$N_{{\rm tot},\, d\lt 200\, {\rm pc}}$| . |
---|---|---|
RAVE | 3261 | 33 792 |
LAMOST | 3729 | 46 729 |
APOGEE | 660 | 5796 |
GALAH | 537 | 6759 |
Hypatia | 660 | 3954 |
Total stars | 8847 | 97 030 |
Total number of binaries | 8407 |
Sample . | |$N_{\rm in\, binary}$| . | |$N_{{\rm tot},\, d\lt 200\, {\rm pc}}$| . |
---|---|---|
RAVE | 3261 | 33 792 |
LAMOST | 3729 | 46 729 |
APOGEE | 660 | 5796 |
GALAH | 537 | 6759 |
Hypatia | 660 | 3954 |
Total stars | 8847 | 97 030 |
Total number of binaries | 8407 |
Sample . | |$N_{\rm in\, binary}$| . | |$N_{{\rm tot},\, d\lt 200\, {\rm pc}}$| . |
---|---|---|
RAVE | 3261 | 33 792 |
LAMOST | 3729 | 46 729 |
APOGEE | 660 | 5796 |
GALAH | 537 | 6759 |
Hypatia | 660 | 3954 |
Total stars | 8847 | 97 030 |
Total number of binaries | 8407 |
Sample . | |$N_{\rm in\, binary}$| . | |$N_{{\rm tot},\, d\lt 200\, {\rm pc}}$| . |
---|---|---|
RAVE | 3261 | 33 792 |
LAMOST | 3729 | 46 729 |
APOGEE | 660 | 5796 |
GALAH | 537 | 6759 |
Hypatia | 660 | 3954 |
Total stars | 8847 | 97 030 |
Total number of binaries | 8407 |
We also construct a spectroscopic ‘control sample’ that consists of the 97 030 stars within 200 pc that were observed by the spectroscopic surveys listed in Table 1 and pass the Gaia quality and magnitude cuts applied to the wide binary sample. Our method for identifying wide binaries is metallicity-blind, and the spectroscopic surveys did not preferentially target or avoid wide binaries. Therefore, any metallicity bias in the spectroscopic binary sample will, at fixed distance, affect the control sample in the same way it affects the binary sample.
Binaries with angular separations of less than a few arcsec may not be spatially resolved by ground-based spectroscopic surveys. The resulting errors in [Fe/H] are expected to be less than 0.1 dex on average, with negligible systematic biases for the mid-resolution optical spectra that constitute the majority of our sample (Schlesinger et al. 2010; El-Badry et al. 2018a).
3 RESULTS
3.1 Metallicity distribution
Fig. 1 compares the metallicity distribution functions (MDFs) of binaries in different separation bins to the MDF of the control sample. Because close binaries are unresolved at large distances, their distributions of heliocentric distance are different from those of the full 200 pc control sample. To avoid biases arising from the distance dependence of the MDF, for each bin in s, we compare to a random subset of the control sample with the same distance distribution as the binaries in that s bin.
At small separations, the MDFs of binaries are biased towards low [Fe/H] relative to the control sample. This bias is strongest in the 50 < s/au < 100 bin but is present in all separation bins up to s = 250 au. No strong bias towards higher or lower [Fe/H] is evident at large separations, though there are hints of a slight excess of binaries with |$\rm [Fe/H]\sim 0$| in the largest separation bin. The latter is likely attributable to age effects: at the widest separations, there is a non-negligible probability for binaries to be dynamically disrupted by gravitational perturbations from other stars and molecular clouds. Lower metallicity binaries are on average older, allowing more time for dynamical disruption.
3.2 Inferring the dependence of binarity on [Fe/H]
We plot the resulting constraints on the binary fraction in Fig. 2, normalizing relative to |$\rm [Fe/H]=0$|. Consistent with the qualitative picture from Fig. 1, the binary fraction becomes metallicity-dependent at s ≲ 250 au. Over |$-0.5 \lt [\rm Fe/H] \lt 0.5$|, the dependence on metallicity is nearly linear, with hints of flattening at lower [Fe/H]. The emergence of metallicity dependence towards smaller separations is quite rapid; there is essentially no dependence at s = 300 au, while at s = 100 au, the binary fraction at |$[\rm Fe/H]= -1$| is a factor of 3 higher than at |$\rm [Fe/H] = 0.5$|. The metallicity dependence at the smallest separations probed by our catalogue is fully consistent with that found at a < 10 au by Moe et al. (2018), though our median constraints lean towards somewhat weaker metallicity dependence at |$\rm [Fe/H] \lt -0.5$|. The uncertainties in our constraints are substantial at small separations due to the small number of binaries in our catalogue with s < 100 au. Nevertheless, the data rule out a metallicity-independent binary fraction with greater than 2 σ significance for all s < 150 au.
3.3 Separation distributions
In Fig. 3, we show inferred intrinsic separation distributions over 50 < s/au < 500 (where the binary selection function is consistent and well-characterized; see Section 2.1) of binaries in four metallicity bins. The relative detection efficiency drops below 50 per cent at an angular separation of θ0 ≈ 1 arcsec, so the maximum distance at which a binary of separation s can be detected is |$d_{{\rm max}}/{\rm pc}\approx {\rm min}\left\lbrace \left(s/{\rm au}\right)/\left(\theta _{0}/{\rm arcsec}\right),\, 200\right\rbrace$|. In inferring the intrinsic separation distribution, we weight each observed binary by the fraction of objects in the control sample at a particular [Fe/H] that are at distances greater than dmax.
Over 50 < s/au < 500, the separation distributions of lower [Fe/H] systems consistently show an excess of smaller separation binaries relative to those of higher [Fe/H] systems. Integrating over all metallicities, the total separation distribution peaks at a ≈ 200 au and is relatively flat over the separations shown in Fig. 3 (Duchêne & Kraus 2013). However, Fig. 3 shows that the peak in the separation distribution occurs at smaller (larger) separations for binaries with low (high) metallicity. Using a weighted two-sample Kolmogorov-Smirnov (KS) test, we verified that the separation distributions for both of the two highest [Fe/H] bins are inconsistent with those of each of the two lowest [Fe/H] bins at at least the 4 σ level (pKS < 3 × 10−5). Indeed, such variation is required to explain a binary fraction that is metallicity dependent at small separations but not at asymptotically large separations (see Moe et al. 2018, their fig. 19).
4 DISCUSSION AND CONCLUSIONS
We have shown that the MDFs of binaries with separations 50 ≲ s/au ≲ 250 exhibit a shortage of high-[Fe/H] binaries and an excess of low-[Fe/H] binaries relative to a control sample subject to the same selection function (Fig. 1). We fit a flexible, parametrized model for the modification of the binary MDF relative to the MDF of all stars, thus constraining the [Fe/H]-dependence of the binary fraction as a function of separation (Fig. 2). Metallicity dependence is weak at s = 250 au but ramps up rapidly with decreasing separation: at 50 < s/au < 100, the binary fraction increases by a factor of 3 over |$-1 \lt \rm [Fe/H] \lt 0.5$|. For these separations, the metallicity dependence is roughly linear over |$-0.5 \lt [\rm Fe/H] \lt 0.5$|. It begins to flatten at |$[\rm Fe/H] \lt -0.5$|, albeit with substantial uncertainty. The separation distribution is similarly metallicity dependent, with low-metallicity binaries concentrated at smaller separations (Fig. 3).
The projected separation s of a wide binary can exceed the semimajor axis a by at most a factor of 2. Projection effects will tend to smooth out the transition between the metallicity-dependent and independent regimes, so the weak metallicity dependence detected at s ≳ 200 au could be a consequence of stronger metallicity dependence at a ∼ 150. However, a and s are usually similar for realistic orbits (see ER18; their fig. B1). For a uniform eccentricity distribution, 16 per cent of randomly observed orbits satisfy s > 1.33a, and 2.3 per cent satisfy s > 1.75a. Metallicity dependence out to s ∼ 250 au thus implies dependence to at least a = 150 au.
In the model proposed by Moe et al. (2018), the binary fraction is metallicity-dependent only at separations where binaries formed primarily via the fragmentation of gravitationally unstable discs: the turbulent core fragmentation process that produces wider binaries is independent of metallicity, at least for the range of |$\rm [Fe/H]$| considered here. Interpreted in terms of this model, our results suggest that 100 < a/au < 200 is the separation below which a substantial fraction of solar-type binaries were formed via disc fragmentation.
In simulations, disc fragmentation typically occurs at separations of a/au ∼ 50–100 (Burkert, Bate & Bodenheimer 1997; Machida et al. 2009; Stamatellos & Whitworth 2009; Kratter et al. 2010), in agreement with observations that find Class 0 binary protostars formed by disc fragmentation to have typical separations of s ∼ 75 au (Tobin et al. 2013, 2016). After fragmentation, the orbital separation can decrease due to viscous dissipation or three-body dynamics (e.g. Moe & Kratter 2018) or increase, e.g. following accretion of high angular momentum gas. Our results imply that systems formed by disc fragmentation constitute a significant fraction of the binary population out to a ∼ 200 au, with wider systems forming primarily through turbulent core fragmentation. Other lines of evidence also point towards a change in the binary formation mechanism at a ∼ 200 au. The masses of the components of solar-type binaries are correlated and inconsistent with random pairings from the initial mass function out to separations of 200 au (Moe & Di Stefano 2017). Similar trends with separation are found for the correlation in accretion rates of binary protostars (White & Ghez 2001) and the mutual inclination of orbits in hierarchical triples (Tokovinin 2017).
It remains important to systematically measure the metallicity dependence of the binary fraction at intermediate separations (10 ≲ a/au ≲ 50) between the regimes probed by close binaries (e.g. Badenes et al. 2018; Moe et al. 2018) and our study. Some previous works have found metallicity dependence in the binary fraction in this regime to be weak (Raghavan et al. 2010; Rastegaev 2010), and others have found evidence of a positive correlation with metallicity, at least for low-mass binaries (Riaz, Gizis & Samaddar 2008; Jao et al. 2009; Lodieu, Zapatero Osorio & Martín 2009; Ziegler et al. 2015). However, the common strategy of photometrically selecting metal-poor subdwarfs from below the main sequence for follow-up imaging can lead to a bias against binaries (Moe et al. 2018). While speckle interferometry and AO + HST imaging likely represent the most promising route to probing the binary fraction at 10 ≲ s/au ≲ 50, studies based on spectroscopically selected metal-poor samples would be less prone to biases against binaries. Constraints on the wobble of astrometric binaries in future Gaia data releases will also probe the intermediate-separation regime.
SUPPORTING INFORMATION
Table 1. Sources of the spectroscopic abundances.
Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
ACKNOWLEDGEMENTS
We thank Max Moe and Carles Badenes for helpful discussions, and the anonymous referee for a constructive report. KE was supported by the NSF GRFP. This project was developed in part at the 2018 NYC Gaia Sprint, hosted by the Center for Computational Astrophysics of the Flatiron Institute in NYC, and in part at the workshop ‘Dynamics of the Milky Way System in the Era of Gaia,’ hosted at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611. This work has made use of data from the ESA Gaia mission, processed by the Gaia Data Processing and Analysis Consortium (DPAC).
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