A Robust Measure of Tidal Circularization in Coeval Binary Populations: The Solar‐Type Spectroscopic Binary Population in the Open Cluster M35

We present an ongoing study on tidal interactions in late-type close binary stars. New results on tidal circularization are combined with existing data to test and constrain theoretical predictions of tidal circularization in the pre-main-sequence (PMS) phase and throughout the main-sequence phase of stellar evolution. Current data suggest that tidal circularization during the PMS phase sets the tidal cutoff period for binary populations younger than ~ 1 Gyr. Binary populations older than ~ 1 Gyr show increasing tidal cutoff periods with age, consistent with active main-sequence tidal circularization.

The extensive stellar radial-velocity surveys of the WIYN Open Cluster Study now allow comprehensive studies of the solar-type hard-binary populations in open clusters as a function of age. We first describe an empirical “initial” hard-binary population as derived from the young open cluster NGC 2168 (M35). Given the limited analyses so far, the cluster binary population is indistinguishable from that of the field. We then compare the hard-binary population in the old open cluster NGC 188 to the binary population in the sophisticated N-body simulations of the old cluster M67 by Hurley et al. The binary populations in the cluster and the simulation show significant differences in binary frequency and fraction of circularized binaries, while otherwise showing similar orbital eccentricity distributions. Since the simulations were designed to match the encounter products in M67, such as blue stragglers, the large reduction in binary fraction indicated by the empirical results likely will also require changes in the simulation physics producing blue stragglers and other anomalous stars arising from stellar dynamics. We present three case studies of stars in open clusters which very likely are products of dynamical encounters between binaries and either single stars or other binaries: the M67 blue straggler S1082, the M67 sub-subgiant S1113, and the horizontal branch star 6819-3002 in the intermediate-age open cluster NGC 6819. Finally, we remind the reader of recent empirical results on the rates of tidal interactions, using tidal circularization periods in open clusters. Every indication is that current theories underestimate the effectiveness of tidal circularization, a result that need to be incorporated into dynamical simulations of dense stellar systems.

In this paper we present an updated compilation of the currently known pre-main sequence (PMS) spectroscopic binaries (SB) for which orbital elements have been determined. In particular we report our results for and discuss the case of the bona-de PMS system RX J1603.9-3938, which has a circular orbit and a period of 7.56 days. This is the longest orbital period for a circular orbit found among the bona-de PMS spectroscopic binaries so far, and we suggest that this system may be thus considered to now set the PMS circularization period. The longer period is compatible with the circularization periods already known for older binary populations such as the Hyades and Praesepe. When considered in the context of the circularization periods for other binary populations of dierent ages, the new PMS circularization period strongly supports the suggestion of Mathieu et al. (1992) that a hybrid scenario (tidal circularization occurring on both PMS phase and on MS phase) could explain the observed circularization periods as a function of age. The apparently circular orbit observed in another PMS system, RX J1301.0-7654a, with an orbital period of nearly 13 days, may perhaps change this picture when the orbit is improved and the system is better understood.

Orbits are presented for 22 spectroscopic binaries in the field of the old open cluster M67. The binary frequency and the distribution of orbital eccentricity are discussed. The detected binary frequency is in the range 9-15 percent, somewhat lower than that found among solar-mass stars in the field. A transition from circular to eccentric orbits among main-sequence binaries at a period between 10.3 and 11.0 days is found, longer than similar transition periods found in younger binary populations. An increase of transition period with cluster age is consistent with the interpretation that the shorter-period orbits have been tidally circularized. A circular orbit at a period of 43 days is found for the cluster giant S1040, consistent with the theoretical expectation that more effective tidal circularization occurs with increasing stellar radius and deepening convective zones.

This thesis presents the analysis of high-resolution, low-signal-to-noise spectroscopic observaitons of a kinematically selected group of about 1300 F-, G-, and K-type dwarfs with proper motions larger than 0.26" per year. The sample includes a significant fraction of stars from the halo of our Galaxy, and the main goal is to characterize the population of spectroscopic binaries in the halo and compare these characteristics with those of the binaries in the disk, to investigate possible differences in the processes of binary star formation. The frequency of spectroscopic binaries with periods less than about 2000 days among the extreme Population II stars is found to be at least 20%, and agrees with the value for Population I. Discrepancies with previous studies which indicated a much lower frequency in the halo are investigated. The distribution of mass ratios (q=M2/M1) is determined here for the first time for the metal-poor binaries, and displays significant differences with the distribution for disk stars. While the latter seems to be essentially flat, the distribution for the halo is found to increase steadily towards q=1, suggesting that Population II systems tend to form with nearly equal-mass components. The difference, however, is shown to be due to a significant contribution from remnants of stellar evolution (white dwarfs), which distort the secondary mass distribution in a sample as old as the halo. The excess over the disk distribution is in good agreement with theory, both qualitatively and quantitatively, and evidence is presented that these binaries with probable white dwarf secondaries tend to have longer orbital periods, as expected from mass transfer or mass loss known to occur during the giant and supergiant phase. After accounting for this effect, the mass distribution for the secondary components in the halo is found to be consistent with that in the Galactic disk. The orbital period distribution and the eccentricity distribution are also similar. Thus, four of the fundamental properties of spectroscopic binaries--the distributions of companion masses, periods, eccentricities, and also the frequency--are comparable in the two populations, which argues that the mechanism that forms binaries is the same, independent of initial conditions in the interstellar medium (chemical composition, turbulence, kinematics). This important conclusion may be relevant for the development of theories of binary star formation. There is clear evidence of orbital evolution among the binaries in this sample, shown by tidal circularization of all orbits with periods shorter than a certain value. The transition period in the halo as marked by the longest circular orbit is seen to be at least as long as 19 days which is longer than that of any other sample of coeval binaries. As predicted by recent theories, this is consistent with the halo being much older, and suggests that tidal circulation is effective not only during the pre-main-sequence phase, but also during the hydrogen-burning stage of stellar evolution.

We present and analyze 120 spectroscopic binary and triple cluster members of the old (4 Gyr) open cluster M67 (NGC 2682). As a cornerstone of stellar astrophysics, M67 is a key cluster in the WIYN Open Cluster Study (WOCS); radial-velocity (RV) observations of M67 are ongoing and extend back over 45 yr, incorporating data from seven different telescopes, and allowing us to detect binaries with orbital periods ≲104 days. Our sample contains 1296 stars (604 cluster members) with magnitudes of 10 ≤ V ≤ 16.5 (about 1.3–0.7 M ⊙), from the giants down to ∼4 mag below the main-sequence turnoff, and extends in radius to 30′ (7.4 pc at a distance of 850 pc, or ∼7 core radii). This paper focuses primarily on the main-sequence binaries, but orbital solutions are also presented for red giants, yellow giants, and sub-subgiants. Out to our period detection limit and within our magnitude and spatial domain, we find a global main-sequence incompleteness-corrected binary fraction of 34% ± 3%, which rises to 70% ± 17% in the cluster center. We derive a tidal circularization period of . We also analyze the incompleteness-corrected distributions of binary orbital elements and masses. The period distribution rises toward longer periods. The eccentricity distribution, beyond P circ, is consistent with a uniform distribution. The mass-ratio distribution is also consistent with a uniform distribution. Overall, these M67 binaries are closely consistent with similar binaries in the galactic field, as well as with the old (7 Gyr) open cluster NGC 188. WOCS. 83.

High sensitivity searches of globular clusters (GC) for radio pulsars by improved pulsar search algorithms and sustained pulsar timing observations have so far yielded some 140 pulsars in more than two dozen GCs. The observed distribution of orbital eccentricity and period of binary radio pulsars in GCs have imprints of the past interaction between single pulsars and binary systems or of binary pulsars and single passing non-compact stars. It is seen that GCs have different groups of pulsars. These may have arisen out of exchange or merger of a component of the binary with the incoming star or a "fly-by" in which the original binary remains intact but undergoes a change of eccentricity and orbital period. We consider the genesis of the distribution of pulsars using analytical and computational tools such as STARLAB, which performs numerical scattering experiments with direct N-body integration. Cluster pulsars with intermediate eccentricities can mostly be accounted for by fly-bys whereas those with high eccentricities are likely to be the result of exchanges and/or mergers of single stars with the binary companion of the pulsar, although there are a few objects which do not easily fit into this description. The corresponding distribution for galactic field pulsars shows notable differences from the GC pulsar orbital period and eccentricity distribution. The long orbital period pulsars in the galactic field with frozen out low eccentricities are largely missing from the globular clusters, and we show that ionization of these systems in GCs cannot alone account for the peculiarities.

Orbital solutions and spectroscopic metallicities are reported for a second set of 40 spectroscopic binaries found in an extended version of the Carney and Latham survey of proper-motion stars. To investigate the distribution of orbital eccentricity versus period for a pure sample of halo binaries, we select only those systems more metal poor than [m/H] = -1.6. It is found that the transition between circular and eccentric orbits occurs at a period of about 19 days. This supports the interpretation that tidal circularization has been more important on the main sequence than during the pre-main-sequence stage for our sample of old binaries in the halo

Based on a sample of 22 main-sequence solar-type spectroscopic binaries, we find the tidal circularization cutoff in the open cluster NGC 188 (age 7 Gyr) to be well defined at a period of 15.0 days. When compared to shorter tidal circularization cutoff periods in the younger clusters M67 and the Hyades, this result establishes that tidal circularization processes are effective in solar-type main-sequence binaries for timescales longer than 1 Gyr. This result is in contrast to the theoretical prediction by Zahn & Bouchet that tidal circularization due to equilibrium tides is ineffective for late-type main-sequence stars, and that tidal circularization cutoff periods are instead set only by pre-main-sequence tidal circularization. The NGC 188 cutoff period is also longer than can be explained by present theories of tidal circularization due to dynamical tides.

We present current results from the ongoing WIYN Open Cluster Study radial-velocity survey for 1410 stars in the young (150 Myr) open cluster M35 (NGC 2168) and establish a benchmark for initial conditions in young open clusters. We find for periods ≲ 1000 days a minimum binary frequency of 0.36 – 0.51. We also analyze the spatial, period and eccentricity distributions of the binary systems and find that the period and eccentricity distributions are well approximated by scaled field distributions from Duquennoy & Mayor (1991). With our large sample size and long baseline, we have a unique understanding of the binary population in this young cluster, making it ideal for defining initial conditions for dynamical simulations.

Context.Many binary stellar systems in which the primary star is beyond the asymptotic giant branch (AGB) evolutionary phase show significant orbital eccentricities, whereas current binary interaction models predict that their orbits are circularised. Aims.In the search for a mechanism to counteract the circularising effect of tidal interaction, we analyse how the orbital parameters in a system are modified under mass loss and mass exchange among its binary components. Methods.We propose a model for enhanced mass loss from the AGB star due to tidal interaction with its companion, which allows a smooth transition between the wind and Roche-lobe overflow mass loss regimes. We explicitly follow its effect along the orbit on the change in eccentricity and orbital semi-major axis, as well as the effect of accretion by the companion. We calculate timescales for the variation in these orbital parameters and compare them to the tidal circularisation timescale. Results.We find that in many cases, due to the enhanced mass loss of the AGB component at orbital phases closer to the periastron, the net eccentricity growth rate in one orbit is comparable to the rate of tidal circularisation. We show that with this eccentricity-enhancing mechanism it is possible to reproduce the orbital period and eccentricity of the Sirius system, which is expected to be circularised under the standard assumptions of binary interaction. We also show that this mechanism may provide an explanation for the eccentricities of most barium star systems, which are expected to be circularised due to tidal dissipation. Conclusions.By proposing a tidally enhanced model of mass loss from AGB stars, we find a mechanism that efficiently works against the tidal circularisation of the orbit. This mechanism can explain the significant eccentricities observed in binary systems containing a white dwarf and a less evolved companion, which are predicted to be circularised due to their proximity, such as Sirius and systems with barium stars.

We perform numerical simulations to investigate tidal evolution of two single-planet systems, that is, WASP-50 and GJ 1214 and a two-planet system CoRoT-7. The results of orbital evolution show that tidal decay and circularization may play a significant role in shaping their final orbits, which is related to the initial orbital data in the simulations. For GJ 1214 system, different cases of initial eccentricity are also considered as only an upper limit of its eccentricity (0.27) is shown, and the outcome suggests a possible maximum initial eccentricity (0.4) in the adopted dynamical model. Moreover, additional runs with alternative values of dissipation factor $Q^\prime_1$ are carried out to explore tidal evolution for GJ 1214b, and these results further indicate that the real $Q^\prime_1$ of GJ 1214b may be much larger than its typical value, which may reasonably suggest that GJ 1214b bears a present-day larger eccentricity, undergoing tidal circularization at a slow rate. For the CoRoT-7 system, tidal forces make two planets migrating towards their host star as well as producing tidal circularization, and in this process tidal effects and mutual gravitational interactions are coupled with each other. Various scenarios of the initial eccentricity of the outer planet have also been done to investigate final planetary configuration. Tidal decay arising from stellar tides may still work for each system as the eccentricity decreases to zero, and this is in association with the remaining lifetime of each planet used to predict its future.

Of the 14 transiting planets that have been detected orbiting eclipsing binaries (“circumbinary planets”), none have been detected with stellar binary orbital periods shorter than 7 days, despite such binaries existing in abundance. The eccentricity–period data for stellar binaries indicate that short-period (<7 days) binaries have had their orbits tidally circularized. We examine here to what extent tidal circularization and shrinkage can conceal circumbinary planets, i.e. whether planets actually exist around short-period binaries, but are not detected because their transit probabilities drop as tides shrink the binary away from the planet. We carry out a population synthesis by initializing a population of eccentric stellar binaries hosting circumbinary planets, and then circularizing and tightening the host orbits using stellar tides. To match the circumbinary transit statistics, stellar binaries must form with eccentricities ≳ 0.2 and periods ≳ 6 days, with circumbinary planets emplaced on exterior stable orbits before tidal circularization; moreover, tidal dissipation must be efficient enough to circularize and shrink binaries out to ∼6–8 days. The resultant binaries that shrink to sub-7 day periods no longer host transiting planets. However, this scenario cannot explain the formation of nearly circular, tight binaries, brought to their present sub-7 day orbits from other processes like disk migration. Still, tidal shrinkage can introduce a bias against finding transiting circumbinary planets, and predicts a population of KIC 3853259 (AB)b analogs consisting of wide-separation, nontransiting planets orbiting tight binaries.

(Abridged) Following on from a recently completed radial-velocity survey of the old (7 Gyr) open cluster NGC 188 in which we study in detail the solar-type hard binaries and blue stragglers of the cluster, here we investigate the dynamical evolution of NGC 188 through a sophisticated N-body model. We employ the observed binary properties of the young (150 Myr) open cluster M35, where possible, to guide our choices for parameters of the initial binary population. At 7 Gyr the main-sequence solar-type hard-binary population in the model matches that of NGC 188 in both binary frequency and distributions of orbital parameters. This agreement between the model and observations is in a large part due to the similarities between the NGC 188 and M35 solar-type binaries. Indeed, among the 7 Gyr main-sequence binaries in the model, only those with P>1000 days show potentially observable evidence for modifications by dynamical encounters. This emphasizes the importance of defining accurate initial conditions for star cluster models, which we propose is best accomplished through comparisons with observations of young open clusters like M35. Furthermore, this suggests that observations of the present-day binaries in even old open clusters can provide valuable information on their primordial binary populations. However, despite the model's successes at matching the true cluster, the model underproduces blue stragglers and produces an overabundance of long-period circular main-sequence--white-dwarf binaries as compared to NGC 188. We conclude that improvements in the physics of mass transfer and common envelope may in fact solve both discrepancies with the observations. This project highlights the unique accessibility of open clusters to both comprehensive observational surveys and full-scale N-body simulations, and underscores the importance of open clusters to the study of star cluster dynamics.

We estimate probability densities of orbital elements, periods, and eccentricities, for the population of extrasolar planetary candidates (EPC) and, separately, for the population of spectroscopic binaries (SB) with solar-type primaries. We construct empirical cumulative distribution functions (CDFs) in order to infer probability distribution functions (PDFs) for orbital periods and eccentricities. We also derive a joint probability density for period-eccentricity pairs in each population. Comparison of respective distributions reveals that in all cases EPC and SB populations are, in the context of orbital elements, indistinguishable from each other to a high degree of statistical significance. Probability densities of orbital periods in both populations have P(exp -1) functional form, whereas the PDFs of eccentricities can he best characterized as a Gaussian with a mean of about 0.35 and standard deviation of about 0.2 turning into a flat distribution at small values of eccentricity. These remarkable similarities between EPC and SB must be taken into account by theories aimed at explaining the origin of extrasolar planetary candidates, and constitute an important clue us to their ultimate nature.