X-Ray Binary Luminosity Function Scaling Relations in Elliptical Galaxies: Evidence for Globular Cluster Seeding of Low-Mass X-Ray Binaries in Galactic Fields
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We report the identification of five short-period variables near the center of the metal-rich globular cluster M71. Our observations consist of multiepoch VI charge coupled device (CCD) images centered on the cluster and covering a 6.3 min x 6.3 min field. Four of these variables are contact eclipsing binaries with periods between 0.35 and 0.41 days; one is a detached or semidetached eclipsing binary with a period of 0.56 days. Two of the variables were first identified as possible eclipsing binaries in an earlier survey by Hodder et al. (1992). We have used a variety of arguments to conclude that all five binary stars are probable members of M71, a result that is consistent with the low number (0.15) of short-period field binaries expected along this line of sight. Based on a simple model of how contact binaries evolve from initially detached binaries, we have determined a lower limit of 1.3% on the frequency of primordial binaries in M71 with initial orbital periods in the range 2.5 - 5 days. This implies that the overall primordial binary frequency, f, is 22(sup +26)(sub -12)% assuming df/d log P = const ( the 'flat' distribution), or f = 57(sup +15)(sub -8)% for df/d log P = 0.032 log P + const as observed for G-dwarf binaries in the solar neighborhood (the 'sloped' distribution). Both estimates of f correspond to binaries with initial periods shorter than 800 yr since any longer-period binaries would have been disrupted over the lifetime of the cluster. Our short-period binary frequency is in excellent agreement with the observed frequency of red-giant binaries observed in globulars if we adopt the flat distribution. For the sloped distribution, our results significantly overestimate the number of red-giant binaries. All of the short-period M71 binaries lie within 1 mag of the luminosity of the cluster turnoff in the color-magnitude diagram despite the fact we should have easily detected similar eclipsing binaries 2 - 2.5 mag fainter than this. We discuss the implications of this on our estimates of the binary frequency in M71 and on the formation of blue stragglers.
The accretion disks that fuel active galactic nuclei (AGNs) may house numerous stars and compact objects, formed in situ or captured from nearby star clusters. Embedded neutron stars and black holes may form binaries and eventually merge, emitting gravitational waves detectable by LIGO/VIRGO. AGN disks are a particularly promising environment for the production of high-mass gravitational-wave events involving black holes in the pair-instability mass gap, and may facilitate electromagnetic counterparts to black hole binary mergers. However, many orders of magnitude separate the typical length scales of binary formation and those on which gravitational waves can drive binary inspirals, making binary mergers inside the disk uncertain. Previous hydrodynamical simulations of binaries have either been restricted to two dimensions entirely, or focused on binaries aligned with the midplane of the disk. Herein we present the first three-dimensional, high-resolution, local-shearing-box, inviscid hydrodynamical simulations of disk-embedded binaries over a range of orbital inclinations. We find that retrograde binaries can shrink up to 4 times as quickly as prograde binaries, and that all binaries not perfectly aligned (or anti-aligned) with the AGN disk are driven into alignment. An important consequence of this is that initially retrograde binaries will traverse the inclinations where von Zeipel–Lidov–Kozai oscillations can drive binary eccentricities to large values, potentially facilitating mergers. We also find that interactions with the AGN disk may excite eccentricities in retrograde binaries and cause the orbits of embedded binaries to precess.
This research includes theoretical studies of the formation and evolution of five types of interacting binary systems. Our main focus has been on developing a number of comprehensive population synthesis codes to study the following types of binary systems: (i) cataclysmic variables (#3, #8, #12, #15), (ii) low- and intermediate-mass X-ray binaries (#13, #20, #21), (iii) high-mass X-ray binaries (#14, #17, #22), (iv) recycled binary millisecond pulsars in globular clusters (#5, #10, #ll), and (v) planetary nebulae which form in interacting binaries (#6, #9). The numbers in parentheses refer to papers published or in preparation that are listed in this paper. These codes take a new unified approach to population synthesis studies. The first step involves a Monte Carlo selection of the primordial binaries, including the constituent masses, and orbital separations and eccentricities. Next, a variety of analytic methods are used to evolve the primary star to the point where either a dynamical episode of mass transfer to the secondary occurs (the common envelope phase), or the system evolves down an alternate path. If the residual core of the primary is greater than 2.5 solar mass, it will evolve to Fe core collapse and the production of a neutron star and a supernova explosion. In the case of systems involving neutron stars, a kick velocity is chosen randomly from an appropriate distribution and added to the orbital dynamics which determine the state of the binary system after the supernova explosion. In the third step, all binaries which commence stable mass transfer from the donor star (the original secondary in the binary system) to the compact object, are followed with a detailed binary evolution code. Finally, we include all the relevant dynamics of the binary system. For example, in the case of LMXBs, the binary system, with its recoil velocity from the supernova explosion, is followed in time through its path in the Galactic potential. For our globular cluster study, detailed three-body calculations are used to follow the interactions of the binary with passing field stars.
The accretion disks that power active galactic nuclei (AGN) are thought to house populations of stars and compact objects; after forming binaries these compact objects may merge, begetting gravitational waves (GWs) such as those detected by LIGO and VIRGO. We present a comprehensive study of the early evolution of binaries within AGN disks as their orbits are influenced by the surrounding gas, focusing on eccentric and unequal-mass binaries. Nearly equal-mass binaries behave similarly to their equal-mass counterparts: Prograde binaries inspiral, albeit somewhat slowly, and have their eccentricities damped; retrograde binaries inspiral ∼2–3 times faster than their prograde counterparts, and those with near-equal masses are driven quickly toward near-unity eccentricities. However, the primaries in retrograde binaries with mass ratios of m 2 /m 1 ≲ 0.4 experience significantly weaker headwinds and retain substantial accretion disks that help damp binary eccentricities, slowing binary inspirals. Additionally, we find that while accretion drives prograde binaries toward equal masses thanks to the exchange of material between the primary and secondary accretion disks, retrograde binaries are driven slowly toward more extreme mass ratios. Prograde binaries, and generally those with low mass ratios, likely accrete for multiple e-folding timescales before merger. On the other hand, high-mass-ratio retrograde binaries may merge before accreting substantially, potentially approaching merger with detectable eccentricity. Future ground-based GW observatories, with their broader frequency coverage, should be particularly useful for studying these populations.
We present an improved catalog of halo wide binaries compiled from an extensive literature search. Most of our binaries stem from the common proper motion binary catalogs by Allen et al. and Chanamé and Gould, but we have also included binaries from the lists of Ryan and Zapatero-Osorio and Martín. All binaries were carefully checked and their distances and systemic radial velocities are included when available. Probable membership to the halo population was tested by means of reduced proper motion diagrams for 251 candidate halo binaries. After eliminating obvious disk binaries, we ended up with 211 probable halo binaries, 150 of which have radial velocities available. We compute galactic orbits for these 150 binaries and calculate the time they spend within the galactic disk. Considering the full sample of 251 candidate halo binaries as well as several subsamples, we find that the distribution of angular separations (or expected major semiaxes) follows a power law f(a) ∼ a {sup –1} (Oepik's relation) up to different limits. For the 50 most disk-like binaries, those that spend their entire lives within z = ±500 pc, this limit is found to be 19,000 AU (0.09 pc), while for the 50 most halo-like binaries, those that spend on average only 18% of their lives within z = ±500 pc, the limit is 63,000 AU (0.31 pc). In a companion paper, we employ this catalog to establish limits on the masses of the halo massive perturbers (massive compact halo objects).
The two Large Magellanic Cloud star clusters, NGC 1805 and NGC 1818, are approximately the same chronological age (∼30 Myr), but show different radial trends in binary frequency. The F-type stars (1.3–2.2 M{sub ⊙}) in NGC 1818 have a binary frequency that decreases toward the core, while the binary frequency for stars of similar mass in NGC 1805 is flat with radius, or perhaps bimodal (with a peak in the core). We show here, through detailed N-body modeling, that both clusters could have formed with the same primordial binary frequency and with binary orbital elements and masses drawn from the same distributions (defined from observations of open clusters and the field of our Galaxy). The observed radial trends in binary frequency for both clusters are best matched with models that have initial substructure. Furthermore, both clusters may be evolving along a very similar dynamical sequence, with the key difference that NGC 1805 is dynamically older than NGC 1818. The F-type binaries in NGC 1818 still show evidence of an initial period of rapid dynamical disruptions (which occur preferentially in the core), while NGC 1805 has already begun to recover a higher core binary frequency, owing to mass segregation (which will eventually produce a distribution in binary frequency that rises only toward the core, as is observed in old Milky Way star clusters). This recovery rate increases for higher-mass binaries, and therefore even at one age in one cluster, we predict a similar dynamical sequence in the radial distribution of the binary frequency as a function of binary primary mass.
High-precision kinematic studies of globular clusters (GCs) require an accurate knowledge of all possible sources of contamination. Among other sources, binary stars can introduce systematic biases in the kinematics. Using a set of Monte Carlo cluster simulations with different concentrations and binary fractions, we investigate the effect of unresolved binaries on proper-motion dispersion profiles, treating the simulations like Hubble Space Telescope proper-motion samples. Since GCs evolve toward a state of partial energy equipartition, more-massive stars lose energy and decrease their velocity dispersion. As a consequence, on average, binaries have a lower velocity dispersion, since they are more-massive kinematic tracers. We show that, in the case of clusters with high binary fractions (initial binary fractions of 50%) and high concentrations (i.e., closer to energy equipartition), unresolved binaries introduce a color-dependent bias in the velocity dispersion of main-sequence stars of the order of 0.1–0.3 km s{sup −1} (corresponding to 1%−6% of the velocity dispersion), with the reddest stars having a lower velocity dispersion, due to the higher fraction of contaminating binaries. This bias depends on the ability to distinguish binaries from single stars, on the details of the color–magnitude diagram and the photometric errors. We apply our analysis to the HSTPROMO data set of NGC 7078 (M15) and show that no effect ascribable to binaries is observed, consistent with the low binary fraction of the cluster. Our work indicates that binaries do not significantly bias proper-motion velocity-dispersion profiles, but should be taken into account in the error budget of kinematic analyses.
We discuss the detectability of gravitationally bound pairs of gas-giant planets (which we call “binary planets”) in extrasolar planetary systems that are formed through orbital instability followed by planet–planet dynamical tides during their close encounters, based on the results of N-body simulations by Ochiai et al. (Paper I). Paper I showed that the formation probability of a binary is as much as ∼10% for three giant planet systems that undergo orbital instability, and after post-capture long-term tidal evolution, the typical binary separation is three to five times the sum of the physical radii of the planets. The binary planets are stable during the main-sequence lifetime of solar-type stars, if the stellarcentric semimajor axis of the binary is larger than 0.3 AU. We show that detecting modulations of transit light curves is the most promising observational method to detect binary planets. Since the likely binary separations are comparable to the stellar diameter, the shape of the transit light curve is different from transit to transit, depending on the phase of the binary’s orbit. The transit durations and depth for binary planet transits are generally longer and deeper than those for the single planet case. We point out that binary planets could exist among the known inflated gas-giant planets or objects classified as false positive detections at orbital radii ≳0.3 AU, propose a binary planet explanation for the CoRoT candidate SRc01 E2 1066, and show that binary planets are likely to be present in, and could be detected using, Kepler-quality data.
We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star–black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc − 3 yr − 1 and the neutron star–black hole merger rate to be between 7.8 and 140 Gpc − 3 yr − 1 , assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc − 3 yr − 1 at a fiducial redshift ( z = 0.2 ). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to ( 1 + z ) κ with κ = 2. 9 − 1.8 + 1.7 for z ≲ 1 . Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from 1.2 − 0.2 + 0.1 to 2.0 − 0.3 + 0.3 M ⊙ . We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of 8.3 − 0.5 + 0.3 and 27.9 − 1.8 + 1.9 M ⊙ . While we continue to find that the mass distribution of a binary’s more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately 60 M ⊙ , which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below χ i ≈ 0.25 . While the majority of spins are preferentially aligned with the orbital angular momentum, we infer evidence of antialigned spins among the binary population. We observe an increase in spin magnitude for systems with more unequal-mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum. Published by the American Physical Society 2023
We created the APOGEE-GALEX-Gaia catalog to study white dwarf (WD) binaries. This database aims to create a minimally biased sample of WD binary systems identified from a combination of GALEX, Gaia, and APOGEE data to increase the number of WD binaries with orbital parameters and chemical compositions. We identify 3414 sources as WD binary candidates, with nondegenerate companions of spectral types between F and M, including main-sequence stars, main-sequence binaries, subgiants, sub-subgiants, red giants, and red clump stars. Among our findings are (a) a total of 1806 systems having inferred WD radii R < 25 R ⊕ , which constitute a more reliable group of WD binary candidates within the main sample; (b) a difference in the metallicity distribution function between WD binary candidates and the control sample of most luminous giants (M H < -3.0); (c) the existence of a population of sub-subgiants with WD companions; (d) evidence for shorter periods in binaries that contain WDs compared to those that do not, as shown by the cumulative distributions of APOGEE radial velocity shifts; (e) evidence for systemic orbital evolution in a sample of 252 WD binaries with orbital periods, based on differences in the period distribution between systems with red clump, main-sequence binary, and sub-subgiant companions and systems with main-sequence or red giant companions; and (f) evidence for chemical enrichment during common envelope (CE) evolution, shown by lower metallicities in wide WD binary candidates (P > 100 days) compared to post-CE (P < 100 days) WD binary candidates.
The problem is addressed to find a 1-1 mapping of the vertices of a binary tree onto those of a target binary tree such that the son of a node on the first binary tree is mapped onto a descendent of the image of that node in the second binary tree. There are two natural measures of the cost of this mapping, namely the dilation cost, i.e., the maximum distance in the target binary tree between the images of vertices that are adjacent in the original tree. The other measure, expansion cost, is defined as the number of extra nodes/edges to be added to the target binary tree in order to ensure a 1-1 mapping. An efficient algorithm to find a mapping of one binary tree onto another is described. It is shown that it is possible to minimize one cost of mapping at the expense of the other. This problem arises when designing pipelined arithmetic logic units (ALU) for special purpose computers. The pipeline is composed of ALU chips connected in the form of a binary tree. The operands to the pipeline can be supplied to the leaf nodes of the binary tree which then process and pass the results up to their parents. The final result is available at the root. As each new application may require a distinct nesting of operations, it is useful to be able to find a good mapping of a new binary tree over existing ALU tree. Another problem arises if every distinct required binary tree is known beforehand. Here it is useful to hardwire the pipeline in the form of a minimal supertree that contains all required binary trees.
Binaries in which both components are brown dwarfs (BDs) are being discovered at an increasing rate, and their properties may hold clues to their origin. We have carried out 200,000 N-body simulations of three identical stellar embryos with masses drawn from a Chabrier IMF and embedded in a molecular core. The bodies are initially non-hierarchical and undergo chaotic motions within the cloud core, while accreting using Bondi–Hoyle accretion. The coupling of dynamics and accretion often leads to one or two dominant bodies controlling the center of the cloud core, while banishing the other(s) to the lower-density outskirts, leading to stunted growth. Eventually each system transforms either to a bound hierarchical configuration or breaks apart into separate single and binary components. The orbital motion is followed for 100 Myr. In order to illustrate 200,000 end-states of such dynamical evolution with accretion, we introduce the “triple diagnostic diagram,” which plots two dimensionless numbers against each other, representing the binary mass ratio and the mass ratio of the third body to the total system mass. Numerous freefloating BD binaries are formed in these simulations, and statistical properties are derived. The separation distribution function is in good correspondence with observations, showing a steep rise at close separations, peaking around 13 AU and declining more gently, reaching zero at separations greater than 200 AU. Unresolved BD triple systems may appear as wider BD binaries. Mass ratios are strongly peaked toward unity, as observed, but this is partially due to the initial assumptions. Eccentricities gradually increase toward higher values, due to the lack of viscous interactions in the simulations, which would both shrink the orbits and decrease their eccentricities. Most newborn triple systems are unstable and while there are 9209 ejected BD binaries at 1 Myr, corresponding to about 4% of the 200,000 simulations, this number has grown to 15,894 at 100 Myr (∼8%). The total binary fraction among freefloating BDs is 0.43, higher than indicated by current observations, which, however, are still incomplete. Also, the gradual breakup of higher-order multiples leads to many more singles, thus lowering the binary fraction. The main threat to newly born triple systems is internal instabilities, not external perturbations. At 1 Myr there are 1325 BD binaries still bound to a star, corresponding to 0.66% of the simulations, but only 253 (0.13%) are stable on timescales >100 Myr. These simulations indicate that dynamical interactions in newborn triple systems of stellar embryos embedded in and accreting from a cloud core naturally form a population of freefloating BD binaries, and this mechanism may constitute a significant pathway for the formation of BD binaries.
Using time-dependent linear theory, we investigate the morphology of the gravitational wake induced by a binary, whose center of mass moves at velocity V{sub cm} against a uniform background of gas. For simplicity, we assume that the components of the binary are on circular orbits about their common center of mass. The consequences of dynamical friction is twofold. First, gas dynamical friction may drag the center of mass of the binary and cause the binary to migrate. Second, drag forces also induce a braking torque, which causes the orbits of the components of the binary to shrink. We compute the drag forces acting on one component of the binary due to the gravitational interaction with its own wake. We show that the dynamical friction force responsible for decelerating the center of mass of the binary is smaller than it is in the point-mass case because of the loss of gravitational focusing. We show that the braking internal torque depends on the Mach numbers of each binary component about their center of mass, and also on the Mach number of the center of mass of the binary. In general, the internal torque decreases with increasing the velocity of the binary relative to the ambient gas cloud. However, this is not always the case. We also mention the relevance of our results to the period distribution of binaries.