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At least 163 records · Page 9

BROWN DWARF BINARIES FROM DISINTEGRATING TRIPLE SYSTEMS

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.

79 ASTRONOMY AND ASTROPHYSICS↗

Binaries traveling through a gaseous medium: dynamical drag forces and internal torques

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.

79 ASTRONOMY AND ASTROPHYSICS↗

MONTE CARLO POPULATION SYNTHESIS OF POST-COMMON-ENVELOPE WHITE DWARF BINARIES AND TYPE Ia SUPERNOVA RATE

Binary population synthesis (BPS) studies provide a comprehensive way to understand the evolution of binaries and their end products. Close white dwarf (WD) binaries have crucial characteristics for examining the influence of unresolved physical parameters on binary evolution. In this paper, we perform Monte Carlo BPS simulations, investigating the population of WD/main-sequence (WD/MS) binaries and double WD binaries using a publicly available binary star evolution code under 37 different assumptions for key physical processes and binary initial conditions. We considered different combinations of the binding energy parameter ( λ {sub g}: considering gravitational energy only; λ {sub b}: considering both gravitational energy and internal energy; and λ {sub e}: considering gravitational energy, internal energy, and entropy of the envelope, with values derived from the MESA code), CE efficiency, critical mass ratio, initial primary mass function, and metallicity. We find that a larger number of post-CE WD/MS binaries in tight orbits are formed when the binding energy parameters are set by λ {sub e} than in those cases where other prescriptions are adopted. We also determine the effects of the other input parameters on the orbital periods and mass distributions of post-CE WD/MS binaries. As they contain at least one CO WD, double WD systems that evolved from WD/MS binaries may explode as type Ia supernovae (SNe Ia) via merging. In this work, we also investigate the frequency of two WD mergers and compare it to the SNe Ia rate. The calculated Galactic SNe Ia rate with λ = λ {sub e} is comparable to the observed SNe Ia rate, ∼8.2 × 10{sup 5} yr{sup 1} – ∼4 × 10{sup 3} yr{sup 1} depending on the other BPS parameters, if a DD system does not require a mass ratio higher than ∼0.8 to become an SNe Ia. On the other hand, a violent merger scenario, which requires the combined mass of two CO WDs ≥ 1.6 M {sub ⊙} and a mass ratio >0.8, results in a much lower SNe Ia rate than is observed.

79 ASTRONOMY AND ASTROPHYSICS↗

WHITE-LIGHT FLARES ON CLOSE BINARIES OBSERVED WITH KEPLER

Based on Kepler data, we present the results of a search for white light flares on 1049 close binaries. We identify 234 flare binaries, of which 6818 flares are detected. We compare the flare-binary fraction in different binary morphologies (“detachedness”). The result shows that the fractions in over-contact and ellipsoidal binaries are approximately 10%–20% lower than those in detached and semi-detached systems. We calculate the binary flare activity level (AL) of all the flare binaries, and discuss its variations along the orbital period ( P {sub orb}) and rotation period ( P {sub rot}, calculated for only detached binaries). We find that the AL increases with decreasing P {sub orb} or P {sub rot}, up to the critical values at P {sub orb} ∼ 3 days or P {sub rot} ∼ 1.5 days, and thereafter the AL starts decreasing no matter how fast the stars rotate. We examine the flaring rate as a function of orbital phase in two eclipsing binaries on which a large number of flares are detected. It appears that there is no correlation between flaring rate and orbital phase in these two binaries. In contrast, when we examine the function with 203 flares on 20 non-eclipse ellipsoidal binaries, bimodal distribution of amplitude-weighted flare numbers shows up at orbital phases 0.25 and 0.75. Such variation could be larger than what is expected from the cross section modification.

79 ASTRONOMY AND ASTROPHYSICS↗

Accretion and orbital inspiral in gas-assisted supermassive black hole binary mergers

Many galaxies are expected to harbor binary supermassive black holes (SMBHs) in their centers. Their interaction with the surrounding gas results in the accretion and exchange of angular momentum via tidal torques, facilitating binary inspiral. Here, we explore the non-trivial coupling between these two processes and analyze how the global properties of externally supplied circumbinary disks depend on the binary accretion rate. By formulating our results in terms of the angular momentum flux driven by internal stresses, we come up with a very simple classification of the possible global disk structures, which differ from the standard constant M-dot accretion disk solution. The suppression of accretion by the binary tides, leading to a significant mass accumulation in the inner disk, accelerates binary inspiral. We show that once the disk region strongly perturbed by the viscously transmitted tidal torque exceeds the binary semimajor axis, the binary can merge in less than its mass-doubling time due to accretion. Thus, unlike the inspirals driven by stellar scattering, the gas-assisted merger can occur even if the binary is embedded in a relatively low-mass disk (lower than its own mass). This is important for resolving the “last parsec” problem for SMBH binaries and understanding powerful gravitational wave sources in the universe. We argue that the enhancement of accretion by the binary found in some recent simulations cannot persist for a long time and should not affect the long-term orbital inspiral. We also review existing simulations of SMBH binary–disk coupling and propose a numerical setup which is particularly well suited to verifying our theoretical predictions.

79 ASTRONOMY AND ASTROPHYSICS↗

A m-ary linear feedback shift register with binary logic

A family of m-ary linear feedback shift registers with binary logic is disclosed. Each m-ary linear feedback shift register with binary logic generates a binary representation of a nonbinary recurring sequence, producible with a m-ary linear feedback shift register without binary logic in which m is greater than 2. The state table of a m-ary linear feedback shift register without binary logic, utilizing sum modulo m feedback, is first tubulated for a given initial state. The entries in the state table are coded in binary and the binary entries are used to set the initial states of the stages of a plurality of binary shift registers. A single feedback logic unit is employed which provides a separate feedback binary digit to each binary register as a function of the states of corresponding stages of the binary registers.

Perlman, M.↗

High-resolution spectroscopy of extremely metal-poor stars from SDSS/Segue. II. Binary fraction

The fraction of binary systems in various stellar populations of the Galaxy and the distribution of their orbital parameters are important but not well-determined factors in studies of star formation, stellar evolution, and Galactic chemical evolution. While observational studies have been carried out for a large sample of nearby stars, including some metal-poor Population II stars, almost no constraints on the binary nature for extremely metal-poor (EMP; [Fe/H] <−3.0) stars have yet been obtained. Here we investigate the fraction of double-lined spectroscopic binaries and carbon-enhanced metal-poor (CEMP) stars, many of which could have formed as pairs of low-mass and intermediate-mass stars, to estimate the lower limit of the fraction of binary systems having short periods. The estimate is based on a sample of very metal-poor stars selected from the Sloan Digital Sky Survey and observed at high spectral resolution in a previous study by Aoki et al. That survey reported 3 double-lined spectroscopic binaries and 11 CEMP stars, which we consider along with a sample of EMP stars from the literature compiled in the SAGA database. We have conducted measurements of the velocity components for stacked absorption features of different spectral lines for each double-lined spectroscopic binary. Our estimate indicates that the fraction of binary stars having orbital periods shorter than 1000 days is at least 10%, and possibly as high as 20% if the majority of CEMP stars are formed in such short-period binaries. This result suggests that the period distribution of EMP binary systems is biased toward short periods, unless the binary fraction of low-mass EMP stars is significantly higher than that of other nearby stars.

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BINARY ASTROMETRIC MICROLENSING WITH GAIA

We investigate whether or not Gaia can specify the binary fractions of massive stellar populations in the Galactic disk through astrometric microlensing. Furthermore, we study whether or not some information about their mass distributions can be inferred via this method. In this regard, we simulate the binary astrometric microlensing events due to massive stellar populations according to the Gaia observing strategy by considering (i) stellar-mass black holes, (ii) neutron stars, (iii) white dwarfs, and (iv) main-sequence stars as microlenses. The Gaia efficiency for detecting the binary signatures in binary astrometric microlensing events is ∼10%–20%. By calculating the optical depth due to the mentioned stellar populations, the numbers of the binary astrometric microlensing events being observed with Gaia with detectable binary signatures, for the binary fraction of about 0.1, are estimated to be 6, 11, 77, and 1316, respectively. Consequently, Gaia can potentially specify the binary fractions of these massive stellar populations. However, the binary fraction of black holes measured with this method has a large uncertainty owing to a low number of the estimated events. Knowing the binary fractions in massive stellar populations helps with studying the gravitational waves. Moreover, we investigate the number of massive microlenses for which Gaia specifies masses through astrometric microlensing of single lenses toward the Galactic bulge. The resulting efficiencies of measuring the mass of mentioned populations are 9.8%, 2.9%, 1.2%, and 0.8%, respectively. The numbers of their astrometric microlensing events being observed in the Gaia era in which the lens mass can be inferred with the relative error less than 0.5 toward the Galactic bulge are estimated as 45, 34, 76, and 786, respectively. Hence, Gaia potentially gives us some information about the mass distribution of these massive stellar populations.

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Binary frequencies in a sample of globular clusters. II. Sample analysis and comparison to models

Binary stars are predicted to have an important role in the evolution of globular clusters, so we obtained binary fractions for 35 globular clusters that were imaged in the F606W and F814W with the Advanced Camera for Surveys on the Hubble Space Telescope. When compared to the values of prior efforts, we find significant discrepancies, despite each group correcting for contamination effects and having performed the appropriate reliability tests. The most reliable binary fractions are obtained when restricting the binary fraction to q⩾0.5. Our analysis indicates that the range of the binary fractions is nearly an order of magnitude for the lowest dynamical ages, suggesting that there is a broad distribution in the binary fraction at globular cluster formation. Dynamical effects also appear to decrease the core binary fractions by a factor of two over a Hubble time, but this is a weak relationship. We confirm a correlation from previous work that the binary fraction within the core–radius decreases with cluster age, indicating that younger clusters formed with higher binary fractions. The strong radial gradient in the binary fraction with cluster radius appears to be a consequence of dynamical interactions. It is often not present in dynamically young clusters, but is nearly always present in dynamically old clusters.

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GALAXY ROTATION AND RAPID SUPERMASSIVE BINARY COALESCENCE

Galaxy mergers usher the supermassive black hole (SMBH) in each galaxy to the center of the potential, where they form an SMBH binary. The binary orbit shrinks by ejecting stars via three-body scattering, but ample work has shown that in spherical galaxy models, the binary separation stalls after ejecting all the stars in its loss cone—this is the well-known final parsec problem. However, it has been shown that SMBH binaries in non-spherical galactic nuclei harden at a nearly constant rate until reaching the gravitational wave regime. Here we use a suite of direct N-body simulations to follow SMBH binary evolution in both corotating and counterrotating flattened galaxy models. For N > 500 K, we find that the evolution of the SMBH binary is convergent and is independent of the particle number. Rotation in general increases the hardening rate of SMBH binaries even more effectively than galaxy geometry alone. SMBH binary hardening rates are similar for co- and counterrotating galaxies. In the corotating case, the center of mass of the SMBH binary settles into an orbit that is in corotation resonance with the background rotating model, and the coalescence time is roughly a few 100 Myr faster than a non-rotating flattened model. We find that counterrotation drives SMBHs to coalesce on a nearly radial orbit promptly after forming a hard binary. We discuss the implications for gravitational wave astronomy, hypervelocity star production, and the effect on the structure of the host galaxy.

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Close substellar-mass companions in stellar wide binaries: discovery and characterization with APOGEE and Gaia DR2

We present a search for close, unresolved companions in a subset of spatially resolved Gaia wide binaries containing main-sequence stars within 200 pc of the Sun, utilizing the APOGEE–Gaia Wide Binary Catalog. A catalogue of 37 wide binaries was created by selecting pairs of stars with nearly identical Gaia positions, parallaxes, and proper motions, and then confirming candidates to be gravitationally bound pairs using APOGEE radial velocities. We identify close, unresolved stellar and substellar candidate companions in these multiple systems using (1) the Gaia binary main sequence and (2) observed periodic radial velocity variations in APOGEE measurements due to the influence of a close substellar-mass companion. The studied wide binary pairs reveal a total of four stellar-mass close companions in four different wide binaries, and four substellar-mass close companion candidates in two wide binaries. The latter are therefore quadruple systems, with one substellar-mass companion orbiting each wide binary component in an S-type orbit. Taken at face value, these candidate systems represent an enhancement of an order of magnitude over the expected occurrence rate of ~2 percent of stars having substellar companions >2 M Jup within ~100-d orbits; we discuss implications and possible explanations for this result. Finally, we compare chemical differences between the components of the wide binaries and the components of the candidate higher-order systems and find that any chemical influence or correlation due to the presence of close companions to wide binary stars is not discernible.

79 ASTRONOMY AND ASTROPHYSICS↗

APPLICATION OF GAS DYNAMICAL FRICTION FOR PLANETESIMALS. II. EVOLUTION OF BINARY PLANETESIMALS

One of the first stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs long before the dispersal of most of the gas from the protoplanetary disk. At this stage gas–planetesimal interactions play a key role in the dynamical evolution of single intermediate-mass planetesimals (m{sub p} ∼ 10{sup 21}–10{sup 25} g) through gas dynamical friction (GDF). A significant fraction of all solar system planetesimals (asteroids and Kuiper-belt objects) are known to be binary planetesimals (BPs). Here, we explore the effects of GDF on the evolution of BPs embedded in a gaseous disk using an N-body code with a fiducial external force accounting for GDF. We find that GDF can induce binary mergers on timescales shorter than the disk lifetime for masses above m{sub p} ≳ 10{sup 22} g at 1 au, independent of the binary initial separation and eccentricity. Such mergers can affect the structure of merger-formed planetesimals, and the GDF-induced binary inspiral can play a role in the evolution of the planetesimal disk. In addition, binaries on eccentric orbits around the star may evolve in the supersonic regime, where the torque reverses and the binary expands, which would enhance the cross section for planetesimal encounters with the binary. Highly inclined binaries with small mass ratios, evolve due to the combined effects of Kozai–Lidov (KL) cycles with GDF which lead to chaotic evolution. Prograde binaries go through semi-regular KL evolution, while retrograde binaries frequently flip their inclination and ∼50% of them are destroyed.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian Characterization of Main-sequence Binaries in the Old Open Cluster NGC 188

The binary fractions of open and globular clusters yield powerful constraints on their dynamical state and evolutionary history. We apply publicly available Bayesian analysis tools to a UBV RIJHK {sub S} photometric catalog of the open cluster NGC 188 to detect and characterize photometric binaries along the cluster main sequence. This technique has the advantage of self-consistently handling photometric errors, missing data in various bandpasses, and star-by-star prior constraints on cluster membership. Simulations are used to verify uncertainties and quantify selection biases in our analysis, illustrating that among binaries with mass ratios >0.5, we recover the binary fraction to better than 7% in the mean, with no significant dependence on binary fraction and a mild dependence on assumed mass-ratio distribution. Using our photometric catalog, we recover the majority (65% ± 11%) of spectroscopically identified main-sequence binaries, including eight of the nine with spectroscopically measured mass ratios. Accounting for incompleteness and systematics, we derive a mass-ratio distribution that rises toward lower mass ratios (within our q > 0.5 analysis domain). We observe a raw binary fraction for solar-type main-sequence stars with mass ratios q > 0.5 of 42% ± 4%, independent of the assumed mass-ratio distribution to within its uncertainties, consistent with literature values for old open clusters but significantly higher than the field solar-type binary fraction. We confirm that the binaries identified by our method are more concentrated than single stars, in agreement with previous studies, and we demonstrate that the binary nature of those candidates that remain unidentified spectroscopically is strongly supported by photometry from Gaia DR2.

79 ASTRONOMY AND ASTROPHYSICS↗

RADIO-SELECTED BINARY ACTIVE GALACTIC NUCLEI FROM THE VERY LARGE ARRAY STRIPE 82 SURVEY

Galaxy mergers play an important role in the growth of galaxies and their supermassive black holes. Simulations suggest that tidal interactions could enhance black hole accretion, which can be tested by the fraction of binary active galactic nuclei (AGNs) among galaxy mergers. However, determining the fraction requires a statistical sample of binaries. We have identified kiloparsec-scale binary AGNs directly from high-resolution radio imaging. Inside the 92 deg{sup 2} covered by the high-resolution Very Large Array survey of the Sloan Digital Sky Survey (SDSS) Stripe 82 field, we identified 22 grade A and 30 grade B candidates of binary radio AGNs with angular separations less than 5'' (10 kpc at z = 0.1). Eight of the candidates have optical spectra for both components from the SDSS spectroscopic surveys and our Keck program. Two grade B candidates are projected pairs, but the remaining six candidates are all compelling cases of binary AGNs based on either emission line ratios or the excess in radio power compared to the Hα-traced star formation rate. Only two of the six binaries were previously discovered by an optical spectroscopic search. Based on these results, we estimate that ∼60% of our binary candidates would be confirmed once we obtain complete spectroscopic information. We conclude that wide-area high-resolution radio surveys offer an efficient method to identify large samples of binary AGNs. These radio-selected binary AGNs complement binaries identified at other wavelengths and are useful for understanding the triggering mechanisms of black hole accretion.

79 ASTRONOMY AND ASTROPHYSICS↗

Stability and coalescence of massive twin binaries

Massive stars are usually found in binaries, and binaries with periods less than 10 days may have a preference for near equal component masses (“twins”). In this paper we investigate the evolution of massive twin binaries all the way to contact and the possibility that these systems can be progenitors of double neutron star binaries. The small orbital separations of observed double neutron star binaries suggest that the progenitor systems underwent a common envelope phase at least once during their evolution. Bethe and Brown proposed that massive binary twins will undergo a common envelope evolution while both components are ascending the red giant branch (RGB) or asymptotic giant branch (AGB) simultaneously, also known as double-core evolution. Using models generated from the stellar evolution code EZ (evolve zero-age main sequence), we determine the range of mass ratios resulting in a contact binary with both components simultaneously ascending the RGB or AGB as a function of the difference in birth times, Δτ. We find that, even for a generous Δτ = 5 Myr, the minimum mass ratio q{sub min}=0.933 for an 8 M{sub ⊙} primary and increases for larger mass primaries. We use a smoothed particle hydrodynamics code, StarSmasher, to study specifically the evolution of q = 1 common envelope systems as a function of initial component mass, age, and orbital separation. We also consider a q = 0.997 system to test the effect of relaxing the constraint of strictly identical components. We find the dynamical stability limit, the largest orbital separation where the binary becomes dynamically unstable, as a function of the component mass and age. Finally, we calculate the efficiency of ejecting matter during the inspiral phase to extrapolate the properties of the remnant binary from our numerical results, assuming the common envelope is completely ejected. We find that for the nominal core masses, there is a minimum orbital separation for a given component mass such that the helium cores survive common envelope evolution in a tightly bound binary and are viable progenitors for double neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Fate of supernova progenitors in massive binary systems

ABSTRACT How massive stars end their lives depends on the core mass, core angular momentum, and hydrogen envelopes at death. However, these key physical facets of stellar evolution can be severely affected by binary interactions. In turn, the effectiveness of binary interactions itself varies greatly depending on the initial conditions of the binaries, making the situation much more complex. We investigate systematically how binary interactions influence core–collapse progenitors and their fates. Binary evolution simulations are performed to survey the parameter space of supernova progenitors in solar metallicity binary systems and to delineate major evolutionary paths. We first study fixed binary mass ratios ($q=M_2/M_1$ = 0.5, 0.7, and 0.9) to elucidate the impacts of initial mass and initial separation on the outcomes, treating separately Type Ibc supernova, Type II supernova, accretion-induced collapse (AIC), rapidly rotating supernova (Ibc-R), black hole formation, and long gamma ray burst (long GRB). We then conduct 12 binary population synthesis model calculations, varying the initial condition distributions and binary evolution parameters, to estimate various supernova fractions. We obtain a Milky Way supernova rate $R_{\rm SN} = (1.78$–$2.47) \times 10^{-2} \, {\rm yr}^{-1}$ which is consistent with observations. We find the rates of AIC, Ibc-R, and long GRB to be $\sim 1/100$ the rate of regular supernovae. Our estimated long GRB rates are higher than the observed long GRB rate and close to the low luminosity GRB rate, although care must be taken considering our models are computed with solar metallicity. Furthering binary modelling and improving the inputs one by one will enable more detailed studies of these and other transients associated with massive stars.

Astronomy & Astrophysics↗

Gravitational waves from supernova mass loss and natal kicks in close binaries

Some fraction of compact binaries that merge within a Hubble time may have formed from two massive stars in isolation. For this isolated-binary formation channel, binaries need to survive two supernova (SN) explosions in addition to surviving common-envelope evolution. For the SN explosions, both the mass loss and natal kicks change the orbital characteristics, producing either a bound or unbound binary. Here we show that gravitational waves (GWs) may be produced not only from the core-collapse SN process, but also from the SN mass loss and SN natal kick during the pre-SN to post-SN binary transition. We model the dynamical evolution of a binary at the time of the second SN explosion with an equation of motion that accounts for the finite time-scales of the SN mass loss and the SN natal kick. From the dynamical evolution of the binary, we calculate the GW burst signals associated with the SN natal kicks. We find that such GW bursts may be of interest to future mid-band GW detectors like DECIGO. We also find that the energy radiated away from the GWs emitted due to the SN mass loss and natal kick may be a significant fraction, ≳ 10 per cent⁠, of the post-SN binary’s orbital energy. For unbound post-SN binaries, the energy radiated away in GWs tends to be higher than that of bound binaries.

79 ASTRONOMY AND ASTROPHYSICS↗

Evolution of Binary Supermassive Black Holes in Rotating Nuclei

The interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binary’s orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binary’s orbital eccentricity as well. We present a general treatment of this problem based on the Fokker–Planck equation for f , defined as the probability distribution for the binary’s orbital elements. First- and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analytic approximations are presented for some of these coefficients. Solutions of the Fokker–Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: (1) the orientation of the binary’s orbit evolves toward alignment with the plane of rotation of the nucleus and (2) binary orbital eccentricity decreases for aligned binaries and increases for counteraligned ones. We find that the diffusive (random-walk) component of a binary’s evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity, and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets.

79 ASTRONOMY AND ASTROPHYSICS↗