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Binary system

A binary system is a gravitationally bound pair of astronomical objects that orbit their common center of mass.^[1] The term most commonly refers to binary stars, where two stars interact through gravity, but it can also describe systems involving other celestial bodies such as black holes, neutron stars, or planets.^[2] Binary systems are prevalent in the universe; estimates suggest that approximately half of all stars in the Milky Way reside in binary or multiple-star configurations.^[1] These systems play a crucial role in astrophysics, enabling precise measurements of stellar masses via orbital dynamics and providing insights into star formation, evolution, and even the potential for habitable exoplanets.^[3] The study of binaries dates back to the early 19th century, when William Herschel recognized that some double stars are physically associated and orbiting each other, rather than mere optical alignments.^[1] Modern observations, aided by telescopes and space missions, continue to reveal the diversity and dynamics of these fundamental stellar partnerships.

Definition and Fundamentals

Core Definition

A binary system in astronomy refers to two celestial bodies of comparable mass that are gravitationally bound to each other and orbit around their common center of mass, or barycenter.^[4] This mutual orbit distinguishes binary systems from hierarchical arrangements like planet-satellite systems. In binaries with comparable masses, the barycenter lies outside both bodies, ensuring neither dominates the dynamics.^[5] Such systems are prevalent throughout the universe, with estimates suggesting that up to half of all stars exist in binaries, though the concept applies broadly to non-stellar objects as well.^[1] The recognition of binary systems originated with binary stars, first systematically identified by William Herschel in 1802, who coined the term "binary" to describe gravitationally bound pairs of stars orbiting each other, distinguishing them from mere optical alignments.^[6] Herschel's observations laid the groundwork for understanding stellar multiplicity, and over time, the binary concept was extended to other celestial pairs, such as asteroids and dwarf planet satellites, where comparable masses allow for similar orbital behaviors.^[4] A key distinction from single-star systems with satellites lies in the mass disparity: in true binaries, the bodies have comparable masses, resulting in a mutual orbit around an external barycenter, whereas in systems like Earth-Moon, the satellite's mass is much smaller (about 1/81 of Earth's), placing the barycenter inside the primary body and rendering it a hierarchical rather than binary configuration.^[7] This criterion ensures that binary dynamics involve balanced gravitational influences, unlike one-sided orbits. Fundamental parameters characterizing binary systems include the orbital separation (semi-major axis, a), which measures the average distance between the bodies; the orbital period (P), the time for one complete revolution; the mass ratio (q = m₂/m₁), indicating relative masses; and the eccentricity (e), describing the orbit's deviation from circularity (0 for circular, approaching 1 for highly elongated).^[8] These parameters, derived from observational data, provide insights into the system's stability and evolution without delving into specific force balances.^[8]

Physical Characteristics

In binary systems, the gravitational interaction between the two components is governed by Newton's law of universal gravitation, which for the two-body problem reduces the dynamics to an equivalent one-body problem using the reduced mass \mu = \frac{m_1 m_2}{m_1 + m_2}, where m_1 and m_2 are the masses of the two bodies. This formulation simplifies the analysis of their mutual orbit, treating the system as a single particle of mass \mu orbiting the total mass M = m_1 + m_2 at a distance equal to the relative separation. The gravitational binding energy arises from this interaction, binding the components against disruptive forces.^[9]^[10] The common center of mass, or barycenter, is the point about which both components orbit, located at a distance from each body proportional to the inverse of their masses. For a binary with semi-major axis a of the relative orbit, the orbital radius of the first component is r_1 = \frac{m_2}{m_1 + m_2} a, and similarly for the second, ensuring the center of mass remains fixed in an inertial frame. This barycenter dynamics dictates the scale of the system's internal motions, with the separation between components typically much smaller than distances to external influences.^[9]^[11] For circular orbits, the total mechanical energy of the binary system is E = -\frac{G m_1 m_2}{2a}, where G is the gravitational constant and a is the semi-major axis, reflecting the balance between negative gravitational potential energy and positive kinetic energy. The virial theorem applies to this bound system, stating that twice the time-averaged kinetic energy equals the absolute value of the time-averaged potential energy, $2\langle K \rangle = -\langle U \rangle, which holds for stable, self-gravitating configurations and implies E = -\langle K \rangle. This theorem underscores the energy partitioning in binary systems over orbital timescales.^[12] Tidal effects in close binaries distort the components due to differential gravitational forces, leading to the concept of the Roche lobe, the region around each star where material is gravitationally bound to it rather than the companion. If a star expands to fill its Roche lobe, mass transfer can occur through the inner Lagrange point. The Roche potential, which defines these lobes, is given by \psi = -\frac{G m_1}{r_1} - \frac{G m_2}{r_2} - \frac{1}{2} \Omega^2 \rho^2, where r_1 and r_2 are distances from the respective masses, \Omega is the orbital angular velocity, and \rho is the cylindrical radius from the rotation axis; the centrifugal term accounts for the rotating frame.^[13]^[14] Angular momentum is conserved in isolated binary systems, with the specific angular momentum of the relative orbit h = \sqrt{G (m_1 + m_2) a (1 - e^2)}, where e is the eccentricity. This quantity remains constant throughout the system's evolution unless external torques act, influencing the stability and separation of the orbit.^[15]

Orbital Mechanics

The orbital mechanics of binary systems are governed by the two-body problem in Newtonian gravity, which describes the mutual motion of two point masses under their gravitational attraction. This problem can be exactly solved by reducing it to an equivalent one-body problem, where the relative motion of the two bodies is equivalent to the motion of a single reduced mass \mu = \frac{m_1 m_2}{m_1 + m_2} orbiting a fixed central mass M = m_1 + m_2 at a distance equal to their separation vector \mathbf{r} = \mathbf{r_1} - \mathbf{r_2}.^[9]^[16] The equations of motion for the relative vector simplify to \ddot{\mathbf{r}} = -\frac{GM}{r^3} \mathbf{r}, yielding closed elliptical orbits for bound systems with total energy E < 0.^[9]^[17] For bound elliptical orbits, Kepler's laws generalize to binary systems. The first law states that the relative orbit is an ellipse with the center of mass at one focus. The second law, conservation of angular momentum, implies equal areas swept in equal times. The third law relates the orbital period T to the semi-major axis a of the relative orbit via T^2 = \frac{4\pi^2}{G(m_1 + m_2)} a^3, or equivalently T = 2\pi \sqrt{\frac{a^3}{G(m_1 + m_2)}}, where a = a_1 + a_2 and a_1, a_2 are the semi-major axes of the individual orbits around the center of mass.^[18]^[19] This relation allows determination of the total mass from observed period and separation. Unbound systems follow parabolic (e=1) or hyperbolic (e>1) trajectories, but binary stars predominantly exhibit bound elliptical orbits with $0 \leq e < 1. The geometry of these orbits is fully specified by six orbital elements: the semi-major axis a, which sets the scale; eccentricity e, describing the orbit's elongation; inclination i, the angle between the orbital plane and the sky plane ($0^\circ \leq i \leq 180^\circ); longitude of the ascending node \Omega, the position angle of the ascending node; argument of pericenter \omega, the angle from the ascending node to pericenter; and mean anomaly M, which specifies the position along the orbit at a given time.^[20]^[21] These elements parameterize the orientation and shape, enabling prediction of positions over time via the solution to Kepler's equation. The vis-viva equation provides the speed v at any separation r in the relative orbit: v^2 = G(m_1 + m_2) \left( \frac{2}{r} - \frac{1}{a} \right), conserving energy across the orbit.^[22] For elliptical orbits, v is maximum at pericenter (r = a(1 - e)) and minimum at apocenter (r = a(1 + e)); in the parabolic limit (a \to \infty), it reduces to escape speed v = \sqrt{2 G (m_1 + m_2)/r}. In hierarchical binaries, where a close inner pair is perturbed by a distant third body, the two-body approximation breaks down due to three-body effects, leading to secular variations in eccentricity and inclination via mechanisms like the Kozai-Lidov resonance.^[23] These perturbations are treated approximately using averaged Hamiltonians, without altering the overall stability for wide outer orbits. For non-hierarchical or multi-body configurations, analytical solutions fail, necessitating numerical N-body integrators such as leapfrog or Bulirsch-Stoer methods to simulate gravitational interactions over time.^[24]^[25]

Classification and Types

Visual and Spectroscopic Binaries

Visual binaries are stellar systems in which the two components can be spatially resolved through direct imaging, allowing astronomers to measure their relative positions and proper motions over time to determine orbital elements. This resolution is possible when the angular separation \theta between the stars is greater than the telescope's diffraction limit, typically on the order of arcseconds for ground-based observations. The angular separation is related to the physical semi-major axis a (in AU) and distance d (in pc) by the formula \theta \approx a / d (in arcseconds), enabling the derivation of absolute orbital sizes when combined with parallax measurements. A classic example is the Sirius system, consisting of Sirius A (a main-sequence A-type star) and Sirius B (a white dwarf companion), with an orbital period of approximately 50 years and an average separation of 20 AU, yielding a total mass of about 3.2 solar masses via Kepler's third law. Spectroscopic binaries are identified through periodic Doppler shifts in the spectral lines of one or both stars, arising from their orbital motion along the line of sight, which manifests as radial velocity variations. The radial velocity semi-amplitude K for a component quantifies this variation and is given by

K = \left( \frac{2\pi G}{P} \right)^{1/3} \frac{m_2 \sin i}{(m_1 + m_2)^{2/3}} \frac{1}{\sqrt{1 - e^2}},

where P is the orbital period, m_1 and m_2 are the masses, i is the inclination, and e is the eccentricity; this formula applies to the observed velocity curve of the primary or secondary. These systems are subdivided into single-lined (SB1), where only one set of spectral lines is visible and Doppler-shifted (often because one star dominates the light), and double-lined (SB2), where lines from both stars are discernible and shift oppositely, allowing measurement of both velocity amplitudes. For SB1 systems, the mass function provides a lower limit on the unseen companion's mass:

f(m) = \frac{P K_1^3 (1 - e^2)^{3/2}}{2\pi G} = \frac{m_2^3 \sin^3 i}{(m_1 + m_2)^2},

where K_1 is the primary's semi-amplitude; assuming a typical \sin^3 i \approx 0.67 statistically yields mass estimates, though individual inclinations remain uncertain without additional data. Astrometric binaries, while not directly resolved visually or spectroscopically, are detected through the periodic wobble in a star's proper motion or position due to the gravitational pull of an unseen companion, effectively measuring the photocenter's orbit. This method is particularly effective for wide orbits or low-mass companions and has been revolutionized by the Gaia mission, which in its Data Release 3 (2022) provided orbital solutions for over 168,000 astrometric binaries, including detections of rare systems like black hole candidates (e.g., Gaia BH1, BH2, BH3) and white dwarf pairs through precise positional measurements spanning 100–1000 day periods. Recent examples include Gaia BH3 (2024), a ~33 solar mass black hole in an 11.6-year orbit with a metal-poor giant star. Gaia's contributions extend to identifying thousands of white dwarf-main-sequence binaries and enabling joint astrometric-radial velocity analyses for refined mass determinations. Stellar binaries are further hierarchically classified by orbital separation into close (typically a \lesssim 10 AU) and wide (a \gtrsim 100 AU) systems, with close binaries prone to evolutionary interactions like mass transfer due to Roche lobe overflow, while wide binaries evolve largely independently. Semi-detached systems represent a subset where one star fills its Roche lobe, leading to mass exchange with the companion (e.g., in Algol-type binaries), often resulting from the initially more massive star evolving faster and becoming the donor. Hierarchical architectures, such as a close binary orbited by a distant third star at separations greater than five times the inner period, stabilize these configurations and are common in multiple-star systems.

Eclipsing and Contact Binaries

Eclipsing binaries are a subclass of binary stars observed through photometric variations caused by one component periodically passing in front of the other along the observer's line of sight. These systems exhibit characteristic light curves with two minima: the primary eclipse, which is deeper and occurs when the hotter or more luminous star is occulted, and the secondary eclipse, which is shallower and happens when the cooler or fainter star is occulted. For eclipses to occur, the orbital inclination must be close to 90°, ensuring the alignment is nearly edge-on. The depth of the eclipse, denoted as Δm, is approximately proportional to (r / a)^2, where r is the stellar radius and a is the orbital separation, reflecting the geometric overlap during the event. Eclipsing binaries are further classified as detached or semi-detached based on whether the stars fill their Roche lobes. In detached systems, both stars lie well within their Roche lobes, resulting in no mass transfer and typically sharp-edged light curve minima due to the spherical shapes of the components. Semi-detached systems, often exemplified by Algol-type binaries, involve one star filling its Roche lobe and transferring mass to its companion, leading to more rounded minima and potential distortions in the light curve. A notable feature in these semi-detached systems is the Algol paradox, where the more massive star appears cooler and less evolved than the less massive one, attributed to the donor star losing mass and thus slowing its evolution while the gainer rejuvenates. Contact binaries represent the extreme case where both stars overfill their Roche lobes and share a common envelope of gas, resulting in continuous light variations beyond just the eclipses due to tidal and gravitational distortions. These overcontact systems, such as those of the W Ursae Majoris (W UMa) type, exhibit light curves with unequal but connected minima and ellipsoidal shapes from the shared envelope. The period-color relation for W UMa binaries indicates that orbital periods increase with redder colors (B-V), linking shorter, bluer (hotter, higher-mass) systems to longer, redder (cooler, lower-mass) ones. Within contact binaries, subtypes include Beta Lyrae systems, which are semi-detached with significant Roche lobe overflow causing continuous light curve variations from the elongated, distorted shapes and mass transfer streams, and W UMa systems, which are fully overcontact with both components enveloped together, leading to more symmetric but still variable light curves. Radial velocity measurements can confirm orbital parameters in these photometric systems. Statistically, 30-50% of stars reside in binary systems, but only about 1% of these are eclipsing for random orientations, as the required near-edge-on inclination is geometrically rare; this fraction aligns with observations from large surveys like Kepler, where eclipsing binaries comprise roughly 1.2% of monitored stars.

Non-Stellar Binary Systems

Non-stellar binary systems encompass pairs of celestial bodies that are neither stars nor involve stellar companions, including asteroids, planetary systems, and compact objects such as black holes and neutron stars. These systems provide critical insights into the formation and dynamics of smaller solar system bodies and exotic remnants of stellar evolution, often revealing processes like rotational fission, tidal interactions, and gravitational wave emission. Unlike stellar binaries, non-stellar pairs typically exhibit wider relative separations and lower masses, allowing for detailed study through direct imaging, occultations, and spacecraft flybys. Their prevalence underscores the ubiquity of binary configurations across diverse environments, from the inner asteroid belt to the outer Kuiper Belt and beyond. Binary asteroids represent a significant subset of non-stellar systems, comprising an estimated 15 ± 4% of near-Earth asteroids as of 2023. These systems often form through the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, where solar radiation torque spins up a rubble-pile asteroid to the point of fission, ejecting material that coalesces into a secondary component. A prominent example is the near-Earth binary (66391) 1999 KW4, a contact binary-like system observed by radar in 2003, featuring a peanut-shaped primary and a smaller satellite, with formation attributed to YORP-induced spin-up leading to equatorial mass shedding. Such binaries enable precise mass determinations via Kepler's third law applied to orbital parameters, aiding in understanding asteroid densities and compositions typically ranging from 1.5 to 3 g/cm³. Planetary binaries, though rarer, highlight extreme mass ratios in non-stellar pairs, as exemplified by the Pluto-Charon system, classified as a dwarf planet binary due to Charon's substantial size—over half of Pluto's diameter—and the location of their common barycenter outside Pluto's radius. Discovered in 1978, this tidally locked pair orbits with a 6.4-day period, and mutual eclipses were directly observed by NASA's New Horizons spacecraft during its 2015 flyby, confirming the system's synchronous rotation and revealing Charon's cryovolcanic surface. The barycenter's external position, approximately 960 km above Pluto's surface, underscores the binary nature, with total system mass about 1.3 × 10^22 kg derived from orbital dynamics. Compact object binaries involve the remnants of massive stars, offering tests of general relativity and multimessenger astronomy. Black hole binaries, such as Cygnus X-1, consist of a stellar-mass black hole (approximately 21 solar masses) orbiting a blue supergiant companion with a 5.6-day period; identified as the first black hole candidate in 1971 from X-ray observations by the Uhuru satellite, it demonstrates accretion-driven X-ray emission and jets. Neutron star binaries, like the Hulse-Taylor pulsar (PSR B1913+16), discovered in 1974, feature two neutron stars (masses around 1.4 solar masses each) in a 7.75-hour orbit, providing the first indirect evidence of gravitational waves through orbital decay matching general relativity predictions at the 0.2% level, as confirmed over decades of timing observations. These systems illustrate post-supernova formation via core collapse and subsequent dynamical pairing. Circumbinary exoplanets, orbiting binary pairs including stellar or compact objects like white dwarfs or brown dwarfs, expand the scope of non-stellar binaries, with stability constrained to regions beyond about three times the binary separation to avoid perturbations. The first confirmed example, Kepler-16b discovered in 2011 via NASA's Kepler mission, is a Saturn-mass gas giant circling a 41-day binary of a K-dwarf and red dwarf, exhibiting mutual eclipses that modulate the planet's transit light curve. Stability simulations indicate such planets reside near dynamical boundaries, with habitable zones potentially offset due to variable stellar irradiation. These systems, detected through transit photometry, suggest formation via disk capture or in situ accretion resilient to binary torques. The prevalence of non-stellar binaries is notably high among trans-Neptunian objects (TNOs), where approximately 10-20% of the population in the Kuiper Belt exhibits binary configurations, based on surveys identifying over 80 such systems by 2018. This elevated fraction, particularly among cold classical TNOs, implies gentle formation environments like gravitational collapse in the protoplanetary disk, contrasting with collision-dominated inner solar system. Binaries in this region facilitate mass estimation via relative astrometry and light curve analysis, revealing low densities (around 1 g/cm³) indicative of icy, porous structures, and informing models of solar system architecture.

Formation and Evolution

Stellar Binary Formation

Stellar binary systems primarily form through fragmentation processes during the collapse of molecular cloud cores into protostars. The dominant mechanisms involve turbulent fragmentation during core collapse and gravitational instability in the ensuing circumstellar disks, both of which lead to the formation of multiple protostellar cores that evolve into bound binary pairs. Numerical simulations of these processes, incorporating realistic radiative transfer and turbulence, indicate that approximately 50-70% of low-mass stars form as part of multiple systems, with binaries comprising the majority.^[26] Fragmentation in protostellar disks arises from core collapse, where turbulent motions in the collapsing cloud induce density perturbations that spawn secondary cores. These simulations demonstrate that radiation feedback from the primary protostar suppresses excessive fragmentation in the inner disk but allows turbulent fragmentation at larger separations, typically beyond 100 AU, resulting in wide binaries. For low-mass systems, this pathway predominates over disk instability due to the heating effects that stabilize the inner regions.^[27] Disk fragmentation occurs when a massive, rapidly accreting circumstellar disk around a young protostar becomes gravitationally unstable, leading to the formation of clumps that collapse into companion stars. This process is governed by the Toomre criterion, where instability arises if the dimensionless parameter Q < 1, indicating that the disk's self-gravity overcomes pressure and rotation support. Such fragmentation favors close binaries with separations under 100 AU and is more efficient in massive disks around higher-mass primaries. The initial mass function (IMF) for binaries shows a strong dependence on primary mass, with higher multiplicity among massive stars. While low-mass stars exhibit binary fractions around 50%, up to 70% of O-type stars form in binary or higher-order systems, reflecting the enhanced role of disk fragmentation in more massive, turbulent environments. Metallicity influences binary formation by affecting cloud cooling rates, which in turn impact fragmentation scales. At lower metallicities, reduced opacity hinders cooling, leading to higher-density fragmentation that favors the formation of closer binaries, whereas solar-metallicity environments allow wider separations through more efficient cooling and disk instabilities.^[28] Observational evidence from Atacama Large Millimeter/submillimeter Array (ALMA) surveys supports these formation channels, revealing binary companions in numerous Class 0 protostars at separations of 50-500 AU. For instance, high-resolution imaging of embedded protostars like IRAS 16293-2422 shows paired outflows and disks indicative of early fragmentation.^[29]^[30]

Dynamical Interactions

In dense stellar environments such as star clusters, binary systems are profoundly influenced by gravitational interactions with single stars and other binaries, leading to modifications in their orbital parameters, formation of new systems, or outright disruption. These dynamical interactions occur frequently due to the high stellar densities, typically on timescales much shorter than the cluster's age, and play a crucial role in the overall energy budget and evolution of the cluster. Three-body encounters, in particular, dominate these processes, allowing for energy and angular momentum exchange that can either tighten existing binaries or eject one component, thereby injecting kinetic energy into the cluster and preventing core collapse in some cases.^[31] Three-body encounters between a binary and a single star can result in ejection of one star or hardening (tightening) of the binary orbit. In such interactions, the incoming single star interacts gravitationally with the binary components, leading to an energy exchange where the binary's binding energy increases if the single star is ejected with excess kinetic energy. The approximate energy change in these encounters, under the impulse approximation for distant flybys, is given by \Delta E \approx \frac{G m_1 m_2 m_3}{b v}, where G is the gravitational constant, m_1 and m_2 are the binary masses, m_3 is the single star mass, b is the impact parameter, and v is the relative velocity; this exchange scales with the masses and inversely with the encounter geometry, often resulting in binaries becoming harder (more tightly bound) by factors of up to 10-100 times their initial energy in close encounters. Simulations show that soft (weakly bound) binaries are prone to ionization, while hard binaries tend to harden further, with ejection events occurring in about 10-20% of strong interactions depending on mass ratios.^[32]^[33] Capture mechanisms enable the formation of new hard binaries through three-body assisted processes, where three single stars interact closely, and two become bound while the third is ejected. This requires the initial encounter to bring the stars within a distance comparable to their mutual Hill radius, with the cross-section for such captures scaling as \sigma \propto \frac{G^2 m^2}{v^4}, reflecting strong gravitational focusing at low relative velocities v; this velocity dependence makes capture more efficient in the dense, low-velocity cores of clusters. These dynamically formed binaries are typically harder than primordial ones and contribute significantly to the population of tight binaries observed in the field.^[34] Many dynamical interactions lead to the formation of hierarchical systems, consisting of an inner close binary orbited by a distant companion. For long-term stability, the separation ratio \Delta = a_\mathrm{out} / a_\mathrm{in} (where a_\mathrm{out} and a_\mathrm{in} are the semi-major axes of the outer and inner orbits, respectively) must exceed 3-5 to prevent chaotic perturbations and ejection of the companion; below this threshold, the system becomes unstable on timescales of $10^3-10^5 orbital periods. This criterion arises from numerical scattering experiments and accounts for eccentricity effects, ensuring the outer orbit dominates the dynamics without disrupting the inner binary. In star clusters, these interactions drive binary dissolution at rates that depend on density and velocity dispersion, with N-body simulations indicating that only about 10% of observed field binaries originate from primordial populations that survive dynamical processing, while the majority result from ongoing dynamical formation and hardening. Dissolution is more rapid for soft binaries in high-density environments, with half-lives of $10^8-10^9 years in typical open clusters, leading to a preference for hard binaries in the ejected field population. A prominent example is the formation of blue stragglers in globular clusters, anomalous main-sequence stars brighter than the cluster turnoff, often produced by mergers of primordial or dynamically hardened binaries during three-body encounters; these mergers occur preferentially in dense cores, accounting for up to 50% of blue stragglers in some clusters like M67.^[35]

Evolutionary Pathways

The evolution of binary star systems is profoundly shaped by mass transfer between the components, which alters their masses, radii, and orbital separation over time. In conservative mass transfer, the total mass and angular momentum of the system are preserved, with material from the donor star fully accreted by the companion, leading to scenarios where the initially less massive star can become the more massive one through reversal of mass ratio.^[36] In contrast, non-conservative mass transfer involves significant mass loss from the system, often through isotropic re-emission from the accretor or expulsion in a Jeans-mode wind from the donor, which can widen the orbit and stabilize the transfer but also reduce the efficiency of angular momentum transport.^[37] Angular momentum loss plays a critical role in driving these processes, particularly via magnetic braking in low-mass binaries, where the torque exerted by magnetized stellar winds scales as \dot{J} \propto \Omega^3, with \Omega denoting the donor's rotation rate, accelerating orbital shrinkage and Roche lobe overflow.^[38] When mass transfer becomes dynamically unstable—typically if the donor expands faster than the Roche lobe can adjust—the system enters a common envelope (CE) phase, where the companion spirals into the donor's envelope, ejecting it through drag-induced energy dissipation. The standard energy formalism for CE evolution balances the binding energy of the envelope, given by E_\mathrm{bind} = -\frac{[G](/page/G) M_\mathrm{env} M_\mathrm{core}}{2\lambda R_\mathrm{env}} (where M_\mathrm{env} and R_\mathrm{env} are the envelope mass and radius, M_\mathrm{core} is the core mass, G is the gravitational constant, and \lambda is a structure parameter accounting for recombination and ionization energies), against the orbital energy released during inspiral to determine the final separation.^[39] Spiral-in timescales during CE are short, often on the order of years to centuries, governed by the drag force and envelope opacity, resulting in tight post-CE orbits that can lead to further interactions or mergers.^[40] These evolutionary pathways culminate in diverse endpoints, including mergers of compact objects that power explosive transients. Double white dwarf (WD) binaries, formed through successive mass transfer and CE phases, can merge if their combined mass exceeds the Chandrasekhar limit of approximately 1.4 M_\odot, igniting a thermonuclear runaway that produces Type Ia supernovae, serving as standardizable candles for cosmology.^[41] Similarly, neutron star (NS) binaries evolve through mass transfer and CE to inspiral via gravitational wave emission, producing short gamma-ray bursts (GRBs) upon merger; the event GW170817 in 2017 provided direct evidence, with the merger triggering a short GRB and an associated kilonova from r-process nucleosynthesis in the ejected material. Binary population synthesis models, such as the BSE code, simulate these pathways across large stellar ensembles and predict that binaries contribute significantly to stripped-envelope supernovae, with approximately 50% of Type Ib/c events arising from mass transfer in progenitor systems that leave behind compact remnants.^[42]

Detection and Observation

Observational Methods

Observational methods for binary systems encompass a range of techniques that leverage emissions across the electromagnetic spectrum to detect and characterize these stellar pairs. In optical imaging, direct resolution of visual binaries relies on high angular precision to separate components, while ultraviolet (UV) spectroscopy probes hot, massive stars and their winds in systems like O-type binaries. Infrared (IR) observations target circumstellar dust disks and cool companions, revealing debris in young systems or obscured low-mass pairs. X-ray emissions, arising from accretion onto compact objects in binaries, provide insights into mass transfer processes, particularly in high-mass X-ray binaries where neutron stars or black holes interact with massive donors.^[43] Ground-based observatories complement space-based platforms, each offering distinct advantages in resolving binary dynamics. Telescopes like the High Accuracy Radial velocity Planet Searcher (HARPS) at the European Southern Observatory enable precise radial velocity measurements for spectroscopic binaries, detecting orbital motions through Doppler shifts with sensitivities down to meters per second. Space missions such as the Hubble Space Telescope (HST) achieve superior angular resolution for close visual binaries, free from atmospheric distortion, while the Transiting Exoplanet Survey Satellite (TESS) excels in photometric monitoring of eclipsing systems via transit-like dips in light curves. These space-based efforts surpass ground-based limits in stability and coverage, particularly for faint or southern-hemisphere targets.^[44] Large-scale surveys have quantified binary populations, informing the prevalence and orbital characteristics of these systems. Spectroscopic surveys like the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) reveal a binary fraction of approximately 41% for field FGK stars, derived from radial velocity variations in thousands of targets. The orbital period distribution for solar-type binaries follows a log-normal profile, peaking at approximately 300 years, which reflects formation mechanisms and dynamical evolution in the solar neighborhood.^[45]^[46] These statistics underscore the ubiquity of binaries among main-sequence stars, with fractions varying by spectral type and metallicity. Interferometry enhances resolution for unresolved binaries, allowing separation of components at sub-milliarcsecond scales. The Very Large Telescope Interferometer (VLTI) achieves angular resolutions below 1 milliarcsecond (mas) in the near- and mid-infrared, enabling astrometric orbits for nearby systems and direct measurement of stellar diameters in close pairs. By combining multiple baselines, VLTI reconstructs fringe patterns to discern companion positions, crucial for systems where traditional imaging falls short.^[47] For compact binaries involving pulsars, timing methods exploit pulse arrival delays to infer orbital parameters. In pulsar-white dwarf or pulsar-neutron star systems, the Shapiro delay—arising from general relativistic time dilation in the companion's gravitational field—manifests as:

\Delta t = \frac{G m}{c^3} \ln \left[ \frac{1 + \cos \theta}{1 - \cos \theta} \right]

where m is the companion mass, c the speed of light, G the gravitational constant, and \theta the angle between the line of sight and the pulsar-companion vector at superior conjunction. This delay, on the order of microseconds for typical masses, enables precise mass determinations and tests of gravity theories. Long-term monitoring with radio telescopes like the Green Bank Telescope accumulates these signals over years, revealing compact orbits inaccessible to other wavelengths.^[48]

Instrumentation and Techniques

The Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO), installed on the European Southern Observatory's (ESO) Very Large Telescope (VLT), achieves radial velocity (RV) precisions down to 10 cm/s, enabling the detection of subtle Doppler shifts in spectroscopic binaries.^[49] This high precision is particularly valuable for identifying double-lined spectroscopic binaries (SB2), where line profile variations reveal the presence of two stellar components through asymmetric broadening or splitting of spectral lines.^[50] Space-based astrometry has revolutionized binary detection through precise positional measurements. The Gaia mission's Data Release 3 (DR3), released in 2022, provides astrometric data for approximately 1.8 billion stars, from which over 800,000 non-single star solutions—including about 181,000 astrometric binaries—have been derived by modeling orbital motions and photocenter wobbles.^[51]^[52] Complementing this, the James Webb Space Telescope (JWST) employs infrared imaging and spectroscopy to observe exoplanets in binary systems, such as potential gas giants orbiting components of nearby binaries like Alpha Centauri, leveraging its high sensitivity to faint companions in crowded fields.^[53] Gravitational wave observatories like the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detect compact binary inspirals through the characteristic "chirp" signal of increasing frequency and amplitude as the components spiral inward.^[54] The detected strain h for such inspirals follows the quadrupole approximation:

h \propto \left( \frac{G M_{\rm chirp}}{c^2} \right)^{5/3} \left( \frac{\pi f}{c^3} \right)^{2/3} \frac{1}{d_L}

where M_{\rm chirp} is the chirp mass, f is the gravitational wave frequency, and d_L is the luminosity distance.^[54] This has enabled the identification of hundreds of binary black hole and neutron star mergers since 2015.^[55] Ground-based high-angular-resolution techniques mitigate atmospheric distortion for visual binaries. The Keck Observatory's adaptive optics (AO) system on the 10-m Keck II telescope corrects wavefront aberrations in real time, achieving sub-arcsecond resolutions to measure separations and position angles in nearby visual binaries with precisions of a few milliarcseconds.^[56] Similarly, speckle imaging reconstructs high-resolution images from short-exposure frames affected by atmospheric seeing, allowing the detection and characterization of close binary companions down to 20-50 milliarcsecond separations using autocorrelation techniques.^[57] Looking ahead, the Extremely Large Telescope (ELT), expected first light in 2028, will feature advanced high-contrast imaging instruments like the High Angular Resolution Monochromatic Imager (HARMONI) and the Mid-infrared ELT Imager and Spectrograph (METIS), enabling the direct imaging of young binaries and their protoplanetary disks at separations below 50 milliarcseconds through extreme AO and coronagraphy.^[58]^[59]

Data Analysis

Data analysis of binary systems involves computational techniques to derive orbital parameters, masses, and other physical properties from observational data such as radial velocities, astrometric positions, and photometric light curves. Orbital fitting typically employs least-squares minimization to determine elements like period P, eccentricity e, inclination i, and semi-amplitude K, by minimizing the residuals between observed and modeled positions or velocities.^[60] This non-linear least-squares approach, often using algorithms like Levenberg-Marquardt, provides initial estimates of the orbital solution. To quantify uncertainties, Monte Carlo Markov Chain (MCMC) methods are widely applied, sampling the posterior distribution of parameters and yielding robust error bars that account for correlations and non-Gaussian likelihoods.^[61] Mass determination in binary systems combines data from visual and spectroscopic observations. For single-lined spectroscopic binaries, where only one radial velocity curve is measurable, the mass function is given by

f(m) = \frac{m_2^3 \sin^3 i}{(m_1 + m_2)^2} = \frac{P K_1^3 (1 - e^2)^{3/2}}{2\pi G},

where m_1 and m_2 are the masses of the observed and unseen components, respectively, providing a lower limit on m_2 since \sin i \leq 1. In visual binaries with spectroscopic follow-up, the angular separation yields the semi-major axis a in AU, allowing full masses via Kepler's third law when combined with P. Double-lined spectroscopic binaries, with both K_1 and K_2 measurable, enable direct computation of the mass ratio m_1 / m_2 = K_2 / K_1 and minimum masses m_1 \sin^3 i = \frac{P K_2 (K_1 + K_2)^2 (1 - e^2)^{3/2}}{2\pi G} and m_2 \sin^3 i = \frac{P K_1 (K_1 + K_2)^2 (1 - e^2)^{3/2}}{2\pi G}, with i from visual or eclipsing data.^[62] Light curve modeling for eclipsing binaries uses synthetic photometry to fit observed flux variations, revealing radii, temperatures, and surface features. The Wilson-Devinney code, a seminal tool since its 1971 introduction, solves the inverse problem by integrating Roche geometry, tidal distortion, and reflection effects over the visible stellar disks.^[63] It incorporates limb darkening laws, such as linear, square-root, or logarithmic forms (e.g., I(\mu)/I(1) = 1 - u (1 - \mu), where \mu = \cos \theta and u is the coefficient), to accurately model the drop in intensity toward the limb due to atmospheric opacity.^[64] Fits adjust parameters like surface brightness ratios and fill-out factors, with uncertainties propagated via covariance matrices from least-squares optimization.^[65] Bayesian inference enhances parameter estimation by incorporating priors and handling complex likelihoods in orbital analysis. For eccentricity distributions, wide binaries often use a flat prior in \log e, reflecting observed near-uniform spacing in logarithmic scale for low-eccentricity systems, as derived from solar-neighborhood samples.^[66] MCMC implementations within Bayesian frameworks, such as those sampling the posterior p(\theta | D) \propto p(D | \theta) p(\theta), provide marginalized distributions for elements like e and \omega, improving robustness over classical methods for sparse or noisy data.^[67] Key error sources in binary data analysis include blending in crowded fields, where unresolved background stars dilute photometric depths or contaminate radial velocities, leading to underestimated radii or masses by up to 10-20% without correction.^[68] Atmospheric effects, such as scintillation and extinction in ground-based observations, introduce scatter in light curves and velocities, mitigated by differential photometry or space-based data but still contributing ~1-5% uncertainties in timings. Multi-periodicity, arising from aliases in unevenly sampled data or additional orbital harmonics, complicates period resolution; Fourier analysis or periodograms resolve this by identifying significant frequencies above noise levels.^[69]

Notable Examples and Applications

Prominent Stellar Binaries

One of the most prominent stellar binary systems is Alpha Centauri AB, the closest known binary to the Sun at a distance of approximately 4.37 light-years.^[70] The two stars, both Sun-like G-type main-sequence stars, orbit each other with a semi-major axis of 23.7 AU and a period of 79.9 years, with their separation varying from a minimum of 11.2 AU to a maximum of 35.6 AU.^[71] This system includes a distant tertiary companion, Proxima Centauri, a red dwarf approximately 13,000 AU from the primary pair, forming a hierarchical triple configuration.^[72] Sirius A and B form another iconic binary, notable as the brightest star system in the night sky, located about 8.6 light-years from Earth.^[73] In 1844, Friedrich Bessel predicted the existence of Sirius B based on irregularities in the proper motion of Sirius A, marking the first detection of an unseen companion through astrometry.^[74] The companion was visually confirmed in 1862 by Alvan Clark using the Alvan Clark refractor telescope, revealing it as the first discovered white dwarf, with Sirius A being an A-type main-sequence star.^[74] The pair orbits with a period of about 50 years and an average separation of 20 AU. The Mizar-Alcor system in the constellation Ursa Major exemplifies an optical double star visible to the naked eye, historically used as a vision test dating back to ancient Arabian and Greek cultures, where the ability to resolve the pair indicated good eyesight.^[75] Although Mizar and Alcor appear close (separated by about 12 arcminutes), they are physically associated and gravitationally bound as part of a wider multiple star system with a large separation of about 12 arcminutes (corresponding to ~0.4 light-years); Alcor is approximately 80 light-years away, similar to Mizar.^[76] Mizar itself is a quadruple system, with Mizar A being the first spectroscopic binary discovered in 1889 by Edward Pickering through analysis of spectral lines showing Doppler shifts.^[77] V404 Cygni stands out as a low-mass X-ray binary containing a stellar-mass black hole, discovered during an outburst in 1989 but gaining renewed attention with a major flare in June 2015 observed across X-ray, optical, and radio wavelengths. In 2024, observations revealed a third, distant companion star approximately 4 billion km away, forming a hierarchical triple system.^[78] The black hole has an estimated mass of 9 solar masses, accreting material from a companion K-type giant star in an orbit with a period of about 6.5 hours.^[79] The 2015 event produced extreme jets and variability, providing key insights into accretion dynamics near black holes.^[80] A more recent example is the young triple stellar system GW Orionis, observed at a distance of about 1,300 light-years, featuring three stars orbiting a common center with a circumtriple protoplanetary disk.^[81] ALMA observations in 2020 revealed a warped and misaligned disk structure, with three distinct dust rings at different inclinations, likely caused by the gravitational torques from the stars' orbits, offering evidence of disk tearing in multiple systems.^[82] This configuration highlights how binary and triple dynamics can influence planet formation.^[83]

Binary Minor Planets

Binary minor planets encompass binary systems among asteroids in the main asteroid belt and trans-Neptunian objects (TNOs) in the Kuiper Belt, providing insights into the formation and evolution of small bodies in the Solar System. The discovery of these systems began with the identification of Pluto's moon Charon in 1978, when photographic plates taken at the United States Naval Observatory revealed periodic elongations or "bumps" on Pluto's disk, later confirmed through mutual occultations and eclipses between 1985 and 1990.^[84] This finding established Pluto-Charon as the first known binary TNO, with Charon comprising about half of Pluto's mass, making it a unique equal-mass pair. The first binary asteroid in the main belt, 90 Antiope, was discovered in August 2000 using adaptive optics imaging at the Keck Observatory, revealing two nearly equal-sized components orbiting each other with a period of about 16.4 hours.^[85] In the Kuiper Belt, binary systems are notably common, with observations suggesting a binary fraction of approximately 10% among TNOs, particularly higher (up to 15-30%) in the cold classical population, based on ground-based and Hubble Space Telescope surveys that have identified over 100 such systems. These binaries often feature components of similar size and albedo, as exemplified by 79360 Sila–Nunam, a cold classical Kuiper Belt object discovered in 1997 and confirmed as a binary in 2001 through adaptive optics and later light curve observations showing mutual eclipses with an orbital period of 12.8 days.^[86] Radar and adaptive optics have been crucial for resolving these distant systems, revealing wide separations and low eccentricities that suggest formation through gravitational collapse or capture in the low-velocity environment of the outer Solar System. In contrast, main belt binaries, comprising about 15% of near-Earth and small main belt asteroids, frequently appear as contact binaries or close pairs formed from rubble-pile progenitors, such as 25143 Itokawa, a peanut-shaped contact binary visited by the Hayabusa mission in 2005, which confirmed its rubble-pile structure with a bulk density of 1.9 g/cm³ and evidence of rotational fission.^[87] The spin-up fission model posits that YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) torque-induced rotational acceleration disrupts loosely bound rubble piles, ejecting material that forms a secondary via reaccumulation, as simulated for systems like Itokawa. In 2023, NASA's Lucy mission imaged the main-belt asteroid 152830 Dinkinesh, revealing a contact binary moon named Selam, consisting of two lobes connected by a neck, supporting the rubble-pile fission model.^[88] Binary minor planets enable precise measurements of bulk density and composition, as the orbital dynamics follow Kepler's third law, allowing density ρ to be derived for synchronous contact binaries modeled as spheres via ρ = 3π / (G P²), where P is the orbital period and G is the gravitational constant; for example, this yields densities around 1-2.5 g/cm³ for main belt systems, indicating porous, ice- or rock-rich interiors. Such measurements reveal compositional gradients, with lower densities in outer Solar System binaries suggesting higher ice fractions compared to the more compact main belt objects. The Double Asteroid Redirection Test (DART) mission targeted the main belt binary 65803 Didymos and its moon Dimorphos in 2022, impacting Dimorphos on September 26 to test kinetic impactor deflection, successfully altering its orbital period by 32 minutes and demonstrating planetary defense techniques on a rubble-pile binary.^[89]

Implications for Astrophysics

Binary systems serve as crucial natural laboratories for testing and refining models of stellar evolution, particularly through observable processes like mass transfer between components. In close binaries, the donor star can transfer material to its companion via Roche lobe overflow, allowing astronomers to directly probe evolutionary stages that are otherwise inaccessible in single stars. This phenomenon provides empirical constraints on mass-loss rates, angular momentum transport, and nucleosynthesis, enabling calibration of single-star models against binary observations. For instance, detached eclipsing binaries yield precise measurements of stellar masses and radii, revealing discrepancies in standard evolutionary tracks that inform adjustments to opacity and convection treatments.^[90]^[6] The prevalence of binaries, known as the binary fraction, offers key insights into galaxy dynamics by constraining the initial mass function (IMF) and star formation efficiency. Observations indicate that binary fractions increase with stellar mass, particularly for O-type stars where they exceed 90%, implying that dynamical interactions in clusters preferentially form or retain massive binaries. This informs the IMF's high-mass end, as binaries contribute significantly to the apparent multiplicity of young stellar populations and affect the efficiency of star formation in molecular clouds, typically estimated at 10-30%. By integrating binary statistics into simulations, researchers refine models of cluster disruption and feedback, linking local star formation to galactic-scale evolution.^[91] Binary mergers are primary sources of gravitational waves, revolutionizing multi-messenger astronomy through detections by observatories like LIGO and Virgo. Compact object binaries, such as neutron star-neutron star (NS-NS) pairs, emit detectable signals during inspiral and merger, providing direct evidence of extreme physics under general relativity. Population analyses from the first three observing runs predict merger rates of 10-100 NS-NS events per year in advanced detector configurations, enabling tests of neutron star equations of state and the distribution of merger delays. These events also trace heavy element production via r-process nucleosynthesis, connecting binary evolution to galactic chemical enrichment.^[92]^[93] Circumbinary planets orbiting binary stars expand the scope of exoplanet habitability by defining habitable zones around paired hosts, where liquid water could persist despite orbital perturbations. Stability analyses show that Earth-like planets can maintain dynamically stable orbits within these zones for billions of years, provided the binary's mass ratio and eccentricity are not extreme; for equal-mass, low-eccentricity binaries, habitable orbits extend inward compared to single-star systems. Climate modeling further demonstrates resilience against stellar flux variations, with circumbinary worlds avoiding global glaciations even under significant insolation changes. This suggests that up to 50-60% of binary systems may support habitable terrestrial planets, broadening the search for life-bearing worlds.^[94]^[95] In cosmology, Type Ia supernovae originating from binary progenitors—such as white dwarf-white dwarf or white dwarf-companion mergers—function as standard candles for measuring cosmic distances, leveraging their consistent peak luminosities. These events, calibrated via Cepheid variables or surface brightness fluctuations, anchor the distance ladder and yield Hubble constant values around 73 km/s/Mpc, contrasting with CMB-derived estimates of 67 km/s/Mpc and fueling the Hubble tension. Enhanced understanding of binary progenitor channels, including mass transfer and ignition mechanisms, promises refined standardization, potentially resolving discrepancies by accounting for environmental dependencies in supernova brightness.^[96]^[97]^[98]

References

[1]
What is binary and how is it used in computing? - TechTarget
Jun 6, 2025 · The binary system is the primary language of computing systems. Inside these systems, a binary number consists of a series of eight bits.
[2]
Binary Number System - GeeksforGeeks
Jul 23, 2025 · The Binary Number System, also known as the base-2 system, uses only two digits, '0' and '1', to represent numbers.
[3]
Binary Number System | Encyclopedia.com
It is more difficult to convert from binary to decimal and from decimal to binary. The advantage of the binary system is its simplicity. A computing device can ...
[4]
Binary Number System - an overview | ScienceDirect Topics
Electronic devices respond to electrical signals, and the binary system provides codes that are easily and reliably deciphered within these devices.Missing: entry - - | Show results with:entry - -
[5]
(PDF) Binary Numbers in Ancient India - Academia.edu
Binary numbers form the basis for the operation of computers. Binary numbers were discovered in the west by German mathematician Gottfried Leibniz in 1695.<|control11|><|separator|>
[6]
Who Discovered the Binary System and Arithmetic? Did Leibniz ...
Gottfried Wilhelm Leibniz (1646-1716) is the self-proclaimed inventor of the binary system and is considered as such by most historians of mathematics.
[7]
[PDF] Development of the Binary Number System and the Foundations of ...
This paper focuses on Leibniz's formalization of the binary system and his work in mathematical logic and computing machines. 2 Numeric Systems. In the most ...Missing: entry - - | Show results with:entry - -
[8]
Computers and the Binary System | Encyclopedia.com
Computers and the Binary System · Input, Processing, Storage, and Output · Hardware · Binary Coding · Storage · Processors and Calculation · Software and Programs.
[9]
Solar System binaries
2005a barycenter resides outside of either of the two gravitationally bound bodies. By this definition, Pluto and Charon qualify as the first known solar ...
[10]
[PDF] Binary Minor Planets - University of Maryland Astronomy
Oct 31, 2005 · We have elected to use the term binary minor planet (or BMP) to mean any mutually orbiting pair of minor planets in our Solar System, where we ...
[11]
Binary star | Definition, Types, & Facts | Britannica
Sep 18, 2025 · Binary star, pair of stars in orbit around their common centre of gravity. A high proportion, perhaps one-half, of all stars in the Milky Way Galaxy are ...
[12]
Binary stars in the new millennium - ScienceDirect.com
The term “binary” was first used by William Herschel in 1802 for double stars which are bound gravitationally and orbiting together. Since then, scientists ...
[13]
Forming equal-mass planetary binaries via pebble accretion
The Earth-Moon system is a binary with a relatively large mass ratio as well, although here the definition of equal mass binary reveals its ambiguity. The ...
[14]
Orbital Parameters of 665 Double-lined Spectroscopic Binaries in ...
Jun 3, 2025 · The mass, orbital period, mass ratio, and eccentricity of binary stars are key parameters that investigate their evolution and interactions ...
[15]
Binary Star Systems - Richard Fitzpatrick
Such systems consist of two stars orbiting about their common center of mass. The distance separating the stars is always much less than the distance to the ...
[16]
[PDF] The Two-Body Problem - UCSB Physics
is the reduced mass of the system. Thus, our problem has effectively been reduced to a one-particle system - mathematically, it is no different than a single.
[17]
Center of Mass - Eclipsing Binary Stars - NAAP - UNL Astronomy
Stars in a binary sytem will orbit around the center of mass (sometimes referred to as the barycenter). The simulator to the right allows you to experiment ...Missing: dynamics radius
[18]
[PDF] ASTR3007/4007/6007, Class 2: Stellar Masses; the Virial Theorem
We define the reduced mass as µ = M1M2/(M1 +M2), so r1 = −(µ/M1)r and r2 = (µ/M2)r. The solution to the problem is that, when the two stars are at an angle θ in ...
[19]
[PDF] Senior astrophysics Lab 4: Roche lobes
In lectures we derived an expression for the effective gravitational potential Φ: Φ = −G. M1 s1. +. M2 s2. −. 1. 2 ω2r2. (1) where s1 and s2 are the distance ...
[20]
A theory of mass transfer in binary stars - Oxford Academic
In this work, we develop a new model of MT based on the assumption that the Roche potential sets up a nozzle converging on the inner Lagrangian point.
[21]
[PDF] Binary Stars Consider a binary composed of two stars of masses M1 ...
Binary Stars. Consider a binary composed of two stars of masses M1 and M2. We define M = M1 + M2 and µ = M1M2/M. If a1 and a2 are the mean.
[22]
[PDF] Orbits 1
Combining the two equations above, we can reduce the two-body problem to an equivalent one-body problem of a particle moving in a ... To determine the orbital ...
[23]
[PDF] Two-body problem Our treatment of one-body gravity is reasonable ...
Our treatment of one-body gravity is reasonable when one object dominates the gravity in a system, as the Sun does in the Solar System.Missing: mechanics | Show results with:mechanics
[24]
Deriving Kepler's Formula for Binary Stars - Imagine the Universe!
Sep 23, 2020 · F_gravity = F_centripetal -> Gm1m2/a^2 = m2a2 omega^2. Now, using Equation (3) to substitute for a2 gives: Gm1m2/a^2 = m2 (m1/(m1+m2)*. We can ...
[25]
[PDF] Johannes Kepler (1571 - 1630) - Physics
T2 = 4π2. G(m1 + m2). (r1 + r2)2. (b) The binary system Cygnus X-1 consists of two stars orbiting about their common center of mass with orbital period 5.6 days ...
[26]
PHY 445/515: Orbital Elements
Orbital Elements of a Binary System ; a, the semi-major axis ; e, the eccentricity of the orbit ; i, the inclination of the orbit to the line of sight ...
[27]
[PDF] 7 Binary Systems
• P – the orbital period. • a – semimajor axis. • e – orbital eccentricity. • I – orbital inclination relative to the plane of the sky. • o – the longitude of ...Missing: elements | Show results with:elements
[28]
[PDF] Orbital Mechanics
The vis viva equation then follows by substituting Eqns. 32 and 33 into 31 and carrying out some algebra: v2 = µ. 2 r. −. 1.
[29]
[PDF] Higher-order effects in the dynamics of hierarchical triple systems
Mar 2, 2021 · We analyze the secular evolution of hierarchical triple systems to second order in the quadrupolar perturbation induced on the inner binary ...
[30]
GANBISS: a new GPU accelerated N-body code for binary star ...
We present a GPU accelerated N-body integrator using the Bulirsch–Stoer method, called GANBISS (GPU accelerated n-body code for binary star systems).
[31]
[PDF] N-body Problem in - DSpace@MIT
Feb 5, 2018 · Abstract. The astrophysical N-body problem describes N point masses interacting with each other through pairwise gravitational forces.
[32]
[PDF] The Inclination Problem Observing Visual Binaries Observing ...
... distance d, then we can calculate a1 and a2 from α1 and α2 using the small-angle formula a1/1 au = (α1/100) (d/1 pc), a2/1 au = (α2/100) (d/1 pc). (3). The ...
[33]
Lecture 10: How Massive is a Star?
Jan 17, 2025 · The total mass of a binary system can be found from the relation M 1 + M 2 = a 3 /P 2 , as long as the values of a & P are known.
[34]
[PDF] Binary Systems and Stellar Parameters
Oct 6, 2020 · BINARY STAR SYSTEMS are classified based on observational characteristics. 1. Optical double: not binaries, but two stars lying along the same ...
[35]
https://arxiv.org/abs/0901.2345
[36]
[PDF] Evolution of Binary Stars
One can have hierarchical systems, in which there is a close binary, and at a much larger distance is a third star (or another binary).
[37]
https://arxiv.org/abs/1804.07092
[38]
[PDF] Eclipsing Binaries - SMU Physics
The Algol Paradox. •This has to do with the rate of evolution of the stars in the binary system. •The less massive star is already a subgiant while the star ...
[39]
https://link.springer.com/article/10.1007/s00159-013-0059-2
[40]
Eclipsing binary statistics – Theory and observation
It is easy to show that the probability of an eclipse of any depth is simply Pe0. = rs + rg, but we want to study the probabil- ity of an eclipse of any ...
[41]
Stellar, brown dwarf and multiple star properties from ...
We report the statistical properties of stars, brown dwarfs and multiple systems obtained from the largest hydrodynamical simulation of star cluster formation ...Stellar, Brown Dwarf And... · 3 Results · 3.4 Multiplicity As A...<|control11|><|separator|>
[42]
THE FORMATION OF LOW-MASS BINARY STAR SYSTEMS VIA ...
We find that protostellar systems with radiation feedback predominately form binaries via turbulent fragmentation, not disk instability, and predict that ...
[43]
Binary formation with different metallicities: dependence on initial ...
As a result, the binary frequency increases as the metallicity decreases, and most stars are born as binary or multiple systems in low-metallicity environments.
[44]
The ALMA Protostellar Interferometric Line Survey (PILS)
The ALMA Protostellar Interferometric Line Survey (PILS). First results from an unbiased submillimeter wavelength line survey of the Class 0 protostellar binary ...
[45]
Binary Evolution in Stellar Dynamics - Oxford Academic
Using an impulsive approximation, it is shown that pairs with low binding energies, i.e. much less than the average kinetic energy of single cluster members, ...
[46]
https://iopscience.iop.org/article/10.1088/0067-0049/190/1/1
[47]
None
### Summary of Key Points on Three-Body Encounters in Clusters for Binary Formation
[48]
Dynamical formation and scattering of hierarchical triples: cross ...
For three-body interactions, the collision cross-section scales with velocity in the same way that the cross-section for exchange does. That is, for v ^ < ...
[49]
[0901.2345] A Binary Origin for Blue Stragglers in Globular Clusters
Jan 15, 2009 · Abstract: Blue stragglers in globular clusters are abnormally massive stars that should have evolved off the stellar main sequence long ago.Missing: seminal | Show results with:seminal
[50]
[PDF] Physics of Binary Star Evolution - arXiv
9.2 Evolution of the Stellar Radius and Cases of Mass Transfer . . . . . . . .327. 9.3 RLO: Reasons for ... 9.5 Examples of Non-conservative Mass Transfer .
[51]
Non-conservative mass transfer in stellar evolution and the case of ...
Apr 19, 2018 · A likely solution to this discrepancy is that a large fraction of the mass flowing from the donor leaves the binary in the form of outflows ...
[52]
[astro-ph/0308361] Magnetic Braking Revisited - arXiv
Aug 20, 2003 · The resulting angular momentum loss rate, \dot J, depends on Omega in the form \dot J \propto Omega^beta where beta ~ 3 for slow rotators ...Missing: proportional | Show results with:proportional
[53]
Common envelope evolution: where we stand and how we can ...
Feb 27, 2013 · In the energy formalism that was adopted, the energy budget for the binary is fixed at the onset of mass transfer and the post-common-envelope ...
[54]
Common envelope evolution on a moving mesh - Oxford Academic
These are known as the energy formalism (Webbink 1984; Livio & Soker 1988) and the angular momentum (or γ) formalism (Nelemans et al. 2000; Nelemans & Tout 2005) ...
[55]
Supernova Type Ia progenitors from merging double white dwarfs
The mass accretion process onto white dwarfs is updated with new efficiencies of mass retention on the surface of the white dwarf. For hydrogen accretion we ...
[56]
Population nucleosynthesis in single and binary stars - I. Model
The binary star code BSE (Hurley et al. 2002) is used alongside the ... These stars explode as type Ib/c supernovae if the (degenerate) core mass in ...
[57]
Ground-Based and Space Observations of Interacting Binaries
Multi-wavelength observational data, obtained from ground-based and space observations are used to compute the physical parameters of the observed ...<|separator|>
[58]
Space-Based Photometry of Binary Stars: From Voyager to TESS
This review traces the binary stars observed and the scientific results obtained from the early days of ultraviolet missions (OAO-2, Voyager, ANS, IUE),Missing: Hubble HARPS<|control11|><|separator|>
[59]
STELLAR LOCI II. A MODEL-FREE ESTIMATE OF THE BINARY ...
... LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of 41% ± 2%. The fractions decrease toward late ...
[60]
ESO - VLTI - Eso.org
Jul 26, 2023 · The VLTI provides milli-arcsec angular resolution at low and intermediate (R=5000) spectral resolution at near and mid-infrared wavelengths.
[61]
Arrival-time analysis for a pulsar in a binary system.
Our timing formula is in a sense merely a parametrization of the arrival times. We show how to measure secular variations in the parameters (i.e., in the ...
[62]
ESO - ESPRESSO - Eso.org
Jul 5, 2021 · The whole system is built to reach the ultimate radial-velocity precision of 10 cm/s over a timespan of 10 years in single UT mode. Read ...
[63]
ESPRESSO at VLT - On-sky performance and first results
ESPRESSO is the new high-resolution spectrograph of ESO's Very Large Telescope (VLT). It was designed for ultra-high radial-velocity (RV) precision and extreme ...
[64]
Gaia Data Release 3 (Gaia DR3) - ESA Cosmos
Contents of Gaia DR3 ; Non-single stars - orbital spectroscopic solutions (SB1 / SB2), 186,905, - ; Non-single stars - eclipsing binaries, 87,073, - ; QSO ...Gaia DR3 events · Gaia DR3 stories · Gaia DR3 previews · Gaia DR3 software tools
[65]
Gaia Data Release 3. Stellar multiplicity, a teaser for ... - NASA ADS
The Gaia DR3 catalogue contains, for the first time, about 800 000 solutions with either orbital elements or trend parameters for astrometric, spectroscopic, ...
[66]
NASA's Webb Finds New Evidence for Planet Around Closest Solar ...
Aug 7, 2025 · Astronomers using NASA's James Webb Space Telescope have found strong evidence of a giant planet orbiting a star in the stellar system ...
[67]
Observation of Gravitational Waves from a Binary Black Hole Merger
Feb 11, 2016 · The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1 . 0 × 1 0 − ...
[68]
Precise Astrometry of Visual Binaries with Adaptive Optics. A Way for ...
We present the results of our study of astrometric stability of 200-in Hale (Mt. Palomar) and 10-m Keck II (Mauna Kea) telescopes, both with Adaptive Optics ...
[69]
Observations of Binary Stars with the Differential Speckle Survey ...
Apr 7, 2020 · We report 370 measures of 170 components of binary and multiple star systems, obtained from speckle imaging observations made with the ...
[70]
Ground-breaking exoplanet science with the ANDES spectrograph ...
May 6, 2025 · High contrast imaging instruments at ELT will examine a volume-limited population of young, non-transiting exoplanets formed with the same ...
[71]
[PDF] Orbital Estimation of Binary Stars - NExScI
• a: semi-major axis of the orbit. • e: eccentricity. • P: orbital period. • T ... The lower the eccentricity the better. Michelson Summer Workshop, July ...Missing: elements | Show results with:elements
[72]
Determination of Orbital Parameters of Binary Star Systems Using ...
MCMC sampling is now a mainstay of orbital analysis, providing statistically rigorous posterior distributions for both circular and elliptical binaries while ...
[73]
[PDF] chapter 18 spectroscopic binary stars 18.1
Thus, since we know P (hence n), e and K1, we can determine a1 sin i – but we cannot determine a1 or i separately. Now the mean motion n is given just before ...
[74]
https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/friedrich-bessel-sirius-b
[75]
Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney ...
Jan 19, 2022 · It offers options for detailed reflection and nonlinear (square-root and logarithmic law) limb darkening, adjustment of spot parameters, an ...
[76]
II. β Aurigae and non-linear limb darkening in light curves
We present the most precise light curve ever obtained of a detached eclipsing binary star and use it investigate the inclusion of non-linear limb darkening laws ...
[77]
https://skyandtelescope.org/astronomy-blogs/explore-night-bob-king/mizar-a-fresh-look-at-an-old-friend03252015/
[78]
Bayesian inference for orbital eccentricities
Highest posterior density intervals (HPDIs) are derived for the true eccentricities ε of spectroscopic binaries with measured values e ≈ 0.Missing: flat | Show results with:flat
[79]
I. Ribas 2,3 - Astronomy & Astrophysics (A&A)
... stars in crowded fields (such as in our case). ... In any case, no systematic errors in the distances of EBs will arise from blending because the analysis can ...
[80]
Binarity and multiperiodicity in high-amplitude δ Scuti stars
We performed a period analysis of the radial velocities, which revealed the main pulsation frequency at f1= 6.802 c d−1, its integer harmonics (2f1, 3f1) and a ...
[81]
The Nearest Neighbor Star - Imagine the Universe! - NASA
Dec 8, 2020 · Alpha Centauri A & B are roughly 4.35 light years away from us. Proxima Centauri is slightly closer at 4.25 light years.Missing: AB | Show results with:AB
[82]
[1007.2293] Recalculating the Orbit of α-Centauri AB - arXiv
Jul 14, 2010 · This paper presents the results of our recalculation of orbital and physical parameters of the system using Thiele-van den Bos method, based on ...
[83]
[1611.03495] Proxima's orbit around Alpha Centauri - arXiv
Nov 10, 2016 · The orbital period of Proxima is approximately 550 000 years. With an excentricity of 0.50 (+0.08 -0.09), Proxima comes within 4.3 (+1.1 -0.9) ...
[84]
Alpha Centauri Stellar System - NASA Scientific Visualization Studio
Jun 13, 2023 · At 4.3 light-years away, Alpha Centauri A and B are the nearest Sun-like stars to our solar system. They orbit with Proxima Centauri as a triple star system.
[85]
Friedrich Bessel: Discoverer of White Dwarf Sirius B | AMNH
Discovering Sirius B long before technology allowed us to see it, or quantum mechanics explained the nature of white dwarfs.Missing: AB binary separation
[86]
Mizar and Alcor in the bend of the Big Dipper - EarthSky
Feb 11, 2024 · Mizar and its fainter companion star Alcor make up one of the most famous double stars in the sky. These two stars are bound to one another by gravity.Missing: eclipsing | Show results with:eclipsing
[87]
An ancient eye test - Mizar and Alcor - Sky & Telescope
Dec 8, 2023 · Mizar and Alcor are two stars that form a binary system clearly visible to the naked eye, located in the handle of the Big Dipper asterism in the constellation ...Missing: eclipsing historical
[88]
Mizar — A Fresh Look at an Old Friend - Sky & Telescope
Mar 25, 2015 · In time he concluded that Mizar A was a binary system. Harvard College Observatory. Pickering examined spectra taken of the star, noting that ...
[89]
[1607.06239] High-energy gamma-ray observations of the accreting ...
Jul 21, 2016 · We report on Fermi/Large Area Telescope observations of the accreting black hole low-mass X-ray binary V404 Cygni during its outburst in June- ...
[90]
THE 2015 DECAY OF THE BLACK HOLE X-RAY BINARY V404 ...
We present simultaneous X-ray and radio observations of the black hole X-ray binary V404 Cygni at the end of its 2015 outburst.
[91]
Black hole awakes after 26 years | University of Oxford
Nov 5, 2015 · On 15 June 2015, V404 Cygni (V404 Cyg), a binary system comprising a sun-like star orbiting a black hole, woke up. A huge outburst of energy ...
[92]
A triple-star system with a misaligned and warped circumstellar disk ...
Sep 4, 2020 · We present observations of the triple-star system GW Orionis, finding evidence for disk tearing. Our images show an eccentric ring that is misaligned with the ...
[93]
ALMA Discovers Misaligned Rings in Planet-Forming Disk Around ...
Sep 3, 2020 · ALMA discovered misaligned rings in a planet-forming disk around GW Orionis, a triple star system, with three rings at different orientations. ...
[94]
Misaligned Planet-Forming Rings around Triple Young Stars | NAOJ
Sep 4, 2020 · ALMA found a peculiar dust ring system around the young triple star GW Orionis. The system has three large, misaligned rings with sufficient dust for planet ...
[95]
45 Years Ago: Astronomers Discover Pluto's Moon Charon - NASA
Jun 23, 2023 · In 1985, Pluto and Charon began a series of mutual eclipses and occultations ... The discovery of Charon refined our understanding of Pluto's size ...
[96]
Discovery of Companions to Asteroids 762 Pulcova and 90 Antiope ...
We present images of two asteroid companions from adaptive optics (AO) observations. These detections bring to four the number of binary systems ever imaged, ...
[97]
[astro-ph/0703134] Binaries in the Kuiper Belt - arXiv
Mar 7, 2007 · The large fraction of transneptunian objects that are binary or multiple, 48 such systems are now known, has been an unanticipated windfall.
[98]
Rotational fission of contact binary asteroids - ScienceDirect.com
Richardson has studied the minimum energy configurations of rubble piles consisting of equal sized spheres, and their response to rapid changes in spin rates ...
[99]
Spin-up of rubble-pile asteroids: Disruption, satellite formation, and ...
The binary systems created in all simulations are analyzed and compared against observed binary near-Earth asteroids and small Main Belt asteroids. The shape ...
[100]
Didymos & Dimorphos - NASA Science
DART intercepted the smaller moonlet asteroid at 7:14 p.m. EDT on Sept. 26, 2022. DART impacted Dimorphos at high speed – about 4 miles or 6.6 kilometers per ...
[101]
The Evolution of Compact Binary Star Systems - PubMed Central - NIH
We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs).
[102]
The Impact of Binaries on the Stellar Initial Mass Function - arXiv
Jun 27, 2018 · A large amount of evidence points to the IMF becoming top-heavy with decreasing metallicity and above a star-formation-rate density of about 0.1 Msun/(pc^3 yr).Missing: efficiency | Show results with:efficiency
[103]
Population of Merging Compact Binaries Inferred Using ...
Mar 29, 2023 · An analysis of gravitational waves from 76 compact binary mergers provides new constraints on the population properties of neutron stars and ...Abstract · Popular Summary
[104]
LIGO-P2100239-v11: The population of merging compact binaries ...
We report on the population properties of 76 compact binary mergers detected with gravitational waves below a false alarm rate of 1 per year.
[105]
The Resilience of Habitable Climates Around Circumbinary Stars
Aug 25, 2020 · Habitable planets in circumbinary systems appear to be remarkably resilient against circumbinary-driven climate variations and can avoid any true climate ...Abstract · Introduction · Analytic Solutions for Earth... · Three-Dimensional Climate...
[106]
Analyzing the Habitable Zones of Circumbinary Planets ... - arXiv
Sep 17, 2021 · Our results indicate that the mass ratio and orbital eccentricity of binary stars are important factors affecting the orbital stability and ...
[107]
Type Ia supernovae as stellar endpoints and cosmological tools
Jun 14, 2011 · Empirically, Type Ia supernovae are the most useful, precise, and mature tools for determining astronomical distances.
[108]
Type Ia supernova progenitors: a contemporary view of a long ...
Dec 2, 2024 · In this review, we give a current update on the different proposed Type Ia supernova progenitors, including descriptions of possible binary star configurations.
[109]
A new measurement of the Hubble constant using Type Ia ...
We present a new calibration of the peak absolute magnitude of Type Ia supernovae (SNe Ia) based on the surface brightness fluctuations (SBF) method.