Equal-mass Systems Research Articles

Three-body recombination at finite energy within an optical model

We investigate three-boson recombination of equal mass systems as function of (negative) scattering length, mass, finite energy, and finite temperature. An optical model with an imaginary potential at short distance reproduces experimental recombination data and allows us to provide a simple parametrization of the recombination rate as function of scattering length and energy. Using the two-body van der Waals length as unit we find that the imaginary potential range and also the potential depth agree to within 30% for lithium and cesium atoms. As opposed to recent studies suggesting universality of the threshold for bound-state formation, our results suggest that the recombination process itself could have universal features.

BINARY FORMATION MECHANISMS: CONSTRAINTS FROM THE COMPANION MASS RATIO DISTRIBUTION

We present a statistical comparison of the mass ratio distribution of companions, as observed in different multiplicity surveys, to the most recent estimate of the single object mass function (Bochanski et al. 2010). The main goal of our analysis is to test whether or not the observed companion mass ratio distribution (CMRD) as a function of primary star mass and star formation environment is consistent with having been drawn from the field star IMF. We consider samples of companions for M dwarfs, solar type and intermediate mass stars, both in the field as well as clusters or associations, and compare them with populations of binaries generated by random pairing from the assumed IMF for a fixed primary mass. With regard to the field we can reject the hypothesis that the CMRD was drawn from the IMF for different primary mass ranges: the observed CMRDs show a larger number of equal-mass systems than predicted by the IMF. This is in agreement with fragmentation theories of binary formation. For the open clusters {\alpha} Persei and the Pleiades we also reject the IMF random- pairing hypothesis. Concerning young star-forming regions, currently we can rule out a connection between the CMRD and the field IMF in Taurus but not in Chamaeleon I. Larger and different samples are needed to better constrain the result as a function of the environment. We also consider other companion mass functions (CMF) and we compare them with observations. Moreover the CMRD both in the field and clusters or associations appears to be independent of separation in the range covered by the observations. Combining therefore the CMRDs of M and G primaries in the field and intermediate mass primary binaries in Sco OB2 for mass ratios, q = M2/M1, from 0.2 to 1, we find that the best chi-square fit follows a power law dN/dq \propto q^{\beta}, with {\beta} = -0.50 \pm 0.29, consistent with previous results.

Binary asteroid systems: Tidal end states and estimates of material properties

The locations of the fully despun, double synchronous end states of tidal evolution, where the rotation rates of both the primary and secondary components in a binary system synchronize with the mean motion about the center of mass, are derived for spherical components. For a given amount of scaled angular momentum J/ J′, the tidal end states are over-plotted on a tidal evolution diagram in terms of mass ratio of the system and the component separation (semimajor axis in units of primary radii). Fully synchronous orbits may not exist for every combination of mass ratio and angular momentum; for example, equal-mass binary systems require J/ J′ > 0.44. When fully synchronous orbits exist for prograde systems, tidal evolution naturally expands the orbit to the stable outer synchronous solution. The location of the unstable inner synchronous orbit is typically within two primary radii and often within the radius of the primary itself. With the exception of nearly equal-mass binaries, binary asteroid systems are in the midst of lengthy tidal evolutions, far from their fully synchronous tidal end states. Of those systems with unequal-mass components, few have even reached the stability limit that splits the fully synchronous orbit curves into unstable inner and stable outer solutions. Calculations of material strength based on limiting the tidal evolution time to the age of the Solar System indicate that binary asteroids in the main belt with 100-km-scale primary components are consistent with being made of monolithic or fractured rock as expected for binaries likely formed from sub-catastrophic impacts in the early Solar System. To tidally evolve in their dynamical lifetime, near-Earth binaries with km-scale primaries or smaller created via a spin-up mechanism must be much weaker mechanically than their main-belt counterparts even if formed in the main belt prior to injection into the near-Earth region. Small main-belt binaries, those having primary components less than 10 km in diameter, could bridge the gap between the large main-belt binaries and the near-Earth binaries, as, depending on the age of the systems, small main-belt binaries could either be as strong as the large main-belt binaries or as weak as the near-Earth binaries. The inherent uncertainty in the age of a binary system is the leading source of error in calculation of material properties, capable of affecting the product of rigidity μ and tidal dissipation function Q by orders of magnitude. Several other issues affecting the calculation of μQ are considered, though these typically affect the calculation by no more than a factor of two. We also find indirect evidence within all three groups of binary asteroids that the semimajor axis of the mutual orbit in a binary system may evolve via another mechanism (or mechanisms) in addition to tides with the binary YORP effect being a likely candidate.

The birth rate of subluminous and overluminous type Ia supernovae

Based on the results of Chen & Li (2009) and Pakmor et al. (2010), we carried out a series of binary population synthesis calculations and considered two treatment of common envelope (CE) evolution, i.e. $\alpha$-formalism and $\gamma$-algorithm. We found that the evolution of birth rate of these peculiar SNe Ia is heavily dependent on how to treat the CE evolution. The over-luminous SNe Ia may only occur for $\alpha$-formalism with low CE ejection efficiency and the delay time of the SNe Ia is between 0.4 and 0.8 Gyr. The upper limit of the contribution rate of the supernovae to all SN Ia is less than 0.3%. The delay time of sub-luminous SNe Ia from equal-mass DD systems is between 0.1 and 0.3 Gyr for $\alpha$-formalism with $\alpha=3.0$, while longer than 9 Gyr for $\alpha=1.0$. The range of the delay time for $\gamma$-algorithm is very wide, i.e. longer than 0.22 Gyr, even as long as 15 Gyr. The sub-luminous SNe Ia from equal-mass DD systems may only account for no more than 1% of all SNe Ia observed. The super-Chandrasekhar mass model of Chen & Li (2009) may account for a part of 2003fg-like supernovae and the equal-mass DD model developed by Pakmor et al. (2010) may explain some 1991bg-like events, too. In addition, based on the comparison between theories and observations, including the birth rate and delay time of the 1991bg-like events, we found that the $\gamma$-algorithm is more likely to be an appropriate prescription of the CE evolution of DD systems than the $\alpha$-formalism if the equal-mass DD systems is the progenitor of 1991bg-like SNe Ia.

THE SEARCH FOR PLANETARY MASS COMPANIONS TO FIELD BROWN DWARFS WITHHST/NICMOS

We present the results of a high-resolution spectral differential imaging survey of 12 nearby, relatively young field L dwarfs (<1 Gyr) carried out with HST/NICMOS to search for planetary mass companions at small physical separations from their host. The survey resolved two brown dwarf binaries: the L dwarf system Kelu-1AB and the newly discovered L/T transition system 2MASS J031059+164815AB. For both systems common proper motion has already been confirmed in follow-up observations which have been published elsewhere. The derived separations of the binaries are smaller than 6 AU and consistent with previous brown dwarf binary statistics. Their mass ratios of q > 0.8 confirm the preference for equal mass systems similar to a large number of other surveys. Furthermore, we found tentative evidence for a companion to the L4 dwarf 2MASS W033703-175807, straddling the brown dwarf/planetary mass boundary and revealing an uncommonly low mass ratio system (q ~ 0.2) compared to the vast majority of previously found brown dwarf binaries. With a derived minimum mass of 10 - 15 Mjup, a planetary nature of the secondary cannot be ruled out yet. However, it seems more likely to be a very low mass brown dwarf secondary at the border of the spectral T/Y transition regime, primarily due to its similarities to recently found very cool T dwarfs. This would make it one of the closest resolved brown dwarf binaries (0.087" $/pm$ 0.015", corresponding to 2.52 $\pm$ 0.44 AU at a distance of 29 pc) with the coolest (Teff ~ 600-630 K) and least massive companion to any L or T dwarf.

Complete phenomenological gravitational waveforms from spinning coalescing binaries

The quest for gravitational waves from coalescing binaries is customarily performed by the LIGO-Virgo collaboration via matched filtering, which requires a detailed knowledge of the signal. Complete analytical coalescence waveforms are currently available only for the non-precessing binary systems. In this paper we introduce complete phenomenological waveforms for the dominant quadrupolar mode of generically spinning systems. These waveforms are constructed by bridging the gap between the analytically known inspiral phase, described by spin Taylor (T4) approximants in the restricted waveform approximation, and the ring-down phase through a phenomenological intermediate phase, calibrated by comparison with specific, numerically generated waveforms, describing equal mass systems with dimension-less spin magnitudes equal to 0.6. The overlap integral between numerical and phenomenological waveforms ranges between 0.95 and 0.99.

DEBRIS DISKS AROUND SOLAR-TYPE STARS: OBSERVATIONS OF THE PLEIADES WITH THESPITZERSPACE TELESCOPE

We present Spitzer MIPS observations at 24 um of 37 solar-type stars in the Pleiades and combine them with previous observations to obtain a sample of 71 stars. We report that 23 stars, or 32 +/- 6.8%, have excesses at 24 um at least 10% above their photospheric emission. We compare our results with studies of debris disks in other open clusters and with a study of A stars to show that debris disks around solar-type stars at 115 Myr occur at nearly the same rate as around A-type stars. We analyze the effects of binarity and X-ray activity on the excess flux. Stars with warm excesses tend not to be in equal-mass binary systems, possibly due to clearing of planetesimals by binary companions in similar orbits. We find that the apparent anti-correlations in the incidence of excess and both the rate of stellar rotation and also the level of activity as judged by X-ray emission are statistically weak.

Parameter estimation for coalescing massive binary black holes with LISA using the full 2-post-Newtonian gravitational waveform and spin-orbit precession

Gravitational waves emitted by binary systems in the inspiral phase carry a complicated structure, consisting in a superposition of different harmonics of the orbital frequency, the amplitude of each of them taking the form of a post-Newtonian series. In addition to that, spinning binaries experience spin-orbit and spin-spin couplings which induce a precession of the orbital angular momentum and of the individual spins. With one exception, previous analyses of the measurement accuracy of gravitational wave experiments for comparable-mass binary systems have neglected either spin-precession effects or subdominant harmonics and amplitude modulations. Here we give the first explicit description of how these effects combine to improve parameter estimation. We consider supermassive black hole binaries as expected to be observed with the planned space-based interferometer LISA, and study the measurement accuracy for several astrophysically interesting parameters obtainable taking into account the full 2PN waveform for spinning bodies, as well as spin-precession effects. We find that for binaries with a total mass in the range ${10}^{5}{M}_{\ensuremath{\bigodot}}&lt;M&lt;{10}^{7}{M}_{\ensuremath{\bigodot}}$ at a redshift of 1, a factor $\ensuremath{\sim}1.5$ is in general gained in accuracy, with the notable exception of the determination of the individual masses in equal-mass systems, for which a factor $\ensuremath{\sim}5$ can be gained. We also find, as could be expected, that using the full waveform helps increasing the upper mass limit for detection, which can be as high as $M={10}^{8}{M}_{\ensuremath{\bigodot}}$ at a redshift of 1, as well as the redshift limit where some information can be extracted from a system, which is roughly $z\ensuremath{\gtrsim}10$ for $M\ensuremath{\le}{10}^{7}{M}_{\ensuremath{\bigodot}}$, 1.5--5 times higher than with the restricted waveform. We computed that the full waveform allows us to use supermassive black hole binaries as standard sirens up to a redshift of $z\ensuremath{\approx}1.6$, about 0.4 larger than what previous studies allowed. We found that for lower unequal-mass binary systems, the measurement accuracy is not as drastically improved as for other systems. This suggests that for these systems, adding parameters such as eccentricity or alternative gravity parameters could be achieved without much loss in the accuracy.

Stellar, brown dwarf and multiple star properties from hydrodynamical simulations of star cluster formation

We report the statistical properties of stars, brown dwarfs and multiple systems obtained from the largest hydrodynamical simulation of star cluster formation to date that resolves masses down to the opacity limit for fragmentation (a few Jupiter masses). The simulation is essentially identical to that of Bate, Bonnell & Bromm except that the initial molecular cloud is larger and more massive. It produces more than 1250 stars and brown dwarfs, providing unprecedented statistical information that can be compared with observational surveys. We find that hydrodynamical/sink particle simulations can reproduce many of the observed stellar properties very well. Binarity as a function of primary mass, the frequency of very-low-mass (VLM) binaries, general trends for the separation and mass ratio distributions of binaries, and the relative orbital orientations of triples systems are all in reasonable agreement with observations. We also examine the radial variations of binarity, velocity dispersion, and mass function in the resulting stellar cluster and the distributions of disc truncation radii due to dynamical interactions. For VLM binaries, we find that their frequency when using small accretion radii and gravitational softening is similar to that expected from observational surveys (approximately 20 percent). We also find that VLM binaries evolve from wide, unequal-mass systems towards close equal-mass systems as they form. The two main deficiencies of the calculations are that they over produce brown dwarfs relative to stars and that there are too few unequal mass binaries with K and G-dwarf primaries. [Abridged]

Size Evolution of the Most Massive Galaxies at 1.7 &lt; z &lt; 3 from GOODS NICMOS Survey Imaging

We measure the sizes of 82 massive (M ≥ 1011 M☉) galaxies at 1.7 ≤ z ≤ 3 utilizing deep HST NICMOS data taken in the GOODS North and South fields. Our sample is almost an order of magnitude larger than previous studies at these redshifts, providing the first statistical study of massive galaxy sizes at z > 2, confirming the extreme compactness of these systems. We split our sample into disk-like (n ≤ 2) and spheroid-like (n > 2) galaxies based on their Sersic indices, and find that at a given stellar mass disk-like galaxies at z ~ 2.3 are a factor of 2.6 ± 0.3 smaller than present-day equal-mass systems, and spheroid-like galaxies at the same redshifts are 4.3 ± 0.7 smaller than comparatively massive elliptical galaxies today. At z > 2 our results are compatible with both a leveling off, or a mild evolution in size. Furthermore, the high density (~2 × 1010 M☉ kpc−3) of massive galaxies at these redshifts, which are similar to present-day globular clusters, possibly makes any further evolution in sizes beyond z = 3 unlikely.

The Initial‐Final Mass Relation: Direct Constraints at the Low‐Mass End

The initial-final mass relation represents a mapping between the mass of a white dwarf remnant and the mass that the hydrogen-burning main-sequence star that created it once had. The empirical relation thus far has been constrained using a sample of ~40 stars in young open clusters, ranging in initial mass from ~2.75 to 7 M☉, and shows a general trend that connects higher mass main-sequence stars with higher mass white dwarfs. In this paper, we present CFHT CFH12K photometric and Keck LRIS multiobject spectroscopic observations of a sample of 22 white dwarfs in two older open clusters, NGC 7789 (t = 1.4 Gyr) and NGC 6819 (t = 2.5 Gyr). We measure masses for the highest signal-to-noise ratio spectra by fitting the Balmer lines to atmosphere models and place the first direct constraints on the low-mass end of the initial-final mass relation. Our results indicate that the observed general trend at higher masses continues down to low masses, with Minitial = 1.6 M☉ main-sequence stars forming Mfinal = 0.54 M☉ white dwarfs. When added to our new data from the very old cluster NGC 6791, the relation is extended down to Minitial = 1.16 M☉ (corresponding to Mfinal = 0.53 M☉). This extension of the relation represents a fourfold increase in the total number of hydrogen-burning stars for which the integrated mass loss can now be calculated from empirical data, assuming a Salpeter initial mass function. The new leverage at the low-mass end is used to derive a purely empirical initial-final mass relation. The sample of white dwarfs in these clusters also shows several interesting systems that we discuss further: a DB (helium) white dwarf, a magnetic white dwarf, a DAB (mixed hydrogen/helium atmosphere or a double degenerate DA+DB) white dwarf(s), and two possible equal-mass DA double degenerate binary systems.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

Free-fall equal-mass three-body systems are numerically studied using symbolic dynamics. We scan the two-dimensional homology map of initial configurations in steps of 0.001 along both axes. States of binary and triple encounters as well as changes of configuration are used to construct symbolic sequences. Symbolic sequences are characterized by Shannon and Markov entropies. Different ergodic components corresponding to different distinct peaks on the histograms of these entropies are revealed.

A wide deep infrared look at the Pleiades with UKIDSS: new constraints on the substellar binary fraction and the low-mass initial mass function

Abstract We present the results of a deep wide-field near-infrared survey of 12 deg2 of the Pleiades conducted as part of the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS) Galactic Cluster Survey (GCS). We have extracted over 340 high-probability proper motion (PM) members down to 0.03 M⊙ using a combination of UKIDSS photometry and PM measurements obtained by cross-correlating the GCS with data from the Two Micron All Sky Survey, the Isaac Newton Telescope and the Canada–France–Hawaii Telescope. Additionally, we have unearthed 73 new candidate brown dwarf (BD) members on the basis of five-band UKIDSS photometry alone. We have identified 23 substellar multiple system candidates out of 63 candidate BDs from the (Y−K, Y) and (J−K, J) colour–magnitude diagrams, yielding a binary frequency of 28–44 per cent in the 0.075−0.030 M⊙ mass range. Our estimate is three times larger than the binary fractions reported from high-resolution imaging surveys of field ultracool dwarfs and Pleiades BDs. However, it is marginally consistent with our earlier ‘peculiar’ photometric binary fraction of 50 ± 10 per cent presented by Pinfield et al., in good agreement with the 32–45 per cent binary fraction derived from the recent Monte Carlo simulations of Maxted &amp; Jeffries and compatible with the 26 ± 10 per cent frequency recently estimated by Basri &amp; Reiners. A tentative estimate of the mass ratios from photometry alone seems to support the hypothesis that binary BDs tend to reside in near equal-mass ratio systems. In addition, the recovery of four Pleiades members targeted by high-resolution imaging surveys for multiplicity studies suggests that half of the binary candidates may have separations below the resolution limit of the Hubble Space Telescope or current adaptive optics facilities at the distance of the Pleiades (a ∼7 au). Finally, we have derived luminosity and mass functions from the sample of photometric candidates with membership probabilities. The mass function is well modelled by a lognormal peaking at 0.24 M⊙ and is in agreement with previous studies in the Pleiades.

N-body models of rotating globular clusters

In this paper we examine the dynamical evolution of rotating globular clusters with direct N-body models. Our initial models are rotating King models, and we obtain results both for equal-mass systems and for systems composed of two mass components. Previous investigations using a Fokker–Planck solver have shown that rotation has a noticeable influence on stellar systems such as globular clusters that evolve by two-body relaxation. In particular, it accelerates their dynamical evolution through the gravogyro instability. We have validated the occurrence of the gravogyro instability with direct N-body models. In the case of systems composed of two mass components, mass segregation takes place, a process that competes with the rotation in the acceleration of the core collapse. The ‘accelerating’ effect of rotation was detected in our isolated two-mass N-body models. Finally, we look at rotating N-body models in a tidal field within the tidal approximation. It turns out that rotation increases the escape rate significantly. A difference between retrograde- and prograde-rotating stellar clusters, with respect to the orbit of the cluster around the Galaxy, occurs. This difference is the result of the presence of a ‘third integral’ and chaotic scattering, respectively.

Collapse of periodic orbits in a driven inelastic particle system

The dynamical behavior of a one-dimensional inelastic particle system with particles of unequal mass traveling between two walls is investigated. The system is driven by adding energy at one of the walls while the other wall is stationary and does not add energy. By deriving analytic solutions for the periodic orbits of this system, we show that there are a countable infinity of critical mass ratios at which the particle dynamics become highly degenerate in the following sense. As the mass ratio passes through these critical points, large numbers of stable periodic orbits can collapse onto a single trivial orbit. We show that the widely studied equal-mass systems represent one of these critical points and are therefore such a degenerate case. We also show that in the elastic limit the number of orbits that collapse onto the single trivial orbit can become arbitrarily large.

Masses of merging compact object binaries

We analyze the distribution of masses of compact object binaries observed in gravitational waves. We simulate the population of such binaries using the Star Track population synthesis code. We find that black hole – black hole binaries observed in gravitational waves will be dominated by the nearly equal mass objects, the black hole – neutron star binaries will mostly be the ones with the mass ratio q < 0.5. The neutron star – neutron star binaries observed in gravitational waves are very likely to include large number of non equal mass systems with small mass ratio, as low as even q ≈ 0.6 − 0.7.

Expected masses of merging compact object binaries observed in gravitational waves

We use the well-tested StarTrack binary population synthesis code to examine the properties of the population of compact object binaries. We calculate the distribution of masses and mass ratios, taking into account weights introduced by observability in gravitational waves during inspiral. We find that in the observability-weighted distribution of double neutron star binaries there are two peaks: one for nearly equal-mass systems, and one for systems consisting of a low- and a high-mass neutron star, q= 0.6–0.7. The observability-weighted distribution of black hole neutron star binaries is concentrated on systems with mass ratio q= 0.3–0.5, while for double black hole binaries the observability-weighted distribution is dominated by massive, nearly equal-mass binaries with q > 0.7.

Metastability in the evolution of triple systems

The dynamical evolution of 15 000 equal-mass triple systems with zero initial velocities (the free-fall three-body problem) is considered. The equations of motion are numerically integrated using regularization of binary and triple encounters. We find 170 triple systems which reach a state where the motions take place within a limited region of phase space during a long time. These regions are concentrated in the zones of regular motions in the vicinities of stable periodic orbits: the von Schubart orbit in the rectilinear problem, the Broucke orbit in the isosceles problem, and the ‘Eight’ orbit. The classification of such metastable orbits is suggested. A change of the types is found during the dynamical evolution of some metastable systems. The triple system leaves the metastable regime after some time, and its evolution is finished by the escape of one body.

Planet Formation is Unlikely in Equal-Mass Binary Systems with [CLC][ITAL]a[/ITAL][/CLC] ∼ 50 AU

We show that planet formation via both gravitational collapse and core accretion is unlikely to occur in equal-mass binary systems with moderate (~50 AU) semimajor axes. Internal thermal energy generation in the disks is sufficient to heat the gas everywhere so that spiral structures quickly decay rather than grow or fragment. This same heating will inhibit dust coagulation because the temperatures rise above the vaporization temperatures of many volatile materials. We consider other processes not included in the model and conclude that our temperatures are conservatively estimated (low), i.e., planet formation is less likely in real systems than in the model.

Monte Carlo simulations of star clusters -- I. First Results

A revision of Stodoíkiewicz's Monte Carlo code is used to simulate evolution of star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The first calculations for isolated, equal-mass N-body systems with three-body energy generation according to Spitzer's formulae show good agreement with direct N-body calculations for N = 2000, 4096 and 10 000 particles. The density, velocity, mass distributions, energy generation, number of binaries, etc., follow the N-body results. Only the number of escapers is slightly too high compared with N-body results, and there is no level-off anisotropy for advanced post-collapse evolution of Monte Carlo models as is seen in N-body simulations for N ≤ 2000. For simulations with N > 10 000 gravothermal oscillations are clearly visible. The calculations of N 2000, 4096, 10 000, 32 000 and 100 000 models take about 2, 6, 20, 130 and 2500 h, respectively. The Monte Carlo code is at least 105 times faster than the N-body one for N = 32 768 with special-purpose hardware. Thus it becomes possible to run several different models to improve statistical quality of the data and run individual models with N as large as 100 000. The Monte Carlo scheme can be regarded as a method which lies in the middle between direct N-body and Fokker-Planck models and combines most advantages of both methods.