Binaries In Globular Clusters Research Articles

The merger of hard binaries in globular clusters as the primary channel for the formation of second-generation stars

ABSTRACT We have recently presented observational evidence which suggests that the origin of the second-generation (G2) stars in globular clusters (GCs) is due to the binary-mediated collision of primordial (G1) low-mass main-sequence (MS) stars. This mechanism avoids both the mass budget problem and the need of external gas for dilution. Here, we report on another piece of evidence supporting this scenario: (1) the fraction of MS binaries is proportional to the fraction of G1 stars in GCs and, at the same time, (2) the smaller the fraction of G1 stars is, the more deficient binaries of higher mass ratio (q>0.7) are. They are, on average, harder than their smaller mass-ratio counterparts due to higher binding energy at a given primary mass. Then (2) implies that (1) is due to the merging/collisions of hard binaries rather than to their disruption. These new results complemented by the present-day data on binaries lead to the following conclusions: (i) the mass-ratio distribution of binaries, particularly short-period ones, with low-mass primaries, MP < 1.5 M⊙, is strongly peaked close to q=1.0, whereas (ii) dynamical processes at high stellar density tend to destroy softer binaries and make hard (nearly) twin binaries to become even harder and favour their mergers and collisions. G2 stars formed this way gain mass that virtually doubles the primary one, 2MP, at which the number of G1 stars is approximately five times smaller than at MP according to the slope of a Milky Way-like initial mass function at MMS < 1.0 M⊙.

A Comparison of Millisecond Pulsar Populations between Globular Clusters and the Galactic Field

We have performed a systematic study of the rotational, orbital, and X-ray properties of millisecond pulsars (MSPs) in globular clusters (GCs) and compared their nature with those of the MSPs in the Galactic field (GF). We found that GC MSPs generally rotate slower than their counterparts in the GF. Different from the expectation of a simple recycling scenario, no evidence for the correlation between the orbital period and the rotation period can be found in the MSP binaries in GCs. There is also an indication that the surface magnetic field of GC MSPs is stronger than those in the GF. All these suggest dynamical interactions in GCs can alter the evolution of MSPs/their progenitors, which can leave an imprint on their X-ray emission properties. While the MSPs in both GF and GCs have similar distributions of X-ray luminosity and hardness, our sample supports the notion that these two populations follow different relations between the X-ray luminosity and spin-down power. We discuss this in terms of both the pulsar emission model and the observational bias.

Radio Detection of an Elusive Millisecond Pulsar in the Globular Cluster NGC 6397

We report the discovery of a new 5.78 ms period millisecond pulsar (MSP), PSR J1740−5340B (NGC 6397B), in an eclipsing binary system discovered with the Parkes radio telescope (now also known as Murriyang) in Australia and confirmed with the MeerKAT radio telescope in South Africa. The measured orbital period, 1.97 days, is the longest among all eclipsing binaries in globular clusters (GCs) and consistent with that of the coincident X-ray source U18, previously suggested to be a “hidden MSP.” Our XMM-Newton observations during NGC 6397B’s radio-quiescent epochs detected no X-ray flares. NGC 6397B is either a transitional MSP or an eclipsing binary in its initial stage of mass transfer after the companion star left the main sequence. The discovery of NGC 6397B potentially reveals a subgroup of extremely faint and heavily obscured binary pulsars, thus providing a plausible explanation for the apparent dearth of binary neutron stars in core-collapsed GCs as well as a critical constraint on the evolution of GCs.

The MAVERIC survey: a catalogue of radio sources in southern globular clusters from the Australia Telescope Compact Array

ABSTRACTRadio continuum observations offer a new window on compact objects in globular clusters compared to typical X-ray or optical studies. As part of the MAVERIC survey, we have used the Australia Telescope Compact Array to carry out a deep (median central noise level ≈4 $\mu$Jy beam-1) radio continuum survey of 26 southern globular clusters at central frequencies of 5.5 and 9.0 GHz. This paper presents a catalogue of 1285 radio continuum sources in the fields of these 26 clusters. Considering the surface density of background sources, we find significant evidence for a population of radio sources in seven of the 26 clusters, and also identify at least 11 previously known compact objects (six pulsars and five X-ray binaries). While the overall density of radio continuum sources with 7.25-GHz flux densities ≳ 20 $\mu$Jy in typical globular clusters is relatively low, the survey has already led to the discovery of several exciting compact binaries, including a candidate ultracompact black hole X-ray binary in 47 Tuc. Many of the unclassified radio sources near the centres of the clusters are likely to be true cluster sources, and multiwavelength follow-up will be necessary to classify these objects and better understand the demographics of accreting compact binaries in globular clusters.

Forming short-period substellar companions in 47 Tucanae – I. Dynamical model and brown dwarf tidal capture rates

ABSTRACT Stars in globular clusters formed and evolved in the most extreme environment: high density and low metallicity. If the formation of stars and planets is at all sensitive to environmental conditions, this should therefore be evident in globular clusters. Observations have indicated that hot Jupiters are at least an order of magnitude less prevalent in the central region of the globular cluster 47 Tucanae (Tuc) than in the field. In this work, we explore the claims in the literature for additional consequences for the low-mass stellar initial mass function. Tidal capture, the mechanism that produces X-ray binaries in globular clusters, applies also to brown dwarfs (BDs). This process produces tight stellar–BD binaries that would be detectable by transit surveys. Applying a Monte Carlo dynamical evolution model, we compute the overall BD capture rates. We find that the number of captures is lower than previous estimates. Capture efficiency increases steeply with stellar mass, which means that mass segregation reduces capture efficiency as BDs and low-mass stars occupy the same regions. The result of this effect is that the current constraints on the short-period companion fraction remain marginally consistent with initially equal numbers of BDs and stars. However, our findings suggest that expanding the sample in 47 Tuc or surveying other globular clusters for close substellar companions can yield constraints on the substellar initial mass function in these environments. We estimate the capture rates in other globular clusters and suggest that 47 Tuc remains a promising target for future transit surveys.

Using binaries in globular clusters to catch sight of intermediate-mass black holes

ABSTRACT The dynamical evolution of globular clusters (GCs) is tied to their binary population, as binaries segregate to the cluster centre, leading to an increased binary fraction in the core. This central overabundance of mainly hard binaries can serve as a source of energy for the cluster and has a significant effect on the observed kinematics, such as artificially increasing the observed line-of-sight velocity dispersion. We analyse the binary fractions and distributions of 95 simulated GCs, with and without an intermediate-mass black hole (IMBH) in their centre. We show that an IMBH will not only halt the segregation of binaries towards the cluster centre, but also, directly and indirectly, disrupt the binaries that segregate, thus, depleting binaries in the cluster core. We illustrate this by showing that clusters with an IMBH have fewer binaries and flatter radial binary distributions than their counterparts without one. These differences in the binary fraction and distribution provide an additional indicator for the presence of a central IMBH in GCs. In addition, we analyse the effects of the binary fraction on the line-of-sight velocity dispersion in the simulated GCs and find that binaries can cause an overestimation of up to $70 \rm {per \, cent}$ of the velocity dispersion within the core radius. Using recent VLT/MUSE observations of NGC 3201 by Giesers et al. (2019), we find an overestimation of $32.2\pm 7.8 \rm {per \, cent}$ in the velocity dispersion that is consistent with the simulations and illustrates the importance of accurately accounting for the binary population when performing kinematic or dynamical analysis.

Zwicky Transient Facility and Globular Clusters: the Period–Luminosity and Period–Luminosity–Color Relations for Late-type Contact Binaries

Abstract In this work, we aimed to derive the gri-band period–luminosity (PL) and period–luminosity–color (PLC) relations for late-type contact binaries, for the first time, located in globular clusters, using the homogeneous light curves collected by the Zwicky Transient Factory (ZTF). We started with 79 contact binaries in 15 globular clusters, and retained 30 contact binaries in 10 globular clusters that have adequate numbers of data points in the ZTF light curves and are unaffected by blending. Magnitudes at mean and maximum light of these contact binaries were determined using a fourth-order Fourier expansion, while extinction corrections were done using the Bayerstar2019 3D reddening map together with adopting the homogeneous distances to their host globular clusters. After removing early-type and “anomaly” contact binaries, our derived gri-band PL and period–Wesenheit (PW) relations exhibited a much larger dispersion with large errors on the fitted coefficients. Nevertheless, the gr-band PL and PW relations based on this small sample of contact binaries in globular clusters were consistent with those based on a larger sample of nearby contact binaries. Good agreements of the PL and PW relations suggested both samples of contact binaries in the local Solar neighborhood and in the distant globular clusters can be combined and used to derive and calibrate the PL, PW, and PLC relations. The final derived gr-band PL, PW, and PLC relations were much improved over those based on the limited sample of contact binaries in the globular clusters.

Mocca-survey Database I: Binary black hole mergers from globular clusters with intermediate mass black holes

ABSTRACT The dynamical formation of black hole binaries in globular clusters that merge due to gravitational waves occurs more frequently in higher stellar density. Meanwhile, the probability to form intermediate mass black holes (IMBHs) also increases with the density. To explore the impact of the formation and growth of IMBHs on the population of stellar mass black hole binaries from globular clusters, we analyse the existing large survey of Monte Carlo globular cluster simulation data (mocca-survey Database I). We show that the number of binary black hole mergers agrees with the prediction based on clusters’ initial properties when the IMBH mass is not massive enough or the IMBH seed forms at a later time. However, binary black hole formation and subsequent merger events are significantly reduced compared to the prediction when the present-day IMBH mass is more massive than ${\sim}10^4\, \rm M_{\odot }$ or the present-day IMBH mass exceeds about 1 per cent of cluster’s initial total mass. By examining the maximum black hole mass in the system at the moment of black hole binary escaping, we find that ∼90 per cent of the merging binary black holes escape before the formation and growth of the IMBH. Furthermore, large fraction of stellar mass black holes are merged into the IMBH or escape as single black holes from globular clusters in cases of massive IMBHs, which can lead to the significant underpopulation of binary black holes merging with gravitational waves by a factor of 2 depending on the clusters’ initial distributions.

New Constraints on the Nuclear Equation of State from the Thermal Emission of Neutron Stars in Quiescent Low-mass X-Ray Binaries

Abstract This paper presents a new analysis of the thermal emission from the neutron star (NS) surface to constrain the dense matter equation of state. We employ an empirical parameterization of the equation of state with a Markov Chain Monte Carlo approach to consistently fit the spectra of quiescent low-mass X-ray binaries in globular clusters with well-measured distances. Despite previous analyses predicting low NS radii, we show that it is possible to reconcile the astrophysical data with nuclear physics knowledge with or without including a prior on the slope of the symmetry energy L sym. With this empirical parameterization of the equation of state, we obtain radii of the order of about 12 km without worsening the fit statistic. More importantly, we obtain the following values for the slope of the symmetry energy, its curvature K sym, and the isoscalar skewness parameter Q sat: MeV, MeV, and MeV. These are the first measurements of the empirical parameters K sym and Q sat. Their values are only weakly impacted by our assumptions, such as the distances or the number of free empirical parameters, provided the latter are taken within a reasonable range. We also study the weak sensitivity of our results to the set of sources analyzed, and we identify a group of sources that dominates the constraints. The resulting masses and radii obtained from this empirical parameterization are also compared to other measurements from electromagnetic observations of NSs and gravitational wave signals from the NS–NS merger GW170817.

Effect of distant encounters on black hole binaries in globular clusters: Systematic increase of in-cluster mergers in the LISA band

We present the first systematic study on how distant weak interactions impact the dynamical evolution of merging binary black holes (BBHs) in dense stellar clusters. Recent studies indicate that dense clusters are likely to significantly contribute to the rate of merging BBHs observable through gravitational waves (GWs), and that many of these mergers will appear with notable eccentricities measurable in the LISA and LIGO sensitivity bands. This is highly interesting, as eccentricity can be used to distinguish between different astrophysical merger channels. However, all of these recent studies are based on various Monte Carlo (MC) techniques that only include strong interactions for the dynamical evolution of BBHs, whereas any binary generally undergoes orders-of-magnitude more weak interactions than strong. It is well known that weak interactions primarily lead to a change in the binary's eccentricity, which for BBHs implies that weak interactions can change their GW inspiral time and thereby their merger probability. With this motivation, we perform MC simulations of BBHs evolving in dense clusters under the influence of both weak and strong interactions. We find that including weak interactions leads to a notable increase in the number of BBHs that merge inside their cluster, which correspondingly leads to a higher number of eccentric LISA sources. These preliminary results illustrate the importance of including weak interactions for accurately modeling how BBHs merge in clusters, and how to link their emitted GW signals to their astrophysical environment.

Analytic computation of the secular effects of encounters on a binary: third-order perturbation, octupole, and post-Newtonian terms; steady-state distribution

ABSTRACTDense stellar systems such as globular clusters are believed to harbour merging binary black holes (BHs). The evolution of such binaries is driven by interactions with other stars, most notably, binary-single interactions. Traditionally, so-called ‘strong’ interactions are believed to be the driving force in this evolution. However, we recently showed that more distant, i.e. ‘weak’ or ‘secular’ encounters, can have important implications for the properties of merging BH binaries in globular clusters. This motivates more detailed understanding of the effects of secular encounters on a binary. In another previous paper, we analytically calculated expressions for the changes of the eccentricity and angular-momentum vectors taking into account second-order perturbation theory, and showed that, for highly eccentric binaries, the new expressions give rise to behaviour that is not captured by first-order theory. Here, we extend our previous work to third-order perturbation theory. We also include terms up to and including octupole order. The latter are non-zero for binaries with unequal component masses. In addition, we consider the effects of post-Newtonian terms, and we determine the steady-state distribution due to the cumulative effect of secular encounters by computing the associated angular-momentum diffusion coefficients, and applying the Fokker–Planck equation. Together with our previous work, the results in this paper provide a framework for incorporating the effects of distant encounters on binaries in models of cluster evolution, such as Monte Carlo codes.

Millisecond Pulsars and Black Holes in Globular Clusters

Abstract Over 100 millisecond radio pulsars (MSPs) have been observed in globular clusters (GCs), motivating theoretical studies of the formation and evolution of these sources through stellar evolution coupled to stellar dynamics. Here we study MSPs in GCs using realistic N-body simulations with our Cluster Monte Carlo code. We show that neutron stars (NSs) formed in electron-capture supernovae (including both accretion-induced and merger-induced collapse of white dwarfs) can be spun up through mass transfer to form MSPs. Both NS formation and spin-up through accretion are greatly enhanced through dynamical interaction processes. We find that our models for average GCs at the present day with masses ≈2 × 105 M ⊙ can produce up to 10–20 MSPs, while a very massive GC model with mass ≈106 M ⊙ can produce close to 100. We show that the number of MSPs is anti-correlated with the total number of stellar-mass black holes (BHs) retained in the host cluster. The radial distributions are also affected: MSPs are more concentrated toward the center in a host cluster with a smaller number of retained BHs. As a result, the number of MSPs in a GC could be used to place constraints on its BH population. Some intrinsic properties of MSP systems in our models (such as the magnetic fields and spin periods) are in good overall agreement with observations, while others (such as the distribution of binary companion types) are less so, and we discuss the possible reasons for such discrepancies. Interestingly, our models also demonstrate the possibility of dynamically forming NS–NS and NS–BH binaries in GCs, although the predicted numbers are very small.

Constraining the mass and radius of neutron stars in globular clusters

We analyze observations of eight quiescent low-mass X-ray binaries in globular clusters and combine them to determine the neutron star mass-radius curve and the equation of state of dense matter. We determine the effect that several uncertainties may have on our results, including uncertainties in the distance, the atmosphere composition, the neutron star maximum mass, the neutron star mass distribution, the possible presence of a hotspot on the neutron star surface, and the prior choice for the equation of state of dense matter. We find that the radius of a 1.4 solar mass neutron star is most likely from 10 to 14 km and that tighter constraints are only possible with stronger assumptions about the nature of the neutron stars, the systematics of the observations, or the nature of dense matter. Strong phase transitions are preferred over other models and interpretations of the data with a Bayes factor of 8 or more, and in this case, the radius is likely smaller than 12 km. However, radii larger than 12 km are preferred if the neutron stars have uneven temperature distributions.

Accreting Black Hole Binaries in Globular Clusters

Abstract We explore the formation of mass-transferring binary systems containing black holes (BHs) within globular clusters (GC). We show that it is possible to form mass-transferring BH binaries with main sequence, giant, and white dwarf companions with a variety of orbital parameters in GCs spanning a large range in present-day properties. All mass-transferring BH binaries found in our models at late times are dynamically created. The BHs in these systems experienced a median of ∼30 dynamical encounters within the cluster before and after acquiring the donor. Furthermore, we show that the presence of mass-transferring BH systems has little correlation with the total number of BHs within the cluster at any time. This is because the net rate of formation of BH–non-BH binaries in a cluster is largely independent of the total number of retained BHs. Our results suggest that the detection of a mass-transferring BH binary in a GC does not necessarily indicate that the host cluster contains a large BH population.

Comprehensive photometric study of an extremely low mass ratio deep contact binary in the globular cluster M 4

Abstract A comprehensive photometric study and an investigation of the orbital period variation of V53 in the globular cluster M 4 are presented. The photometric study reveals that the mass ratio and the contact degree of V53 are q ∼ 0.078 and f ∼ 69%, respectively. The observed variation in the light curve can be explained by adjusting the spot parameters. V53 belongs to extreme mass ratio (q ≤ 0.25), deep contact (f ≥ 50%) binaries, and its mass ratio is close to the minimum mass ratio predicted by theoretical studies, making it a potential object for studying the evolution of binaries and the formation of blue stragglers and FK Com-type stars. The orbital period of V53 shows a long-term decrease at a rate of dp/dt = 5.89(±0.02) × 10−8 d yr−1. This secular period decrease may be caused by the combination of mass transfer from the more massive component to the less massive component and an angular momentum loss via magnetic braking. As this mass transfer and angular momentum loss continues, V53 will ultimately evolve into a single fast-rotation star. By studying the statistics of all the contact binaries in globular clusters that have been analyzed, we found a possible correlation between the contact degree and whether or not a contact binary is a blue straggler. A contact binary is likely to become a blue straggler when its fill-out factor is more than 46.25(±2.05)%. More samples should be introduced to confirm this preliminary result in the future.

CHANDRA ACIS SURVEY OF X-RAY POINT SOURCES IN NEARBY GALAXIES. II. X-RAY LUMINOSITY FUNCTIONS AND ULTRALUMINOUS X-RAY SOURCES

ABSTRACT Based on the recently completed Chandra/ACIS survey of X-ray point sources in nearby galaxies, we study the X-ray luminosity functions (XLFs) for X-ray point sources in different types of galaxies and the statistical properties of ultraluminous X-ray sources (ULXs). Uniform procedures are developed to compute the detection threshold, to estimate the foreground/background contamination, and to calculate the XLFs for individual galaxies and groups of galaxies, resulting in an XLF library of 343 galaxies of different types. With the large number of surveyed galaxies, we have studied the XLFs and ULX properties across different host galaxy types, and confirm with good statistics that the XLF slope flattens from lenticular (α ∼ 1.50 ± 0.07) to elliptical (∼1.21 ± 0.02), to spirals (∼0.80 ± 0.02), to peculiars (∼0.55 ± 0.30), and to irregulars (∼0.26 ± 0.10). The XLF break dividing the neutron star and black hole binaries is also confirmed, albeit at quite different break luminosities for different types of galaxies. A radial dependency is found for ellipticals, with a flatter XLF slope for sources located between D 25 and 2D 25, suggesting the XLF slopes in the outer region of early-type galaxies are dominated by low-mass X-ray binaries in globular clusters. This study shows that the ULX rate in early-type galaxies is 0.24 ± 0.05 ULXs per surveyed galaxy, on a 5σ confidence level. The XLF for ULXs in late-type galaxies extends smoothly until it drops abruptly around 4 × 1040 erg s−1, and this break may suggest a mild boundary between the stellar black hole population possibly including 30 M ⊙ black holes with super-Eddington radiation and intermediate mass black holes.

Dynamically formed black hole+millisecond pulsar binaries in globular clusters

The discovery of a binary comprising a black hole (BH) and a millisecond pulsar (MSP) would yield insights into stellar evolution and facilitate exquisitely sensitive tests of general relativity. Globular clusters (GCs) are known to harbor large MSP populations and recent studies suggest that GCs may also retain a substantial population of stellar mass BHs. We modeled the formation of BH+MSP binaries in GCs through exchange interactions between binary and single stars. We found that in dense, massive clusters most of the dynamically formed BH+MSP binaries will have orbital periods of 2 to 10 days, regardless of the mass of the BH, the number of BHs retained by the cluster, and the nature of the GC's binary population. The size of the BH+MSP population is sensitive to several uncertain parameters, including the BH mass function, the BH retention fraction, and the binary fraction in GCs. Based on our models, we estimate that there are $0.6\pm0.2$ dynamically formed BH+MSP binaries in the Milky Way GC system, and place an upper limit on the size of this population of $\sim 10$. Interestingly, we find that BH+MSP binaries will be rare even if GCs retain large BH populations.

Can very compact and very massive neutron stars both exist?

The existence of neutron stars with masses of $\sim 2\,M_{\odot}$ requires a stiff equation of state at high densities. On the other hand, the necessary appearance also at high densities of new degrees of freedom, such as hyperons and $\Delta$ resonances, can lead to a strong softening of the equation of state with resulting maximum masses of $\sim 1.5\, M_{\odot}$ and radii smaller than $\sim 10$ km. Hints for the existence of compact stellar objects with very small radii have been found in recent statistical analysis of quiescent low-mass X-ray binaries in globular clusters. We propose an interpretation of these two apparently contradicting measurements, large masses and small radii, in terms of two separate families of compact stars: hadronic stars, whose equation of state is soft, can be very compact, while quark stars, whose equation of state is stiff, can be very massive. In this respect an early appearance of $\Delta$ resonances is crucial to guarantee the stability of the branch of hadronic stars. Our proposal could be tested by measurements of radii with an error of $\sim 1$ km, which is within reach of the planned LOFT satellite, and it would be further strengthened by the discovery of compact stars heavier than $\sim 2\,M_{\odot}$.

BLACK HOLE TRIPLE DYNAMICS: A BREAKDOWN OF THE ORBIT AVERAGE APPROXIMATION AND IMPLICATIONS FOR GRAVITATIONAL WAVE DETECTIONS

Coalescing black hole (BH) binaries forming in the dense core of globular clusters (GCs) are expected to be one the brightest sources of gravitational wave (GW) radiation for the next generation of ground-based laser interferometers. Favorable conditions for merger are initiated by the Kozai resonance in which the gravitational interaction with a third distant object, typically another BH, induces quasi-periodic variations of the inner BH binary eccentricity. In this paper we perform high precision N-body simulations of the long term evolution of hierarchical BH triples and investigate the conditions that lead to the merging of the BH binary and the way it might become an observable source of GW radiation. We find that the secular orbit average treatment, adopted in previous works, does not reliably describe the dynamics of these systems if the binary is orbited by the outer BH on a highly inclined orbit at a moderate distance. During the high eccentricity phase of a Kozai cycle the torque due to the outer BH can drive the binary to extremely large eccentricities in a fraction of the binary's orbital period. This occurs before relativistic terms become important to the evolution and allows the binary GW signal to reach large GW frequencies (>~10 Hz) at high eccentricities. We show that ~50 % of coalescing BH binaries driven by the Kozai mechanism in GCs will have eccentricities larger than 0.1, with 10 % of them being extremely eccentric, (1-e)<~10^-5, when they first chirp in the frequency band of ground based laser interferometers. This implies that a large fraction of such GW sources could be missed if conventional quasi-circular templates are used for analysis of GW detectors data. The efficient detection of all coalescing BH binaries in GCs will therefore require template banks of eccentric inspiral waveforms for matched-filtering and dedicated search strategies.

On the disruption of pulsar and X-ray binaries in globular clusters

The stellar encounter rate Gamma has been shown to be strongly correlated with the number of X-ray binaries in clusters and also to the number of radio pulsars. However, the pulsar populations in different clusters show remarkably different characteristics: in some GCs the population is dominated by binary systems, in others by single pulsars and exotic systems that result from exchange encounters. In this paper, we describe a second dynamical parameter for globular clusters, the encounter rate for a single binary, gamma. We find that this parameter provides a good characterization of the differences between the pulsar populations of different globular clusters. The higher gamma is for any particular globular cluster the more isolated pulsars and products of exchange interactions are observed. Furthermore, we also find that slow and "young" pulsars are found almost exclusively in clusters with a high gamma; this suggests that these kinds of objects are formed by the disruption of X-ray binaries, thus halting the recycling of a previously dead neutron star. We discuss the implications of this for the nature of young pulsars and for the formation of neutron stars in globular clusters.