arXiv subjects

Nathan W. C. Leigh

Publications and source records attributed to Nathan W. C. Leigh.

At least 55 records · Page 3Linked to original sources

arXiv2019

A Triple Origin for Twin Blue Stragglers in Close Binaries

We propose a formation mechanism for twin blue stragglers (BSs) in compact binaries that involves mass transfer from an evolved outer tertiary companion on to the inner binary via a circumbinary disk. We apply this scenario to the observed double BS system Binary 7782 in the old open cluster NGC 188, and show that its observed properties are naturally reproduced within the context of the proposed model. We predict the following properties for twin BSs: (1) For the outer tertiary orbit, the initial orbital period should lie between 220 days $\lesssim$ P$_{\rm out}$ $\lesssim$ 1100 days, assuming initial masses for the inner binary components of $m_{\rm 1} = 1.1$ M$_{\odot}$ and $m_{\rm 2} =$ 0.9 M$_{\odot}$ and an outer tertiary mass of $m_{\rm 3} = 1.4$ M$_{\odot}$. After Roche-lobe overflow, the outer star turns into a white dwarf (WD) of mass 0.43 to 0.54\,\MSun. There is a correlation between the mass of this WD and the outer orbital period: more massive WDs will be on wider orbits. (3) The rotational axes of both BSs will be aligned with each other and the orbital plane of the outer tertiary WD. (4) The BSs will have roughly equal masses, independent of their initial masses (since the lower mass star accretes the most). The dominant accretor should, therefore, be more enriched by the accreted material. Hence, one of the BSs will appear to be more enriched by either He, C and O or by s-process elements, if the donor started Roche lobe overflow on, respectively, the red giant or asymptotic giant branch. (5) Relative to old clusters, twin BSs in close binaries formed from the proposed mechanism should be more frequent in the Galactic field and open clusters with ages $\lesssim$ 4-6 Gyr, since then the donor will have a radiative envelope. (6) The orbit of the binary BS will have a small semi-major axis (typically $\aplt 0.3$\,au) and be close to circular ($e \aplt 0.2$).

astro-ph.SR↗

arXiv2018

Implementing Tidal and Gravitational Wave Energy Losses in Few-body Codes: A Fast and Easy Drag Force Model

We present a drag force model for evolving chaotic few-body interactions with the inclusion of orbital energy losses, such as tidal dissipation and gravitational wave (GW) emission. The main effect from such losses is the formation of two-body captures, that for compact objects result in GW mergers, and for stars lead to either compact binaries, mergers or disruptions. Studying the inclusion of energy loss terms in few-body interactions is therefore likely to be important for modeling and understanding the variety of transients that soon will be observed by current and upcoming surveys. However, including especially tides in few-body codes has been shown to be technically difficult and computationally heavy, which has lead to very few systematic tidal studies. In this paper we derive a drag force term that can be used to model the effects from tidal, as well as other, energy losses in few-body interactions, if the two-body orbit averaged energy loss is known a priori. This drag force model is very fast to evolve, and gives results in agreement with other approaches, including the impulsive and affine tide approximations.

astro-ph.HE↗

arXiv2018

Small-N collisional dynamics IV: Order in the realm of not-so-small-N

In this paper, the fourth in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We focus once again on the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and interactions that produce direct collisions between any two particles. Our long-term goal is to predict the probability of a given collision event occurring over the course of an interaction, as a function of the numbers and properties of the particles. In previous papers, we varied the number of interacting particles, as well as the distributions of particle radii and masses. Here, we refine the methods developed in these preceding studies, and arrive at a final and robust methodology that can be used to study collisional dynamics in a variety of astrophysical contexts, ranging from stars in star clusters, galaxies in galaxy groups and clusters and even the collisional growth of planetesimals in protoplanetary disks. We further present and refine the concept of a Collision Rate Diagram (CRD), the primary tool we use to quantify the relative rates for different collision scenarios to occur. The agreement between our final theoretical model and the results of numerical scattering simulations is excellent.

astro-ph.SR↗

arXiv2018

When do star clusters become multiple star systems? II. Toward a half-life formalism with four bodies

We present a half-life formalism for describing the disruption of gravitationally-bound few-body systems, with a focus on binary-binary scattering. For negative total encounter energies, the four-body problem has three possible decay products in the point particle limit. For each decay product and a given set of initial conditions, we obtain directly from numerical scattering simulations the half-life for the distribution of disruption times. As in radioactive decay, the half-lives should provide a direct prediction for the relative fractions of each decay product. We test this prediction with simulated data and find good agreement with our hypothesis. We briefly discuss applications of this feature of the gravitational four-body problem to populations of black holes in globular clusters. This paper, the second in the series, builds on extending the remarkable similarity between gravitational chaos at the macroscopic scale and radioactive decay at the microscopic scale to larger-N systems.

astro-ph.SR↗

arXiv2018

Illustrating chaos: A schematic discretization of the general three-body problem in Newtonian gravity

We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular momentum-space. Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta. These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state. As shown via an illustrative example for the bound case, prolonged excursions of one of the particles, which by far dominates the computational cost of the simulations, are reduced to a single discrete transformation in energy- and angular momentum-space, thereby potentially mitigating any computational expense. We further generalize our formalism to sequences of (unbound) three-body interactions, as occur in dense stellar environments during binary hardening. Finally, we provide a method for dynamically evolving entire populations of binaries via three-body scattering interactions, using a purely analytic formalism. In principle, the techniques presented here are adaptable to other three-body problems that conserve energy and angular momentum.

astro-ph.SR↗

arXiv2017

On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening

We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disk components hosting a super-massive black hole (SMBH). We determine the total number of encounters $N_{\rm GW}$ needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disk components. Using a Monte Carlo approach, we refine our calculations for $N_{\rm GW}$ to include gravitational wave emission between scattering events. For astrophysically plausible models we find that typically $N_{\rm GW} \lesssim$ 10. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low velocity dispersions and no significant Keplerian component; and (2) migration traps in disks around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disk. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation- and dispersion-supported components. Because disks enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.

astro-ph.GA↗

arXiv2017

The Evolution of Kicked Stellar-Mass Black Holes in Star Cluster Environments

We consider how dynamical friction acts on black holes that receive a velocity kick while located at the center of a gravitational potential, analogous to a star cluster, due to either a natal kick or the anisotropic emission of gravitational waves during a black hole-black hole merger. Our investigation specifically focuses on how well various Chandrasekhar-based dynamical friction models can predict the orbital decay of kicked black holes with $m_{bh} \lesssim 100 M_\odot$ due to an inhomogeneous background stellar field. In general, the orbital evolution of a kicked black hole follows that of a damped oscillator where two-body encounters and dynamical friction serve as sources of damping. However, we find models for approximating the effects of dynamical friction do not accurately predict the amount of energy lost by the black hole if the initial kick velocity $v_{k}$ is greater than the stellar velocity dispersion $σ$. For all kick velocities, we also find that two-body encounters with nearby stars can cause the energy evolution of a kicked BH to stray significantly from standard dynamical friction theory as encounters can sometimes lead to an energy gain. For larger kick velocities, we find the orbital decay of a black hole departs from classical theory completely as the black hole's orbital amplitude decays linearly with time as opposed to exponentially. Therefore, we have developed a linear decay formalism which scales linearly with black hole mass and $\frac{v_{k}}σ$ in order to account for the variations in the local gravitational potential.

astro-ph.GA↗

arXiv2017

Small-N collisional dynamics III: The battle for the realm of not-so-small-N

In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that produce direct collisions between any two stars. Our long-term goal is to construct an equation that gives the probability of a given collision event occurring over the course of the interaction, as a function of the total encounter energy and angular momentum as well as the numbers and properties of the particles. In previous papers, we varied the number of interacting particles and the distribution of particle radii, for all equal mass particles. Here, we focus on the effects of different combinations of particle masses. We develop an analytic formalism for calculating the time-scales for different collision scenarios to occur. Our analytic time-scales reproduce the simulated time-scales when gravitational focusing is included. We present a method for calculating the relative rates for different types of collisions to occur, assuming two different limits for the particle orbits; radial and tangential. These limits yield relative collision probabilities that bracket the probabilities we obtain directly from numerical scattering experiments, and are designed to reveal important information about the (time-averaged) trajectories of the particles as a function of the interaction parameters. Finally, we present a Collision Rate Diagram (CRD), which directly compares the predictions of our analytic rates to the simulations and quantifies the quality of the agreement. The CRD will facilitate refining our analytic collision rates in future work, as we expand in to the remaining parameter space.

astro-ph.SR↗

arXiv2017

Mass Evaporation Rate of Globular Clusters in a Strong Tidal Field

The mass evaporation rate of globular clusters evolving in a strong Galactic tidal field is derived through the analysis of large, multi-mass $N$-body simulations. For comparison, we also study the same evaporation rates using MOCCA Monte Carlo models for globular cluster evolution. Our results show that the mass evaporation rate is a dynamical value; that is, far from a constant single number found in earlier analytical work and commonly used in the literature. Moreover, the evaporation rate derived with these simulations is higher than values previously published. These models also show that the value of the mass evaporation rate depends on the strength of the tidal field. We give an analytical estimate of the mass evaporation rate as a function of time and galactocentric distance xi(R_{GC},t). Upon extrapolating this formula to smaller R_{GC} values, our results provide tentative evidence for a very high xi value at small R_{GC}. Our results suggest that the corresponding mass loss in the inner Galactic potential could be high and it should be accounted for when star clusters pass within it. This has direct relevance to nuclear cluster formation/growth via the infall of globular clusters through dynamical friction. As an illustrative example, we estimate how the evaporation rate increases for a ~10^5 solar masses globular cluster that decays through dynamical friction into the galactic centre. We discuss the findings of this work in relation to the formation of nuclear star clusters by inspiraling globular clusters.

astro-ph.GA↗

arXiv2017

Formation of runaway stars in a star-cluster potential

We study the formation of runaway stars due to binary-binary (2+2) interactions in young star-forming clusters and/or associations. This is done using a combination of analytic methods and numerical simulations of 2+2 scattering interactions, both in isolation and in a homogeneous background potential. We focus on interactions that produce two single stars and a binary, and study the outcomes as a function of the depth of the background potential, within a range typical of cluster cores. As reference parameters for the observational properties, we use those observed for the system of runaway stars AE Aur and $μ$ Col and binary $ι$ Ori. We find that the outcome fractions have no appreciable dependence on the depth of the potential, and neither do the velocities of the ejected single stars. However, as the potential gets deeper and a larger fraction of binaries remain trapped, two binary populations emerge, with the escaped component having higher speeds and shorter semi-major axes than the trapped one. Additionally, we find that the relative angles between the ejected products are generally large. In particular, the angle between the ejected fastest star and the escaped binary is typically $\gtrsim 120-135^{\circ}$, with a peak at around $160^{\circ}$. However, as the potential gets deeper, the angle distribution becomes broader. Finally, we discuss the implications of our results for the interpretation of the properties of the runaway stars AE Aur and $μ$ Col.

astro-ph.GA↗

arXiv2017

On the Origin of Sub-subgiant Stars. III. Formation Frequencies

Sub-subgiants are a new class of stars that are optically redder than normal main-sequence stars and fainter than normal subgiant stars. Sub-subgiants, and the possibly related red stragglers (which fall to the red of the giant branch), occupy a region of the color-magnitude diagram that is predicted to be devoid of stars by standard stellar evolution theory. In previous papers we presented the observed demographics of these sources and defined possible theoretical formation channels through isolated binary evolution, the rapid stripping of a subgiant's envelope, and stellar collisions. Sub-subgiants offer key tests for single- and binary-star evolution and stellar collision models. In this paper, we synthesize these findings to discuss the formation frequencies through each of these channels. The empirical data, our analytic formation rate calculations, and analyses of sub-subgiants in a large grid of Monte Carlo globular cluster models suggest that the binary evolution channels may be the most prevalent, though all channels appear to be viable routes to sub-subgiant creation (especially in higher-mass globular clusters). Multiple formation channels may operate simultaneously to produce the observed sub-subgiant population. Finally, many of these formation pathways can produce stars in both the sub-subgiant and red straggler (and blue straggler) regions of the color-magnitude diagram, in some cases as different stages along the same evolutionary sequence.

astro-ph.SR↗

arXiv2017

An analytic method for identifying dynamically-formed runaway stars

In this paper, we study the 3-body products (two single stars and a binary) of binary-binary (2+2) scattering interactions. This is done using a combination of analytic methods and numerical simulations of 2+2 scattering interactions, both in isolation and in a homogeneous background potential. We derive analytically a simple formula relating the angle between the velocity vectors of the two ejected single stars and the orbital separation of the remaining binary. We compare our analytic formulation to numerical scattering simulations, and illustrate that the agreement is excellent, both in isolation and in a homogeneous background potential. Our results are ideally suited for application to the GAIA database, which is expected to identify many hundred runaway stars. The analytic relation presented here has the potential to identify runaway stars formed dynamically with high confidence. Finally, by applying our method to the runaways AE Aur and $μ$ Col, we illustrate that it can be used to constrain the history of the background potential, which was denser than the presently observed density in the case of the Trapezium cluster.

astro-ph.GA↗

arXiv2017

On the Origin of Sub-subgiant Stars. I. Demographics

Sub-subgiants are stars observed to be redder than normal main-sequence stars and fainter than normal subgiant (and giant) stars in an optical color-magnitude diagram. The red straggler stars, which lie redward of the red giant branch, may be related and are often grouped together with the sub-subgiants in the literature. These stars defy our standard theory of single-star evolution, and are important tests for binary evolution and stellar collision models. In total, we identify 65 sub-subgiants and red stragglers in 16 open and globular star clusters from the literature; 50 of these, including 43 sub-subgiants, pass our strict membership selection criteria (though the remaining sources may also be cluster members). In addition to their unique location on the color-magnitude diagram, we find that at least 58% (25/43) of sub-subgiants in this sample are X-ray sources with typical 0.5-2.5 keV luminosities of order 10^30 - 10^31 erg/s. Their X-ray luminosities and optical-to-X-ray flux ratios are similar to those of RS CVn active binaries. At least 65% (28/43) of the sub-subgiants in our sample are variables, 21 of which are known to be radial-velocity binaries. Typical variability periods are <15 days. At least 33% (14/43) of the sub-subgiants are H-alpha emitters. These observational demographics provide strong evidence that binarity is important for sub-subgiant formation. Finally, we find that the number of sub-subgiants per unit mass increases toward lower-mass clusters, such that the open clusters in our sample have the highest specific frequencies of sub-subgiants.

astro-ph.SR↗

arXiv2017

MOCCA-SURVEY database I. Accreting white dwarf binary systems in globular clusters -- III. Cataclysmic variables -- Implications of model assumptions

In this third of a series of papers related to cataclysmic variables (CVs) and related objects, we analyse the population of CVs in a set of 12 globular cluster models evolved with the MOCCA Monte Carlo code, for two initial binary populations (IBPs), two choices of common-envelope phase (CEP) parameters, and three different models for the evolution of CVs and the treatment of angular momentum loss. When more realistic models and parameters are considered, we find that present-day cluster CV duty cycles are extremely-low ($\lesssim 0.1$ per cent) which makes their detection during outbursts rather difficult. Additionally, the IBP plays a significant role in shaping the CV population properties, and models that follow the Kroupa IBP are less affected by enhanced angular momentum loss. We also predict from our simulations that CVs formed dynamically in the past few Gyr (massive CVs) correspond to bright CVs (as expected), and that faint CVs formed several Gyr ago (dynamically or not) represent the overwhelming majority. Regarding the CV formation rate, we rule out the notion that it is similar irrespective of the cluster properties. Finally, we discuss the differences in the present-day CV properties related to the IBPs, the initial cluster conditions, the CEP parameters, formation channels, the CV evolution models, and the angular momentum loss treatments.

astro-ph.GA↗

arXiv2017

Numerical study of the chaotic N=4 problem in a background potential

We perform a large suite of $N=4$ numerical scattering experiments between two identical binaries consisting of identical point particles in a (continuous) background potential. For investigative purposes, albeit without loss of generality, we assume that the potential corresponds to a uniform (natal or star-forming) gas medium. We explore a range of constant gas densities, from $n=10~ {\rm cm}^{-3}$ to $10^{5}~ {\rm cm}^{-3}$. These densities are relevant for various astrophysical environments, including molecular clouds (i.e., star-forming regions) and denser, fragmented cores within these clouds. Our primary goal is to characterize the effects of the background potential on the subsequent stellar dynamics. We consider the outcome probabilities as well as the properties of any binaries formed during the binary-binary encounters, such as the distributions of binary binding energies and eccentricities. We also present the final velocity distributions of the ejected single stars. The background potential has two important effects on the stellar dynamics: 1) The potential acts to reset the zero-point of the total system energy, which in turn affects the types and properties of the products of the encounter; 2) For higher $n$ and weakly bound systems (i.e., large semimajor axes), the stellar dynamics are significantly affected when stars become trapped in the potential, oscillating around the system centre of mass (CM). This, in turn, increases the number of scattering events between stars (single, binary or triple) near the CM and makes it harder for single stars to escape to infinity. This ultimately leads to the preferential ionization of triples and wide binaries and the survival of compact binaries, with the single stars escaping at very high ejection velocities.

astro-ph.SR↗

arXiv2017

A novel mechanism for the distance-redshift relation

We consider a novel mechanism to account for the observed distance-redshift relation. This is done by presenting a toy model for the large-scale matter distribution in a static Universe. Our model mainly concerns particles with masses far below those in the Standard Model of Particle Physics. The model is founded on three main assumptions: (1) a mass spectrum dN$_{\rm i}$/dm$_{\rm i}$ $=$ $β$m$_{\rm i}^{-α}$ (where $α$ and $β$ are both positive constants) for low-mass particles with m$_{\rm i}$ $\ll$ 10$^{-22}$ eV $\ll$ M$_{\rm P}$, where M$_{\rm P}$ is the Planck mass; (2) a particle mass-wavelength relation of the form $λ_{\rm i} =$ $\hbar$/$δ_{\rm i}$m$_{\rm i}$c, where $δ_{\rm i} =$ $η$m$_{\rm i}^γ$ and $η$ and $γ$ are both constants; and (3) For such low-mass particles, locality can only be defined on large spatial scales, comparable to or exceeding the particle wavelengths. We use our model to derive the cosmological redshift characteristic of the Standard Model of Cosmology, which becomes a gravitational redshift in our model. We compare the results of our model to empirical data and show that, in order to reproduce the sub-linear form of the observed distance-redshift relation, our model requires $α$ + $γ$ $<$ 0. We further place our toy model in the context of the Friedmann Universe via a superposition of Einstein Universes, each with its own scale factor a$_{\rm i}$. Given the overwhelming evidence supporting an expanding Universe, we then address possible modifications to our base model that would be required to account for the available empirical constraints, including the addition of some initial expansion. Finally, we consider potentially observable distinctions between the cosmological redshift and our proposed mechanism to account for the observed distance-redshift relation.

astro-ph.CO↗

arXiv2016

The chaotic four-body problem in Newtonian gravity I: Identical point-particles

In this paper, we study the chaotic four-body problem in Newtonian gravity. Assuming point particles and total encounter energies $\le$ 0, the problem has three possible outcomes. We describe each outcome as a series of discrete transformations in energy space, using the diagrams first presented in Leigh \& Geller (2012; see the Appendix). Furthermore, we develop a formalism for calculating probabilities for these outcomes to occur, expressed using the density of escape configurations per unit energy, and based on the Monaghan description originally developed for the three-body problem. We compare this analytic formalism to results from a series of binary-binary encounters with identical point particles, simulated using the \texttt{FEWBODY} code. Each of our three encounter outcomes produces a unique velocity distribution for the escaping star(s). Thus, these distributions can potentially be used to constrain the origins of dynamically-formed populations, via a direct comparison between the predicted and observed velocity distributions. Finally, we show that, for encounters that form stable triples, the simulated single star escape velocity distributions are the same as for the three-body problem. This is also the case for the other two encounter outcomes, but only at low virial ratios. This suggests that single and binary stars processed via single-binary and binary-binary encounters in dense star clusters should have a unique velocity distribution relative to the underlying Maxwellian distribution (provided the relaxation time is sufficiently long), which can be calculated analytically.

astro-ph.SR↗

arXiv2016

On the origins of enigmatic stellar populations in Local Group galactic nuclei

We consider the origins of enigmatic stellar populations in four Local Group galactic nuclei, specifically the Milky Way, M31, M32 and M33. These are centrally concentrated blue stars, found in three out of the four nuclear star clusters (NSCs) considered here. Their origins are unknown, but could include blue straggler (BS) stars, extended horizontal branch stars and young recently formed stars. Here, we calculate order-of-magnitude estimates for various collision rates, as a function of the host NSC environment and distance from the cluster centre. These rates are sufficiently high that BSs, formed via collisions between main sequence (MS) stars, could contribute non-negligibly ($\sim$ 1-10% in mass) to every surface brightness profile, with the exception of the Milky Way. Stellar evolution models show that the envelopes of red giant branch (RGB) stars must be nearly completely stripped to significantly affect their photometric appearance, which requires multiple collisions. Hence, the collision rates for individual RGB stars are only sufficiently high in the inner $\lesssim$ 0.1 pc of M31 and M32 for RGB destruction to occur. Collisions between white dwarfs and MS stars, which should ablate the stars, could offer a steady and significant supply of gas in every NSC in our sample. The gas could either fragment to form new stars, or accrete onto old MS stars already present. Thus, collisional processes could contribute significantly to the observed blue excesses in M31 and M33; future studies should be aimed at better constraining theoretical predictions to compliment existing and future observational data.

astro-ph.GA↗