Evolution of binary stars and the effect of tides on binary populations

Christopher A. Tout; Jarrod R. Hurley; Onno R. Pols

REVIEW

Evolution of binary stars and the effect of tides on binary populations

Jarrod R. Hurley, Christopher A. Tout, Onno R. Pols

Astrophysics · Submitted 14 Jan 2002 · 2 references

Pith's verdict: The BSE code paper: the algorithm and the semi-latus rectum result are the real contributions, while the abstract's claim that tides are 'necessary' outruns what the paper's own Section 5 concedes.

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CitationChristopher A. Tout, Jarrod R. Hurley, Onno R. Pols. "Evolution of binary stars and the effect of tides on binary populations." arXiv:astro-ph/0201220 (2002). https://pith.science/paper/BPLRT2OP

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Bottom line: this is the BSE code paper, and it is what you cite when you run binary population synthesis. The code is the contribution. The tides result is a sensitivity study of one module, not the general quantification the abstract advertises, and the authors say as much themselves in Section 5. Read it for the algorithm and for the semi-latus rectum argument; discount the percentage shifts in Table 5 accordingly. What is genuinely new: a fast binary evolution algorithm that carries eccentric orbits and stellar spins with convective, radiative and degenerate damping all active, at 0.14 s per binary. The individual damping laws are imported from Hut (1981), Zahn (1977), Campbell (1984) and Rasio et al. (1996). That is fine, those are published. The assembly is the work, and it is done carefully. The semi-latus rectum result in Section 4.2.3 is the durable export: because circularization precedes Roche-lobe overflow and tides conserve angular momentum, systems with the same initial l evolve identically regardless of e. That is a real, checkable statement, and it changes how you set up initial conditions. Where it is soft: the stress-test note is right. Models A through G vary alpha_CE, the IMF, Z and eccentricity, but never the tidal coefficients in eqs. 30, 42 and 47. So the percentage shifts in Table 5 are a single point in a space that the paper's own Section 3.3 and Figure 6 show to be violently nonlinear. A 10% change in alpha_CE flips an Algol into an ELD SNIa. A factor-of-few error in the damping normalization, which nobody has calibrated against a sample of pre-RLOF binaries, could move systems across those boundaries and change the sign of individual shifts. The error column in Table 5 is seed noise only. The abstract/body mismatch is real. Sentence s6 says tides are necessary for accurate conclusions; Section 5 says the differences are generally not enough to confirm one way or another. The body is the honest one, and it is to the authors' credit that they wrote it. Minor: eqs. 15 to 17 are attributed to Gair and Snellgrove, private communication, which is load-bearing and unpublished, and the code ships on request only. Who should read it: anyone running population synthesis, and anyone who wants the tidal timescale formulae collected in one place. Yes to peer review. It is a methods paper of record.

Referee report

Significance

If the differential result holds, it is a useful and durable statement: every population-synthesis rate table computed without tides carries a systematic error of the order of tens of per cent in several channels, and the sign of the error is not uniform across populations. The paper's real and lasting contributions are the algorithm itself, its public availability (Section 6), and the controlled A-versus-B design: identical grid, identical initial conditions, one switch. The reported percent-level errors from repeated random seeds (Table 5, final column) are a genuine and welcome piece of rigour that much of the contemporary population-synthesis literature lacked. The analytic argument that systems with equal semi-latus rectum circularize to the same separation before Roche-lobe overflow, so that the outcome is nearly independent of initial eccentricity, is a clean and falsifiable claim, and the comparison of the predicted double-degenerate period distribution with the 22 systems supplied by Marsh (Fig. 11) is exactly the kind of direct observational test the field needs. The paper is also commendably explicit about which parameters are uncertain and about where its own model is a

Major objections (5)

[Abstract, sentence s6, versus Section 5] The abstract states that the comparison 'show[s] that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work', but Section 5 concludes that the differences 'are generally not enough to confirm one way or another whether tidal evolution helps to explain the observed binary populations'. These two statements are in direct tension, and the abstract version is the one that will be quoted. The defensible claim supported by Section 4 is narrower: switching tides off shifts several predicted rates by tens of per cent, with the shift large enough to matter for the interpretation of any individual channel but not large enough to discriminate between models on current data. I would ask the authors to bring the abstract into line with Section 5, or to supply the additional evidence that would justify the stronger wording.
[Section 4.1.4, Table 4, and Section 2.3] The headline percentage shifts are single-point estimates: Models A through G vary the common-envelope efficiency, the secondary-mass distribution, metallicity and initial eccentricity, but no model varies the tidal damping coefficients themselves (eqs. 30, 42 and 47). The paper's own Section 3.3 and Figure 6 demonstrate that the outcomes are strongly nonlinear, with a change of 'less than 10%' in alpha_CE flipping an Algol into an edge-lit detonation and with a region of parameter space in which small changes in initial separation or mass move systems between coalescence and survival. Given that sensitivity, a factor-of-a-few change in the tidal strength, which is well inside the uncertainty of the uncalibrated prescriptions, could move systems across those boundaries and change the sign of individual shifts. At minimum the authors should add one model with the tidal timescales scaled by a constant factor (say 0.1 and 10) and report how the entries of Table 5 respond, so that the reader can see whether the quoted percentages are robust or are artefacts of one calibration.
[Section 2.3 and Section 4.3] The tidal damping normalizations are never checked against the observations that directly constrain them. The classical test is the period or separation at which eccentric orbits in open clusters and in field binaries become circular, and the corresponding synchronization boundary; these data existed well before this paper. Instead the only observational contact is indirect, through the double-degenerate period distribution in Figure 11 and the general rate comparisons of Section 4.3. Since the entire A-versus-B experiment measures the sensitivity of the population to this one module, a short subsection comparing the predicted circularization and synchronization boundaries with the observed ones (for example the (a/R)_circ values tabulated in Table 1 against the observed cutoff for the relevant mass range) would substantially strengthen the case that the module is calibrated rather than merely plausible.
[Abstract, sentence s7, and Section 4.2.3, Figures 7 and 8] The claim that 'it is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries' rests on the statement that plotting semi-latus rectum on the vertical axis of Figure 8 'appears virtually identical' to Figure 7. That is a visual comparison at a single fixed primary mass of 3.2 solar masses, whereas the claim is general. Table 5 shows that Models A and F do differ appreciably in several channels (for example the persistent NS LMXB rate differs by a factor of about three), and the paper attributes this to wider orbits interacting at periastron. The conditional form of the argument, that results are eccentricity-independent only if initial separations are drawn from the semi-latus-rectum distribution, is the important one, and no model in Table 4 actually adopts that distribution. I would ask for a quantitative statement: run one model with separations drawn from the semi-latus-rectum distribution and report the resulting rates alongside Model A, or soften the abstract to state the conditional claim explicitly.
[Section 4.3.5 and Section 5] Model A is designated the standard partly because Model C (alpha_CE = 1) 'fails to produce anywhere near enough' double degenerates, and the same double-degenerate observations are then used in Section 4.3.5 to validate Model A. This is a mild but real circularity in the parameter selection: the model is chosen by its agreement with a constraint and then reported as agreeing with that constraint. The paper is transparent about the choice, which is to its credit, but the reader cannot tell how much of the claimed success of Model A is independent evidence. A sentence in Section 4.3.5 or Section 5 stating explicitly which observational comparisons were used to fix alpha_CE and which are therefore independent tests would resolve this.

Minor objections (7)

[Eqs. (30) and (47)] Please check the printed forms of these two conversions. Combining eq. (29) with eq. (28) gives (k/T)_c = (2/21) f_conv (M_env/M) / tau_conv, i.e. tau_conv in the denominator, whereas eq. (30) as typeset appears to have tau_conv multiplying. Similarly, combining eq. (46) with eq. (27) gives (k/T)_d = (11.3 x 10^7 / 3) r_g^2 (L/M)^{5/7} approximately 3.8 x 10^7 r_g^2 (L/M)^{5/7} yr^{-1}, whereas eq. (47) quotes 2.564 x 10^{-8}. If these are typesetting slips they should be corrected; if not, the derivation should be shown.
[Eq. (42)] The printed form of eq. (42) appears dimensionally inconsistent with eq. (41): equating eq. (41) with eq. (28) gives (k/T)_r proportional to M^{1/2} R a^{-5/2}, not M R^2 a^{-5}. The prefactor 1.9782 x 10^4 is indeed (GM_sun/R_sun^3)^{1/2} in inverse years, which supports the former. Please verify the exponents.
[Section 2.7.1 and Table 3] Section 2.7.1 states that 'generally alpha_CE approximately 1 is used', while Table 3 lists the default as 3.0 and Model A adopts 3.0. A sentence reconciling the recommended default with the value used in the population synthesis would avoid confusion.
[Section 4.3.3] The finding that imposing the Eddington limit raises the persistent NS LMXB birth rate but lowers the total number, making the model inconsistent with the observed catalogue, is interesting and is dispatched in two sentences. It deserves a slightly fuller discussion, since it is one of the few places where an optional switch is disfavoured by data.
[Figures 5 to 8] The captions for Figures 5 to 8 do not state what is plotted on each axis, and the explanation of the indices i and j appears only in the caption of Figure 5. Each caption should be self-contained, and the symbol conventions (plus, cross, filled square) should be repeated or cross-referenced.
[Section 4.1.2] The paper recommends in the abstract that initial separations be distributed according to the observed distribution of semi-latera recta, but the flat-in-ln(a) distribution of eq. (100) is used in every model and is explicitly noted to be contrary to Eggleton, Fitchett & Tout (1989). A short statement of what the observed semi-latus-rectum distribution looks like, and how the rates of Table 5 would be expected to move under it, would make the recommendation actionable.
[Typographical] A number of typographical errors should be corrected: 'desiginated' (Section 1), 'possble' (Section 2.6), 'rejuvanation' (Section 2.6.6), 'efficency' (Section 2.7.1), 'preceeding' (Section 2.8), and 'cooling cooling track' (Section 4.2.2).

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The paper

The paper claims

Tides are not a detail: switching them off moves predicted binary-star birth rates by tens to hundreds of per cent, and the quantity that really fixes a binary's fate is the semi-latus rectum, not the period or the semi-major axis.

The reading

The authors want to know whether the tides a star raises on its companion — the friction that spins a binary into co-rotation and rounds out an eccentric orbit — change what population-synthesis studies predict about how many cataclysmic variables, X-ray binaries, double white dwarfs and Type Ia supernovae the Galaxy should produce. Their answer is yes, by amounts that matter: with tidal evolution switched off, the predicted birth rate of classical cataclysmic variables falls by roughly 35 per cent, subdwarf-B binaries rise by about 23 per cent, double degenerates rise by about 10 per cent, and the rate at which helium white dwarfs explode rises by about 190 per cent. The vehicle is a fast binary-evolution code that grafts tidal circularization and synchronization onto an already published single-star prescription, so that several hundred thousand binaries can be carried to 15 Gyr in hours rather than years. A second, quieter claim follows from the same bookkeeping: because orbits almost always circularize before Roche-lobe overflow, the later evolution of an interacting binary is fixed by its semi-latus rectum $l = a(1-e^2)$ rather than by its period or semi-major axis. If the authors are right, every earlier rate table computed without tides carries a systematic offset of this size, and the correct way to draw initial separations is from a distribution in $l$.

What carries the argument

The load-bearing object is the pair of weak-friction tidal evolution equations of Hut (1981) — one for $de/dt$, one for $dΩ_{spin}/dt$ — driven by three different damping prescriptions selected by stellar structure. For stars with convective envelopes the damping is turbulent viscosity, with $(k/T)_c = (2/21) f_{conv} τ_{conv} (M_{env}/M)$ yr$^{-1}$, where $τ_{conv}$ is the eddy turnover time of the largest convective cells and $f_{conv} = 1$ only while the tidal pumping period exceeds $2τ_{conv}$. For radiative envelopes it is Zahn's dynamical tide, with $(k/T)_r$ built from a tidal coefficient $E_2 = 1.592×10^{-9} M^{2.84}$. For degenerate stars it is Campbell's estimate $(k/T)_d = 2.564×10^{-8} r_g^2 (L/M)^{5/7}$ yr$^{-1}$. The equations are integrated by exchanging angular momentum between the orbit and the stellar spins, with the star prevented from being spun past its equilibrium rate $Ω_{spin,eq}(e)$, and the semi-major axis updated through the change in $J_{orb}$ rather than directly. This machinery is what makes the A-versus-B comparison possible: it is the only module toggled between the two populations, so the reported rate shifts are a direct measurement of the population's sensitivity to tidal strength.

Extended reading notes

Core claim

The paper's central claim is that tidal dissipation is a load-bearing ingredient of binary population synthesis, not a refinement. The authors build it into a rapid evolution code — convective damping of the equilibrium tide, radiative damping of the dynamical tide, and degenerate damping for white dwarfs — and then run the same large grid of binaries twice, once with tides and once without, comparing birth rates and present-day Galactic numbers for some forty classes of system and event. The differences are systematic and often large: classical cataclysmic variables down about 35 per cent without tides, subdwarf-B binaries up about 23 per cent, double degenerates up about 10 per cent, exploding helium white dwarfs up about 190 per cent, and roughly 55 per cent more Algols currently in the Galaxy. The authors also argue that the effect is not chaotic but organised by an invariant: tidal interaction conserves orbital angular momentum, and since $l = h^2/(GM_b)$ is conserved while an orbit circularizes, two systems born with the same $l$ but different eccentricities reach Roche-lobe overflow at the same separation and thereafter evolve identically. Hence the recommendation that initial separations be drawn from an observed distribution of semi-latera recta, and that an eccentricity distribution is unnecessary for interacting binaries.

Load-bearing premise

The whole comparison rests on three theoretical tidal-damping normalizations — convective, radiative and degenerate — that are adopted from analytic theory and never calibrated against an observed sample of pre-mass-transfer binaries, yet are applied to stars that are simultaneously expanding, losing mass and changing structure.

Editorial extensions

If this is right

Any population-synthesis rate table computed without tidal circularization and synchronization carries a systematic error of order tens of per cent in the classes that matter most for surveys — cataclysmic variables, Algols, subdwarf-B binaries and double degenerates — so comparisons between such tables and observed samples are comparing a model bias against observational selection effects.
The overproduction of exploding helium white dwarfs when tides are omitted (a factor of roughly three) is in direct conflict with the observed Type Ia and Type Ib supernova rates, which gives an independent argument for including tides rather than a purely internal one.
Initial separations in population synthesis should be drawn from a distribution of semi-latera recta $l = a(1-e^2)$, since systems sharing $l$ circularize to the same separation before Roche-lobe overflow; an eccentricity distribution is then redundant for interacting binaries, though it still matters for wide systems that never interact, such as barium stars.
The period distribution of double white dwarfs, when weighted by each system's gravitational-radiation merger time, matches the observed sample better with tides included, which suggests tides are needed to reproduce individual orbital characteristics and not just aggregate rates.
The common-envelope efficiency $α_{CE}$ is constrained from the same runs: $α_{CE}=1$ produces far too few double degenerates, while $α_{CE}=3$ is consistent with the observed double-degenerate fraction, so the tidal model and the envelope energetics have to be calibrated together.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the population-level shifts are as sensitive to the tidal normalization as the paper's own internal comparison suggests, then the natural next test is the inverse one: fit the tidal strength to the observed eccentricity-period distribution of pre-Roche-lobe binaries (subgiant and giant companions in eccentric orbits) and then re-run the population synthesis with the fitted value, rather than ad
The semi-latus rectum argument implies that published initial-separation distributions expressed in period or semi-major axis are not merely inconvenient but systematically wrong for eccentric populations, since converting between them requires an eccentricity distribution that the argument says is irrelevant. Re-expressing existing population-synthesis grids in $l$ would make previously incompara
Because the same angular momentum bookkeeping that circularizes an orbit also spins up the envelope, the model predicts that stars in close detached binaries should be rotating faster than single stars of the same mass and age — a prediction that is checkable now with rotational-velocity surveys of binary versus single field stars, independent of any population synthesis.
The reported excess of Type Ib/c supernovae across nearly all models, which the authors attribute to stripped helium stars from relatively low-mass progenitors, suggests the tension may lie in the helium-star mass-loss prescription rather than in the binary interaction physics; lowering that mass-loss rate would be a cleaner fix than adjusting the tidal model.

Original abstract

We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,944 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.85 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.75 · mentions code or data availability 0.04.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems.	contribution 0.69	0.93	0.04	asserted 1.00
s1	In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included.	method 0.91	0.66	0.02	asserted 1.00
s2	In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms.	method 0.94	0.76	0.03	asserted 0.99
s3	We use this algorithm to study the formation and evolution of various binary systems.	contribution 0.85	0.92	0.03	asserted 0.77
s4	We also investigate the effect that tidal friction has on the outcome of binary evolution.	contribution 0.99	0.88	0.05	unclear 0.58
s5	Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events.	method 0.93	0.96	0.04	asserted 0.96
s6	By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work.	interpretation 0.62	0.96	0.85	asserted 1.00
s7	Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity.	result 0.70	0.86	0.14	asserted 1.00
s8	It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.	interpretation 0.76	0.82	0.24	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.77 · evidence from simulation or computation 1.00.

What was examined, and what was not

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arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
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P abstract

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 2.** The evolution of the spins of the primary (∗ points) and secondary (+ points) stars, and the orbital spin (× points), as a function of the eccentricity of the orbit for the example of Algol evolution, shown until the end of the first phase of mass transfer. The points at zero eccentricity have been slightly displaced so that the co-rotation of the stars with the orbit can be clearly seen. the tide raised on the 0.9 M⊙ secondary acts to circularize the system so that at a time T = 413 Myr, when the 2.9 M⊙ primary reaches the end of its MS lifetime, the eccentricity has fallen to…

**Figure 3.** The evolution of stellar mass with binary period for the example of Algol evolution, until the end of the first phase of mass transfer. The primary mass decreases from 2.9 M⊙ to 0.42 M⊙ (∗ points) and the secondary mass increases from 0.9 M⊙ to 2.85 M⊙ (+ points) while the period initially decreases owing to circularization of the orbit and then increases as a result of the nearly conservative mass transfer. The observed parameters for the Algol systems RY Gem (solid triangles) and TT Hya (solid squares) are also shown. the evolution of the mass of the stars with the orbital period…

**Figure 5.** The region of parameter space from which cataclysmic variables (CVs) form when the initial mass of one star is fixed at 3.2 M⊙. Systems formed from Model A are shown as + symbols, from Model B as × symbols, with any overlap as filled squares. The indices i and j can assume the value of either 1 or 2 depending on which mass represents the primary star on the ZAMS, i.e. if the 3.2 M⊙ star is the more massive then i = 1 and j = 2. lobe, by which time the HeMS star has become a COWD and the resulting CE evolution leaves a COWD/HeMS pair in a close orbit. When the new HeMS evolves to…

**Figure 6.** The region of parameter space from which double-degenerate (DD) binaries form when the initial mass of one star is fixed at 1.6 M⊙. Systems formed from Model A are shown as + symbols, from Model B as × symbols, with any overlap as filled squares. The unstable behaviour of some near equal-mass systems is due to the relatively short lifetime of the GB stage. In this case there is a range of separations where the first phase of RLOF begins with both stars on the GB and CE gives a HeWD-HeWD pair. If the mass of either star changes slightly then one star is still on the MS when RLOF…

**Figure 7.** The region of parameter space from which CV, Algol and X-ray binaries form when the initial mass of one star is fixed at 3.2 M⊙ in Model A. or decrease the separation depending on the size of the velocity kick. After some time the MS star evolves to fill its Roche-lobe, by which time any eccentricity induced in the orbit by the supernova has been removed by the tides and a persistent NS LMXB is formed. If tides are not included then the orbit of the HeHG-MS pair is much wider so that the second RLOF phase occurs when the primary is on the GB, a CE forms and a DD NS-HeWD binary is…

**Figure 8.** The region of parameter space from which CV, Algol and X-ray binaries form when the initial mass of one star is fixed at 3.2 M⊙ in Model F. WD binaries, of which there are noticeably more formed in Model B. A typical RLOF+CE WDWD DD formation scenario in Model B begins with M1 = 2.2 M⊙, M2 = 1.6 M⊙ and P = 2 d. The primary fills its Roche-lobe on the HG when P = 1.9 d. RLOF ends on the GB just before the primary becomes a CHeB star, loses what little is left of its envelope, and moves to the HeMS. Now M1 = 0.35 M⊙, M2 = 3.45 M⊙ and P = 60 d. The orbit has widened as a result of the…

**Figure 9.** The probability, as a function of time, of a binary being found as a member of certain individual populations of Model A. We assume that all stars are born at the same time. The individual populations shown are: blue stragglers (full line), cataclysmic variables (dashed line), Algols (dash-dot line), persistent X-ray binaries (dotted line) and double-degenerates (dash-dot-dot-dot line). Each population includes contributions from each of its sub-populations listed in

**Figure 10.** The apparent magnitude distribution of Algol systems identified by Brancewicz & Dworak (1980). The magnitudes are taken from Wood et al. (1980). A best fit to the data for m ≤ 9.5 is shown by the full line. have a primary mass greater than 1 M⊙ as a function of their apparent magnitude. The apparent brightness of a star is linked to its distance and bolometric luminosity by l = L 4πd2 (107) which defines a volume V = 4π 3 L 4πl3/2 . (108) Assuming that the stars are uniformly distributed within this volume the number of stars out to apparent brightness l is Nl (m) = A l−3/2 n…

**Figure 11.** The distribution of periods of WDWD DD systems at formation in Model A (full line). The same distribution weighted by the gravitational radiation timescale of each system is shown for Model A (dashed line) and Model B (dotted line). Also shown are the periods of 22 observed DD systems (asterisks) provided by Marsh (private communication) Note that the vertical positioning of these points bears no relation to any physical parameters. 0.03 yr−1 for the DD birth rate but his model uses αCE = 1 (although Han accounts for the ionization energy in calculating the envelope binding energy…

Showing 9 of the paper's 11 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/0201220 by the authors.

References

Works cited (2)

[1]

c© 2000 RAS, MNRAS 000, 1–36 34 J. R. Hurley, C. A. Tout and O. R. Pols Alexander M.E., 1973, Astrophys. Space Sci., 23, 459 Bailey V.C., 1999, Ph.D. Thesis, Cambridge University Bailey V.C., Davies M.B., 1999, MNRAS, 308, 257 Beloborodov A.M., 1998, MNRAS, 297, 739 Benz W., Hills J.G., 1992, ApJ, 389, 546 Binney J., Tremaine S., 1987, Galactic Dynamics. ...

View on Pith 1995
[2]

Now the binary eclipses if π/2 −ψ <i<π/ 2 (A25) where ψ = arcsin(1/3) = π2 − arccos(1/3). (A26) Therefore the fraction of systems which are likely to be eclipsing is P = ∫ π/2 arccos(1/3) sinidi = 1/3. (A27) c© 2000 RAS, MNRAS 000, 1–36

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Turning five EBLM single-lined binaries into double-lined systems yields dynamical M-dwarf masses and shows that single-lined estimates run systematically high because binary light inflates isochrone radii.
From the Milky Way to the Early Universe: How Metallicity Shapes the Formation of Double Neutron Stars
astro-ph.SR 2026-10 conditional novelty 6.0 of 10

Merger efficiency of double neutron stars rises toward low metallicity, yet most cosmic mergers still come from 0.1 to 1 solar metallicity progenitors.

Show 13 more citing papers

Inferring the population properties of galactic binaries from LISA's stochastic foreground
astro-ph.HE 2026-02 unverdicted novelty 6.0 of 10

A neural posterior estimator trained on simulated LISA foreground spectra recovers galactic binary population parameters, including total number, with good accuracy in validation tests.
Gamma-ray emission from decays of boosted nuclei in protomagnetar jets
astro-ph.HE 2025-02 conditional novelty 6.0 of 10

Doppler-boosted, time-dilated radioactive decay lines from nuclei in protomagnetar jets could be detected by INTEGRAL/SPI and e-ASTROGAM from a supernova at 10 kpc.
Astrophysics and cosmology with a decihertz gravitational-wave detector: TianGO
gr-qc 2019-08 conditional novelty 6.0 of 10

A decihertz space gravitational-wave detector paired with a ground network would localize compact binary mergers far more precisely than the ground network alone, supporting standard-siren cosmology, early warning, an...
Spin orientations of merging black holes formed from the evolution of stellar binaries
astro-ph.HE 2018-08 conditional novelty 6.0 of 10

Black-hole binary spin misalignments split into three precession morphologies whose relative fractions track whether stellar tides realigned a spin before the second core collapse, giving a measurable handle on massiv...
Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation
gr-qc 2013-02 conditional novelty 6.0 of 10

A toy model of black-hole binary formation predicts that efficient tidal alignment locks spins into a resonant plane, with the preferred angle set by whether mass transfer reversed the mass ratio.
Formation and Detectability of PSR J0653+0443-like Extremely Eccentric Binary Neutron Stars in the Milky Way
astro-ph.HE 2026-10 conditional novelty 5.0 of 10

Only about 0.6% of Milky Way binary neutron stars detectable by FAST should have orbital eccentricity above 0.99, so PSR J0653+0443 is rare but consistent with standard binary evolution.
On the origin of the short-period Blue Straggler Stars in Collinder 261: a binary evolution approach
astro-ph.SR 2026-10 conditional novelty 5.0 of 10

Mass-transfer binary evolution reproduces the positions and short periods of the eclipsing blue stragglers in Collinder 261, with an efficiency near 0.5 needed to match the faintest systems.
Joint constraints on the field-cluster mixing fraction, common envelope efficiency, and globular cluster radii from a population of binary hole mergers via deep learning
astro-ph.HE 2020-11 conditional novelty 5.0 of 10

Fitting a two-channel mixture model to 44 gravitational-wave events yields a field-formation fraction of 0.20, a common envelope efficiency of 2.26, and a cluster virial radius of 2.71 pc, with the efficiency constrai...
Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries
astro-ph.HE 2015-12 conditional novelty 5.0 of 10

Chemically homogeneous evolution in tidally locked massive binaries yields a local binary black hole merger rate of about 10 Gpc^-3 yr^-1, peaking near 20 at z about 0.5, with typical total masses of 50 to 110 solar masses.
Diagnosing the Properties and Evolutionary Fates of Black Hole and Wolf-Rayet X-ray Binaries as Potential Gravitational Wave Sources for the LIGO-Virgo-KAGRA Network
astro-ph.HE 2025-10 unverdicted novelty 4.0 of 10

MESA binary evolution simulations with revised Bondi-Hoyle accretion efficiency and observational constraints yield lower BH mass upper limits for IC 10 X-1 and NGC 300 X-1 and predict Hubble-time BBH mergers for all ...
Science with the Einstein Telescope: a comparison of different designs
gr-qc 2023-03 unverdicted novelty 3.0 of 10

The paper evaluates how triangular versus two-L-shaped geometries, arm lengths, and presence of low-frequency instruments affect the science reach of the Einstein Telescope for compact binaries, multi-messenger events...
Relativistic Binaries in Globular Clusters
astro-ph.SR 2011-10 accept novelty 2.0 of 10

Dense globular clusters build tight binaries of white dwarfs, neutron stars, and black holes through dynamical encounters, making them over-abundant relative to the Galactic field and prime targets for gravitational-w...
The first decade of gravitational-wave measurements of black hole spins
gr-qc 2026-06 unverdicted novelty 1.0 of 10

A review summarizing formation-channel predictions, waveform effects, and population-level constraints on stellar-mass black hole spins from the first decade of gravitational-wave observations.

How later papers used it

617 later papers cite it

Evidence: substantial. 598 of the citing papers share no author with it, and 448 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 1,252 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

16 later papers by other authors are listed below: 16 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 17 of 437 papers with this label · 1 by the same authors

Used the same formalism as described in this paper for the common envelope phase, depending on two free parameters, α and λ.

The cosmic merger rate of stellar black hole binaries from the Illustris simulation (2017) · 1.00 · paraphrased: the licence does not allow quoting
In order to calculate the binary effect for core-collapse progenitors, we use the binary population synthesis method developed by Ref. [ref] .

Impact of binary interactions on the diffuse supernova neutrino background (2020) · Population synthesis · 1.00
Generated a cosmological population of BBH mergers from isolated binary evolution using a code based on an updated version of this paper.

Joint constraints on the field-cluster mixing fraction, common envelope efficiency, and globular cluster radii from a population of binary hole mergers via deep learning (2020) · 1.00 · paraphrased: the licence does not allow quoting
Carried out Monte Carlo simulations of a large population of synthetic binaries using the semi-analytic model of this paper to assess effects on observable separation distributions.

Imprints of white dwarf recoil in the separation distribution of Gaia wide binaries (2018) · 1.00 · paraphrased: the licence does not allow quoting
Our binary star model is based on the BSE model [ref] .

Merger rate density of binary black holes through isolated Population I, II, III and extremely metal-poor binary star evolution (2021) · Single and binary star models · 1.00
Modeled wind mass transfer and Roche-lobe overflow mass transfer as described in another work and largely based on this paper.

The role of accretion efficiency, natal kicks, and angular momentum transport in the formation of the Gaia black holes (2026) · 1.00 · paraphrased: the licence does not allow quoting
Performed its modelling of single and binary star evolution using the rapid binary-star evolution algorithm bse presented in this paper.

Stellar multiplicity in high-resolution spectroscopic surveys. I. Application to APOGEE subgiants and giants (2018) · 1.00 · paraphrased: the licence does not allow quoting
We carried out post-CE binary population synthesis with the BSE code [ref] adopting the methodology described in detail in [ref] .

Formation of long-period post-common-envelope binaries I. No extra energy is needed to explain oxygen-neon white dwarfs paired with AFGK-type main-sequence stars (2024) · Binary population models · 1.00
Used the Binary Star Evolution (BSE) code from this paper, which models angular momentum loss in binaries, as the most important part of MOCCA for producing CVs and related objects.

MOCCA-SURVEY database I. Accreting white dwarf binary systems in globular clusters -- III. Cataclysmic variables -- Implications of model assumptions (2017) · 1.00 · paraphrased: the licence does not allow quoting
Modeled details such as mass transfer rate, stellar aging/rejuvenation, and conditions for unstable transfer according to this paper.

A statistical view on stable and unstable Roche lobe overflow of a tertiary star onto the inner binary in triple systems (2021) · 1.00 · paraphrased: the licence does not allow quoting
For wind mass loss, we apply the standard prescriptions applied in [ref] ; however, the mass loss prescription for the AGB is coded from [ref] which considers the rapid mass loss in AGB stars before the super–wind phase.

Probing Binary Architectures of Lithium-Rich Giants in GALAH with COSMIC and Stellar Models (2025) · Section · 1.00
In order to definitively rule out that these are post-common envelope binaries, we decided to reconstruct the common envelope phase using the same algorithm described in detail in [ref] , based on the binary star evolution (BSE) code from [ref] .

The White Dwarf Binary Pathways Survey -- IX. Three long period white dwarf plus subgiant binaries (2022) · Past evolution · 1.00
Used a modified version of COSMIC, an updated version of BSE from this paper, to generate the populations of binaries in the GBTDS.

LISA Galactic Binaries in the Roman Galactic Bulge Time-Domain Survey (2022) · 1.00 · paraphrased: the licence does not allow quoting
Binary and stellar evolution is fully coupled to the dynamical evolution of the clusters and is calculated by the publicly available software [ref] , which is based on [ref] and [ref] .

The dominant mechanism(s) for populating the outskirts of star clusters with neutron star binaries (2023) · The code and initial conditions · 1.00
Computed the evolution of around 2×10^6 binary systems with the bse population synthesis code of this paper.

Modelling nova populations in galaxies (2016) · 1.00 · paraphrased: the licence does not allow quoting
Carried out binary population synthesis with the code of this paper, recently modified and calibrated, to test the origin of WD magnetic fields during CE evolution.

Are white dwarf magnetic fields in close binaries generated during common-envelope evolution? (2019) · 0.99 · paraphrased: the licence does not allow quoting

By the same authors

Synthesised a population of binaries with the BSE code of this paper for a CE efficiency parameter α in the range 0.1–0.9.

Magnetic Fields in Interacting Binaries (2018) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

92 arXiv papers cite this in 172 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 71 sentences without a confident label

Contests it 2 papers

For the radiative damping of the dynamical tide relevant to WR stars, [equation] after accounting for the typo in Eq. (42) of [ref] .

Pathways for producing binary black holes with large misaligned spins in the isolated formation channel · Tides · contest 0.73
These results challenge the simplified stability prescriptions commonly adopted in rapid population-synthesis codes [ref] , which may either overestimate or underestimate the prevalence of SMT depending on the adopted assumptions [ref] .

How Common Are Common Envelopes? Quantifying Their Role in Forming Gravitational-Wave Sources · Mass Transfer and Binary Interactions as the Dominant Uncertainty · contest 0.71

Uses its method or tool 56 papers

To evolve a model population of binaries up to AIC, we have used the state-of-the-art binary-star evolution (BSE) code [ref] .

Millisecond Pulsars from Accretion Induced Collapse as the Origin of the Galactic Centre Gamma-ray Excess Signal · Generation of reference data set · 1.00
In order to calculate the binary effect for core-collapse progenitors, we use the binary population synthesis method developed by Ref. [ref] .

Impact of binary interactions on the diffuse supernova neutrino background · Population synthesis · 1.00
We generate a cosmological population of BBH mergers originating from isolated binary evolution using [ref] , which is based on an updated version of [ref] .

Joint constraints on the field-cluster mixing fraction, common envelope efficiency, and globular cluster radii from a population of binary hole mergers via deep learning · Introduction · 1.00

Uses its data or values 5 papers

We adopt the following empirically-motivated, “off-the-shelf” parameter choices (see ssec:initparams for detailed justifications and motivations): i) We assume a binary star fraction of 70% [ref] ; ii) We draw $M_1,ZAMS$ from the initial mass function of [ref] iii) Secondary masses are drawn from a flat mass ratio distribution [ref] ; iv) Initial eccentricities are set to zero; v) Orbital periods at zero age are drawn from a log-uniform distribution and range from $10$ days to $10^4$ days [ref] ; vi) The common envelope efficiency factor (see sec:CE) is set to $α_CE=1$ [ref] ; vii) The binding energy parameter $λ_b$ is calculated using the Cambridge STARS code [ref] ; and viii) Magnetic fields are assigned to each nascent AIC NS via random sampling from the log-normal magnetic field distribution of [ref] .

Millisecond Pulsars from Accretion Induced Collapse as the Origin of the Galactic Centre Gamma-ray Excess Signal · Generation of reference data set · 0.82
We find their polytropic $q_crit=4$ [ref] .

Adiabatic Mass Loss In Binary Stars. VI. Massive Helium Binary Stars · Estimation of the non-conserved polytropic criterion · 0.81
Here, we assume the same values of $q_c$ as in the original paper by [ref] , apart from the case of a red giant branch star donor for which we adopt the formalism by [ref] .

The role of accretion efficiency, natal kicks, and angular momentum transport in the formation of the Gaia black holes · Common-envelope (CE) evolution · 0.81

Compares with it 4 papers

Compared to the original [ref] formalism, our framework yields higher helium and carbon-oxygen core masses, leading to more massive compact remnants.

Evolution of Massive Main-sequence Stars in Rapid Population Synthesis. I. Framework and Implementation · Conclusion · 0.90
In our companion paper [ref] , we present our fiducial tidal model in contrast to the commonly used prescriptions from [ref] and [ref] , which we abbreviate as Z77.

Modern tidal interaction models for rapid binary population synthesis: II. Binary black hole formation, mergers, and spins · Comparison to Zahn (1977) · 0.89
Compared with the conserved polytropic criterion, which are $q_crit=1.6$ [ref] or $q_crit=3$ [ref] for HeMS and $q_crit=4$ for HeHG [ref] , the adiabatic models predict that the parameter space of unstable mass transfer for HeMS is wider, while for HeHG it is narrower.

Adiabatic Mass Loss In Binary Stars. VI. Massive Helium Binary Stars · Discussion · 0.99

Cites it as background 8 papers

Previous population synthesis studies of post-CE WD+MS systems have generally adopted MT stability criteria based on polytropic stellar models [ref] .

Influence of mass-transfer stability on the formation of post-common-envelope binaries · Introduction · 0.80
[ref] examined the evolution and rates of rotating helium stars with and without a companion using the equations of [ref] to parameterize binary evolution.

Simulations of Interacting Binary Systems -- Pathways to Radio Bright GRB Progenitors · Introduction · 0.81
An analytical description of the effect of an SN-kick on a binary system was studied in great details for circular binaries [ref] , mainly for neutron stellar systems.

SNe Kicks in Hierarchical Triple Systems · INTRODUCTION · 0.92

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

c© 2000 RAS, MNRAS 000, 1–36 34 J. R. Hurley, C. A. Tout and O. R. Pols Alexander M.E., 1973, Astrophys. Space Sci., 23, 459 Bailey V.C., 1999, Ph.D. Thesis, Cambridge University Bailey V.C., Davies M.B., 1999, MNRAS, 308, 257 Beloborodov A.M., 1998, MNRAS, 297, 739 Benz W., Hills J.G., 1992, ApJ, 389, 546 Binney J., Tremaine S., 1987, Galactic Dynamics. ...

View on Pith 1995

[2] [2]

Now the binary eclipses if π/2 −ψ <i<π/ 2 (A25) where ψ = arcsin(1/3) = π2 − arccos(1/3). (A26) Therefore the fraction of systems which are likely to be eclipsing is P = ∫ π/2 arccos(1/3) sinidi = 1/3. (A27) c© 2000 RAS, MNRAS 000, 1–36

View on Pith 2000